0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.WnzIjun5Hb true 0.13/0.35 % Computer : n024.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 960 0.13/0.35 % WCLimit : 120 0.13/0.35 % DateTime : Tue Aug 9 01:59:22 EDT 2022 0.13/0.36 % CPUTime : 0.13/0.36 % Running portfolio for 960 s 0.13/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.36 % Number of cores: 8 0.13/0.36 % Python version: Python 3.6.8 0.13/0.36 % Running in HO mode 0.42/0.61 % Total configuration time : 828 0.42/0.61 % Estimated wc time : 1656 0.42/0.61 % Estimated cpu time (8 cpus) : 207.0 0.53/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.53/0.71 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.53/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.53/0.72 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.53/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.53/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.55/0.77 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 47.77/7.19 % Solved by lams/20_acsne_simpl.sh. 47.77/7.19 % done 407 iterations in 6.183s 47.77/7.19 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 47.77/7.19 % SZS output start Refutation 47.77/7.19 thf(a_type, type, a: $tType). 47.77/7.19 thf('#sk4_type', type, '#sk4': a). 47.77/7.19 thf('#sk30_type', type, '#sk30': a > a > $o). 47.77/7.19 thf('#sk103_type', type, '#sk103': (a > a > $o) > a). 47.77/7.19 thf('#sk796_type', type, '#sk796': (a > a > $o) > a). 47.77/7.19 thf('#sk3_type', type, '#sk3': a). 47.77/7.19 thf('#form522_type', type, '#form522': (a > a > $o) > $o). 47.77/7.19 thf('#sk722_type', type, '#sk722': (a > a > $o) > a). 47.77/7.19 thf('#sk348_type', type, '#sk348': (a > a > $o) > a). 47.77/7.19 thf('#sk12_type', type, '#sk12': a). 47.77/7.19 thf('#sk21_type', type, '#sk21': a > a > $o). 47.77/7.19 thf('#sk260_type', type, '#sk260': (a > a > $o) > a). 47.77/7.19 thf('#sk47_type', type, '#sk47': (a > a > $o) > a). 47.77/7.19 thf('#sk221_type', type, '#sk221': (a > a > $o) > a). 47.77/7.19 thf('#sk77_type', type, '#sk77': (a > a > $o) > a). 47.77/7.19 thf('#sk6_type', type, '#sk6': a). 47.77/7.19 thf('#sk130_type', type, '#sk130': (a > a > $o) > a). 47.77/7.19 thf('#sk2_type', type, '#sk2': a > a > $o). 47.77/7.19 thf('#sk269_type', type, '#sk269': (a > a > $o) > a). 47.77/7.19 thf('#sk8_type', type, '#sk8': a). 47.77/7.19 thf('#sk10_type', type, '#sk10': a). 47.77/7.19 thf('#sk7_type', type, '#sk7': a). 47.77/7.19 thf('#sk157_type', type, '#sk157': (a > a > $o) > a). 47.77/7.19 thf('#form1026_type', type, '#form1026': $o). 47.77/7.19 thf('#form721_type', type, '#form721': (a > a > $o) > $o). 47.77/7.19 thf('#form9_type', type, '#form9': $o). 47.77/7.19 thf('#form11_type', type, '#form11': $o). 47.77/7.19 thf('#sk5_type', type, '#sk5': a > a > $o). 47.77/7.19 thf('#sk1_type', type, '#sk1': a > a > $o). 47.77/7.19 thf('#form94_type', type, '#form94': $o). 47.77/7.19 thf('#sk192_type', type, '#sk192': (a > a > $o) > a). 47.77/7.19 thf('#form813_type', type, '#form813': (a > a > $o) > $o). 47.77/7.19 thf('#form336_type', type, '#form336': (a > a > $o) > $o). 47.77/7.19 thf(cTHM250G_pme, conjecture, 47.77/7.19 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 47.77/7.19 ( ( ![Xp1:( a > a > $o )]: 47.77/7.19 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 47.77/7.19 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xz ) ) ) & 47.77/7.19 ( ![Xx0:a,Xy0:a]: 47.77/7.19 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 47.77/7.19 ( Xp1 @ Xx @ Xy ) ) ) | 47.77/7.19 ( ~( ( ( ![Xx0:a,Xy0:a,Xz:a]: 47.77/7.19 ( ( ( ![Xp1:( a > a > $o )]: 47.77/7.19 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 47.77/7.19 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 47.77/7.19 ( ![Xx1:a,Xy1:a]: 47.77/7.19 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 47.77/7.19 ( ![Xp1:( a > a > $o )]: 47.77/7.19 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 47.77/7.19 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 47.77/7.19 ( ![Xx1:a,Xy1:a]: 47.77/7.19 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 47.77/7.19 ( Xp1 @ Xy0 @ Xz ) ) ) ) => 47.77/7.19 ( ![Xp1:( a > a > $o )]: 47.77/7.19 ( ( ( ![Xx1:a,Xy1:a]: 47.77/7.19 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 47.77/7.19 ( ![Xx1:a,Xy1:a,Xz0:a]: 47.77/7.19 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) & 47.77/7.19 ( ![Xx0:a,Xy0:a]: 47.77/7.19 ( ( ( ![Xp1:( a > a > $o )]: 47.77/7.19 ( ( ( ![Xx1:a,Xy1:a]: 47.77/7.19 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) & 47.77/7.19 ( ![Xx1:a,Xy1:a,Xz:a]: 47.77/7.19 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 47.77/7.19 ( ![Xp1:( a > a > $o )]: 47.77/7.19 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 47.77/7.19 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xz ) ) ) & 47.77/7.19 ( ![Xx1:a,Xy1:a]: 47.77/7.19 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 47.77/7.19 ( ![Xp1:( a > a > $o )]: 47.77/7.19 ( ( ( ![Xx1:a,Xy1:a]: 47.77/7.19 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 47.77/7.19 ( ![Xx1:a,Xy1:a,Xz:a]: 47.77/7.19 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) ) => 47.77/7.19 ( ![Xp1:( a > a > $o )]: 47.77/7.19 ( ( ( ![Xx0:a,Xy0:a]: 47.77/7.19 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 47.77/7.19 ( ![Xx0:a,Xy0:a,Xz:a]: 47.77/7.19 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 47.77/7.19 ( Xp1 @ Xx @ Xy ) ) ) ) ) ))). 47.77/7.19 thf(zf_stmt_0, negated_conjecture, 47.77/7.19 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 47.77/7.19 ( ( ![Xp1:( a > a > $o )]: 47.77/7.19 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 47.77/7.19 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xz ) ) ) & 47.77/7.19 ( ![Xx0:a,Xy0:a]: 47.77/7.19 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 47.77/7.19 ( Xp1 @ Xx @ Xy ) ) ) | 47.77/7.19 ( ~( ( ( ![Xx0:a,Xy0:a,Xz:a]: 47.77/7.19 ( ( ( ![Xp1:( a > a > $o )]: 47.77/7.19 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 47.77/7.19 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 47.77/7.19 ( ![Xx1:a,Xy1:a]: 47.77/7.19 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 47.77/7.19 ( ![Xp1:( a > a > $o )]: 47.77/7.19 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 47.77/7.19 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 47.77/7.19 ( ![Xx1:a,Xy1:a]: 47.77/7.19 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 47.77/7.19 ( Xp1 @ Xy0 @ Xz ) ) ) ) => 47.77/7.19 ( ![Xp1:( a > a > $o )]: 47.77/7.19 ( ( ( ![Xx1:a,Xy1:a]: 47.77/7.19 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 47.77/7.19 ( ![Xx1:a,Xy1:a,Xz0:a]: 47.77/7.19 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) & 47.77/7.19 ( ![Xx0:a,Xy0:a]: 47.77/7.19 ( ( ( ![Xp1:( a > a > $o )]: 47.77/7.19 ( ( ( ![Xx1:a,Xy1:a]: 47.77/7.19 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) & 47.77/7.19 ( ![Xx1:a,Xy1:a,Xz:a]: 47.77/7.19 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 47.77/7.19 ( ![Xp1:( a > a > $o )]: 47.77/7.19 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 47.77/7.19 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xz ) ) ) & 47.77/7.19 ( ![Xx1:a,Xy1:a]: 47.77/7.19 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 47.77/7.19 ( ![Xp1:( a > a > $o )]: 47.77/7.19 ( ( ( ![Xx1:a,Xy1:a]: 47.77/7.19 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 47.77/7.19 ( ![Xx1:a,Xy1:a,Xz:a]: 47.77/7.19 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 47.77/7.19 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) ) => 47.77/7.19 ( ![Xp1:( a > a > $o )]: 47.77/7.19 ( ( ( ![Xx0:a,Xy0:a]: 47.77/7.19 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 47.77/7.19 ( ![Xx0:a,Xy0:a,Xz:a]: 47.77/7.19 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 47.77/7.19 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 47.77/7.19 ( Xp1 @ Xx @ Xy ) ) ) ) ) ) )), 47.77/7.19 inference('cnf.neg', [status(esa)], [cTHM250G_pme])). 47.77/7.19 thf(zip_derived_cl0, plain, 47.77/7.19 (~ (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.19 (((!!) @ (^[Y1 : a > a > $o]: 47.77/7.19 (((!!) @ (^[Y2 : a]: 47.77/7.19 (((!!) @ (^[Y3 : a]: 47.77/7.19 (((((!!) @ (^[Y4 : 47.77/7.19 a > a > $o]: 47.77/7.19 (( 47.77/7.19 (( 47.77/7.19 (( 47.77/7.19 (!!) @ ( 47.77/7.19 ^[Y5 : a]: 47.77/7.19 (( 47.77/7.19 (!!) @ ( 47.77/7.19 ^[Y6 : a]: 47.77/7.19 (( 47.77/7.19 (!!) @ ( 47.77/7.19 ^[Y7 : a]: 47.77/7.19 (( 47.77/7.19 (( 47.77/7.19 (Y4 @ 47.77/7.19 Y6 @ 47.77/7.19 Y7) & 47.77/7.19 (Y4 @ 47.77/7.19 Y5 @ Y6))) => 47.77/7.19 (Y4 @ 47.77/7.19 Y5 @ Y7)))))))))))) & 47.77/7.19 (( 47.77/7.19 (!!) @ ( 47.77/7.19 ^[Y5 : a]: 47.77/7.19 (( 47.77/7.19 (!!) @ ( 47.77/7.19 ^[Y6 : a]: 47.77/7.19 (( 47.77/7.19 (( 47.77/7.19 (Y1 @ 47.77/7.19 Y5 @ 47.77/7.19 Y6) | 47.77/7.19 (Y0 @ 47.77/7.19 Y5 @ Y6))) => 47.77/7.19 (Y4 @ 47.77/7.19 Y5 @ Y6))))))))))) => 47.77/7.19 (Y4 @ 47.77/7.19 Y2 @ Y3)))))) | 47.77/7.19 (((~) @ (((( 47.77/7.19 (( 47.77/7.19 (!!) @ ( 47.77/7.19 ^[Y4 : a]: 47.77/7.19 (( 47.77/7.19 (!!) @ ( 47.77/7.19 ^[Y5 : a]: 47.77/7.19 (( 47.77/7.19 (!!) @ ( 47.77/7.19 ^[Y6 : a]: 47.77/7.19 (( 47.77/7.19 (( 47.77/7.19 (( 47.77/7.19 (!!) @ ( 47.77/7.19 ^[Y7 : 47.77/7.19 a > a > $o]: 47.77/7.19 (( 47.77/7.19 (( 47.77/7.19 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y9 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y10 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y7 @ 47.77/7.20 Y8 @ 47.77/7.20 Y9) & 47.77/7.20 (Y7 @ 47.77/7.20 Y9 @ Y10))) => 47.77/7.20 (Y7 @ 47.77/7.20 Y8 @ Y10)))))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y9 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y1 @ 47.77/7.20 Y8 @ 47.77/7.20 Y9) | 47.77/7.20 (Y0 @ 47.77/7.20 Y8 @ Y9))) => 47.77/7.20 (Y7 @ 47.77/7.20 Y8 @ Y9))))))))))) => 47.77/7.20 (Y7 @ 47.77/7.20 Y4 @ Y5)))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y9 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y10 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y7 @ 47.77/7.20 Y9 @ 47.77/7.20 Y10) & 47.77/7.20 (Y7 @ 47.77/7.20 Y8 @ Y9))) => 47.77/7.20 (Y7 @ 47.77/7.20 Y8 @ Y10)))))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y9 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y1 @ 47.77/7.20 Y8 @ 47.77/7.20 Y9) | 47.77/7.20 (Y0 @ 47.77/7.20 Y8 @ Y9))) => 47.77/7.20 (Y7 @ 47.77/7.20 Y8 @ Y9))))))))))) => 47.77/7.20 (Y7 @ 47.77/7.20 Y5 @ Y6)))))))) => 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y9 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y0 @ 47.77/7.20 Y8 @ 47.77/7.20 Y9) | 47.77/7.20 (Y1 @ 47.77/7.20 Y8 @ Y9))) => 47.77/7.20 (Y7 @ 47.77/7.20 Y8 @ Y9))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y9 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y10 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y7 @ 47.77/7.20 Y9 @ 47.77/7.20 Y10) & 47.77/7.20 (Y7 @ 47.77/7.20 Y8 @ Y9))) => 47.77/7.20 (Y7 @ 47.77/7.20 Y8 @ Y10)))))))))))))) => 47.77/7.20 (Y7 @ 47.77/7.20 Y4 @ Y6))))))))))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (Y1 @ 47.77/7.20 Y7 @ 47.77/7.20 Y8) => 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ Y8))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y9 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y6 @ 47.77/7.20 Y8 @ 47.77/7.20 Y9) & 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ Y8))) => 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ Y9)))))))))))))) => 47.77/7.20 (Y6 @ 47.77/7.20 Y4 @ Y5)))))) | 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y9 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y6 @ 47.77/7.20 Y8 @ 47.77/7.20 Y9) & 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ Y8))) => 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ Y9)))))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (Y0 @ 47.77/7.20 Y7 @ 47.77/7.20 Y8) => 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ Y8))))))))))) => 47.77/7.20 (Y6 @ 47.77/7.20 Y4 @ Y5)))))))) => 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y1 @ 47.77/7.20 Y7 @ 47.77/7.20 Y8) | 47.77/7.20 (Y0 @ 47.77/7.20 Y7 @ Y8))) => 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ Y8))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y9 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ 47.77/7.20 Y8) & 47.77/7.20 (Y6 @ 47.77/7.20 Y8 @ Y9))) => 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ Y9)))))))))))))) => 47.77/7.20 (Y6 @ 47.77/7.20 Y4 @ Y5)))))))))))))))) => 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y1 @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) | 47.77/7.20 (Y0 @ 47.77/7.20 Y5 @ Y6))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y6))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) & 47.77/7.20 (Y4 @ 47.77/7.20 Y6 @ Y7))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y7)))))))))))))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y2 @ Y3))))))))))))))))))))))))), 47.77/7.20 inference('cnf', [status(esa)], [zf_stmt_0])). 47.77/7.20 thf(zip_derived_cl1, plain, 47.77/7.20 (~ (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((!!) @ (^[Y3 : a > a > $o]: 47.77/7.20 (((((((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y3 @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) & 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y6)))))))))))) & 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y0 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))))))))))) => 47.77/7.20 (Y3 @ Y1 @ Y2)))))) | 47.77/7.20 (((~) @ (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y9 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ 47.77/7.20 Y8) & 47.77/7.20 (Y6 @ 47.77/7.20 Y8 @ Y9))) => 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ Y9)))))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y0 @ 47.77/7.20 Y7 @ 47.77/7.20 Y8) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y7 @ Y8))) => 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ Y8))))))))))) => 47.77/7.20 (Y6 @ 47.77/7.20 Y3 @ Y4)))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y9 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y6 @ 47.77/7.20 Y8 @ 47.77/7.20 Y9) & 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ Y8))) => 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ Y9)))))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y0 @ 47.77/7.20 Y7 @ 47.77/7.20 Y8) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y7 @ Y8))) => 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ Y8))))))))))) => 47.77/7.20 (Y6 @ 47.77/7.20 Y4 @ Y5)))))))) => 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y7 @ 47.77/7.20 Y8) | 47.77/7.20 (Y0 @ 47.77/7.20 Y7 @ Y8))) => 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ Y8))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y9 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y6 @ 47.77/7.20 Y8 @ 47.77/7.20 Y9) & 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ Y8))) => 47.77/7.20 (Y6 @ 47.77/7.20 Y7 @ Y9)))))))))))))) => 47.77/7.20 (Y6 @ 47.77/7.20 Y3 @ Y5))))))))))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (Y0 @ 47.77/7.20 Y6 @ 47.77/7.20 Y7) => 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ Y7))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y5 @ 47.77/7.20 Y7 @ 47.77/7.20 Y8) & 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ Y7))) => 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ Y8)))))))))))))) => 47.77/7.20 (Y5 @ 47.77/7.20 Y3 @ Y4)))))) | 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y5 @ 47.77/7.20 Y7 @ 47.77/7.20 Y8) & 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ Y7))) => 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ Y8)))))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y6 @ 47.77/7.20 Y7) => 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ Y7))))))))))) => 47.77/7.20 (Y5 @ 47.77/7.20 Y3 @ Y4)))))))) => 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y0 @ 47.77/7.20 Y6 @ 47.77/7.20 Y7) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y6 @ Y7))) => 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ Y7))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ 47.77/7.20 Y7) & 47.77/7.20 (Y5 @ 47.77/7.20 Y7 @ Y8))) => 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ Y8)))))))))))))) => 47.77/7.20 (Y5 @ 47.77/7.20 Y3 @ Y4)))))))))))))))) => 47.77/7.20 (((!!) @ (^[Y3 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y0 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y3 @ 47.77/7.20 Y5 @ Y6))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y6)))))))))))))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y1 @ Y2)))))))))))))))))))))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 47.77/7.20 thf(zip_derived_cl2, plain, 47.77/7.20 (~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (((( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ Y4) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))) | 47.77/7.20 (((~) @ (((((((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ 47.77/7.20 Y7) & 47.77/7.20 (Y5 @ 47.77/7.20 Y7 @ Y8))) => 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ Y8)))))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y6 @ 47.77/7.20 Y7) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y6 @ Y7))) => 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ Y7))))))))))) => 47.77/7.20 (Y5 @ 47.77/7.20 Y2 @ Y3)))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y5 @ 47.77/7.20 Y7 @ 47.77/7.20 Y8) & 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ Y7))) => 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ Y8)))))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y6 @ 47.77/7.20 Y7) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y6 @ Y7))) => 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ Y7))))))))))) => 47.77/7.20 (Y5 @ 47.77/7.20 Y3 @ Y4)))))))) => 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y6 @ 47.77/7.20 Y7) | 47.77/7.20 ('#sk2' @ 47.77/7.20 Y6 @ Y7))) => 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ Y7))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y8 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y5 @ 47.77/7.20 Y7 @ 47.77/7.20 Y8) & 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ Y7))) => 47.77/7.20 (Y5 @ 47.77/7.20 Y6 @ Y8)))))))))))))) => 47.77/7.20 (Y5 @ 47.77/7.20 Y2 @ Y4))))))))))))))))) & 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) => 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y6))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y4 @ 47.77/7.20 Y6 @ 47.77/7.20 Y7) & 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y6))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y7)))))))))))))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y2 @ Y3)))))) | 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y4 @ 47.77/7.20 Y6 @ 47.77/7.20 Y7) & 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y6))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y7)))))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) => 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y6))))))))))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y2 @ Y3)))))))) => 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y5 @ Y6))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y6))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) & 47.77/7.20 (Y4 @ 47.77/7.20 Y6 @ Y7))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y7)))))))))))))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y2 @ Y3)))))))))))))))) => 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ ( 47.77/7.20 ^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) & 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1))))))))))))))))))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 47.77/7.20 thf(zip_derived_cl3, plain, 47.77/7.20 (~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((((!!) @ (^[Y1 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (((( 47.77/7.20 (Y1 @ 47.77/7.20 Y3 @ Y4) & 47.77/7.20 (Y1 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y1 @ 47.77/7.20 Y2 @ Y4)))))))))))) & 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 ((((('#sk2' @ 47.77/7.20 Y2 @ Y3) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y1 @ Y2 @ Y3))))))))))) => 47.77/7.20 (Y1 @ '#sk3' @ Y0)))))) | 47.77/7.20 (((~) @ (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) & 47.77/7.20 (Y4 @ 47.77/7.20 Y6 @ Y7))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y7)))))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y5 @ Y6))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y6))))))))))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y1 @ Y2)))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y4 @ 47.77/7.20 Y6 @ 47.77/7.20 Y7) & 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y6))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y7)))))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y5 @ Y6))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y6))))))))))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y2 @ Y3)))))))) => 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : 47.77/7.20 a > a > $o]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) | 47.77/7.20 ('#sk2' @ 47.77/7.20 Y5 @ Y6))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y6))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y7 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y4 @ 47.77/7.20 Y6 @ 47.77/7.20 Y7) & 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y6))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y5 @ Y7)))))))))))))) => 47.77/7.20 (Y4 @ 47.77/7.20 Y1 @ Y3))))))))))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((((!!) @ ( 47.77/7.20 ^[Y3 : 47.77/7.20 a > a > $o]: 47.77/7.20 (((( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y3 @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) & 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y6)))))))))))))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y1 @ Y2)))))) | 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y3 : 47.77/7.20 a > a > $o]: 47.77/7.20 (((( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y3 @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) & 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y6)))))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))))))))))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y1 @ Y2)))))))) => 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y3 : a > a > $o]: 47.77/7.20 (((((( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y3 @ 47.77/7.20 Y5 @ Y6))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y6)))))))))))))) => 47.77/7.20 (Y3 @ Y1 @ 47.77/7.20 Y2)))))))))))))))) => 47.77/7.20 (((!!) @ (^[Y1 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y3 : a]: 47.77/7.20 ((((('#sk2' @ 47.77/7.20 Y2 @ Y3) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y1 @ Y2 @ 47.77/7.20 Y3))))))))) & 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y1 @ 47.77/7.20 Y2 @ 47.77/7.20 Y3) & 47.77/7.20 (Y1 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y1 @ 47.77/7.20 Y2 @ Y4)))))))))))))) => 47.77/7.20 (Y1 @ '#sk3' @ Y0)))))))))))))))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 47.77/7.20 thf(zip_derived_cl4, plain, 47.77/7.20 (~ (((((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y2 @ 47.77/7.20 Y3) & (Y0 @ 47.77/7.20 Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.20 ('#sk1' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.20 (Y0 @ '#sk3' @ '#sk4')))))) | 47.77/7.20 (((~) @ (((((((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((((!!) @ ( 47.77/7.20 ^[Y3 : 47.77/7.20 a > a > $o]: 47.77/7.20 (((( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y3 @ 47.77/7.20 Y5 @ Y6))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y6)))))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))))))))))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y0 @ Y1)))))) & 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y3 : 47.77/7.20 a > a > $o]: 47.77/7.20 (((( 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y3 @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) & 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y6)))))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))))))))))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y1 @ Y2)))))))) => 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y3 : a > a > $o]: 47.77/7.20 (((((( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) | 47.77/7.20 ('#sk2' @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))))))))) & 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y3 @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) & 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y6)))))))))))))) => 47.77/7.20 (Y3 @ Y0 @ 47.77/7.20 Y2))))))))))))))))) & 47.77/7.20 (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ ( 47.77/7.20 ^[Y3 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y3 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))) | 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ ( 47.77/7.20 ^[Y3 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))) & 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y3 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ ( 47.77/7.20 ^[Y3 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y3 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) & 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))))))))))) => 47.77/7.20 (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk2' @ 47.77/7.20 Y1 @ Y2) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y3 : a]: 47.77/7.20 (((((Y0 @ 47.77/7.20 Y1 @ Y2) & 47.77/7.20 (Y0 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y0 @ Y1 @ 47.77/7.20 Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk3' @ '#sk4'))))))))))))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 47.77/7.20 thf(zip_derived_cl6, plain, 47.77/7.20 ( (((((((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((((!!) @ (^[Y3 : a > a > $o]: 47.77/7.20 (((((((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y3 @ 47.77/7.20 Y5 @ Y6))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y6)))))))))))) & 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))))))))))) => 47.77/7.20 (Y3 @ Y0 @ 47.77/7.20 Y1)))))) & 47.77/7.20 (((!!) @ (^[Y3 : a > a > $o]: 47.77/7.20 (((((((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y3 @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) & 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y6)))))))))))) & 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))))))))))) => 47.77/7.20 (Y3 @ Y1 @ 47.77/7.20 Y2)))))))) => 47.77/7.20 (((!!) @ (^[Y3 : a > a > $o]: 47.77/7.20 (((((((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) | 47.77/7.20 ('#sk2' @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))))))))) & 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y3 @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) & 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y6)))))))))))))) => 47.77/7.20 (Y3 @ Y0 @ Y2))))))))))))))))) & 47.77/7.20 (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))) | 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) & 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))))))))))) => 47.77/7.20 (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.20 ('#sk1' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y1 @ 47.77/7.20 Y2) & (Y0 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk3' @ '#sk4'))))))))), 47.77/7.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 47.77/7.20 thf(zip_derived_cl8, plain, 47.77/7.20 ((~ (((((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((((!!) @ (^[Y3 : a > a > $o]: 47.77/7.20 (((((((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y3 @ 47.77/7.20 Y5 @ Y6))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y6)))))))))))) & 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))))))))))) => 47.77/7.20 (Y3 @ Y0 @ 47.77/7.20 Y1)))))) & 47.77/7.20 (((!!) @ (^[Y3 : a > a > $o]: 47.77/7.20 (((((((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y3 @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) & 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y6)))))))))))) & 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))))))))))) => 47.77/7.20 (Y3 @ Y1 @ 47.77/7.20 Y2)))))))) => 47.77/7.20 (((!!) @ (^[Y3 : a > a > $o]: 47.77/7.20 (((((((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) | 47.77/7.20 ('#sk2' @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))))))))) & 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y3 @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) & 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y6)))))))))))))) => 47.77/7.20 (Y3 @ Y0 @ Y2))))))))))))))))) & 47.77/7.20 (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))) | 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) & 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))))))))))) 47.77/7.20 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.20 ('#sk1' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y1 @ 47.77/7.20 Y2) & (Y0 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk3' @ '#sk4')))))))), 47.77/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 47.77/7.20 thf(zip_derived_cl11, plain, 47.77/7.20 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((((!!) @ (^[Y3 : a > a > $o]: 47.77/7.20 (((((((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y3 @ 47.77/7.20 Y5 @ Y6))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y6)))))))))))) & 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))))))))))) => 47.77/7.20 (Y3 @ Y0 @ Y1)))))) & 47.77/7.20 (((!!) @ (^[Y3 : a > a > $o]: 47.77/7.20 (((((((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y3 @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) & 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y6)))))))))))) & 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))))))))))) => 47.77/7.20 (Y3 @ Y1 @ Y2)))))))) => 47.77/7.20 (((!!) @ (^[Y3 : a > a > $o]: 47.77/7.20 (((((((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) | 47.77/7.20 ('#sk2' @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))))))))) & 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y6 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y3 @ 47.77/7.20 Y5 @ 47.77/7.20 Y6) & 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y3 @ 47.77/7.20 Y4 @ Y6)))))))))))))) => 47.77/7.20 (Y3 @ Y0 @ Y2))))))))))))))))) 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))) | 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) & 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))))))))) 47.77/7.20 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.20 ('#sk1' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y1 @ 47.77/7.20 Y2) & (Y0 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk3' @ '#sk4')))))))), 47.77/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl8])). 47.77/7.20 thf(zip_derived_cl14, plain, 47.77/7.20 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) & 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))))) => 47.77/7.20 (Y2 @ '#sk6' @ Y0)))))) & 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (((( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) | 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ '#sk6' @ Y1)))))))))))))) 47.77/7.20 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.20 ('#sk1' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y1 @ 47.77/7.20 Y2) & (Y0 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk3' @ '#sk4')))))) 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))) | 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) & 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))))))))))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl11])). 47.77/7.20 thf(zip_derived_cl17, plain, 47.77/7.20 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((((((!!) @ (^[Y1 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (( 47.77/7.20 (Y1 @ 47.77/7.20 Y2 @ 47.77/7.20 Y3) & 47.77/7.20 (Y1 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y1 @ 47.77/7.20 Y2 @ Y4)))))))))))) & 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 ((((('#sk2' @ 47.77/7.20 Y2 @ 47.77/7.20 Y3) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y1 @ Y2 @ 47.77/7.20 Y3))))))))))) => 47.77/7.20 (Y1 @ '#sk6' @ '#sk7')))))) & 47.77/7.20 (((!!) @ (^[Y1 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (( 47.77/7.20 (Y1 @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) & 47.77/7.20 (Y1 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y1 @ 47.77/7.20 Y2 @ Y4)))))))))))) & 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 ((((('#sk2' @ 47.77/7.20 Y2 @ 47.77/7.20 Y3) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y1 @ Y2 @ 47.77/7.20 Y3))))))))))) => 47.77/7.20 (Y1 @ '#sk7' @ Y0)))))))) => 47.77/7.20 (((!!) @ (^[Y1 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 ((((('#sk1' @ 47.77/7.20 Y2 @ Y3) | 47.77/7.20 ('#sk2' @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y1 @ Y2 @ 47.77/7.20 Y3))))))))) & 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (((( 47.77/7.20 (Y1 @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) & 47.77/7.20 (Y1 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y1 @ 47.77/7.20 Y2 @ Y4)))))))))))))) => 47.77/7.20 (Y1 @ '#sk6' @ Y0))))))))))) 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))) | 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) & 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))))))))) 47.77/7.20 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.20 ('#sk1' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y1 @ 47.77/7.20 Y2) & (Y0 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk3' @ '#sk4')))))))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl14])). 47.77/7.20 thf(zip_derived_cl20, plain, 47.77/7.20 ((~ (((((((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ 47.77/7.20 Y1 @ 47.77/7.20 Y2) & 47.77/7.20 (Y0 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y0 @ Y1 @ 47.77/7.20 Y3)))))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.20 ('#sk1' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.20 (Y0 @ '#sk6' @ '#sk7')))))) & 47.77/7.20 (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ 47.77/7.20 Y2 @ 47.77/7.20 Y3) & 47.77/7.20 (Y0 @ 47.77/7.20 Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ 47.77/7.20 Y3)))))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.20 ('#sk1' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.20 (Y0 @ '#sk7' @ '#sk8')))))))) => 47.77/7.20 (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk1' @ Y1 @ Y2) | 47.77/7.20 ('#sk2' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y2 @ 47.77/7.20 Y3) & 47.77/7.20 (Y0 @ Y1 @ 47.77/7.20 Y2))) => 47.77/7.20 (Y0 @ Y1 @ 47.77/7.20 Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk6' @ '#sk8')))))))) 47.77/7.20 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.20 ('#sk1' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y1 @ 47.77/7.20 Y2) & (Y0 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk3' @ '#sk4')))))) 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))) | 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) & 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))))))))))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl17])). 47.77/7.20 thf(zip_derived_cl24, plain, 47.77/7.20 ((~ (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk1' @ Y1 @ Y2) | 47.77/7.20 ('#sk2' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y2 @ 47.77/7.20 Y3) & (Y0 @ 47.77/7.20 Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk6' @ '#sk8')))))) 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))) | 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) & 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))))))))) 47.77/7.20 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.20 ('#sk1' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y1 @ 47.77/7.20 Y2) & (Y0 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk3' @ '#sk4')))))))), 47.77/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 47.77/7.20 thf(zip_derived_cl30, plain, 47.77/7.20 (( ('#form9') 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))) | 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) & 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))))))))))), 47.77/7.20 define([status(thm)])). 47.77/7.20 thf(zip_derived_cl31, plain, 47.77/7.20 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((((((!!) @ (^[Y1 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 ((('#sk2' @ 47.77/7.20 Y2 @ Y3) => 47.77/7.20 (Y1 @ Y2 @ 47.77/7.20 Y3))))))))) & 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (( 47.77/7.20 (Y1 @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) & 47.77/7.20 (Y1 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y1 @ 47.77/7.20 Y2 @ Y4)))))))))))))) => 47.77/7.20 (Y1 @ '#sk10' @ Y0)))))) | 47.77/7.20 (((!!) @ (^[Y1 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (( 47.77/7.20 (Y1 @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) & 47.77/7.20 (Y1 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y1 @ 47.77/7.20 Y2 @ Y4)))))))))))) & 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 ((('#sk1' @ 47.77/7.20 Y2 @ Y3) => 47.77/7.20 (Y1 @ Y2 @ 47.77/7.20 Y3))))))))))) => 47.77/7.20 (Y1 @ '#sk10' @ Y0)))))))) => 47.77/7.20 (((!!) @ (^[Y1 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 ((((('#sk2' @ 47.77/7.20 Y2 @ Y3) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y1 @ Y2 @ 47.77/7.20 Y3))))))))) & 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (((( 47.77/7.20 (Y1 @ 47.77/7.20 Y2 @ 47.77/7.20 Y3) & 47.77/7.20 (Y1 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y1 @ 47.77/7.20 Y2 @ Y4)))))))))))))) => 47.77/7.20 (Y1 @ '#sk10' @ Y0))))))))))) 47.77/7.20 | ('#form9'))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])). 47.77/7.20 thf(zip_derived_cl42, plain, 47.77/7.20 ((~ (((((((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((('#sk2' @ Y1 @ Y2) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ 47.77/7.20 Y2 @ 47.77/7.20 Y3) & 47.77/7.20 (Y0 @ 47.77/7.20 Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ 47.77/7.20 Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk10' @ '#sk12')))))) | 47.77/7.20 (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ 47.77/7.20 Y2 @ 47.77/7.20 Y3) & 47.77/7.20 (Y0 @ 47.77/7.20 Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ 47.77/7.20 Y3)))))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((('#sk1' @ Y1 @ Y2) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.20 (Y0 @ '#sk10' @ '#sk12')))))))) => 47.77/7.20 (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.20 ('#sk1' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y1 @ 47.77/7.20 Y2) & 47.77/7.20 (Y0 @ Y2 @ 47.77/7.20 Y3))) => 47.77/7.20 (Y0 @ Y1 @ 47.77/7.20 Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk10' @ '#sk12')))))))) 47.77/7.20 | ('#form9'))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl31])). 47.77/7.20 thf(zip_derived_cl49, plain, 47.77/7.20 ((~ (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.20 ('#sk1' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y1 @ 47.77/7.20 Y2) & (Y0 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk10' @ '#sk12')))))) 47.77/7.20 | ('#form9'))), 47.77/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])). 47.77/7.20 thf(zip_derived_cl67, plain, 47.77/7.20 ((~ (((((((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.20 Y1))) => 47.77/7.20 ('#sk30' @ Y0 @ Y1))))))))) & 47.77/7.20 (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk30' @ Y0 @ Y1) & 47.77/7.20 ('#sk30' @ Y1 @ Y2))) => 47.77/7.20 ('#sk30' @ Y0 @ Y2)))))))))))))) => 47.77/7.20 ('#sk30' @ '#sk10' @ '#sk12'))) 47.77/7.20 | ('#form9'))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl49])). 47.77/7.20 thf(zip_derived_cl80, plain, 47.77/7.20 ((~ ('#sk30' @ '#sk10' @ '#sk12') | ('#form9'))), 47.77/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 47.77/7.20 thf(zip_derived_cl48, plain, 47.77/7.20 (( (((((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((('#sk2' @ Y1 @ Y2) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y2 @ 47.77/7.20 Y3) & (Y0 @ 47.77/7.20 Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk10' @ '#sk12')))))) | 47.77/7.20 (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y2 @ 47.77/7.20 Y3) & (Y0 @ 47.77/7.20 Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((('#sk1' @ Y1 @ Y2) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.20 (Y0 @ '#sk10' @ '#sk12')))))))) 47.77/7.20 | ('#form9'))), 47.77/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])). 47.77/7.20 thf(zip_derived_cl63, plain, 47.77/7.20 (( (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((('#sk2' @ Y1 @ Y2) => (Y0 @ 47.77/7.20 Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y2 @ 47.77/7.20 Y3) & (Y0 @ 47.77/7.20 Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk10' @ '#sk12')))))) 47.77/7.20 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y2 @ 47.77/7.20 Y3) & (Y0 @ 47.77/7.20 Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((('#sk1' @ Y1 @ Y2) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.20 (Y0 @ '#sk10' @ '#sk12')))))) 47.77/7.20 | ('#form9'))), 47.77/7.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl48])). 47.77/7.20 thf(zip_derived_cl73, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 ( (((((((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 47.77/7.20 (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((X2 @ Y1 @ Y2) & (X2 @ 47.77/7.20 Y0 @ Y1))) => 47.77/7.20 (X2 @ Y0 @ Y2)))))))))))))) => 47.77/7.20 (X2 @ '#sk10' @ '#sk12'))) 47.77/7.20 | ('#form9') 47.77/7.20 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ 47.77/7.20 Y2 @ Y3) & 47.77/7.20 (Y0 @ 47.77/7.20 Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ 47.77/7.20 Y3)))))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((('#sk1' @ Y1 @ Y2) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.20 (Y0 @ '#sk10' @ '#sk12')))))))), 47.77/7.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 47.77/7.20 thf(zip_derived_cl86, plain, 47.77/7.20 ((~ ('#form94') 47.77/7.20 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y2 @ 47.77/7.20 Y3) & (Y0 @ 47.77/7.20 Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((('#sk1' @ Y1 @ Y2) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.20 (Y0 @ '#sk10' @ '#sk12')))))))), 47.77/7.20 define([status(thm)])). 47.77/7.20 thf(zip_derived_cl87, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 ( (((((((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((X2 @ Y1 @ Y2) & (X2 @ 47.77/7.20 Y0 @ Y1))) => 47.77/7.20 (X2 @ Y0 @ Y2)))))))))))) & 47.77/7.20 (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 47.77/7.20 (X2 @ '#sk10' @ '#sk12'))) 47.77/7.20 | ~ ('#form94'))), 47.77/7.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl86])). 47.77/7.20 thf(zip_derived_cl88, plain, 47.77/7.20 (( (((((((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk30' @ Y1 @ Y2) & 47.77/7.20 ('#sk30' @ Y0 @ Y1))) => 47.77/7.20 ('#sk30' @ Y0 @ Y2)))))))))))) & 47.77/7.20 (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk1' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 47.77/7.20 Y1))))))))))) => 47.77/7.20 ('#sk30' @ '#sk10' @ '#sk12'))) 47.77/7.20 | ~ ('#form94'))), 47.77/7.20 inference('triggered_bool_instantiation', [status(thm)], 47.77/7.20 [zip_derived_cl87])). 47.77/7.20 thf(zip_derived_cl195, plain, 47.77/7.20 ((~ (((((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk30' @ Y1 @ Y2) & 47.77/7.20 ('#sk30' @ Y0 @ Y1))) => 47.77/7.20 ('#sk30' @ Y0 @ Y2)))))))))))) & 47.77/7.20 (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk1' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))))) 47.77/7.20 | ('#sk30' @ '#sk10' @ '#sk12') 47.77/7.20 | ~ ('#form94'))), 47.77/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl88])). 47.77/7.20 thf(zip_derived_cl196, plain, 47.77/7.20 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk30' @ Y1 @ Y2) & 47.77/7.20 ('#sk30' @ Y0 @ Y1))) => 47.77/7.20 ('#sk30' @ Y0 @ Y2)))))))))))) 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk1' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))) 47.77/7.20 | ~ ('#form94') 47.77/7.20 | ('#sk30' @ '#sk10' @ '#sk12'))), 47.77/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl195])). 47.77/7.20 thf(zip_derived_cl87, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 ( (((((((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((X2 @ Y1 @ Y2) & (X2 @ 47.77/7.20 Y0 @ Y1))) => 47.77/7.20 (X2 @ Y0 @ Y2)))))))))))) & 47.77/7.20 (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 47.77/7.20 (X2 @ '#sk10' @ '#sk12'))) 47.77/7.20 | ~ ('#form94'))), 47.77/7.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl86])). 47.77/7.20 thf(zip_derived_cl103, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 (~ (((((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((X2 @ Y1 @ Y2) & (X2 @ 47.77/7.20 Y0 @ Y1))) => 47.77/7.20 (X2 @ Y0 @ Y2)))))))))))) & 47.77/7.20 (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) 47.77/7.20 | (X2 @ '#sk10' @ '#sk12') 47.77/7.20 | ~ ('#form94'))), 47.77/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl87])). 47.77/7.20 thf(zip_derived_cl113, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 (~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((X2 @ Y1 @ Y2) & (X2 @ 47.77/7.20 Y0 @ Y1))) => 47.77/7.20 (X2 @ Y0 @ Y2)))))))))))) 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 47.77/7.20 | ~ ('#form94') 47.77/7.20 | (X2 @ '#sk10' @ '#sk12'))), 47.77/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl103])). 47.77/7.20 thf(zip_derived_cl124, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 (~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((((X2 @ Y0 @ Y1) & (X2 @ 47.77/7.20 ('#sk130' @ X2) @ Y0))) => 47.77/7.20 (X2 @ ('#sk130' @ X2) @ Y1))))))))) 47.77/7.20 | (X2 @ '#sk10' @ '#sk12') 47.77/7.20 | ~ ('#form94') 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl113])). 47.77/7.20 thf(zip_derived_cl136, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 (~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((((X2 @ ('#sk192' @ X2) @ Y0) & (X2 @ 47.77/7.20 ('#sk130' @ X2) @ ('#sk192' @ X2)))) => 47.77/7.20 (X2 @ ('#sk130' @ X2) @ Y0)))))) 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 47.77/7.20 | ~ ('#form94') 47.77/7.20 | (X2 @ '#sk10' @ '#sk12'))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl124])). 47.77/7.20 thf(zip_derived_cl150, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 (~ (((((X2 @ ('#sk192' @ X2) @ ('#sk260' @ X2)) & (X2 @ 47.77/7.20 ('#sk130' @ X2) @ ('#sk192' @ X2)))) => 47.77/7.20 (X2 @ ('#sk130' @ X2) @ ('#sk260' @ X2)))) 47.77/7.20 | (X2 @ '#sk10' @ '#sk12') 47.77/7.20 | ~ ('#form94') 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl136])). 47.77/7.20 thf(zip_derived_cl169, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 (~ (X2 @ ('#sk130' @ X2) @ ('#sk260' @ X2)) 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 47.77/7.20 | ~ ('#form94') 47.77/7.20 | (X2 @ '#sk10' @ '#sk12'))), 47.77/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl150])). 47.77/7.20 thf(zip_derived_cl176, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 ( ('#form721' @ X2) 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 47.77/7.20 define([status(thm)])). 47.77/7.20 thf(zip_derived_cl197, plain, 47.77/7.20 ((~ ('#form721' @ '#sk30') 47.77/7.20 | ('#sk30' @ '#sk10' @ '#sk12') 47.77/7.20 | ~ ('#form94') 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk30' @ Y1 @ Y2) & 47.77/7.20 ('#sk30' @ Y0 @ Y1))) => 47.77/7.20 ('#sk30' @ Y0 @ Y2)))))))))))))), 47.77/7.20 inference('renaming', [status(thm)], 47.77/7.20 [zip_derived_cl196, zip_derived_cl176])). 47.77/7.20 thf(zip_derived_cl198, plain, 47.77/7.20 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((((('#sk30' @ Y0 @ Y1) & ('#sk30' @ 47.77/7.20 ('#sk130' @ '#sk30') @ Y0))) => 47.77/7.20 ('#sk30' @ ('#sk130' @ '#sk30') @ Y1))))))))) 47.77/7.20 | ~ ('#form94') 47.77/7.20 | ('#sk30' @ '#sk10' @ '#sk12') 47.77/7.20 | ~ ('#form721' @ '#sk30'))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl197])). 47.77/7.20 thf(zip_derived_cl199, plain, 47.77/7.20 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.20 ((((('#sk30' @ ('#sk192' @ '#sk30') @ Y0) & ('#sk30' @ 47.77/7.20 ('#sk130' @ '#sk30') @ ('#sk192' @ '#sk30')))) => 47.77/7.20 ('#sk30' @ ('#sk130' @ '#sk30') @ Y0)))))) 47.77/7.20 | ~ ('#form721' @ '#sk30') 47.77/7.20 | ('#sk30' @ '#sk10' @ '#sk12') 47.77/7.20 | ~ ('#form94'))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl198])). 47.77/7.20 thf(zip_derived_cl200, plain, 47.77/7.20 ((~ ((((('#sk30' @ ('#sk192' @ '#sk30') @ ('#sk260' @ '#sk30')) & 47.77/7.20 ('#sk30' @ ('#sk130' @ '#sk30') @ ('#sk192' @ '#sk30')))) => 47.77/7.20 ('#sk30' @ ('#sk130' @ '#sk30') @ ('#sk260' @ '#sk30')))) 47.77/7.20 | ~ ('#form94') 47.77/7.20 | ('#sk30' @ '#sk10' @ '#sk12') 47.77/7.20 | ~ ('#form721' @ '#sk30'))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl199])). 47.77/7.20 thf(zip_derived_cl73, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 ( (((((((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 47.77/7.20 (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((X2 @ Y1 @ Y2) & (X2 @ 47.77/7.20 Y0 @ Y1))) => 47.77/7.20 (X2 @ Y0 @ Y2)))))))))))))) => 47.77/7.20 (X2 @ '#sk10' @ '#sk12'))) 47.77/7.20 | ('#form9') 47.77/7.20 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ 47.77/7.20 Y2 @ Y3) & 47.77/7.20 (Y0 @ 47.77/7.20 Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ 47.77/7.20 Y3)))))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((('#sk1' @ Y1 @ Y2) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.20 (Y0 @ '#sk10' @ '#sk12')))))))), 47.77/7.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 47.77/7.20 thf(zip_derived_cl86, plain, 47.77/7.20 ((~ ('#form94') 47.77/7.20 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y2 @ 47.77/7.20 Y3) & (Y0 @ 47.77/7.20 Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((('#sk1' @ Y1 @ Y2) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.20 (Y0 @ '#sk10' @ '#sk12')))))))), 47.77/7.20 define([status(thm)])). 47.77/7.20 thf(zip_derived_cl93, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 ( ('#form94') 47.77/7.20 | ('#form9') 47.77/7.20 | (((((((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 47.77/7.20 (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((X2 @ Y1 @ Y2) & 47.77/7.20 (X2 @ Y0 @ Y1))) => 47.77/7.20 (X2 @ Y0 @ Y2)))))))))))))) => 47.77/7.20 (X2 @ '#sk10' @ '#sk12'))))), 47.77/7.20 inference('renaming', [status(thm)], [zip_derived_cl73, zip_derived_cl86])). 47.77/7.20 thf(zip_derived_cl102, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 (~ (((((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 47.77/7.20 (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((X2 @ Y1 @ Y2) & (X2 @ 47.77/7.20 Y0 @ Y1))) => 47.77/7.20 (X2 @ Y0 @ Y2)))))))))))))) 47.77/7.20 | (X2 @ '#sk10' @ '#sk12') 47.77/7.20 | ('#form9') 47.77/7.20 | ('#form94'))), 47.77/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl93])). 47.77/7.20 thf(zip_derived_cl112, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 (~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((X2 @ Y1 @ Y2) & (X2 @ 47.77/7.20 Y0 @ Y1))) => 47.77/7.20 (X2 @ Y0 @ Y2)))))))))))) 47.77/7.20 | ('#form94') 47.77/7.20 | ('#form9') 47.77/7.20 | (X2 @ '#sk10' @ '#sk12'))), 47.77/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl102])). 47.77/7.20 thf(zip_derived_cl123, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 (~ (((!!) @ (^[Y0 : a]: 47.77/7.20 ((('#sk2' @ ('#sk269' @ X2) @ Y0) => (X2 @ 47.77/7.20 ('#sk269' @ X2) @ Y0)))))) 47.77/7.20 | (X2 @ '#sk10' @ '#sk12') 47.77/7.20 | ('#form9') 47.77/7.20 | ('#form94') 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((X2 @ Y1 @ Y2) & (X2 @ 47.77/7.20 Y0 @ Y1))) => 47.77/7.20 (X2 @ Y0 @ Y2)))))))))))))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl112])). 47.77/7.20 thf(zip_derived_cl135, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 (~ ((('#sk2' @ ('#sk269' @ X2) @ ('#sk348' @ X2)) => (X2 @ 47.77/7.20 ('#sk269' @ X2) @ ('#sk348' @ X2)))) 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((X2 @ Y1 @ Y2) & (X2 @ 47.77/7.20 Y0 @ Y1))) => 47.77/7.20 (X2 @ Y0 @ Y2)))))))))))) 47.77/7.20 | ('#form94') 47.77/7.20 | ('#form9') 47.77/7.20 | (X2 @ '#sk10' @ '#sk12'))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl123])). 47.77/7.20 thf(zip_derived_cl148, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 ( ('#sk2' @ ('#sk269' @ X2) @ ('#sk348' @ X2)) 47.77/7.20 | (X2 @ '#sk10' @ '#sk12') 47.77/7.20 | ('#form9') 47.77/7.20 | ('#form94') 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((((X2 @ Y1 @ Y2) & (X2 @ 47.77/7.20 Y0 @ Y1))) => 47.77/7.20 (X2 @ Y0 @ Y2)))))))))))))), 47.77/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl135])). 47.77/7.20 thf(zip_derived_cl166, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 (~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((((X2 @ Y0 @ Y1) & (X2 @ 47.77/7.20 ('#sk130' @ X2) @ Y0))) => 47.77/7.20 (X2 @ ('#sk130' @ X2) @ Y1))))))))) 47.77/7.20 | ('#form94') 47.77/7.20 | ('#form9') 47.77/7.20 | (X2 @ '#sk10' @ '#sk12') 47.77/7.20 | ('#sk2' @ ('#sk269' @ X2) @ ('#sk348' @ X2)))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl148])). 47.77/7.20 thf(zip_derived_cl172, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 (~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((((X2 @ ('#sk192' @ X2) @ Y0) & (X2 @ 47.77/7.20 ('#sk130' @ X2) @ ('#sk192' @ X2)))) => 47.77/7.20 (X2 @ ('#sk130' @ X2) @ Y0)))))) 47.77/7.20 | ('#sk2' @ ('#sk269' @ X2) @ ('#sk348' @ X2)) 47.77/7.20 | (X2 @ '#sk10' @ '#sk12') 47.77/7.20 | ('#form9') 47.77/7.20 | ('#form94'))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl166])). 47.77/7.20 thf(zip_derived_cl179, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 (~ (((((X2 @ ('#sk192' @ X2) @ ('#sk260' @ X2)) & (X2 @ 47.77/7.20 ('#sk130' @ X2) @ ('#sk192' @ X2)))) => 47.77/7.20 (X2 @ ('#sk130' @ X2) @ ('#sk260' @ X2)))) 47.77/7.20 | ('#form94') 47.77/7.20 | ('#form9') 47.77/7.20 | (X2 @ '#sk10' @ '#sk12') 47.77/7.20 | ('#sk2' @ ('#sk269' @ X2) @ ('#sk348' @ X2)))), 47.77/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl172])). 47.77/7.20 thf(zip_derived_cl184, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 ( ('#form813' @ X2) 47.77/7.20 | ~ (((((X2 @ ('#sk192' @ X2) @ ('#sk260' @ X2)) & (X2 @ 47.77/7.20 ('#sk130' @ X2) @ ('#sk192' @ X2)))) => 47.77/7.20 (X2 @ ('#sk130' @ X2) @ ('#sk260' @ X2)))))), 47.77/7.20 define([status(thm)])). 47.77/7.20 thf(zip_derived_cl201, plain, 47.77/7.20 ((~ ('#form813' @ '#sk30') 47.77/7.20 | ~ ('#form721' @ '#sk30') 47.77/7.20 | ('#sk30' @ '#sk10' @ '#sk12') 47.77/7.20 | ~ ('#form94'))), 47.77/7.20 inference('renaming', [status(thm)], 47.77/7.20 [zip_derived_cl200, zip_derived_cl184])). 47.77/7.20 thf(zip_derived_cl168, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 ( (((X2 @ ('#sk192' @ X2) @ ('#sk260' @ X2)) & (X2 @ 47.77/7.20 ('#sk130' @ X2) @ ('#sk192' @ X2)))) 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 47.77/7.20 | ~ ('#form94') 47.77/7.20 | (X2 @ '#sk10' @ '#sk12'))), 47.77/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl150])). 47.77/7.20 thf(zip_derived_cl174, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 ( (X2 @ ('#sk192' @ X2) @ ('#sk260' @ X2)) 47.77/7.20 | (X2 @ '#sk10' @ '#sk12') 47.77/7.20 | ~ ('#form94') 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 47.77/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl168])). 47.77/7.20 thf(zip_derived_cl176, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 ( ('#form721' @ X2) 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 47.77/7.20 define([status(thm)])). 47.77/7.20 thf(zip_derived_cl181, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 (~ ('#form721' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 47.77/7.20 | ~ ('#form94') 47.77/7.20 | (X2 @ '#sk10' @ '#sk12') 47.77/7.20 | (X2 @ ('#sk192' @ X2) @ ('#sk260' @ X2)))), 47.77/7.20 inference('renaming', [status(thm)], 47.77/7.20 [zip_derived_cl174, zip_derived_cl176])). 47.77/7.20 thf(zip_derived_cl189, plain, 47.77/7.20 (![X2 : a > a > $o]: 47.77/7.20 (~ ('#form721' @ X2) 47.77/7.20 | ~ ('#form94') 47.77/7.20 | (X2 @ '#sk10' @ '#sk12') 47.77/7.20 | (X2 @ ('#sk192' @ X2) @ ('#sk260' @ X2)))), 47.77/7.20 inference('ho_norm', [status(thm)], [zip_derived_cl181])). 47.77/7.20 thf(zip_derived_cl24, plain, 47.77/7.20 ((~ (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk1' @ Y1 @ Y2) | 47.77/7.20 ('#sk2' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y2 @ 47.77/7.20 Y3) & (Y0 @ 47.77/7.20 Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk6' @ '#sk8')))))) 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))) | 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) & 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))))))))) 47.77/7.20 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.20 ('#sk1' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y1 @ 47.77/7.20 Y2) & (Y0 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk3' @ '#sk4')))))))), 47.77/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 47.77/7.20 thf(zip_derived_cl30, plain, 47.77/7.20 (( ('#form9') 47.77/7.20 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))) | 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ 47.77/7.20 Y5) & 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 (( 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.20 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (( 47.77/7.20 ('#sk2' @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) | 47.77/7.20 ('#sk1' @ 47.77/7.20 Y3 @ Y4))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y4))))))))) & 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((!!) @ ( 47.77/7.20 ^[Y4 : a]: 47.77/7.20 ( 47.77/7.20 ( 47.77/7.20 (!!) @ ( 47.77/7.20 ^[Y5 : a]: 47.77/7.20 (( 47.77/7.20 (( 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ 47.77/7.20 Y4) & 47.77/7.20 (Y2 @ 47.77/7.20 Y4 @ Y5))) => 47.77/7.20 (Y2 @ 47.77/7.20 Y3 @ Y5)))))))))))))) => 47.77/7.20 (Y2 @ Y0 @ Y1)))))))))))))))), 47.77/7.20 define([status(thm)])). 47.77/7.20 thf(zip_derived_cl32, plain, 47.77/7.20 ((~ ('#form9') 47.77/7.20 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.20 ('#sk1' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y1 @ 47.77/7.20 Y2) & (Y0 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk3' @ '#sk4')))))) 47.77/7.20 | ~ (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk1' @ Y1 @ Y2) | 47.77/7.20 ('#sk2' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y2 @ 47.77/7.20 Y3) & 47.77/7.20 (Y0 @ Y1 @ 47.77/7.20 Y2))) => 47.77/7.20 (Y0 @ Y1 @ 47.77/7.20 Y3)))))))))))))) => 47.77/7.20 (Y0 @ '#sk6' @ '#sk8')))))))), 47.77/7.20 inference('renaming', [status(thm)], [zip_derived_cl24, zip_derived_cl30])). 47.77/7.20 thf(zip_derived_cl23, plain, 47.77/7.20 (( (((((!!) @ (^[Y0 : a > a > $o]: 47.77/7.20 (((((((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 (((!!) @ (^[Y3 : a]: 47.77/7.20 (((((Y0 @ Y1 @ 47.77/7.20 Y2) & (Y0 @ 47.77/7.20 Y2 @ Y3))) => 47.77/7.20 (Y0 @ Y1 @ Y3)))))))))))) & 47.77/7.20 (((!!) @ (^[Y1 : a]: 47.77/7.20 (((!!) @ (^[Y2 : a]: 47.77/7.20 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.20 ('#sk1' @ Y1 @ Y2))) => 47.77/7.20 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.20 (Y0 @ '#sk6' @ '#sk7')))))) & 47.77/7.21 (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y2 @ 47.77/7.21 Y3) & (Y0 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.21 ('#sk1' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.21 (Y0 @ '#sk7' @ '#sk8')))))))) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 ('#sk2' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ 47.77/7.21 Y5) & 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))) | 47.77/7.21 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ 47.77/7.21 Y5) & 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 ('#sk1' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.21 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 ( 47.77/7.21 ( 47.77/7.21 (( 47.77/7.21 ('#sk2' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) | 47.77/7.21 ('#sk1' @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 ( 47.77/7.21 ( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) & 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ Y5))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))))))))))) 47.77/7.21 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.21 ('#sk1' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y1 @ 47.77/7.21 Y2) & (Y0 @ 47.77/7.21 Y2 @ Y3))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.21 (Y0 @ '#sk3' @ '#sk4')))))))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 47.77/7.21 thf(zip_derived_cl28, plain, 47.77/7.21 (( (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y1 @ 47.77/7.21 Y2) & (Y0 @ 47.77/7.21 Y2 @ Y3))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.21 ('#sk1' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.21 (Y0 @ '#sk6' @ '#sk7')))))) 47.77/7.21 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.21 ('#sk1' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y1 @ 47.77/7.21 Y2) & (Y0 @ 47.77/7.21 Y2 @ Y3))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.21 (Y0 @ '#sk3' @ '#sk4')))))) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 ('#sk2' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ 47.77/7.21 Y5) & 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))) | 47.77/7.21 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ 47.77/7.21 Y5) & 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 ('#sk1' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.21 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 ( 47.77/7.21 ( 47.77/7.21 (( 47.77/7.21 ('#sk2' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) | 47.77/7.21 ('#sk1' @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 ( 47.77/7.21 ( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) & 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ Y5))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))))))))))))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])). 47.77/7.21 thf(zip_derived_cl34, plain, 47.77/7.21 ((~ ('#form11') 47.77/7.21 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.21 ('#sk1' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y1 @ 47.77/7.21 Y2) & (Y0 @ 47.77/7.21 Y2 @ Y3))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.21 (Y0 @ '#sk3' @ '#sk4')))))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl41, plain, 47.77/7.21 (( ('#form11') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk1' @ Y1 @ Y2) | 47.77/7.21 ('#sk2' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y2 @ 47.77/7.21 Y3) & 47.77/7.21 (Y0 @ Y1 @ 47.77/7.21 Y2))) => 47.77/7.21 (Y0 @ Y1 @ 47.77/7.21 Y3)))))))))))))) => 47.77/7.21 (Y0 @ '#sk6' @ '#sk8')))))) 47.77/7.21 | ~ ('#form9'))), 47.77/7.21 inference('renaming', [status(thm)], [zip_derived_cl32, zip_derived_cl34])). 47.77/7.21 thf(zip_derived_cl47, plain, 47.77/7.21 ((~ (((((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 ('#sk21' @ Y0 @ Y1))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk21' @ Y1 @ Y2) & 47.77/7.21 ('#sk21' @ Y0 @ Y1))) => 47.77/7.21 ('#sk21' @ Y0 @ Y2)))))))))))))) => 47.77/7.21 ('#sk21' @ '#sk6' @ '#sk8'))) 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl41])). 47.77/7.21 thf(zip_derived_cl62, plain, 47.77/7.21 ((~ ('#sk21' @ '#sk6' @ '#sk8') | ('#form11') | ~ ('#form9'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 47.77/7.21 thf(zip_derived_cl73, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( (((((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((((X2 @ Y1 @ Y2) & (X2 @ 47.77/7.21 Y0 @ Y1))) => 47.77/7.21 (X2 @ Y0 @ Y2)))))))))))))) => 47.77/7.21 (X2 @ '#sk10' @ '#sk12'))) 47.77/7.21 | ('#form9') 47.77/7.21 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ 47.77/7.21 Y2 @ Y3) & 47.77/7.21 (Y0 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ 47.77/7.21 Y3)))))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((('#sk1' @ Y1 @ Y2) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.21 (Y0 @ '#sk10' @ '#sk12')))))))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 47.77/7.21 thf(zip_derived_cl74, plain, 47.77/7.21 (( (((((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 47.77/7.21 Y1))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk30' @ Y1 @ Y2) & 47.77/7.21 ('#sk30' @ Y0 @ Y1))) => 47.77/7.21 ('#sk30' @ Y0 @ Y2)))))))))))))) => 47.77/7.21 ('#sk30' @ '#sk10' @ '#sk12'))) 47.77/7.21 | ('#form9') 47.77/7.21 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y2 @ 47.77/7.21 Y3) & (Y0 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((('#sk1' @ Y1 @ Y2) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.21 (Y0 @ '#sk10' @ '#sk12')))))))), 47.77/7.21 inference('triggered_bool_instantiation', [status(thm)], 47.77/7.21 [zip_derived_cl73])). 47.77/7.21 thf(zip_derived_cl86, plain, 47.77/7.21 ((~ ('#form94') 47.77/7.21 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y2 @ 47.77/7.21 Y3) & (Y0 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((('#sk1' @ Y1 @ Y2) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.21 (Y0 @ '#sk10' @ '#sk12')))))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl285, plain, 47.77/7.21 (( ('#form94') 47.77/7.21 | ('#form9') 47.77/7.21 | (((((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 47.77/7.21 Y1))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk30' @ Y1 @ Y2) & 47.77/7.21 ('#sk30' @ Y0 @ Y1))) => 47.77/7.21 ('#sk30' @ Y0 @ Y2)))))))))))))) => 47.77/7.21 ('#sk30' @ '#sk10' @ '#sk12'))))), 47.77/7.21 inference('renaming', [status(thm)], [zip_derived_cl74, zip_derived_cl86])). 47.77/7.21 thf(zip_derived_cl286, plain, 47.77/7.21 ((~ (((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk30' @ Y1 @ Y2) & 47.77/7.21 ('#sk30' @ Y0 @ Y1))) => 47.77/7.21 ('#sk30' @ Y0 @ Y2)))))))))))))) 47.77/7.21 | ('#sk30' @ '#sk10' @ '#sk12') 47.77/7.21 | ('#form9') 47.77/7.21 | ('#form94'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl285])). 47.77/7.21 thf(zip_derived_cl80, plain, 47.77/7.21 ((~ ('#sk30' @ '#sk10' @ '#sk12') | ('#form9'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 47.77/7.21 thf(zip_derived_cl287, plain, 47.77/7.21 (( ('#form94') 47.77/7.21 | ('#form9') 47.77/7.21 | ~ (((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 47.77/7.21 Y1))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk30' @ Y1 @ Y2) & 47.77/7.21 ('#sk30' @ Y0 @ Y1))) => 47.77/7.21 ('#sk30' @ Y0 @ Y2)))))))))))))))), 47.77/7.21 inference('clc', [status(thm)], [zip_derived_cl286, zip_derived_cl80])). 47.77/7.21 thf(zip_derived_cl288, plain, 47.77/7.21 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk30' @ Y1 @ Y2) & 47.77/7.21 ('#sk30' @ Y0 @ Y1))) => 47.77/7.21 ('#sk30' @ Y0 @ Y2)))))))))))) 47.77/7.21 | ('#form9') 47.77/7.21 | ('#form94'))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl287])). 47.77/7.21 thf(zip_derived_cl289, plain, 47.77/7.21 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.21 ((('#sk2' @ ('#sk269' @ '#sk30') @ Y0) => ('#sk30' @ 47.77/7.21 ('#sk269' @ '#sk30') @ Y0)))))) 47.77/7.21 | ('#form94') 47.77/7.21 | ('#form9') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk30' @ Y1 @ Y2) & 47.77/7.21 ('#sk30' @ Y0 @ Y1))) => 47.77/7.21 ('#sk30' @ Y0 @ Y2)))))))))))))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl288])). 47.77/7.21 thf(zip_derived_cl290, plain, 47.77/7.21 ((~ ((('#sk2' @ ('#sk269' @ '#sk30') @ ('#sk348' @ '#sk30')) => 47.77/7.21 ('#sk30' @ ('#sk269' @ '#sk30') @ ('#sk348' @ '#sk30')))) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk30' @ Y1 @ Y2) & 47.77/7.21 ('#sk30' @ Y0 @ Y1))) => 47.77/7.21 ('#sk30' @ Y0 @ Y2)))))))))))) 47.77/7.21 | ('#form9') 47.77/7.21 | ('#form94'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl289])). 47.77/7.21 thf(zip_derived_cl291, plain, 47.77/7.21 (( ('#sk2' @ ('#sk269' @ '#sk30') @ ('#sk348' @ '#sk30')) 47.77/7.21 | ('#form94') 47.77/7.21 | ('#form9') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk30' @ Y1 @ Y2) & 47.77/7.21 ('#sk30' @ Y0 @ Y1))) => 47.77/7.21 ('#sk30' @ Y0 @ Y2)))))))))))))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl290])). 47.77/7.21 thf(zip_derived_cl293, plain, 47.77/7.21 (( ('#form1026') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk30' @ Y1 @ Y2) & 47.77/7.21 ('#sk30' @ Y0 @ Y1))) => 47.77/7.21 ('#sk30' @ Y0 @ Y2)))))))))))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl294, plain, 47.77/7.21 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk30' @ Y0 @ Y1) & ('#sk30' @ 47.77/7.21 ('#sk130' @ '#sk30') @ Y0))) => 47.77/7.21 ('#sk30' @ ('#sk130' @ '#sk30') @ Y1))))))))) 47.77/7.21 | ('#form1026'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl293])). 47.77/7.21 thf(zip_derived_cl297, plain, 47.77/7.21 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.21 ((((('#sk30' @ ('#sk192' @ '#sk30') @ Y0) & ('#sk30' @ 47.77/7.21 ('#sk130' @ '#sk30') @ ('#sk192' @ '#sk30')))) => 47.77/7.21 ('#sk30' @ ('#sk130' @ '#sk30') @ Y0)))))) 47.77/7.21 | ('#form1026'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl294])). 47.77/7.21 thf(zip_derived_cl298, plain, 47.77/7.21 ((~ ((((('#sk30' @ ('#sk192' @ '#sk30') @ ('#sk260' @ '#sk30')) & 47.77/7.21 ('#sk30' @ ('#sk130' @ '#sk30') @ ('#sk192' @ '#sk30')))) => 47.77/7.21 ('#sk30' @ ('#sk130' @ '#sk30') @ ('#sk260' @ '#sk30')))) 47.77/7.21 | ('#form1026'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl297])). 47.77/7.21 thf(zip_derived_cl299, plain, 47.77/7.21 (( ((('#sk30' @ ('#sk192' @ '#sk30') @ ('#sk260' @ '#sk30')) & 47.77/7.21 ('#sk30' @ ('#sk130' @ '#sk30') @ ('#sk192' @ '#sk30')))) 47.77/7.21 | ('#form1026'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl298])). 47.77/7.21 thf(zip_derived_cl302, plain, 47.77/7.21 (( ('#sk30' @ ('#sk130' @ '#sk30') @ ('#sk192' @ '#sk30')) 47.77/7.21 | ('#form1026'))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl299])). 47.77/7.21 thf(zip_derived_cl176, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( ('#form721' @ X2) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl177, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((!!) @ (^[Y0 : a]: 47.77/7.21 ((('#sk1' @ ('#sk722' @ X2) @ Y0) => (X2 @ 47.77/7.21 ('#sk722' @ X2) @ Y0)))))) 47.77/7.21 | ('#form721' @ X2))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl176])). 47.77/7.21 thf(zip_derived_cl183, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ ((('#sk1' @ ('#sk722' @ X2) @ ('#sk796' @ X2)) => (X2 @ 47.77/7.21 ('#sk722' @ X2) @ ('#sk796' @ X2)))) 47.77/7.21 | ('#form721' @ X2))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl177])). 47.77/7.21 thf(zip_derived_cl191, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( ('#sk1' @ ('#sk722' @ X2) @ ('#sk796' @ X2)) | ('#form721' @ X2))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl183])). 47.77/7.21 thf(zip_derived_cl300, plain, 47.77/7.21 ((~ ('#sk30' @ ('#sk130' @ '#sk30') @ ('#sk260' @ '#sk30')) 47.77/7.21 | ('#form1026'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl298])). 47.77/7.21 thf(zip_derived_cl301, plain, 47.77/7.21 (( ('#sk30' @ ('#sk192' @ '#sk30') @ ('#sk260' @ '#sk30')) 47.77/7.21 | ('#form1026'))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl299])). 47.77/7.21 thf(zip_derived_cl291, plain, 47.77/7.21 (( ('#sk2' @ ('#sk269' @ '#sk30') @ ('#sk348' @ '#sk30')) 47.77/7.21 | ('#form94') 47.77/7.21 | ('#form9') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk30' @ Y1 @ Y2) & 47.77/7.21 ('#sk30' @ Y0 @ Y1))) => 47.77/7.21 ('#sk30' @ Y0 @ Y2)))))))))))))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl290])). 47.77/7.21 thf(zip_derived_cl293, plain, 47.77/7.21 (( ('#form1026') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk30' @ Y1 @ Y2) & 47.77/7.21 ('#sk30' @ Y0 @ Y1))) => 47.77/7.21 ('#sk30' @ Y0 @ Y2)))))))))))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl295, plain, 47.77/7.21 ((~ ('#form1026') 47.77/7.21 | ('#form9') 47.77/7.21 | ('#form94') 47.77/7.21 | ('#sk2' @ ('#sk269' @ '#sk30') @ ('#sk348' @ '#sk30')))), 47.77/7.21 inference('renaming', [status(thm)], 47.77/7.21 [zip_derived_cl291, zip_derived_cl293])). 47.77/7.21 thf(zip_derived_cl292, plain, 47.77/7.21 ((~ ('#sk30' @ ('#sk269' @ '#sk30') @ ('#sk348' @ '#sk30')) 47.77/7.21 | ('#form94') 47.77/7.21 | ('#form9') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk30' @ Y1 @ Y2) & 47.77/7.21 ('#sk30' @ Y0 @ Y1))) => 47.77/7.21 ('#sk30' @ Y0 @ Y2)))))))))))))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl290])). 47.77/7.21 thf(zip_derived_cl293, plain, 47.77/7.21 (( ('#form1026') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk30' @ Y1 @ Y2) & 47.77/7.21 ('#sk30' @ Y0 @ Y1))) => 47.77/7.21 ('#sk30' @ Y0 @ Y2)))))))))))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl296, plain, 47.77/7.21 ((~ ('#form1026') 47.77/7.21 | ('#form9') 47.77/7.21 | ('#form94') 47.77/7.21 | ~ ('#sk30' @ ('#sk269' @ '#sk30') @ ('#sk348' @ '#sk30')))), 47.77/7.21 inference('renaming', [status(thm)], 47.77/7.21 [zip_derived_cl292, zip_derived_cl293])). 47.77/7.21 thf(zip_derived_cl79, plain, 47.77/7.21 (( (((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 47.77/7.21 ('#sk30' @ Y0 @ Y1))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk30' @ Y0 @ Y1) & 47.77/7.21 ('#sk30' @ Y1 @ Y2))) => 47.77/7.21 ('#sk30' @ Y0 @ Y2)))))))))))))) 47.77/7.21 | ('#form9'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 47.77/7.21 thf(zip_derived_cl94, plain, 47.77/7.21 (( (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 47.77/7.21 ('#sk30' @ Y0 @ Y1))))))))) 47.77/7.21 | ('#form9'))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl79])). 47.77/7.21 thf(zip_derived_cl104, plain, 47.77/7.21 (![X2 : a]: 47.77/7.21 ( (((!!) @ (^[Y0 : a]: 47.77/7.21 ((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) => 47.77/7.21 ('#sk30' @ X2 @ Y0)))))) 47.77/7.21 | ('#form9'))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])). 47.77/7.21 thf(zip_derived_cl114, plain, 47.77/7.21 (![X2 : a, X4 : a]: 47.77/7.21 ( ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) => ('#sk30' @ X2 @ X4))) 47.77/7.21 | ('#form9'))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl104])). 47.77/7.21 thf(zip_derived_cl125, plain, 47.77/7.21 (![X2 : a, X4 : a]: 47.77/7.21 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 47.77/7.21 | ('#sk30' @ X2 @ X4) 47.77/7.21 | ('#form9'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl114])). 47.77/7.21 thf(zip_derived_cl138, plain, 47.77/7.21 (![X2 : a, X4 : a]: 47.77/7.21 (~ ('#sk1' @ X2 @ X4) | ('#form9') | ('#sk30' @ X2 @ X4))), 47.77/7.21 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl125])). 47.77/7.21 thf(zip_derived_cl192, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (X2 @ ('#sk722' @ X2) @ ('#sk796' @ X2)) | ('#form721' @ X2))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl183])). 47.77/7.21 thf(zip_derived_cl29, plain, 47.77/7.21 (( (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y2 @ 47.77/7.21 Y3) & (Y0 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.21 ('#sk1' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.21 (Y0 @ '#sk7' @ '#sk8')))))) 47.77/7.21 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.21 ('#sk1' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y1 @ 47.77/7.21 Y2) & (Y0 @ 47.77/7.21 Y2 @ Y3))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.21 (Y0 @ '#sk3' @ '#sk4')))))) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 ('#sk2' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ 47.77/7.21 Y5) & 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))) | 47.77/7.21 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ 47.77/7.21 Y5) & 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 ('#sk1' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.21 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 ( 47.77/7.21 ( 47.77/7.21 (( 47.77/7.21 ('#sk2' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) | 47.77/7.21 ('#sk1' @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 ( 47.77/7.21 ( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) & 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ Y5))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))))))))))))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])). 47.77/7.21 thf(zip_derived_cl34, plain, 47.77/7.21 ((~ ('#form11') 47.77/7.21 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.21 ('#sk1' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y1 @ 47.77/7.21 Y2) & (Y0 @ 47.77/7.21 Y2 @ Y3))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.21 (Y0 @ '#sk3' @ '#sk4')))))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl40, plain, 47.77/7.21 (( ('#form11') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 ('#sk2' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ 47.77/7.21 Y5) & 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))) | 47.77/7.21 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ 47.77/7.21 Y5) & 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 ('#sk1' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.21 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 ( 47.77/7.21 ( 47.77/7.21 (( 47.77/7.21 ('#sk2' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) | 47.77/7.21 ('#sk1' @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 ( 47.77/7.21 ( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) & 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ Y5))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))))))))))) 47.77/7.21 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y2 @ 47.77/7.21 Y3) & (Y0 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.21 ('#sk1' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.21 (Y0 @ '#sk7' @ '#sk8')))))))), 47.77/7.21 inference('renaming', [status(thm)], [zip_derived_cl29, zip_derived_cl34])). 47.77/7.21 thf(zip_derived_cl30, plain, 47.77/7.21 (( ('#form9') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 ('#sk2' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ 47.77/7.21 Y5) & 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))) | 47.77/7.21 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ 47.77/7.21 Y5) & 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 ('#sk1' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.21 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 ( 47.77/7.21 ( 47.77/7.21 (( 47.77/7.21 ('#sk2' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) | 47.77/7.21 ('#sk1' @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 ( 47.77/7.21 ( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) & 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ Y5))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))))))))))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl45, plain, 47.77/7.21 ((~ ('#form9') 47.77/7.21 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y2 @ 47.77/7.21 Y3) & (Y0 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.21 ('#sk1' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.21 (Y0 @ '#sk7' @ '#sk8')))))) 47.77/7.21 | ('#form11'))), 47.77/7.21 inference('renaming', [status(thm)], [zip_derived_cl40, zip_derived_cl30])). 47.77/7.21 thf(zip_derived_cl56, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( (((((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((((X2 @ Y1 @ Y2) & (X2 @ 47.77/7.21 Y0 @ Y1))) => 47.77/7.21 (X2 @ Y0 @ Y2)))))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))))) => 47.77/7.21 (X2 @ '#sk7' @ '#sk8'))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9'))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl45])). 47.77/7.21 thf(zip_derived_cl57, plain, 47.77/7.21 (( (((((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk21' @ Y1 @ Y2) & 47.77/7.21 ('#sk21' @ Y0 @ Y1))) => 47.77/7.21 ('#sk21' @ Y0 @ Y2)))))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 ('#sk21' @ Y0 @ Y1))))))))))) => 47.77/7.21 ('#sk21' @ '#sk7' @ '#sk8'))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9'))), 47.77/7.21 inference('triggered_bool_instantiation', [status(thm)], 47.77/7.21 [zip_derived_cl56])). 47.77/7.21 thf(zip_derived_cl332, plain, 47.77/7.21 ((~ (((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk21' @ Y1 @ Y2) & 47.77/7.21 ('#sk21' @ Y0 @ Y1))) => 47.77/7.21 ('#sk21' @ Y0 @ Y2)))))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 47.77/7.21 ('#sk21' @ Y0 @ Y1))))))))))) 47.77/7.21 | ('#sk21' @ '#sk7' @ '#sk8') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 47.77/7.21 thf(zip_derived_cl333, plain, 47.77/7.21 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk21' @ Y1 @ Y2) & 47.77/7.21 ('#sk21' @ Y0 @ Y1))) => 47.77/7.21 ('#sk21' @ Y0 @ Y2)))))))))))) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 47.77/7.21 ('#sk21' @ Y0 @ Y1))))))))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#sk21' @ '#sk7' @ '#sk8'))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl332])). 47.77/7.21 thf(zip_derived_cl56, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( (((((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((((X2 @ Y1 @ Y2) & (X2 @ 47.77/7.21 Y0 @ Y1))) => 47.77/7.21 (X2 @ Y0 @ Y2)))))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))))) => 47.77/7.21 (X2 @ '#sk7' @ '#sk8'))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9'))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl45])). 47.77/7.21 thf(zip_derived_cl70, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((((X2 @ Y1 @ Y2) & (X2 @ 47.77/7.21 Y0 @ Y1))) => 47.77/7.21 (X2 @ Y0 @ Y2)))))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))))) 47.77/7.21 | (X2 @ '#sk7' @ '#sk8') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl56])). 47.77/7.21 thf(zip_derived_cl83, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((((X2 @ Y1 @ Y2) & (X2 @ 47.77/7.21 Y0 @ Y1))) => 47.77/7.21 (X2 @ Y0 @ Y2)))))))))))) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | (X2 @ '#sk7' @ '#sk8'))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl70])). 47.77/7.21 thf(zip_derived_cl99, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((((X2 @ Y0 @ Y1) & (X2 @ 47.77/7.21 ('#sk130' @ X2) @ Y0))) => 47.77/7.21 (X2 @ ('#sk130' @ X2) @ Y1))))))))) 47.77/7.21 | (X2 @ '#sk7' @ '#sk8') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl83])). 47.77/7.21 thf(zip_derived_cl109, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((((X2 @ ('#sk192' @ X2) @ Y0) & (X2 @ 47.77/7.21 ('#sk130' @ X2) @ ('#sk192' @ X2)))) => 47.77/7.21 (X2 @ ('#sk130' @ X2) @ Y0)))))) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | (X2 @ '#sk7' @ '#sk8'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl99])). 47.77/7.21 thf(zip_derived_cl119, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((((X2 @ ('#sk192' @ X2) @ ('#sk260' @ X2)) & (X2 @ 47.77/7.21 ('#sk130' @ X2) @ ('#sk192' @ X2)))) => 47.77/7.21 (X2 @ ('#sk130' @ X2) @ ('#sk260' @ X2)))) 47.77/7.21 | (X2 @ '#sk7' @ '#sk8') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl109])). 47.77/7.21 thf(zip_derived_cl131, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( ('#form336' @ X2) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl334, plain, 47.77/7.21 ((~ ('#form336' @ '#sk21') 47.77/7.21 | ('#sk21' @ '#sk7' @ '#sk8') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk21' @ Y1 @ Y2) & 47.77/7.21 ('#sk21' @ Y0 @ Y1))) => 47.77/7.21 ('#sk21' @ Y0 @ Y2)))))))))))))), 47.77/7.21 inference('renaming', [status(thm)], 47.77/7.21 [zip_derived_cl333, zip_derived_cl131])). 47.77/7.21 thf(zip_derived_cl335, plain, 47.77/7.21 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk21' @ Y0 @ Y1) & ('#sk21' @ 47.77/7.21 ('#sk130' @ '#sk21') @ Y0))) => 47.77/7.21 ('#sk21' @ ('#sk130' @ '#sk21') @ Y1))))))))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#sk21' @ '#sk7' @ '#sk8') 47.77/7.21 | ~ ('#form336' @ '#sk21'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl334])). 47.77/7.21 thf(zip_derived_cl336, plain, 47.77/7.21 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.21 ((((('#sk21' @ ('#sk192' @ '#sk21') @ Y0) & ('#sk21' @ 47.77/7.21 ('#sk130' @ '#sk21') @ ('#sk192' @ '#sk21')))) => 47.77/7.21 ('#sk21' @ ('#sk130' @ '#sk21') @ Y0)))))) 47.77/7.21 | ~ ('#form336' @ '#sk21') 47.77/7.21 | ('#sk21' @ '#sk7' @ '#sk8') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl335])). 47.77/7.21 thf(zip_derived_cl337, plain, 47.77/7.21 ((~ ((((('#sk21' @ ('#sk192' @ '#sk21') @ ('#sk260' @ '#sk21')) & 47.77/7.21 ('#sk21' @ ('#sk130' @ '#sk21') @ ('#sk192' @ '#sk21')))) => 47.77/7.21 ('#sk21' @ ('#sk130' @ '#sk21') @ ('#sk260' @ '#sk21')))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#sk21' @ '#sk7' @ '#sk8') 47.77/7.21 | ~ ('#form336' @ '#sk21'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl336])). 47.77/7.21 thf(zip_derived_cl184, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( ('#form813' @ X2) 47.77/7.21 | ~ (((((X2 @ ('#sk192' @ X2) @ ('#sk260' @ X2)) & (X2 @ 47.77/7.21 ('#sk130' @ X2) @ ('#sk192' @ X2)))) => 47.77/7.21 (X2 @ ('#sk130' @ X2) @ ('#sk260' @ X2)))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl338, plain, 47.77/7.21 ((~ ('#form813' @ '#sk21') 47.77/7.21 | ~ ('#form336' @ '#sk21') 47.77/7.21 | ('#sk21' @ '#sk7' @ '#sk8') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11'))), 47.77/7.21 inference('renaming', [status(thm)], 47.77/7.21 [zip_derived_cl337, zip_derived_cl184])). 47.77/7.21 thf(zip_derived_cl137, plain, 47.77/7.21 (![X2 : a, X4 : a]: 47.77/7.21 (~ ('#sk2' @ X2 @ X4) | ('#form9') | ('#sk30' @ X2 @ X4))), 47.77/7.21 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl125])). 47.77/7.21 thf(zip_derived_cl184, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( ('#form813' @ X2) 47.77/7.21 | ~ (((((X2 @ ('#sk192' @ X2) @ ('#sk260' @ X2)) & (X2 @ 47.77/7.21 ('#sk130' @ X2) @ ('#sk192' @ X2)))) => 47.77/7.21 (X2 @ ('#sk130' @ X2) @ ('#sk260' @ X2)))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl185, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( (((X2 @ ('#sk192' @ X2) @ ('#sk260' @ X2)) & (X2 @ 47.77/7.21 ('#sk130' @ X2) @ ('#sk192' @ X2)))) 47.77/7.21 | ('#form813' @ X2))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl184])). 47.77/7.21 thf(zip_derived_cl193, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( (X2 @ ('#sk192' @ X2) @ ('#sk260' @ X2)) | ('#form813' @ X2))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl185])). 47.77/7.21 thf(zip_derived_cl28, plain, 47.77/7.21 (( (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y1 @ 47.77/7.21 Y2) & (Y0 @ 47.77/7.21 Y2 @ Y3))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.21 ('#sk1' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.21 (Y0 @ '#sk6' @ '#sk7')))))) 47.77/7.21 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.21 ('#sk1' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y1 @ 47.77/7.21 Y2) & (Y0 @ 47.77/7.21 Y2 @ Y3))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.21 (Y0 @ '#sk3' @ '#sk4')))))) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 ('#sk2' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ 47.77/7.21 Y5) & 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))) | 47.77/7.21 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ 47.77/7.21 Y5) & 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 ('#sk1' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.21 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 ( 47.77/7.21 ( 47.77/7.21 (( 47.77/7.21 ('#sk2' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) | 47.77/7.21 ('#sk1' @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 ( 47.77/7.21 ( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) & 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ Y5))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))))))))))))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])). 47.77/7.21 thf(zip_derived_cl34, plain, 47.77/7.21 ((~ ('#form11') 47.77/7.21 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.21 ('#sk1' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y1 @ 47.77/7.21 Y2) & (Y0 @ 47.77/7.21 Y2 @ Y3))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.21 (Y0 @ '#sk3' @ '#sk4')))))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl39, plain, 47.77/7.21 (( ('#form11') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 ('#sk2' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ 47.77/7.21 Y5) & 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))) | 47.77/7.21 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ 47.77/7.21 Y5) & 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 ('#sk1' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.21 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 ( 47.77/7.21 ( 47.77/7.21 (( 47.77/7.21 ('#sk2' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) | 47.77/7.21 ('#sk1' @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 ( 47.77/7.21 ( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) & 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ Y5))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))))))))))) 47.77/7.21 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y1 @ 47.77/7.21 Y2) & (Y0 @ 47.77/7.21 Y2 @ Y3))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.21 ('#sk1' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.21 (Y0 @ '#sk6' @ '#sk7')))))))), 47.77/7.21 inference('renaming', [status(thm)], [zip_derived_cl28, zip_derived_cl34])). 47.77/7.21 thf(zip_derived_cl30, plain, 47.77/7.21 (( ('#form9') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((((((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 ('#sk2' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ 47.77/7.21 Y5) & 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))) | 47.77/7.21 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ 47.77/7.21 Y5) & 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 (( 47.77/7.21 ('#sk1' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))))) => 47.77/7.21 (((!!) @ (^[Y2 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 ( 47.77/7.21 ( 47.77/7.21 (( 47.77/7.21 ('#sk2' @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) | 47.77/7.21 ('#sk1' @ 47.77/7.21 Y3 @ Y4))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y4))))))))) & 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((!!) @ ( 47.77/7.21 ^[Y4 : a]: 47.77/7.21 ( 47.77/7.21 ( 47.77/7.21 (!!) @ ( 47.77/7.21 ^[Y5 : a]: 47.77/7.21 (( 47.77/7.21 (( 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ 47.77/7.21 Y4) & 47.77/7.21 (Y2 @ 47.77/7.21 Y4 @ Y5))) => 47.77/7.21 (Y2 @ 47.77/7.21 Y3 @ Y5)))))))))))))) => 47.77/7.21 (Y2 @ Y0 @ Y1)))))))))))))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl43, plain, 47.77/7.21 ((~ ('#form9') 47.77/7.21 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y1 @ 47.77/7.21 Y2) & (Y0 @ 47.77/7.21 Y2 @ Y3))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.21 ('#sk1' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.21 (Y0 @ '#sk6' @ '#sk7')))))) 47.77/7.21 | ('#form11'))), 47.77/7.21 inference('renaming', [status(thm)], [zip_derived_cl39, zip_derived_cl30])). 47.77/7.21 thf(zip_derived_cl50, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( (((((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((((X2 @ Y0 @ Y1) & (X2 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (X2 @ Y0 @ Y2)))))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))))) => 47.77/7.21 (X2 @ '#sk6' @ '#sk7'))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9'))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 47.77/7.21 thf(zip_derived_cl51, plain, 47.77/7.21 (( (((((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk21' @ Y0 @ Y1) & 47.77/7.21 ('#sk21' @ Y1 @ Y2))) => 47.77/7.21 ('#sk21' @ Y0 @ Y2)))))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 ('#sk21' @ Y0 @ Y1))))))))))) => 47.77/7.21 ('#sk21' @ '#sk6' @ '#sk7'))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9'))), 47.77/7.21 inference('triggered_bool_instantiation', [status(thm)], 47.77/7.21 [zip_derived_cl50])). 47.77/7.21 thf(zip_derived_cl267, plain, 47.77/7.21 ((~ (((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk21' @ Y0 @ Y1) & 47.77/7.21 ('#sk21' @ Y1 @ Y2))) => 47.77/7.21 ('#sk21' @ Y0 @ Y2)))))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 47.77/7.21 ('#sk21' @ Y0 @ Y1))))))))))) 47.77/7.21 | ('#sk21' @ '#sk6' @ '#sk7') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 47.77/7.21 thf(zip_derived_cl268, plain, 47.77/7.21 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk21' @ Y0 @ Y1) & 47.77/7.21 ('#sk21' @ Y1 @ Y2))) => 47.77/7.21 ('#sk21' @ Y0 @ Y2)))))))))))) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 47.77/7.21 ('#sk21' @ Y0 @ Y1))))))))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#sk21' @ '#sk6' @ '#sk7'))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl267])). 47.77/7.21 thf(zip_derived_cl131, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( ('#form336' @ X2) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl269, plain, 47.77/7.21 ((~ ('#form336' @ '#sk21') 47.77/7.21 | ('#sk21' @ '#sk6' @ '#sk7') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk21' @ Y0 @ Y1) & 47.77/7.21 ('#sk21' @ Y1 @ Y2))) => 47.77/7.21 ('#sk21' @ Y0 @ Y2)))))))))))))), 47.77/7.21 inference('renaming', [status(thm)], 47.77/7.21 [zip_derived_cl268, zip_derived_cl131])). 47.77/7.21 thf(zip_derived_cl270, plain, 47.77/7.21 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk21' @ ('#sk103' @ '#sk21') @ Y0) & 47.77/7.21 ('#sk21' @ Y0 @ Y1))) => 47.77/7.21 ('#sk21' @ ('#sk103' @ '#sk21') @ Y1))))))))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#sk21' @ '#sk6' @ '#sk7') 47.77/7.21 | ~ ('#form336' @ '#sk21'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl269])). 47.77/7.21 thf(zip_derived_cl271, plain, 47.77/7.21 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.21 ((((('#sk21' @ ('#sk103' @ '#sk21') @ 47.77/7.21 ('#sk157' @ '#sk21')) & ('#sk21' @ 47.77/7.21 ('#sk157' @ '#sk21') @ Y0))) => 47.77/7.21 ('#sk21' @ ('#sk103' @ '#sk21') @ Y0)))))) 47.77/7.21 | ~ ('#form336' @ '#sk21') 47.77/7.21 | ('#sk21' @ '#sk6' @ '#sk7') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl270])). 47.77/7.21 thf(zip_derived_cl272, plain, 47.77/7.21 ((~ ((((('#sk21' @ ('#sk103' @ '#sk21') @ ('#sk157' @ '#sk21')) & 47.77/7.21 ('#sk21' @ ('#sk157' @ '#sk21') @ ('#sk221' @ '#sk21')))) => 47.77/7.21 ('#sk21' @ ('#sk103' @ '#sk21') @ ('#sk221' @ '#sk21')))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#sk21' @ '#sk6' @ '#sk7') 47.77/7.21 | ~ ('#form336' @ '#sk21'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl271])). 47.77/7.21 thf(zip_derived_cl273, plain, 47.77/7.21 (( ((('#sk21' @ ('#sk103' @ '#sk21') @ ('#sk157' @ '#sk21')) & 47.77/7.21 ('#sk21' @ ('#sk157' @ '#sk21') @ ('#sk221' @ '#sk21')))) 47.77/7.21 | ~ ('#form336' @ '#sk21') 47.77/7.21 | ('#sk21' @ '#sk6' @ '#sk7') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl272])). 47.77/7.21 thf(zip_derived_cl34, plain, 47.77/7.21 ((~ ('#form11') 47.77/7.21 | (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.21 ('#sk1' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y1 @ 47.77/7.21 Y2) & (Y0 @ 47.77/7.21 Y2 @ Y3))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))))) => 47.77/7.21 (Y0 @ '#sk3' @ '#sk4')))))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl35, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( (((((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((((X2 @ Y0 @ Y1) & (X2 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (X2 @ Y0 @ Y2)))))))))))))) => 47.77/7.21 (X2 @ '#sk3' @ '#sk4'))) 47.77/7.21 | ~ ('#form11'))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 47.77/7.21 thf(zip_derived_cl44, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((((X2 @ Y0 @ Y1) & (X2 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (X2 @ Y0 @ Y2)))))))))))))) 47.77/7.21 | (X2 @ '#sk3' @ '#sk4') 47.77/7.21 | ~ ('#form11'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 47.77/7.21 thf(zip_derived_cl55, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((((X2 @ Y0 @ Y1) & (X2 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (X2 @ Y0 @ Y2)))))))))))) 47.77/7.21 | ~ ('#form11') 47.77/7.21 | (X2 @ '#sk3' @ '#sk4'))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl44])). 47.77/7.21 thf(zip_derived_cl69, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((!!) @ (^[Y0 : a]: 47.77/7.21 ((((('#sk2' @ ('#sk47' @ X2) @ Y0) | ('#sk1' @ 47.77/7.21 ('#sk47' @ X2) @ Y0))) => 47.77/7.21 (X2 @ ('#sk47' @ X2) @ Y0)))))) 47.77/7.21 | (X2 @ '#sk3' @ '#sk4') 47.77/7.21 | ~ ('#form11') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((((X2 @ Y0 @ Y1) & (X2 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (X2 @ Y0 @ Y2)))))))))))))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl55])). 47.77/7.21 thf(zip_derived_cl82, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ ((((('#sk2' @ ('#sk47' @ X2) @ ('#sk77' @ X2)) | ('#sk1' @ 47.77/7.21 ('#sk47' @ X2) @ ('#sk77' @ X2)))) => 47.77/7.21 (X2 @ ('#sk47' @ X2) @ ('#sk77' @ X2)))) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((((X2 @ Y0 @ Y1) & (X2 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (X2 @ Y0 @ Y2)))))))))))) 47.77/7.21 | ~ ('#form11') 47.77/7.21 | (X2 @ '#sk3' @ '#sk4'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl69])). 47.77/7.21 thf(zip_derived_cl98, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (X2 @ ('#sk47' @ X2) @ ('#sk77' @ X2)) 47.77/7.21 | (X2 @ '#sk3' @ '#sk4') 47.77/7.21 | ~ ('#form11') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((((X2 @ Y0 @ Y1) & (X2 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (X2 @ Y0 @ Y2)))))))))))))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 47.77/7.21 thf(zip_derived_cl108, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((((X2 @ ('#sk103' @ X2) @ Y0) & (X2 @ 47.77/7.21 Y0 @ Y1))) => 47.77/7.21 (X2 @ ('#sk103' @ X2) @ Y1))))))))) 47.77/7.21 | ~ ('#form11') 47.77/7.21 | (X2 @ '#sk3' @ '#sk4') 47.77/7.21 | ~ (X2 @ ('#sk47' @ X2) @ ('#sk77' @ X2)))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl98])). 47.77/7.21 thf(zip_derived_cl118, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((((X2 @ ('#sk103' @ X2) @ ('#sk157' @ X2)) & (X2 @ 47.77/7.21 ('#sk157' @ X2) @ Y0))) => 47.77/7.21 (X2 @ ('#sk103' @ X2) @ Y0)))))) 47.77/7.21 | ~ (X2 @ ('#sk47' @ X2) @ ('#sk77' @ X2)) 47.77/7.21 | (X2 @ '#sk3' @ '#sk4') 47.77/7.21 | ~ ('#form11'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl108])). 47.77/7.21 thf(zip_derived_cl130, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((((X2 @ ('#sk103' @ X2) @ ('#sk157' @ X2)) & (X2 @ 47.77/7.21 ('#sk157' @ X2) @ ('#sk221' @ X2)))) => 47.77/7.21 (X2 @ ('#sk103' @ X2) @ ('#sk221' @ X2)))) 47.77/7.21 | ~ ('#form11') 47.77/7.21 | (X2 @ '#sk3' @ '#sk4') 47.77/7.21 | ~ (X2 @ ('#sk47' @ X2) @ ('#sk77' @ X2)))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl118])). 47.77/7.21 thf(zip_derived_cl143, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( (((X2 @ ('#sk103' @ X2) @ ('#sk157' @ X2)) & (X2 @ 47.77/7.21 ('#sk157' @ X2) @ ('#sk221' @ X2)))) 47.77/7.21 | ~ (X2 @ ('#sk47' @ X2) @ ('#sk77' @ X2)) 47.77/7.21 | (X2 @ '#sk3' @ '#sk4') 47.77/7.21 | ~ ('#form11'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl130])). 47.77/7.21 thf(zip_derived_cl158, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ ('#form522' @ X2) 47.77/7.21 | (((X2 @ ('#sk103' @ X2) @ ('#sk157' @ X2)) & (X2 @ 47.77/7.21 ('#sk157' @ X2) @ ('#sk221' @ X2)))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl275, plain, 47.77/7.21 (( ('#form522' @ '#sk21') 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#sk21' @ '#sk6' @ '#sk7') 47.77/7.21 | ~ ('#form336' @ '#sk21'))), 47.77/7.21 inference('renaming', [status(thm)], 47.77/7.21 [zip_derived_cl273, zip_derived_cl158])). 47.77/7.21 thf(zip_derived_cl95, plain, 47.77/7.21 (( (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk30' @ Y0 @ Y1) & 47.77/7.21 ('#sk30' @ Y1 @ Y2))) => 47.77/7.21 ('#sk30' @ Y0 @ Y2)))))))))))) 47.77/7.21 | ('#form9'))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl79])). 47.77/7.21 thf(zip_derived_cl105, plain, 47.77/7.21 (![X2 : a]: 47.77/7.21 ( (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk30' @ X2 @ Y0) & ('#sk30' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 ('#sk30' @ X2 @ Y1))))))))) 47.77/7.21 | ('#form9'))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl95])). 47.77/7.21 thf(zip_derived_cl115, plain, 47.77/7.21 (![X2 : a, X4 : a]: 47.77/7.21 ( (((!!) @ (^[Y0 : a]: 47.77/7.21 ((((('#sk30' @ X2 @ X4) & ('#sk30' @ X4 @ Y0))) => 47.77/7.21 ('#sk30' @ X2 @ Y0)))))) 47.77/7.21 | ('#form9'))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl105])). 47.77/7.21 thf(zip_derived_cl126, plain, 47.77/7.21 (![X2 : a, X4 : a, X6 : a]: 47.77/7.21 ( ((((('#sk30' @ X2 @ X4) & ('#sk30' @ X4 @ X6))) => ('#sk30' @ X2 @ 47.77/7.21 X6))) 47.77/7.21 | ('#form9'))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl115])). 47.77/7.21 thf(zip_derived_cl139, plain, 47.77/7.21 (![X2 : a, X4 : a, X6 : a]: 47.77/7.21 (~ ((('#sk30' @ X2 @ X4) & ('#sk30' @ X4 @ X6))) 47.77/7.21 | ('#sk30' @ X2 @ X6) 47.77/7.21 | ('#form9'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl126])). 47.77/7.21 thf(zip_derived_cl151, plain, 47.77/7.21 (![X2 : a, X4 : a, X6 : a]: 47.77/7.21 (~ ('#sk30' @ X2 @ X4) 47.77/7.21 | ~ ('#sk30' @ X4 @ X6) 47.77/7.21 | ('#form9') 47.77/7.21 | ('#sk30' @ X2 @ X6))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl139])). 47.77/7.21 thf(zip_derived_cl186, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (X2 @ ('#sk130' @ X2) @ ('#sk260' @ X2)) | ('#form813' @ X2))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl184])). 47.77/7.21 thf(zip_derived_cl194, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( (X2 @ ('#sk130' @ X2) @ ('#sk192' @ X2)) | ('#form813' @ X2))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl185])). 47.77/7.21 thf(zip_derived_cl50, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( (((((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((((X2 @ Y0 @ Y1) & (X2 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (X2 @ Y0 @ Y2)))))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))))) => 47.77/7.21 (X2 @ '#sk6' @ '#sk7'))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9'))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 47.77/7.21 thf(zip_derived_cl68, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((((X2 @ Y0 @ Y1) & (X2 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (X2 @ Y0 @ Y2)))))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))))) 47.77/7.21 | (X2 @ '#sk6' @ '#sk7') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])). 47.77/7.21 thf(zip_derived_cl81, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((((X2 @ Y0 @ Y1) & (X2 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (X2 @ Y0 @ Y2)))))))))))) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | (X2 @ '#sk6' @ '#sk7'))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl68])). 47.77/7.21 thf(zip_derived_cl96, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((((X2 @ ('#sk103' @ X2) @ Y0) & (X2 @ 47.77/7.21 Y0 @ Y1))) => 47.77/7.21 (X2 @ ('#sk103' @ X2) @ Y1))))))))) 47.77/7.21 | (X2 @ '#sk6' @ '#sk7') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl81])). 47.77/7.21 thf(zip_derived_cl106, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((((X2 @ ('#sk103' @ X2) @ ('#sk157' @ X2)) & (X2 @ 47.77/7.21 ('#sk157' @ X2) @ Y0))) => 47.77/7.21 (X2 @ ('#sk103' @ X2) @ Y0)))))) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | (X2 @ '#sk6' @ '#sk7'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 47.77/7.21 thf(zip_derived_cl116, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((((X2 @ ('#sk103' @ X2) @ ('#sk157' @ X2)) & (X2 @ 47.77/7.21 ('#sk157' @ X2) @ ('#sk221' @ X2)))) => 47.77/7.21 (X2 @ ('#sk103' @ X2) @ ('#sk221' @ X2)))) 47.77/7.21 | (X2 @ '#sk6' @ '#sk7') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl106])). 47.77/7.21 thf(zip_derived_cl128, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (X2 @ ('#sk103' @ X2) @ ('#sk221' @ X2)) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | (X2 @ '#sk6' @ '#sk7'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl116])). 47.77/7.21 thf(zip_derived_cl131, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( ('#form336' @ X2) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl141, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ ('#form336' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 47.77/7.21 | (X2 @ '#sk6' @ '#sk7') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11') 47.77/7.21 | ~ (X2 @ ('#sk103' @ X2) @ ('#sk221' @ X2)))), 47.77/7.21 inference('renaming', [status(thm)], 47.77/7.21 [zip_derived_cl128, zip_derived_cl131])). 47.77/7.21 thf(zip_derived_cl155, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ ('#form336' @ X2) 47.77/7.21 | (X2 @ '#sk6' @ '#sk7') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11') 47.77/7.21 | ~ (X2 @ ('#sk103' @ X2) @ ('#sk221' @ X2)))), 47.77/7.21 inference('ho_norm', [status(thm)], [zip_derived_cl141])). 47.77/7.21 thf(zip_derived_cl61, plain, 47.77/7.21 (( (((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 47.77/7.21 ('#sk21' @ Y0 @ Y1))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk21' @ Y1 @ Y2) & 47.77/7.21 ('#sk21' @ Y0 @ Y1))) => 47.77/7.21 ('#sk21' @ Y0 @ Y2)))))))))))))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 47.77/7.21 thf(zip_derived_cl71, plain, 47.77/7.21 (( (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 47.77/7.21 ('#sk21' @ Y0 @ Y1))))))))) 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11'))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl61])). 47.77/7.21 thf(zip_derived_cl84, plain, 47.77/7.21 (![X2 : a]: 47.77/7.21 ( (((!!) @ (^[Y0 : a]: 47.77/7.21 ((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) => 47.77/7.21 ('#sk21' @ X2 @ Y0)))))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9'))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl71])). 47.77/7.21 thf(zip_derived_cl100, plain, 47.77/7.21 (![X2 : a, X4 : a]: 47.77/7.21 ( ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) => ('#sk21' @ X2 @ X4))) 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11'))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl84])). 47.77/7.21 thf(zip_derived_cl110, plain, 47.77/7.21 (![X2 : a, X4 : a]: 47.77/7.21 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 47.77/7.21 | ('#sk21' @ X2 @ X4) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 47.77/7.21 thf(zip_derived_cl120, plain, 47.77/7.21 (![X2 : a, X4 : a]: 47.77/7.21 (~ ('#sk1' @ X2 @ X4) 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11') 47.77/7.21 | ('#sk21' @ X2 @ X4))), 47.77/7.21 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl110])). 47.77/7.21 thf(zip_derived_cl121, plain, 47.77/7.21 (![X2 : a, X4 : a]: 47.77/7.21 (~ ('#sk2' @ X2 @ X4) 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11') 47.77/7.21 | ('#sk21' @ X2 @ X4))), 47.77/7.21 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl110])). 47.77/7.21 thf(zip_derived_cl72, plain, 47.77/7.21 (( (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk21' @ Y1 @ Y2) & 47.77/7.21 ('#sk21' @ Y0 @ Y1))) => 47.77/7.21 ('#sk21' @ Y0 @ Y2)))))))))))) 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11'))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl61])). 47.77/7.21 thf(zip_derived_cl85, plain, 47.77/7.21 (![X2 : a]: 47.77/7.21 ( (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk21' @ Y0 @ Y1) & ('#sk21' @ X2 @ 47.77/7.21 Y0))) => 47.77/7.21 ('#sk21' @ X2 @ Y1))))))))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9'))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl72])). 47.77/7.21 thf(zip_derived_cl101, plain, 47.77/7.21 (![X2 : a, X4 : a]: 47.77/7.21 ( (((!!) @ (^[Y0 : a]: 47.77/7.21 ((((('#sk21' @ X4 @ Y0) & ('#sk21' @ X2 @ X4))) => 47.77/7.21 ('#sk21' @ X2 @ Y0)))))) 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11'))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 47.77/7.21 thf(zip_derived_cl111, plain, 47.77/7.21 (![X2 : a, X4 : a, X6 : a]: 47.77/7.21 ( ((((('#sk21' @ X4 @ X6) & ('#sk21' @ X2 @ X4))) => ('#sk21' @ X2 @ 47.77/7.21 X6))) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9'))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl101])). 47.77/7.21 thf(zip_derived_cl122, plain, 47.77/7.21 (![X2 : a, X4 : a, X6 : a]: 47.77/7.21 (~ ((('#sk21' @ X4 @ X6) & ('#sk21' @ X2 @ X4))) 47.77/7.21 | ('#sk21' @ X2 @ X6) 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#form11'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl111])). 47.77/7.21 thf(zip_derived_cl134, plain, 47.77/7.21 (![X2 : a, X4 : a, X6 : a]: 47.77/7.21 (~ ('#sk21' @ X4 @ X6) 47.77/7.21 | ~ ('#sk21' @ X2 @ X4) 47.77/7.21 | ('#form11') 47.77/7.21 | ~ ('#form9') 47.77/7.21 | ('#sk21' @ X2 @ X6))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl122])). 47.77/7.21 thf(zip_derived_cl35, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( (((((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((((X2 @ Y0 @ Y1) & (X2 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (X2 @ Y0 @ Y2)))))))))))))) => 47.77/7.21 (X2 @ '#sk3' @ '#sk4'))) 47.77/7.21 | ~ ('#form11'))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 47.77/7.21 thf(zip_derived_cl36, plain, 47.77/7.21 (( (((((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 ('#sk5' @ Y0 @ Y1))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk5' @ Y0 @ Y1) & 47.77/7.21 ('#sk5' @ Y1 @ Y2))) => 47.77/7.21 ('#sk5' @ Y0 @ Y2)))))))))))))) => 47.77/7.21 ('#sk5' @ '#sk3' @ '#sk4'))) 47.77/7.21 | ~ ('#form11'))), 47.77/7.21 inference('triggered_bool_instantiation', [status(thm)], 47.77/7.21 [zip_derived_cl35])). 47.77/7.21 thf(zip_derived_cl5, plain, 47.77/7.21 (~ (((!!) @ (^[Y0 : a > a > $o]: 47.77/7.21 (((((((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 (((!!) @ (^[Y3 : a]: 47.77/7.21 (((((Y0 @ Y2 @ 47.77/7.21 Y3) & (Y0 @ 47.77/7.21 Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y3)))))))))))) & 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk2' @ Y1 @ Y2) | 47.77/7.21 ('#sk1' @ Y1 @ Y2))) => 47.77/7.21 (Y0 @ Y1 @ Y2))))))))))) => 47.77/7.21 (Y0 @ '#sk3' @ '#sk4'))))))), 47.77/7.21 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 47.77/7.21 thf(zip_derived_cl7, plain, 47.77/7.21 (~ (((((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk5' @ Y1 @ Y2) & 47.77/7.21 ('#sk5' @ Y0 @ Y1))) => 47.77/7.21 ('#sk5' @ Y0 @ Y2)))))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 ('#sk5' @ Y0 @ Y1))))))))))) => 47.77/7.21 ('#sk5' @ '#sk3' @ '#sk4')))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl5])). 47.77/7.21 thf(zip_derived_cl10, plain, (~ ('#sk5' @ '#sk3' @ '#sk4')), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 47.77/7.21 thf(zip_derived_cl229, plain, 47.77/7.21 (( (((((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 ('#sk5' @ Y0 @ Y1))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk5' @ Y0 @ Y1) & 47.77/7.21 ('#sk5' @ Y1 @ Y2))) => 47.77/7.21 ('#sk5' @ Y0 @ Y2)))))))))))))) => 47.77/7.21 ($false))) 47.77/7.21 | ~ ('#form11'))), 47.77/7.21 inference('demod', [status(thm)], [zip_derived_cl36, zip_derived_cl10])). 47.77/7.21 thf(zip_derived_cl230, plain, 47.77/7.21 (( (((~) @ (((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 47.77/7.21 Y0 @ Y1))) => 47.77/7.21 ('#sk5' @ Y0 @ Y1))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk5' @ Y0 @ Y1) & 47.77/7.21 ('#sk5' @ Y1 @ Y2))) => 47.77/7.21 ('#sk5' @ Y0 @ Y2)))))))))))))))) 47.77/7.21 | ~ ('#form11'))), 47.77/7.21 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl229])). 47.77/7.21 thf(zip_derived_cl231, plain, 47.77/7.21 ((~ (((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 47.77/7.21 ('#sk5' @ Y0 @ Y1))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk5' @ Y0 @ Y1) & 47.77/7.21 ('#sk5' @ Y1 @ Y2))) => 47.77/7.21 ('#sk5' @ Y0 @ Y2)))))))))))))) 47.77/7.21 | ~ ('#form11'))), 47.77/7.21 inference('simplify nested equalities', [status(thm)], 47.77/7.21 [zip_derived_cl230])). 47.77/7.21 thf(zip_derived_cl232, plain, 47.77/7.21 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 47.77/7.21 ('#sk5' @ Y0 @ Y1))))))))) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk5' @ Y0 @ Y1) & 47.77/7.21 ('#sk5' @ Y1 @ Y2))) => 47.77/7.21 ('#sk5' @ Y0 @ Y2)))))))))))) 47.77/7.21 | ~ ('#form11'))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl231])). 47.77/7.21 thf(zip_derived_cl131, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( ('#form336' @ X2) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl233, plain, 47.77/7.21 ((~ ('#form336' @ '#sk5') 47.77/7.21 | ~ ('#form11') 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk5' @ Y0 @ Y1) & 47.77/7.21 ('#sk5' @ Y1 @ Y2))) => 47.77/7.21 ('#sk5' @ Y0 @ Y2)))))))))))))), 47.77/7.21 inference('renaming', [status(thm)], 47.77/7.21 [zip_derived_cl232, zip_derived_cl131])). 47.77/7.21 thf(zip_derived_cl234, plain, 47.77/7.21 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk5' @ ('#sk103' @ '#sk5') @ Y0) & 47.77/7.21 ('#sk5' @ Y0 @ Y1))) => 47.77/7.21 ('#sk5' @ ('#sk103' @ '#sk5') @ Y1))))))))) 47.77/7.21 | ~ ('#form11') 47.77/7.21 | ~ ('#form336' @ '#sk5'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl233])). 47.77/7.21 thf(zip_derived_cl235, plain, 47.77/7.21 ((~ (((!!) @ (^[Y0 : a]: 47.77/7.21 ((((('#sk5' @ ('#sk103' @ '#sk5') @ 47.77/7.21 ('#sk157' @ '#sk5')) & ('#sk5' @ 47.77/7.21 ('#sk157' @ '#sk5') @ Y0))) => 47.77/7.21 ('#sk5' @ ('#sk103' @ '#sk5') @ Y0)))))) 47.77/7.21 | ~ ('#form336' @ '#sk5') 47.77/7.21 | ~ ('#form11'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl234])). 47.77/7.21 thf(zip_derived_cl236, plain, 47.77/7.21 ((~ ((((('#sk5' @ ('#sk103' @ '#sk5') @ ('#sk157' @ '#sk5')) & ('#sk5' @ 47.77/7.21 ('#sk157' @ '#sk5') @ ('#sk221' @ '#sk5')))) => 47.77/7.21 ('#sk5' @ ('#sk103' @ '#sk5') @ ('#sk221' @ '#sk5')))) 47.77/7.21 | ~ ('#form11') 47.77/7.21 | ~ ('#form336' @ '#sk5'))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl235])). 47.77/7.21 thf(zip_derived_cl237, plain, 47.77/7.21 (( ((('#sk5' @ ('#sk103' @ '#sk5') @ ('#sk157' @ '#sk5')) & ('#sk5' @ 47.77/7.21 ('#sk157' @ '#sk5') @ ('#sk221' @ '#sk5')))) 47.77/7.21 | ~ ('#form336' @ '#sk5') 47.77/7.21 | ~ ('#form11'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl236])). 47.77/7.21 thf(zip_derived_cl158, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ ('#form522' @ X2) 47.77/7.21 | (((X2 @ ('#sk103' @ X2) @ ('#sk157' @ X2)) & (X2 @ 47.77/7.21 ('#sk157' @ X2) @ ('#sk221' @ X2)))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl239, plain, 47.77/7.21 (( ('#form522' @ '#sk5') | ~ ('#form11') | ~ ('#form336' @ '#sk5'))), 47.77/7.21 inference('renaming', [status(thm)], 47.77/7.21 [zip_derived_cl237, zip_derived_cl158])). 47.77/7.21 thf(zip_derived_cl238, plain, 47.77/7.21 ((~ ('#sk5' @ ('#sk103' @ '#sk5') @ ('#sk221' @ '#sk5')) 47.77/7.21 | ~ ('#form336' @ '#sk5') 47.77/7.21 | ~ ('#form11'))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl236])). 47.77/7.21 thf(zip_derived_cl131, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( ('#form336' @ X2) 47.77/7.21 | ~ (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 47.77/7.21 Y1))) => 47.77/7.21 (X2 @ Y0 @ Y1))))))))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl132, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (((!!) @ (^[Y0 : a]: 47.77/7.21 ((((('#sk2' @ ('#sk47' @ X2) @ Y0) | ('#sk1' @ 47.77/7.21 ('#sk47' @ X2) @ Y0))) => 47.77/7.21 (X2 @ ('#sk47' @ X2) @ Y0)))))) 47.77/7.21 | ('#form336' @ X2))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl131])). 47.77/7.21 thf(zip_derived_cl147, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ ((((('#sk2' @ ('#sk47' @ X2) @ ('#sk77' @ X2)) | ('#sk1' @ 47.77/7.21 ('#sk47' @ X2) @ ('#sk77' @ X2)))) => 47.77/7.21 (X2 @ ('#sk47' @ X2) @ ('#sk77' @ X2)))) 47.77/7.21 | ('#form336' @ X2))), 47.77/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl132])). 47.77/7.21 thf(zip_derived_cl164, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( ((('#sk2' @ ('#sk47' @ X2) @ ('#sk77' @ X2)) | ('#sk1' @ 47.77/7.21 ('#sk47' @ X2) @ ('#sk77' @ X2)))) 47.77/7.21 | ('#form336' @ X2))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl147])). 47.77/7.21 thf(zip_derived_cl171, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( ('#sk2' @ ('#sk47' @ X2) @ ('#sk77' @ X2)) 47.77/7.21 | ('#sk1' @ ('#sk47' @ X2) @ ('#sk77' @ X2)) 47.77/7.21 | ('#form336' @ X2))), 47.77/7.21 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl164])). 47.77/7.21 thf(zip_derived_cl165, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ (X2 @ ('#sk47' @ X2) @ ('#sk77' @ X2)) | ('#form336' @ X2))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl147])). 47.77/7.21 thf(zip_derived_cl9, plain, 47.77/7.21 ( (((((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk5' @ Y1 @ Y2) & 47.77/7.21 ('#sk5' @ Y0 @ Y1))) => 47.77/7.21 ('#sk5' @ Y0 @ Y2)))))))))))) & 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 47.77/7.21 ('#sk5' @ Y0 @ Y1)))))))))))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 47.77/7.21 thf(zip_derived_cl13, plain, 47.77/7.21 ( (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 47.77/7.21 ('#sk5' @ Y0 @ Y1)))))))))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl9])). 47.77/7.21 thf(zip_derived_cl16, plain, 47.77/7.21 (![X2 : a]: 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 ((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) => 47.77/7.21 ('#sk5' @ X2 @ Y0))))))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 47.77/7.21 thf(zip_derived_cl19, plain, 47.77/7.21 (![X2 : a, X4 : a]: 47.77/7.21 ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) => ('#sk5' @ X2 @ X4)))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 47.77/7.21 thf(zip_derived_cl22, plain, 47.77/7.21 (![X2 : a, X4 : a]: 47.77/7.21 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) | ('#sk5' @ X2 @ X4))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 47.77/7.21 thf(zip_derived_cl27, plain, 47.77/7.21 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 47.77/7.21 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl22])). 47.77/7.21 thf(zip_derived_cl26, plain, 47.77/7.21 (![X2 : a, X4 : a]: (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 47.77/7.21 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl22])). 47.77/7.21 thf(zip_derived_cl158, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 (~ ('#form522' @ X2) 47.77/7.21 | (((X2 @ ('#sk103' @ X2) @ ('#sk157' @ X2)) & (X2 @ 47.77/7.21 ('#sk157' @ X2) @ ('#sk221' @ X2)))))), 47.77/7.21 define([status(thm)])). 47.77/7.21 thf(zip_derived_cl160, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( (X2 @ ('#sk157' @ X2) @ ('#sk221' @ X2)) | ~ ('#form522' @ X2))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl158])). 47.77/7.21 thf(zip_derived_cl159, plain, 47.77/7.21 (![X2 : a > a > $o]: 47.77/7.21 ( (X2 @ ('#sk103' @ X2) @ ('#sk157' @ X2)) | ~ ('#form522' @ X2))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl158])). 47.77/7.21 thf(zip_derived_cl12, plain, 47.77/7.21 ( (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 (((!!) @ (^[Y2 : a]: 47.77/7.21 ((((('#sk5' @ Y1 @ Y2) & ('#sk5' @ 47.77/7.21 Y0 @ Y1))) => 47.77/7.21 ('#sk5' @ Y0 @ Y2))))))))))))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl9])). 47.77/7.21 thf(zip_derived_cl15, plain, 47.77/7.21 (![X2 : a]: 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 (((!!) @ (^[Y1 : a]: 47.77/7.21 ((((('#sk5' @ Y0 @ Y1) & ('#sk5' @ X2 @ Y0))) => 47.77/7.21 ('#sk5' @ X2 @ Y1)))))))))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])). 47.77/7.21 thf(zip_derived_cl18, plain, 47.77/7.21 (![X2 : a, X4 : a]: 47.77/7.21 (((!!) @ (^[Y0 : a]: 47.77/7.21 ((((('#sk5' @ X4 @ Y0) & ('#sk5' @ X2 @ X4))) => 47.77/7.21 ('#sk5' @ X2 @ Y0))))))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 47.77/7.21 thf(zip_derived_cl21, plain, 47.77/7.21 (![X2 : a, X4 : a, X6 : a]: 47.77/7.21 ((((('#sk5' @ X4 @ X6) & ('#sk5' @ X2 @ X4))) => ('#sk5' @ X2 @ X6)))), 47.77/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])). 47.77/7.21 thf(zip_derived_cl25, plain, 47.77/7.21 (![X2 : a, X4 : a, X6 : a]: 47.77/7.21 (~ ((('#sk5' @ X4 @ X6) & ('#sk5' @ X2 @ X4))) | ('#sk5' @ X2 @ X6))), 47.77/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 47.77/7.21 thf(zip_derived_cl33, plain, 47.77/7.21 (![X2 : a, X4 : a, X6 : a]: 47.77/7.21 (~ ('#sk5' @ X4 @ X6) | ~ ('#sk5' @ X2 @ X4) | ('#sk5' @ X2 @ X6))), 47.77/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl25])). 47.77/7.21 thf(zip_derived_cl5906, plain, ($false), 47.77/7.21 inference('eprover', [status(thm)], 47.77/7.21 [zip_derived_cl80, zip_derived_cl201, zip_derived_cl189, 47.77/7.21 zip_derived_cl62, zip_derived_cl302, zip_derived_cl191, 47.77/7.21 zip_derived_cl300, zip_derived_cl301, zip_derived_cl295, 47.77/7.21 zip_derived_cl296, zip_derived_cl138, zip_derived_cl192, 47.77/7.21 zip_derived_cl338, zip_derived_cl137, zip_derived_cl193, 47.77/7.21 zip_derived_cl275, zip_derived_cl151, zip_derived_cl186, 47.77/7.21 zip_derived_cl194, zip_derived_cl155, zip_derived_cl120, 47.77/7.21 zip_derived_cl121, zip_derived_cl134, zip_derived_cl239, 47.77/7.21 zip_derived_cl238, zip_derived_cl171, zip_derived_cl165, 47.77/7.21 zip_derived_cl27, zip_derived_cl26, zip_derived_cl160, 47.77/7.21 zip_derived_cl159, zip_derived_cl33])). 47.77/7.21 47.77/7.21 % SZS output end Refutation 47.77/7.21 47.77/7.21 47.77/7.21 % Terminating... 47.77/7.31 % Runner terminated. 47.77/7.32 % Zipperpin 1.5 exiting 47.77/7.32 EOF