0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Msq1i4lkwe true 0.13/0.34 % Computer : n004.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 02:04:35 EDT 2022 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 960 s 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.34 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.50/0.62 % Total configuration time : 828 0.50/0.62 % Estimated wc time : 1656 0.50/0.62 % Estimated cpu time (8 cpus) : 207.0 0.54/0.69 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.54/0.71 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.54/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.55/0.73 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.55/0.73 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.55/0.75 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 54.32/7.41 % Solved by lams/20_acsne_simpl.sh. 54.32/7.41 % done 432 iterations in 6.509s 54.32/7.41 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 54.32/7.41 % SZS output start Refutation 54.32/7.41 thf(a_type, type, a: $tType). 54.32/7.41 thf('#sk4_type', type, '#sk4': a). 54.32/7.41 thf('#sk30_type', type, '#sk30': a > a > $o). 54.32/7.41 thf('#sk238_type', type, '#sk238': (a > a > $o) > a). 54.32/7.41 thf('#form367_type', type, '#form367': (a > a > $o) > $o). 54.32/7.41 thf('#sk173_type', type, '#sk173': (a > a > $o) > a). 54.32/7.41 thf('#sk3_type', type, '#sk3': a). 54.32/7.41 thf('#sk658_type', type, '#sk658': (a > a > $o) > a). 54.32/7.41 thf('#sk12_type', type, '#sk12': a). 54.32/7.41 thf('#sk21_type', type, '#sk21': a > a > $o). 54.32/7.41 thf('#sk47_type', type, '#sk47': (a > a > $o) > a). 54.32/7.41 thf('#sk112_type', type, '#sk112': (a > a > $o) > a). 54.32/7.41 thf('#sk592_type', type, '#sk592': (a > a > $o) > a). 54.32/7.41 thf('#sk121_type', type, '#sk121': (a > a > $o) > a). 54.32/7.41 thf('#sk314_type', type, '#sk314': (a > a > $o) > a). 54.32/7.41 thf('#sk6_type', type, '#sk6': a). 54.32/7.41 thf('#sk350_type', type, '#sk350': (a > a > $o) > a). 54.32/7.41 thf('#sk2_type', type, '#sk2': a > a > $o). 54.32/7.41 thf('#form172_type', type, '#form172': (a > a > $o) > $o). 54.32/7.41 thf('#sk8_type', type, '#sk8': a). 54.32/7.41 thf('#sk10_type', type, '#sk10': a). 54.32/7.41 thf('#sk7_type', type, '#sk7': a). 54.32/7.41 thf('#form91_type', type, '#form91': $o). 54.32/7.41 thf('#sk74_type', type, '#sk74': (a > a > $o) > a). 54.32/7.41 thf('#form9_type', type, '#form9': $o). 54.32/7.41 thf('#form591_type', type, '#form591': (a > a > $o) > $o). 54.32/7.41 thf('#form11_type', type, '#form11': $o). 54.32/7.41 thf('#sk5_type', type, '#sk5': a > a > $o). 54.32/7.41 thf('#sk1_type', type, '#sk1': a > a > $o). 54.32/7.41 thf('#sk464_type', type, '#sk464': (a > a > $o) > a). 54.32/7.41 thf('#sk255_type', type, '#sk255': (a > a > $o) > a). 54.32/7.41 thf('#form787_type', type, '#form787': (a > a > $o) > $o). 54.32/7.41 thf('#sk228_type', type, '#sk228': (a > a > $o) > a). 54.32/7.41 thf('#sk368_type', type, '#sk368': (a > a > $o) > a). 54.32/7.41 thf(cTHM250H_pme, conjecture, 54.32/7.41 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 54.32/7.41 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 54.32/7.41 ( ( ( ![Xp1:( a > a > $o )]: 54.32/7.41 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 54.32/7.41 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 54.32/7.41 ( ![Xx1:a,Xy1:a]: 54.32/7.41 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 54.32/7.41 ( Xp1 @ Xy0 @ Xz ) ) ) & 54.32/7.41 ( ![Xp1:( a > a > $o )]: 54.32/7.41 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 54.32/7.41 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 54.32/7.41 ( ![Xx1:a,Xy1:a]: 54.32/7.41 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 54.32/7.41 ( ![Xp1:( a > a > $o )]: 54.32/7.41 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 54.32/7.41 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 54.32/7.41 ( ![Xx1:a,Xy1:a]: 54.32/7.41 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) & 54.32/7.41 ( ![Xx0:a,Xy0:a]: 54.32/7.41 ( ( ( ![Xp1:( a > a > $o )]: 54.32/7.41 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 54.32/7.41 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xz ) ) ) & 54.32/7.41 ( ![Xx1:a,Xy1:a]: 54.32/7.41 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 54.32/7.41 ( ![Xp1:( a > a > $o )]: 54.32/7.41 ( ( ( ![Xx1:a,Xy1:a]: 54.32/7.41 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) & 54.32/7.41 ( ![Xx1:a,Xy1:a,Xz:a]: 54.32/7.41 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 54.32/7.41 ( ![Xp1:( a > a > $o )]: 54.32/7.41 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 54.32/7.41 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xz ) ) ) & 54.32/7.41 ( ![Xx1:a,Xy1:a]: 54.32/7.41 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) & 54.32/7.41 ( ~( ![Xp1:( a > a > $o )]: 54.32/7.41 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 54.32/7.41 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xz ) ) ) & 54.32/7.41 ( ![Xx0:a,Xy0:a]: 54.32/7.41 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 54.32/7.41 ( Xp1 @ Xx @ Xy ) ) ) ) ) | 54.32/7.41 ( ![Xp1:( a > a > $o )]: 54.32/7.41 ( ( ( ![Xx0:a,Xy0:a]: 54.32/7.41 ( ( ( R @ Xx0 @ Xy0 ) | ( S @ Xx0 @ Xy0 ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 54.32/7.41 ( ![Xx0:a,Xy0:a,Xz:a]: 54.32/7.41 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 54.32/7.41 ( Xp1 @ Xx @ Xy ) ) ) ))). 54.32/7.41 thf(zf_stmt_0, negated_conjecture, 54.32/7.41 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 54.32/7.41 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 54.32/7.41 ( ( ( ![Xp1:( a > a > $o )]: 54.32/7.41 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 54.32/7.41 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 54.32/7.41 ( ![Xx1:a,Xy1:a]: 54.32/7.41 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 54.32/7.41 ( Xp1 @ Xy0 @ Xz ) ) ) & 54.32/7.41 ( ![Xp1:( a > a > $o )]: 54.32/7.41 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 54.32/7.41 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 54.32/7.41 ( ![Xx1:a,Xy1:a]: 54.32/7.41 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 54.32/7.41 ( ![Xp1:( a > a > $o )]: 54.32/7.41 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 54.32/7.41 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 54.32/7.41 ( ![Xx1:a,Xy1:a]: 54.32/7.41 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) & 54.32/7.41 ( ![Xx0:a,Xy0:a]: 54.32/7.41 ( ( ( ![Xp1:( a > a > $o )]: 54.32/7.41 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 54.32/7.41 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xz ) ) ) & 54.32/7.41 ( ![Xx1:a,Xy1:a]: 54.32/7.41 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 54.32/7.41 ( ![Xp1:( a > a > $o )]: 54.32/7.41 ( ( ( ![Xx1:a,Xy1:a]: 54.32/7.41 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) & 54.32/7.41 ( ![Xx1:a,Xy1:a,Xz:a]: 54.32/7.41 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 54.32/7.41 ( ![Xp1:( a > a > $o )]: 54.32/7.41 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 54.32/7.41 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xz ) ) ) & 54.32/7.41 ( ![Xx1:a,Xy1:a]: 54.32/7.41 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 54.32/7.41 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) & 54.32/7.41 ( ~( ![Xp1:( a > a > $o )]: 54.32/7.41 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 54.32/7.41 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xz ) ) ) & 54.32/7.41 ( ![Xx0:a,Xy0:a]: 54.32/7.41 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 54.32/7.41 ( Xp1 @ Xx @ Xy ) ) ) ) ) | 54.32/7.41 ( ![Xp1:( a > a > $o )]: 54.32/7.41 ( ( ( ![Xx0:a,Xy0:a]: 54.32/7.41 ( ( ( R @ Xx0 @ Xy0 ) | ( S @ Xx0 @ Xy0 ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 54.32/7.41 ( ![Xx0:a,Xy0:a,Xz:a]: 54.32/7.41 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 54.32/7.41 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 54.32/7.41 ( Xp1 @ Xx @ Xy ) ) ) ) )), 54.32/7.41 inference('cnf.neg', [status(esa)], [cTHM250H_pme])). 54.32/7.41 thf(zip_derived_cl0, plain, 54.32/7.41 (~ (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((!!) @ (^[Y1 : a > a > $o]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y9 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y10 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y7 @ 54.32/7.41 Y8 @ 54.32/7.41 Y9) & 54.32/7.41 (Y7 @ 54.32/7.41 Y9 @ Y10))) => 54.32/7.41 (Y7 @ 54.32/7.41 Y8 @ Y10)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y9 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y0 @ 54.32/7.41 Y8 @ 54.32/7.41 Y9) | 54.32/7.41 (Y1 @ 54.32/7.41 Y8 @ Y9))) => 54.32/7.41 (Y7 @ 54.32/7.41 Y8 @ Y9))))))))))) => 54.32/7.41 (Y7 @ 54.32/7.41 Y5 @ Y6)))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y9 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y10 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y7 @ 54.32/7.41 Y9 @ 54.32/7.41 Y10) & 54.32/7.41 (Y7 @ 54.32/7.41 Y8 @ Y9))) => 54.32/7.41 (Y7 @ 54.32/7.41 Y8 @ Y10)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y9 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y1 @ 54.32/7.41 Y8 @ 54.32/7.41 Y9) | 54.32/7.41 (Y0 @ 54.32/7.41 Y8 @ Y9))) => 54.32/7.41 (Y7 @ 54.32/7.41 Y8 @ Y9))))))))))) => 54.32/7.41 (Y7 @ 54.32/7.41 Y4 @ Y5)))))))) => 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y9 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y10 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y7 @ 54.32/7.41 Y8 @ 54.32/7.41 Y9) & 54.32/7.41 (Y7 @ 54.32/7.41 Y9 @ Y10))) => 54.32/7.41 (Y7 @ 54.32/7.41 Y8 @ Y10)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y9 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y1 @ 54.32/7.41 Y8 @ 54.32/7.41 Y9) | 54.32/7.41 (Y0 @ 54.32/7.41 Y8 @ Y9))) => 54.32/7.41 (Y7 @ 54.32/7.41 Y8 @ Y9))))))))))) => 54.32/7.41 (Y7 @ 54.32/7.41 Y4 @ Y6))))))))))))))))) & 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y9 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y6 @ 54.32/7.41 Y8 @ 54.32/7.41 Y9) & 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ Y8))) => 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ Y9)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (Y1 @ 54.32/7.41 Y7 @ 54.32/7.41 Y8) => 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ Y8))))))))))) => 54.32/7.41 (Y6 @ 54.32/7.41 Y4 @ Y5)))))) | 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (Y0 @ 54.32/7.41 Y7 @ 54.32/7.41 Y8) => 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ Y8))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y9 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ 54.32/7.41 Y8) & 54.32/7.41 (Y6 @ 54.32/7.41 Y8 @ Y9))) => 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ Y9)))))))))))))) => 54.32/7.41 (Y6 @ 54.32/7.41 Y4 @ Y5)))))))) => 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y9 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ 54.32/7.41 Y8) & 54.32/7.41 (Y6 @ 54.32/7.41 Y8 @ Y9))) => 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ Y9)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y0 @ 54.32/7.41 Y7 @ 54.32/7.41 Y8) | 54.32/7.41 (Y1 @ 54.32/7.41 Y7 @ Y8))) => 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ Y8))))))))))) => 54.32/7.41 (Y6 @ 54.32/7.41 Y4 @ Y5)))))))))))))) & 54.32/7.41 (((~) @ (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y4 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) & 54.32/7.41 (Y4 @ 54.32/7.41 Y6 @ Y7))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y7)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y1 @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) | 54.32/7.41 (Y0 @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y6))))))))))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y2 @ Y3)))))))))) | 54.32/7.41 (((!!) @ (^[Y4 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y0 @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) | 54.32/7.41 (Y1 @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y6))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y4 @ 54.32/7.41 Y6 @ 54.32/7.41 Y7) & 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y7)))))))))))))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y2 @ Y3))))))))))))))))))))), 54.32/7.41 inference('cnf', [status(esa)], [zf_stmt_0])). 54.32/7.41 thf(zip_derived_cl1, plain, 54.32/7.41 (~ (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y9 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ 54.32/7.41 Y8) & 54.32/7.41 (Y6 @ 54.32/7.41 Y8 @ Y9))) => 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ Y9)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y7 @ 54.32/7.41 Y8) | 54.32/7.41 (Y0 @ 54.32/7.41 Y7 @ Y8))) => 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ Y8))))))))))) => 54.32/7.41 (Y6 @ 54.32/7.41 Y4 @ Y5)))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y9 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y6 @ 54.32/7.41 Y8 @ 54.32/7.41 Y9) & 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ Y8))) => 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ Y9)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y0 @ 54.32/7.41 Y7 @ 54.32/7.41 Y8) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y7 @ Y8))) => 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ Y8))))))))))) => 54.32/7.41 (Y6 @ 54.32/7.41 Y3 @ Y4)))))))) => 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y9 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ 54.32/7.41 Y8) & 54.32/7.41 (Y6 @ 54.32/7.41 Y8 @ Y9))) => 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ Y9)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y0 @ 54.32/7.41 Y7 @ 54.32/7.41 Y8) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y7 @ Y8))) => 54.32/7.41 (Y6 @ 54.32/7.41 Y7 @ Y8))))))))))) => 54.32/7.41 (Y6 @ 54.32/7.41 Y3 @ Y5))))))))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (((((( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y5 @ 54.32/7.41 Y7 @ 54.32/7.41 Y8) & 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ Y7))) => 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ Y8)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (Y0 @ 54.32/7.41 Y6 @ 54.32/7.41 Y7) => 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ Y7))))))))))) => 54.32/7.41 (Y5 @ 54.32/7.41 Y3 @ Y4)))))) | 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y6 @ 54.32/7.41 Y7) => 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ Y7))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ 54.32/7.41 Y7) & 54.32/7.41 (Y5 @ 54.32/7.41 Y7 @ Y8))) => 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ Y8)))))))))))))) => 54.32/7.41 (Y5 @ 54.32/7.41 Y3 @ Y4)))))))) => 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y5 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ 54.32/7.41 Y7) & 54.32/7.41 (Y5 @ 54.32/7.41 Y7 @ Y8))) => 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ Y8)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y6 @ 54.32/7.41 Y7) | 54.32/7.41 (Y0 @ 54.32/7.41 Y6 @ Y7))) => 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ Y7))))))))))) => 54.32/7.41 (Y5 @ 54.32/7.41 Y3 @ Y4)))))))))))))) & 54.32/7.41 (((~) @ (((!!) @ (^[Y3 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y3 @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y6)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y0 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))))))))))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y1 @ Y2)))))))))) | 54.32/7.41 (((!!) @ (^[Y3 : a > a > $o]: 54.32/7.41 (((((((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) | 54.32/7.41 (Y0 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))))))))) & 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y3 @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) & 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y6)))))))))))))) => 54.32/7.41 (Y3 @ Y1 @ Y2)))))))))))))))))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 54.32/7.41 thf(zip_derived_cl2, plain, 54.32/7.41 (~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (((((( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ 54.32/7.41 Y7) & 54.32/7.41 (Y5 @ 54.32/7.41 Y7 @ Y8))) => 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ Y8)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y6 @ 54.32/7.41 Y7) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y6 @ Y7))) => 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ Y7))))))))))) => 54.32/7.41 (Y5 @ 54.32/7.41 Y3 @ Y4)))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y5 @ 54.32/7.41 Y7 @ 54.32/7.41 Y8) & 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ Y7))) => 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ Y8)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y6 @ 54.32/7.41 Y7) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y6 @ Y7))) => 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ Y7))))))))))) => 54.32/7.41 (Y5 @ 54.32/7.41 Y2 @ Y3)))))))) => 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y5 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y8 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ 54.32/7.41 Y7) & 54.32/7.41 (Y5 @ 54.32/7.41 Y7 @ Y8))) => 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ Y8)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y6 @ 54.32/7.41 Y7) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y6 @ Y7))) => 54.32/7.41 (Y5 @ 54.32/7.41 Y6 @ Y7))))))))))) => 54.32/7.41 (Y5 @ 54.32/7.41 Y2 @ Y4))))))))))))))))) & 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((((!!) @ ( 54.32/7.41 ^[Y4 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y4 @ 54.32/7.41 Y6 @ 54.32/7.41 Y7) & 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y7)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) => 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y6))))))))))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y2 @ Y3)))))) | 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) => 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y6))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) & 54.32/7.41 (Y4 @ 54.32/7.41 Y6 @ Y7))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y7)))))))))))))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y2 @ Y3)))))))) => 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : 54.32/7.41 a > a > $o]: 54.32/7.41 (((( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) & 54.32/7.41 (Y4 @ 54.32/7.41 Y6 @ Y7))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y7)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y6))))))))))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y2 @ Y3)))))))))))))) & 54.32/7.41 (((~) @ (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ ( 54.32/7.41 ^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))))) | 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (((( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ Y4) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1))))))))))))))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 54.32/7.41 thf(zip_derived_cl3, plain, 54.32/7.41 (~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((((!!) @ ( 54.32/7.41 ^[Y4 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) & 54.32/7.41 (Y4 @ 54.32/7.41 Y6 @ Y7))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y7)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y6))))))))))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y2 @ Y3)))))) & 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : 54.32/7.41 a > a > $o]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y4 @ 54.32/7.41 Y6 @ 54.32/7.41 Y7) & 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y7)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y6))))))))))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y1 @ Y2)))))))) => 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : 54.32/7.41 a > a > $o]: 54.32/7.41 (((( 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y7 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) & 54.32/7.41 (Y4 @ 54.32/7.41 Y6 @ Y7))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y7)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y5 @ Y6))))))))))) => 54.32/7.41 (Y4 @ 54.32/7.41 Y1 @ Y3))))))))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((((!!) @ (^[Y3 : a > a > $o]: 54.32/7.41 (((((( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y3 @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) & 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y6)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))))))))))) => 54.32/7.41 (Y3 @ Y1 @ 54.32/7.41 Y2)))))) | 54.32/7.41 (((!!) @ (^[Y3 : a > a > $o]: 54.32/7.41 (((((( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y3 @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y6)))))))))))))) => 54.32/7.41 (Y3 @ Y1 @ 54.32/7.41 Y2)))))))) => 54.32/7.41 (((!!) @ (^[Y3 : a > a > $o]: 54.32/7.41 (((((((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y3 @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y6)))))))))))) & 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))))))))))) => 54.32/7.41 (Y3 @ Y1 @ Y2)))))))))))))) & 54.32/7.41 (((~) @ (((!!) @ (^[Y1 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y1 @ 54.32/7.41 Y2 @ 54.32/7.41 Y3) & 54.32/7.41 (Y1 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y1 @ 54.32/7.41 Y2 @ Y4)))))))))))) & 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y3 : a]: 54.32/7.41 ((((('#sk2' @ 54.32/7.41 Y2 @ Y3) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y1 @ Y2 @ 54.32/7.41 Y3))))))))))) => 54.32/7.41 (Y1 @ '#sk3' @ Y0)))))))))) | 54.32/7.41 (((!!) @ (^[Y1 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 ((((('#sk1' @ 54.32/7.41 Y2 @ Y3) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y1 @ Y2 @ Y3))))))))) & 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (((( 54.32/7.41 (Y1 @ 54.32/7.41 Y3 @ Y4) & 54.32/7.41 (Y1 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y1 @ 54.32/7.41 Y2 @ Y4)))))))))))))) => 54.32/7.41 (Y1 @ '#sk3' @ Y0)))))))))))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 54.32/7.41 thf(zip_derived_cl4, plain, 54.32/7.41 (~ (((((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((((!!) @ (^[Y3 : a > a > $o]: 54.32/7.41 (((((( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y3 @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y6)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))))))))))) => 54.32/7.41 (Y3 @ Y1 @ 54.32/7.41 Y2)))))) & 54.32/7.41 (((!!) @ (^[Y3 : a > a > $o]: 54.32/7.41 (((((( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y3 @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) & 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y6)))))))))))) & 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))))))))))) => 54.32/7.41 (Y3 @ Y0 @ 54.32/7.41 Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y3 : a > a > $o]: 54.32/7.41 (((((((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y3 @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y6)))))))))))) & 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))))))))))) => 54.32/7.41 (Y3 @ Y0 @ Y2))))))))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))) | 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))))))))) & 54.32/7.41 (((~) @ (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y3 : a]: 54.32/7.41 (((((Y0 @ 54.32/7.41 Y1 @ Y2) & 54.32/7.41 (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ 54.32/7.41 Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ 54.32/7.41 Y1 @ Y2) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4')))))))))) | 54.32/7.41 (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk1' @ Y1 @ Y2) | 54.32/7.41 ('#sk2' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y2 @ 54.32/7.41 Y3) & (Y0 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4'))))))))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 54.32/7.41 thf(zip_derived_cl5, plain, 54.32/7.41 (~ (((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((((!!) @ (^[Y3 : a > a > $o]: 54.32/7.41 (((((((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y3 @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y6)))))))))))) & 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))))))))))) => 54.32/7.41 (Y3 @ Y1 @ Y2)))))) & 54.32/7.41 (((!!) @ (^[Y3 : a > a > $o]: 54.32/7.41 (((((((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y3 @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) & 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y6)))))))))))) & 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))))))))))) => 54.32/7.41 (Y3 @ Y0 @ Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y3 : a > a > $o]: 54.32/7.41 (((((((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y3 @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y6)))))))))))) & 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))))))))))) => 54.32/7.41 (Y3 @ Y0 @ Y2))))))))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))) | 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))))))))) & 54.32/7.41 (((~) @ (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y0 @ 54.32/7.41 Y1 @ 54.32/7.41 Y2) & 54.32/7.41 (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ 54.32/7.41 Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ 54.32/7.41 Y2) | ('#sk1' @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4'))))))))))), 54.32/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 54.32/7.41 thf(zip_derived_cl7, plain, 54.32/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((((!!) @ (^[Y3 : a > a > $o]: 54.32/7.41 (((((((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y3 @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y6)))))))))))) & 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))))))))))) => 54.32/7.41 (Y3 @ Y1 @ Y2)))))) & 54.32/7.41 (((!!) @ (^[Y3 : a > a > $o]: 54.32/7.41 (((((((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y3 @ 54.32/7.41 Y5 @ 54.32/7.41 Y6) & 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y6)))))))))))) & 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))))))))))) => 54.32/7.41 (Y3 @ Y0 @ Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y3 : a > a > $o]: 54.32/7.41 (((((((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y6 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y3 @ 54.32/7.41 Y5 @ Y6))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y6)))))))))))) & 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y3 @ 54.32/7.41 Y4 @ Y5))))))))))) => 54.32/7.41 (Y3 @ Y0 @ Y2))))))))))))))))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))) | 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))))))))) 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4')))))))), 54.32/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl5])). 54.32/7.41 thf(zip_derived_cl9, plain, 54.32/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))) & 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ '#sk6' @ Y0)))))))) => 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (((( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ '#sk6' @ Y1)))))))))))))) 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4')))))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))) | 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))))))))))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl7])). 54.32/7.41 thf(zip_derived_cl12, plain, 54.32/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((((((!!) @ (^[Y1 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 (Y1 @ 54.32/7.41 Y2 @ 54.32/7.41 Y3) & 54.32/7.41 (Y1 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y1 @ 54.32/7.41 Y2 @ Y4)))))))))))) & 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 ((((('#sk1' @ 54.32/7.41 Y2 @ 54.32/7.41 Y3) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y1 @ Y2 @ 54.32/7.41 Y3))))))))))) => 54.32/7.41 (Y1 @ '#sk7' @ Y0)))))) & 54.32/7.41 (((!!) @ (^[Y1 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 (Y1 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y1 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y1 @ 54.32/7.41 Y2 @ Y4)))))))))))) & 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 ((((('#sk2' @ 54.32/7.41 Y2 @ 54.32/7.41 Y3) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y1 @ Y2 @ 54.32/7.41 Y3))))))))))) => 54.32/7.41 (Y1 @ '#sk6' @ '#sk7')))))))) => 54.32/7.41 (((!!) @ (^[Y1 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (((( 54.32/7.41 (Y1 @ 54.32/7.41 Y2 @ 54.32/7.41 Y3) & 54.32/7.41 (Y1 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y1 @ 54.32/7.41 Y2 @ Y4)))))))))))) & 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 ((((('#sk2' @ 54.32/7.41 Y2 @ Y3) | 54.32/7.41 ('#sk1' @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y1 @ Y2 @ 54.32/7.41 Y3))))))))))) => 54.32/7.41 (Y1 @ '#sk6' @ Y0))))))))))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))) | 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))))))))) 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4')))))))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl9])). 54.32/7.41 thf(zip_derived_cl15, plain, 54.32/7.41 ((~ (((((((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ 54.32/7.41 Y1 @ 54.32/7.41 Y2) & 54.32/7.41 (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ 54.32/7.41 Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk1' @ Y1 @ Y2) | 54.32/7.41 ('#sk2' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk7' @ '#sk8')))))) & 54.32/7.41 (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ 54.32/7.41 Y2 @ 54.32/7.41 Y3) & 54.32/7.41 (Y0 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ 54.32/7.41 Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk6' @ '#sk7')))))))) => 54.32/7.41 (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & 54.32/7.41 (Y0 @ Y2 @ 54.32/7.41 Y3))) => 54.32/7.41 (Y0 @ Y1 @ 54.32/7.41 Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk6' @ '#sk8')))))))) 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4')))))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))) | 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))))))))))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 54.32/7.41 thf(zip_derived_cl19, plain, 54.32/7.41 ((~ (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk6' @ '#sk8')))))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))) | 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))))))))) 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4')))))))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 54.32/7.41 thf(zip_derived_cl24, plain, 54.32/7.41 (( ('#form9') 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))) | 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))))))))))), 54.32/7.41 define([status(thm)])). 54.32/7.41 thf(zip_derived_cl25, plain, 54.32/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((((((!!) @ (^[Y1 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 (Y1 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y1 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y1 @ 54.32/7.41 Y2 @ Y4)))))))))))) & 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 ((('#sk2' @ 54.32/7.41 Y2 @ Y3) => 54.32/7.41 (Y1 @ Y2 @ 54.32/7.41 Y3))))))))))) => 54.32/7.41 (Y1 @ '#sk10' @ Y0)))))) | 54.32/7.41 (((!!) @ (^[Y1 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 ((('#sk1' @ 54.32/7.41 Y2 @ Y3) => 54.32/7.41 (Y1 @ Y2 @ 54.32/7.41 Y3))))))))) & 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 (Y1 @ 54.32/7.41 Y2 @ 54.32/7.41 Y3) & 54.32/7.41 (Y1 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y1 @ 54.32/7.41 Y2 @ Y4)))))))))))))) => 54.32/7.41 (Y1 @ '#sk10' @ Y0)))))))) => 54.32/7.41 (((!!) @ (^[Y1 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (((( 54.32/7.41 (Y1 @ 54.32/7.41 Y2 @ 54.32/7.41 Y3) & 54.32/7.41 (Y1 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y1 @ 54.32/7.41 Y2 @ Y4)))))))))))) & 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 ((((('#sk1' @ 54.32/7.41 Y2 @ Y3) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y1 @ Y2 @ 54.32/7.41 Y3))))))))))) => 54.32/7.41 (Y1 @ '#sk10' @ Y0))))))))))) 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl24])). 54.32/7.41 thf(zip_derived_cl37, plain, 54.32/7.41 ((~ (((((((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ 54.32/7.41 Y2 @ 54.32/7.41 Y3) & 54.32/7.41 (Y0 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ 54.32/7.41 Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((('#sk2' @ Y1 @ Y2) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk10' @ '#sk12')))))) | 54.32/7.41 (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((('#sk1' @ Y1 @ Y2) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ 54.32/7.41 Y1 @ 54.32/7.41 Y2) & 54.32/7.41 (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ 54.32/7.41 Y3)))))))))))))) => 54.32/7.41 (Y0 @ '#sk10' @ '#sk12')))))))) => 54.32/7.41 (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & 54.32/7.41 (Y0 @ Y2 @ 54.32/7.41 Y3))) => 54.32/7.41 (Y0 @ Y1 @ 54.32/7.41 Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk1' @ Y1 @ Y2) | 54.32/7.41 ('#sk2' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk10' @ '#sk12')))))))) 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl25])). 54.32/7.41 thf(zip_derived_cl47, plain, 54.32/7.41 ((~ (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk1' @ Y1 @ Y2) | 54.32/7.41 ('#sk2' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk10' @ '#sk12')))))) 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 54.32/7.41 thf(zip_derived_cl66, plain, 54.32/7.41 ((~ (((((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk30' @ Y0 @ Y1) & 54.32/7.41 ('#sk30' @ Y1 @ Y2))) => 54.32/7.41 ('#sk30' @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.32/7.41 Y1))) => 54.32/7.41 ('#sk30' @ Y0 @ Y1))))))))))) => 54.32/7.41 ('#sk30' @ '#sk10' @ '#sk12'))) 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 54.32/7.41 thf(zip_derived_cl79, plain, 54.32/7.41 ((~ ('#sk30' @ '#sk10' @ '#sk12') | ('#form9'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl66])). 54.32/7.41 thf(zip_derived_cl46, plain, 54.32/7.41 (( (((((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y2 @ 54.32/7.41 Y3) & (Y0 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((('#sk2' @ Y1 @ Y2) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk10' @ '#sk12')))))) | 54.32/7.41 (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((('#sk1' @ Y1 @ Y2) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))))) => 54.32/7.41 (Y0 @ '#sk10' @ '#sk12')))))))) 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 54.32/7.41 thf(zip_derived_cl62, plain, 54.32/7.41 (( (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y2 @ 54.32/7.41 Y3) & (Y0 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((('#sk2' @ Y1 @ Y2) => (Y0 @ 54.32/7.41 Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk10' @ '#sk12')))))) 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((('#sk1' @ Y1 @ Y2) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))))) => 54.32/7.41 (Y0 @ '#sk10' @ '#sk12')))))) 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl46])). 54.32/7.41 thf(zip_derived_cl72, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( (((((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((X2 @ Y1 @ Y2) & (X2 @ 54.32/7.41 Y0 @ Y1))) => 54.32/7.41 (X2 @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 54.32/7.41 (X2 @ '#sk10' @ '#sk12'))) 54.32/7.41 | ('#form9') 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((('#sk1' @ Y1 @ Y2) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ 54.32/7.41 Y1 @ Y2) & 54.32/7.41 (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ 54.32/7.41 Y3)))))))))))))) => 54.32/7.41 (Y0 @ '#sk10' @ '#sk12')))))))), 54.32/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl62])). 54.32/7.41 thf(zip_derived_cl85, plain, 54.32/7.41 ((~ ('#form91') 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((('#sk1' @ Y1 @ Y2) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))))) => 54.32/7.41 (Y0 @ '#sk10' @ '#sk12')))))))), 54.32/7.41 define([status(thm)])). 54.32/7.41 thf(zip_derived_cl86, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( (((((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (X2 @ Y0 @ Y2)))))))))))))) => 54.32/7.41 (X2 @ '#sk10' @ '#sk12'))) 54.32/7.41 | ~ ('#form91'))), 54.32/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 54.32/7.41 thf(zip_derived_cl101, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (X2 @ Y0 @ Y2)))))))))))))) 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ~ ('#form91'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl86])). 54.32/7.41 thf(zip_derived_cl113, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (X2 @ Y0 @ Y2)))))))))))) 54.32/7.41 | ~ ('#form91') 54.32/7.41 | (X2 @ '#sk10' @ '#sk12'))), 54.32/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl101])). 54.32/7.41 thf(zip_derived_cl125, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((!!) @ (^[Y0 : a]: 54.32/7.41 ((('#sk1' @ ('#sk255' @ X2) @ Y0) => (X2 @ 54.32/7.41 ('#sk255' @ X2) @ Y0)))))) 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ~ ('#form91') 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (X2 @ Y0 @ Y2)))))))))))))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl113])). 54.32/7.41 thf(zip_derived_cl139, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ ((('#sk1' @ ('#sk255' @ X2) @ ('#sk350' @ X2)) => (X2 @ 54.32/7.41 ('#sk255' @ X2) @ ('#sk350' @ X2)))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (X2 @ Y0 @ Y2)))))))))))) 54.32/7.41 | ~ ('#form91') 54.32/7.41 | (X2 @ '#sk10' @ '#sk12'))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl125])). 54.32/7.41 thf(zip_derived_cl153, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (X2 @ ('#sk255' @ X2) @ ('#sk350' @ X2)) 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ~ ('#form91') 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (X2 @ Y0 @ Y2)))))))))))))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl139])). 54.32/7.41 thf(zip_derived_cl163, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((X2 @ ('#sk47' @ X2) @ Y0) & (X2 @ 54.32/7.41 Y0 @ Y1))) => 54.32/7.41 (X2 @ ('#sk47' @ X2) @ Y1))))))))) 54.32/7.41 | ~ ('#form91') 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ~ (X2 @ ('#sk255' @ X2) @ ('#sk350' @ X2)))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl153])). 54.32/7.41 thf(zip_derived_cl174, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ 54.32/7.41 ('#sk74' @ X2) @ Y0))) => 54.32/7.41 (X2 @ ('#sk47' @ X2) @ Y0)))))) 54.32/7.41 | ~ (X2 @ ('#sk255' @ X2) @ ('#sk350' @ X2)) 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ~ ('#form91'))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl163])). 54.32/7.41 thf(zip_derived_cl180, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ 54.32/7.41 ('#sk74' @ X2) @ ('#sk112' @ X2)))) => 54.32/7.41 (X2 @ ('#sk47' @ X2) @ ('#sk112' @ X2)))) 54.32/7.41 | ~ ('#form91') 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ~ (X2 @ ('#sk255' @ X2) @ ('#sk350' @ X2)))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl174])). 54.32/7.41 thf(zip_derived_cl188, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (X2 @ ('#sk47' @ X2) @ ('#sk112' @ X2)) 54.32/7.41 | ~ (X2 @ ('#sk255' @ X2) @ ('#sk350' @ X2)) 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ~ ('#form91'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl180])). 54.32/7.41 thf(zip_derived_cl152, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( ('#sk1' @ ('#sk255' @ X2) @ ('#sk350' @ X2)) 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ~ ('#form91') 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (X2 @ Y0 @ Y2)))))))))))))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl139])). 54.32/7.41 thf(zip_derived_cl162, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((X2 @ ('#sk47' @ X2) @ Y0) & (X2 @ 54.32/7.41 Y0 @ Y1))) => 54.32/7.41 (X2 @ ('#sk47' @ X2) @ Y1))))))))) 54.32/7.41 | ~ ('#form91') 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ('#sk1' @ ('#sk255' @ X2) @ ('#sk350' @ X2)))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl152])). 54.32/7.41 thf(zip_derived_cl173, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ 54.32/7.41 ('#sk74' @ X2) @ Y0))) => 54.32/7.41 (X2 @ ('#sk47' @ X2) @ Y0)))))) 54.32/7.41 | ('#sk1' @ ('#sk255' @ X2) @ ('#sk350' @ X2)) 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ~ ('#form91'))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl162])). 54.32/7.41 thf(zip_derived_cl179, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ 54.32/7.41 ('#sk74' @ X2) @ ('#sk112' @ X2)))) => 54.32/7.41 (X2 @ ('#sk47' @ X2) @ ('#sk112' @ X2)))) 54.32/7.41 | ~ ('#form91') 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ('#sk1' @ ('#sk255' @ X2) @ ('#sk350' @ X2)))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl173])). 54.32/7.41 thf(zip_derived_cl186, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (X2 @ ('#sk47' @ X2) @ ('#sk112' @ X2)) 54.32/7.41 | ('#sk1' @ ('#sk255' @ X2) @ ('#sk350' @ X2)) 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ~ ('#form91'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])). 54.32/7.41 thf(zip_derived_cl187, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( (((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ ('#sk74' @ X2) @ 54.32/7.41 ('#sk112' @ X2)))) 54.32/7.41 | ~ (X2 @ ('#sk255' @ X2) @ ('#sk350' @ X2)) 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ~ ('#form91'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl180])). 54.32/7.41 thf(zip_derived_cl185, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( (((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ ('#sk74' @ X2) @ 54.32/7.41 ('#sk112' @ X2)))) 54.32/7.41 | ('#sk1' @ ('#sk255' @ X2) @ ('#sk350' @ X2)) 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ~ ('#form91'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])). 54.32/7.41 thf(zip_derived_cl189, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ ('#form787' @ X2) 54.32/7.41 | (((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ ('#sk74' @ X2) @ 54.32/7.41 ('#sk112' @ X2)))))), 54.32/7.41 define([status(thm)])). 54.32/7.41 thf(zip_derived_cl193, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( ('#form787' @ X2) 54.32/7.41 | ~ ('#form91') 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ~ (X2 @ ('#sk255' @ X2) @ ('#sk350' @ X2)))), 54.32/7.41 inference('renaming', [status(thm)], 54.32/7.41 [zip_derived_cl187, zip_derived_cl189])). 54.32/7.41 thf(zip_derived_cl185, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( (((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ ('#sk74' @ X2) @ 54.32/7.41 ('#sk112' @ X2)))) 54.32/7.41 | ('#sk1' @ ('#sk255' @ X2) @ ('#sk350' @ X2)) 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ~ ('#form91'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])). 54.32/7.41 thf(zip_derived_cl189, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ ('#form787' @ X2) 54.32/7.41 | (((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ ('#sk74' @ X2) @ 54.32/7.41 ('#sk112' @ X2)))))), 54.32/7.41 define([status(thm)])). 54.32/7.41 thf(zip_derived_cl192, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( ('#form787' @ X2) 54.32/7.41 | ~ ('#form91') 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ('#sk1' @ ('#sk255' @ X2) @ ('#sk350' @ X2)))), 54.32/7.41 inference('renaming', [status(thm)], 54.32/7.41 [zip_derived_cl185, zip_derived_cl189])). 54.32/7.41 thf(zip_derived_cl78, plain, 54.32/7.41 (( (((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk30' @ Y0 @ Y1) & 54.32/7.41 ('#sk30' @ Y1 @ Y2))) => 54.32/7.41 ('#sk30' @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 54.32/7.41 ('#sk30' @ Y0 @ Y1))))))))))) 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl66])). 54.32/7.41 thf(zip_derived_cl94, plain, 54.32/7.41 (( (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 54.32/7.41 ('#sk30' @ Y0 @ Y1))))))))) 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl78])). 54.32/7.41 thf(zip_derived_cl103, plain, 54.32/7.41 (![X2 : a]: 54.32/7.41 ( (((!!) @ (^[Y0 : a]: 54.32/7.41 ((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) => 54.32/7.41 ('#sk30' @ X2 @ Y0)))))) 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])). 54.32/7.41 thf(zip_derived_cl115, plain, 54.32/7.41 (![X2 : a, X4 : a]: 54.32/7.41 ( ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) => ('#sk30' @ X2 @ X4))) 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl103])). 54.32/7.41 thf(zip_derived_cl127, plain, 54.32/7.41 (![X2 : a, X4 : a]: 54.32/7.41 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 54.32/7.41 | ('#sk30' @ X2 @ X4) 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl115])). 54.32/7.41 thf(zip_derived_cl141, plain, 54.32/7.41 (![X2 : a, X4 : a]: 54.32/7.41 (~ ('#sk1' @ X2 @ X4) | ('#form9') | ('#sk30' @ X2 @ X4))), 54.32/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl127])). 54.32/7.41 thf(zip_derived_cl72, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( (((((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((X2 @ Y1 @ Y2) & (X2 @ 54.32/7.41 Y0 @ Y1))) => 54.32/7.41 (X2 @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 54.32/7.41 (X2 @ '#sk10' @ '#sk12'))) 54.32/7.41 | ('#form9') 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((('#sk1' @ Y1 @ Y2) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ 54.32/7.41 Y1 @ Y2) & 54.32/7.41 (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ 54.32/7.41 Y3)))))))))))))) => 54.32/7.41 (Y0 @ '#sk10' @ '#sk12')))))))), 54.32/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl62])). 54.32/7.41 thf(zip_derived_cl73, plain, 54.32/7.41 (( (((((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk30' @ Y1 @ Y2) & 54.32/7.41 ('#sk30' @ Y0 @ Y1))) => 54.32/7.41 ('#sk30' @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 54.32/7.41 Y1))))))))))) => 54.32/7.41 ('#sk30' @ '#sk10' @ '#sk12'))) 54.32/7.41 | ('#form9') 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((('#sk1' @ Y1 @ Y2) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))))) => 54.32/7.41 (Y0 @ '#sk10' @ '#sk12')))))))), 54.32/7.41 inference('triggered_bool_instantiation', [status(thm)], 54.32/7.41 [zip_derived_cl72])). 54.32/7.41 thf(zip_derived_cl85, plain, 54.32/7.41 ((~ ('#form91') 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((('#sk1' @ Y1 @ Y2) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))))) => 54.32/7.41 (Y0 @ '#sk10' @ '#sk12')))))))), 54.32/7.41 define([status(thm)])). 54.32/7.41 thf(zip_derived_cl334, plain, 54.32/7.41 (( ('#form91') 54.32/7.41 | ('#form9') 54.32/7.41 | (((((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk30' @ Y1 @ Y2) & 54.32/7.41 ('#sk30' @ Y0 @ Y1))) => 54.32/7.41 ('#sk30' @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 54.32/7.41 Y1))))))))))) => 54.32/7.41 ('#sk30' @ '#sk10' @ '#sk12'))))), 54.32/7.41 inference('renaming', [status(thm)], [zip_derived_cl73, zip_derived_cl85])). 54.32/7.41 thf(zip_derived_cl335, plain, 54.32/7.41 ((~ (((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk30' @ Y1 @ Y2) & 54.32/7.41 ('#sk30' @ Y0 @ Y1))) => 54.32/7.41 ('#sk30' @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))))) 54.32/7.41 | ('#sk30' @ '#sk10' @ '#sk12') 54.32/7.41 | ('#form9') 54.32/7.41 | ('#form91'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl334])). 54.32/7.41 thf(zip_derived_cl79, plain, 54.32/7.41 ((~ ('#sk30' @ '#sk10' @ '#sk12') | ('#form9'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl66])). 54.32/7.41 thf(zip_derived_cl336, plain, 54.32/7.41 (( ('#form91') 54.32/7.41 | ('#form9') 54.32/7.41 | ~ (((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk30' @ Y1 @ Y2) & 54.32/7.41 ('#sk30' @ Y0 @ Y1))) => 54.32/7.41 ('#sk30' @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 54.32/7.41 Y1))))))))))))), 54.32/7.41 inference('clc', [status(thm)], [zip_derived_cl335, zip_derived_cl79])). 54.32/7.41 thf(zip_derived_cl337, plain, 54.32/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk30' @ Y1 @ Y2) & 54.32/7.41 ('#sk30' @ Y0 @ Y1))) => 54.32/7.41 ('#sk30' @ Y0 @ Y2)))))))))))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))) 54.32/7.41 | ('#form9') 54.32/7.41 | ('#form91'))), 54.32/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl336])). 54.32/7.41 thf(zip_derived_cl72, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( (((((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((X2 @ Y1 @ Y2) & (X2 @ 54.32/7.41 Y0 @ Y1))) => 54.32/7.41 (X2 @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 54.32/7.41 (X2 @ '#sk10' @ '#sk12'))) 54.32/7.41 | ('#form9') 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((('#sk1' @ Y1 @ Y2) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ 54.32/7.41 Y1 @ Y2) & 54.32/7.41 (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ 54.32/7.41 Y3)))))))))))))) => 54.32/7.41 (Y0 @ '#sk10' @ '#sk12')))))))), 54.32/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl62])). 54.32/7.41 thf(zip_derived_cl85, plain, 54.32/7.41 ((~ ('#form91') 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((('#sk1' @ Y1 @ Y2) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))))) => 54.32/7.41 (Y0 @ '#sk10' @ '#sk12')))))))), 54.32/7.41 define([status(thm)])). 54.32/7.41 thf(zip_derived_cl92, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( ('#form91') 54.32/7.41 | ('#form9') 54.32/7.41 | (((((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((X2 @ Y1 @ Y2) & 54.32/7.41 (X2 @ Y0 @ Y1))) => 54.32/7.41 (X2 @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 54.32/7.41 (X2 @ '#sk10' @ '#sk12'))))), 54.32/7.41 inference('renaming', [status(thm)], [zip_derived_cl72, zip_derived_cl85])). 54.32/7.41 thf(zip_derived_cl100, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((X2 @ Y1 @ Y2) & (X2 @ 54.32/7.41 Y0 @ Y1))) => 54.32/7.41 (X2 @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ('#form9') 54.32/7.41 | ('#form91'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])). 54.32/7.41 thf(zip_derived_cl112, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((X2 @ Y1 @ Y2) & (X2 @ 54.32/7.41 Y0 @ Y1))) => 54.32/7.41 (X2 @ Y0 @ Y2)))))))))))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 54.32/7.41 | ('#form91') 54.32/7.41 | ('#form9') 54.32/7.41 | (X2 @ '#sk10' @ '#sk12'))), 54.32/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl100])). 54.32/7.41 thf(zip_derived_cl124, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.41 ('#sk121' @ X2) @ Y0))) => 54.32/7.41 (X2 @ ('#sk121' @ X2) @ Y1))))))))) 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ('#form9') 54.32/7.41 | ('#form91') 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl112])). 54.32/7.41 thf(zip_derived_cl138, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((((X2 @ ('#sk228' @ X2) @ Y0) & (X2 @ 54.32/7.41 ('#sk121' @ X2) @ ('#sk228' @ X2)))) => 54.32/7.41 (X2 @ ('#sk121' @ X2) @ Y0)))))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 54.32/7.41 | ('#form91') 54.32/7.41 | ('#form9') 54.32/7.41 | (X2 @ '#sk10' @ '#sk12'))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl124])). 54.32/7.41 thf(zip_derived_cl151, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((((X2 @ ('#sk228' @ X2) @ ('#sk314' @ X2)) & (X2 @ 54.32/7.41 ('#sk121' @ X2) @ ('#sk228' @ X2)))) => 54.32/7.41 (X2 @ ('#sk121' @ X2) @ ('#sk314' @ X2)))) 54.32/7.41 | (X2 @ '#sk10' @ '#sk12') 54.32/7.41 | ('#form9') 54.32/7.41 | ('#form91') 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl138])). 54.32/7.41 thf(zip_derived_cl161, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (X2 @ ('#sk121' @ X2) @ ('#sk314' @ X2)) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 54.32/7.41 | ('#form91') 54.32/7.41 | ('#form9') 54.32/7.41 | (X2 @ '#sk10' @ '#sk12'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl151])). 54.32/7.41 thf(zip_derived_cl170, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( ('#form591' @ X2) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 54.32/7.41 define([status(thm)])). 54.32/7.41 thf(zip_derived_cl338, plain, 54.32/7.41 ((~ ('#form591' @ '#sk30') 54.32/7.41 | ('#form91') 54.32/7.41 | ('#form9') 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk30' @ Y1 @ Y2) & 54.32/7.41 ('#sk30' @ Y0 @ Y1))) => 54.32/7.41 ('#sk30' @ Y0 @ Y2)))))))))))))), 54.32/7.41 inference('renaming', [status(thm)], 54.32/7.41 [zip_derived_cl337, zip_derived_cl170])). 54.32/7.41 thf(zip_derived_cl339, plain, 54.32/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk30' @ Y0 @ Y1) & ('#sk30' @ 54.32/7.41 ('#sk121' @ '#sk30') @ Y0))) => 54.32/7.41 ('#sk30' @ ('#sk121' @ '#sk30') @ Y1))))))))) 54.32/7.41 | ('#form9') 54.32/7.41 | ('#form91') 54.32/7.41 | ~ ('#form591' @ '#sk30'))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl338])). 54.32/7.41 thf(zip_derived_cl340, plain, 54.32/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.32/7.41 ((((('#sk30' @ ('#sk228' @ '#sk30') @ Y0) & ('#sk30' @ 54.32/7.41 ('#sk121' @ '#sk30') @ ('#sk228' @ '#sk30')))) => 54.32/7.41 ('#sk30' @ ('#sk121' @ '#sk30') @ Y0)))))) 54.32/7.41 | ~ ('#form591' @ '#sk30') 54.32/7.41 | ('#form91') 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl339])). 54.32/7.41 thf(zip_derived_cl341, plain, 54.32/7.41 ((~ ((((('#sk30' @ ('#sk228' @ '#sk30') @ ('#sk314' @ '#sk30')) & 54.32/7.41 ('#sk30' @ ('#sk121' @ '#sk30') @ ('#sk228' @ '#sk30')))) => 54.32/7.41 ('#sk30' @ ('#sk121' @ '#sk30') @ ('#sk314' @ '#sk30')))) 54.32/7.41 | ('#form9') 54.32/7.41 | ('#form91') 54.32/7.41 | ~ ('#form591' @ '#sk30'))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl340])). 54.32/7.41 thf(zip_derived_cl342, plain, 54.32/7.41 (( ((('#sk30' @ ('#sk228' @ '#sk30') @ ('#sk314' @ '#sk30')) & 54.32/7.41 ('#sk30' @ ('#sk121' @ '#sk30') @ ('#sk228' @ '#sk30')))) 54.32/7.41 | ~ ('#form591' @ '#sk30') 54.32/7.41 | ('#form91') 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl341])). 54.32/7.41 thf(zip_derived_cl345, plain, 54.32/7.41 (( ('#sk30' @ ('#sk121' @ '#sk30') @ ('#sk228' @ '#sk30')) 54.32/7.41 | ('#form9') 54.32/7.41 | ('#form91') 54.32/7.41 | ~ ('#form591' @ '#sk30'))), 54.32/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl342])). 54.32/7.41 thf(zip_derived_cl344, plain, 54.32/7.41 (( ('#sk30' @ ('#sk228' @ '#sk30') @ ('#sk314' @ '#sk30')) 54.32/7.41 | ('#form9') 54.32/7.41 | ('#form91') 54.32/7.41 | ~ ('#form591' @ '#sk30'))), 54.32/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl342])). 54.32/7.41 thf(zip_derived_cl343, plain, 54.32/7.41 ((~ ('#sk30' @ ('#sk121' @ '#sk30') @ ('#sk314' @ '#sk30')) 54.32/7.41 | ~ ('#form591' @ '#sk30') 54.32/7.41 | ('#form91') 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl341])). 54.32/7.41 thf(zip_derived_cl93, plain, 54.32/7.41 (( (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk30' @ Y0 @ Y1) & 54.32/7.41 ('#sk30' @ Y1 @ Y2))) => 54.32/7.41 ('#sk30' @ Y0 @ Y2)))))))))))) 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl78])). 54.32/7.41 thf(zip_derived_cl102, plain, 54.32/7.41 (![X2 : a]: 54.32/7.41 ( (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk30' @ X2 @ Y0) & ('#sk30' @ Y0 @ 54.32/7.41 Y1))) => 54.32/7.41 ('#sk30' @ X2 @ Y1))))))))) 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl93])). 54.32/7.41 thf(zip_derived_cl114, plain, 54.32/7.41 (![X2 : a, X4 : a]: 54.32/7.41 ( (((!!) @ (^[Y0 : a]: 54.32/7.41 ((((('#sk30' @ X2 @ X4) & ('#sk30' @ X4 @ Y0))) => 54.32/7.41 ('#sk30' @ X2 @ Y0)))))) 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl102])). 54.32/7.41 thf(zip_derived_cl126, plain, 54.32/7.41 (![X2 : a, X4 : a, X6 : a]: 54.32/7.41 ( ((((('#sk30' @ X2 @ X4) & ('#sk30' @ X4 @ X6))) => ('#sk30' @ X2 @ 54.32/7.41 X6))) 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl114])). 54.32/7.41 thf(zip_derived_cl140, plain, 54.32/7.41 (![X2 : a, X4 : a, X6 : a]: 54.32/7.41 (~ ((('#sk30' @ X2 @ X4) & ('#sk30' @ X4 @ X6))) 54.32/7.41 | ('#sk30' @ X2 @ X6) 54.32/7.41 | ('#form9'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl126])). 54.32/7.41 thf(zip_derived_cl154, plain, 54.32/7.41 (![X2 : a, X4 : a, X6 : a]: 54.32/7.41 (~ ('#sk30' @ X2 @ X4) 54.32/7.41 | ~ ('#sk30' @ X4 @ X6) 54.32/7.41 | ('#form9') 54.32/7.41 | ('#sk30' @ X2 @ X6))), 54.32/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl140])). 54.32/7.41 thf(zip_derived_cl170, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( ('#form591' @ X2) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 54.32/7.41 define([status(thm)])). 54.32/7.41 thf(zip_derived_cl171, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((!!) @ (^[Y0 : a]: 54.32/7.41 ((('#sk2' @ ('#sk592' @ X2) @ Y0) => (X2 @ 54.32/7.41 ('#sk592' @ X2) @ Y0)))))) 54.32/7.41 | ('#form591' @ X2))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl170])). 54.32/7.41 thf(zip_derived_cl178, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ ((('#sk2' @ ('#sk592' @ X2) @ ('#sk658' @ X2)) => (X2 @ 54.32/7.41 ('#sk592' @ X2) @ ('#sk658' @ X2)))) 54.32/7.41 | ('#form591' @ X2))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl171])). 54.32/7.41 thf(zip_derived_cl183, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( ('#sk2' @ ('#sk592' @ X2) @ ('#sk658' @ X2)) | ('#form591' @ X2))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl178])). 54.32/7.41 thf(zip_derived_cl142, plain, 54.32/7.41 (![X2 : a, X4 : a]: 54.32/7.41 (~ ('#sk2' @ X2 @ X4) | ('#form9') | ('#sk30' @ X2 @ X4))), 54.32/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl127])). 54.32/7.41 thf(zip_derived_cl184, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (X2 @ ('#sk592' @ X2) @ ('#sk658' @ X2)) | ('#form591' @ X2))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl178])). 54.32/7.41 thf(zip_derived_cl19, plain, 54.32/7.41 ((~ (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk6' @ '#sk8')))))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))) | 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))))))))) 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4')))))))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 54.32/7.41 thf(zip_derived_cl24, plain, 54.32/7.41 (( ('#form9') 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))) | 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))))))))))), 54.32/7.41 define([status(thm)])). 54.32/7.41 thf(zip_derived_cl26, plain, 54.32/7.41 ((~ ('#form9') 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4')))))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & 54.32/7.41 (Y0 @ Y2 @ 54.32/7.41 Y3))) => 54.32/7.41 (Y0 @ Y1 @ 54.32/7.41 Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk6' @ '#sk8')))))))), 54.32/7.41 inference('renaming', [status(thm)], [zip_derived_cl19, zip_derived_cl24])). 54.32/7.41 thf(zip_derived_cl18, plain, 54.32/7.41 (( (((((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk1' @ Y1 @ Y2) | 54.32/7.41 ('#sk2' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk7' @ '#sk8')))))) & 54.32/7.41 (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y2 @ 54.32/7.41 Y3) & (Y0 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk6' @ '#sk7')))))))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))) | 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))))))))) 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4')))))))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 54.32/7.41 thf(zip_derived_cl22, plain, 54.32/7.41 (( (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk1' @ Y1 @ Y2) | 54.32/7.41 ('#sk2' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk7' @ '#sk8')))))) 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4')))))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))) | 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))))))))))), 54.32/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])). 54.32/7.41 thf(zip_derived_cl29, plain, 54.32/7.41 ((~ ('#form11') 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4')))))))), 54.32/7.41 define([status(thm)])). 54.32/7.41 thf(zip_derived_cl36, plain, 54.32/7.41 (( ('#form11') 54.32/7.41 | ~ (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & 54.32/7.41 (Y0 @ Y2 @ 54.32/7.41 Y3))) => 54.32/7.41 (Y0 @ Y1 @ 54.32/7.41 Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk6' @ '#sk8')))))) 54.32/7.41 | ~ ('#form9'))), 54.32/7.41 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl29])). 54.32/7.41 thf(zip_derived_cl45, plain, 54.32/7.41 ((~ (((((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk21' @ Y0 @ Y1) & 54.32/7.41 ('#sk21' @ Y1 @ Y2))) => 54.32/7.41 ('#sk21' @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.41 Y1))) => 54.32/7.41 ('#sk21' @ Y0 @ Y1))))))))))) => 54.32/7.41 ('#sk21' @ '#sk6' @ '#sk8'))) 54.32/7.41 | ~ ('#form9') 54.32/7.41 | ('#form11'))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl36])). 54.32/7.41 thf(zip_derived_cl61, plain, 54.32/7.41 ((~ ('#sk21' @ '#sk6' @ '#sk8') | ('#form11') | ~ ('#form9'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 54.32/7.41 thf(zip_derived_cl23, plain, 54.32/7.41 (( (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y2 @ 54.32/7.41 Y3) & (Y0 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk6' @ '#sk7')))))) 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4')))))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))) | 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))))))))))), 54.32/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])). 54.32/7.41 thf(zip_derived_cl29, plain, 54.32/7.41 ((~ ('#form11') 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4')))))))), 54.32/7.41 define([status(thm)])). 54.32/7.41 thf(zip_derived_cl35, plain, 54.32/7.41 (( ('#form11') 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))) | 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))))))))) 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y2 @ 54.32/7.41 Y3) & (Y0 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk6' @ '#sk7')))))))), 54.32/7.41 inference('renaming', [status(thm)], [zip_derived_cl23, zip_derived_cl29])). 54.32/7.41 thf(zip_derived_cl24, plain, 54.32/7.41 (( ('#form9') 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))) | 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.41 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) & 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ Y5))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y5)))))))))))) & 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 ( 54.32/7.41 ( 54.32/7.41 (( 54.32/7.41 ('#sk1' @ 54.32/7.41 Y3 @ 54.32/7.41 Y4) | 54.32/7.41 ('#sk2' @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))))))))))) => 54.32/7.41 (Y2 @ Y0 @ Y1)))))))))))))))), 54.32/7.41 define([status(thm)])). 54.32/7.41 thf(zip_derived_cl43, plain, 54.32/7.41 ((~ ('#form9') 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y2 @ 54.32/7.41 Y3) & (Y0 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk6' @ '#sk7')))))) 54.32/7.41 | ('#form11'))), 54.32/7.41 inference('renaming', [status(thm)], [zip_derived_cl35, zip_derived_cl24])). 54.32/7.41 thf(zip_derived_cl55, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( (((((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((X2 @ Y1 @ Y2) & (X2 @ 54.32/7.41 Y0 @ Y1))) => 54.32/7.41 (X2 @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.41 Y1))) => 54.32/7.41 (X2 @ Y0 @ Y1))))))))))) => 54.32/7.41 (X2 @ '#sk6' @ '#sk7'))) 54.32/7.41 | ('#form11') 54.32/7.41 | ~ ('#form9'))), 54.32/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 54.32/7.41 thf(zip_derived_cl69, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((X2 @ Y1 @ Y2) & (X2 @ 54.32/7.41 Y0 @ Y1))) => 54.32/7.41 (X2 @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.41 Y1))) => 54.32/7.41 (X2 @ Y0 @ Y1))))))))))) 54.32/7.41 | (X2 @ '#sk6' @ '#sk7') 54.32/7.41 | ~ ('#form9') 54.32/7.41 | ('#form11'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 54.32/7.41 thf(zip_derived_cl82, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((X2 @ Y1 @ Y2) & (X2 @ 54.32/7.41 Y0 @ Y1))) => 54.32/7.41 (X2 @ Y0 @ Y2)))))))))))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.41 Y1))) => 54.32/7.41 (X2 @ Y0 @ Y1))))))))) 54.32/7.41 | ('#form11') 54.32/7.41 | ~ ('#form9') 54.32/7.41 | (X2 @ '#sk6' @ '#sk7'))), 54.32/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 54.32/7.41 thf(zip_derived_cl97, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.41 ('#sk121' @ X2) @ Y0))) => 54.32/7.41 (X2 @ ('#sk121' @ X2) @ Y1))))))))) 54.32/7.41 | (X2 @ '#sk6' @ '#sk7') 54.32/7.41 | ~ ('#form9') 54.32/7.41 | ('#form11') 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.41 Y1))) => 54.32/7.41 (X2 @ Y0 @ Y1))))))))))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl82])). 54.32/7.41 thf(zip_derived_cl97, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.41 ('#sk121' @ X2) @ Y0))) => 54.32/7.41 (X2 @ ('#sk121' @ X2) @ Y1))))))))) 54.32/7.41 | (X2 @ '#sk6' @ '#sk7') 54.32/7.41 | ~ ('#form9') 54.32/7.41 | ('#form11') 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.41 Y1))) => 54.32/7.41 (X2 @ Y0 @ Y1))))))))))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl82])). 54.32/7.41 thf(zip_derived_cl107, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( ('#form172' @ X2) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.41 Y1))) => 54.32/7.41 (X2 @ Y0 @ Y1))))))))))), 54.32/7.41 define([status(thm)])). 54.32/7.41 thf(zip_derived_cl109, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ ('#form172' @ X2) 54.32/7.41 | ('#form11') 54.32/7.41 | ~ ('#form9') 54.32/7.41 | (X2 @ '#sk6' @ '#sk7') 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.41 ('#sk121' @ X2) @ Y0))) => 54.32/7.41 (X2 @ ('#sk121' @ X2) @ Y1))))))))))), 54.32/7.41 inference('renaming', [status(thm)], 54.32/7.41 [zip_derived_cl97, zip_derived_cl107])). 54.32/7.41 thf(zip_derived_cl119, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((((X2 @ ('#sk228' @ X2) @ Y0) & (X2 @ 54.32/7.41 ('#sk121' @ X2) @ ('#sk228' @ X2)))) => 54.32/7.41 (X2 @ ('#sk121' @ X2) @ Y0)))))) 54.32/7.41 | (X2 @ '#sk6' @ '#sk7') 54.32/7.41 | ~ ('#form9') 54.32/7.41 | ('#form11') 54.32/7.41 | ~ ('#form172' @ X2))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl109])). 54.32/7.41 thf(zip_derived_cl134, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (((((X2 @ ('#sk228' @ X2) @ ('#sk314' @ X2)) & (X2 @ 54.32/7.41 ('#sk121' @ X2) @ ('#sk228' @ X2)))) => 54.32/7.41 (X2 @ ('#sk121' @ X2) @ ('#sk314' @ X2)))) 54.32/7.41 | ~ ('#form172' @ X2) 54.32/7.41 | ('#form11') 54.32/7.41 | ~ ('#form9') 54.32/7.41 | (X2 @ '#sk6' @ '#sk7'))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl119])). 54.32/7.41 thf(zip_derived_cl148, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( (((X2 @ ('#sk228' @ X2) @ ('#sk314' @ X2)) & (X2 @ 54.32/7.41 ('#sk121' @ X2) @ ('#sk228' @ X2)))) 54.32/7.41 | (X2 @ '#sk6' @ '#sk7') 54.32/7.41 | ~ ('#form9') 54.32/7.41 | ('#form11') 54.32/7.41 | ~ ('#form172' @ X2))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl134])). 54.32/7.41 thf(zip_derived_cl159, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( (X2 @ ('#sk121' @ X2) @ ('#sk228' @ X2)) 54.32/7.41 | ~ ('#form172' @ X2) 54.32/7.41 | ('#form11') 54.32/7.41 | ~ ('#form9') 54.32/7.41 | (X2 @ '#sk6' @ '#sk7'))), 54.32/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl148])). 54.32/7.41 thf(zip_derived_cl149, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ (X2 @ ('#sk121' @ X2) @ ('#sk314' @ X2)) 54.32/7.41 | (X2 @ '#sk6' @ '#sk7') 54.32/7.41 | ~ ('#form9') 54.32/7.41 | ('#form11') 54.32/7.41 | ~ ('#form172' @ X2))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl134])). 54.32/7.41 thf(zip_derived_cl29, plain, 54.32/7.41 ((~ ('#form11') 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4')))))))), 54.32/7.41 define([status(thm)])). 54.32/7.41 thf(zip_derived_cl30, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( (((((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (X2 @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.41 Y1))) => 54.32/7.41 (X2 @ Y0 @ Y1))))))))))) => 54.32/7.41 (X2 @ '#sk3' @ '#sk4'))) 54.32/7.41 | ~ ('#form11'))), 54.32/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl29])). 54.32/7.41 thf(zip_derived_cl31, plain, 54.32/7.41 (( (((((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk5' @ Y0 @ Y1) & 54.32/7.41 ('#sk5' @ Y1 @ Y2))) => 54.32/7.41 ('#sk5' @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.41 Y1))) => 54.32/7.41 ('#sk5' @ Y0 @ Y1))))))))))) => 54.32/7.41 ('#sk5' @ '#sk3' @ '#sk4'))) 54.32/7.41 | ~ ('#form11'))), 54.32/7.41 inference('triggered_bool_instantiation', [status(thm)], 54.32/7.41 [zip_derived_cl30])). 54.32/7.41 thf(zip_derived_cl6, plain, 54.32/7.41 (~ (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk1' @ Y1 @ Y2) | 54.32/7.41 ('#sk2' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y2 @ 54.32/7.41 Y3) & (Y0 @ 54.32/7.41 Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4'))))))), 54.32/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 54.32/7.41 thf(zip_derived_cl8, plain, 54.32/7.41 (~ (((((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.32/7.41 Y1))) => 54.32/7.41 ('#sk5' @ Y0 @ Y1))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk5' @ Y1 @ Y2) & 54.32/7.41 ('#sk5' @ Y0 @ Y1))) => 54.32/7.41 ('#sk5' @ Y0 @ Y2)))))))))))))) => 54.32/7.41 ('#sk5' @ '#sk3' @ '#sk4')))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 54.32/7.41 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk3' @ '#sk4')), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 54.32/7.41 thf(zip_derived_cl230, plain, 54.32/7.41 (( (((((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk5' @ Y0 @ Y1) & 54.32/7.41 ('#sk5' @ Y1 @ Y2))) => 54.32/7.41 ('#sk5' @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.41 Y1))) => 54.32/7.41 ('#sk5' @ Y0 @ Y1))))))))))) => 54.32/7.41 ($false))) 54.32/7.41 | ~ ('#form11'))), 54.32/7.41 inference('demod', [status(thm)], [zip_derived_cl31, zip_derived_cl11])). 54.32/7.41 thf(zip_derived_cl231, plain, 54.32/7.41 (( (((~) @ (((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk5' @ Y0 @ Y1) & 54.32/7.41 ('#sk5' @ Y1 @ Y2))) => 54.32/7.41 ('#sk5' @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 54.32/7.41 Y0 @ Y1))) => 54.32/7.41 ('#sk5' @ Y0 @ Y1))))))))))))) 54.32/7.41 | ~ ('#form11'))), 54.32/7.41 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl230])). 54.32/7.41 thf(zip_derived_cl232, plain, 54.32/7.41 ((~ (((((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk5' @ Y0 @ Y1) & 54.32/7.41 ('#sk5' @ Y1 @ Y2))) => 54.32/7.41 ('#sk5' @ Y0 @ Y2)))))))))))) & 54.32/7.41 (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 54.32/7.41 ('#sk5' @ Y0 @ Y1))))))))))) 54.32/7.41 | ~ ('#form11'))), 54.32/7.41 inference('simplify nested equalities', [status(thm)], 54.32/7.41 [zip_derived_cl231])). 54.32/7.41 thf(zip_derived_cl233, plain, 54.32/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk5' @ Y0 @ Y1) & 54.32/7.41 ('#sk5' @ Y1 @ Y2))) => 54.32/7.41 ('#sk5' @ Y0 @ Y2)))))))))))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 54.32/7.41 ('#sk5' @ Y0 @ Y1))))))))) 54.32/7.41 | ~ ('#form11'))), 54.32/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl232])). 54.32/7.41 thf(zip_derived_cl107, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( ('#form172' @ X2) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.41 Y1))) => 54.32/7.41 (X2 @ Y0 @ Y1))))))))))), 54.32/7.41 define([status(thm)])). 54.32/7.41 thf(zip_derived_cl234, plain, 54.32/7.41 ((~ ('#form172' @ '#sk5') 54.32/7.41 | ~ ('#form11') 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk5' @ Y0 @ Y1) & 54.32/7.41 ('#sk5' @ Y1 @ Y2))) => 54.32/7.41 ('#sk5' @ Y0 @ Y2)))))))))))))), 54.32/7.41 inference('renaming', [status(thm)], 54.32/7.41 [zip_derived_cl233, zip_derived_cl107])). 54.32/7.41 thf(zip_derived_cl235, plain, 54.32/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 ((((('#sk5' @ ('#sk47' @ '#sk5') @ Y0) & 54.32/7.41 ('#sk5' @ Y0 @ Y1))) => 54.32/7.41 ('#sk5' @ ('#sk47' @ '#sk5') @ Y1))))))))) 54.32/7.41 | ~ ('#form11') 54.32/7.41 | ~ ('#form172' @ '#sk5'))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl234])). 54.32/7.41 thf(zip_derived_cl236, plain, 54.32/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.32/7.41 ((((('#sk5' @ ('#sk47' @ '#sk5') @ ('#sk74' @ '#sk5')) & 54.32/7.41 ('#sk5' @ ('#sk74' @ '#sk5') @ Y0))) => 54.32/7.41 ('#sk5' @ ('#sk47' @ '#sk5') @ Y0)))))) 54.32/7.41 | ~ ('#form172' @ '#sk5') 54.32/7.41 | ~ ('#form11'))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl235])). 54.32/7.41 thf(zip_derived_cl237, plain, 54.32/7.41 ((~ ((((('#sk5' @ ('#sk47' @ '#sk5') @ ('#sk74' @ '#sk5')) & ('#sk5' @ 54.32/7.41 ('#sk74' @ '#sk5') @ ('#sk112' @ '#sk5')))) => 54.32/7.41 ('#sk5' @ ('#sk47' @ '#sk5') @ ('#sk112' @ '#sk5')))) 54.32/7.41 | ~ ('#form11') 54.32/7.41 | ~ ('#form172' @ '#sk5'))), 54.32/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl236])). 54.32/7.41 thf(zip_derived_cl238, plain, 54.32/7.41 (( ((('#sk5' @ ('#sk47' @ '#sk5') @ ('#sk74' @ '#sk5')) & ('#sk5' @ 54.32/7.41 ('#sk74' @ '#sk5') @ ('#sk112' @ '#sk5')))) 54.32/7.41 | ~ ('#form172' @ '#sk5') 54.32/7.41 | ~ ('#form11'))), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl237])). 54.32/7.41 thf(zip_derived_cl189, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 (~ ('#form787' @ X2) 54.32/7.41 | (((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ ('#sk74' @ X2) @ 54.32/7.41 ('#sk112' @ X2)))))), 54.32/7.41 define([status(thm)])). 54.32/7.41 thf(zip_derived_cl240, plain, 54.32/7.41 (( ('#form787' @ '#sk5') | ~ ('#form11') | ~ ('#form172' @ '#sk5'))), 54.32/7.41 inference('renaming', [status(thm)], 54.32/7.41 [zip_derived_cl238, zip_derived_cl189])). 54.32/7.41 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk3' @ '#sk4')), 54.32/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 54.32/7.41 thf(zip_derived_cl158, plain, 54.32/7.41 (![X2 : a > a > $o]: 54.32/7.41 ( (X2 @ ('#sk228' @ X2) @ ('#sk314' @ X2)) 54.32/7.41 | ~ ('#form172' @ X2) 54.32/7.41 | ('#form11') 54.32/7.41 | ~ ('#form9') 54.32/7.41 | (X2 @ '#sk6' @ '#sk7'))), 54.32/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl148])). 54.32/7.41 thf(zip_derived_cl22, plain, 54.32/7.41 (( (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk1' @ Y1 @ Y2) | 54.32/7.41 ('#sk2' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk7' @ '#sk8')))))) 54.32/7.41 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 (((!!) @ (^[Y3 : a]: 54.32/7.41 (((((Y0 @ Y1 @ 54.32/7.41 Y2) & (Y0 @ 54.32/7.41 Y2 @ Y3))) => 54.32/7.41 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((!!) @ (^[Y2 : a]: 54.32/7.41 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.41 ('#sk1' @ Y1 @ Y2))) => 54.32/7.41 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.41 (Y0 @ '#sk3' @ '#sk4')))))) 54.32/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.41 (((!!) @ (^[Y1 : a]: 54.32/7.41 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.41 (((((((!!) @ (^[Y3 : a]: 54.32/7.41 (((!!) @ ( 54.32/7.41 ^[Y4 : a]: 54.32/7.41 (( 54.32/7.41 (!!) @ ( 54.32/7.41 ^[Y5 : a]: 54.32/7.41 (( 54.32/7.41 (( 54.32/7.41 (Y2 @ 54.32/7.41 Y4 @ 54.32/7.41 Y5) & 54.32/7.41 (Y2 @ 54.32/7.41 Y3 @ Y4))) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y5)))))))))))) & 54.32/7.42 (((!!) @ (^[Y3 : a]: 54.32/7.42 (((!!) @ ( 54.32/7.42 ^[Y4 : a]: 54.32/7.42 (( 54.32/7.42 ('#sk2' @ 54.32/7.42 Y3 @ 54.32/7.42 Y4) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y4))))))))))) => 54.32/7.42 (Y2 @ Y0 @ Y1)))))) | 54.32/7.42 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.42 (((((((!!) @ (^[Y3 : a]: 54.32/7.42 (((!!) @ ( 54.32/7.42 ^[Y4 : a]: 54.32/7.42 (( 54.32/7.42 ('#sk1' @ 54.32/7.42 Y3 @ 54.32/7.42 Y4) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y4))))))))) & 54.32/7.42 (((!!) @ (^[Y3 : a]: 54.32/7.42 (((!!) @ ( 54.32/7.42 ^[Y4 : a]: 54.32/7.42 (( 54.32/7.42 (!!) @ ( 54.32/7.42 ^[Y5 : a]: 54.32/7.42 (( 54.32/7.42 (( 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ 54.32/7.42 Y4) & 54.32/7.42 (Y2 @ 54.32/7.42 Y4 @ Y5))) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y5)))))))))))))) => 54.32/7.42 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.42 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.42 (((((((!!) @ (^[Y3 : a]: 54.32/7.42 (((!!) @ ( 54.32/7.42 ^[Y4 : a]: 54.32/7.42 ( 54.32/7.42 ( 54.32/7.42 (!!) @ ( 54.32/7.42 ^[Y5 : a]: 54.32/7.42 (( 54.32/7.42 (( 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ 54.32/7.42 Y4) & 54.32/7.42 (Y2 @ 54.32/7.42 Y4 @ Y5))) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y5)))))))))))) & 54.32/7.42 (((!!) @ (^[Y3 : a]: 54.32/7.42 (((!!) @ ( 54.32/7.42 ^[Y4 : a]: 54.32/7.42 ( 54.32/7.42 ( 54.32/7.42 (( 54.32/7.42 ('#sk1' @ 54.32/7.42 Y3 @ 54.32/7.42 Y4) | 54.32/7.42 ('#sk2' @ 54.32/7.42 Y3 @ Y4))) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y4))))))))))) => 54.32/7.42 (Y2 @ Y0 @ Y1)))))))))))))))), 54.32/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])). 54.32/7.42 thf(zip_derived_cl29, plain, 54.32/7.42 ((~ ('#form11') 54.32/7.42 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.42 (((((((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 (((!!) @ (^[Y3 : a]: 54.32/7.42 (((((Y0 @ Y1 @ 54.32/7.42 Y2) & (Y0 @ 54.32/7.42 Y2 @ Y3))) => 54.32/7.42 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 ((((('#sk2' @ Y1 @ Y2) | 54.32/7.42 ('#sk1' @ Y1 @ Y2))) => 54.32/7.42 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.42 (Y0 @ '#sk3' @ '#sk4')))))))), 54.32/7.42 define([status(thm)])). 54.32/7.42 thf(zip_derived_cl34, plain, 54.32/7.42 (( ('#form11') 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.42 (((((((!!) @ (^[Y3 : a]: 54.32/7.42 (((!!) @ ( 54.32/7.42 ^[Y4 : a]: 54.32/7.42 (( 54.32/7.42 (!!) @ ( 54.32/7.42 ^[Y5 : a]: 54.32/7.42 (( 54.32/7.42 (( 54.32/7.42 (Y2 @ 54.32/7.42 Y4 @ 54.32/7.42 Y5) & 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y4))) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y5)))))))))))) & 54.32/7.42 (((!!) @ (^[Y3 : a]: 54.32/7.42 (((!!) @ ( 54.32/7.42 ^[Y4 : a]: 54.32/7.42 (( 54.32/7.42 ('#sk2' @ 54.32/7.42 Y3 @ 54.32/7.42 Y4) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y4))))))))))) => 54.32/7.42 (Y2 @ Y0 @ Y1)))))) | 54.32/7.42 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.42 (((((((!!) @ (^[Y3 : a]: 54.32/7.42 (((!!) @ ( 54.32/7.42 ^[Y4 : a]: 54.32/7.42 (( 54.32/7.42 ('#sk1' @ 54.32/7.42 Y3 @ 54.32/7.42 Y4) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y4))))))))) & 54.32/7.42 (((!!) @ (^[Y3 : a]: 54.32/7.42 (((!!) @ ( 54.32/7.42 ^[Y4 : a]: 54.32/7.42 (( 54.32/7.42 (!!) @ ( 54.32/7.42 ^[Y5 : a]: 54.32/7.42 (( 54.32/7.42 (( 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ 54.32/7.42 Y4) & 54.32/7.42 (Y2 @ 54.32/7.42 Y4 @ Y5))) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y5)))))))))))))) => 54.32/7.42 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.42 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.42 (((((((!!) @ (^[Y3 : a]: 54.32/7.42 (((!!) @ ( 54.32/7.42 ^[Y4 : a]: 54.32/7.42 ( 54.32/7.42 ( 54.32/7.42 (!!) @ ( 54.32/7.42 ^[Y5 : a]: 54.32/7.42 (( 54.32/7.42 (( 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ 54.32/7.42 Y4) & 54.32/7.42 (Y2 @ 54.32/7.42 Y4 @ Y5))) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y5)))))))))))) & 54.32/7.42 (((!!) @ (^[Y3 : a]: 54.32/7.42 (((!!) @ ( 54.32/7.42 ^[Y4 : a]: 54.32/7.42 ( 54.32/7.42 ( 54.32/7.42 (( 54.32/7.42 ('#sk1' @ 54.32/7.42 Y3 @ 54.32/7.42 Y4) | 54.32/7.42 ('#sk2' @ 54.32/7.42 Y3 @ Y4))) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y4))))))))))) => 54.32/7.42 (Y2 @ Y0 @ Y1)))))))))))))) 54.32/7.42 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.42 (((((((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 (((!!) @ (^[Y3 : a]: 54.32/7.42 (((((Y0 @ Y1 @ 54.32/7.42 Y2) & (Y0 @ 54.32/7.42 Y2 @ Y3))) => 54.32/7.42 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 ((((('#sk1' @ Y1 @ Y2) | 54.32/7.42 ('#sk2' @ Y1 @ Y2))) => 54.32/7.42 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.42 (Y0 @ '#sk7' @ '#sk8')))))))), 54.32/7.42 inference('renaming', [status(thm)], [zip_derived_cl22, zip_derived_cl29])). 54.32/7.42 thf(zip_derived_cl24, plain, 54.32/7.42 (( ('#form9') 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((((((!!) @ (^[Y2 : a > a > $o]: 54.32/7.42 (((((((!!) @ (^[Y3 : a]: 54.32/7.42 (((!!) @ ( 54.32/7.42 ^[Y4 : a]: 54.32/7.42 (( 54.32/7.42 (!!) @ ( 54.32/7.42 ^[Y5 : a]: 54.32/7.42 (( 54.32/7.42 (( 54.32/7.42 (Y2 @ 54.32/7.42 Y4 @ 54.32/7.42 Y5) & 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y4))) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y5)))))))))))) & 54.32/7.42 (((!!) @ (^[Y3 : a]: 54.32/7.42 (((!!) @ ( 54.32/7.42 ^[Y4 : a]: 54.32/7.42 (( 54.32/7.42 ('#sk2' @ 54.32/7.42 Y3 @ 54.32/7.42 Y4) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y4))))))))))) => 54.32/7.42 (Y2 @ Y0 @ Y1)))))) | 54.32/7.42 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.42 (((((((!!) @ (^[Y3 : a]: 54.32/7.42 (((!!) @ ( 54.32/7.42 ^[Y4 : a]: 54.32/7.42 (( 54.32/7.42 ('#sk1' @ 54.32/7.42 Y3 @ 54.32/7.42 Y4) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y4))))))))) & 54.32/7.42 (((!!) @ (^[Y3 : a]: 54.32/7.42 (((!!) @ ( 54.32/7.42 ^[Y4 : a]: 54.32/7.42 (( 54.32/7.42 (!!) @ ( 54.32/7.42 ^[Y5 : a]: 54.32/7.42 (( 54.32/7.42 (( 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ 54.32/7.42 Y4) & 54.32/7.42 (Y2 @ 54.32/7.42 Y4 @ Y5))) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y5)))))))))))))) => 54.32/7.42 (Y2 @ Y0 @ Y1)))))))) => 54.32/7.42 (((!!) @ (^[Y2 : a > a > $o]: 54.32/7.42 (((((((!!) @ (^[Y3 : a]: 54.32/7.42 (((!!) @ ( 54.32/7.42 ^[Y4 : a]: 54.32/7.42 ( 54.32/7.42 ( 54.32/7.42 (!!) @ ( 54.32/7.42 ^[Y5 : a]: 54.32/7.42 (( 54.32/7.42 (( 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ 54.32/7.42 Y4) & 54.32/7.42 (Y2 @ 54.32/7.42 Y4 @ Y5))) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y5)))))))))))) & 54.32/7.42 (((!!) @ (^[Y3 : a]: 54.32/7.42 (((!!) @ ( 54.32/7.42 ^[Y4 : a]: 54.32/7.42 ( 54.32/7.42 ( 54.32/7.42 (( 54.32/7.42 ('#sk1' @ 54.32/7.42 Y3 @ 54.32/7.42 Y4) | 54.32/7.42 ('#sk2' @ 54.32/7.42 Y3 @ Y4))) => 54.32/7.42 (Y2 @ 54.32/7.42 Y3 @ Y4))))))))))) => 54.32/7.42 (Y2 @ Y0 @ Y1)))))))))))))))), 54.32/7.42 define([status(thm)])). 54.32/7.42 thf(zip_derived_cl41, plain, 54.32/7.42 ((~ ('#form9') 54.32/7.42 | (((!!) @ (^[Y0 : a > a > $o]: 54.32/7.42 (((((((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 (((!!) @ (^[Y3 : a]: 54.32/7.42 (((((Y0 @ Y1 @ 54.32/7.42 Y2) & (Y0 @ 54.32/7.42 Y2 @ Y3))) => 54.32/7.42 (Y0 @ Y1 @ Y3)))))))))))) & 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 ((((('#sk1' @ Y1 @ Y2) | 54.32/7.42 ('#sk2' @ Y1 @ Y2))) => 54.32/7.42 (Y0 @ Y1 @ Y2))))))))))) => 54.32/7.42 (Y0 @ '#sk7' @ '#sk8')))))) 54.32/7.42 | ('#form11'))), 54.32/7.42 inference('renaming', [status(thm)], [zip_derived_cl34, zip_derived_cl24])). 54.32/7.42 thf(zip_derived_cl49, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 ( (((((((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.42 Y1 @ Y2))) => 54.32/7.42 (X2 @ Y0 @ Y2)))))))))))) & 54.32/7.42 (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))))) => 54.32/7.42 (X2 @ '#sk7' @ '#sk8'))) 54.32/7.42 | ('#form11') 54.32/7.42 | ~ ('#form9'))), 54.32/7.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 54.32/7.42 thf(zip_derived_cl67, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ (((((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.42 Y1 @ Y2))) => 54.32/7.42 (X2 @ Y0 @ Y2)))))))))))) & 54.32/7.42 (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))))) 54.32/7.42 | (X2 @ '#sk7' @ '#sk8') 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#form11'))), 54.32/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 54.32/7.42 thf(zip_derived_cl80, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.42 Y1 @ Y2))) => 54.32/7.42 (X2 @ Y0 @ Y2)))))))))))) 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))) 54.32/7.42 | ('#form11') 54.32/7.42 | ~ ('#form9') 54.32/7.42 | (X2 @ '#sk7' @ '#sk8'))), 54.32/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl67])). 54.32/7.42 thf(zip_derived_cl95, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((((X2 @ ('#sk47' @ X2) @ Y0) & (X2 @ 54.32/7.42 Y0 @ Y1))) => 54.32/7.42 (X2 @ ('#sk47' @ X2) @ Y1))))))))) 54.32/7.42 | (X2 @ '#sk7' @ '#sk8') 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#form11') 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))))), 54.32/7.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl80])). 54.32/7.42 thf(zip_derived_cl104, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ 54.32/7.42 ('#sk74' @ X2) @ Y0))) => 54.32/7.42 (X2 @ ('#sk47' @ X2) @ Y0)))))) 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))) 54.32/7.42 | ('#form11') 54.32/7.42 | ~ ('#form9') 54.32/7.42 | (X2 @ '#sk7' @ '#sk8'))), 54.32/7.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl95])). 54.32/7.42 thf(zip_derived_cl116, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ (((((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ 54.32/7.42 ('#sk74' @ X2) @ ('#sk112' @ X2)))) => 54.32/7.42 (X2 @ ('#sk47' @ X2) @ ('#sk112' @ X2)))) 54.32/7.42 | (X2 @ '#sk7' @ '#sk8') 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#form11') 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))))), 54.32/7.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl104])). 54.32/7.42 thf(zip_derived_cl129, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ (X2 @ ('#sk47' @ X2) @ ('#sk112' @ X2)) 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))) 54.32/7.42 | ('#form11') 54.32/7.42 | ~ ('#form9') 54.32/7.42 | (X2 @ '#sk7' @ '#sk8'))), 54.32/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl116])). 54.32/7.42 thf(zip_derived_cl145, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 ( ('#form367' @ X2) 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))))), 54.32/7.42 define([status(thm)])). 54.32/7.42 thf(zip_derived_cl146, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ (((!!) @ (^[Y0 : a]: 54.32/7.42 ((((('#sk1' @ ('#sk368' @ X2) @ Y0) | ('#sk2' @ 54.32/7.42 ('#sk368' @ X2) @ Y0))) => 54.32/7.42 (X2 @ ('#sk368' @ X2) @ Y0)))))) 54.32/7.42 | ('#form367' @ X2))), 54.32/7.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl145])). 54.32/7.42 thf(zip_derived_cl157, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ ((((('#sk1' @ ('#sk368' @ X2) @ ('#sk464' @ X2)) | ('#sk2' @ 54.32/7.42 ('#sk368' @ X2) @ ('#sk464' @ X2)))) => 54.32/7.42 (X2 @ ('#sk368' @ X2) @ ('#sk464' @ X2)))) 54.32/7.42 | ('#form367' @ X2))), 54.32/7.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl146])). 54.32/7.42 thf(zip_derived_cl166, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 ( ((('#sk1' @ ('#sk368' @ X2) @ ('#sk464' @ X2)) | ('#sk2' @ 54.32/7.42 ('#sk368' @ X2) @ ('#sk464' @ X2)))) 54.32/7.42 | ('#form367' @ X2))), 54.32/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl157])). 54.32/7.42 thf(zip_derived_cl175, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 ( ('#sk1' @ ('#sk368' @ X2) @ ('#sk464' @ X2)) 54.32/7.42 | ('#sk2' @ ('#sk368' @ X2) @ ('#sk464' @ X2)) 54.32/7.42 | ('#form367' @ X2))), 54.32/7.42 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl166])). 54.32/7.42 thf(zip_derived_cl49, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 ( (((((((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.42 Y1 @ Y2))) => 54.32/7.42 (X2 @ Y0 @ Y2)))))))))))) & 54.32/7.42 (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))))) => 54.32/7.42 (X2 @ '#sk7' @ '#sk8'))) 54.32/7.42 | ('#form11') 54.32/7.42 | ~ ('#form9'))), 54.32/7.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 54.32/7.42 thf(zip_derived_cl50, plain, 54.32/7.42 (( (((((((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 ((((('#sk21' @ Y0 @ Y1) & 54.32/7.42 ('#sk21' @ Y1 @ Y2))) => 54.32/7.42 ('#sk21' @ Y0 @ Y2)))))))))))) & 54.32/7.42 (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 ('#sk21' @ Y0 @ Y1))))))))))) => 54.32/7.42 ('#sk21' @ '#sk7' @ '#sk8'))) 54.32/7.42 | ('#form11') 54.32/7.42 | ~ ('#form9'))), 54.32/7.42 inference('triggered_bool_instantiation', [status(thm)], 54.32/7.42 [zip_derived_cl49])). 54.32/7.42 thf(zip_derived_cl299, plain, 54.32/7.42 ((~ (((((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 ((((('#sk21' @ Y0 @ Y1) & 54.32/7.42 ('#sk21' @ Y1 @ Y2))) => 54.32/7.42 ('#sk21' @ Y0 @ Y2)))))))))))) & 54.32/7.42 (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 54.32/7.42 ('#sk21' @ Y0 @ Y1))))))))))) 54.32/7.42 | ('#sk21' @ '#sk7' @ '#sk8') 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#form11'))), 54.32/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])). 54.32/7.42 thf(zip_derived_cl300, plain, 54.32/7.42 ((~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 ((((('#sk21' @ Y0 @ Y1) & 54.32/7.42 ('#sk21' @ Y1 @ Y2))) => 54.32/7.42 ('#sk21' @ Y0 @ Y2)))))))))))) 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 54.32/7.42 ('#sk21' @ Y0 @ Y1))))))))) 54.32/7.42 | ('#form11') 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#sk21' @ '#sk7' @ '#sk8'))), 54.32/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl299])). 54.32/7.42 thf(zip_derived_cl145, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 ( ('#form367' @ X2) 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))))), 54.32/7.42 define([status(thm)])). 54.32/7.42 thf(zip_derived_cl301, plain, 54.32/7.42 ((~ ('#form367' @ '#sk21') 54.32/7.42 | ('#sk21' @ '#sk7' @ '#sk8') 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#form11') 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 ((((('#sk21' @ Y0 @ Y1) & 54.32/7.42 ('#sk21' @ Y1 @ Y2))) => 54.32/7.42 ('#sk21' @ Y0 @ Y2)))))))))))))), 54.32/7.42 inference('renaming', [status(thm)], 54.32/7.42 [zip_derived_cl300, zip_derived_cl145])). 54.32/7.42 thf(zip_derived_cl302, plain, 54.32/7.42 ((~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk21' @ ('#sk47' @ '#sk21') @ Y0) & 54.32/7.42 ('#sk21' @ Y0 @ Y1))) => 54.32/7.42 ('#sk21' @ ('#sk47' @ '#sk21') @ Y1))))))))) 54.32/7.42 | ('#form11') 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#sk21' @ '#sk7' @ '#sk8') 54.32/7.42 | ~ ('#form367' @ '#sk21'))), 54.32/7.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl301])). 54.32/7.42 thf(zip_derived_cl303, plain, 54.32/7.42 ((~ (((!!) @ (^[Y0 : a]: 54.32/7.42 ((((('#sk21' @ ('#sk47' @ '#sk21') @ 54.32/7.42 ('#sk74' @ '#sk21')) & ('#sk21' @ 54.32/7.42 ('#sk74' @ '#sk21') @ Y0))) => 54.32/7.42 ('#sk21' @ ('#sk47' @ '#sk21') @ Y0)))))) 54.32/7.42 | ~ ('#form367' @ '#sk21') 54.32/7.42 | ('#sk21' @ '#sk7' @ '#sk8') 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#form11'))), 54.32/7.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl302])). 54.32/7.42 thf(zip_derived_cl304, plain, 54.32/7.42 ((~ ((((('#sk21' @ ('#sk47' @ '#sk21') @ ('#sk74' @ '#sk21')) & 54.32/7.42 ('#sk21' @ ('#sk74' @ '#sk21') @ ('#sk112' @ '#sk21')))) => 54.32/7.42 ('#sk21' @ ('#sk47' @ '#sk21') @ ('#sk112' @ '#sk21')))) 54.32/7.42 | ('#form11') 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#sk21' @ '#sk7' @ '#sk8') 54.32/7.42 | ~ ('#form367' @ '#sk21'))), 54.32/7.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl303])). 54.32/7.42 thf(zip_derived_cl305, plain, 54.32/7.42 (( ((('#sk21' @ ('#sk47' @ '#sk21') @ ('#sk74' @ '#sk21')) & ('#sk21' @ 54.32/7.42 ('#sk74' @ '#sk21') @ ('#sk112' @ '#sk21')))) 54.32/7.42 | ~ ('#form367' @ '#sk21') 54.32/7.42 | ('#sk21' @ '#sk7' @ '#sk8') 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#form11'))), 54.32/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl304])). 54.32/7.42 thf(zip_derived_cl189, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ ('#form787' @ X2) 54.32/7.42 | (((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ ('#sk74' @ X2) @ 54.32/7.42 ('#sk112' @ X2)))))), 54.32/7.42 define([status(thm)])). 54.32/7.42 thf(zip_derived_cl307, plain, 54.32/7.42 (( ('#form787' @ '#sk21') 54.32/7.42 | ('#form11') 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#sk21' @ '#sk7' @ '#sk8') 54.32/7.42 | ~ ('#form367' @ '#sk21'))), 54.32/7.42 inference('renaming', [status(thm)], 54.32/7.42 [zip_derived_cl305, zip_derived_cl189])). 54.32/7.42 thf(zip_derived_cl107, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 ( ('#form172' @ X2) 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))))), 54.32/7.42 define([status(thm)])). 54.32/7.42 thf(zip_derived_cl108, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ (((!!) @ (^[Y0 : a]: 54.32/7.42 ((((('#sk2' @ ('#sk173' @ X2) @ Y0) | ('#sk1' @ 54.32/7.42 ('#sk173' @ X2) @ Y0))) => 54.32/7.42 (X2 @ ('#sk173' @ X2) @ Y0)))))) 54.32/7.42 | ('#form172' @ X2))), 54.32/7.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl107])). 54.32/7.42 thf(zip_derived_cl120, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ ((((('#sk2' @ ('#sk173' @ X2) @ ('#sk238' @ X2)) | ('#sk1' @ 54.32/7.42 ('#sk173' @ X2) @ ('#sk238' @ X2)))) => 54.32/7.42 (X2 @ ('#sk173' @ X2) @ ('#sk238' @ X2)))) 54.32/7.42 | ('#form172' @ X2))), 54.32/7.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl108])). 54.32/7.42 thf(zip_derived_cl135, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 ( ((('#sk2' @ ('#sk173' @ X2) @ ('#sk238' @ X2)) | ('#sk1' @ 54.32/7.42 ('#sk173' @ X2) @ ('#sk238' @ X2)))) 54.32/7.42 | ('#form172' @ X2))), 54.32/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl120])). 54.32/7.42 thf(zip_derived_cl150, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 ( ('#sk2' @ ('#sk173' @ X2) @ ('#sk238' @ X2)) 54.32/7.42 | ('#sk1' @ ('#sk173' @ X2) @ ('#sk238' @ X2)) 54.32/7.42 | ('#form172' @ X2))), 54.32/7.42 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl135])). 54.32/7.42 thf(zip_derived_cl136, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ (X2 @ ('#sk173' @ X2) @ ('#sk238' @ X2)) | ('#form172' @ X2))), 54.32/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl120])). 54.32/7.42 thf(zip_derived_cl30, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 ( (((((((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.42 Y1 @ Y2))) => 54.32/7.42 (X2 @ Y0 @ Y2)))))))))))) & 54.32/7.42 (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))))) => 54.32/7.42 (X2 @ '#sk3' @ '#sk4'))) 54.32/7.42 | ~ ('#form11'))), 54.32/7.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl29])). 54.32/7.42 thf(zip_derived_cl42, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ (((((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.42 Y1 @ Y2))) => 54.32/7.42 (X2 @ Y0 @ Y2)))))))))))) & 54.32/7.42 (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))))) 54.32/7.42 | (X2 @ '#sk3' @ '#sk4') 54.32/7.42 | ~ ('#form11'))), 54.32/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl30])). 54.32/7.42 thf(zip_derived_cl54, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 (((((X2 @ Y0 @ Y1) & (X2 @ 54.32/7.42 Y1 @ Y2))) => 54.32/7.42 (X2 @ Y0 @ Y2)))))))))))) 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))) 54.32/7.42 | ~ ('#form11') 54.32/7.42 | (X2 @ '#sk3' @ '#sk4'))), 54.32/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl42])). 54.32/7.42 thf(zip_derived_cl68, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((((X2 @ ('#sk47' @ X2) @ Y0) & (X2 @ 54.32/7.42 Y0 @ Y1))) => 54.32/7.42 (X2 @ ('#sk47' @ X2) @ Y1))))))))) 54.32/7.42 | (X2 @ '#sk3' @ '#sk4') 54.32/7.42 | ~ ('#form11') 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))))), 54.32/7.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl54])). 54.32/7.42 thf(zip_derived_cl81, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ 54.32/7.42 ('#sk74' @ X2) @ Y0))) => 54.32/7.42 (X2 @ ('#sk47' @ X2) @ Y0)))))) 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))) 54.32/7.42 | ~ ('#form11') 54.32/7.42 | (X2 @ '#sk3' @ '#sk4'))), 54.32/7.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl68])). 54.32/7.42 thf(zip_derived_cl96, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ (((((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ 54.32/7.42 ('#sk74' @ X2) @ ('#sk112' @ X2)))) => 54.32/7.42 (X2 @ ('#sk47' @ X2) @ ('#sk112' @ X2)))) 54.32/7.42 | (X2 @ '#sk3' @ '#sk4') 54.32/7.42 | ~ ('#form11') 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))))), 54.32/7.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl81])). 54.32/7.42 thf(zip_derived_cl106, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ (X2 @ ('#sk47' @ X2) @ ('#sk112' @ X2)) 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))) 54.32/7.42 | ~ ('#form11') 54.32/7.42 | (X2 @ '#sk3' @ '#sk4'))), 54.32/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 54.32/7.42 thf(zip_derived_cl107, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 ( ('#form172' @ X2) 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))))), 54.32/7.42 define([status(thm)])). 54.32/7.42 thf(zip_derived_cl118, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ ('#form172' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 54.32/7.42 | (X2 @ '#sk3' @ '#sk4') 54.32/7.42 | ~ ('#form11') 54.32/7.42 | ~ (X2 @ ('#sk47' @ X2) @ ('#sk112' @ X2)))), 54.32/7.42 inference('renaming', [status(thm)], 54.32/7.42 [zip_derived_cl106, zip_derived_cl107])). 54.32/7.42 thf(zip_derived_cl133, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ ('#form172' @ X2) 54.32/7.42 | (X2 @ '#sk3' @ '#sk4') 54.32/7.42 | ~ ('#form11') 54.32/7.42 | ~ (X2 @ ('#sk47' @ X2) @ ('#sk112' @ X2)))), 54.32/7.42 inference('ho_norm', [status(thm)], [zip_derived_cl118])). 54.32/7.42 thf(zip_derived_cl129, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ (X2 @ ('#sk47' @ X2) @ ('#sk112' @ X2)) 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))) 54.32/7.42 | ('#form11') 54.32/7.42 | ~ ('#form9') 54.32/7.42 | (X2 @ '#sk7' @ '#sk8'))), 54.32/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl116])). 54.32/7.42 thf(zip_derived_cl145, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 ( ('#form367' @ X2) 54.32/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 (X2 @ Y0 @ Y1))))))))))), 54.32/7.42 define([status(thm)])). 54.32/7.42 thf(zip_derived_cl147, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ ('#form367' @ X2) 54.32/7.42 | (X2 @ '#sk7' @ '#sk8') 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#form11') 54.32/7.42 | ~ (X2 @ ('#sk47' @ X2) @ ('#sk112' @ X2)))), 54.32/7.42 inference('renaming', [status(thm)], 54.32/7.42 [zip_derived_cl129, zip_derived_cl145])). 54.32/7.42 thf(zip_derived_cl10, plain, 54.32/7.42 ( (((((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 54.32/7.42 ('#sk5' @ Y0 @ Y1))))))))) & 54.32/7.42 (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 ((((('#sk5' @ Y1 @ Y2) & 54.32/7.42 ('#sk5' @ Y0 @ Y1))) => 54.32/7.42 ('#sk5' @ Y0 @ Y2))))))))))))))), 54.32/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 54.32/7.42 thf(zip_derived_cl13, plain, 54.32/7.42 ( (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 54.32/7.42 ('#sk5' @ Y0 @ Y1)))))))))), 54.32/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 54.32/7.42 thf(zip_derived_cl16, plain, 54.32/7.42 (![X2 : a]: 54.32/7.42 (((!!) @ (^[Y0 : a]: 54.32/7.42 ((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) => 54.32/7.42 ('#sk5' @ X2 @ Y0))))))), 54.32/7.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 54.32/7.42 thf(zip_derived_cl20, plain, 54.32/7.42 (![X2 : a, X4 : a]: 54.32/7.42 ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) => ('#sk5' @ X2 @ X4)))), 54.32/7.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 54.32/7.42 thf(zip_derived_cl27, plain, 54.32/7.42 (![X2 : a, X4 : a]: 54.32/7.42 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) | ('#sk5' @ X2 @ X4))), 54.32/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 54.32/7.42 thf(zip_derived_cl39, plain, 54.32/7.42 (![X2 : a, X4 : a]: (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 54.32/7.42 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl27])). 54.32/7.42 thf(zip_derived_cl38, plain, 54.32/7.42 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 54.32/7.42 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl27])). 54.32/7.42 thf(zip_derived_cl60, plain, 54.32/7.42 (( (((((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 ((((('#sk21' @ Y0 @ Y1) & 54.32/7.42 ('#sk21' @ Y1 @ Y2))) => 54.32/7.42 ('#sk21' @ Y0 @ Y2)))))))))))) & 54.32/7.42 (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 54.32/7.42 ('#sk21' @ Y0 @ Y1))))))))))) 54.32/7.42 | ('#form11') 54.32/7.42 | ~ ('#form9'))), 54.32/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 54.32/7.42 thf(zip_derived_cl71, plain, 54.32/7.42 (( (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 54.32/7.42 ('#sk21' @ Y0 @ Y1))))))))) 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#form11'))), 54.32/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl60])). 54.32/7.42 thf(zip_derived_cl84, plain, 54.32/7.42 (![X2 : a]: 54.32/7.42 ( (((!!) @ (^[Y0 : a]: 54.32/7.42 ((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) => 54.32/7.42 ('#sk21' @ X2 @ Y0)))))) 54.32/7.42 | ('#form11') 54.32/7.42 | ~ ('#form9'))), 54.32/7.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl71])). 54.32/7.42 thf(zip_derived_cl99, plain, 54.32/7.42 (![X2 : a, X4 : a]: 54.32/7.42 ( ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) => ('#sk21' @ X2 @ X4))) 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#form11'))), 54.32/7.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl84])). 54.32/7.42 thf(zip_derived_cl111, plain, 54.32/7.42 (![X2 : a, X4 : a]: 54.32/7.42 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 54.32/7.42 | ('#sk21' @ X2 @ X4) 54.32/7.42 | ('#form11') 54.32/7.42 | ~ ('#form9'))), 54.32/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl99])). 54.32/7.42 thf(zip_derived_cl122, plain, 54.32/7.42 (![X2 : a, X4 : a]: 54.32/7.42 (~ ('#sk2' @ X2 @ X4) 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#form11') 54.32/7.42 | ('#sk21' @ X2 @ X4))), 54.32/7.42 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl111])). 54.32/7.42 thf(zip_derived_cl123, plain, 54.32/7.42 (![X2 : a, X4 : a]: 54.32/7.42 (~ ('#sk1' @ X2 @ X4) 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#form11') 54.32/7.42 | ('#sk21' @ X2 @ X4))), 54.32/7.42 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl111])). 54.32/7.42 thf(zip_derived_cl167, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ (X2 @ ('#sk368' @ X2) @ ('#sk464' @ X2)) | ('#form367' @ X2))), 54.32/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl157])). 54.32/7.42 thf(zip_derived_cl189, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 (~ ('#form787' @ X2) 54.32/7.42 | (((X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) & (X2 @ ('#sk74' @ X2) @ 54.32/7.42 ('#sk112' @ X2)))))), 54.32/7.42 define([status(thm)])). 54.32/7.42 thf(zip_derived_cl190, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 ( (X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) | ~ ('#form787' @ X2))), 54.32/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl189])). 54.32/7.42 thf(zip_derived_cl14, plain, 54.32/7.42 ( (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 ((((('#sk5' @ Y1 @ Y2) & ('#sk5' @ 54.32/7.42 Y0 @ Y1))) => 54.32/7.42 ('#sk5' @ Y0 @ Y2))))))))))))), 54.32/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 54.32/7.42 thf(zip_derived_cl17, plain, 54.32/7.42 (![X2 : a]: 54.32/7.42 (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk5' @ Y0 @ Y1) & ('#sk5' @ X2 @ Y0))) => 54.32/7.42 ('#sk5' @ X2 @ Y1)))))))))), 54.32/7.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 54.32/7.42 thf(zip_derived_cl21, plain, 54.32/7.42 (![X2 : a, X4 : a]: 54.32/7.42 (((!!) @ (^[Y0 : a]: 54.32/7.42 ((((('#sk5' @ X4 @ Y0) & ('#sk5' @ X2 @ X4))) => 54.32/7.42 ('#sk5' @ X2 @ Y0))))))), 54.32/7.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 54.32/7.42 thf(zip_derived_cl28, plain, 54.32/7.42 (![X2 : a, X4 : a, X6 : a]: 54.32/7.42 ((((('#sk5' @ X4 @ X6) & ('#sk5' @ X2 @ X4))) => ('#sk5' @ X2 @ X6)))), 54.32/7.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl21])). 54.32/7.42 thf(zip_derived_cl40, plain, 54.32/7.42 (![X2 : a, X4 : a, X6 : a]: 54.32/7.42 (~ ((('#sk5' @ X4 @ X6) & ('#sk5' @ X2 @ X4))) | ('#sk5' @ X2 @ X6))), 54.32/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl28])). 54.32/7.42 thf(zip_derived_cl48, plain, 54.32/7.42 (![X2 : a, X4 : a, X6 : a]: 54.32/7.42 (~ ('#sk5' @ X4 @ X6) | ~ ('#sk5' @ X2 @ X4) | ('#sk5' @ X2 @ X6))), 54.32/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl40])). 54.32/7.42 thf(zip_derived_cl191, plain, 54.32/7.42 (![X2 : a > a > $o]: 54.32/7.42 ( (X2 @ ('#sk74' @ X2) @ ('#sk112' @ X2)) | ~ ('#form787' @ X2))), 54.32/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl189])). 54.32/7.42 thf(zip_derived_cl70, plain, 54.32/7.42 (( (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 (((!!) @ (^[Y2 : a]: 54.32/7.42 ((((('#sk21' @ Y0 @ Y1) & 54.32/7.42 ('#sk21' @ Y1 @ Y2))) => 54.32/7.42 ('#sk21' @ Y0 @ Y2)))))))))))) 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#form11'))), 54.32/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl60])). 54.32/7.42 thf(zip_derived_cl83, plain, 54.32/7.42 (![X2 : a]: 54.32/7.42 ( (((!!) @ (^[Y0 : a]: 54.32/7.42 (((!!) @ (^[Y1 : a]: 54.32/7.42 ((((('#sk21' @ X2 @ Y0) & ('#sk21' @ Y0 @ 54.32/7.42 Y1))) => 54.32/7.42 ('#sk21' @ X2 @ Y1))))))))) 54.32/7.42 | ('#form11') 54.32/7.42 | ~ ('#form9'))), 54.32/7.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl70])). 54.32/7.42 thf(zip_derived_cl98, plain, 54.32/7.42 (![X2 : a, X4 : a]: 54.32/7.42 ( (((!!) @ (^[Y0 : a]: 54.32/7.42 ((((('#sk21' @ X2 @ X4) & ('#sk21' @ X4 @ Y0))) => 54.32/7.42 ('#sk21' @ X2 @ Y0)))))) 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#form11'))), 54.32/7.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl83])). 54.32/7.42 thf(zip_derived_cl110, plain, 54.32/7.42 (![X2 : a, X4 : a, X6 : a]: 54.32/7.42 ( ((((('#sk21' @ X2 @ X4) & ('#sk21' @ X4 @ X6))) => ('#sk21' @ X2 @ 54.32/7.42 X6))) 54.32/7.42 | ('#form11') 54.32/7.42 | ~ ('#form9'))), 54.32/7.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl98])). 54.32/7.42 thf(zip_derived_cl121, plain, 54.32/7.42 (![X2 : a, X4 : a, X6 : a]: 54.32/7.42 (~ ((('#sk21' @ X2 @ X4) & ('#sk21' @ X4 @ X6))) 54.32/7.42 | ('#sk21' @ X2 @ X6) 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#form11'))), 54.32/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl110])). 54.32/7.42 thf(zip_derived_cl137, plain, 54.32/7.42 (![X2 : a, X4 : a, X6 : a]: 54.32/7.42 (~ ('#sk21' @ X2 @ X4) 54.32/7.42 | ~ ('#sk21' @ X4 @ X6) 54.32/7.42 | ('#form11') 54.32/7.42 | ~ ('#form9') 54.32/7.42 | ('#sk21' @ X2 @ X6))), 54.32/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl121])). 54.32/7.42 thf(zip_derived_cl6548, plain, ($false), 54.32/7.42 inference('eprover', [status(thm)], 54.32/7.42 [zip_derived_cl79, zip_derived_cl188, zip_derived_cl186, 54.32/7.42 zip_derived_cl193, zip_derived_cl192, zip_derived_cl141, 54.32/7.42 zip_derived_cl345, zip_derived_cl344, zip_derived_cl343, 54.32/7.42 zip_derived_cl154, zip_derived_cl183, zip_derived_cl142, 54.32/7.42 zip_derived_cl184, zip_derived_cl61, zip_derived_cl159, 54.32/7.42 zip_derived_cl149, zip_derived_cl240, zip_derived_cl11, 54.32/7.42 zip_derived_cl158, zip_derived_cl175, zip_derived_cl307, 54.32/7.42 zip_derived_cl150, zip_derived_cl136, zip_derived_cl133, 54.32/7.42 zip_derived_cl147, zip_derived_cl39, zip_derived_cl38, 54.32/7.42 zip_derived_cl122, zip_derived_cl123, zip_derived_cl167, 54.32/7.42 zip_derived_cl190, zip_derived_cl48, zip_derived_cl191, 54.32/7.42 zip_derived_cl137])). 54.32/7.42 54.32/7.42 % SZS output end Refutation 54.32/7.42 54.32/7.42 54.32/7.42 % Terminating... 54.32/7.45 % Runner terminated. 54.32/7.46 % Zipperpin 1.5 exiting 54.32/7.46 EOF