0.03/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.jRb3vwg6Kw true 0.11/0.33 % Computer : n020.cluster.edu 0.11/0.33 % Model : x86_64 x86_64 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.33 % Memory : 8042.1875MB 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.33 % CPULimit : 1920 0.11/0.33 % WCLimit : 240 0.11/0.33 % DateTime : Wed Jul 30 02:37:04 EDT 2025 0.11/0.33 % CPUTime : 0.11/0.33 % Running portfolio for 1920 s 0.11/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.11/0.34 % Number of cores: 8 0.11/0.34 % Python version: Python 3.6.8 0.11/0.34 % Running in HO mode 0.47/0.62 % Total configuration time : 828 0.47/0.62 % Estimated wc time : 1656 0.47/0.62 % Estimated cpu time (8 cpus) : 207.0 0.48/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.48/0.69 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.48/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.48/0.70 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.48/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.48/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.48/0.70 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.48/0.70 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 50.80/7.00 % Solved by lams/20_acsne_simpl.sh. 50.80/7.00 % done 598 iterations in 6.165s 50.80/7.00 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 50.80/7.00 % SZS output start Refutation 50.80/7.00 thf(a_type, type, a: $tType). 50.80/7.00 thf('#sk4_type', type, '#sk4': a). 50.80/7.00 thf('#sk266_type', type, '#sk266': (a > a > $o) > a). 50.80/7.00 thf('#sk30_type', type, '#sk30': a > a > $o). 50.80/7.00 thf('#sk318_type', type, '#sk318': (a > a > $o) > a). 50.80/7.00 thf('#sk3_type', type, '#sk3': a). 50.80/7.00 thf('#sk366_type', type, '#sk366': (a > a > $o) > a). 50.80/7.00 thf('#sk12_type', type, '#sk12': a). 50.80/7.00 thf('#sk21_type', type, '#sk21': a > a > $o). 50.80/7.00 thf('#sk355_type', type, '#sk355': (a > a > $o) > a). 50.80/7.00 thf('#sk100_type', type, '#sk100': (a > a > $o) > a). 50.80/7.00 thf('#sk151_type', type, '#sk151': (a > a > $o) > a). 50.80/7.00 thf('#form213_type', type, '#form213': (a > a > $o) > $o). 50.80/7.00 thf('#sk47_type', type, '#sk47': (a > a > $o) > a). 50.80/7.00 thf('#sk456_type', type, '#sk456': (a > a > $o) > a). 50.80/7.00 thf('#sk599_type', type, '#sk599': (a > a > $o) > a). 50.80/7.00 thf('#sk6_type', type, '#sk6': a). 50.80/7.00 thf('#sk2_type', type, '#sk2': a > a > $o). 50.80/7.00 thf('#form230_type', type, '#form230': (a > a > $o) > $o). 50.80/7.00 thf('#sk8_type', type, '#sk8': a). 50.80/7.00 thf('#sk10_type', type, '#sk10': a). 50.80/7.00 thf('#sk7_type', type, '#sk7': a). 50.80/7.00 thf('#form91_type', type, '#form91': $o). 50.80/7.00 thf('#sk74_type', type, '#sk74': (a > a > $o) > a). 50.80/7.00 thf('#sk469_type', type, '#sk469': (a > a > $o) > a). 50.80/7.00 thf('#form9_type', type, '#form9': $o). 50.80/7.00 thf('#form11_type', type, '#form11': $o). 50.80/7.00 thf('#sk5_type', type, '#sk5': a > a > $o). 50.80/7.00 thf('#sk1_type', type, '#sk1': a > a > $o). 50.80/7.00 thf('#sk113_type', type, '#sk113': (a > a > $o) > a). 50.80/7.00 thf('#form598_type', type, '#form598': (a > a > $o) > $o). 50.80/7.00 thf('#sk637_type', type, '#sk637': (a > a > $o) > a). 50.80/7.00 thf('#sk231_type', type, '#sk231': (a > a > $o) > a). 50.80/7.00 thf(cTHM250G_pme, conjecture, 50.80/7.00 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 50.80/7.00 ( ( ![Xp1:( a > a > $o )]: 50.80/7.00 ( ( ( ![Xx0:a,Xy0:a]: 50.80/7.00 ( ( ( R @ Xx0 @ Xy0 ) | ( S @ Xx0 @ Xy0 ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 50.80/7.00 ( ![Xx0:a,Xy0:a,Xz:a]: 50.80/7.00 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 50.80/7.00 ( Xp1 @ Xx @ Xy ) ) ) | 50.80/7.00 ( ~( ( ( ![Xx0:a,Xy0:a,Xz:a]: 50.80/7.00 ( ( ( ![Xp1:( a > a > $o )]: 50.80/7.00 ( ( ( ![Xx1:a,Xy1:a]: 50.80/7.00 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 50.80/7.00 ( ![Xx1:a,Xy1:a,Xz0:a]: 50.80/7.00 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 50.80/7.00 ( Xp1 @ Xy0 @ Xz ) ) ) & 50.80/7.00 ( ![Xp1:( a > a > $o )]: 50.80/7.00 ( ( ( ![Xx1:a,Xy1:a]: 50.80/7.00 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 50.80/7.00 ( ![Xx1:a,Xy1:a,Xz0:a]: 50.80/7.00 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 50.80/7.00 ( ![Xp1:( a > a > $o )]: 50.80/7.00 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 50.80/7.00 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 50.80/7.00 ( ![Xx1:a,Xy1:a]: 50.80/7.00 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) & 50.80/7.00 ( ![Xx0:a,Xy0:a]: 50.80/7.00 ( ( ( ![Xp1:( a > a > $o )]: 50.80/7.00 ( ( ( ![Xx1:a,Xy1:a]: 50.80/7.00 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) & 50.80/7.00 ( ![Xx1:a,Xy1:a,Xz:a]: 50.80/7.00 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 50.80/7.00 ( ![Xp1:( a > a > $o )]: 50.80/7.00 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 50.80/7.00 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xz ) ) ) & 50.80/7.00 ( ![Xx1:a,Xy1:a]: 50.80/7.00 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 50.80/7.00 ( ![Xp1:( a > a > $o )]: 50.80/7.00 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 50.80/7.00 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xz ) ) ) & 50.80/7.00 ( ![Xx1:a,Xy1:a]: 50.80/7.00 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) ) => 50.80/7.00 ( ![Xp1:( a > a > $o )]: 50.80/7.00 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 50.80/7.00 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xz ) ) ) & 50.80/7.00 ( ![Xx0:a,Xy0:a]: 50.80/7.00 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 50.80/7.00 ( Xp1 @ Xx @ Xy ) ) ) ) ) ))). 50.80/7.00 thf(zf_stmt_0, negated_conjecture, 50.80/7.00 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 50.80/7.00 ( ( ![Xp1:( a > a > $o )]: 50.80/7.00 ( ( ( ![Xx0:a,Xy0:a]: 50.80/7.00 ( ( ( R @ Xx0 @ Xy0 ) | ( S @ Xx0 @ Xy0 ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 50.80/7.00 ( ![Xx0:a,Xy0:a,Xz:a]: 50.80/7.00 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 50.80/7.00 ( Xp1 @ Xx @ Xy ) ) ) | 50.80/7.00 ( ~( ( ( ![Xx0:a,Xy0:a,Xz:a]: 50.80/7.00 ( ( ( ![Xp1:( a > a > $o )]: 50.80/7.00 ( ( ( ![Xx1:a,Xy1:a]: 50.80/7.00 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 50.80/7.00 ( ![Xx1:a,Xy1:a,Xz0:a]: 50.80/7.00 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 50.80/7.00 ( Xp1 @ Xy0 @ Xz ) ) ) & 50.80/7.00 ( ![Xp1:( a > a > $o )]: 50.80/7.00 ( ( ( ![Xx1:a,Xy1:a]: 50.80/7.00 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 50.80/7.00 ( ![Xx1:a,Xy1:a,Xz0:a]: 50.80/7.00 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 50.80/7.00 ( ![Xp1:( a > a > $o )]: 50.80/7.00 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 50.80/7.00 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 50.80/7.00 ( ![Xx1:a,Xy1:a]: 50.80/7.00 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) & 50.80/7.00 ( ![Xx0:a,Xy0:a]: 50.80/7.00 ( ( ( ![Xp1:( a > a > $o )]: 50.80/7.00 ( ( ( ![Xx1:a,Xy1:a]: 50.80/7.00 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) & 50.80/7.00 ( ![Xx1:a,Xy1:a,Xz:a]: 50.80/7.00 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 50.80/7.00 ( ![Xp1:( a > a > $o )]: 50.80/7.00 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 50.80/7.00 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xz ) ) ) & 50.80/7.00 ( ![Xx1:a,Xy1:a]: 50.80/7.00 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 50.80/7.00 ( ![Xp1:( a > a > $o )]: 50.80/7.00 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 50.80/7.00 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xz ) ) ) & 50.80/7.00 ( ![Xx1:a,Xy1:a]: 50.80/7.00 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 50.80/7.00 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) ) => 50.80/7.00 ( ![Xp1:( a > a > $o )]: 50.80/7.00 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 50.80/7.00 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xz ) ) ) & 50.80/7.00 ( ![Xx0:a,Xy0:a]: 50.80/7.00 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 50.80/7.00 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 50.80/7.00 ( Xp1 @ Xx @ Xy ) ) ) ) ) ) )), 50.80/7.00 inference('cnf.neg', [status(esa)], [cTHM250G_pme])). 50.80/7.00 thf(zip_derived_cl0, plain, 50.80/7.00 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((!!) @ (^[Y1 : a > a > $o]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((!!) @ (^[Y4 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y0 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) | 50.80/7.00 (Y1 @ 50.80/7.00 Y5 @ Y6))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y6))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) & 50.80/7.00 (Y4 @ 50.80/7.00 Y6 @ Y7))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y7)))))))))))))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y2 @ Y3)))))) | 50.80/7.00 (((~) @ (((( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y9 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y0 @ 50.80/7.00 Y8 @ 50.80/7.00 Y9) | 50.80/7.00 (Y1 @ 50.80/7.00 Y8 @ Y9))) => 50.80/7.00 (Y7 @ 50.80/7.00 Y8 @ Y9))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y9 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y10 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y7 @ 50.80/7.00 Y9 @ 50.80/7.00 Y10) & 50.80/7.00 (Y7 @ 50.80/7.00 Y8 @ Y9))) => 50.80/7.00 (Y7 @ 50.80/7.00 Y8 @ Y10)))))))))))))) => 50.80/7.00 (Y7 @ 50.80/7.00 Y5 @ Y6)))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y9 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y0 @ 50.80/7.00 Y8 @ 50.80/7.00 Y9) | 50.80/7.00 (Y1 @ 50.80/7.00 Y8 @ Y9))) => 50.80/7.00 (Y7 @ 50.80/7.00 Y8 @ Y9))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y9 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y10 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y7 @ 50.80/7.00 Y9 @ 50.80/7.00 Y10) & 50.80/7.00 (Y7 @ 50.80/7.00 Y8 @ Y9))) => 50.80/7.00 (Y7 @ 50.80/7.00 Y8 @ Y10)))))))))))))) => 50.80/7.00 (Y7 @ 50.80/7.00 Y4 @ Y5)))))))) => 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y9 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y10 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y7 @ 50.80/7.00 Y9 @ 50.80/7.00 Y10) & 50.80/7.00 (Y7 @ 50.80/7.00 Y8 @ Y9))) => 50.80/7.00 (Y7 @ 50.80/7.00 Y8 @ Y10)))))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y9 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y1 @ 50.80/7.00 Y8 @ 50.80/7.00 Y9) | 50.80/7.00 (Y0 @ 50.80/7.00 Y8 @ Y9))) => 50.80/7.00 (Y7 @ 50.80/7.00 Y8 @ Y9))))))))))) => 50.80/7.00 (Y7 @ 50.80/7.00 Y4 @ Y6))))))))))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (Y1 @ 50.80/7.00 Y7 @ 50.80/7.00 Y8) => 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ Y8))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y9 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y6 @ 50.80/7.00 Y8 @ 50.80/7.00 Y9) & 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ Y8))) => 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ Y9)))))))))))))) => 50.80/7.00 (Y6 @ 50.80/7.00 Y4 @ Y5)))))) | 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y9 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ 50.80/7.00 Y8) & 50.80/7.00 (Y6 @ 50.80/7.00 Y8 @ Y9))) => 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ Y9)))))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (Y0 @ 50.80/7.00 Y7 @ 50.80/7.00 Y8) => 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ Y8))))))))))) => 50.80/7.00 (Y6 @ 50.80/7.00 Y4 @ Y5)))))))) => 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y9 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ 50.80/7.00 Y8) & 50.80/7.00 (Y6 @ 50.80/7.00 Y8 @ Y9))) => 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ Y9)))))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y0 @ 50.80/7.00 Y7 @ 50.80/7.00 Y8) | 50.80/7.00 (Y1 @ 50.80/7.00 Y7 @ Y8))) => 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ Y8))))))))))) => 50.80/7.00 (Y6 @ 50.80/7.00 Y4 @ Y5)))))))))))))))) => 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y4 @ 50.80/7.00 Y6 @ 50.80/7.00 Y7) & 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y6))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y7)))))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y1 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) | 50.80/7.00 (Y0 @ 50.80/7.00 Y5 @ Y6))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y6))))))))))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y2 @ Y3))))))))))))))))))))))))), 50.80/7.00 inference('cnf', [status(esa)], [zf_stmt_0])). 50.80/7.00 thf(zip_derived_cl1, plain, 50.80/7.00 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((((!!) @ (^[Y3 : a > a > $o]: 50.80/7.00 (((((((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) | 50.80/7.00 (Y0 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))))))))) & 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) & 50.80/7.00 (Y3 @ 50.80/7.00 Y5 @ Y6))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y6)))))))))))))) => 50.80/7.00 (Y3 @ Y1 @ Y2)))))) | 50.80/7.00 (((~) @ (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y7 @ 50.80/7.00 Y8) | 50.80/7.00 (Y0 @ 50.80/7.00 Y7 @ Y8))) => 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ Y8))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y9 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y6 @ 50.80/7.00 Y8 @ 50.80/7.00 Y9) & 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ Y8))) => 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ Y9)))))))))))))) => 50.80/7.00 (Y6 @ 50.80/7.00 Y4 @ Y5)))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y7 @ 50.80/7.00 Y8) | 50.80/7.00 (Y0 @ 50.80/7.00 Y7 @ Y8))) => 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ Y8))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y9 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y6 @ 50.80/7.00 Y8 @ 50.80/7.00 Y9) & 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ Y8))) => 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ Y9)))))))))))))) => 50.80/7.00 (Y6 @ 50.80/7.00 Y3 @ Y4)))))))) => 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y9 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y6 @ 50.80/7.00 Y8 @ 50.80/7.00 Y9) & 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ Y8))) => 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ Y9)))))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y0 @ 50.80/7.00 Y7 @ 50.80/7.00 Y8) | 50.80/7.00 ('#sk1' @ 50.80/7.00 Y7 @ Y8))) => 50.80/7.00 (Y6 @ 50.80/7.00 Y7 @ Y8))))))))))) => 50.80/7.00 (Y6 @ 50.80/7.00 Y3 @ Y5))))))))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (Y0 @ 50.80/7.00 Y6 @ 50.80/7.00 Y7) => 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ Y7))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y5 @ 50.80/7.00 Y7 @ 50.80/7.00 Y8) & 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ Y7))) => 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ Y8)))))))))))))) => 50.80/7.00 (Y5 @ 50.80/7.00 Y3 @ Y4)))))) | 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ 50.80/7.00 Y7) & 50.80/7.00 (Y5 @ 50.80/7.00 Y7 @ Y8))) => 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ Y8)))))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y6 @ 50.80/7.00 Y7) => 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ Y7))))))))))) => 50.80/7.00 (Y5 @ 50.80/7.00 Y3 @ Y4)))))))) => 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ 50.80/7.00 Y7) & 50.80/7.00 (Y5 @ 50.80/7.00 Y7 @ Y8))) => 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ Y8)))))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y6 @ 50.80/7.00 Y7) | 50.80/7.00 (Y0 @ 50.80/7.00 Y6 @ Y7))) => 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ Y7))))))))))) => 50.80/7.00 (Y5 @ 50.80/7.00 Y3 @ Y4)))))))))))))))) => 50.80/7.00 (((!!) @ (^[Y3 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y3 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) & 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y6)))))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y0 @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) | 50.80/7.00 ('#sk1' @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))))))))))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y1 @ Y2)))))))))))))))))))))), 50.80/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 50.80/7.00 thf(zip_derived_cl2, plain, 50.80/7.00 (~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (((( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ Y4) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))) | 50.80/7.00 (((~) @ (((((((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y6 @ 50.80/7.00 Y7) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y6 @ Y7))) => 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ Y7))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y5 @ 50.80/7.00 Y7 @ 50.80/7.00 Y8) & 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ Y7))) => 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ Y8)))))))))))))) => 50.80/7.00 (Y5 @ 50.80/7.00 Y3 @ Y4)))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y6 @ 50.80/7.00 Y7) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y6 @ Y7))) => 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ Y7))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y5 @ 50.80/7.00 Y7 @ 50.80/7.00 Y8) & 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ Y7))) => 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ Y8)))))))))))))) => 50.80/7.00 (Y5 @ 50.80/7.00 Y2 @ Y3)))))))) => 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y8 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y5 @ 50.80/7.00 Y7 @ 50.80/7.00 Y8) & 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ Y7))) => 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ Y8)))))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y6 @ 50.80/7.00 Y7) | 50.80/7.00 ('#sk1' @ 50.80/7.00 Y6 @ Y7))) => 50.80/7.00 (Y5 @ 50.80/7.00 Y6 @ Y7))))))))))) => 50.80/7.00 (Y5 @ 50.80/7.00 Y2 @ Y4))))))))))))))))) & 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) => 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y6))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y4 @ 50.80/7.00 Y6 @ 50.80/7.00 Y7) & 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y6))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y7)))))))))))))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y2 @ Y3)))))) | 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) & 50.80/7.00 (Y4 @ 50.80/7.00 Y6 @ Y7))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y7)))))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) => 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y6))))))))))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y2 @ Y3)))))))) => 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) & 50.80/7.00 (Y4 @ 50.80/7.00 Y6 @ Y7))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y7)))))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y5 @ Y6))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y6))))))))))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y2 @ Y3)))))))))))))))) => 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ ( 50.80/7.00 ^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) & 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) | 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1))))))))))))))))))), 50.80/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 50.80/7.00 thf(zip_derived_cl3, plain, 50.80/7.00 (~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((((!!) @ (^[Y1 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 ((((('#sk1' @ 50.80/7.00 Y2 @ Y3) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y1 @ Y2 @ Y3))))))))) & 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (((( 50.80/7.00 (Y1 @ 50.80/7.00 Y2 @ Y3) & 50.80/7.00 (Y1 @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y1 @ 50.80/7.00 Y2 @ Y4)))))))))))))) => 50.80/7.00 (Y1 @ '#sk3' @ Y0)))))) | 50.80/7.00 (((~) @ (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y5 @ Y6))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y6))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y4 @ 50.80/7.00 Y6 @ 50.80/7.00 Y7) & 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y6))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y7)))))))))))))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y2 @ Y3)))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y5 @ Y6))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y6))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y4 @ 50.80/7.00 Y6 @ 50.80/7.00 Y7) & 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y6))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y7)))))))))))))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y1 @ Y2)))))))) => 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : 50.80/7.00 a > a > $o]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y7 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y4 @ 50.80/7.00 Y6 @ 50.80/7.00 Y7) & 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y6))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y7)))))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) | 50.80/7.00 ('#sk1' @ 50.80/7.00 Y5 @ Y6))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y5 @ Y6))))))))))) => 50.80/7.00 (Y4 @ 50.80/7.00 Y1 @ Y3))))))))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((((((!!) @ ( 50.80/7.00 ^[Y3 : 50.80/7.00 a > a > $o]: 50.80/7.00 (((( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y3 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) & 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y6)))))))))))))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y1 @ Y2)))))) | 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y3 : 50.80/7.00 a > a > $o]: 50.80/7.00 (((( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) & 50.80/7.00 (Y3 @ 50.80/7.00 Y5 @ Y6))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y6)))))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))))))))))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y1 @ Y2)))))))) => 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y3 : a > a > $o]: 50.80/7.00 (((((( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) & 50.80/7.00 (Y3 @ 50.80/7.00 Y5 @ Y6))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y6)))))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))))))))))) => 50.80/7.00 (Y3 @ Y1 @ 50.80/7.00 Y2)))))))))))))))) => 50.80/7.00 (((!!) @ (^[Y1 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y1 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y1 @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y1 @ 50.80/7.00 Y2 @ Y4)))))))))))) & 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y3 : a]: 50.80/7.00 ((((('#sk2' @ 50.80/7.00 Y2 @ Y3) | 50.80/7.00 ('#sk1' @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y1 @ Y2 @ 50.80/7.00 Y3))))))))))) => 50.80/7.00 (Y1 @ '#sk3' @ Y0)))))))))))))))), 50.80/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 50.80/7.00 thf(zip_derived_cl4, plain, 50.80/7.00 (~ (((((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((((('#sk1' @ Y1 @ Y2) | 50.80/7.00 ('#sk2' @ Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y1 @ 50.80/7.00 Y2) & (Y0 @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.80/7.00 (Y0 @ '#sk3' @ '#sk4')))))) | 50.80/7.00 (((~) @ (((((((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((((((!!) @ ( 50.80/7.00 ^[Y3 : 50.80/7.00 a > a > $o]: 50.80/7.00 (((( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y3 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) & 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y6)))))))))))))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y1 @ Y2)))))) & 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y3 : 50.80/7.00 a > a > $o]: 50.80/7.00 (((( 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y3 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) & 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y6)))))))))))))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y0 @ Y1)))))))) => 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y3 : a > a > $o]: 50.80/7.00 (((((( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y3 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) & 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y6)))))))))))) & 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) | 50.80/7.00 ('#sk1' @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))))))))))) => 50.80/7.00 (Y3 @ Y0 @ 50.80/7.00 Y2))))))))))))))))) & 50.80/7.00 (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ ( 50.80/7.00 ^[Y3 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))) & 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y3 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) & 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))) | 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ ( 50.80/7.00 ^[Y3 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y3 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ ( 50.80/7.00 ^[Y3 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y3 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))))))))))) => 50.80/7.00 (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y3 : a]: 50.80/7.00 (((((Y0 @ 50.80/7.00 Y2 @ Y3) & 50.80/7.00 (Y0 @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ 50.80/7.00 Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((((('#sk2' @ 50.80/7.00 Y1 @ Y2) | 50.80/7.00 ('#sk1' @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk3' @ '#sk4'))))))))))))), 50.80/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 50.80/7.00 thf(zip_derived_cl6, plain, 50.80/7.00 ( (((((((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((((((!!) @ (^[Y3 : a > a > $o]: 50.80/7.00 (((((((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))))))))) & 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y3 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) & 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y6)))))))))))))) => 50.80/7.00 (Y3 @ Y1 @ 50.80/7.00 Y2)))))) & 50.80/7.00 (((!!) @ (^[Y3 : a > a > $o]: 50.80/7.00 (((((((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))))))))) & 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y3 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) & 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y6)))))))))))))) => 50.80/7.00 (Y3 @ Y0 @ 50.80/7.00 Y1)))))))) => 50.80/7.00 (((!!) @ (^[Y3 : a > a > $o]: 50.80/7.00 (((((((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y3 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) & 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y6)))))))))))) & 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) | 50.80/7.00 ('#sk1' @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))))))))))) => 50.80/7.00 (Y3 @ Y0 @ Y2))))))))))))))))) & 50.80/7.00 (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) & 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))) | 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))))))))))) => 50.80/7.00 (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y2 @ 50.80/7.00 Y3) & (Y0 @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.00 ('#sk1' @ Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk3' @ '#sk4'))))))))), 50.80/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 50.80/7.00 thf(zip_derived_cl8, plain, 50.80/7.00 ((~ (((((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((((((!!) @ (^[Y3 : a > a > $o]: 50.80/7.00 (((((((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))))))))) & 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y3 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) & 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y6)))))))))))))) => 50.80/7.00 (Y3 @ Y1 @ 50.80/7.00 Y2)))))) & 50.80/7.00 (((!!) @ (^[Y3 : a > a > $o]: 50.80/7.00 (((((((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))))))))) & 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y3 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) & 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y6)))))))))))))) => 50.80/7.00 (Y3 @ Y0 @ 50.80/7.00 Y1)))))))) => 50.80/7.00 (((!!) @ (^[Y3 : a > a > $o]: 50.80/7.00 (((((((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y3 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) & 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y6)))))))))))) & 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) | 50.80/7.00 ('#sk1' @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))))))))))) => 50.80/7.00 (Y3 @ Y0 @ Y2))))))))))))))))) & 50.80/7.00 (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) & 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))) | 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))))))))))) 50.80/7.00 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y2 @ 50.80/7.00 Y3) & (Y0 @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.00 ('#sk1' @ Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk3' @ '#sk4')))))))), 50.80/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 50.80/7.00 thf(zip_derived_cl11, plain, 50.80/7.00 ((~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((((((!!) @ (^[Y3 : a > a > $o]: 50.80/7.00 (((((((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))))))))) & 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y3 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) & 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y6)))))))))))))) => 50.80/7.00 (Y3 @ Y1 @ Y2)))))) & 50.80/7.00 (((!!) @ (^[Y3 : a > a > $o]: 50.80/7.00 (((((((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))))))))) & 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y3 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) & 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y6)))))))))))))) => 50.80/7.00 (Y3 @ Y0 @ Y1)))))))) => 50.80/7.00 (((!!) @ (^[Y3 : a > a > $o]: 50.80/7.00 (((((((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y6 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y3 @ 50.80/7.00 Y5 @ 50.80/7.00 Y6) & 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y6)))))))))))) & 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) | 50.80/7.00 ('#sk1' @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y3 @ 50.80/7.00 Y4 @ Y5))))))))))) => 50.80/7.00 (Y3 @ Y0 @ Y2))))))))))))))))) 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) & 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))) | 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))))))))) 50.80/7.00 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y2 @ 50.80/7.00 Y3) & (Y0 @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.00 ('#sk1' @ Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk3' @ '#sk4')))))))), 50.80/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl8])). 50.80/7.00 thf(zip_derived_cl14, plain, 50.80/7.00 ((~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) & 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))) & 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) & 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))))) => 50.80/7.00 (Y2 @ '#sk6' @ Y0)))))))) => 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) & 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (((( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) | 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ '#sk6' @ Y1)))))))))))))) 50.80/7.00 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y2 @ 50.80/7.00 Y3) & (Y0 @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.00 ('#sk1' @ Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk3' @ '#sk4')))))) 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) & 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))) | 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))))))))))), 50.80/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl11])). 50.80/7.00 thf(zip_derived_cl17, plain, 50.80/7.00 ((~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((((((!!) @ (^[Y1 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 ((((('#sk1' @ 50.80/7.00 Y2 @ 50.80/7.00 Y3) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y1 @ Y2 @ 50.80/7.00 Y3))))))))) & 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (( 50.80/7.00 (Y1 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y1 @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y1 @ 50.80/7.00 Y2 @ Y4)))))))))))))) => 50.80/7.00 (Y1 @ '#sk7' @ Y0)))))) & 50.80/7.00 (((!!) @ (^[Y1 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 ((((('#sk1' @ 50.80/7.00 Y2 @ 50.80/7.00 Y3) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y1 @ Y2 @ 50.80/7.00 Y3))))))))) & 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (( 50.80/7.00 (Y1 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y1 @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y1 @ 50.80/7.00 Y2 @ Y4)))))))))))))) => 50.80/7.00 (Y1 @ '#sk6' @ '#sk7')))))))) => 50.80/7.00 (((!!) @ (^[Y1 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (((( 50.80/7.00 (Y1 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y1 @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y1 @ 50.80/7.00 Y2 @ Y4)))))))))))) & 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 ((((('#sk2' @ 50.80/7.00 Y2 @ Y3) | 50.80/7.00 ('#sk1' @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y1 @ Y2 @ 50.80/7.00 Y3))))))))))) => 50.80/7.00 (Y1 @ '#sk6' @ Y0))))))))))) 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) & 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))) | 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))))))))) 50.80/7.00 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y2 @ 50.80/7.00 Y3) & (Y0 @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.00 ('#sk1' @ Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk3' @ '#sk4')))))))), 50.80/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl14])). 50.80/7.00 thf(zip_derived_cl20, plain, 50.80/7.00 ((~ (((((((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((((('#sk1' @ Y1 @ Y2) | 50.80/7.00 ('#sk2' @ Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ 50.80/7.00 Y2 @ 50.80/7.00 Y3) & 50.80/7.00 (Y0 @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ 50.80/7.00 Y3)))))))))))))) => 50.80/7.00 (Y0 @ '#sk7' @ '#sk8')))))) & 50.80/7.00 (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((((('#sk1' @ Y1 @ Y2) | 50.80/7.00 ('#sk2' @ Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ 50.80/7.00 Y2 @ 50.80/7.00 Y3) & 50.80/7.00 (Y0 @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ 50.80/7.00 Y3)))))))))))))) => 50.80/7.00 (Y0 @ '#sk6' @ '#sk7')))))))) => 50.80/7.00 (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y2 @ 50.80/7.00 Y3) & 50.80/7.00 (Y0 @ Y1 @ 50.80/7.00 Y2))) => 50.80/7.00 (Y0 @ Y1 @ 50.80/7.00 Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.00 ('#sk1' @ Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk6' @ '#sk8')))))))) 50.80/7.00 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y2 @ 50.80/7.00 Y3) & (Y0 @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.00 ('#sk1' @ Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk3' @ '#sk4')))))) 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) & 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))) | 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))))))))))), 50.80/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl17])). 50.80/7.00 thf(zip_derived_cl24, plain, 50.80/7.00 ((~ (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y2 @ 50.80/7.00 Y3) & (Y0 @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.00 ('#sk1' @ Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk6' @ '#sk8')))))) 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) & 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))) | 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))))))))) 50.80/7.00 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y2 @ 50.80/7.00 Y3) & (Y0 @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.00 ('#sk1' @ Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk3' @ '#sk4')))))))), 50.80/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 50.80/7.00 thf(zip_derived_cl30, plain, 50.80/7.00 (( ('#form9') 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ 50.80/7.00 Y5) & 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))) | 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.00 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (!!) @ ( 50.80/7.00 ^[Y5 : a]: 50.80/7.00 (( 50.80/7.00 (( 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y2 @ 50.80/7.00 Y4 @ Y5))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y5)))))))))))) & 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (( 50.80/7.00 ('#sk1' @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y2 @ 50.80/7.00 Y3 @ Y4))))))))))) => 50.80/7.00 (Y2 @ Y0 @ Y1)))))))))))))))), 50.80/7.00 define([status(thm)])). 50.80/7.00 thf(zip_derived_cl31, plain, 50.80/7.00 ((~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((((((!!) @ (^[Y1 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 ((('#sk2' @ 50.80/7.00 Y2 @ Y3) => 50.80/7.00 (Y1 @ Y2 @ 50.80/7.00 Y3))))))))) & 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (( 50.80/7.00 (Y1 @ 50.80/7.00 Y3 @ 50.80/7.00 Y4) & 50.80/7.00 (Y1 @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y1 @ 50.80/7.00 Y2 @ Y4)))))))))))))) => 50.80/7.00 (Y1 @ '#sk10' @ Y0)))))) | 50.80/7.00 (((!!) @ (^[Y1 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 ( 50.80/7.00 ( 50.80/7.00 (( 50.80/7.00 (Y1 @ 50.80/7.00 Y2 @ 50.80/7.00 Y3) & 50.80/7.00 (Y1 @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y1 @ 50.80/7.00 Y2 @ Y4)))))))))))) & 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 ((('#sk1' @ 50.80/7.00 Y2 @ Y3) => 50.80/7.00 (Y1 @ Y2 @ 50.80/7.00 Y3))))))))))) => 50.80/7.00 (Y1 @ '#sk10' @ Y0)))))))) => 50.80/7.00 (((!!) @ (^[Y1 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((!!) @ ( 50.80/7.00 ^[Y4 : a]: 50.80/7.00 (((( 50.80/7.00 (Y1 @ 50.80/7.00 Y2 @ 50.80/7.00 Y3) & 50.80/7.00 (Y1 @ 50.80/7.00 Y3 @ Y4))) => 50.80/7.00 (Y1 @ 50.80/7.00 Y2 @ Y4)))))))))))) & 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 ((((('#sk1' @ 50.80/7.00 Y2 @ Y3) | 50.80/7.00 ('#sk2' @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y1 @ Y2 @ 50.80/7.00 Y3))))))))))) => 50.80/7.00 (Y1 @ '#sk10' @ Y0))))))))))) 50.80/7.00 | ('#form9'))), 50.80/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])). 50.80/7.00 thf(zip_derived_cl42, plain, 50.80/7.00 ((~ (((((((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((('#sk2' @ Y1 @ Y2) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ 50.80/7.00 Y2 @ 50.80/7.00 Y3) & 50.80/7.00 (Y0 @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ 50.80/7.00 Y3)))))))))))))) => 50.80/7.00 (Y0 @ '#sk10' @ '#sk12')))))) | 50.80/7.00 (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ 50.80/7.00 Y1 @ 50.80/7.00 Y2) & 50.80/7.00 (Y0 @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y0 @ Y1 @ 50.80/7.00 Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((('#sk1' @ Y1 @ Y2) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk10' @ '#sk12')))))))) => 50.80/7.00 (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y1 @ 50.80/7.00 Y2) & 50.80/7.00 (Y0 @ Y2 @ 50.80/7.00 Y3))) => 50.80/7.00 (Y0 @ Y1 @ 50.80/7.00 Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((((('#sk1' @ Y1 @ Y2) | 50.80/7.00 ('#sk2' @ Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk10' @ '#sk12')))))))) 50.80/7.00 | ('#form9'))), 50.80/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl31])). 50.80/7.00 thf(zip_derived_cl48, plain, 50.80/7.00 (( (((((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((('#sk2' @ Y1 @ Y2) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y2 @ 50.80/7.00 Y3) & (Y0 @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.80/7.00 (Y0 @ '#sk10' @ '#sk12')))))) | 50.80/7.00 (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y1 @ 50.80/7.00 Y2) & (Y0 @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((('#sk1' @ Y1 @ Y2) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk10' @ '#sk12')))))))) 50.80/7.00 | ('#form9'))), 50.80/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])). 50.80/7.00 thf(zip_derived_cl63, plain, 50.80/7.00 (( (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((('#sk2' @ Y1 @ Y2) => (Y0 @ 50.80/7.00 Y1 @ Y2))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y2 @ 50.80/7.00 Y3) & (Y0 @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.80/7.00 (Y0 @ '#sk10' @ '#sk12')))))) 50.80/7.00 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y1 @ 50.80/7.00 Y2) & (Y0 @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((('#sk1' @ Y1 @ Y2) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk10' @ '#sk12')))))) 50.80/7.00 | ('#form9'))), 50.80/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl48])). 50.80/7.00 thf(zip_derived_cl73, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 ( (((((((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 50.80/7.00 (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.00 Y0 @ Y1))) => 50.80/7.00 (X2 @ Y0 @ Y2)))))))))))))) => 50.80/7.00 (X2 @ '#sk10' @ '#sk12'))) 50.80/7.00 | ('#form9') 50.80/7.00 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ 50.80/7.00 Y1 @ Y2) & 50.80/7.00 (Y0 @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y0 @ Y1 @ 50.80/7.00 Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((('#sk1' @ Y1 @ Y2) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk10' @ '#sk12')))))))), 50.80/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 50.80/7.00 thf(zip_derived_cl86, plain, 50.80/7.00 ((~ ('#form91') 50.80/7.00 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y1 @ 50.80/7.00 Y2) & (Y0 @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((('#sk1' @ Y1 @ Y2) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk10' @ '#sk12')))))))), 50.80/7.00 define([status(thm)])). 50.80/7.00 thf(zip_derived_cl87, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 ( (((((((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((((X2 @ Y0 @ Y1) & (X2 @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (X2 @ Y0 @ Y2)))))))))))) & 50.80/7.00 (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 50.80/7.00 (X2 @ '#sk10' @ '#sk12'))) 50.80/7.00 | ~ ('#form91'))), 50.80/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl86])). 50.80/7.00 thf(zip_derived_cl102, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 (~ (((((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((((X2 @ Y0 @ Y1) & (X2 @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (X2 @ Y0 @ Y2)))))))))))) & 50.80/7.00 (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) 50.80/7.00 | (X2 @ '#sk10' @ '#sk12') 50.80/7.00 | ~ ('#form91'))), 50.80/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl87])). 50.80/7.00 thf(zip_derived_cl112, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 (~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((((X2 @ Y0 @ Y1) & (X2 @ 50.80/7.00 Y1 @ Y2))) => 50.80/7.00 (X2 @ Y0 @ Y2)))))))))))) 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 50.80/7.00 | ~ ('#form91') 50.80/7.00 | (X2 @ '#sk10' @ '#sk12'))), 50.80/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl102])). 50.80/7.00 thf(zip_derived_cl128, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 (~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((((X2 @ ('#sk266' @ X2) @ Y0) & (X2 @ 50.80/7.00 Y0 @ Y1))) => 50.80/7.00 (X2 @ ('#sk266' @ X2) @ Y1))))))))) 50.80/7.00 | (X2 @ '#sk10' @ '#sk12') 50.80/7.00 | ~ ('#form91') 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.80/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl112])). 50.80/7.00 thf(zip_derived_cl143, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 (~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((((X2 @ ('#sk266' @ X2) @ ('#sk366' @ X2)) & (X2 @ 50.80/7.00 ('#sk366' @ X2) @ Y0))) => 50.80/7.00 (X2 @ ('#sk266' @ X2) @ Y0)))))) 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 50.80/7.00 | ~ ('#form91') 50.80/7.00 | (X2 @ '#sk10' @ '#sk12'))), 50.80/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl128])). 50.80/7.00 thf(zip_derived_cl155, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 (~ (((((X2 @ ('#sk266' @ X2) @ ('#sk366' @ X2)) & (X2 @ 50.80/7.00 ('#sk366' @ X2) @ ('#sk469' @ X2)))) => 50.80/7.00 (X2 @ ('#sk266' @ X2) @ ('#sk469' @ X2)))) 50.80/7.00 | (X2 @ '#sk10' @ '#sk12') 50.80/7.00 | ~ ('#form91') 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.80/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl143])). 50.80/7.00 thf(zip_derived_cl162, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 ( (((X2 @ ('#sk266' @ X2) @ ('#sk366' @ X2)) & (X2 @ 50.80/7.00 ('#sk366' @ X2) @ ('#sk469' @ X2)))) 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 50.80/7.00 | ~ ('#form91') 50.80/7.00 | (X2 @ '#sk10' @ '#sk12'))), 50.80/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl155])). 50.80/7.00 thf(zip_derived_cl166, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 ( (X2 @ ('#sk266' @ X2) @ ('#sk366' @ X2)) 50.80/7.00 | (X2 @ '#sk10' @ '#sk12') 50.80/7.00 | ~ ('#form91') 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.80/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl162])). 50.80/7.00 thf(zip_derived_cl163, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 (~ (X2 @ ('#sk266' @ X2) @ ('#sk469' @ X2)) 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 50.80/7.00 | ~ ('#form91') 50.80/7.00 | (X2 @ '#sk10' @ '#sk12'))), 50.80/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl155])). 50.80/7.00 thf(zip_derived_cl168, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 ( ('#form598' @ X2) 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.80/7.00 define([status(thm)])). 50.80/7.00 thf(zip_derived_cl171, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 (~ ('#form598' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 50.80/7.00 | ~ ('#form91') 50.80/7.00 | (X2 @ '#sk10' @ '#sk12') 50.80/7.00 | (X2 @ ('#sk266' @ X2) @ ('#sk366' @ X2)))), 50.80/7.00 inference('renaming', [status(thm)], 50.80/7.00 [zip_derived_cl166, zip_derived_cl168])). 50.80/7.00 thf(zip_derived_cl174, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 (~ ('#form598' @ X2) 50.80/7.00 | ~ ('#form91') 50.80/7.00 | (X2 @ '#sk10' @ '#sk12') 50.80/7.00 | (X2 @ ('#sk266' @ X2) @ ('#sk366' @ X2)))), 50.80/7.00 inference('ho_norm', [status(thm)], [zip_derived_cl171])). 50.80/7.00 thf(zip_derived_cl49, plain, 50.80/7.00 ((~ (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y1 @ 50.80/7.00 Y2) & (Y0 @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((((('#sk1' @ Y1 @ Y2) | 50.80/7.00 ('#sk2' @ Y1 @ Y2))) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk10' @ '#sk12')))))) 50.80/7.00 | ('#form9'))), 50.80/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])). 50.80/7.00 thf(zip_derived_cl67, plain, 50.80/7.00 ((~ (((((((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((((('#sk30' @ Y0 @ Y1) & 50.80/7.00 ('#sk30' @ Y1 @ Y2))) => 50.80/7.00 ('#sk30' @ Y0 @ Y2)))))))))))) & 50.80/7.00 (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.80/7.00 Y1))) => 50.80/7.00 ('#sk30' @ Y0 @ Y1))))))))))) => 50.80/7.00 ('#sk30' @ '#sk10' @ '#sk12'))) 50.80/7.00 | ('#form9'))), 50.80/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl49])). 50.80/7.00 thf(zip_derived_cl80, plain, 50.80/7.00 ((~ ('#sk30' @ '#sk10' @ '#sk12') | ('#form9'))), 50.80/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 50.80/7.00 thf(zip_derived_cl163, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 (~ (X2 @ ('#sk266' @ X2) @ ('#sk469' @ X2)) 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 50.80/7.00 | ~ ('#form91') 50.80/7.00 | (X2 @ '#sk10' @ '#sk12'))), 50.80/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl155])). 50.80/7.00 thf(zip_derived_cl168, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 ( ('#form598' @ X2) 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.80/7.00 define([status(thm)])). 50.80/7.00 thf(zip_derived_cl170, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 (~ ('#form598' @ X2) 50.80/7.00 | (X2 @ '#sk10' @ '#sk12') 50.80/7.00 | ~ ('#form91') 50.80/7.00 | ~ (X2 @ ('#sk266' @ X2) @ ('#sk469' @ X2)))), 50.80/7.00 inference('renaming', [status(thm)], 50.80/7.00 [zip_derived_cl163, zip_derived_cl168])). 50.80/7.00 thf(zip_derived_cl168, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 ( ('#form598' @ X2) 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.80/7.00 define([status(thm)])). 50.80/7.00 thf(zip_derived_cl169, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 (~ (((!!) @ (^[Y0 : a]: 50.80/7.00 ((('#sk1' @ ('#sk599' @ X2) @ Y0) => (X2 @ 50.80/7.00 ('#sk599' @ X2) @ Y0)))))) 50.80/7.00 | ('#form598' @ X2))), 50.80/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl168])). 50.80/7.00 thf(zip_derived_cl173, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 (~ ((('#sk1' @ ('#sk599' @ X2) @ ('#sk637' @ X2)) => (X2 @ 50.80/7.00 ('#sk599' @ X2) @ ('#sk637' @ X2)))) 50.80/7.00 | ('#form598' @ X2))), 50.80/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl169])). 50.80/7.00 thf(zip_derived_cl176, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 ( ('#sk1' @ ('#sk599' @ X2) @ ('#sk637' @ X2)) | ('#form598' @ X2))), 50.80/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl173])). 50.80/7.00 thf(zip_derived_cl167, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 ( (X2 @ ('#sk366' @ X2) @ ('#sk469' @ X2)) 50.80/7.00 | (X2 @ '#sk10' @ '#sk12') 50.80/7.00 | ~ ('#form91') 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.80/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl162])). 50.80/7.00 thf(zip_derived_cl168, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 ( ('#form598' @ X2) 50.80/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.80/7.00 define([status(thm)])). 50.80/7.00 thf(zip_derived_cl172, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 (~ ('#form598' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 50.80/7.00 | ~ ('#form91') 50.80/7.00 | (X2 @ '#sk10' @ '#sk12') 50.80/7.00 | (X2 @ ('#sk366' @ X2) @ ('#sk469' @ X2)))), 50.80/7.00 inference('renaming', [status(thm)], 50.80/7.00 [zip_derived_cl167, zip_derived_cl168])). 50.80/7.00 thf(zip_derived_cl175, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 (~ ('#form598' @ X2) 50.80/7.00 | ~ ('#form91') 50.80/7.00 | (X2 @ '#sk10' @ '#sk12') 50.80/7.00 | (X2 @ ('#sk366' @ X2) @ ('#sk469' @ X2)))), 50.80/7.00 inference('ho_norm', [status(thm)], [zip_derived_cl172])). 50.80/7.00 thf(zip_derived_cl73, plain, 50.80/7.00 (![X2 : a > a > $o]: 50.80/7.00 ( (((((((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 50.80/7.00 (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.00 Y0 @ Y1))) => 50.80/7.00 (X2 @ Y0 @ Y2)))))))))))))) => 50.80/7.00 (X2 @ '#sk10' @ '#sk12'))) 50.80/7.00 | ('#form9') 50.80/7.00 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ 50.80/7.00 Y1 @ Y2) & 50.80/7.00 (Y0 @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y0 @ Y1 @ 50.80/7.00 Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((('#sk1' @ Y1 @ Y2) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk10' @ '#sk12')))))))), 50.80/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 50.80/7.00 thf(zip_derived_cl74, plain, 50.80/7.00 (( (((((((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 50.80/7.00 Y1))))))))) & 50.80/7.00 (((!!) @ (^[Y0 : a]: 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((((('#sk30' @ Y1 @ Y2) & 50.80/7.00 ('#sk30' @ Y0 @ Y1))) => 50.80/7.00 ('#sk30' @ Y0 @ Y2)))))))))))))) => 50.80/7.00 ('#sk30' @ '#sk10' @ '#sk12'))) 50.80/7.00 | ('#form9') 50.80/7.00 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y1 @ 50.80/7.00 Y2) & (Y0 @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.00 (((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 ((('#sk1' @ Y1 @ Y2) => 50.80/7.00 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.00 (Y0 @ '#sk10' @ '#sk12')))))))), 50.80/7.00 inference('triggered_bool_instantiation', [status(thm)], 50.80/7.00 [zip_derived_cl73])). 50.80/7.00 thf(zip_derived_cl86, plain, 50.80/7.00 ((~ ('#form91') 50.80/7.00 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.00 (((((((!!) @ (^[Y1 : a]: 50.80/7.00 (((!!) @ (^[Y2 : a]: 50.80/7.00 (((!!) @ (^[Y3 : a]: 50.80/7.00 (((((Y0 @ Y1 @ 50.80/7.00 Y2) & (Y0 @ 50.80/7.00 Y2 @ Y3))) => 50.80/7.00 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((('#sk1' @ Y1 @ Y2) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.01 (Y0 @ '#sk10' @ '#sk12')))))))), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(zip_derived_cl333, plain, 50.80/7.01 (( ('#form91') 50.80/7.01 | ('#form9') 50.80/7.01 | (((((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 50.80/7.01 Y1))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk30' @ Y1 @ Y2) & 50.80/7.01 ('#sk30' @ Y0 @ Y1))) => 50.80/7.01 ('#sk30' @ Y0 @ Y2)))))))))))))) => 50.80/7.01 ('#sk30' @ '#sk10' @ '#sk12'))))), 50.80/7.01 inference('renaming', [status(thm)], [zip_derived_cl74, zip_derived_cl86])). 50.80/7.01 thf(zip_derived_cl334, plain, 50.80/7.01 ((~ (((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk30' @ Y1 @ Y2) & 50.80/7.01 ('#sk30' @ Y0 @ Y1))) => 50.80/7.01 ('#sk30' @ Y0 @ Y2)))))))))))))) 50.80/7.01 | ('#sk30' @ '#sk10' @ '#sk12') 50.80/7.01 | ('#form9') 50.80/7.01 | ('#form91'))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl333])). 50.80/7.01 thf(zip_derived_cl80, plain, 50.80/7.01 ((~ ('#sk30' @ '#sk10' @ '#sk12') | ('#form9'))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 50.80/7.01 thf(zip_derived_cl335, plain, 50.80/7.01 (( ('#form91') 50.80/7.01 | ('#form9') 50.80/7.01 | ~ (((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 50.80/7.01 Y1))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk30' @ Y1 @ Y2) & 50.80/7.01 ('#sk30' @ Y0 @ Y1))) => 50.80/7.01 ('#sk30' @ Y0 @ Y2)))))))))))))))), 50.80/7.01 inference('clc', [status(thm)], [zip_derived_cl334, zip_derived_cl80])). 50.80/7.01 thf(zip_derived_cl336, plain, 50.80/7.01 ((~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk30' @ Y1 @ Y2) & 50.80/7.01 ('#sk30' @ Y0 @ Y1))) => 50.80/7.01 ('#sk30' @ Y0 @ Y2)))))))))))) 50.80/7.01 | ('#form9') 50.80/7.01 | ('#form91'))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl335])). 50.80/7.01 thf(zip_derived_cl23, plain, 50.80/7.01 (( (((((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk1' @ Y1 @ Y2) | 50.80/7.01 ('#sk2' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))))) => 50.80/7.01 (Y0 @ '#sk7' @ '#sk8')))))) & 50.80/7.01 (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk1' @ Y1 @ Y2) | 50.80/7.01 ('#sk2' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))))) => 50.80/7.01 (Y0 @ '#sk6' @ '#sk7')))))))) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ 50.80/7.01 Y5) & 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))) | 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) | 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))))))))) 50.80/7.01 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.01 ('#sk1' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.01 (Y0 @ '#sk3' @ '#sk4')))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 50.80/7.01 thf(zip_derived_cl28, plain, 50.80/7.01 (( (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk1' @ Y1 @ Y2) | 50.80/7.01 ('#sk2' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))))) => 50.80/7.01 (Y0 @ '#sk7' @ '#sk8')))))) 50.80/7.01 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.01 ('#sk1' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.01 (Y0 @ '#sk3' @ '#sk4')))))) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ 50.80/7.01 Y5) & 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))) | 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) | 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))))))))))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])). 50.80/7.01 thf(zip_derived_cl28, plain, 50.80/7.01 (( (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk1' @ Y1 @ Y2) | 50.80/7.01 ('#sk2' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))))) => 50.80/7.01 (Y0 @ '#sk7' @ '#sk8')))))) 50.80/7.01 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.01 ('#sk1' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.01 (Y0 @ '#sk3' @ '#sk4')))))) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ 50.80/7.01 Y5) & 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))) | 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) | 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))))))))))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])). 50.80/7.01 thf(zip_derived_cl34, plain, 50.80/7.01 ((~ ('#form11') 50.80/7.01 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.01 ('#sk1' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.01 (Y0 @ '#sk3' @ '#sk4')))))))), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(zip_derived_cl39, plain, 50.80/7.01 (( ('#form11') 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ 50.80/7.01 Y5) & 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))) | 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) | 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))))))))) 50.80/7.01 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk1' @ Y1 @ Y2) | 50.80/7.01 ('#sk2' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))))) => 50.80/7.01 (Y0 @ '#sk7' @ '#sk8')))))))), 50.80/7.01 inference('renaming', [status(thm)], [zip_derived_cl28, zip_derived_cl34])). 50.80/7.01 thf(zip_derived_cl30, plain, 50.80/7.01 (( ('#form9') 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ 50.80/7.01 Y5) & 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))) | 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) | 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))))))))))), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(zip_derived_cl43, plain, 50.80/7.01 ((~ ('#form9') 50.80/7.01 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk1' @ Y1 @ Y2) | 50.80/7.01 ('#sk2' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))))) => 50.80/7.01 (Y0 @ '#sk7' @ '#sk8')))))) 50.80/7.01 | ('#form11'))), 50.80/7.01 inference('renaming', [status(thm)], [zip_derived_cl39, zip_derived_cl30])). 50.80/7.01 thf(zip_derived_cl50, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( (((((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 (X2 @ Y0 @ Y1))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))))) => 50.80/7.01 (X2 @ '#sk7' @ '#sk8'))) 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ('#form9'))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 50.80/7.01 thf(zip_derived_cl68, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 (X2 @ Y0 @ Y1))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))))) 50.80/7.01 | (X2 @ '#sk7' @ '#sk8') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#form11'))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])). 50.80/7.01 thf(zip_derived_cl81, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y1))))))))) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))) 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | (X2 @ '#sk7' @ '#sk8'))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl68])). 50.80/7.01 thf(zip_derived_cl96, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (((!!) @ (^[Y0 : a]: 50.80/7.01 ((((('#sk1' @ ('#sk100' @ X2) @ Y0) | ('#sk2' @ 50.80/7.01 ('#sk100' @ X2) @ Y0))) => 50.80/7.01 (X2 @ ('#sk100' @ X2) @ Y0)))))) 50.80/7.01 | (X2 @ '#sk7' @ '#sk8') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#form11') 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl81])). 50.80/7.01 thf(zip_derived_cl105, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ ((((('#sk1' @ ('#sk100' @ X2) @ ('#sk151' @ X2)) | ('#sk2' @ 50.80/7.01 ('#sk100' @ X2) @ ('#sk151' @ X2)))) => 50.80/7.01 (X2 @ ('#sk100' @ X2) @ ('#sk151' @ X2)))) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))) 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | (X2 @ '#sk7' @ '#sk8'))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 50.80/7.01 thf(zip_derived_cl115, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( ('#form213' @ X2) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(zip_derived_cl337, plain, 50.80/7.01 ((~ ('#form213' @ '#sk30') 50.80/7.01 | ('#form91') 50.80/7.01 | ('#form9') 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))))), 50.80/7.01 inference('renaming', [status(thm)], 50.80/7.01 [zip_derived_cl336, zip_derived_cl115])). 50.80/7.01 thf(zip_derived_cl338, plain, 50.80/7.01 ((~ (((!!) @ (^[Y0 : a]: 50.80/7.01 ((('#sk2' @ ('#sk355' @ '#sk30') @ Y0) => ('#sk30' @ 50.80/7.01 ('#sk355' @ '#sk30') @ Y0)))))) 50.80/7.01 | ('#form9') 50.80/7.01 | ('#form91') 50.80/7.01 | ~ ('#form213' @ '#sk30'))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl337])). 50.80/7.01 thf(zip_derived_cl339, plain, 50.80/7.01 ((~ ((('#sk2' @ ('#sk355' @ '#sk30') @ ('#sk456' @ '#sk30')) => 50.80/7.01 ('#sk30' @ ('#sk355' @ '#sk30') @ ('#sk456' @ '#sk30')))) 50.80/7.01 | ~ ('#form213' @ '#sk30') 50.80/7.01 | ('#form91') 50.80/7.01 | ('#form9'))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl338])). 50.80/7.01 thf(zip_derived_cl340, plain, 50.80/7.01 (( ('#sk2' @ ('#sk355' @ '#sk30') @ ('#sk456' @ '#sk30')) 50.80/7.01 | ('#form9') 50.80/7.01 | ('#form91') 50.80/7.01 | ~ ('#form213' @ '#sk30'))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl339])). 50.80/7.01 thf(zip_derived_cl341, plain, 50.80/7.01 ((~ ('#sk30' @ ('#sk355' @ '#sk30') @ ('#sk456' @ '#sk30')) 50.80/7.01 | ('#form9') 50.80/7.01 | ('#form91') 50.80/7.01 | ~ ('#form213' @ '#sk30'))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl339])). 50.80/7.01 thf(zip_derived_cl79, plain, 50.80/7.01 (( (((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk30' @ Y0 @ Y1) & 50.80/7.01 ('#sk30' @ Y1 @ Y2))) => 50.80/7.01 ('#sk30' @ Y0 @ Y2)))))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 50.80/7.01 ('#sk30' @ Y0 @ Y1))))))))))) 50.80/7.01 | ('#form9'))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 50.80/7.01 thf(zip_derived_cl95, plain, 50.80/7.01 (( (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 50.80/7.01 ('#sk30' @ Y0 @ Y1))))))))) 50.80/7.01 | ('#form9'))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl79])). 50.80/7.01 thf(zip_derived_cl104, plain, 50.80/7.01 (![X2 : a]: 50.80/7.01 ( (((!!) @ (^[Y0 : a]: 50.80/7.01 ((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) => 50.80/7.01 ('#sk30' @ X2 @ Y0)))))) 50.80/7.01 | ('#form9'))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl95])). 50.80/7.01 thf(zip_derived_cl114, plain, 50.80/7.01 (![X2 : a, X4 : a]: 50.80/7.01 ( ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) => ('#sk30' @ X2 @ X4))) 50.80/7.01 | ('#form9'))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl104])). 50.80/7.01 thf(zip_derived_cl130, plain, 50.80/7.01 (![X2 : a, X4 : a]: 50.80/7.01 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 50.80/7.01 | ('#sk30' @ X2 @ X4) 50.80/7.01 | ('#form9'))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl114])). 50.80/7.01 thf(zip_derived_cl145, plain, 50.80/7.01 (![X2 : a, X4 : a]: 50.80/7.01 (~ ('#sk1' @ X2 @ X4) | ('#form9') | ('#sk30' @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl130])). 50.80/7.01 thf(zip_derived_cl177, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (X2 @ ('#sk599' @ X2) @ ('#sk637' @ X2)) | ('#form598' @ X2))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl173])). 50.80/7.01 thf(zip_derived_cl146, plain, 50.80/7.01 (![X2 : a, X4 : a]: 50.80/7.01 (~ ('#sk2' @ X2 @ X4) | ('#form9') | ('#sk30' @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl130])). 50.80/7.01 thf(zip_derived_cl24, plain, 50.80/7.01 ((~ (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.01 ('#sk1' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.01 (Y0 @ '#sk6' @ '#sk8')))))) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ 50.80/7.01 Y5) & 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))) | 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) | 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))))))))) 50.80/7.01 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.01 ('#sk1' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.01 (Y0 @ '#sk3' @ '#sk4')))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 50.80/7.01 thf(zip_derived_cl30, plain, 50.80/7.01 (( ('#form9') 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ 50.80/7.01 Y5) & 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))) | 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) | 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))))))))))), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(zip_derived_cl32, plain, 50.80/7.01 ((~ ('#form9') 50.80/7.01 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.01 ('#sk1' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.01 (Y0 @ '#sk3' @ '#sk4')))))) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & 50.80/7.01 (Y0 @ Y1 @ 50.80/7.01 Y2))) => 50.80/7.01 (Y0 @ Y1 @ 50.80/7.01 Y3)))))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.01 ('#sk1' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.01 (Y0 @ '#sk6' @ '#sk8')))))))), 50.80/7.01 inference('renaming', [status(thm)], [zip_derived_cl24, zip_derived_cl30])). 50.80/7.01 thf(zip_derived_cl34, plain, 50.80/7.01 ((~ ('#form11') 50.80/7.01 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.01 ('#sk1' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.01 (Y0 @ '#sk3' @ '#sk4')))))))), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(zip_derived_cl41, plain, 50.80/7.01 (( ('#form11') 50.80/7.01 | ~ (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & 50.80/7.01 (Y0 @ Y1 @ 50.80/7.01 Y2))) => 50.80/7.01 (Y0 @ Y1 @ 50.80/7.01 Y3)))))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.01 ('#sk1' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.01 (Y0 @ '#sk6' @ '#sk8')))))) 50.80/7.01 | ~ ('#form9'))), 50.80/7.01 inference('renaming', [status(thm)], [zip_derived_cl32, zip_derived_cl34])). 50.80/7.01 thf(zip_derived_cl47, plain, 50.80/7.01 ((~ (((((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk21' @ Y1 @ Y2) & 50.80/7.01 ('#sk21' @ Y0 @ Y1))) => 50.80/7.01 ('#sk21' @ Y0 @ Y2)))))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 ('#sk21' @ Y0 @ Y1))))))))))) => 50.80/7.01 ('#sk21' @ '#sk6' @ '#sk8'))) 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#form11'))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl41])). 50.80/7.01 thf(zip_derived_cl62, plain, 50.80/7.01 ((~ ('#sk21' @ '#sk6' @ '#sk8') | ('#form11') | ~ ('#form9'))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 50.80/7.01 thf(zip_derived_cl94, plain, 50.80/7.01 (( (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk30' @ Y0 @ Y1) & 50.80/7.01 ('#sk30' @ Y1 @ Y2))) => 50.80/7.01 ('#sk30' @ Y0 @ Y2)))))))))))) 50.80/7.01 | ('#form9'))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl79])). 50.80/7.01 thf(zip_derived_cl103, plain, 50.80/7.01 (![X2 : a]: 50.80/7.01 ( (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk30' @ X2 @ Y0) & ('#sk30' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 ('#sk30' @ X2 @ Y1))))))))) 50.80/7.01 | ('#form9'))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])). 50.80/7.01 thf(zip_derived_cl113, plain, 50.80/7.01 (![X2 : a, X4 : a]: 50.80/7.01 ( (((!!) @ (^[Y0 : a]: 50.80/7.01 ((((('#sk30' @ X2 @ X4) & ('#sk30' @ X4 @ Y0))) => 50.80/7.01 ('#sk30' @ X2 @ Y0)))))) 50.80/7.01 | ('#form9'))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl103])). 50.80/7.01 thf(zip_derived_cl129, plain, 50.80/7.01 (![X2 : a, X4 : a, X6 : a]: 50.80/7.01 ( ((((('#sk30' @ X2 @ X4) & ('#sk30' @ X4 @ X6))) => ('#sk30' @ X2 @ 50.80/7.01 X6))) 50.80/7.01 | ('#form9'))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl113])). 50.80/7.01 thf(zip_derived_cl144, plain, 50.80/7.01 (![X2 : a, X4 : a, X6 : a]: 50.80/7.01 (~ ((('#sk30' @ X2 @ X4) & ('#sk30' @ X4 @ X6))) 50.80/7.01 | ('#sk30' @ X2 @ X6) 50.80/7.01 | ('#form9'))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl129])). 50.80/7.01 thf(zip_derived_cl156, plain, 50.80/7.01 (![X2 : a, X4 : a, X6 : a]: 50.80/7.01 (~ ('#sk30' @ X2 @ X4) 50.80/7.01 | ~ ('#sk30' @ X4 @ X6) 50.80/7.01 | ('#form9') 50.80/7.01 | ('#sk30' @ X2 @ X6))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl144])). 50.80/7.01 thf(zip_derived_cl61, plain, 50.80/7.01 (( (((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk21' @ Y1 @ Y2) & 50.80/7.01 ('#sk21' @ Y0 @ Y1))) => 50.80/7.01 ('#sk21' @ Y0 @ Y2)))))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 50.80/7.01 ('#sk21' @ Y0 @ Y1))))))))))) 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ('#form9'))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 50.80/7.01 thf(zip_derived_cl71, plain, 50.80/7.01 (( (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk21' @ Y1 @ Y2) & 50.80/7.01 ('#sk21' @ Y0 @ Y1))) => 50.80/7.01 ('#sk21' @ Y0 @ Y2)))))))))))) 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#form11'))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl61])). 50.80/7.01 thf(zip_derived_cl84, plain, 50.80/7.01 (![X2 : a]: 50.80/7.01 ( (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk21' @ Y0 @ Y1) & ('#sk21' @ X2 @ 50.80/7.01 Y0))) => 50.80/7.01 ('#sk21' @ X2 @ Y1))))))))) 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ('#form9'))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl71])). 50.80/7.01 thf(zip_derived_cl99, plain, 50.80/7.01 (![X2 : a, X4 : a]: 50.80/7.01 ( (((!!) @ (^[Y0 : a]: 50.80/7.01 ((((('#sk21' @ X4 @ Y0) & ('#sk21' @ X2 @ X4))) => 50.80/7.01 ('#sk21' @ X2 @ Y0)))))) 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#form11'))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl84])). 50.80/7.01 thf(zip_derived_cl109, plain, 50.80/7.01 (![X2 : a, X4 : a, X6 : a]: 50.80/7.01 ( ((((('#sk21' @ X4 @ X6) & ('#sk21' @ X2 @ X4))) => ('#sk21' @ X2 @ 50.80/7.01 X6))) 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ('#form9'))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl99])). 50.80/7.01 thf(zip_derived_cl124, plain, 50.80/7.01 (![X2 : a, X4 : a, X6 : a]: 50.80/7.01 (~ ((('#sk21' @ X4 @ X6) & ('#sk21' @ X2 @ X4))) 50.80/7.01 | ('#sk21' @ X2 @ X6) 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#form11'))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl109])). 50.80/7.01 thf(zip_derived_cl140, plain, 50.80/7.01 (![X2 : a, X4 : a, X6 : a]: 50.80/7.01 (~ ('#sk21' @ X4 @ X6) 50.80/7.01 | ~ ('#sk21' @ X2 @ X4) 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#sk21' @ X2 @ X6))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl124])). 50.80/7.01 thf(zip_derived_cl105, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ ((((('#sk1' @ ('#sk100' @ X2) @ ('#sk151' @ X2)) | ('#sk2' @ 50.80/7.01 ('#sk100' @ X2) @ ('#sk151' @ X2)))) => 50.80/7.01 (X2 @ ('#sk100' @ X2) @ ('#sk151' @ X2)))) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))) 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | (X2 @ '#sk7' @ '#sk8'))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 50.80/7.01 thf(zip_derived_cl115, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( ('#form213' @ X2) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(zip_derived_cl117, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ ('#form213' @ X2) 50.80/7.01 | (X2 @ '#sk7' @ '#sk8') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ((((('#sk1' @ ('#sk100' @ X2) @ ('#sk151' @ X2)) | ('#sk2' @ 50.80/7.01 ('#sk100' @ X2) @ ('#sk151' @ X2)))) => 50.80/7.01 (X2 @ ('#sk100' @ X2) @ ('#sk151' @ X2)))))), 50.80/7.01 inference('renaming', [status(thm)], 50.80/7.01 [zip_derived_cl105, zip_derived_cl115])). 50.80/7.01 thf(zip_derived_cl131, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( ((('#sk1' @ ('#sk100' @ X2) @ ('#sk151' @ X2)) | ('#sk2' @ 50.80/7.01 ('#sk100' @ X2) @ ('#sk151' @ X2)))) 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | (X2 @ '#sk7' @ '#sk8') 50.80/7.01 | ~ ('#form213' @ X2))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl117])). 50.80/7.01 thf(zip_derived_cl147, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( ('#sk1' @ ('#sk100' @ X2) @ ('#sk151' @ X2)) 50.80/7.01 | ('#sk2' @ ('#sk100' @ X2) @ ('#sk151' @ X2)) 50.80/7.01 | ~ ('#form213' @ X2) 50.80/7.01 | (X2 @ '#sk7' @ '#sk8') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#form11'))), 50.80/7.01 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl131])). 50.80/7.01 thf(zip_derived_cl132, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (X2 @ ('#sk100' @ X2) @ ('#sk151' @ X2)) 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | (X2 @ '#sk7' @ '#sk8') 50.80/7.01 | ~ ('#form213' @ X2))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl117])). 50.80/7.01 thf(zip_derived_cl29, plain, 50.80/7.01 (( (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk1' @ Y1 @ Y2) | 50.80/7.01 ('#sk2' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))))) => 50.80/7.01 (Y0 @ '#sk6' @ '#sk7')))))) 50.80/7.01 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.01 ('#sk1' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.01 (Y0 @ '#sk3' @ '#sk4')))))) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ 50.80/7.01 Y5) & 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))) | 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) | 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))))))))))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])). 50.80/7.01 thf(zip_derived_cl34, plain, 50.80/7.01 ((~ ('#form11') 50.80/7.01 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.01 ('#sk1' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.01 (Y0 @ '#sk3' @ '#sk4')))))))), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(zip_derived_cl40, plain, 50.80/7.01 (( ('#form11') 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ 50.80/7.01 Y5) & 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))) | 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) | 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))))))))) 50.80/7.01 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk1' @ Y1 @ Y2) | 50.80/7.01 ('#sk2' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))))) => 50.80/7.01 (Y0 @ '#sk6' @ '#sk7')))))))), 50.80/7.01 inference('renaming', [status(thm)], [zip_derived_cl29, zip_derived_cl34])). 50.80/7.01 thf(zip_derived_cl30, plain, 50.80/7.01 (( ('#form9') 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((((((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ 50.80/7.01 Y5) & 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))) | 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))) => 50.80/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y5 : a]: 50.80/7.01 (( 50.80/7.01 (( 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) & 50.80/7.01 (Y2 @ 50.80/7.01 Y4 @ Y5))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y5)))))))))))) & 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : a]: 50.80/7.01 ( 50.80/7.01 ( 50.80/7.01 (( 50.80/7.01 ('#sk1' @ 50.80/7.01 Y3 @ 50.80/7.01 Y4) | 50.80/7.01 ('#sk2' @ 50.80/7.01 Y3 @ Y4))) => 50.80/7.01 (Y2 @ 50.80/7.01 Y3 @ Y4))))))))))) => 50.80/7.01 (Y2 @ Y0 @ Y1)))))))))))))))), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(zip_derived_cl45, plain, 50.80/7.01 ((~ ('#form9') 50.80/7.01 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk1' @ Y1 @ Y2) | 50.80/7.01 ('#sk2' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))))) => 50.80/7.01 (Y0 @ '#sk6' @ '#sk7')))))) 50.80/7.01 | ('#form11'))), 50.80/7.01 inference('renaming', [status(thm)], [zip_derived_cl40, zip_derived_cl30])). 50.80/7.01 thf(zip_derived_cl56, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( (((((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 (X2 @ Y0 @ Y1))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))))) => 50.80/7.01 (X2 @ '#sk6' @ '#sk7'))) 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ('#form9'))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl45])). 50.80/7.01 thf(zip_derived_cl70, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 (X2 @ Y0 @ Y1))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))))) 50.80/7.01 | (X2 @ '#sk6' @ '#sk7') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#form11'))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl56])). 50.80/7.01 thf(zip_derived_cl83, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y1))))))))) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))) 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | (X2 @ '#sk6' @ '#sk7'))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl70])). 50.80/7.01 thf(zip_derived_cl98, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (((!!) @ (^[Y0 : a]: 50.80/7.01 ((((('#sk1' @ ('#sk100' @ X2) @ Y0) | ('#sk2' @ 50.80/7.01 ('#sk100' @ X2) @ Y0))) => 50.80/7.01 (X2 @ ('#sk100' @ X2) @ Y0)))))) 50.80/7.01 | (X2 @ '#sk6' @ '#sk7') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#form11') 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl83])). 50.80/7.01 thf(zip_derived_cl108, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ ((((('#sk1' @ ('#sk100' @ X2) @ ('#sk151' @ X2)) | ('#sk2' @ 50.80/7.01 ('#sk100' @ X2) @ ('#sk151' @ X2)))) => 50.80/7.01 (X2 @ ('#sk100' @ X2) @ ('#sk151' @ X2)))) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))) 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | (X2 @ '#sk6' @ '#sk7'))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl98])). 50.80/7.01 thf(zip_derived_cl115, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( ('#form213' @ X2) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(zip_derived_cl123, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ ('#form213' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 50.80/7.01 | (X2 @ '#sk6' @ '#sk7') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ((((('#sk1' @ ('#sk100' @ X2) @ ('#sk151' @ X2)) | ('#sk2' @ 50.80/7.01 ('#sk100' @ X2) @ ('#sk151' @ X2)))) => 50.80/7.01 (X2 @ ('#sk100' @ X2) @ ('#sk151' @ X2)))))), 50.80/7.01 inference('renaming', [status(thm)], 50.80/7.01 [zip_derived_cl108, zip_derived_cl115])). 50.80/7.01 thf(zip_derived_cl137, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ ('#form213' @ X2) 50.80/7.01 | (X2 @ '#sk6' @ '#sk7') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ((((('#sk1' @ ('#sk100' @ X2) @ ('#sk151' @ X2)) | ('#sk2' @ 50.80/7.01 ('#sk100' @ X2) @ ('#sk151' @ X2)))) => 50.80/7.01 (X2 @ ('#sk100' @ X2) @ ('#sk151' @ X2)))))), 50.80/7.01 inference('ho_norm', [status(thm)], [zip_derived_cl123])). 50.80/7.01 thf(zip_derived_cl138, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( ((('#sk1' @ ('#sk100' @ X2) @ ('#sk151' @ X2)) | ('#sk2' @ 50.80/7.01 ('#sk100' @ X2) @ ('#sk151' @ X2)))) 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | (X2 @ '#sk6' @ '#sk7') 50.80/7.01 | ~ ('#form213' @ X2))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])). 50.80/7.01 thf(zip_derived_cl153, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( ('#sk1' @ ('#sk100' @ X2) @ ('#sk151' @ X2)) 50.80/7.01 | ('#sk2' @ ('#sk100' @ X2) @ ('#sk151' @ X2)) 50.80/7.01 | ~ ('#form213' @ X2) 50.80/7.01 | (X2 @ '#sk6' @ '#sk7') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#form11'))), 50.80/7.01 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl138])). 50.80/7.01 thf(zip_derived_cl72, plain, 50.80/7.01 (( (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 50.80/7.01 ('#sk21' @ Y0 @ Y1))))))))) 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#form11'))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl61])). 50.80/7.01 thf(zip_derived_cl85, plain, 50.80/7.01 (![X2 : a]: 50.80/7.01 ( (((!!) @ (^[Y0 : a]: 50.80/7.01 ((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) => 50.80/7.01 ('#sk21' @ X2 @ Y0)))))) 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ('#form9'))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl72])). 50.80/7.01 thf(zip_derived_cl100, plain, 50.80/7.01 (![X2 : a, X4 : a]: 50.80/7.01 ( ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) => ('#sk21' @ X2 @ X4))) 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#form11'))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 50.80/7.01 thf(zip_derived_cl110, plain, 50.80/7.01 (![X2 : a, X4 : a]: 50.80/7.01 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 50.80/7.01 | ('#sk21' @ X2 @ X4) 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ('#form9'))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 50.80/7.01 thf(zip_derived_cl126, plain, 50.80/7.01 (![X2 : a, X4 : a]: 50.80/7.01 (~ ('#sk1' @ X2 @ X4) 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#form11') 50.80/7.01 | ('#sk21' @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl110])). 50.80/7.01 thf(zip_derived_cl115, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( ('#form213' @ X2) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(zip_derived_cl116, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((((X2 @ Y0 @ Y1) & (X2 @ 50.80/7.01 ('#sk47' @ X2) @ Y0))) => 50.80/7.01 (X2 @ ('#sk47' @ X2) @ Y1))))))))) 50.80/7.01 | ('#form213' @ X2))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl115])). 50.80/7.01 thf(zip_derived_cl133, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((((X2 @ ('#sk74' @ X2) @ Y0) & (X2 @ 50.80/7.01 ('#sk47' @ X2) @ ('#sk74' @ X2)))) => 50.80/7.01 (X2 @ ('#sk47' @ X2) @ Y0)))))) 50.80/7.01 | ('#form213' @ X2))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl116])). 50.80/7.01 thf(zip_derived_cl148, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (((((X2 @ ('#sk74' @ X2) @ ('#sk113' @ X2)) & (X2 @ 50.80/7.01 ('#sk47' @ X2) @ ('#sk74' @ X2)))) => 50.80/7.01 (X2 @ ('#sk47' @ X2) @ ('#sk113' @ X2)))) 50.80/7.01 | ('#form213' @ X2))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl133])). 50.80/7.01 thf(zip_derived_cl157, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( (((X2 @ ('#sk74' @ X2) @ ('#sk113' @ X2)) & (X2 @ ('#sk47' @ X2) @ 50.80/7.01 ('#sk74' @ X2)))) 50.80/7.01 | ('#form213' @ X2))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl148])). 50.80/7.01 thf(zip_derived_cl165, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( (X2 @ ('#sk47' @ X2) @ ('#sk74' @ X2)) | ('#form213' @ X2))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl157])). 50.80/7.01 thf(zip_derived_cl34, plain, 50.80/7.01 ((~ ('#form11') 50.80/7.01 | (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y2 @ 50.80/7.01 Y3) & (Y0 @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk2' @ Y1 @ Y2) | 50.80/7.01 ('#sk1' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))))) => 50.80/7.01 (Y0 @ '#sk3' @ '#sk4')))))))), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(zip_derived_cl35, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( (((((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 (X2 @ Y0 @ Y1))))))))))) => 50.80/7.01 (X2 @ '#sk3' @ '#sk4'))) 50.80/7.01 | ~ ('#form11'))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 50.80/7.01 thf(zip_derived_cl36, plain, 50.80/7.01 (( (((((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk5' @ Y1 @ Y2) & 50.80/7.01 ('#sk5' @ Y0 @ Y1))) => 50.80/7.01 ('#sk5' @ Y0 @ Y2)))))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 ('#sk5' @ Y0 @ Y1))))))))))) => 50.80/7.01 ('#sk5' @ '#sk3' @ '#sk4'))) 50.80/7.01 | ~ ('#form11'))), 50.80/7.01 inference('triggered_bool_instantiation', [status(thm)], 50.80/7.01 [zip_derived_cl35])). 50.80/7.01 thf(zip_derived_cl5, plain, 50.80/7.01 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.80/7.01 (((((((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk1' @ Y1 @ Y2) | 50.80/7.01 ('#sk2' @ Y1 @ Y2))) => 50.80/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((!!) @ (^[Y3 : a]: 50.80/7.01 (((((Y0 @ Y1 @ 50.80/7.01 Y2) & (Y0 @ 50.80/7.01 Y2 @ Y3))) => 50.80/7.01 (Y0 @ Y1 @ Y3)))))))))))))) => 50.80/7.01 (Y0 @ '#sk3' @ '#sk4'))))))), 50.80/7.01 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 50.80/7.01 thf(zip_derived_cl7, plain, 50.80/7.01 (~ (((((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 ('#sk5' @ Y0 @ Y1))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk5' @ Y0 @ Y1) & 50.80/7.01 ('#sk5' @ Y1 @ Y2))) => 50.80/7.01 ('#sk5' @ Y0 @ Y2)))))))))))))) => 50.80/7.01 ('#sk5' @ '#sk3' @ '#sk4')))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl5])). 50.80/7.01 thf(zip_derived_cl10, plain, (~ ('#sk5' @ '#sk3' @ '#sk4')), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 50.80/7.01 thf(zip_derived_cl218, plain, 50.80/7.01 (( (((((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk5' @ Y1 @ Y2) & 50.80/7.01 ('#sk5' @ Y0 @ Y1))) => 50.80/7.01 ('#sk5' @ Y0 @ Y2)))))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 ('#sk5' @ Y0 @ Y1))))))))))) => 50.80/7.01 ($false))) 50.80/7.01 | ~ ('#form11'))), 50.80/7.01 inference('demod', [status(thm)], [zip_derived_cl36, zip_derived_cl10])). 50.80/7.01 thf(zip_derived_cl219, plain, 50.80/7.01 (( (((~) @ (((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk5' @ Y1 @ Y2) & 50.80/7.01 ('#sk5' @ Y0 @ Y1))) => 50.80/7.01 ('#sk5' @ Y0 @ Y2)))))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 ('#sk5' @ Y0 @ Y1))))))))))))) 50.80/7.01 | ~ ('#form11'))), 50.80/7.01 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl218])). 50.80/7.01 thf(zip_derived_cl220, plain, 50.80/7.01 ((~ (((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk5' @ Y1 @ Y2) & 50.80/7.01 ('#sk5' @ Y0 @ Y1))) => 50.80/7.01 ('#sk5' @ Y0 @ Y2)))))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 50.80/7.01 ('#sk5' @ Y0 @ Y1))))))))))) 50.80/7.01 | ~ ('#form11'))), 50.80/7.01 inference('simplify nested equalities', [status(thm)], 50.80/7.01 [zip_derived_cl219])). 50.80/7.01 thf(zip_derived_cl221, plain, 50.80/7.01 ((~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk5' @ Y1 @ Y2) & 50.80/7.01 ('#sk5' @ Y0 @ Y1))) => 50.80/7.01 ('#sk5' @ Y0 @ Y2)))))))))))) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 50.80/7.01 ('#sk5' @ Y0 @ Y1))))))))) 50.80/7.01 | ~ ('#form11'))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl220])). 50.80/7.01 thf(zip_derived_cl115, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( ('#form213' @ X2) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(zip_derived_cl222, plain, 50.80/7.01 ((~ ('#form213' @ '#sk5') 50.80/7.01 | ~ ('#form11') 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 50.80/7.01 ('#sk5' @ Y0 @ Y1))))))))))), 50.80/7.01 inference('renaming', [status(thm)], 50.80/7.01 [zip_derived_cl221, zip_derived_cl115])). 50.80/7.01 thf(zip_derived_cl35, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( (((((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 (X2 @ Y0 @ Y1))))))))))) => 50.80/7.01 (X2 @ '#sk3' @ '#sk4'))) 50.80/7.01 | ~ ('#form11'))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 50.80/7.01 thf(zip_derived_cl44, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 (X2 @ Y0 @ Y1))))))))))) 50.80/7.01 | (X2 @ '#sk3' @ '#sk4') 50.80/7.01 | ~ ('#form11'))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 50.80/7.01 thf(zip_derived_cl55, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.80/7.01 Y0 @ Y1))) => 50.80/7.01 (X2 @ Y0 @ Y2)))))))))))) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 (X2 @ Y0 @ Y1))))))))) 50.80/7.01 | ~ ('#form11') 50.80/7.01 | (X2 @ '#sk3' @ '#sk4'))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl44])). 50.80/7.01 thf(zip_derived_cl69, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((((X2 @ Y0 @ Y1) & (X2 @ 50.80/7.01 ('#sk47' @ X2) @ Y0))) => 50.80/7.01 (X2 @ ('#sk47' @ X2) @ Y1))))))))) 50.80/7.01 | (X2 @ '#sk3' @ '#sk4') 50.80/7.01 | ~ ('#form11') 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 (X2 @ Y0 @ Y1))))))))))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl55])). 50.80/7.01 thf(zip_derived_cl82, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((((X2 @ ('#sk74' @ X2) @ Y0) & (X2 @ 50.80/7.01 ('#sk47' @ X2) @ ('#sk74' @ X2)))) => 50.80/7.01 (X2 @ ('#sk47' @ X2) @ Y0)))))) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 (X2 @ Y0 @ Y1))))))))) 50.80/7.01 | ~ ('#form11') 50.80/7.01 | (X2 @ '#sk3' @ '#sk4'))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl69])). 50.80/7.01 thf(zip_derived_cl97, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (((((X2 @ ('#sk74' @ X2) @ ('#sk113' @ X2)) & (X2 @ 50.80/7.01 ('#sk47' @ X2) @ ('#sk74' @ X2)))) => 50.80/7.01 (X2 @ ('#sk47' @ X2) @ ('#sk113' @ X2)))) 50.80/7.01 | (X2 @ '#sk3' @ '#sk4') 50.80/7.01 | ~ ('#form11') 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 (X2 @ Y0 @ Y1))))))))))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl82])). 50.80/7.01 thf(zip_derived_cl107, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (X2 @ ('#sk47' @ X2) @ ('#sk113' @ X2)) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 (X2 @ Y0 @ Y1))))))))) 50.80/7.01 | ~ ('#form11') 50.80/7.01 | (X2 @ '#sk3' @ '#sk4'))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])). 50.80/7.01 thf(zip_derived_cl120, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( ('#form230' @ X2) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 (X2 @ Y0 @ Y1))))))))))), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(zip_derived_cl223, plain, 50.80/7.01 ((~ ('#form230' @ '#sk5') | ~ ('#form11') | ~ ('#form213' @ '#sk5'))), 50.80/7.01 inference('renaming', [status(thm)], 50.80/7.01 [zip_derived_cl222, zip_derived_cl120])). 50.80/7.01 thf(zip_derived_cl125, plain, 50.80/7.01 (![X2 : a, X4 : a]: 50.80/7.01 (~ ('#sk2' @ X2 @ X4) 50.80/7.01 | ~ ('#form9') 50.80/7.01 | ('#form11') 50.80/7.01 | ('#sk21' @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl110])). 50.80/7.01 thf(zip_derived_cl139, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (X2 @ ('#sk100' @ X2) @ ('#sk151' @ X2)) 50.80/7.01 | ('#form11') 50.80/7.01 | ~ ('#form9') 50.80/7.01 | (X2 @ '#sk6' @ '#sk7') 50.80/7.01 | ~ ('#form213' @ X2))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])). 50.80/7.01 thf(zip_derived_cl164, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( (X2 @ ('#sk74' @ X2) @ ('#sk113' @ X2)) | ('#form213' @ X2))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl157])). 50.80/7.01 thf(zip_derived_cl158, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (X2 @ ('#sk47' @ X2) @ ('#sk113' @ X2)) | ('#form213' @ X2))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl148])). 50.80/7.01 thf(zip_derived_cl120, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( ('#form230' @ X2) 50.80/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.80/7.01 Y1))) => 50.80/7.01 (X2 @ Y0 @ Y1))))))))))), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(zip_derived_cl121, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (((!!) @ (^[Y0 : a]: 50.80/7.01 ((((('#sk2' @ ('#sk231' @ X2) @ Y0) | ('#sk1' @ 50.80/7.01 ('#sk231' @ X2) @ Y0))) => 50.80/7.01 (X2 @ ('#sk231' @ X2) @ Y0)))))) 50.80/7.01 | ('#form230' @ X2))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl120])). 50.80/7.01 thf(zip_derived_cl136, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ ((((('#sk2' @ ('#sk231' @ X2) @ ('#sk318' @ X2)) | ('#sk1' @ 50.80/7.01 ('#sk231' @ X2) @ ('#sk318' @ X2)))) => 50.80/7.01 (X2 @ ('#sk231' @ X2) @ ('#sk318' @ X2)))) 50.80/7.01 | ('#form230' @ X2))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl121])). 50.80/7.01 thf(zip_derived_cl151, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( ((('#sk2' @ ('#sk231' @ X2) @ ('#sk318' @ X2)) | ('#sk1' @ 50.80/7.01 ('#sk231' @ X2) @ ('#sk318' @ X2)))) 50.80/7.01 | ('#form230' @ X2))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl136])). 50.80/7.01 thf(zip_derived_cl159, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 ( ('#sk2' @ ('#sk231' @ X2) @ ('#sk318' @ X2)) 50.80/7.01 | ('#sk1' @ ('#sk231' @ X2) @ ('#sk318' @ X2)) 50.80/7.01 | ('#form230' @ X2))), 50.80/7.01 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl151])). 50.80/7.01 thf(zip_derived_cl9, plain, 50.80/7.01 ( (((((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 50.80/7.01 ('#sk5' @ Y0 @ Y1))))))))) & 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk5' @ Y0 @ Y1) & 50.80/7.01 ('#sk5' @ Y1 @ Y2))) => 50.80/7.01 ('#sk5' @ Y0 @ Y2))))))))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 50.80/7.01 thf(zip_derived_cl13, plain, 50.80/7.01 ( (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 (((!!) @ (^[Y2 : a]: 50.80/7.01 ((((('#sk5' @ Y0 @ Y1) & ('#sk5' @ 50.80/7.01 Y1 @ Y2))) => 50.80/7.01 ('#sk5' @ Y0 @ Y2))))))))))))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl9])). 50.80/7.01 thf(zip_derived_cl16, plain, 50.80/7.01 (![X2 : a]: 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk5' @ X2 @ Y0) & ('#sk5' @ Y0 @ Y1))) => 50.80/7.01 ('#sk5' @ X2 @ Y1)))))))))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 50.80/7.01 thf(zip_derived_cl19, plain, 50.80/7.01 (![X2 : a, X4 : a]: 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 ((((('#sk5' @ X2 @ X4) & ('#sk5' @ X4 @ Y0))) => 50.80/7.01 ('#sk5' @ X2 @ Y0))))))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 50.80/7.01 thf(zip_derived_cl22, plain, 50.80/7.01 (![X2 : a, X4 : a, X6 : a]: 50.80/7.01 ((((('#sk5' @ X2 @ X4) & ('#sk5' @ X4 @ X6))) => ('#sk5' @ X2 @ X6)))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 50.80/7.01 thf(zip_derived_cl27, plain, 50.80/7.01 (![X2 : a, X4 : a, X6 : a]: 50.80/7.01 (~ ((('#sk5' @ X2 @ X4) & ('#sk5' @ X4 @ X6))) | ('#sk5' @ X2 @ X6))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 50.80/7.01 thf(zip_derived_cl33, plain, 50.80/7.01 (![X2 : a, X4 : a, X6 : a]: 50.80/7.01 (~ ('#sk5' @ X2 @ X4) | ~ ('#sk5' @ X4 @ X6) | ('#sk5' @ X2 @ X6))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl27])). 50.80/7.01 thf(zip_derived_cl12, plain, 50.80/7.01 ( (((!!) @ (^[Y0 : a]: 50.80/7.01 (((!!) @ (^[Y1 : a]: 50.80/7.01 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 50.80/7.01 ('#sk5' @ Y0 @ Y1)))))))))), 50.80/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl9])). 50.80/7.01 thf(zip_derived_cl15, plain, 50.80/7.01 (![X2 : a]: 50.80/7.01 (((!!) @ (^[Y0 : a]: 50.80/7.01 ((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) => 50.80/7.01 ('#sk5' @ X2 @ Y0))))))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])). 50.80/7.01 thf(zip_derived_cl18, plain, 50.80/7.01 (![X2 : a, X4 : a]: 50.80/7.01 ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) => ('#sk5' @ X2 @ X4)))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 50.80/7.01 thf(zip_derived_cl21, plain, 50.80/7.01 (![X2 : a, X4 : a]: 50.80/7.01 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) | ('#sk5' @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 50.80/7.01 thf(zip_derived_cl25, plain, 50.80/7.01 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl21])). 50.80/7.01 thf(zip_derived_cl26, plain, 50.80/7.01 (![X2 : a, X4 : a]: (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl21])). 50.80/7.01 thf(zip_derived_cl152, plain, 50.80/7.01 (![X2 : a > a > $o]: 50.80/7.01 (~ (X2 @ ('#sk231' @ X2) @ ('#sk318' @ X2)) | ('#form230' @ X2))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl136])). 50.80/7.01 thf(zip_derived_cl4247, plain, ($false), 50.80/7.01 inference('eprover', [status(thm)], 50.80/7.01 [zip_derived_cl174, zip_derived_cl80, zip_derived_cl170, 50.80/7.01 zip_derived_cl176, zip_derived_cl175, zip_derived_cl340, 50.80/7.01 zip_derived_cl341, zip_derived_cl145, zip_derived_cl177, 50.80/7.01 zip_derived_cl146, zip_derived_cl62, zip_derived_cl156, 50.80/7.01 zip_derived_cl140, zip_derived_cl147, zip_derived_cl132, 50.80/7.01 zip_derived_cl153, zip_derived_cl126, zip_derived_cl165, 50.80/7.01 zip_derived_cl223, zip_derived_cl125, zip_derived_cl139, 50.80/7.01 zip_derived_cl164, zip_derived_cl158, zip_derived_cl159, 50.80/7.01 zip_derived_cl33, zip_derived_cl25, zip_derived_cl26, 50.80/7.01 zip_derived_cl152])). 50.80/7.01 50.80/7.01 % SZS output end Refutation 50.80/7.01 50.80/7.01 50.80/7.01 % Terminating... 51.63/7.15 % Runner terminated. 51.63/7.17 % Zipperpin 1.5 exiting 51.63/7.18 EOF