0.05/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.KZuPf1LcZ7 true 0.10/0.32 % Computer : n012.cluster.edu 0.10/0.32 % Model : x86_64 x86_64 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.32 % Memory : 8042.1875MB 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.32 % CPULimit : 1440 0.10/0.32 % WCLimit : 180 0.10/0.32 % DateTime : Thu Jul 4 06:59:09 EDT 2024 0.10/0.32 % CPUTime : 0.10/0.32 % Running portfolio for 1440 s 0.10/0.32 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.10/0.32 % Number of cores: 8 0.10/0.32 % Python version: Python 3.6.8 0.10/0.32 % Running in HO mode 0.15/0.61 % Total configuration time : 828 0.15/0.61 % Estimated wc time : 1656 0.15/0.61 % Estimated cpu time (8 cpus) : 207.0 0.73/0.72 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.73/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 1.04/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 1.04/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 1.12/0.83 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 1.31/1.13 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 1.32/1.14 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 1.32/1.16 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 71.03/14.26 % Solved by lams/20_acsne_simpl.sh. 71.03/14.26 % done 147 iterations in 12.615s 71.03/14.26 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 71.03/14.26 % SZS output start Refutation 71.03/14.26 thf(a_type, type, a: $tType). 71.03/14.26 thf('#sk4_type', type, '#sk4': a). 71.03/14.26 thf('#sk621_type', type, '#sk621': (a > a > $o) > a). 71.03/14.26 thf('#sk30_type', type, '#sk30': a > a > $o). 71.03/14.26 thf('#sk3_type', type, '#sk3': a). 71.03/14.26 thf('#sk533_type', type, '#sk533': (a > a > $o) > a). 71.03/14.26 thf('#sk597_type', type, '#sk597': (a > a > $o) > a). 71.03/14.26 thf('#sk12_type', type, '#sk12': a). 71.03/14.26 thf('#sk21_type', type, '#sk21': a > a > $o). 71.03/14.26 thf('#sk47_type', type, '#sk47': (a > a > $o) > a). 71.03/14.26 thf('#sk112_type', type, '#sk112': (a > a > $o) > a). 71.03/14.26 thf('#sk121_type', type, '#sk121': (a > a > $o) > a). 71.03/14.26 thf('#sk509_type', type, '#sk509': (a > a > $o) > a). 71.03/14.26 thf('#sk175_type', type, '#sk175': (a > a > $o) > a). 71.03/14.26 thf('#sk6_type', type, '#sk6': a). 71.03/14.26 thf('#sk421_type', type, '#sk421': (a > a > $o) > a). 71.03/14.26 thf('#sk2_type', type, '#sk2': a > a > $o). 71.03/14.26 thf('#form434_type', type, '#form434': (a > a > $o) > $o). 71.03/14.26 thf('#sk334_type', type, '#sk334': (a > a > $o) > a). 71.03/14.26 thf('#sk514_type', type, '#sk514': (a > a > $o) > a). 71.03/14.26 thf('#sk8_type', type, '#sk8': a). 71.03/14.26 thf('#sk10_type', type, '#sk10': a). 71.03/14.26 thf('#sk7_type', type, '#sk7': a). 71.03/14.26 thf('#form91_type', type, '#form91': $o). 71.03/14.26 thf('#sk277_type', type, '#sk277': (a > a > $o) > a). 71.03/14.26 thf('#sk74_type', type, '#sk74': (a > a > $o) > a). 71.03/14.26 thf('#form9_type', type, '#form9': $o). 71.03/14.26 thf('#form11_type', type, '#form11': $o). 71.03/14.26 thf('#sk5_type', type, '#sk5': a > a > $o). 71.03/14.26 thf('#sk1_type', type, '#sk1': a > a > $o). 71.03/14.26 thf('#sk205_type', type, '#sk205': (a > a > $o) > a). 71.03/14.26 thf('#form204_type', type, '#form204': (a > a > $o) > $o). 71.03/14.26 thf(cTHM250G_pme, conjecture, 71.03/14.26 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 71.03/14.26 ( ( ![Xp1:( a > a > $o )]: 71.03/14.26 ( ( ( ![Xx0:a,Xy0:a]: 71.03/14.26 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 71.03/14.26 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 71.03/14.26 ( ![Xx0:a,Xy0:a,Xz:a]: 71.03/14.26 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 71.03/14.26 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 71.03/14.27 ( Xp1 @ Xx @ Xy ) ) ) | 71.03/14.27 ( ~( ( ( ![Xx0:a,Xy0:a,Xz:a]: 71.03/14.27 ( ( ( ![Xp1:( a > a > $o )]: 71.03/14.27 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 71.03/14.27 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 71.03/14.27 ( ![Xx1:a,Xy1:a]: 71.03/14.27 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 71.03/14.27 ( Xp1 @ Xy0 @ Xz ) ) ) & 71.03/14.27 ( ![Xp1:( a > a > $o )]: 71.03/14.27 ( ( ( ![Xx1:a,Xy1:a]: 71.03/14.27 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 71.03/14.27 ( ![Xx1:a,Xy1:a,Xz0:a]: 71.03/14.27 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 71.03/14.27 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 71.03/14.27 ( ![Xp1:( a > a > $o )]: 71.03/14.27 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 71.03/14.27 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 71.03/14.27 ( ![Xx1:a,Xy1:a]: 71.03/14.27 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 71.03/14.27 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) & 71.03/14.27 ( ![Xx0:a,Xy0:a]: 71.03/14.27 ( ( ( ![Xp1:( a > a > $o )]: 71.03/14.27 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 71.03/14.27 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xz ) ) ) & 71.03/14.27 ( ![Xx1:a,Xy1:a]: 71.03/14.27 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 71.03/14.27 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 71.03/14.27 ( ![Xp1:( a > a > $o )]: 71.03/14.27 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 71.03/14.27 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xz ) ) ) & 71.03/14.27 ( ![Xx1:a,Xy1:a]: 71.03/14.27 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 71.03/14.27 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 71.03/14.27 ( ![Xp1:( a > a > $o )]: 71.03/14.27 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 71.03/14.27 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xz ) ) ) & 71.03/14.27 ( ![Xx1:a,Xy1:a]: 71.03/14.27 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 71.03/14.27 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) ) => 71.03/14.27 ( ![Xp1:( a > a > $o )]: 71.03/14.27 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 71.03/14.27 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 71.03/14.27 ( Xp1 @ Xx0 @ Xz ) ) ) & 71.03/14.27 ( ![Xx0:a,Xy0:a]: 71.03/14.27 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 71.03/14.27 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 71.03/14.27 ( Xp1 @ Xx @ Xy ) ) ) ) ) ))). 71.03/14.27 thf(zf_stmt_0, negated_conjecture, 71.03/14.27 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 71.03/14.27 ( ( ![Xp1:( a > a > $o )]: 71.03/14.27 ( ( ( ![Xx0:a,Xy0:a]: 71.03/14.27 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 71.03/14.27 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 71.03/14.27 ( ![Xx0:a,Xy0:a,Xz:a]: 71.03/14.27 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 71.03/14.27 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 71.03/14.27 ( Xp1 @ Xx @ Xy ) ) ) | 71.03/14.27 ( ~( ( ( ![Xx0:a,Xy0:a,Xz:a]: 71.03/14.27 ( ( ( ![Xp1:( a > a > $o )]: 71.03/14.27 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 71.03/14.27 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 71.03/14.27 ( ![Xx1:a,Xy1:a]: 71.03/14.27 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 71.03/14.27 ( Xp1 @ Xy0 @ Xz ) ) ) & 71.03/14.27 ( ![Xp1:( a > a > $o )]: 71.03/14.27 ( ( ( ![Xx1:a,Xy1:a]: 71.03/14.27 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 71.03/14.27 ( ![Xx1:a,Xy1:a,Xz0:a]: 71.03/14.27 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 71.03/14.27 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 71.03/14.27 ( ![Xp1:( a > a > $o )]: 71.03/14.27 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 71.03/14.27 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 71.03/14.27 ( ![Xx1:a,Xy1:a]: 71.03/14.27 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 71.03/14.27 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) & 71.03/14.27 ( ![Xx0:a,Xy0:a]: 71.03/14.27 ( ( ( ![Xp1:( a > a > $o )]: 71.03/14.27 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 71.03/14.27 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xz ) ) ) & 71.03/14.27 ( ![Xx1:a,Xy1:a]: 71.03/14.27 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 71.03/14.27 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 71.03/14.27 ( ![Xp1:( a > a > $o )]: 71.03/14.27 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 71.03/14.27 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xz ) ) ) & 71.03/14.27 ( ![Xx1:a,Xy1:a]: 71.03/14.27 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 71.03/14.27 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 71.03/14.27 ( ![Xp1:( a > a > $o )]: 71.03/14.27 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 71.03/14.27 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xz ) ) ) & 71.03/14.27 ( ![Xx1:a,Xy1:a]: 71.03/14.27 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 71.03/14.27 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 71.03/14.27 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) ) => 71.03/14.27 ( ![Xp1:( a > a > $o )]: 71.03/14.27 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 71.03/14.27 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 71.03/14.27 ( Xp1 @ Xx0 @ Xz ) ) ) & 71.03/14.27 ( ![Xx0:a,Xy0:a]: 71.03/14.27 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 71.03/14.27 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 71.03/14.27 ( Xp1 @ Xx @ Xy ) ) ) ) ) ) )), 71.03/14.27 inference('cnf.neg', [status(esa)], [cTHM250G_pme])). 71.03/14.27 thf(zip_derived_cl0, plain, 71.03/14.27 (~ (((!!) @ (^[Y0 : a > a > $o]: 71.03/14.27 (((!!) @ (^[Y1 : a > a > $o]: 71.03/14.27 (((!!) @ (^[Y2 : a]: 71.03/14.27 (((!!) @ (^[Y3 : a]: 71.03/14.27 (((((!!) @ (^[Y4 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y1 @ 71.03/14.27 Y5 @ 71.03/14.27 Y6) | 71.03/14.27 (Y0 @ 71.03/14.27 Y5 @ Y6))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y6))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ 71.03/14.27 Y6) & 71.03/14.27 (Y4 @ 71.03/14.27 Y6 @ Y7))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y7)))))))))))))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y2 @ Y3)))))) | 71.03/14.27 (((~) @ (((( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y9 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y10 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y7 @ 71.03/14.27 Y8 @ 71.03/14.27 Y9) & 71.03/14.27 (Y7 @ 71.03/14.27 Y9 @ Y10))) => 71.03/14.27 (Y7 @ 71.03/14.27 Y8 @ Y10)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y9 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y1 @ 71.03/14.27 Y8 @ 71.03/14.27 Y9) | 71.03/14.27 (Y0 @ 71.03/14.27 Y8 @ Y9))) => 71.03/14.27 (Y7 @ 71.03/14.27 Y8 @ Y9))))))))))) => 71.03/14.27 (Y7 @ 71.03/14.27 Y5 @ Y6)))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y9 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y0 @ 71.03/14.27 Y8 @ 71.03/14.27 Y9) | 71.03/14.27 (Y1 @ 71.03/14.27 Y8 @ Y9))) => 71.03/14.27 (Y7 @ 71.03/14.27 Y8 @ Y9))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y9 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y10 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y7 @ 71.03/14.27 Y9 @ 71.03/14.27 Y10) & 71.03/14.27 (Y7 @ 71.03/14.27 Y8 @ Y9))) => 71.03/14.27 (Y7 @ 71.03/14.27 Y8 @ Y10)))))))))))))) => 71.03/14.27 (Y7 @ 71.03/14.27 Y4 @ Y5)))))))) => 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y9 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y10 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y7 @ 71.03/14.27 Y9 @ 71.03/14.27 Y10) & 71.03/14.27 (Y7 @ 71.03/14.27 Y8 @ Y9))) => 71.03/14.27 (Y7 @ 71.03/14.27 Y8 @ Y10)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y9 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y0 @ 71.03/14.27 Y8 @ 71.03/14.27 Y9) | 71.03/14.27 (Y1 @ 71.03/14.27 Y8 @ Y9))) => 71.03/14.27 (Y7 @ 71.03/14.27 Y8 @ Y9))))))))))) => 71.03/14.27 (Y7 @ 71.03/14.27 Y4 @ Y6))))))))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y9 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ 71.03/14.27 Y8) & 71.03/14.27 (Y6 @ 71.03/14.27 Y8 @ Y9))) => 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ Y9)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (Y0 @ 71.03/14.27 Y7 @ 71.03/14.27 Y8) => 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ Y8))))))))))) => 71.03/14.27 (Y6 @ 71.03/14.27 Y4 @ Y5)))))) | 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y9 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ 71.03/14.27 Y8) & 71.03/14.27 (Y6 @ 71.03/14.27 Y8 @ Y9))) => 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ Y9)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (Y1 @ 71.03/14.27 Y7 @ 71.03/14.27 Y8) => 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ Y8))))))))))) => 71.03/14.27 (Y6 @ 71.03/14.27 Y4 @ Y5)))))))) => 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y9 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y6 @ 71.03/14.27 Y8 @ 71.03/14.27 Y9) & 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ Y8))) => 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ Y9)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y0 @ 71.03/14.27 Y7 @ 71.03/14.27 Y8) | 71.03/14.27 (Y1 @ 71.03/14.27 Y7 @ Y8))) => 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ Y8))))))))))) => 71.03/14.27 (Y6 @ 71.03/14.27 Y4 @ Y5)))))))))))))))) => 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ 71.03/14.27 Y6) & 71.03/14.27 (Y4 @ 71.03/14.27 Y6 @ Y7))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y7)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y1 @ 71.03/14.27 Y5 @ 71.03/14.27 Y6) | 71.03/14.27 (Y0 @ 71.03/14.27 Y5 @ Y6))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y6))))))))))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y2 @ Y3))))))))))))))))))))))))), 71.03/14.27 inference('cnf', [status(esa)], [zf_stmt_0])). 71.03/14.27 thf(zip_derived_cl1, plain, 71.03/14.27 (~ (((!!) @ (^[Y0 : a > a > $o]: 71.03/14.27 (((!!) @ (^[Y1 : a]: 71.03/14.27 (((!!) @ (^[Y2 : a]: 71.03/14.27 (((((!!) @ (^[Y3 : a > a > $o]: 71.03/14.27 (((((((!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (((!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y0 @ 71.03/14.27 Y4 @ 71.03/14.27 Y5) | 71.03/14.27 ('#sk1' @ 71.03/14.27 Y4 @ Y5))) => 71.03/14.27 (Y3 @ 71.03/14.27 Y4 @ Y5))))))))) & 71.03/14.27 (((!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (((!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y3 @ 71.03/14.27 Y4 @ 71.03/14.27 Y5) & 71.03/14.27 (Y3 @ 71.03/14.27 Y5 @ Y6))) => 71.03/14.27 (Y3 @ 71.03/14.27 Y4 @ Y6)))))))))))))) => 71.03/14.27 (Y3 @ Y1 @ Y2)))))) | 71.03/14.27 (((~) @ (((((((!!) @ (^[Y3 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y9 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ 71.03/14.27 Y8) & 71.03/14.27 (Y6 @ 71.03/14.27 Y8 @ Y9))) => 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ Y9)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y0 @ 71.03/14.27 Y7 @ 71.03/14.27 Y8) | 71.03/14.27 ('#sk1' @ 71.03/14.27 Y7 @ Y8))) => 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ Y8))))))))))) => 71.03/14.27 (Y6 @ 71.03/14.27 Y4 @ Y5)))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 ('#sk1' @ 71.03/14.27 Y7 @ 71.03/14.27 Y8) | 71.03/14.27 (Y0 @ 71.03/14.27 Y7 @ Y8))) => 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ Y8))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y9 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y6 @ 71.03/14.27 Y8 @ 71.03/14.27 Y9) & 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ Y8))) => 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ Y9)))))))))))))) => 71.03/14.27 (Y6 @ 71.03/14.27 Y3 @ Y4)))))))) => 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y9 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y6 @ 71.03/14.27 Y8 @ 71.03/14.27 Y9) & 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ Y8))) => 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ Y9)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 ('#sk1' @ 71.03/14.27 Y7 @ 71.03/14.27 Y8) | 71.03/14.27 (Y0 @ 71.03/14.27 Y7 @ Y8))) => 71.03/14.27 (Y6 @ 71.03/14.27 Y7 @ Y8))))))))))) => 71.03/14.27 (Y6 @ 71.03/14.27 Y3 @ Y5))))))))))))))))) & 71.03/14.27 (((!!) @ (^[Y3 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ 71.03/14.27 Y7) & 71.03/14.27 (Y5 @ 71.03/14.27 Y7 @ Y8))) => 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ Y8)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 ('#sk1' @ 71.03/14.27 Y6 @ 71.03/14.27 Y7) => 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ Y7))))))))))) => 71.03/14.27 (Y5 @ 71.03/14.27 Y3 @ Y4)))))) | 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ 71.03/14.27 Y7) & 71.03/14.27 (Y5 @ 71.03/14.27 Y7 @ Y8))) => 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ Y8)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (Y0 @ 71.03/14.27 Y6 @ 71.03/14.27 Y7) => 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ Y7))))))))))) => 71.03/14.27 (Y5 @ 71.03/14.27 Y3 @ Y4)))))))) => 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y5 @ 71.03/14.27 Y7 @ 71.03/14.27 Y8) & 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ Y7))) => 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ Y8)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 ('#sk1' @ 71.03/14.27 Y6 @ 71.03/14.27 Y7) | 71.03/14.27 (Y0 @ 71.03/14.27 Y6 @ Y7))) => 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ Y7))))))))))) => 71.03/14.27 (Y5 @ 71.03/14.27 Y3 @ Y4)))))))))))))))) => 71.03/14.27 (((!!) @ (^[Y3 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y3 @ 71.03/14.27 Y4 @ 71.03/14.27 Y5) & 71.03/14.27 (Y3 @ 71.03/14.27 Y5 @ Y6))) => 71.03/14.27 (Y3 @ 71.03/14.27 Y4 @ Y6)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y0 @ 71.03/14.27 Y4 @ 71.03/14.27 Y5) | 71.03/14.27 ('#sk1' @ 71.03/14.27 Y4 @ Y5))) => 71.03/14.27 (Y3 @ 71.03/14.27 Y4 @ Y5))))))))))) => 71.03/14.27 (Y3 @ 71.03/14.27 Y1 @ Y2)))))))))))))))))))))), 71.03/14.27 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 71.03/14.27 thf(zip_derived_cl2, plain, 71.03/14.27 (~ (((!!) @ (^[Y0 : a]: 71.03/14.27 (((!!) @ (^[Y1 : a]: 71.03/14.27 (((((!!) @ (^[Y2 : a > a > $o]: 71.03/14.27 (((((((!!) @ (^[Y3 : a]: 71.03/14.27 (((!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (((( 71.03/14.27 ('#sk2' @ 71.03/14.27 Y3 @ Y4) | 71.03/14.27 ('#sk1' @ 71.03/14.27 Y3 @ Y4))) => 71.03/14.27 (Y2 @ 71.03/14.27 Y3 @ Y4))))))))) & 71.03/14.27 (((!!) @ (^[Y3 : a]: 71.03/14.27 (((!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (((!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y2 @ 71.03/14.27 Y3 @ 71.03/14.27 Y4) & 71.03/14.27 (Y2 @ 71.03/14.27 Y4 @ Y5))) => 71.03/14.27 (Y2 @ 71.03/14.27 Y3 @ Y5)))))))))))))) => 71.03/14.27 (Y2 @ Y0 @ Y1)))))) | 71.03/14.27 (((~) @ (((((((!!) @ (^[Y2 : a]: 71.03/14.27 (((!!) @ (^[Y3 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ 71.03/14.27 Y7) & 71.03/14.27 (Y5 @ 71.03/14.27 Y7 @ Y8))) => 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ Y8)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 ('#sk2' @ 71.03/14.27 Y6 @ 71.03/14.27 Y7) | 71.03/14.27 ('#sk1' @ 71.03/14.27 Y6 @ Y7))) => 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ Y7))))))))))) => 71.03/14.27 (Y5 @ 71.03/14.27 Y3 @ Y4)))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 ('#sk1' @ 71.03/14.27 Y6 @ 71.03/14.27 Y7) | 71.03/14.27 ('#sk2' @ 71.03/14.27 Y6 @ Y7))) => 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ Y7))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y5 @ 71.03/14.27 Y7 @ 71.03/14.27 Y8) & 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ Y7))) => 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ Y8)))))))))))))) => 71.03/14.27 (Y5 @ 71.03/14.27 Y2 @ Y3)))))))) => 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y8 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y5 @ 71.03/14.27 Y7 @ 71.03/14.27 Y8) & 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ Y7))) => 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ Y8)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 ('#sk1' @ 71.03/14.27 Y6 @ 71.03/14.27 Y7) | 71.03/14.27 ('#sk2' @ 71.03/14.27 Y6 @ Y7))) => 71.03/14.27 (Y5 @ 71.03/14.27 Y6 @ Y7))))))))))) => 71.03/14.27 (Y5 @ 71.03/14.27 Y2 @ Y4))))))))))))))))) & 71.03/14.27 (((!!) @ (^[Y2 : a]: 71.03/14.27 (((!!) @ (^[Y3 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ 71.03/14.27 Y6) & 71.03/14.27 (Y4 @ 71.03/14.27 Y6 @ Y7))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y7)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 ('#sk1' @ 71.03/14.27 Y5 @ 71.03/14.27 Y6) => 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y6))))))))))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y2 @ Y3)))))) | 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ 71.03/14.27 Y6) & 71.03/14.27 (Y4 @ 71.03/14.27 Y6 @ Y7))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y7)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 ('#sk2' @ 71.03/14.27 Y5 @ 71.03/14.27 Y6) => 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y6))))))))))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y2 @ Y3)))))))) => 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y4 @ 71.03/14.27 Y6 @ 71.03/14.27 Y7) & 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y6))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y7)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 ('#sk1' @ 71.03/14.27 Y5 @ 71.03/14.27 Y6) | 71.03/14.27 ('#sk2' @ 71.03/14.27 Y5 @ Y6))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y6))))))))))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y2 @ Y3)))))))))))))))) => 71.03/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.03/14.27 (((((((!!) @ ( 71.03/14.27 ^[Y3 : a]: 71.03/14.27 (((!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y2 @ 71.03/14.27 Y3 @ 71.03/14.27 Y4) & 71.03/14.27 (Y2 @ 71.03/14.27 Y4 @ Y5))) => 71.03/14.27 (Y2 @ 71.03/14.27 Y3 @ Y5)))))))))))) & 71.03/14.27 (((!!) @ ( 71.03/14.27 ^[Y3 : a]: 71.03/14.27 (((!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 ('#sk2' @ 71.03/14.27 Y3 @ 71.03/14.27 Y4) | 71.03/14.27 ('#sk1' @ 71.03/14.27 Y3 @ Y4))) => 71.03/14.27 (Y2 @ 71.03/14.27 Y3 @ Y4))))))))))) => 71.03/14.27 (Y2 @ Y0 @ Y1))))))))))))))))))), 71.03/14.27 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 71.03/14.27 thf(zip_derived_cl3, plain, 71.03/14.27 (~ (((!!) @ (^[Y0 : a]: 71.03/14.27 (((((!!) @ (^[Y1 : a > a > $o]: 71.03/14.27 (((((((!!) @ (^[Y2 : a]: 71.03/14.27 (((!!) @ (^[Y3 : a]: 71.03/14.27 ((((('#sk2' @ 71.03/14.27 Y2 @ Y3) | 71.03/14.27 ('#sk1' @ 71.03/14.27 Y2 @ Y3))) => 71.03/14.27 (Y1 @ Y2 @ Y3))))))))) & 71.03/14.27 (((!!) @ (^[Y2 : a]: 71.03/14.27 (((!!) @ (^[Y3 : a]: 71.03/14.27 (((!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (((( 71.03/14.27 (Y1 @ 71.03/14.27 Y2 @ Y3) & 71.03/14.27 (Y1 @ 71.03/14.27 Y3 @ Y4))) => 71.03/14.27 (Y1 @ 71.03/14.27 Y2 @ Y4)))))))))))))) => 71.03/14.27 (Y1 @ '#sk3' @ Y0)))))) | 71.03/14.27 (((~) @ (((((((!!) @ (^[Y1 : a]: 71.03/14.27 (((!!) @ (^[Y2 : a]: 71.03/14.27 (((!!) @ (^[Y3 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ 71.03/14.27 Y6) & 71.03/14.27 (Y4 @ 71.03/14.27 Y6 @ Y7))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y7)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 ('#sk2' @ 71.03/14.27 Y5 @ 71.03/14.27 Y6) | 71.03/14.27 ('#sk1' @ 71.03/14.27 Y5 @ Y6))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y6))))))))))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y2 @ Y3)))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 ('#sk1' @ 71.03/14.27 Y5 @ 71.03/14.27 Y6) | 71.03/14.27 ('#sk2' @ 71.03/14.27 Y5 @ Y6))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y6))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y4 @ 71.03/14.27 Y6 @ 71.03/14.27 Y7) & 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y6))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y7)))))))))))))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y1 @ Y2)))))))) => 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : 71.03/14.27 a > a > $o]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y7 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y4 @ 71.03/14.27 Y6 @ 71.03/14.27 Y7) & 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y6))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y7)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 ('#sk1' @ 71.03/14.27 Y5 @ 71.03/14.27 Y6) | 71.03/14.27 ('#sk2' @ 71.03/14.27 Y5 @ Y6))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y5 @ Y6))))))))))) => 71.03/14.27 (Y4 @ 71.03/14.27 Y1 @ Y3))))))))))))))))) & 71.03/14.27 (((!!) @ (^[Y1 : a]: 71.03/14.27 (((!!) @ (^[Y2 : a]: 71.03/14.27 (((((((!!) @ ( 71.03/14.27 ^[Y3 : 71.03/14.27 a > a > $o]: 71.03/14.27 (((( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y3 @ 71.03/14.27 Y4 @ 71.03/14.27 Y5) & 71.03/14.27 (Y3 @ 71.03/14.27 Y5 @ Y6))) => 71.03/14.27 (Y3 @ 71.03/14.27 Y4 @ Y6)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 ('#sk1' @ 71.03/14.27 Y4 @ 71.03/14.27 Y5) => 71.03/14.27 (Y3 @ 71.03/14.27 Y4 @ Y5))))))))))) => 71.03/14.27 (Y3 @ 71.03/14.27 Y1 @ Y2)))))) | 71.03/14.27 (((!!) @ ( 71.03/14.27 ^[Y3 : 71.03/14.27 a > a > $o]: 71.03/14.27 (((( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y3 @ 71.03/14.27 Y4 @ 71.03/14.27 Y5) & 71.03/14.27 (Y3 @ 71.03/14.27 Y5 @ Y6))) => 71.03/14.27 (Y3 @ 71.03/14.27 Y4 @ Y6)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 ('#sk2' @ 71.03/14.27 Y4 @ 71.03/14.27 Y5) => 71.03/14.27 (Y3 @ 71.03/14.27 Y4 @ Y5))))))))))) => 71.03/14.27 (Y3 @ 71.03/14.27 Y1 @ Y2)))))))) => 71.03/14.27 (((!!) @ ( 71.03/14.27 ^[Y3 : a > a > $o]: 71.03/14.27 (((((( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y3 @ 71.03/14.27 Y5 @ 71.03/14.27 Y6) & 71.03/14.27 (Y3 @ 71.03/14.27 Y4 @ Y5))) => 71.03/14.27 (Y3 @ 71.03/14.27 Y4 @ Y6)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 ('#sk1' @ 71.03/14.27 Y4 @ 71.03/14.27 Y5) | 71.03/14.27 ('#sk2' @ 71.03/14.27 Y4 @ Y5))) => 71.03/14.27 (Y3 @ 71.03/14.27 Y4 @ Y5))))))))))) => 71.03/14.27 (Y3 @ Y1 @ 71.03/14.27 Y2)))))))))))))))) => 71.03/14.27 (((!!) @ (^[Y1 : a > a > $o]: 71.03/14.27 (((((((!!) @ (^[Y2 : a]: 71.03/14.27 (((!!) @ ( 71.03/14.27 ^[Y3 : a]: 71.03/14.27 (((!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y1 @ 71.03/14.27 Y2 @ 71.03/14.27 Y3) & 71.03/14.27 (Y1 @ 71.03/14.27 Y3 @ Y4))) => 71.03/14.27 (Y1 @ 71.03/14.27 Y2 @ Y4)))))))))))) & 71.03/14.27 (((!!) @ (^[Y2 : a]: 71.03/14.27 (((!!) @ ( 71.03/14.27 ^[Y3 : a]: 71.03/14.27 ((((('#sk2' @ 71.03/14.27 Y2 @ Y3) | 71.03/14.27 ('#sk1' @ 71.03/14.27 Y2 @ Y3))) => 71.03/14.27 (Y1 @ Y2 @ 71.03/14.27 Y3))))))))))) => 71.03/14.27 (Y1 @ '#sk3' @ Y0)))))))))))))))), 71.03/14.27 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 71.03/14.27 thf(zip_derived_cl4, plain, 71.03/14.27 (~ (((((!!) @ (^[Y0 : a > a > $o]: 71.03/14.27 (((((((!!) @ (^[Y1 : a]: 71.03/14.27 (((!!) @ (^[Y2 : a]: 71.03/14.27 ((((('#sk2' @ Y1 @ Y2) | 71.03/14.27 ('#sk1' @ Y1 @ Y2))) => 71.03/14.27 (Y0 @ Y1 @ Y2))))))))) & 71.03/14.27 (((!!) @ (^[Y1 : a]: 71.03/14.27 (((!!) @ (^[Y2 : a]: 71.03/14.27 (((!!) @ (^[Y3 : a]: 71.03/14.27 (((((Y0 @ Y1 @ 71.03/14.27 Y2) & (Y0 @ 71.03/14.27 Y2 @ Y3))) => 71.03/14.27 (Y0 @ Y1 @ Y3)))))))))))))) => 71.03/14.27 (Y0 @ '#sk3' @ '#sk4')))))) | 71.03/14.27 (((~) @ (((((((!!) @ (^[Y0 : a]: 71.03/14.27 (((!!) @ (^[Y1 : a]: 71.03/14.27 (((!!) @ (^[Y2 : a]: 71.03/14.27 (((((((!!) @ ( 71.03/14.27 ^[Y3 : 71.03/14.27 a > a > $o]: 71.03/14.27 (((( 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y6 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 (Y3 @ 71.03/14.27 Y4 @ 71.03/14.27 Y5) & 71.03/14.27 (Y3 @ 71.03/14.27 Y5 @ Y6))) => 71.03/14.27 (Y3 @ 71.03/14.27 Y4 @ Y6)))))))))))) & 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y4 : a]: 71.03/14.27 (( 71.03/14.27 (!!) @ ( 71.03/14.27 ^[Y5 : a]: 71.03/14.27 (( 71.03/14.27 (( 71.03/14.27 ('#sk2' @ 71.03/14.27 Y4 @ 71.03/14.27 Y5) | 71.15/14.27 ('#sk1' @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))))))))))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y1 @ Y2)))))) & 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y3 : 71.15/14.27 a > a > $o]: 71.15/14.27 (((( 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))))))))) & 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y6 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y3 @ 71.15/14.27 Y5 @ 71.15/14.27 Y6) & 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y6)))))))))))))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y0 @ Y1)))))))) => 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y3 : a > a > $o]: 71.15/14.27 (((((( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y6 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y3 @ 71.15/14.27 Y5 @ 71.15/14.27 Y6) & 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y6)))))))))))) & 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))))))))))) => 71.15/14.27 (Y3 @ Y0 @ 71.15/14.27 Y2))))))))))))))))) & 71.15/14.27 (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ ( 71.15/14.27 ^[Y3 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y3 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))) | 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ ( 71.15/14.27 ^[Y3 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y3 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ ( 71.15/14.27 ^[Y3 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y3 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))))))))))) => 71.15/14.27 (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y3 : a]: 71.15/14.27 (((((Y0 @ 71.15/14.27 Y1 @ Y2) & 71.15/14.27 (Y0 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y0 @ Y1 @ 71.15/14.27 Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk2' @ 71.15/14.27 Y1 @ Y2) | 71.15/14.27 ('#sk1' @ 71.15/14.27 Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk3' @ '#sk4'))))))))))))), 71.15/14.27 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 71.15/14.27 thf(zip_derived_cl6, plain, 71.15/14.27 ( (((((((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((((((!!) @ (^[Y3 : a > a > $o]: 71.15/14.27 (((((((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y6 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y3 @ 71.15/14.27 Y5 @ Y6))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y6)))))))))))) & 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) | 71.15/14.27 ('#sk1' @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))))))))))) => 71.15/14.27 (Y3 @ Y1 @ 71.15/14.27 Y2)))))) & 71.15/14.27 (((!!) @ (^[Y3 : a > a > $o]: 71.15/14.27 (((((((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))))))))) & 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y6 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y3 @ 71.15/14.27 Y5 @ 71.15/14.27 Y6) & 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y6)))))))))))))) => 71.15/14.27 (Y3 @ Y0 @ 71.15/14.27 Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y3 : a > a > $o]: 71.15/14.27 (((((((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y6 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y3 @ 71.15/14.27 Y5 @ 71.15/14.27 Y6) & 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y6)))))))))))) & 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))))))))))) => 71.15/14.27 (Y3 @ Y0 @ Y2))))))))))))))))) & 71.15/14.27 (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))) | 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))))))))))) => 71.15/14.27 (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y1 @ 71.15/14.27 Y2) & (Y0 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.27 ('#sk1' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk3' @ '#sk4'))))))))), 71.15/14.27 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 71.15/14.27 thf(zip_derived_cl8, plain, 71.15/14.27 ((~ (((((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((((((!!) @ (^[Y3 : a > a > $o]: 71.15/14.27 (((((((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y6 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y3 @ 71.15/14.27 Y5 @ Y6))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y6)))))))))))) & 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) | 71.15/14.27 ('#sk1' @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))))))))))) => 71.15/14.27 (Y3 @ Y1 @ 71.15/14.27 Y2)))))) & 71.15/14.27 (((!!) @ (^[Y3 : a > a > $o]: 71.15/14.27 (((((((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))))))))) & 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y6 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y3 @ 71.15/14.27 Y5 @ 71.15/14.27 Y6) & 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y6)))))))))))))) => 71.15/14.27 (Y3 @ Y0 @ 71.15/14.27 Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y3 : a > a > $o]: 71.15/14.27 (((((((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y6 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y3 @ 71.15/14.27 Y5 @ 71.15/14.27 Y6) & 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y6)))))))))))) & 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))))))))))) => 71.15/14.27 (Y3 @ Y0 @ Y2))))))))))))))))) & 71.15/14.27 (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))) | 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))))))))))) 71.15/14.27 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y1 @ 71.15/14.27 Y2) & (Y0 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.27 ('#sk1' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk3' @ '#sk4')))))))), 71.15/14.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 71.15/14.27 thf(zip_derived_cl11, plain, 71.15/14.27 ((~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((((((!!) @ (^[Y3 : a > a > $o]: 71.15/14.27 (((((((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y6 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y3 @ 71.15/14.27 Y5 @ Y6))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y6)))))))))))) & 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) | 71.15/14.27 ('#sk1' @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))))))))))) => 71.15/14.27 (Y3 @ Y1 @ Y2)))))) & 71.15/14.27 (((!!) @ (^[Y3 : a > a > $o]: 71.15/14.27 (((((((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))))))))) & 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y6 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y3 @ 71.15/14.27 Y5 @ 71.15/14.27 Y6) & 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y6)))))))))))))) => 71.15/14.27 (Y3 @ Y0 @ Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y3 : a > a > $o]: 71.15/14.27 (((((((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y6 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y3 @ 71.15/14.27 Y5 @ 71.15/14.27 Y6) & 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y6)))))))))))) & 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y3 @ 71.15/14.27 Y4 @ Y5))))))))))) => 71.15/14.27 (Y3 @ Y0 @ Y2))))))))))))))))) 71.15/14.27 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))) | 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))))))))) 71.15/14.27 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y1 @ 71.15/14.27 Y2) & (Y0 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.27 ('#sk1' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk3' @ '#sk4')))))))), 71.15/14.27 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl8])). 71.15/14.27 thf(zip_derived_cl14, plain, 71.15/14.27 ((~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) | 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))) & 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))))) => 71.15/14.27 (Y2 @ '#sk6' @ Y0)))))))) => 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (((( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ '#sk6' @ Y1)))))))))))))) 71.15/14.27 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y1 @ 71.15/14.27 Y2) & (Y0 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.27 ('#sk1' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk3' @ '#sk4')))))) 71.15/14.27 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))) | 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))))))))))), 71.15/14.27 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl11])). 71.15/14.27 thf(zip_derived_cl17, plain, 71.15/14.27 ((~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((((((!!) @ (^[Y1 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (( 71.15/14.27 (Y1 @ 71.15/14.27 Y2 @ 71.15/14.27 Y3) & 71.15/14.27 (Y1 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y1 @ 71.15/14.27 Y2 @ Y4)))))))))))) & 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 ((((('#sk2' @ 71.15/14.27 Y2 @ 71.15/14.27 Y3) | 71.15/14.27 ('#sk1' @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y1 @ Y2 @ 71.15/14.27 Y3))))))))))) => 71.15/14.27 (Y1 @ '#sk7' @ Y0)))))) & 71.15/14.27 (((!!) @ (^[Y1 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 ((((('#sk1' @ 71.15/14.27 Y2 @ 71.15/14.27 Y3) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y1 @ Y2 @ 71.15/14.27 Y3))))))))) & 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (( 71.15/14.27 (Y1 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y1 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y1 @ 71.15/14.27 Y2 @ Y4)))))))))))))) => 71.15/14.27 (Y1 @ '#sk6' @ '#sk7')))))))) => 71.15/14.27 (((!!) @ (^[Y1 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (((( 71.15/14.27 (Y1 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y1 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y1 @ 71.15/14.27 Y2 @ Y4)))))))))))) & 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 ((((('#sk1' @ 71.15/14.27 Y2 @ Y3) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y1 @ Y2 @ 71.15/14.27 Y3))))))))))) => 71.15/14.27 (Y1 @ '#sk6' @ Y0))))))))))) 71.15/14.27 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))) | 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))))))))) 71.15/14.27 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y1 @ 71.15/14.27 Y2) & (Y0 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.27 ('#sk1' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk3' @ '#sk4')))))))), 71.15/14.27 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl14])). 71.15/14.27 thf(zip_derived_cl20, plain, 71.15/14.27 ((~ (((((((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ 71.15/14.27 Y1 @ 71.15/14.27 Y2) & 71.15/14.27 (Y0 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y0 @ Y1 @ 71.15/14.27 Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.27 ('#sk1' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk7' @ '#sk8')))))) & 71.15/14.27 (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk1' @ Y1 @ Y2) | 71.15/14.27 ('#sk2' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ 71.15/14.27 Y2 @ 71.15/14.27 Y3) & 71.15/14.27 (Y0 @ 71.15/14.27 Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ 71.15/14.27 Y3)))))))))))))) => 71.15/14.27 (Y0 @ '#sk6' @ '#sk7')))))))) => 71.15/14.27 (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y2 @ 71.15/14.27 Y3) & 71.15/14.27 (Y0 @ Y1 @ 71.15/14.27 Y2))) => 71.15/14.27 (Y0 @ Y1 @ 71.15/14.27 Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk1' @ Y1 @ Y2) | 71.15/14.27 ('#sk2' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk6' @ '#sk8')))))))) 71.15/14.27 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y1 @ 71.15/14.27 Y2) & (Y0 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.27 ('#sk1' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk3' @ '#sk4')))))) 71.15/14.27 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))) | 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))))))))))), 71.15/14.27 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl17])). 71.15/14.27 thf(zip_derived_cl23, plain, 71.15/14.27 (( (((((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y1 @ 71.15/14.27 Y2) & (Y0 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.27 ('#sk1' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk7' @ '#sk8')))))) & 71.15/14.27 (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk1' @ Y1 @ Y2) | 71.15/14.27 ('#sk2' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y2 @ 71.15/14.27 Y3) & (Y0 @ 71.15/14.27 Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))))) => 71.15/14.27 (Y0 @ '#sk6' @ '#sk7')))))))) 71.15/14.27 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))) | 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))))))))) 71.15/14.27 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y1 @ 71.15/14.27 Y2) & (Y0 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.27 ('#sk1' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk3' @ '#sk4')))))))), 71.15/14.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 71.15/14.27 thf(zip_derived_cl29, plain, 71.15/14.27 (( (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk1' @ Y1 @ Y2) | 71.15/14.27 ('#sk2' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y2 @ 71.15/14.27 Y3) & (Y0 @ 71.15/14.27 Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))))) => 71.15/14.27 (Y0 @ '#sk6' @ '#sk7')))))) 71.15/14.27 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y1 @ 71.15/14.27 Y2) & (Y0 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.27 ('#sk1' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk3' @ '#sk4')))))) 71.15/14.27 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))) | 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))))))))))), 71.15/14.27 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])). 71.15/14.27 thf(zip_derived_cl28, plain, 71.15/14.27 (( (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y1 @ 71.15/14.27 Y2) & (Y0 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.27 ('#sk1' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk7' @ '#sk8')))))) 71.15/14.27 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y1 @ 71.15/14.27 Y2) & (Y0 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.27 ('#sk1' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk3' @ '#sk4')))))) 71.15/14.27 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))) | 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))))))))))), 71.15/14.27 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])). 71.15/14.27 thf(zip_derived_cl34, plain, 71.15/14.27 ((~ ('#form11') 71.15/14.27 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y1 @ 71.15/14.27 Y2) & (Y0 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.27 ('#sk1' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk3' @ '#sk4')))))))), 71.15/14.27 define([status(thm)])). 71.15/14.27 thf(zip_derived_cl40, plain, 71.15/14.27 (( ('#form11') 71.15/14.27 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))) | 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))))))))) 71.15/14.27 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk1' @ Y1 @ Y2) | 71.15/14.27 ('#sk2' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y2 @ 71.15/14.27 Y3) & (Y0 @ 71.15/14.27 Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))))) => 71.15/14.27 (Y0 @ '#sk6' @ '#sk7')))))))), 71.15/14.27 inference('renaming', [status(thm)], [zip_derived_cl29, zip_derived_cl34])). 71.15/14.27 thf(zip_derived_cl24, plain, 71.15/14.27 ((~ (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y2 @ 71.15/14.27 Y3) & (Y0 @ 71.15/14.27 Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk1' @ Y1 @ Y2) | 71.15/14.27 ('#sk2' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk6' @ '#sk8')))))) 71.15/14.27 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))) | 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))))))))) 71.15/14.27 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y1 @ 71.15/14.27 Y2) & (Y0 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.27 ('#sk1' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk3' @ '#sk4')))))))), 71.15/14.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 71.15/14.27 thf(zip_derived_cl30, plain, 71.15/14.27 (( ('#form9') 71.15/14.27 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))) | 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))))))))))), 71.15/14.27 define([status(thm)])). 71.15/14.27 thf(zip_derived_cl45, plain, 71.15/14.27 ((~ ('#form9') 71.15/14.27 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk1' @ Y1 @ Y2) | 71.15/14.27 ('#sk2' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y2 @ 71.15/14.27 Y3) & (Y0 @ 71.15/14.27 Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))))) => 71.15/14.27 (Y0 @ '#sk6' @ '#sk7')))))) 71.15/14.27 | ('#form11'))), 71.15/14.27 inference('renaming', [status(thm)], [zip_derived_cl40, zip_derived_cl30])). 71.15/14.27 thf(zip_derived_cl56, plain, 71.15/14.27 (![X2 : a > a > $o]: 71.15/14.27 ( (((((((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 71.15/14.27 Y1))) => 71.15/14.27 (X2 @ Y0 @ Y1))))))))) & 71.15/14.27 (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((((X2 @ Y1 @ Y2) & (X2 @ 71.15/14.27 Y0 @ Y1))) => 71.15/14.27 (X2 @ Y0 @ Y2)))))))))))))) => 71.15/14.27 (X2 @ '#sk6' @ '#sk7'))) 71.15/14.27 | ('#form11') 71.15/14.27 | ~ ('#form9'))), 71.15/14.27 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl45])). 71.15/14.27 thf(zip_derived_cl70, plain, 71.15/14.27 (![X2 : a > a > $o]: 71.15/14.27 (~ (((((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 71.15/14.27 Y1))) => 71.15/14.27 (X2 @ Y0 @ Y1))))))))) & 71.15/14.27 (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((((X2 @ Y1 @ Y2) & (X2 @ 71.15/14.27 Y0 @ Y1))) => 71.15/14.27 (X2 @ Y0 @ Y2)))))))))))))) 71.15/14.27 | (X2 @ '#sk6' @ '#sk7') 71.15/14.27 | ~ ('#form9') 71.15/14.27 | ('#form11'))), 71.15/14.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl56])). 71.15/14.27 thf(zip_derived_cl83, plain, 71.15/14.27 (![X2 : a > a > $o]: 71.15/14.27 (~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 71.15/14.27 (X2 @ Y0 @ Y1))))))))) 71.15/14.27 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((((X2 @ Y1 @ Y2) & (X2 @ 71.15/14.27 Y0 @ Y1))) => 71.15/14.27 (X2 @ Y0 @ Y2)))))))))))) 71.15/14.27 | ('#form11') 71.15/14.27 | ~ ('#form9') 71.15/14.27 | (X2 @ '#sk6' @ '#sk7'))), 71.15/14.27 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl70])). 71.15/14.27 thf(zip_derived_cl98, plain, 71.15/14.27 (![X2 : a > a > $o]: 71.15/14.27 (~ (((!!) @ (^[Y0 : a]: 71.15/14.27 ((((('#sk1' @ ('#sk121' @ X2) @ Y0) | ('#sk2' @ 71.15/14.27 ('#sk121' @ X2) @ Y0))) => 71.15/14.27 (X2 @ ('#sk121' @ X2) @ Y0)))))) 71.15/14.27 | (X2 @ '#sk6' @ '#sk7') 71.15/14.27 | ~ ('#form9') 71.15/14.27 | ('#form11') 71.15/14.27 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((((X2 @ Y1 @ Y2) & (X2 @ 71.15/14.27 Y0 @ Y1))) => 71.15/14.27 (X2 @ Y0 @ Y2)))))))))))))), 71.15/14.27 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl83])). 71.15/14.27 thf(zip_derived_cl108, plain, 71.15/14.27 (![X2 : a > a > $o]: 71.15/14.27 (~ ((((('#sk1' @ ('#sk121' @ X2) @ ('#sk175' @ X2)) | ('#sk2' @ 71.15/14.27 ('#sk121' @ X2) @ ('#sk175' @ X2)))) => 71.15/14.27 (X2 @ ('#sk121' @ X2) @ ('#sk175' @ X2)))) 71.15/14.27 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((((X2 @ Y1 @ Y2) & (X2 @ 71.15/14.27 Y0 @ Y1))) => 71.15/14.27 (X2 @ Y0 @ Y2)))))))))))) 71.15/14.27 | ('#form11') 71.15/14.27 | ~ ('#form9') 71.15/14.27 | (X2 @ '#sk6' @ '#sk7'))), 71.15/14.27 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl98])). 71.15/14.27 thf(zip_derived_cl121, plain, 71.15/14.27 (![X2 : a > a > $o]: 71.15/14.27 (~ (X2 @ ('#sk121' @ X2) @ ('#sk175' @ X2)) 71.15/14.27 | (X2 @ '#sk6' @ '#sk7') 71.15/14.27 | ~ ('#form9') 71.15/14.27 | ('#form11') 71.15/14.27 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((((X2 @ Y1 @ Y2) & (X2 @ 71.15/14.27 Y0 @ Y1))) => 71.15/14.27 (X2 @ Y0 @ Y2)))))))))))))), 71.15/14.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 71.15/14.27 thf(zip_derived_cl136, plain, 71.15/14.27 (![X2 : a > a > $o]: 71.15/14.27 (~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((((X2 @ Y0 @ Y1) & (X2 @ 71.15/14.27 ('#sk334' @ X2) @ Y0))) => 71.15/14.27 (X2 @ ('#sk334' @ X2) @ Y1))))))))) 71.15/14.27 | ('#form11') 71.15/14.27 | ~ ('#form9') 71.15/14.27 | (X2 @ '#sk6' @ '#sk7') 71.15/14.27 | ~ (X2 @ ('#sk121' @ X2) @ ('#sk175' @ X2)))), 71.15/14.27 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl121])). 71.15/14.27 thf(zip_derived_cl148, plain, 71.15/14.27 (![X2 : a > a > $o]: 71.15/14.27 (~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((((X2 @ ('#sk421' @ X2) @ Y0) & (X2 @ 71.15/14.27 ('#sk334' @ X2) @ ('#sk421' @ X2)))) => 71.15/14.27 (X2 @ ('#sk334' @ X2) @ Y0)))))) 71.15/14.27 | ~ (X2 @ ('#sk121' @ X2) @ ('#sk175' @ X2)) 71.15/14.27 | (X2 @ '#sk6' @ '#sk7') 71.15/14.27 | ~ ('#form9') 71.15/14.27 | ('#form11'))), 71.15/14.27 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl136])). 71.15/14.27 thf(zip_derived_cl158, plain, 71.15/14.27 (![X2 : a > a > $o]: 71.15/14.27 (~ (((((X2 @ ('#sk421' @ X2) @ ('#sk509' @ X2)) & (X2 @ 71.15/14.27 ('#sk334' @ X2) @ ('#sk421' @ X2)))) => 71.15/14.27 (X2 @ ('#sk334' @ X2) @ ('#sk509' @ X2)))) 71.15/14.27 | ('#form11') 71.15/14.27 | ~ ('#form9') 71.15/14.27 | (X2 @ '#sk6' @ '#sk7') 71.15/14.27 | ~ (X2 @ ('#sk121' @ X2) @ ('#sk175' @ X2)))), 71.15/14.27 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl148])). 71.15/14.27 thf(zip_derived_cl165, plain, 71.15/14.27 (![X2 : a > a > $o]: 71.15/14.27 (~ (X2 @ ('#sk334' @ X2) @ ('#sk509' @ X2)) 71.15/14.27 | ~ (X2 @ ('#sk121' @ X2) @ ('#sk175' @ X2)) 71.15/14.27 | (X2 @ '#sk6' @ '#sk7') 71.15/14.27 | ~ ('#form9') 71.15/14.27 | ('#form11'))), 71.15/14.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])). 71.15/14.27 thf(zip_derived_cl164, plain, 71.15/14.27 (![X2 : a > a > $o]: 71.15/14.27 ( (((X2 @ ('#sk421' @ X2) @ ('#sk509' @ X2)) & (X2 @ 71.15/14.27 ('#sk334' @ X2) @ ('#sk421' @ X2)))) 71.15/14.27 | ~ (X2 @ ('#sk121' @ X2) @ ('#sk175' @ X2)) 71.15/14.27 | (X2 @ '#sk6' @ '#sk7') 71.15/14.27 | ~ ('#form9') 71.15/14.27 | ('#form11'))), 71.15/14.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])). 71.15/14.27 thf(zip_derived_cl172, plain, 71.15/14.27 (![X2 : a > a > $o]: 71.15/14.27 ( (X2 @ ('#sk421' @ X2) @ ('#sk509' @ X2)) 71.15/14.27 | ('#form11') 71.15/14.27 | ~ ('#form9') 71.15/14.27 | (X2 @ '#sk6' @ '#sk7') 71.15/14.27 | ~ (X2 @ ('#sk121' @ X2) @ ('#sk175' @ X2)))), 71.15/14.27 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl164])). 71.15/14.27 thf(zip_derived_cl24, plain, 71.15/14.27 ((~ (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y2 @ 71.15/14.27 Y3) & (Y0 @ 71.15/14.27 Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk1' @ Y1 @ Y2) | 71.15/14.27 ('#sk2' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk6' @ '#sk8')))))) 71.15/14.27 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))) | 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) | 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))))))))) 71.15/14.27 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((((Y0 @ Y1 @ 71.15/14.27 Y2) & (Y0 @ 71.15/14.27 Y2 @ Y3))) => 71.15/14.27 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((!!) @ (^[Y2 : a]: 71.15/14.27 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.27 ('#sk1' @ Y1 @ Y2))) => 71.15/14.27 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.27 (Y0 @ '#sk3' @ '#sk4')))))))), 71.15/14.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 71.15/14.27 thf(zip_derived_cl30, plain, 71.15/14.27 (( ('#form9') 71.15/14.27 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.27 (((!!) @ (^[Y1 : a]: 71.15/14.27 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk1' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))) | 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) & 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ Y5))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 (( 71.15/14.27 ('#sk2' @ 71.15/14.27 Y3 @ 71.15/14.27 Y4) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))))))))))) => 71.15/14.27 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.27 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.27 (((((((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.27 (!!) @ ( 71.15/14.27 ^[Y5 : a]: 71.15/14.27 (( 71.15/14.27 (( 71.15/14.27 (Y2 @ 71.15/14.27 Y4 @ 71.15/14.27 Y5) & 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y4))) => 71.15/14.27 (Y2 @ 71.15/14.27 Y3 @ Y5)))))))))))) & 71.15/14.27 (((!!) @ (^[Y3 : a]: 71.15/14.27 (((!!) @ ( 71.15/14.27 ^[Y4 : a]: 71.15/14.27 ( 71.15/14.27 ( 71.15/14.28 (( 71.15/14.28 ('#sk1' @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) | 71.15/14.28 ('#sk2' @ 71.15/14.28 Y3 @ Y4))) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y4))))))))))) => 71.15/14.28 (Y2 @ Y0 @ Y1)))))))))))))))), 71.15/14.28 define([status(thm)])). 71.15/14.28 thf(zip_derived_cl32, plain, 71.15/14.28 ((~ ('#form9') 71.15/14.28 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((((Y0 @ Y1 @ 71.15/14.28 Y2) & (Y0 @ 71.15/14.28 Y2 @ Y3))) => 71.15/14.28 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.28 ('#sk1' @ Y1 @ Y2))) => 71.15/14.28 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.28 (Y0 @ '#sk3' @ '#sk4')))))) 71.15/14.28 | ~ (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((((Y0 @ Y2 @ 71.15/14.28 Y3) & 71.15/14.28 (Y0 @ Y1 @ 71.15/14.28 Y2))) => 71.15/14.28 (Y0 @ Y1 @ 71.15/14.28 Y3)))))))))))) & 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 ((((('#sk1' @ Y1 @ Y2) | 71.15/14.28 ('#sk2' @ Y1 @ Y2))) => 71.15/14.28 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.28 (Y0 @ '#sk6' @ '#sk8')))))))), 71.15/14.28 inference('renaming', [status(thm)], [zip_derived_cl24, zip_derived_cl30])). 71.15/14.28 thf(zip_derived_cl34, plain, 71.15/14.28 ((~ ('#form11') 71.15/14.28 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((((Y0 @ Y1 @ 71.15/14.28 Y2) & (Y0 @ 71.15/14.28 Y2 @ Y3))) => 71.15/14.28 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.28 ('#sk1' @ Y1 @ Y2))) => 71.15/14.28 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.28 (Y0 @ '#sk3' @ '#sk4')))))))), 71.15/14.28 define([status(thm)])). 71.15/14.28 thf(zip_derived_cl41, plain, 71.15/14.28 (( ('#form11') 71.15/14.28 | ~ (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((((Y0 @ Y2 @ 71.15/14.28 Y3) & 71.15/14.28 (Y0 @ Y1 @ 71.15/14.28 Y2))) => 71.15/14.28 (Y0 @ Y1 @ 71.15/14.28 Y3)))))))))))) & 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 ((((('#sk1' @ Y1 @ Y2) | 71.15/14.28 ('#sk2' @ Y1 @ Y2))) => 71.15/14.28 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.28 (Y0 @ '#sk6' @ '#sk8')))))) 71.15/14.28 | ~ ('#form9'))), 71.15/14.28 inference('renaming', [status(thm)], [zip_derived_cl32, zip_derived_cl34])). 71.15/14.28 thf(zip_derived_cl47, plain, 71.15/14.28 ((~ (((((((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 ((((('#sk21' @ Y1 @ Y2) & 71.15/14.28 ('#sk21' @ Y0 @ Y1))) => 71.15/14.28 ('#sk21' @ Y0 @ Y2)))))))))))) & 71.15/14.28 (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 71.15/14.28 Y1))) => 71.15/14.28 ('#sk21' @ Y0 @ Y1))))))))))) => 71.15/14.28 ('#sk21' @ '#sk6' @ '#sk8'))) 71.15/14.28 | ~ ('#form9') 71.15/14.28 | ('#form11'))), 71.15/14.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl41])). 71.15/14.28 thf(zip_derived_cl62, plain, 71.15/14.28 ((~ ('#sk21' @ '#sk6' @ '#sk8') | ('#form11') | ~ ('#form9'))), 71.15/14.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 71.15/14.28 thf(zip_derived_cl173, plain, 71.15/14.28 (![X2 : a > a > $o]: 71.15/14.28 ( (X2 @ ('#sk334' @ X2) @ ('#sk421' @ X2)) 71.15/14.28 | ('#form11') 71.15/14.28 | ~ ('#form9') 71.15/14.28 | (X2 @ '#sk6' @ '#sk7') 71.15/14.28 | ~ (X2 @ ('#sk121' @ X2) @ ('#sk175' @ X2)))), 71.15/14.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl164])). 71.15/14.28 thf(zip_derived_cl28, plain, 71.15/14.28 (( (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((((Y0 @ Y1 @ 71.15/14.28 Y2) & (Y0 @ 71.15/14.28 Y2 @ Y3))) => 71.15/14.28 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.28 ('#sk1' @ Y1 @ Y2))) => 71.15/14.28 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.28 (Y0 @ '#sk7' @ '#sk8')))))) 71.15/14.28 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((((Y0 @ Y1 @ 71.15/14.28 Y2) & (Y0 @ 71.15/14.28 Y2 @ Y3))) => 71.15/14.28 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.28 ('#sk1' @ Y1 @ Y2))) => 71.15/14.28 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.28 (Y0 @ '#sk3' @ '#sk4')))))) 71.15/14.28 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 (( 71.15/14.28 (!!) @ ( 71.15/14.28 ^[Y5 : a]: 71.15/14.28 (( 71.15/14.28 (( 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) & 71.15/14.28 (Y2 @ 71.15/14.28 Y4 @ Y5))) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y5)))))))))))) & 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 (( 71.15/14.28 ('#sk1' @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y4))))))))))) => 71.15/14.28 (Y2 @ Y0 @ Y1)))))) | 71.15/14.28 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 (( 71.15/14.28 (!!) @ ( 71.15/14.28 ^[Y5 : a]: 71.15/14.28 (( 71.15/14.28 (( 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) & 71.15/14.28 (Y2 @ 71.15/14.28 Y4 @ Y5))) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y5)))))))))))) & 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 (( 71.15/14.28 ('#sk2' @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y4))))))))))) => 71.15/14.28 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.28 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 ( 71.15/14.28 ( 71.15/14.28 (!!) @ ( 71.15/14.28 ^[Y5 : a]: 71.15/14.28 (( 71.15/14.28 (( 71.15/14.28 (Y2 @ 71.15/14.28 Y4 @ 71.15/14.28 Y5) & 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y4))) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y5)))))))))))) & 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 ( 71.15/14.28 ( 71.15/14.28 (( 71.15/14.28 ('#sk1' @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) | 71.15/14.28 ('#sk2' @ 71.15/14.28 Y3 @ Y4))) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y4))))))))))) => 71.15/14.28 (Y2 @ Y0 @ Y1)))))))))))))))), 71.15/14.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])). 71.15/14.28 thf(zip_derived_cl34, plain, 71.15/14.28 ((~ ('#form11') 71.15/14.28 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((((Y0 @ Y1 @ 71.15/14.28 Y2) & (Y0 @ 71.15/14.28 Y2 @ Y3))) => 71.15/14.28 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.28 ('#sk1' @ Y1 @ Y2))) => 71.15/14.28 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.28 (Y0 @ '#sk3' @ '#sk4')))))))), 71.15/14.28 define([status(thm)])). 71.15/14.28 thf(zip_derived_cl39, plain, 71.15/14.28 (( ('#form11') 71.15/14.28 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 (( 71.15/14.28 (!!) @ ( 71.15/14.28 ^[Y5 : a]: 71.15/14.28 (( 71.15/14.28 (( 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) & 71.15/14.28 (Y2 @ 71.15/14.28 Y4 @ Y5))) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y5)))))))))))) & 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 (( 71.15/14.28 ('#sk1' @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y4))))))))))) => 71.15/14.28 (Y2 @ Y0 @ Y1)))))) | 71.15/14.28 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 (( 71.15/14.28 (!!) @ ( 71.15/14.28 ^[Y5 : a]: 71.15/14.28 (( 71.15/14.28 (( 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) & 71.15/14.28 (Y2 @ 71.15/14.28 Y4 @ Y5))) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y5)))))))))))) & 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 (( 71.15/14.28 ('#sk2' @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y4))))))))))) => 71.15/14.28 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.28 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 ( 71.15/14.28 ( 71.15/14.28 (!!) @ ( 71.15/14.28 ^[Y5 : a]: 71.15/14.28 (( 71.15/14.28 (( 71.15/14.28 (Y2 @ 71.15/14.28 Y4 @ 71.15/14.28 Y5) & 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y4))) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y5)))))))))))) & 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 ( 71.15/14.28 ( 71.15/14.28 (( 71.15/14.28 ('#sk1' @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) | 71.15/14.28 ('#sk2' @ 71.15/14.28 Y3 @ Y4))) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y4))))))))))) => 71.15/14.28 (Y2 @ Y0 @ Y1)))))))))))))) 71.15/14.28 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((((Y0 @ Y1 @ 71.15/14.28 Y2) & (Y0 @ 71.15/14.28 Y2 @ Y3))) => 71.15/14.28 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.28 ('#sk1' @ Y1 @ Y2))) => 71.15/14.28 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.28 (Y0 @ '#sk7' @ '#sk8')))))))), 71.15/14.28 inference('renaming', [status(thm)], [zip_derived_cl28, zip_derived_cl34])). 71.15/14.28 thf(zip_derived_cl30, plain, 71.15/14.28 (( ('#form9') 71.15/14.28 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 (( 71.15/14.28 (!!) @ ( 71.15/14.28 ^[Y5 : a]: 71.15/14.28 (( 71.15/14.28 (( 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) & 71.15/14.28 (Y2 @ 71.15/14.28 Y4 @ Y5))) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y5)))))))))))) & 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 (( 71.15/14.28 ('#sk1' @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y4))))))))))) => 71.15/14.28 (Y2 @ Y0 @ Y1)))))) | 71.15/14.28 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 (( 71.15/14.28 (!!) @ ( 71.15/14.28 ^[Y5 : a]: 71.15/14.28 (( 71.15/14.28 (( 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) & 71.15/14.28 (Y2 @ 71.15/14.28 Y4 @ Y5))) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y5)))))))))))) & 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 (( 71.15/14.28 ('#sk2' @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y4))))))))))) => 71.15/14.28 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.28 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 ( 71.15/14.28 ( 71.15/14.28 (!!) @ ( 71.15/14.28 ^[Y5 : a]: 71.15/14.28 (( 71.15/14.28 (( 71.15/14.28 (Y2 @ 71.15/14.28 Y4 @ 71.15/14.28 Y5) & 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y4))) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y5)))))))))))) & 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 ( 71.15/14.28 ( 71.15/14.28 (( 71.15/14.28 ('#sk1' @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) | 71.15/14.28 ('#sk2' @ 71.15/14.28 Y3 @ Y4))) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y4))))))))))) => 71.15/14.28 (Y2 @ Y0 @ Y1)))))))))))))))), 71.15/14.28 define([status(thm)])). 71.15/14.28 thf(zip_derived_cl43, plain, 71.15/14.28 ((~ ('#form9') 71.15/14.28 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((((Y0 @ Y1 @ 71.15/14.28 Y2) & (Y0 @ 71.15/14.28 Y2 @ Y3))) => 71.15/14.28 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.28 ('#sk1' @ Y1 @ Y2))) => 71.15/14.28 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.28 (Y0 @ '#sk7' @ '#sk8')))))) 71.15/14.28 | ('#form11'))), 71.15/14.28 inference('renaming', [status(thm)], [zip_derived_cl39, zip_derived_cl30])). 71.15/14.28 thf(zip_derived_cl50, plain, 71.15/14.28 (![X2 : a > a > $o]: 71.15/14.28 ( (((((((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 (((((X2 @ Y0 @ Y1) & (X2 @ 71.15/14.28 Y1 @ Y2))) => 71.15/14.28 (X2 @ Y0 @ Y2)))))))))))) & 71.15/14.28 (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 71.15/14.28 Y1))) => 71.15/14.28 (X2 @ Y0 @ Y1))))))))))) => 71.15/14.28 (X2 @ '#sk7' @ '#sk8'))) 71.15/14.28 | ('#form11') 71.15/14.28 | ~ ('#form9'))), 71.15/14.28 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 71.15/14.28 thf(zip_derived_cl51, plain, 71.15/14.28 (( (((((((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 ((((('#sk21' @ Y0 @ Y1) & 71.15/14.28 ('#sk21' @ Y1 @ Y2))) => 71.15/14.28 ('#sk21' @ Y0 @ Y2)))))))))))) & 71.15/14.28 (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 71.15/14.28 Y1))) => 71.15/14.28 ('#sk21' @ Y0 @ Y1))))))))))) => 71.15/14.28 ('#sk21' @ '#sk7' @ '#sk8'))) 71.15/14.28 | ('#form11') 71.15/14.28 | ~ ('#form9'))), 71.15/14.28 inference('triggered_bool_instantiation', [status(thm)], 71.15/14.28 [zip_derived_cl50])). 71.15/14.28 thf(zip_derived_cl247, plain, 71.15/14.28 ((~ (((((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 ((((('#sk21' @ Y0 @ Y1) & 71.15/14.28 ('#sk21' @ Y1 @ Y2))) => 71.15/14.28 ('#sk21' @ Y0 @ Y2)))))))))))) & 71.15/14.28 (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 71.15/14.28 ('#sk21' @ Y0 @ Y1))))))))))) 71.15/14.28 | ('#sk21' @ '#sk7' @ '#sk8') 71.15/14.28 | ~ ('#form9') 71.15/14.28 | ('#form11'))), 71.15/14.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 71.15/14.28 thf(zip_derived_cl248, plain, 71.15/14.28 ((~ (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 ((((('#sk21' @ Y0 @ Y1) & 71.15/14.28 ('#sk21' @ Y1 @ Y2))) => 71.15/14.28 ('#sk21' @ Y0 @ Y2)))))))))))) 71.15/14.28 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 71.15/14.28 ('#sk21' @ Y0 @ Y1))))))))) 71.15/14.28 | ('#form11') 71.15/14.28 | ~ ('#form9') 71.15/14.28 | ('#sk21' @ '#sk7' @ '#sk8'))), 71.15/14.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl247])). 71.15/14.28 thf(zip_derived_cl50, plain, 71.15/14.28 (![X2 : a > a > $o]: 71.15/14.28 ( (((((((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 (((((X2 @ Y0 @ Y1) & (X2 @ 71.15/14.28 Y1 @ Y2))) => 71.15/14.28 (X2 @ Y0 @ Y2)))))))))))) & 71.15/14.28 (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 71.15/14.28 Y1))) => 71.15/14.28 (X2 @ Y0 @ Y1))))))))))) => 71.15/14.28 (X2 @ '#sk7' @ '#sk8'))) 71.15/14.28 | ('#form11') 71.15/14.28 | ~ ('#form9'))), 71.15/14.28 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 71.15/14.28 thf(zip_derived_cl68, plain, 71.15/14.28 (![X2 : a > a > $o]: 71.15/14.28 (~ (((((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 (((((X2 @ Y0 @ Y1) & (X2 @ 71.15/14.28 Y1 @ Y2))) => 71.15/14.28 (X2 @ Y0 @ Y2)))))))))))) & 71.15/14.28 (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 71.15/14.28 Y1))) => 71.15/14.28 (X2 @ Y0 @ Y1))))))))))) 71.15/14.28 | (X2 @ '#sk7' @ '#sk8') 71.15/14.28 | ~ ('#form9') 71.15/14.28 | ('#form11'))), 71.15/14.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])). 71.15/14.28 thf(zip_derived_cl81, plain, 71.15/14.28 (![X2 : a > a > $o]: 71.15/14.28 (~ (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 (((((X2 @ Y0 @ Y1) & (X2 @ 71.15/14.28 Y1 @ Y2))) => 71.15/14.28 (X2 @ Y0 @ Y2)))))))))))) 71.15/14.28 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 71.15/14.28 Y1))) => 71.15/14.28 (X2 @ Y0 @ Y1))))))))) 71.15/14.28 | ('#form11') 71.15/14.28 | ~ ('#form9') 71.15/14.28 | (X2 @ '#sk7' @ '#sk8'))), 71.15/14.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl68])). 71.15/14.28 thf(zip_derived_cl96, plain, 71.15/14.28 (![X2 : a > a > $o]: 71.15/14.28 (~ (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((((X2 @ ('#sk47' @ X2) @ Y0) & (X2 @ 71.15/14.28 Y0 @ Y1))) => 71.15/14.28 (X2 @ ('#sk47' @ X2) @ Y1))))))))) 71.15/14.28 | (X2 @ '#sk7' @ '#sk8') 71.15/14.28 | ~ ('#form9') 71.15/14.28 | ('#form11') 71.15/14.28 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 71.15/14.28 Y1))) => 71.15/14.28 (X2 @ Y0 @ Y1))))))))))), 71.15/14.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl81])). 71.15/14.28 thf(zip_derived_cl105, plain, 71.15/14.28 (![X2 : a > a > $o]: 71.15/14.28 (~ (((!!) @ (^[Y0 : a]: 71.15/14.28 (((((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ 71.15/14.28 ('#sk74' @ X2) @ Y0))) => 71.15/14.28 (X2 @ ('#sk47' @ X2) @ Y0)))))) 71.15/14.28 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 71.15/14.28 Y1))) => 71.15/14.28 (X2 @ Y0 @ Y1))))))))) 71.15/14.28 | ('#form11') 71.15/14.28 | ~ ('#form9') 71.15/14.28 | (X2 @ '#sk7' @ '#sk8'))), 71.15/14.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 71.15/14.28 thf(zip_derived_cl115, plain, 71.15/14.28 (![X2 : a > a > $o]: 71.15/14.28 ( ('#form204' @ X2) 71.15/14.28 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 71.15/14.28 Y1))) => 71.15/14.28 (X2 @ Y0 @ Y1))))))))))), 71.15/14.28 define([status(thm)])). 71.15/14.28 thf(zip_derived_cl249, plain, 71.15/14.28 ((~ ('#form204' @ '#sk21') 71.15/14.28 | ('#sk21' @ '#sk7' @ '#sk8') 71.15/14.28 | ~ ('#form9') 71.15/14.28 | ('#form11') 71.15/14.28 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 ((((('#sk21' @ Y0 @ Y1) & 71.15/14.28 ('#sk21' @ Y1 @ Y2))) => 71.15/14.28 ('#sk21' @ Y0 @ Y2)))))))))))))), 71.15/14.28 inference('renaming', [status(thm)], 71.15/14.28 [zip_derived_cl248, zip_derived_cl115])). 71.15/14.28 thf(zip_derived_cl250, plain, 71.15/14.28 ((~ (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 ((((('#sk21' @ ('#sk47' @ '#sk21') @ Y0) & 71.15/14.28 ('#sk21' @ Y0 @ Y1))) => 71.15/14.28 ('#sk21' @ ('#sk47' @ '#sk21') @ Y1))))))))) 71.15/14.28 | ('#form11') 71.15/14.28 | ~ ('#form9') 71.15/14.28 | ('#sk21' @ '#sk7' @ '#sk8') 71.15/14.28 | ~ ('#form204' @ '#sk21'))), 71.15/14.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl249])). 71.15/14.28 thf(zip_derived_cl251, plain, 71.15/14.28 ((~ (((!!) @ (^[Y0 : a]: 71.15/14.28 ((((('#sk21' @ ('#sk47' @ '#sk21') @ 71.15/14.28 ('#sk74' @ '#sk21')) & ('#sk21' @ 71.15/14.28 ('#sk74' @ '#sk21') @ Y0))) => 71.15/14.28 ('#sk21' @ ('#sk47' @ '#sk21') @ Y0)))))) 71.15/14.28 | ~ ('#form204' @ '#sk21') 71.15/14.28 | ('#sk21' @ '#sk7' @ '#sk8') 71.15/14.28 | ~ ('#form9') 71.15/14.28 | ('#form11'))), 71.15/14.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl250])). 71.15/14.28 thf(zip_derived_cl30, plain, 71.15/14.28 (( ('#form9') 71.15/14.28 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((((((!!) @ (^[Y2 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 (( 71.15/14.28 (!!) @ ( 71.15/14.28 ^[Y5 : a]: 71.15/14.28 (( 71.15/14.28 (( 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) & 71.15/14.28 (Y2 @ 71.15/14.28 Y4 @ Y5))) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y5)))))))))))) & 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 (( 71.15/14.28 ('#sk1' @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y4))))))))))) => 71.15/14.28 (Y2 @ Y0 @ Y1)))))) | 71.15/14.28 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 (( 71.15/14.28 (!!) @ ( 71.15/14.28 ^[Y5 : a]: 71.15/14.28 (( 71.15/14.28 (( 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) & 71.15/14.28 (Y2 @ 71.15/14.28 Y4 @ Y5))) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y5)))))))))))) & 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 (( 71.15/14.28 ('#sk2' @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y4))))))))))) => 71.15/14.28 (Y2 @ Y0 @ Y1)))))))) => 71.15/14.28 (((!!) @ (^[Y2 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 ( 71.15/14.28 ( 71.15/14.28 (!!) @ ( 71.15/14.28 ^[Y5 : a]: 71.15/14.28 (( 71.15/14.28 (( 71.15/14.28 (Y2 @ 71.15/14.28 Y4 @ 71.15/14.28 Y5) & 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y4))) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y5)))))))))))) & 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 ( 71.15/14.28 ( 71.15/14.28 (( 71.15/14.28 ('#sk1' @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) | 71.15/14.28 ('#sk2' @ 71.15/14.28 Y3 @ Y4))) => 71.15/14.28 (Y2 @ 71.15/14.28 Y3 @ Y4))))))))))) => 71.15/14.28 (Y2 @ Y0 @ Y1)))))))))))))))), 71.15/14.28 define([status(thm)])). 71.15/14.28 thf(zip_derived_cl31, plain, 71.15/14.28 ((~ (((!!) @ (^[Y0 : a]: 71.15/14.28 (((((((!!) @ (^[Y1 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y2 : a]: 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 ( 71.15/14.28 ( 71.15/14.28 (( 71.15/14.28 (Y1 @ 71.15/14.28 Y2 @ 71.15/14.28 Y3) & 71.15/14.28 (Y1 @ 71.15/14.28 Y3 @ Y4))) => 71.15/14.28 (Y1 @ 71.15/14.28 Y2 @ Y4)))))))))))) & 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 ((('#sk1' @ 71.15/14.28 Y2 @ Y3) => 71.15/14.28 (Y1 @ Y2 @ 71.15/14.28 Y3))))))))))) => 71.15/14.28 (Y1 @ '#sk10' @ Y0)))))) | 71.15/14.28 (((!!) @ (^[Y1 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y2 : a]: 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 ( 71.15/14.28 ( 71.15/14.28 (( 71.15/14.28 (Y1 @ 71.15/14.28 Y2 @ 71.15/14.28 Y3) & 71.15/14.28 (Y1 @ 71.15/14.28 Y3 @ Y4))) => 71.15/14.28 (Y1 @ 71.15/14.28 Y2 @ Y4)))))))))))) & 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 ((('#sk2' @ 71.15/14.28 Y2 @ Y3) => 71.15/14.28 (Y1 @ Y2 @ 71.15/14.28 Y3))))))))))) => 71.15/14.28 (Y1 @ '#sk10' @ Y0)))))))) => 71.15/14.28 (((!!) @ (^[Y1 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y2 : a]: 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((!!) @ ( 71.15/14.28 ^[Y4 : a]: 71.15/14.28 (((( 71.15/14.28 (Y1 @ 71.15/14.28 Y3 @ 71.15/14.28 Y4) & 71.15/14.28 (Y1 @ 71.15/14.28 Y2 @ Y3))) => 71.15/14.28 (Y1 @ 71.15/14.28 Y2 @ Y4)))))))))))) & 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 ((((('#sk1' @ 71.15/14.28 Y2 @ Y3) | 71.15/14.28 ('#sk2' @ 71.15/14.28 Y2 @ Y3))) => 71.15/14.28 (Y1 @ Y2 @ 71.15/14.28 Y3))))))))))) => 71.15/14.28 (Y1 @ '#sk10' @ Y0))))))))))) 71.15/14.28 | ('#form9'))), 71.15/14.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])). 71.15/14.28 thf(zip_derived_cl42, plain, 71.15/14.28 ((~ (((((((!!) @ (^[Y0 : a > a > $o]: 71.15/14.28 (((((((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 (((!!) @ (^[Y3 : a]: 71.15/14.28 (((((Y0 @ 71.15/14.28 Y1 @ 71.15/14.28 Y2) & 71.15/14.28 (Y0 @ 71.15/14.28 Y2 @ Y3))) => 71.15/14.28 (Y0 @ Y1 @ 71.15/14.28 Y3)))))))))))) & 71.15/14.28 (((!!) @ (^[Y1 : a]: 71.15/14.28 (((!!) @ (^[Y2 : a]: 71.15/14.28 ((('#sk1' @ Y1 @ Y2) => 71.15/14.28 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.29 (Y0 @ '#sk10' @ '#sk12')))))) | 71.15/14.29 (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.29 (((((((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((!!) @ (^[Y3 : a]: 71.15/14.29 (((((Y0 @ 71.15/14.29 Y1 @ 71.15/14.29 Y2) & 71.15/14.29 (Y0 @ 71.15/14.29 Y2 @ Y3))) => 71.15/14.29 (Y0 @ Y1 @ 71.15/14.29 Y3)))))))))))) & 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((('#sk2' @ Y1 @ Y2) => 71.15/14.29 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.29 (Y0 @ '#sk10' @ '#sk12')))))))) => 71.15/14.29 (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.29 (((((((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((!!) @ (^[Y3 : a]: 71.15/14.29 (((((Y0 @ Y2 @ 71.15/14.29 Y3) & 71.15/14.29 (Y0 @ Y1 @ 71.15/14.29 Y2))) => 71.15/14.29 (Y0 @ Y1 @ 71.15/14.29 Y3)))))))))))) & 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk1' @ Y1 @ Y2) | 71.15/14.29 ('#sk2' @ Y1 @ Y2))) => 71.15/14.29 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.29 (Y0 @ '#sk10' @ '#sk12')))))))) 71.15/14.29 | ('#form9'))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl31])). 71.15/14.29 thf(zip_derived_cl48, plain, 71.15/14.29 (( (((((!!) @ (^[Y0 : a > a > $o]: 71.15/14.29 (((((((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((!!) @ (^[Y3 : a]: 71.15/14.29 (((((Y0 @ Y1 @ 71.15/14.29 Y2) & (Y0 @ 71.15/14.29 Y2 @ Y3))) => 71.15/14.29 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((('#sk1' @ Y1 @ Y2) => 71.15/14.29 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.29 (Y0 @ '#sk10' @ '#sk12')))))) | 71.15/14.29 (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.29 (((((((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((!!) @ (^[Y3 : a]: 71.15/14.29 (((((Y0 @ Y1 @ 71.15/14.29 Y2) & (Y0 @ 71.15/14.29 Y2 @ Y3))) => 71.15/14.29 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((('#sk2' @ Y1 @ Y2) => 71.15/14.29 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.29 (Y0 @ '#sk10' @ '#sk12')))))))) 71.15/14.29 | ('#form9'))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])). 71.15/14.29 thf(zip_derived_cl63, plain, 71.15/14.29 (( (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.29 (((((((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((!!) @ (^[Y3 : a]: 71.15/14.29 (((((Y0 @ Y1 @ 71.15/14.29 Y2) & (Y0 @ 71.15/14.29 Y2 @ Y3))) => 71.15/14.29 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 71.15/14.29 Y1 @ Y2))))))))))) => 71.15/14.29 (Y0 @ '#sk10' @ '#sk12')))))) 71.15/14.29 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.29 (((((((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((!!) @ (^[Y3 : a]: 71.15/14.29 (((((Y0 @ Y1 @ 71.15/14.29 Y2) & (Y0 @ 71.15/14.29 Y2 @ Y3))) => 71.15/14.29 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((('#sk2' @ Y1 @ Y2) => 71.15/14.29 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.29 (Y0 @ '#sk10' @ '#sk12')))))) 71.15/14.29 | ('#form9'))), 71.15/14.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl48])). 71.15/14.29 thf(zip_derived_cl73, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( (((((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((((X2 @ Y0 @ Y1) & (X2 @ 71.15/14.29 Y1 @ Y2))) => 71.15/14.29 (X2 @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 71.15/14.29 (X2 @ '#sk10' @ '#sk12'))) 71.15/14.29 | ('#form9') 71.15/14.29 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.29 (((((((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((!!) @ (^[Y3 : a]: 71.15/14.29 (((((Y0 @ 71.15/14.29 Y1 @ Y2) & 71.15/14.29 (Y0 @ 71.15/14.29 Y2 @ Y3))) => 71.15/14.29 (Y0 @ Y1 @ 71.15/14.29 Y3)))))))))))) & 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((('#sk2' @ Y1 @ Y2) => 71.15/14.29 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.29 (Y0 @ '#sk10' @ '#sk12')))))))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 71.15/14.29 thf(zip_derived_cl73, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( (((((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((((X2 @ Y0 @ Y1) & (X2 @ 71.15/14.29 Y1 @ Y2))) => 71.15/14.29 (X2 @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 71.15/14.29 (X2 @ '#sk10' @ '#sk12'))) 71.15/14.29 | ('#form9') 71.15/14.29 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.29 (((((((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((!!) @ (^[Y3 : a]: 71.15/14.29 (((((Y0 @ 71.15/14.29 Y1 @ Y2) & 71.15/14.29 (Y0 @ 71.15/14.29 Y2 @ Y3))) => 71.15/14.29 (Y0 @ Y1 @ 71.15/14.29 Y3)))))))))))) & 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((('#sk2' @ Y1 @ Y2) => 71.15/14.29 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.29 (Y0 @ '#sk10' @ '#sk12')))))))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 71.15/14.29 thf(zip_derived_cl86, plain, 71.15/14.29 ((~ ('#form91') 71.15/14.29 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.29 (((((((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((!!) @ (^[Y3 : a]: 71.15/14.29 (((((Y0 @ Y1 @ 71.15/14.29 Y2) & (Y0 @ 71.15/14.29 Y2 @ Y3))) => 71.15/14.29 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((('#sk2' @ Y1 @ Y2) => 71.15/14.29 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.29 (Y0 @ '#sk10' @ '#sk12')))))))), 71.15/14.29 define([status(thm)])). 71.15/14.29 thf(zip_derived_cl93, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( ('#form91') 71.15/14.29 | ('#form9') 71.15/14.29 | (((((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((((X2 @ Y0 @ Y1) & 71.15/14.29 (X2 @ Y1 @ Y2))) => 71.15/14.29 (X2 @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 71.15/14.29 (X2 @ '#sk10' @ '#sk12'))))), 71.15/14.29 inference('renaming', [status(thm)], [zip_derived_cl73, zip_derived_cl86])). 71.15/14.29 thf(zip_derived_cl101, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((((X2 @ Y0 @ Y1) & (X2 @ 71.15/14.29 Y1 @ Y2))) => 71.15/14.29 (X2 @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) 71.15/14.29 | (X2 @ '#sk10' @ '#sk12') 71.15/14.29 | ('#form9') 71.15/14.29 | ('#form91'))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl93])). 71.15/14.29 thf(zip_derived_cl111, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((((X2 @ Y0 @ Y1) & (X2 @ 71.15/14.29 Y1 @ Y2))) => 71.15/14.29 (X2 @ Y0 @ Y2)))))))))))) 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 71.15/14.29 | ('#form91') 71.15/14.29 | ('#form9') 71.15/14.29 | (X2 @ '#sk10' @ '#sk12'))), 71.15/14.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl101])). 71.15/14.29 thf(zip_derived_cl125, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((((X2 @ ('#sk47' @ X2) @ Y0) & (X2 @ 71.15/14.29 Y0 @ Y1))) => 71.15/14.29 (X2 @ ('#sk47' @ X2) @ Y1))))))))) 71.15/14.29 | (X2 @ '#sk10' @ '#sk12') 71.15/14.29 | ('#form9') 71.15/14.29 | ('#form91') 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl111])). 71.15/14.29 thf(zip_derived_cl138, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ 71.15/14.29 ('#sk74' @ X2) @ Y0))) => 71.15/14.29 (X2 @ ('#sk47' @ X2) @ Y0)))))) 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 71.15/14.29 | ('#form91') 71.15/14.29 | ('#form9') 71.15/14.29 | (X2 @ '#sk10' @ '#sk12'))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl125])). 71.15/14.29 thf(zip_derived_cl149, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( ('#form434' @ X2) 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ 71.15/14.29 ('#sk74' @ X2) @ Y0))) => 71.15/14.29 (X2 @ ('#sk47' @ X2) @ Y0)))))))), 71.15/14.29 define([status(thm)])). 71.15/14.29 thf(zip_derived_cl252, plain, 71.15/14.29 ((~ ('#form434' @ '#sk21') 71.15/14.29 | ('#form11') 71.15/14.29 | ~ ('#form9') 71.15/14.29 | ('#sk21' @ '#sk7' @ '#sk8') 71.15/14.29 | ~ ('#form204' @ '#sk21'))), 71.15/14.29 inference('renaming', [status(thm)], 71.15/14.29 [zip_derived_cl251, zip_derived_cl149])). 71.15/14.29 thf(zip_derived_cl120, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( ((('#sk1' @ ('#sk121' @ X2) @ ('#sk175' @ X2)) | ('#sk2' @ 71.15/14.29 ('#sk121' @ X2) @ ('#sk175' @ X2)))) 71.15/14.29 | (X2 @ '#sk6' @ '#sk7') 71.15/14.29 | ~ ('#form9') 71.15/14.29 | ('#form11') 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((((X2 @ Y1 @ Y2) & (X2 @ 71.15/14.29 Y0 @ Y1))) => 71.15/14.29 (X2 @ Y0 @ Y2)))))))))))))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 71.15/14.29 thf(zip_derived_cl135, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( ('#sk1' @ ('#sk121' @ X2) @ ('#sk175' @ X2)) 71.15/14.29 | ('#sk2' @ ('#sk121' @ X2) @ ('#sk175' @ X2)) 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((((X2 @ Y1 @ Y2) & (X2 @ 71.15/14.29 Y0 @ Y1))) => 71.15/14.29 (X2 @ Y0 @ Y2)))))))))))) 71.15/14.29 | ('#form11') 71.15/14.29 | ~ ('#form9') 71.15/14.29 | (X2 @ '#sk6' @ '#sk7'))), 71.15/14.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl120])). 71.15/14.29 thf(zip_derived_cl147, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((((X2 @ Y0 @ Y1) & (X2 @ 71.15/14.29 ('#sk334' @ X2) @ Y0))) => 71.15/14.29 (X2 @ ('#sk334' @ X2) @ Y1))))))))) 71.15/14.29 | (X2 @ '#sk6' @ '#sk7') 71.15/14.29 | ~ ('#form9') 71.15/14.29 | ('#form11') 71.15/14.29 | ('#sk2' @ ('#sk121' @ X2) @ ('#sk175' @ X2)) 71.15/14.29 | ('#sk1' @ ('#sk121' @ X2) @ ('#sk175' @ X2)))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl135])). 71.15/14.29 thf(zip_derived_cl157, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((((X2 @ ('#sk421' @ X2) @ Y0) & (X2 @ 71.15/14.29 ('#sk334' @ X2) @ ('#sk421' @ X2)))) => 71.15/14.29 (X2 @ ('#sk334' @ X2) @ Y0)))))) 71.15/14.29 | ('#sk1' @ ('#sk121' @ X2) @ ('#sk175' @ X2)) 71.15/14.29 | ('#sk2' @ ('#sk121' @ X2) @ ('#sk175' @ X2)) 71.15/14.29 | ('#form11') 71.15/14.29 | ~ ('#form9') 71.15/14.29 | (X2 @ '#sk6' @ '#sk7'))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl147])). 71.15/14.29 thf(zip_derived_cl163, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (((((X2 @ ('#sk421' @ X2) @ ('#sk509' @ X2)) & (X2 @ 71.15/14.29 ('#sk334' @ X2) @ ('#sk421' @ X2)))) => 71.15/14.29 (X2 @ ('#sk334' @ X2) @ ('#sk509' @ X2)))) 71.15/14.29 | (X2 @ '#sk6' @ '#sk7') 71.15/14.29 | ~ ('#form9') 71.15/14.29 | ('#form11') 71.15/14.29 | ('#sk2' @ ('#sk121' @ X2) @ ('#sk175' @ X2)) 71.15/14.29 | ('#sk1' @ ('#sk121' @ X2) @ ('#sk175' @ X2)))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl157])). 71.15/14.29 thf(zip_derived_cl171, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (X2 @ ('#sk334' @ X2) @ ('#sk509' @ X2)) 71.15/14.29 | ('#sk1' @ ('#sk121' @ X2) @ ('#sk175' @ X2)) 71.15/14.29 | ('#sk2' @ ('#sk121' @ X2) @ ('#sk175' @ X2)) 71.15/14.29 | ('#form11') 71.15/14.29 | ~ ('#form9') 71.15/14.29 | (X2 @ '#sk6' @ '#sk7'))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl163])). 71.15/14.29 thf(zip_derived_cl170, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( (((X2 @ ('#sk421' @ X2) @ ('#sk509' @ X2)) & (X2 @ 71.15/14.29 ('#sk334' @ X2) @ ('#sk421' @ X2)))) 71.15/14.29 | ('#sk1' @ ('#sk121' @ X2) @ ('#sk175' @ X2)) 71.15/14.29 | ('#sk2' @ ('#sk121' @ X2) @ ('#sk175' @ X2)) 71.15/14.29 | ('#form11') 71.15/14.29 | ~ ('#form9') 71.15/14.29 | (X2 @ '#sk6' @ '#sk7'))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl163])). 71.15/14.29 thf(zip_derived_cl178, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( (X2 @ ('#sk421' @ X2) @ ('#sk509' @ X2)) 71.15/14.29 | (X2 @ '#sk6' @ '#sk7') 71.15/14.29 | ~ ('#form9') 71.15/14.29 | ('#form11') 71.15/14.29 | ('#sk2' @ ('#sk121' @ X2) @ ('#sk175' @ X2)) 71.15/14.29 | ('#sk1' @ ('#sk121' @ X2) @ ('#sk175' @ X2)))), 71.15/14.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl170])). 71.15/14.29 thf(zip_derived_cl61, plain, 71.15/14.29 (( (((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk21' @ Y1 @ Y2) & 71.15/14.29 ('#sk21' @ Y0 @ Y1))) => 71.15/14.29 ('#sk21' @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 71.15/14.29 ('#sk21' @ Y0 @ Y1))))))))))) 71.15/14.29 | ('#form11') 71.15/14.29 | ~ ('#form9'))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 71.15/14.29 thf(zip_derived_cl71, plain, 71.15/14.29 (( (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk21' @ Y1 @ Y2) & 71.15/14.29 ('#sk21' @ Y0 @ Y1))) => 71.15/14.29 ('#sk21' @ Y0 @ Y2)))))))))))) 71.15/14.29 | ~ ('#form9') 71.15/14.29 | ('#form11'))), 71.15/14.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl61])). 71.15/14.29 thf(zip_derived_cl84, plain, 71.15/14.29 (![X2 : a]: 71.15/14.29 ( (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk21' @ Y0 @ Y1) & ('#sk21' @ X2 @ 71.15/14.29 Y0))) => 71.15/14.29 ('#sk21' @ X2 @ Y1))))))))) 71.15/14.29 | ('#form11') 71.15/14.29 | ~ ('#form9'))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl71])). 71.15/14.29 thf(zip_derived_cl99, plain, 71.15/14.29 (![X2 : a, X4 : a]: 71.15/14.29 ( (((!!) @ (^[Y0 : a]: 71.15/14.29 ((((('#sk21' @ X4 @ Y0) & ('#sk21' @ X2 @ X4))) => 71.15/14.29 ('#sk21' @ X2 @ Y0)))))) 71.15/14.29 | ~ ('#form9') 71.15/14.29 | ('#form11'))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl84])). 71.15/14.29 thf(zip_derived_cl109, plain, 71.15/14.29 (![X2 : a, X4 : a, X6 : a]: 71.15/14.29 ( ((((('#sk21' @ X4 @ X6) & ('#sk21' @ X2 @ X4))) => ('#sk21' @ X2 @ 71.15/14.29 X6))) 71.15/14.29 | ('#form11') 71.15/14.29 | ~ ('#form9'))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl99])). 71.15/14.29 thf(zip_derived_cl122, plain, 71.15/14.29 (![X2 : a, X4 : a, X6 : a]: 71.15/14.29 (~ ((('#sk21' @ X4 @ X6) & ('#sk21' @ X2 @ X4))) 71.15/14.29 | ('#sk21' @ X2 @ X6) 71.15/14.29 | ~ ('#form9') 71.15/14.29 | ('#form11'))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl109])). 71.15/14.29 thf(zip_derived_cl137, plain, 71.15/14.29 (![X2 : a, X4 : a, X6 : a]: 71.15/14.29 (~ ('#sk21' @ X4 @ X6) 71.15/14.29 | ~ ('#sk21' @ X2 @ X4) 71.15/14.29 | ('#form11') 71.15/14.29 | ~ ('#form9') 71.15/14.29 | ('#sk21' @ X2 @ X6))), 71.15/14.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl122])). 71.15/14.29 thf(zip_derived_cl72, plain, 71.15/14.29 (( (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 71.15/14.29 ('#sk21' @ Y0 @ Y1))))))))) 71.15/14.29 | ~ ('#form9') 71.15/14.29 | ('#form11'))), 71.15/14.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl61])). 71.15/14.29 thf(zip_derived_cl85, plain, 71.15/14.29 (![X2 : a]: 71.15/14.29 ( (((!!) @ (^[Y0 : a]: 71.15/14.29 ((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) => 71.15/14.29 ('#sk21' @ X2 @ Y0)))))) 71.15/14.29 | ('#form11') 71.15/14.29 | ~ ('#form9'))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl72])). 71.15/14.29 thf(zip_derived_cl100, plain, 71.15/14.29 (![X2 : a, X4 : a]: 71.15/14.29 ( ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) => ('#sk21' @ X2 @ X4))) 71.15/14.29 | ~ ('#form9') 71.15/14.29 | ('#form11'))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 71.15/14.29 thf(zip_derived_cl110, plain, 71.15/14.29 (![X2 : a, X4 : a]: 71.15/14.29 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 71.15/14.29 | ('#sk21' @ X2 @ X4) 71.15/14.29 | ('#form11') 71.15/14.29 | ~ ('#form9'))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 71.15/14.29 thf(zip_derived_cl124, plain, 71.15/14.29 (![X2 : a, X4 : a]: 71.15/14.29 (~ ('#sk2' @ X2 @ X4) 71.15/14.29 | ~ ('#form9') 71.15/14.29 | ('#form11') 71.15/14.29 | ('#sk21' @ X2 @ X4))), 71.15/14.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl110])). 71.15/14.29 thf(zip_derived_cl123, plain, 71.15/14.29 (![X2 : a, X4 : a]: 71.15/14.29 (~ ('#sk1' @ X2 @ X4) 71.15/14.29 | ~ ('#form9') 71.15/14.29 | ('#form11') 71.15/14.29 | ('#sk21' @ X2 @ X4))), 71.15/14.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl110])). 71.15/14.29 thf(zip_derived_cl179, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( (X2 @ ('#sk334' @ X2) @ ('#sk421' @ X2)) 71.15/14.29 | (X2 @ '#sk6' @ '#sk7') 71.15/14.29 | ~ ('#form9') 71.15/14.29 | ('#form11') 71.15/14.29 | ('#sk2' @ ('#sk121' @ X2) @ ('#sk175' @ X2)) 71.15/14.29 | ('#sk1' @ ('#sk121' @ X2) @ ('#sk175' @ X2)))), 71.15/14.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl170])). 71.15/14.29 thf(zip_derived_cl34, plain, 71.15/14.29 ((~ ('#form11') 71.15/14.29 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.29 (((((((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((!!) @ (^[Y3 : a]: 71.15/14.29 (((((Y0 @ Y1 @ 71.15/14.29 Y2) & (Y0 @ 71.15/14.29 Y2 @ Y3))) => 71.15/14.29 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.29 ('#sk1' @ Y1 @ Y2))) => 71.15/14.29 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.29 (Y0 @ '#sk3' @ '#sk4')))))))), 71.15/14.29 define([status(thm)])). 71.15/14.29 thf(zip_derived_cl35, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( (((((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((((X2 @ Y0 @ Y1) & (X2 @ 71.15/14.29 Y1 @ Y2))) => 71.15/14.29 (X2 @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 71.15/14.29 Y1))) => 71.15/14.29 (X2 @ Y0 @ Y1))))))))))) => 71.15/14.29 (X2 @ '#sk3' @ '#sk4'))) 71.15/14.29 | ~ ('#form11'))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 71.15/14.29 thf(zip_derived_cl36, plain, 71.15/14.29 (( (((((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk5' @ Y0 @ Y1) & 71.15/14.29 ('#sk5' @ Y1 @ Y2))) => 71.15/14.29 ('#sk5' @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 71.15/14.29 Y1))) => 71.15/14.29 ('#sk5' @ Y0 @ Y1))))))))))) => 71.15/14.29 ('#sk5' @ '#sk3' @ '#sk4'))) 71.15/14.29 | ~ ('#form11'))), 71.15/14.29 inference('triggered_bool_instantiation', [status(thm)], 71.15/14.29 [zip_derived_cl35])). 71.15/14.29 thf(zip_derived_cl5, plain, 71.15/14.29 (~ (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.29 (((((((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk2' @ Y1 @ Y2) | 71.15/14.29 ('#sk1' @ Y1 @ Y2))) => 71.15/14.29 (Y0 @ Y1 @ Y2))))))))) & 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((!!) @ (^[Y3 : a]: 71.15/14.29 (((((Y0 @ Y1 @ 71.15/14.29 Y2) & (Y0 @ 71.15/14.29 Y2 @ Y3))) => 71.15/14.29 (Y0 @ Y1 @ Y3)))))))))))))) => 71.15/14.29 (Y0 @ '#sk3' @ '#sk4'))))))), 71.15/14.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 71.15/14.29 thf(zip_derived_cl7, plain, 71.15/14.29 (~ (((((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 71.15/14.29 Y1))) => 71.15/14.29 ('#sk5' @ Y0 @ Y1))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk5' @ Y0 @ Y1) & 71.15/14.29 ('#sk5' @ Y1 @ Y2))) => 71.15/14.29 ('#sk5' @ Y0 @ Y2)))))))))))))) => 71.15/14.29 ('#sk5' @ '#sk3' @ '#sk4')))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl5])). 71.15/14.29 thf(zip_derived_cl10, plain, (~ ('#sk5' @ '#sk3' @ '#sk4')), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 71.15/14.29 thf(zip_derived_cl221, plain, 71.15/14.29 (( (((((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk5' @ Y0 @ Y1) & 71.15/14.29 ('#sk5' @ Y1 @ Y2))) => 71.15/14.29 ('#sk5' @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 71.15/14.29 Y1))) => 71.15/14.29 ('#sk5' @ Y0 @ Y1))))))))))) => 71.15/14.29 ($false))) 71.15/14.29 | ~ ('#form11'))), 71.15/14.29 inference('demod', [status(thm)], [zip_derived_cl36, zip_derived_cl10])). 71.15/14.29 thf(zip_derived_cl222, plain, 71.15/14.29 (( (((~) @ (((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk5' @ Y0 @ Y1) & 71.15/14.29 ('#sk5' @ Y1 @ Y2))) => 71.15/14.29 ('#sk5' @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 71.15/14.29 Y0 @ Y1))) => 71.15/14.29 ('#sk5' @ Y0 @ Y1))))))))))))) 71.15/14.29 | ~ ('#form11'))), 71.15/14.29 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl221])). 71.15/14.29 thf(zip_derived_cl223, plain, 71.15/14.29 ((~ (((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk5' @ Y0 @ Y1) & 71.15/14.29 ('#sk5' @ Y1 @ Y2))) => 71.15/14.29 ('#sk5' @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 71.15/14.29 ('#sk5' @ Y0 @ Y1))))))))))) 71.15/14.29 | ~ ('#form11'))), 71.15/14.29 inference('simplify nested equalities', [status(thm)], 71.15/14.29 [zip_derived_cl222])). 71.15/14.29 thf(zip_derived_cl224, plain, 71.15/14.29 ((~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk5' @ Y0 @ Y1) & 71.15/14.29 ('#sk5' @ Y1 @ Y2))) => 71.15/14.29 ('#sk5' @ Y0 @ Y2)))))))))))) 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 71.15/14.29 ('#sk5' @ Y0 @ Y1))))))))) 71.15/14.29 | ~ ('#form11'))), 71.15/14.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl223])). 71.15/14.29 thf(zip_derived_cl115, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( ('#form204' @ X2) 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 71.15/14.29 Y1))) => 71.15/14.29 (X2 @ Y0 @ Y1))))))))))), 71.15/14.29 define([status(thm)])). 71.15/14.29 thf(zip_derived_cl225, plain, 71.15/14.29 ((~ ('#form204' @ '#sk5') 71.15/14.29 | ~ ('#form11') 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk5' @ Y0 @ Y1) & 71.15/14.29 ('#sk5' @ Y1 @ Y2))) => 71.15/14.29 ('#sk5' @ Y0 @ Y2)))))))))))))), 71.15/14.29 inference('renaming', [status(thm)], 71.15/14.29 [zip_derived_cl224, zip_derived_cl115])). 71.15/14.29 thf(zip_derived_cl226, plain, 71.15/14.29 ((~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk5' @ ('#sk47' @ '#sk5') @ Y0) & 71.15/14.29 ('#sk5' @ Y0 @ Y1))) => 71.15/14.29 ('#sk5' @ ('#sk47' @ '#sk5') @ Y1))))))))) 71.15/14.29 | ~ ('#form11') 71.15/14.29 | ~ ('#form204' @ '#sk5'))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl225])). 71.15/14.29 thf(zip_derived_cl227, plain, 71.15/14.29 ((~ (((!!) @ (^[Y0 : a]: 71.15/14.29 ((((('#sk5' @ ('#sk47' @ '#sk5') @ ('#sk74' @ '#sk5')) & 71.15/14.29 ('#sk5' @ ('#sk74' @ '#sk5') @ Y0))) => 71.15/14.29 ('#sk5' @ ('#sk47' @ '#sk5') @ Y0)))))) 71.15/14.29 | ~ ('#form204' @ '#sk5') 71.15/14.29 | ~ ('#form11'))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl226])). 71.15/14.29 thf(zip_derived_cl149, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( ('#form434' @ X2) 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ 71.15/14.29 ('#sk74' @ X2) @ Y0))) => 71.15/14.29 (X2 @ ('#sk47' @ X2) @ Y0)))))))), 71.15/14.29 define([status(thm)])). 71.15/14.29 thf(zip_derived_cl228, plain, 71.15/14.29 ((~ ('#form434' @ '#sk5') | ~ ('#form11') | ~ ('#form204' @ '#sk5'))), 71.15/14.29 inference('renaming', [status(thm)], 71.15/14.29 [zip_derived_cl227, zip_derived_cl149])). 71.15/14.29 thf(zip_derived_cl49, plain, 71.15/14.29 ((~ (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.29 (((((((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((!!) @ (^[Y3 : a]: 71.15/14.29 (((((Y0 @ Y2 @ 71.15/14.29 Y3) & (Y0 @ 71.15/14.29 Y1 @ Y2))) => 71.15/14.29 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk1' @ Y1 @ Y2) | 71.15/14.29 ('#sk2' @ Y1 @ Y2))) => 71.15/14.29 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.29 (Y0 @ '#sk10' @ '#sk12')))))) 71.15/14.29 | ('#form9'))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])). 71.15/14.29 thf(zip_derived_cl67, plain, 71.15/14.29 ((~ (((((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk30' @ Y1 @ Y2) & 71.15/14.29 ('#sk30' @ Y0 @ Y1))) => 71.15/14.29 ('#sk30' @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 71.15/14.29 Y1))) => 71.15/14.29 ('#sk30' @ Y0 @ Y1))))))))))) => 71.15/14.29 ('#sk30' @ '#sk10' @ '#sk12'))) 71.15/14.29 | ('#form9'))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl49])). 71.15/14.29 thf(zip_derived_cl80, plain, 71.15/14.29 ((~ ('#sk30' @ '#sk10' @ '#sk12') | ('#form9'))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 71.15/14.29 thf(zip_derived_cl79, plain, 71.15/14.29 (( (((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk30' @ Y1 @ Y2) & 71.15/14.29 ('#sk30' @ Y0 @ Y1))) => 71.15/14.29 ('#sk30' @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 71.15/14.29 ('#sk30' @ Y0 @ Y1))))))))))) 71.15/14.29 | ('#form9'))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 71.15/14.29 thf(zip_derived_cl95, plain, 71.15/14.29 (( (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 71.15/14.29 ('#sk30' @ Y0 @ Y1))))))))) 71.15/14.29 | ('#form9'))), 71.15/14.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl79])). 71.15/14.29 thf(zip_derived_cl104, plain, 71.15/14.29 (![X2 : a]: 71.15/14.29 ( (((!!) @ (^[Y0 : a]: 71.15/14.29 ((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) => 71.15/14.29 ('#sk30' @ X2 @ Y0)))))) 71.15/14.29 | ('#form9'))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl95])). 71.15/14.29 thf(zip_derived_cl114, plain, 71.15/14.29 (![X2 : a, X4 : a]: 71.15/14.29 ( ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) => ('#sk30' @ X2 @ X4))) 71.15/14.29 | ('#form9'))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl104])). 71.15/14.29 thf(zip_derived_cl128, plain, 71.15/14.29 (![X2 : a, X4 : a]: 71.15/14.29 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 71.15/14.29 | ('#sk30' @ X2 @ X4) 71.15/14.29 | ('#form9'))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl114])). 71.15/14.29 thf(zip_derived_cl142, plain, 71.15/14.29 (![X2 : a, X4 : a]: 71.15/14.29 (~ ('#sk2' @ X2 @ X4) | ('#form9') | ('#sk30' @ X2 @ X4))), 71.15/14.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl128])). 71.15/14.29 thf(zip_derived_cl86, plain, 71.15/14.29 ((~ ('#form91') 71.15/14.29 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.29 (((((((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((!!) @ (^[Y3 : a]: 71.15/14.29 (((((Y0 @ Y1 @ 71.15/14.29 Y2) & (Y0 @ 71.15/14.29 Y2 @ Y3))) => 71.15/14.29 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((('#sk2' @ Y1 @ Y2) => 71.15/14.29 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.29 (Y0 @ '#sk10' @ '#sk12')))))))), 71.15/14.29 define([status(thm)])). 71.15/14.29 thf(zip_derived_cl87, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( (((((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((((X2 @ Y0 @ Y1) & (X2 @ 71.15/14.29 Y1 @ Y2))) => 71.15/14.29 (X2 @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 71.15/14.29 (X2 @ '#sk10' @ '#sk12'))) 71.15/14.29 | ~ ('#form91'))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl86])). 71.15/14.29 thf(zip_derived_cl102, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((((X2 @ Y0 @ Y1) & (X2 @ 71.15/14.29 Y1 @ Y2))) => 71.15/14.29 (X2 @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) 71.15/14.29 | (X2 @ '#sk10' @ '#sk12') 71.15/14.29 | ~ ('#form91'))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl87])). 71.15/14.29 thf(zip_derived_cl112, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((((X2 @ Y0 @ Y1) & (X2 @ 71.15/14.29 Y1 @ Y2))) => 71.15/14.29 (X2 @ Y0 @ Y2)))))))))))) 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 71.15/14.29 | ~ ('#form91') 71.15/14.29 | (X2 @ '#sk10' @ '#sk12'))), 71.15/14.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl102])). 71.15/14.29 thf(zip_derived_cl126, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((((X2 @ ('#sk47' @ X2) @ Y0) & (X2 @ 71.15/14.29 Y0 @ Y1))) => 71.15/14.29 (X2 @ ('#sk47' @ X2) @ Y1))))))))) 71.15/14.29 | (X2 @ '#sk10' @ '#sk12') 71.15/14.29 | ~ ('#form91') 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl112])). 71.15/14.29 thf(zip_derived_cl139, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ 71.15/14.29 ('#sk74' @ X2) @ Y0))) => 71.15/14.29 (X2 @ ('#sk47' @ X2) @ Y0)))))) 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 71.15/14.29 | ~ ('#form91') 71.15/14.29 | (X2 @ '#sk10' @ '#sk12'))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl126])). 71.15/14.29 thf(zip_derived_cl149, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( ('#form434' @ X2) 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ 71.15/14.29 ('#sk74' @ X2) @ Y0))) => 71.15/14.29 (X2 @ ('#sk47' @ X2) @ Y0)))))))), 71.15/14.29 define([status(thm)])). 71.15/14.29 thf(zip_derived_cl152, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ ('#form434' @ X2) 71.15/14.29 | (X2 @ '#sk10' @ '#sk12') 71.15/14.29 | ~ ('#form91') 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 71.15/14.29 inference('renaming', [status(thm)], 71.15/14.29 [zip_derived_cl139, zip_derived_cl149])). 71.15/14.29 thf(zip_derived_cl162, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (((!!) @ (^[Y0 : a]: 71.15/14.29 ((('#sk2' @ ('#sk533' @ X2) @ Y0) => (X2 @ 71.15/14.29 ('#sk533' @ X2) @ Y0)))))) 71.15/14.29 | ~ ('#form91') 71.15/14.29 | (X2 @ '#sk10' @ '#sk12') 71.15/14.29 | ~ ('#form434' @ X2))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl152])). 71.15/14.29 thf(zip_derived_cl169, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ ((('#sk2' @ ('#sk533' @ X2) @ ('#sk621' @ X2)) => (X2 @ 71.15/14.29 ('#sk533' @ X2) @ ('#sk621' @ X2)))) 71.15/14.29 | ~ ('#form434' @ X2) 71.15/14.29 | (X2 @ '#sk10' @ '#sk12') 71.15/14.29 | ~ ('#form91'))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl162])). 71.15/14.29 thf(zip_derived_cl177, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (X2 @ ('#sk533' @ X2) @ ('#sk621' @ X2)) 71.15/14.29 | ~ ('#form91') 71.15/14.29 | (X2 @ '#sk10' @ '#sk12') 71.15/14.29 | ~ ('#form434' @ X2))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl169])). 71.15/14.29 thf(zip_derived_cl115, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( ('#form204' @ X2) 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 71.15/14.29 Y1))) => 71.15/14.29 (X2 @ Y0 @ Y1))))))))))), 71.15/14.29 define([status(thm)])). 71.15/14.29 thf(zip_derived_cl116, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (((!!) @ (^[Y0 : a]: 71.15/14.29 ((((('#sk2' @ ('#sk205' @ X2) @ Y0) | ('#sk1' @ 71.15/14.29 ('#sk205' @ X2) @ Y0))) => 71.15/14.29 (X2 @ ('#sk205' @ X2) @ Y0)))))) 71.15/14.29 | ('#form204' @ X2))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl115])). 71.15/14.29 thf(zip_derived_cl130, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ ((((('#sk2' @ ('#sk205' @ X2) @ ('#sk277' @ X2)) | ('#sk1' @ 71.15/14.29 ('#sk205' @ X2) @ ('#sk277' @ X2)))) => 71.15/14.29 (X2 @ ('#sk205' @ X2) @ ('#sk277' @ X2)))) 71.15/14.29 | ('#form204' @ X2))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl116])). 71.15/14.29 thf(zip_derived_cl145, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( ((('#sk2' @ ('#sk205' @ X2) @ ('#sk277' @ X2)) | ('#sk1' @ 71.15/14.29 ('#sk205' @ X2) @ ('#sk277' @ X2)))) 71.15/14.29 | ('#form204' @ X2))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl130])). 71.15/14.29 thf(zip_derived_cl156, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( ('#sk2' @ ('#sk205' @ X2) @ ('#sk277' @ X2)) 71.15/14.29 | ('#sk1' @ ('#sk205' @ X2) @ ('#sk277' @ X2)) 71.15/14.29 | ('#form204' @ X2))), 71.15/14.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl145])). 71.15/14.29 thf(zip_derived_cl9, plain, 71.15/14.29 ( (((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 71.15/14.29 ('#sk5' @ Y0 @ Y1))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk5' @ Y0 @ Y1) & 71.15/14.29 ('#sk5' @ Y1 @ Y2))) => 71.15/14.29 ('#sk5' @ Y0 @ Y2))))))))))))))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 71.15/14.29 thf(zip_derived_cl13, plain, 71.15/14.29 ( (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk5' @ Y0 @ Y1) & ('#sk5' @ 71.15/14.29 Y1 @ Y2))) => 71.15/14.29 ('#sk5' @ Y0 @ Y2))))))))))))), 71.15/14.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl9])). 71.15/14.29 thf(zip_derived_cl16, plain, 71.15/14.29 (![X2 : a]: 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk5' @ X2 @ Y0) & ('#sk5' @ Y0 @ Y1))) => 71.15/14.29 ('#sk5' @ X2 @ Y1)))))))))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 71.15/14.29 thf(zip_derived_cl19, plain, 71.15/14.29 (![X2 : a, X4 : a]: 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 ((((('#sk5' @ X2 @ X4) & ('#sk5' @ X4 @ Y0))) => 71.15/14.29 ('#sk5' @ X2 @ Y0))))))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 71.15/14.29 thf(zip_derived_cl22, plain, 71.15/14.29 (![X2 : a, X4 : a, X6 : a]: 71.15/14.29 ((((('#sk5' @ X2 @ X4) & ('#sk5' @ X4 @ X6))) => ('#sk5' @ X2 @ X6)))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 71.15/14.29 thf(zip_derived_cl27, plain, 71.15/14.29 (![X2 : a, X4 : a, X6 : a]: 71.15/14.29 (~ ((('#sk5' @ X2 @ X4) & ('#sk5' @ X4 @ X6))) | ('#sk5' @ X2 @ X6))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 71.15/14.29 thf(zip_derived_cl33, plain, 71.15/14.29 (![X2 : a, X4 : a, X6 : a]: 71.15/14.29 (~ ('#sk5' @ X2 @ X4) | ~ ('#sk5' @ X4 @ X6) | ('#sk5' @ X2 @ X6))), 71.15/14.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl27])). 71.15/14.29 thf(zip_derived_cl176, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( ('#sk2' @ ('#sk533' @ X2) @ ('#sk621' @ X2)) 71.15/14.29 | ~ ('#form91') 71.15/14.29 | (X2 @ '#sk10' @ '#sk12') 71.15/14.29 | ~ ('#form434' @ X2))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl169])). 71.15/14.29 thf(zip_derived_cl12, plain, 71.15/14.29 ( (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 71.15/14.29 ('#sk5' @ Y0 @ Y1)))))))))), 71.15/14.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl9])). 71.15/14.29 thf(zip_derived_cl15, plain, 71.15/14.29 (![X2 : a]: 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 ((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) => 71.15/14.29 ('#sk5' @ X2 @ Y0))))))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])). 71.15/14.29 thf(zip_derived_cl18, plain, 71.15/14.29 (![X2 : a, X4 : a]: 71.15/14.29 ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) => ('#sk5' @ X2 @ X4)))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 71.15/14.29 thf(zip_derived_cl21, plain, 71.15/14.29 (![X2 : a, X4 : a]: 71.15/14.29 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) | ('#sk5' @ X2 @ X4))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 71.15/14.29 thf(zip_derived_cl25, plain, 71.15/14.29 (![X2 : a, X4 : a]: (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 71.15/14.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl21])). 71.15/14.29 thf(zip_derived_cl26, plain, 71.15/14.29 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 71.15/14.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl21])). 71.15/14.29 thf(zip_derived_cl146, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (X2 @ ('#sk205' @ X2) @ ('#sk277' @ X2)) | ('#form204' @ X2))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl130])). 71.15/14.29 thf(zip_derived_cl73, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( (((((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((((X2 @ Y0 @ Y1) & (X2 @ 71.15/14.29 Y1 @ Y2))) => 71.15/14.29 (X2 @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 71.15/14.29 (X2 @ '#sk10' @ '#sk12'))) 71.15/14.29 | ('#form9') 71.15/14.29 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.29 (((((((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((!!) @ (^[Y3 : a]: 71.15/14.29 (((((Y0 @ 71.15/14.29 Y1 @ Y2) & 71.15/14.29 (Y0 @ 71.15/14.29 Y2 @ Y3))) => 71.15/14.29 (Y0 @ Y1 @ 71.15/14.29 Y3)))))))))))) & 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((('#sk2' @ Y1 @ Y2) => 71.15/14.29 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.29 (Y0 @ '#sk10' @ '#sk12')))))))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 71.15/14.29 thf(zip_derived_cl74, plain, 71.15/14.29 (( (((((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk30' @ Y0 @ Y1) & 71.15/14.29 ('#sk30' @ Y1 @ Y2))) => 71.15/14.29 ('#sk30' @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk1' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 71.15/14.29 Y1))))))))))) => 71.15/14.29 ('#sk30' @ '#sk10' @ '#sk12'))) 71.15/14.29 | ('#form9') 71.15/14.29 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.29 (((((((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((!!) @ (^[Y3 : a]: 71.15/14.29 (((((Y0 @ Y1 @ 71.15/14.29 Y2) & (Y0 @ 71.15/14.29 Y2 @ Y3))) => 71.15/14.29 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((('#sk2' @ Y1 @ Y2) => 71.15/14.29 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.29 (Y0 @ '#sk10' @ '#sk12')))))))), 71.15/14.29 inference('triggered_bool_instantiation', [status(thm)], 71.15/14.29 [zip_derived_cl73])). 71.15/14.29 thf(zip_derived_cl86, plain, 71.15/14.29 ((~ ('#form91') 71.15/14.29 | (((!!) @ (^[Y0 : a > a > $o]: 71.15/14.29 (((((((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 (((!!) @ (^[Y3 : a]: 71.15/14.29 (((((Y0 @ Y1 @ 71.15/14.29 Y2) & (Y0 @ 71.15/14.29 Y2 @ Y3))) => 71.15/14.29 (Y0 @ Y1 @ Y3)))))))))))) & 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((('#sk2' @ Y1 @ Y2) => 71.15/14.29 (Y0 @ Y1 @ Y2))))))))))) => 71.15/14.29 (Y0 @ '#sk10' @ '#sk12')))))))), 71.15/14.29 define([status(thm)])). 71.15/14.29 thf(zip_derived_cl259, plain, 71.15/14.29 (( ('#form91') 71.15/14.29 | ('#form9') 71.15/14.29 | (((((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk30' @ Y0 @ Y1) & 71.15/14.29 ('#sk30' @ Y1 @ Y2))) => 71.15/14.29 ('#sk30' @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk1' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 71.15/14.29 Y1))))))))))) => 71.15/14.29 ('#sk30' @ '#sk10' @ '#sk12'))))), 71.15/14.29 inference('renaming', [status(thm)], [zip_derived_cl74, zip_derived_cl86])). 71.15/14.29 thf(zip_derived_cl260, plain, 71.15/14.29 ((~ (((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk30' @ Y0 @ Y1) & 71.15/14.29 ('#sk30' @ Y1 @ Y2))) => 71.15/14.29 ('#sk30' @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk1' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))))) 71.15/14.29 | ('#sk30' @ '#sk10' @ '#sk12') 71.15/14.29 | ('#form9') 71.15/14.29 | ('#form91'))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl259])). 71.15/14.29 thf(zip_derived_cl80, plain, 71.15/14.29 ((~ ('#sk30' @ '#sk10' @ '#sk12') | ('#form9'))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 71.15/14.29 thf(zip_derived_cl261, plain, 71.15/14.29 (( ('#form91') 71.15/14.29 | ('#form9') 71.15/14.29 | ~ (((((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk30' @ Y0 @ Y1) & 71.15/14.29 ('#sk30' @ Y1 @ Y2))) => 71.15/14.29 ('#sk30' @ Y0 @ Y2)))))))))))) & 71.15/14.29 (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk1' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 71.15/14.29 Y1))))))))))))), 71.15/14.29 inference('clc', [status(thm)], [zip_derived_cl260, zip_derived_cl80])). 71.15/14.29 thf(zip_derived_cl262, plain, 71.15/14.29 ((~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk30' @ Y0 @ Y1) & 71.15/14.29 ('#sk30' @ Y1 @ Y2))) => 71.15/14.29 ('#sk30' @ Y0 @ Y2)))))))))))) 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk1' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))) 71.15/14.29 | ('#form9') 71.15/14.29 | ('#form91'))), 71.15/14.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl261])). 71.15/14.29 thf(zip_derived_cl263, plain, 71.15/14.29 ((~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk30' @ ('#sk47' @ '#sk30') @ Y0) & 71.15/14.29 ('#sk30' @ Y0 @ Y1))) => 71.15/14.29 ('#sk30' @ ('#sk47' @ '#sk30') @ Y1))))))))) 71.15/14.29 | ('#form91') 71.15/14.29 | ('#form9') 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk1' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl262])). 71.15/14.29 thf(zip_derived_cl264, plain, 71.15/14.29 ((~ (((!!) @ (^[Y0 : a]: 71.15/14.29 ((((('#sk30' @ ('#sk47' @ '#sk30') @ 71.15/14.29 ('#sk74' @ '#sk30')) & ('#sk30' @ 71.15/14.29 ('#sk74' @ '#sk30') @ Y0))) => 71.15/14.29 ('#sk30' @ ('#sk47' @ '#sk30') @ Y0)))))) 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk1' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))) 71.15/14.29 | ('#form9') 71.15/14.29 | ('#form91'))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl263])). 71.15/14.29 thf(zip_derived_cl149, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( ('#form434' @ X2) 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ 71.15/14.29 ('#sk74' @ X2) @ Y0))) => 71.15/14.29 (X2 @ ('#sk47' @ X2) @ Y0)))))))), 71.15/14.29 define([status(thm)])). 71.15/14.29 thf(zip_derived_cl265, plain, 71.15/14.29 ((~ ('#form434' @ '#sk30') 71.15/14.29 | ('#form91') 71.15/14.29 | ('#form9') 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((('#sk1' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))))), 71.15/14.29 inference('renaming', [status(thm)], 71.15/14.29 [zip_derived_cl264, zip_derived_cl149])). 71.15/14.29 thf(zip_derived_cl266, plain, 71.15/14.29 ((~ (((!!) @ (^[Y0 : a]: 71.15/14.29 ((('#sk1' @ ('#sk514' @ '#sk30') @ Y0) => ('#sk30' @ 71.15/14.29 ('#sk514' @ '#sk30') @ Y0)))))) 71.15/14.29 | ('#form9') 71.15/14.29 | ('#form91') 71.15/14.29 | ~ ('#form434' @ '#sk30'))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl265])). 71.15/14.29 thf(zip_derived_cl267, plain, 71.15/14.29 ((~ ((('#sk1' @ ('#sk514' @ '#sk30') @ ('#sk597' @ '#sk30')) => 71.15/14.29 ('#sk30' @ ('#sk514' @ '#sk30') @ ('#sk597' @ '#sk30')))) 71.15/14.29 | ~ ('#form434' @ '#sk30') 71.15/14.29 | ('#form91') 71.15/14.29 | ('#form9'))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl266])). 71.15/14.29 thf(zip_derived_cl269, plain, 71.15/14.29 ((~ ('#sk30' @ ('#sk514' @ '#sk30') @ ('#sk597' @ '#sk30')) 71.15/14.29 | ('#form9') 71.15/14.29 | ('#form91') 71.15/14.29 | ~ ('#form434' @ '#sk30'))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl267])). 71.15/14.29 thf(zip_derived_cl268, plain, 71.15/14.29 (( ('#sk1' @ ('#sk514' @ '#sk30') @ ('#sk597' @ '#sk30')) 71.15/14.29 | ('#form9') 71.15/14.29 | ('#form91') 71.15/14.29 | ~ ('#form434' @ '#sk30'))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl267])). 71.15/14.29 thf(zip_derived_cl141, plain, 71.15/14.29 (![X2 : a, X4 : a]: 71.15/14.29 (~ ('#sk1' @ X2 @ X4) | ('#form9') | ('#sk30' @ X2 @ X4))), 71.15/14.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl128])). 71.15/14.29 thf(zip_derived_cl149, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( ('#form434' @ X2) 71.15/14.29 | ~ (((!!) @ (^[Y0 : a]: 71.15/14.29 (((((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ 71.15/14.29 ('#sk74' @ X2) @ Y0))) => 71.15/14.29 (X2 @ ('#sk47' @ X2) @ Y0)))))))), 71.15/14.29 define([status(thm)])). 71.15/14.29 thf(zip_derived_cl150, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (((((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ 71.15/14.29 ('#sk74' @ X2) @ ('#sk112' @ X2)))) => 71.15/14.29 (X2 @ ('#sk47' @ X2) @ ('#sk112' @ X2)))) 71.15/14.29 | ('#form434' @ X2))), 71.15/14.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl149])). 71.15/14.29 thf(zip_derived_cl160, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( (((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ ('#sk74' @ X2) @ 71.15/14.29 ('#sk112' @ X2)))) 71.15/14.29 | ('#form434' @ X2))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl150])). 71.15/14.29 thf(zip_derived_cl168, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( (X2 @ ('#sk74' @ X2) @ ('#sk112' @ X2)) | ('#form434' @ X2))), 71.15/14.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl160])). 71.15/14.29 thf(zip_derived_cl161, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 (~ (X2 @ ('#sk47' @ X2) @ ('#sk112' @ X2)) | ('#form434' @ X2))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl150])). 71.15/14.29 thf(zip_derived_cl167, plain, 71.15/14.29 (![X2 : a > a > $o]: 71.15/14.29 ( (X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) | ('#form434' @ X2))), 71.15/14.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl160])). 71.15/14.29 thf(zip_derived_cl94, plain, 71.15/14.29 (( (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 (((!!) @ (^[Y2 : a]: 71.15/14.29 ((((('#sk30' @ Y1 @ Y2) & 71.15/14.29 ('#sk30' @ Y0 @ Y1))) => 71.15/14.29 ('#sk30' @ Y0 @ Y2)))))))))))) 71.15/14.29 | ('#form9'))), 71.15/14.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl79])). 71.15/14.29 thf(zip_derived_cl103, plain, 71.15/14.29 (![X2 : a]: 71.15/14.29 ( (((!!) @ (^[Y0 : a]: 71.15/14.29 (((!!) @ (^[Y1 : a]: 71.15/14.29 ((((('#sk30' @ Y0 @ Y1) & ('#sk30' @ X2 @ 71.15/14.29 Y0))) => 71.15/14.29 ('#sk30' @ X2 @ Y1))))))))) 71.15/14.29 | ('#form9'))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])). 71.15/14.29 thf(zip_derived_cl113, plain, 71.15/14.29 (![X2 : a, X4 : a]: 71.15/14.29 ( (((!!) @ (^[Y0 : a]: 71.15/14.29 ((((('#sk30' @ X4 @ Y0) & ('#sk30' @ X2 @ X4))) => 71.15/14.29 ('#sk30' @ X2 @ Y0)))))) 71.15/14.29 | ('#form9'))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl103])). 71.15/14.29 thf(zip_derived_cl127, plain, 71.15/14.29 (![X2 : a, X4 : a, X6 : a]: 71.15/14.29 ( ((((('#sk30' @ X4 @ X6) & ('#sk30' @ X2 @ X4))) => ('#sk30' @ X2 @ 71.15/14.29 X6))) 71.15/14.29 | ('#form9'))), 71.15/14.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl113])). 71.15/14.29 thf(zip_derived_cl140, plain, 71.15/14.29 (![X2 : a, X4 : a, X6 : a]: 71.15/14.29 (~ ((('#sk30' @ X4 @ X6) & ('#sk30' @ X2 @ X4))) 71.15/14.29 | ('#sk30' @ X2 @ X6) 71.15/14.29 | ('#form9'))), 71.15/14.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 71.15/14.29 thf(zip_derived_cl153, plain, 71.15/14.29 (![X2 : a, X4 : a, X6 : a]: 71.15/14.29 (~ ('#sk30' @ X4 @ X6) 71.15/14.29 | ~ ('#sk30' @ X2 @ X4) 71.15/14.29 | ('#form9') 71.15/14.29 | ('#sk30' @ X2 @ X6))), 71.15/14.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl140])). 71.15/14.29 thf(zip_derived_cl1557, plain, ($false), 71.15/14.29 inference('eprover', [status(thm)], 71.15/14.29 [zip_derived_cl165, zip_derived_cl172, zip_derived_cl62, 71.15/14.29 zip_derived_cl173, zip_derived_cl252, zip_derived_cl171, 71.15/14.29 zip_derived_cl178, zip_derived_cl137, zip_derived_cl124, 71.15/14.29 zip_derived_cl123, zip_derived_cl179, zip_derived_cl228, 71.15/14.29 zip_derived_cl80, zip_derived_cl142, zip_derived_cl177, 71.15/14.29 zip_derived_cl156, zip_derived_cl33, zip_derived_cl176, 71.15/14.29 zip_derived_cl25, zip_derived_cl26, zip_derived_cl146, 71.15/14.29 zip_derived_cl269, zip_derived_cl268, zip_derived_cl141, 71.15/14.29 zip_derived_cl168, zip_derived_cl161, zip_derived_cl167, 71.15/14.29 zip_derived_cl153])). 71.15/14.29 71.15/14.29 % SZS output end Refutation 71.15/14.29 71.15/14.29 71.15/14.29 % Terminating... 71.99/14.47 % Runner terminated. 72.00/14.49 % Zipperpin 1.5 exiting 72.00/14.51 EOF