0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Cu5Hn7y6BO true 0.14/0.34 % Computer : n022.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 1440 0.14/0.34 % WCLimit : 180 0.14/0.34 % DateTime : Thu Jul 4 06:48:09 EDT 2024 0.14/0.34 % CPUTime : 0.14/0.34 % Running portfolio for 1440 s 0.14/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.35 % Number of cores: 8 0.14/0.35 % Python version: Python 3.6.8 0.14/0.35 % Running in HO mode 0.56/0.66 % Total configuration time : 828 0.56/0.66 % Estimated wc time : 1656 0.56/0.66 % Estimated cpu time (8 cpus) : 207.0 0.57/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.57/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.57/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.57/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.57/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.57/0.77 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.57/0.77 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.57/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 50.75/7.03 % Solved by lams/20_acsne_simpl.sh. 50.75/7.03 % done 884 iterations in 6.097s 50.75/7.03 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 50.75/7.03 % SZS output start Refutation 50.75/7.03 thf(a_type, type, a: $tType). 50.75/7.03 thf('#sk4_type', type, '#sk4': a). 50.75/7.03 thf('#sk343_type', type, '#sk343': (a > a > $o) > a). 50.75/7.03 thf('#sk3_type', type, '#sk3': a). 50.75/7.03 thf('#sk582_type', type, '#sk582': (a > a > $o) > a). 50.75/7.03 thf('#form185_type', type, '#form185': (a > a > $o) > $o). 50.75/7.03 thf('#sk626_type', type, '#sk626': (a > a > $o) > a). 50.75/7.03 thf('#sk139_type', type, '#sk139': (a > a > $o) > a). 50.75/7.03 thf('#sk6_type', type, '#sk6': a). 50.75/7.03 thf('#sk20_type', type, '#sk20': a). 50.75/7.03 thf('#sk2_type', type, '#sk2': a > a > $o). 50.75/7.03 thf('#sk8_type', type, '#sk8': a > a > $o). 50.75/7.03 thf('#sk88_type', type, '#sk88': a > a > $o). 50.75/7.03 thf('#sk10_type', type, '#sk10': a). 50.75/7.03 thf('#sk87_type', type, '#sk87': (a > a > $o) > a). 50.75/7.03 thf('#sk7_type', type, '#sk7': a). 50.75/7.03 thf('#form19_type', type, '#form19': $o). 50.75/7.03 thf('#sk38_type', type, '#sk38': a). 50.75/7.03 thf('#form29_type', type, '#form29': $o). 50.75/7.03 thf('#sk186_type', type, '#sk186': (a > a > $o) > a). 50.75/7.03 thf('#form9_type', type, '#form9': $o). 50.75/7.03 thf('#sk105_type', type, '#sk105': (a > a > $o) > a). 50.75/7.03 thf('#form360_type', type, '#form360': (a > a > $o) > $o). 50.75/7.03 thf('#sk128_type', type, '#sk128': (a > a > $o) > a). 50.75/7.03 thf('#sk5_type', type, '#sk5': a > a > $o). 50.75/7.03 thf('#sk1_type', type, '#sk1': a > a > $o). 50.75/7.03 thf('#form581_type', type, '#form581': (a > a > $o) > $o). 50.75/7.03 thf('#sk441_type', type, '#sk441': (a > a > $o) > a). 50.75/7.03 thf('#sk247_type', type, '#sk247': (a > a > $o) > a). 50.75/7.03 thf('#sk361_type', type, '#sk361': (a > a > $o) > a). 50.75/7.03 thf('#sk119_type', type, '#sk119': (a > a > $o) > a). 50.75/7.03 thf('#sk258_type', type, '#sk258': (a > a > $o) > a). 50.75/7.03 thf('#sk199_type', type, '#sk199': (a > a > $o) > a). 50.75/7.03 thf(cTHM250D_pme, conjecture, 50.75/7.03 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 50.75/7.03 ( ( ( ( ![Xx0:a,Xy0:a]: 50.75/7.03 ( ( ( ![Xp1:( a > a > $o )]: 50.75/7.03 ( ( ( ![Xx1:a,Xy1:a]: 50.75/7.03 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) & 50.75/7.03 ( ![Xx1:a,Xy1:a,Xz:a]: 50.75/7.03 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 50.75/7.03 ( ![Xp1:( a > a > $o )]: 50.75/7.03 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 50.75/7.03 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xz ) ) ) & 50.75/7.03 ( ![Xx1:a,Xy1:a]: 50.75/7.03 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 50.75/7.03 ( ![Xp1:( a > a > $o )]: 50.75/7.03 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 50.75/7.03 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xz ) ) ) & 50.75/7.03 ( ![Xx1:a,Xy1:a]: 50.75/7.03 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) & 50.75/7.03 ( ![Xx0:a,Xy0:a,Xz:a]: 50.75/7.03 ( ( ( ![Xp1:( a > a > $o )]: 50.75/7.03 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 50.75/7.03 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 50.75/7.03 ( ![Xx1:a,Xy1:a]: 50.75/7.03 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.75/7.03 ( Xp1 @ Xy0 @ Xz ) ) ) & 50.75/7.03 ( ![Xp1:( a > a > $o )]: 50.75/7.03 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 50.75/7.03 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 50.75/7.03 ( ![Xx1:a,Xy1:a]: 50.75/7.03 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 50.75/7.03 ( ![Xp1:( a > a > $o )]: 50.75/7.03 ( ( ( ![Xx1:a,Xy1:a]: 50.75/7.03 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 50.75/7.03 ( ![Xx1:a,Xy1:a,Xz0:a]: 50.75/7.03 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) ) => 50.75/7.03 ( ![Xp1:( a > a > $o )]: 50.75/7.03 ( ( ( ![Xx0:a,Xy0:a]: 50.75/7.03 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 50.75/7.03 ( ![Xx0:a,Xy0:a,Xz:a]: 50.75/7.03 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 50.75/7.03 ( Xp1 @ Xx @ Xy ) ) ) ) => 50.75/7.03 ( ![Xp1:( a > a > $o )]: 50.75/7.03 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 50.75/7.03 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xz ) ) ) & 50.75/7.03 ( ![Xx0:a,Xy0:a]: 50.75/7.03 ( ( ( R @ Xx0 @ Xy0 ) | ( S @ Xx0 @ Xy0 ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 50.75/7.03 ( Xp1 @ Xx @ Xy ) ) ) ))). 50.75/7.03 thf(zf_stmt_0, negated_conjecture, 50.75/7.03 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 50.75/7.03 ( ( ( ( ![Xx0:a,Xy0:a]: 50.75/7.03 ( ( ( ![Xp1:( a > a > $o )]: 50.75/7.03 ( ( ( ![Xx1:a,Xy1:a]: 50.75/7.03 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) & 50.75/7.03 ( ![Xx1:a,Xy1:a,Xz:a]: 50.75/7.03 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 50.75/7.03 ( ![Xp1:( a > a > $o )]: 50.75/7.03 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 50.75/7.03 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xz ) ) ) & 50.75/7.03 ( ![Xx1:a,Xy1:a]: 50.75/7.03 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 50.75/7.03 ( ![Xp1:( a > a > $o )]: 50.75/7.03 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 50.75/7.03 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xz ) ) ) & 50.75/7.03 ( ![Xx1:a,Xy1:a]: 50.75/7.03 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) & 50.75/7.03 ( ![Xx0:a,Xy0:a,Xz:a]: 50.75/7.03 ( ( ( ![Xp1:( a > a > $o )]: 50.75/7.03 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 50.75/7.03 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 50.75/7.03 ( ![Xx1:a,Xy1:a]: 50.75/7.03 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.75/7.03 ( Xp1 @ Xy0 @ Xz ) ) ) & 50.75/7.03 ( ![Xp1:( a > a > $o )]: 50.75/7.03 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 50.75/7.03 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 50.75/7.03 ( ![Xx1:a,Xy1:a]: 50.75/7.03 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 50.75/7.03 ( ![Xp1:( a > a > $o )]: 50.75/7.03 ( ( ( ![Xx1:a,Xy1:a]: 50.75/7.03 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 50.75/7.03 ( ![Xx1:a,Xy1:a,Xz0:a]: 50.75/7.03 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 50.75/7.03 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) ) => 50.75/7.03 ( ![Xp1:( a > a > $o )]: 50.75/7.03 ( ( ( ![Xx0:a,Xy0:a]: 50.75/7.03 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 50.75/7.03 ( ![Xx0:a,Xy0:a,Xz:a]: 50.75/7.03 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 50.75/7.03 ( Xp1 @ Xx @ Xy ) ) ) ) => 50.75/7.03 ( ![Xp1:( a > a > $o )]: 50.75/7.03 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 50.75/7.03 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xz ) ) ) & 50.75/7.03 ( ![Xx0:a,Xy0:a]: 50.75/7.03 ( ( ( R @ Xx0 @ Xy0 ) | ( S @ Xx0 @ Xy0 ) ) => 50.75/7.03 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 50.75/7.03 ( Xp1 @ Xx @ Xy ) ) ) ) )), 50.75/7.03 inference('cnf.neg', [status(esa)], [cTHM250D_pme])). 50.75/7.03 thf(zip_derived_cl0, plain, 50.75/7.03 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((!!) @ (^[Y1 : a > a > $o]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (Y0 @ 50.75/7.03 Y7 @ 50.75/7.03 Y8) => 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ Y8))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y9 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y6 @ 50.75/7.03 Y8 @ 50.75/7.03 Y9) & 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ Y8))) => 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ Y9)))))))))))))) => 50.75/7.03 (Y6 @ 50.75/7.03 Y4 @ Y5)))))) | 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y9 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ 50.75/7.03 Y8) & 50.75/7.03 (Y6 @ 50.75/7.03 Y8 @ Y9))) => 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ Y9)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (Y1 @ 50.75/7.03 Y7 @ 50.75/7.03 Y8) => 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ Y8))))))))))) => 50.75/7.03 (Y6 @ 50.75/7.03 Y4 @ Y5)))))))) => 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y9 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y6 @ 50.75/7.03 Y8 @ 50.75/7.03 Y9) & 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ Y8))) => 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ Y9)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y1 @ 50.75/7.03 Y7 @ 50.75/7.03 Y8) | 50.75/7.03 (Y0 @ 50.75/7.03 Y7 @ Y8))) => 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ Y8))))))))))) => 50.75/7.03 (Y6 @ 50.75/7.03 Y4 @ Y5)))))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y9 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y10 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y7 @ 50.75/7.03 Y8 @ 50.75/7.03 Y9) & 50.75/7.03 (Y7 @ 50.75/7.03 Y9 @ Y10))) => 50.75/7.03 (Y7 @ 50.75/7.03 Y8 @ Y10)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y9 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y0 @ 50.75/7.03 Y8 @ 50.75/7.03 Y9) | 50.75/7.03 (Y1 @ 50.75/7.03 Y8 @ Y9))) => 50.75/7.03 (Y7 @ 50.75/7.03 Y8 @ Y9))))))))))) => 50.75/7.03 (Y7 @ 50.75/7.03 Y5 @ Y6)))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y9 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y10 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y7 @ 50.75/7.03 Y9 @ 50.75/7.03 Y10) & 50.75/7.03 (Y7 @ 50.75/7.03 Y8 @ Y9))) => 50.75/7.03 (Y7 @ 50.75/7.03 Y8 @ Y10)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y9 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y1 @ 50.75/7.03 Y8 @ 50.75/7.03 Y9) | 50.75/7.03 (Y0 @ 50.75/7.03 Y8 @ Y9))) => 50.75/7.03 (Y7 @ 50.75/7.03 Y8 @ Y9))))))))))) => 50.75/7.03 (Y7 @ 50.75/7.03 Y4 @ Y5)))))))) => 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y9 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y1 @ 50.75/7.03 Y8 @ 50.75/7.03 Y9) | 50.75/7.03 (Y0 @ 50.75/7.03 Y8 @ Y9))) => 50.75/7.03 (Y7 @ 50.75/7.03 Y8 @ Y9))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y9 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y10 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y7 @ 50.75/7.03 Y8 @ 50.75/7.03 Y9) & 50.75/7.03 (Y7 @ 50.75/7.03 Y9 @ Y10))) => 50.75/7.03 (Y7 @ 50.75/7.03 Y8 @ Y10)))))))))))))) => 50.75/7.03 (Y7 @ 50.75/7.03 Y4 @ Y6))))))))))))))))))) => 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a > a > $o]: 50.75/7.03 (((((( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y1 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) | 50.75/7.03 (Y0 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y6))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y4 @ 50.75/7.03 Y6 @ 50.75/7.03 Y7) & 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y7)))))))))))))) => 50.75/7.03 (Y4 @ Y2 @ 50.75/7.03 Y3)))))))) => 50.75/7.03 (((!!) @ (^[Y4 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y4 @ 50.75/7.03 Y6 @ Y7))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y7)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y0 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) | 50.75/7.03 (Y1 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y6))))))))))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y2 @ Y3))))))))))))))))))))), 50.75/7.03 inference('cnf', [status(esa)], [zf_stmt_0])). 50.75/7.03 thf(zip_derived_cl1, plain, 50.75/7.03 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (((( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y6 @ 50.75/7.03 Y7) => 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ Y7))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y5 @ 50.75/7.03 Y7 @ 50.75/7.03 Y8) & 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ Y7))) => 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ Y8)))))))))))))) => 50.75/7.03 (Y5 @ 50.75/7.03 Y3 @ Y4)))))) | 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ 50.75/7.03 Y7) & 50.75/7.03 (Y5 @ 50.75/7.03 Y7 @ Y8))) => 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ Y8)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (Y0 @ 50.75/7.03 Y6 @ 50.75/7.03 Y7) => 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ Y7))))))))))) => 50.75/7.03 (Y5 @ 50.75/7.03 Y3 @ Y4)))))))) => 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y5 @ 50.75/7.03 Y7 @ 50.75/7.03 Y8) & 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ Y7))) => 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ Y8)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y0 @ 50.75/7.03 Y6 @ 50.75/7.03 Y7) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y6 @ Y7))) => 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ Y7))))))))))) => 50.75/7.03 (Y5 @ 50.75/7.03 Y3 @ Y4)))))))))))))) & 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y9 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ 50.75/7.03 Y8) & 50.75/7.03 (Y6 @ 50.75/7.03 Y8 @ Y9))) => 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ Y9)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y7 @ 50.75/7.03 Y8) | 50.75/7.03 (Y0 @ 50.75/7.03 Y7 @ Y8))) => 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ Y8))))))))))) => 50.75/7.03 (Y6 @ 50.75/7.03 Y4 @ Y5)))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y9 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y6 @ 50.75/7.03 Y8 @ 50.75/7.03 Y9) & 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ Y8))) => 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ Y9)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y0 @ 50.75/7.03 Y7 @ 50.75/7.03 Y8) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y7 @ Y8))) => 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ Y8))))))))))) => 50.75/7.03 (Y6 @ 50.75/7.03 Y3 @ Y4)))))))) => 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y0 @ 50.75/7.03 Y7 @ 50.75/7.03 Y8) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y7 @ Y8))) => 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ Y8))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y9 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ 50.75/7.03 Y8) & 50.75/7.03 (Y6 @ 50.75/7.03 Y8 @ Y9))) => 50.75/7.03 (Y6 @ 50.75/7.03 Y7 @ Y9)))))))))))))) => 50.75/7.03 (Y6 @ 50.75/7.03 Y3 @ Y5))))))))))))))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y0 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y1 @ Y2)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 (Y0 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ Y2)))))))))))))))))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 50.75/7.03 thf(zip_derived_cl2, plain, 50.75/7.03 (~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((((((((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) => 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y6))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y4 @ 50.75/7.03 Y6 @ 50.75/7.03 Y7) & 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y7)))))))))))))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y2 @ Y3)))))) | 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y4 @ 50.75/7.03 Y6 @ Y7))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y7)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) => 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y6))))))))))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y2 @ Y3)))))))) => 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y4 @ 50.75/7.03 Y6 @ 50.75/7.03 Y7) & 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y7)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y6))))))))))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y2 @ Y3)))))))))))))) & 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (((( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ 50.75/7.03 Y7) & 50.75/7.03 (Y5 @ 50.75/7.03 Y7 @ Y8))) => 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ Y8)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y6 @ 50.75/7.03 Y7) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y6 @ Y7))) => 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ Y7))))))))))) => 50.75/7.03 (Y5 @ 50.75/7.03 Y3 @ Y4)))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y5 @ 50.75/7.03 Y7 @ 50.75/7.03 Y8) & 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ Y7))) => 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ Y8)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y6 @ 50.75/7.03 Y7) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y6 @ Y7))) => 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ Y7))))))))))) => 50.75/7.03 (Y5 @ 50.75/7.03 Y2 @ Y3)))))))) => 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y6 @ 50.75/7.03 Y7) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y6 @ Y7))) => 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ Y7))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y8 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ 50.75/7.03 Y7) & 50.75/7.03 (Y5 @ 50.75/7.03 Y7 @ Y8))) => 50.75/7.03 (Y5 @ 50.75/7.03 Y6 @ Y8)))))))))))))) => 50.75/7.03 (Y5 @ 50.75/7.03 Y2 @ Y4))))))))))))))))))) => 50.75/7.03 (((!!) @ (^[Y2 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))))))))) & 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y2 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y5)))))))))))))) => 50.75/7.03 (Y2 @ Y0 @ Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y2 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) & 50.75/7.03 (Y2 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y5)))))))))))) & 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (((( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y3 @ Y4) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))))))))))) => 50.75/7.03 (Y2 @ Y0 @ Y1))))))))))))))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 50.75/7.03 thf(zip_derived_cl3, plain, 50.75/7.03 (~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : 50.75/7.03 a > a > $o]: 50.75/7.03 (((( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y1 @ Y2)))))) | 50.75/7.03 (((!!) @ (^[Y3 : 50.75/7.03 a > a > $o]: 50.75/7.03 (((( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y1 @ Y2)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y4 @ 50.75/7.03 Y6 @ Y7))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y7)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y6))))))))))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y2 @ Y3)))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y4 @ 50.75/7.03 Y6 @ 50.75/7.03 Y7) & 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y7)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y6))))))))))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y1 @ Y2)))))))) => 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : 50.75/7.03 a > a > $o]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y6))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y7 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y4 @ 50.75/7.03 Y6 @ Y7))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y5 @ Y7)))))))))))))) => 50.75/7.03 (Y4 @ 50.75/7.03 Y1 @ Y3))))))))))))))))))) => 50.75/7.03 (((!!) @ (^[Y1 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 ((((('#sk2' @ 50.75/7.03 Y2 @ Y3) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y1 @ Y2 @ 50.75/7.03 Y3))))))))) & 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y1 @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) & 50.75/7.03 (Y1 @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y1 @ 50.75/7.03 Y2 @ Y4)))))))))))))) => 50.75/7.03 (Y1 @ '#sk3' @ Y0)))))))) => 50.75/7.03 (((!!) @ (^[Y1 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (((( 50.75/7.03 (Y1 @ 50.75/7.03 Y2 @ Y3) & 50.75/7.03 (Y1 @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y1 @ 50.75/7.03 Y2 @ Y4)))))))))))) & 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 ((((('#sk1' @ 50.75/7.03 Y2 @ Y3) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y1 @ Y2 @ Y3))))))))))) => 50.75/7.03 (Y1 @ '#sk3' @ Y0)))))))))))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 50.75/7.03 thf(zip_derived_cl4, plain, 50.75/7.03 (~ (((((((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((((((!!) @ (^[Y2 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y3 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))))))))) & 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y2 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y5)))))))))))))) => 50.75/7.03 (Y2 @ Y0 @ Y1)))))) | 50.75/7.03 (((!!) @ (^[Y2 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y3 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) & 50.75/7.03 (Y2 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y5)))))))))))) & 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))))))))))) => 50.75/7.03 (Y2 @ Y0 @ Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y2 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y3 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y2 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y5)))))))))))) & 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))))))))))) => 50.75/7.03 (Y2 @ Y0 @ Y1)))))))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : 50.75/7.03 a > a > $o]: 50.75/7.03 (((( 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 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@ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y2))))))))))))))))))) => 50.75/7.03 (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ 50.75/7.03 Y2 @ Y3) & 50.75/7.03 (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ 50.75/7.03 Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4')))))))) => 50.75/7.03 (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y1 @ 50.75/7.03 Y2) & (Y0 @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk1' @ Y1 @ Y2) | 50.75/7.03 ('#sk2' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4'))))))))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 50.75/7.03 thf(zip_derived_cl5, plain, 50.75/7.03 ( (((((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((((((!!) @ (^[Y2 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))))))))) & 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y2 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y5)))))))))))))) => 50.75/7.03 (Y2 @ Y0 @ Y1)))))) | 50.75/7.03 (((!!) @ (^[Y2 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) & 50.75/7.03 (Y2 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y5)))))))))))) & 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))))))))))) => 50.75/7.03 (Y2 @ Y0 @ Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y2 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y2 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y5)))))))))))) & 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))))))))))) => 50.75/7.03 (Y2 @ Y0 @ Y1)))))))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ Y2))))))))))))))))))) => 50.75/7.03 (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4'))))))))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 50.75/7.03 thf(zip_derived_cl7, plain, 50.75/7.03 ((~ (((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((((((!!) @ (^[Y2 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))))))))) & 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y2 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y5)))))))))))))) => 50.75/7.03 (Y2 @ Y0 @ Y1)))))) | 50.75/7.03 (((!!) @ (^[Y2 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) & 50.75/7.03 (Y2 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y5)))))))))))) & 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))))))))))) => 50.75/7.03 (Y2 @ Y0 @ Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y2 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y2 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 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50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ Y2))))))))))))))))))) 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4')))))))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 50.75/7.03 thf(zip_derived_cl9, plain, 50.75/7.03 ((~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((((((!!) @ (^[Y2 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))))))))) & 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y2 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y5)))))))))))))) => 50.75/7.03 (Y2 @ Y0 @ Y1)))))) | 50.75/7.03 (((!!) @ (^[Y2 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) & 50.75/7.03 (Y2 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y5)))))))))))) & 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))))))))))) => 50.75/7.03 (Y2 @ Y0 @ Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y2 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y2 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y5)))))))))))) & 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (((( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))))))))))) => 50.75/7.03 (Y2 @ Y0 @ Y1)))))))))))))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ Y2))))))))))))))))) 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4')))))))), 50.75/7.03 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl7])). 50.75/7.03 thf(zip_derived_cl12, plain, 50.75/7.03 ((~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((((((!!) @ (^[Y1 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 ((('#sk1' @ 50.75/7.03 Y2 @ Y3) => 50.75/7.03 (Y1 @ Y2 @ 50.75/7.03 Y3))))))))) & 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (( 50.75/7.03 (Y1 @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) & 50.75/7.03 (Y1 @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y1 @ 50.75/7.03 Y2 @ Y4)))))))))))))) => 50.75/7.03 (Y1 @ '#sk6' @ Y0)))))) | 50.75/7.03 (((!!) @ (^[Y1 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (( 50.75/7.03 (Y1 @ 50.75/7.03 Y2 @ 50.75/7.03 Y3) & 50.75/7.03 (Y1 @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y1 @ 50.75/7.03 Y2 @ Y4)))))))))))) & 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 ((('#sk2' @ 50.75/7.03 Y2 @ Y3) => 50.75/7.03 (Y1 @ Y2 @ 50.75/7.03 Y3))))))))))) => 50.75/7.03 (Y1 @ '#sk6' @ Y0)))))))) => 50.75/7.03 (((!!) @ (^[Y1 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (((( 50.75/7.03 (Y1 @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) & 50.75/7.03 (Y1 @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y1 @ 50.75/7.03 Y2 @ Y4)))))))))))) & 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 ((((('#sk2' @ 50.75/7.03 Y2 @ Y3) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y1 @ Y2 @ 50.75/7.03 Y3))))))))))) => 50.75/7.03 (Y1 @ '#sk6' @ Y0))))))))))) 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4')))))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ Y2))))))))))))))))))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl9])). 50.75/7.03 thf(zip_derived_cl15, plain, 50.75/7.03 ((~ (((((((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((('#sk1' @ Y1 @ Y2) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ 50.75/7.03 Y2 @ 50.75/7.03 Y3) & 50.75/7.03 (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ 50.75/7.03 Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk6' @ '#sk7')))))) | 50.75/7.03 (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ 50.75/7.03 Y1 @ 50.75/7.03 Y2) & 50.75/7.03 (Y0 @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y0 @ Y1 @ 50.75/7.03 Y3)))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((('#sk2' @ Y1 @ Y2) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.03 (Y0 @ '#sk6' @ '#sk7')))))))) => 50.75/7.03 (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & 50.75/7.03 (Y0 @ Y1 @ 50.75/7.03 Y2))) => 50.75/7.03 (Y0 @ Y1 @ 50.75/7.03 Y3)))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.03 (Y0 @ '#sk6' @ '#sk7')))))))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ Y2))))))))))))))))) 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4')))))))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 50.75/7.03 thf(zip_derived_cl19, plain, 50.75/7.03 ((~ (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.03 (Y0 @ '#sk6' @ '#sk7')))))) 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4')))))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ Y2))))))))))))))))))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 50.75/7.03 thf(zip_derived_cl23, plain, 50.75/7.03 ((~ (((((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk8' @ Y1 @ Y2) & 50.75/7.03 ('#sk8' @ Y0 @ Y1))) => 50.75/7.03 ('#sk8' @ Y0 @ Y2)))))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 ('#sk8' @ Y0 @ Y1))))))))))) => 50.75/7.03 ('#sk8' @ '#sk6' @ '#sk7'))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ Y2))))))))))))))))) 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4')))))))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 50.75/7.03 thf(zip_derived_cl31, plain, 50.75/7.03 (( ('#form9') 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ Y2))))))))))))))))))), 50.75/7.03 define([status(thm)])). 50.75/7.03 thf(zip_derived_cl32, plain, 50.75/7.03 ((~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((((((!!) @ (^[Y2 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) & 50.75/7.03 (Y2 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y5)))))))))))) & 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))))))))))) => 50.75/7.03 (Y2 @ Y0 @ Y1)))))) & 50.75/7.03 (((!!) @ (^[Y2 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y2 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y5)))))))))))) & 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))))))))))) => 50.75/7.03 (Y2 @ '#sk10' @ Y0)))))))) => 50.75/7.03 (((!!) @ (^[Y2 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (((( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y4))))))))) & 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) & 50.75/7.03 (Y2 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y2 @ 50.75/7.03 Y3 @ Y5)))))))))))))) => 50.75/7.03 (Y2 @ '#sk10' @ Y1)))))))))))))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl31])). 50.75/7.03 thf(zip_derived_cl45, plain, 50.75/7.03 ((~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((((((!!) @ (^[Y1 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (( 50.75/7.03 (Y1 @ 50.75/7.03 Y2 @ 50.75/7.03 Y3) & 50.75/7.03 (Y1 @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y1 @ 50.75/7.03 Y2 @ Y4)))))))))))) & 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 ((((('#sk1' @ 50.75/7.03 Y2 @ 50.75/7.03 Y3) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y1 @ Y2 @ 50.75/7.03 Y3))))))))))) => 50.75/7.03 (Y1 @ '#sk20' @ Y0)))))) & 50.75/7.03 (((!!) @ (^[Y1 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (( 50.75/7.03 (Y1 @ 50.75/7.03 Y3 @ 50.75/7.03 Y4) & 50.75/7.03 (Y1 @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y1 @ 50.75/7.03 Y2 @ Y4)))))))))))) & 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 ((((('#sk2' @ 50.75/7.03 Y2 @ 50.75/7.03 Y3) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y1 @ Y2 @ 50.75/7.03 Y3))))))))))) => 50.75/7.03 (Y1 @ '#sk10' @ '#sk20')))))))) => 50.75/7.03 (((!!) @ (^[Y1 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 ((((('#sk2' @ 50.75/7.03 Y2 @ Y3) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y1 @ Y2 @ 50.75/7.03 Y3))))))))) & 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (((( 50.75/7.03 (Y1 @ 50.75/7.03 Y2 @ 50.75/7.03 Y3) & 50.75/7.03 (Y1 @ 50.75/7.03 Y3 @ Y4))) => 50.75/7.03 (Y1 @ 50.75/7.03 Y2 @ Y4)))))))))))))) => 50.75/7.03 (Y1 @ '#sk10' @ Y0))))))))))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl32])). 50.75/7.03 thf(zip_derived_cl57, plain, 50.75/7.03 ((~ (((((((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ 50.75/7.03 Y1 @ 50.75/7.03 Y2) & 50.75/7.03 (Y0 @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y0 @ Y1 @ 50.75/7.03 Y3)))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk1' @ Y1 @ Y2) | 50.75/7.03 ('#sk2' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.03 (Y0 @ '#sk20' @ '#sk38')))))) & 50.75/7.03 (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ 50.75/7.03 Y2 @ 50.75/7.03 Y3) & 50.75/7.03 (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ 50.75/7.03 Y3)))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.03 (Y0 @ '#sk10' @ '#sk20')))))))) => 50.75/7.03 (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y1 @ 50.75/7.03 Y2) & 50.75/7.03 (Y0 @ Y2 @ 50.75/7.03 Y3))) => 50.75/7.03 (Y0 @ Y1 @ 50.75/7.03 Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk10' @ '#sk38')))))))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl45])). 50.75/7.03 thf(zip_derived_cl64, plain, 50.75/7.03 ((~ (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y1 @ 50.75/7.03 Y2) & (Y0 @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk10' @ '#sk38')))))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 50.75/7.03 thf(zip_derived_cl75, plain, 50.75/7.03 ((~ (((((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 ('#sk88' @ Y0 @ Y1))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk88' @ Y0 @ Y1) & 50.75/7.03 ('#sk88' @ Y1 @ Y2))) => 50.75/7.03 ('#sk88' @ Y0 @ Y2)))))))))))))) => 50.75/7.03 ('#sk88' @ '#sk10' @ '#sk38'))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl64])). 50.75/7.03 thf(zip_derived_cl94, plain, 50.75/7.03 ((~ ('#sk88' @ '#sk10' @ '#sk38') | ('#form9'))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 50.75/7.03 thf(zip_derived_cl63, plain, 50.75/7.03 (( (((((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y1 @ 50.75/7.03 Y2) & (Y0 @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk1' @ Y1 @ Y2) | 50.75/7.03 ('#sk2' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.03 (Y0 @ '#sk20' @ '#sk38')))))) & 50.75/7.03 (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.03 (Y0 @ '#sk10' @ '#sk20')))))))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 50.75/7.03 thf(zip_derived_cl71, plain, 50.75/7.03 (( (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.03 (Y0 @ '#sk10' @ '#sk20')))))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl63])). 50.75/7.03 thf(zip_derived_cl87, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( (((((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((X2 @ Y1 @ Y2) & (X2 @ 50.75/7.03 Y0 @ Y1))) => 50.75/7.03 (X2 @ Y0 @ Y2)))))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))))) => 50.75/7.03 (X2 @ '#sk10' @ '#sk20'))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl71])). 50.75/7.03 thf(zip_derived_cl102, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ (((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((X2 @ Y1 @ Y2) & (X2 @ 50.75/7.03 Y0 @ Y1))) => 50.75/7.03 (X2 @ Y0 @ Y2)))))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))))) 50.75/7.03 | (X2 @ '#sk10' @ '#sk20') 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl87])). 50.75/7.03 thf(zip_derived_cl115, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((X2 @ Y1 @ Y2) & (X2 @ 50.75/7.03 Y0 @ Y1))) => 50.75/7.03 (X2 @ Y0 @ Y2)))))))))))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))) 50.75/7.03 | ('#form9') 50.75/7.03 | (X2 @ '#sk10' @ '#sk20'))), 50.75/7.03 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl102])). 50.75/7.03 thf(zip_derived_cl18, plain, 50.75/7.03 (( (((((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((('#sk1' @ Y1 @ Y2) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk6' @ '#sk7')))))) | 50.75/7.03 (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y1 @ 50.75/7.03 Y2) & (Y0 @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((('#sk2' @ Y1 @ Y2) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.03 (Y0 @ '#sk6' @ '#sk7')))))))) 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4')))))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ Y2))))))))))))))))))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 50.75/7.03 thf(zip_derived_cl22, plain, 50.75/7.03 (( (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 50.75/7.03 Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk6' @ '#sk7')))))) 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y1 @ 50.75/7.03 Y2) & (Y0 @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((('#sk2' @ Y1 @ Y2) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.03 (Y0 @ '#sk6' @ '#sk7')))))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ Y2))))))))))))))))) 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4')))))))), 50.75/7.03 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl18])). 50.75/7.03 thf(zip_derived_cl26, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( (((((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((X2 @ Y1 @ Y2) & (X2 @ 50.75/7.03 Y0 @ Y1))) => 50.75/7.03 (X2 @ Y0 @ Y2)))))))))))))) => 50.75/7.03 (X2 @ '#sk6' @ '#sk7'))) 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ 50.75/7.03 Y2 @ Y3) & 50.75/7.03 (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ 50.75/7.03 Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4')))))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : 50.75/7.03 a > a > $o]: 50.75/7.03 (((((( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : 50.75/7.03 a > a > $o]: 50.75/7.03 (((((( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y2))))))))))))))))) 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ 50.75/7.03 Y1 @ Y2) & 50.75/7.03 (Y0 @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y0 @ Y1 @ 50.75/7.03 Y3)))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((('#sk2' @ Y1 @ Y2) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.03 (Y0 @ '#sk6' @ '#sk7')))))))), 50.75/7.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 50.75/7.03 thf(zip_derived_cl26, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( (((((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((X2 @ Y1 @ Y2) & (X2 @ 50.75/7.03 Y0 @ Y1))) => 50.75/7.03 (X2 @ Y0 @ Y2)))))))))))))) => 50.75/7.03 (X2 @ '#sk6' @ '#sk7'))) 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ 50.75/7.03 Y2 @ Y3) & 50.75/7.03 (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ 50.75/7.03 Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4')))))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : 50.75/7.03 a > a > $o]: 50.75/7.03 (((((( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : 50.75/7.03 a > a > $o]: 50.75/7.03 (((((( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y2))))))))))))))))) 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ 50.75/7.03 Y1 @ Y2) & 50.75/7.03 (Y0 @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y0 @ Y1 @ 50.75/7.03 Y3)))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((('#sk2' @ Y1 @ Y2) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.03 (Y0 @ '#sk6' @ '#sk7')))))))), 50.75/7.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 50.75/7.03 thf(zip_derived_cl37, plain, 50.75/7.03 ((~ ('#form19') 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4')))))))), 50.75/7.03 define([status(thm)])). 50.75/7.03 thf(zip_derived_cl43, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( ('#form19') 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ 50.75/7.03 Y1 @ Y2) & 50.75/7.03 (Y0 @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y0 @ Y1 @ 50.75/7.03 Y3)))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((('#sk2' @ Y1 @ Y2) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.03 (Y0 @ '#sk6' @ '#sk7')))))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : 50.75/7.03 a > a > $o]: 50.75/7.03 (((((( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : 50.75/7.03 a > a > $o]: 50.75/7.03 (((((( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y2))))))))))))))))) 50.75/7.03 | (((((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((X2 @ Y1 @ Y2) & 50.75/7.03 (X2 @ Y0 @ Y1))) => 50.75/7.03 (X2 @ Y0 @ Y2)))))))))))))) => 50.75/7.03 (X2 @ '#sk6' @ '#sk7'))))), 50.75/7.03 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl37])). 50.75/7.03 thf(zip_derived_cl43, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( ('#form19') 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ 50.75/7.03 Y1 @ Y2) & 50.75/7.03 (Y0 @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y0 @ Y1 @ 50.75/7.03 Y3)))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((('#sk2' @ Y1 @ Y2) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.03 (Y0 @ '#sk6' @ '#sk7')))))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : 50.75/7.03 a > a > $o]: 50.75/7.03 (((((( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : 50.75/7.03 a > a > $o]: 50.75/7.03 (((((( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y2))))))))))))))))) 50.75/7.03 | (((((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((X2 @ Y1 @ Y2) & 50.75/7.03 (X2 @ Y0 @ Y1))) => 50.75/7.03 (X2 @ Y0 @ Y2)))))))))))))) => 50.75/7.03 (X2 @ '#sk6' @ '#sk7'))))), 50.75/7.03 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl37])). 50.75/7.03 thf(zip_derived_cl47, plain, 50.75/7.03 ((~ ('#form29') 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y1 @ 50.75/7.03 Y2) & (Y0 @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((('#sk2' @ Y1 @ Y2) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.03 (Y0 @ '#sk6' @ '#sk7')))))))), 50.75/7.03 define([status(thm)])). 50.75/7.03 thf(zip_derived_cl53, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( ('#form29') 50.75/7.03 | (((((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((X2 @ Y1 @ Y2) & 50.75/7.03 (X2 @ Y0 @ Y1))) => 50.75/7.03 (X2 @ Y0 @ Y2)))))))))))))) => 50.75/7.03 (X2 @ '#sk6' @ '#sk7'))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : 50.75/7.03 a > a > $o]: 50.75/7.03 (((((( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : 50.75/7.03 a > a > $o]: 50.75/7.03 (((((( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y2))))))))))))))))) 50.75/7.03 | ('#form19'))), 50.75/7.03 inference('renaming', [status(thm)], [zip_derived_cl43, zip_derived_cl47])). 50.75/7.03 thf(zip_derived_cl31, plain, 50.75/7.03 (( ('#form9') 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ Y2))))))))))))))))))), 50.75/7.03 define([status(thm)])). 50.75/7.03 thf(zip_derived_cl58, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ ('#form9') 50.75/7.03 | ('#form19') 50.75/7.03 | (((((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((X2 @ Y1 @ Y2) & 50.75/7.03 (X2 @ Y0 @ Y1))) => 50.75/7.03 (X2 @ Y0 @ Y2)))))))))))))) => 50.75/7.03 (X2 @ '#sk6' @ '#sk7'))) 50.75/7.03 | ('#form29'))), 50.75/7.03 inference('renaming', [status(thm)], [zip_derived_cl53, zip_derived_cl31])). 50.75/7.03 thf(zip_derived_cl65, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ (((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((X2 @ Y1 @ Y2) & (X2 @ 50.75/7.03 Y0 @ Y1))) => 50.75/7.03 (X2 @ Y0 @ Y2)))))))))))))) 50.75/7.03 | (X2 @ '#sk6' @ '#sk7') 50.75/7.03 | ('#form29') 50.75/7.03 | ('#form19') 50.75/7.03 | ~ ('#form9'))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 50.75/7.03 thf(zip_derived_cl76, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((X2 @ Y1 @ Y2) & (X2 @ 50.75/7.03 Y0 @ Y1))) => 50.75/7.03 (X2 @ Y0 @ Y2)))))))))))) 50.75/7.03 | ~ ('#form9') 50.75/7.03 | ('#form19') 50.75/7.03 | ('#form29') 50.75/7.03 | (X2 @ '#sk6' @ '#sk7'))), 50.75/7.03 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl65])). 50.75/7.03 thf(zip_derived_cl95, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ (((!!) @ (^[Y0 : a]: 50.75/7.03 ((('#sk1' @ ('#sk128' @ X2) @ Y0) => (X2 @ 50.75/7.03 ('#sk128' @ X2) @ Y0)))))) 50.75/7.03 | (X2 @ '#sk6' @ '#sk7') 50.75/7.03 | ('#form29') 50.75/7.03 | ('#form19') 50.75/7.03 | ~ ('#form9') 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((X2 @ Y1 @ Y2) & (X2 @ 50.75/7.03 Y0 @ Y1))) => 50.75/7.03 (X2 @ Y0 @ Y2)))))))))))))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl76])). 50.75/7.03 thf(zip_derived_cl105, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( ('#form185' @ X2) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((X2 @ Y1 @ Y2) & (X2 @ 50.75/7.03 Y0 @ Y1))) => 50.75/7.03 (X2 @ Y0 @ Y2)))))))))))))), 50.75/7.03 define([status(thm)])). 50.75/7.03 thf(zip_derived_cl127, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ ('#form185' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 50.75/7.03 | (X2 @ '#sk10' @ '#sk20') 50.75/7.03 | ('#form9') 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))))), 50.75/7.03 inference('renaming', [status(thm)], 50.75/7.03 [zip_derived_cl115, zip_derived_cl105])). 50.75/7.03 thf(zip_derived_cl139, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ ('#form185' @ X2) 50.75/7.03 | (X2 @ '#sk10' @ '#sk20') 50.75/7.03 | ('#form9') 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))))), 50.75/7.03 inference('ho_norm', [status(thm)], [zip_derived_cl127])). 50.75/7.03 thf(zip_derived_cl140, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ (((!!) @ (^[Y0 : a]: 50.75/7.03 ((((('#sk2' @ ('#sk87' @ X2) @ Y0) | ('#sk1' @ 50.75/7.03 ('#sk87' @ X2) @ Y0))) => 50.75/7.03 (X2 @ ('#sk87' @ X2) @ Y0)))))) 50.75/7.03 | ('#form9') 50.75/7.03 | (X2 @ '#sk10' @ '#sk20') 50.75/7.03 | ~ ('#form185' @ X2))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl139])). 50.75/7.03 thf(zip_derived_cl149, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ ((((('#sk2' @ ('#sk87' @ X2) @ ('#sk119' @ X2)) | ('#sk1' @ 50.75/7.03 ('#sk87' @ X2) @ ('#sk119' @ X2)))) => 50.75/7.03 (X2 @ ('#sk87' @ X2) @ ('#sk119' @ X2)))) 50.75/7.03 | ~ ('#form185' @ X2) 50.75/7.03 | (X2 @ '#sk10' @ '#sk20') 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl140])). 50.75/7.03 thf(zip_derived_cl161, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( ((('#sk2' @ ('#sk87' @ X2) @ ('#sk119' @ X2)) | ('#sk1' @ 50.75/7.03 ('#sk87' @ X2) @ ('#sk119' @ X2)))) 50.75/7.03 | ('#form9') 50.75/7.03 | (X2 @ '#sk10' @ '#sk20') 50.75/7.03 | ~ ('#form185' @ X2))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl149])). 50.75/7.03 thf(zip_derived_cl169, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( ('#sk2' @ ('#sk87' @ X2) @ ('#sk119' @ X2)) 50.75/7.03 | ('#sk1' @ ('#sk87' @ X2) @ ('#sk119' @ X2)) 50.75/7.03 | ~ ('#form185' @ X2) 50.75/7.03 | (X2 @ '#sk10' @ '#sk20') 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl161])). 50.75/7.03 thf(zip_derived_cl70, plain, 50.75/7.03 (( (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y1 @ 50.75/7.03 Y2) & (Y0 @ 50.75/7.03 Y2 @ Y3))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk1' @ Y1 @ Y2) | 50.75/7.03 ('#sk2' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.03 (Y0 @ '#sk20' @ '#sk38')))))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl63])). 50.75/7.03 thf(zip_derived_cl81, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( (((((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((X2 @ Y0 @ Y1) & (X2 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (X2 @ Y0 @ Y2)))))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))))) => 50.75/7.03 (X2 @ '#sk20' @ '#sk38'))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl70])). 50.75/7.03 thf(zip_derived_cl101, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ (((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((X2 @ Y0 @ Y1) & (X2 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (X2 @ Y0 @ Y2)))))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))))) 50.75/7.03 | (X2 @ '#sk20' @ '#sk38') 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 50.75/7.03 thf(zip_derived_cl114, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((X2 @ Y0 @ Y1) & (X2 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (X2 @ Y0 @ Y2)))))))))))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))) 50.75/7.03 | ('#form9') 50.75/7.03 | (X2 @ '#sk20' @ '#sk38'))), 50.75/7.03 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl101])). 50.75/7.03 thf(zip_derived_cl126, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((((X2 @ ('#sk105' @ X2) @ Y0) & (X2 @ 50.75/7.03 Y0 @ Y1))) => 50.75/7.03 (X2 @ ('#sk105' @ X2) @ Y1))))))))) 50.75/7.03 | (X2 @ '#sk20' @ '#sk38') 50.75/7.03 | ('#form9') 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl114])). 50.75/7.03 thf(zip_derived_cl138, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((((X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) & (X2 @ 50.75/7.03 ('#sk139' @ X2) @ Y0))) => 50.75/7.03 (X2 @ ('#sk105' @ X2) @ Y0)))))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))) 50.75/7.03 | ('#form9') 50.75/7.03 | (X2 @ '#sk20' @ '#sk38'))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl126])). 50.75/7.03 thf(zip_derived_cl148, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ (((((X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) & (X2 @ 50.75/7.03 ('#sk139' @ X2) @ ('#sk199' @ X2)))) => 50.75/7.03 (X2 @ ('#sk105' @ X2) @ ('#sk199' @ X2)))) 50.75/7.03 | (X2 @ '#sk20' @ '#sk38') 50.75/7.03 | ('#form9') 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl138])). 50.75/7.03 thf(zip_derived_cl159, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( (((X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) & (X2 @ 50.75/7.03 ('#sk139' @ X2) @ ('#sk199' @ X2)))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))) 50.75/7.03 | ('#form9') 50.75/7.03 | (X2 @ '#sk20' @ '#sk38'))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl148])). 50.75/7.03 thf(zip_derived_cl164, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( (X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) 50.75/7.03 | (X2 @ '#sk20' @ '#sk38') 50.75/7.03 | ('#form9') 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))))), 50.75/7.03 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl159])). 50.75/7.03 thf(zip_derived_cl160, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ (X2 @ ('#sk105' @ X2) @ ('#sk199' @ X2)) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))) 50.75/7.03 | ('#form9') 50.75/7.03 | (X2 @ '#sk20' @ '#sk38'))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl148])). 50.75/7.03 thf(zip_derived_cl166, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( ('#form581' @ X2) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))))), 50.75/7.03 define([status(thm)])). 50.75/7.03 thf(zip_derived_cl170, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ ('#form581' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 50.75/7.03 | ('#form9') 50.75/7.03 | (X2 @ '#sk20' @ '#sk38') 50.75/7.03 | (X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)))), 50.75/7.03 inference('renaming', [status(thm)], 50.75/7.03 [zip_derived_cl164, zip_derived_cl166])). 50.75/7.03 thf(zip_derived_cl173, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ ('#form581' @ X2) 50.75/7.03 | ('#form9') 50.75/7.03 | (X2 @ '#sk20' @ '#sk38') 50.75/7.03 | (X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)))), 50.75/7.03 inference('ho_norm', [status(thm)], [zip_derived_cl170])). 50.75/7.03 thf(zip_derived_cl162, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ (X2 @ ('#sk87' @ X2) @ ('#sk119' @ X2)) 50.75/7.03 | ('#form9') 50.75/7.03 | (X2 @ '#sk10' @ '#sk20') 50.75/7.03 | ~ ('#form185' @ X2))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl149])). 50.75/7.03 thf(zip_derived_cl166, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( ('#form581' @ X2) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))))), 50.75/7.03 define([status(thm)])). 50.75/7.03 thf(zip_derived_cl167, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ (((!!) @ (^[Y0 : a]: 50.75/7.03 ((((('#sk1' @ ('#sk582' @ X2) @ Y0) | ('#sk2' @ 50.75/7.03 ('#sk582' @ X2) @ Y0))) => 50.75/7.03 (X2 @ ('#sk582' @ X2) @ Y0)))))) 50.75/7.03 | ('#form581' @ X2))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl166])). 50.75/7.03 thf(zip_derived_cl172, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ ((((('#sk1' @ ('#sk582' @ X2) @ ('#sk626' @ X2)) | ('#sk2' @ 50.75/7.03 ('#sk582' @ X2) @ ('#sk626' @ X2)))) => 50.75/7.03 (X2 @ ('#sk582' @ X2) @ ('#sk626' @ X2)))) 50.75/7.03 | ('#form581' @ X2))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl167])). 50.75/7.03 thf(zip_derived_cl175, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( ((('#sk1' @ ('#sk582' @ X2) @ ('#sk626' @ X2)) | ('#sk2' @ 50.75/7.03 ('#sk582' @ X2) @ ('#sk626' @ X2)))) 50.75/7.03 | ('#form581' @ X2))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl172])). 50.75/7.03 thf(zip_derived_cl177, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( ('#sk1' @ ('#sk582' @ X2) @ ('#sk626' @ X2)) 50.75/7.03 | ('#sk2' @ ('#sk582' @ X2) @ ('#sk626' @ X2)) 50.75/7.03 | ('#form581' @ X2))), 50.75/7.03 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl175])). 50.75/7.03 thf(zip_derived_cl160, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ (X2 @ ('#sk105' @ X2) @ ('#sk199' @ X2)) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))) 50.75/7.03 | ('#form9') 50.75/7.03 | (X2 @ '#sk20' @ '#sk38'))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl148])). 50.75/7.03 thf(zip_derived_cl166, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( ('#form581' @ X2) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))))), 50.75/7.03 define([status(thm)])). 50.75/7.03 thf(zip_derived_cl168, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ ('#form581' @ X2) 50.75/7.03 | (X2 @ '#sk20' @ '#sk38') 50.75/7.03 | ('#form9') 50.75/7.03 | ~ (X2 @ ('#sk105' @ X2) @ ('#sk199' @ X2)))), 50.75/7.03 inference('renaming', [status(thm)], 50.75/7.03 [zip_derived_cl160, zip_derived_cl166])). 50.75/7.03 thf(zip_derived_cl93, plain, 50.75/7.03 (( (((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 50.75/7.03 ('#sk88' @ Y0 @ Y1))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk88' @ Y0 @ Y1) & 50.75/7.03 ('#sk88' @ Y1 @ Y2))) => 50.75/7.03 ('#sk88' @ Y0 @ Y2)))))))))))))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 50.75/7.03 thf(zip_derived_cl103, plain, 50.75/7.03 (( (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 50.75/7.03 ('#sk88' @ Y0 @ Y1))))))))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl93])). 50.75/7.03 thf(zip_derived_cl116, plain, 50.75/7.03 (![X2 : a]: 50.75/7.03 ( (((!!) @ (^[Y0 : a]: 50.75/7.03 ((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) => 50.75/7.03 ('#sk88' @ X2 @ Y0)))))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl103])). 50.75/7.03 thf(zip_derived_cl128, plain, 50.75/7.03 (![X2 : a, X4 : a]: 50.75/7.03 ( ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) => ('#sk88' @ X2 @ X4))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl116])). 50.75/7.03 thf(zip_derived_cl141, plain, 50.75/7.03 (![X2 : a, X4 : a]: 50.75/7.03 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 50.75/7.03 | ('#sk88' @ X2 @ X4) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl128])). 50.75/7.03 thf(zip_derived_cl150, plain, 50.75/7.03 (![X2 : a, X4 : a]: 50.75/7.03 (~ ('#sk2' @ X2 @ X4) | ('#form9') | ('#sk88' @ X2 @ X4))), 50.75/7.03 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl141])). 50.75/7.03 thf(zip_derived_cl165, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( (X2 @ ('#sk139' @ X2) @ ('#sk199' @ X2)) 50.75/7.03 | (X2 @ '#sk20' @ '#sk38') 50.75/7.03 | ('#form9') 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))))), 50.75/7.03 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl159])). 50.75/7.03 thf(zip_derived_cl166, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( ('#form581' @ X2) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 (X2 @ Y0 @ Y1))))))))))), 50.75/7.03 define([status(thm)])). 50.75/7.03 thf(zip_derived_cl171, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ ('#form581' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 50.75/7.03 | ('#form9') 50.75/7.03 | (X2 @ '#sk20' @ '#sk38') 50.75/7.03 | (X2 @ ('#sk139' @ X2) @ ('#sk199' @ X2)))), 50.75/7.03 inference('renaming', [status(thm)], 50.75/7.03 [zip_derived_cl165, zip_derived_cl166])). 50.75/7.03 thf(zip_derived_cl174, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ ('#form581' @ X2) 50.75/7.03 | ('#form9') 50.75/7.03 | (X2 @ '#sk20' @ '#sk38') 50.75/7.03 | (X2 @ ('#sk139' @ X2) @ ('#sk199' @ X2)))), 50.75/7.03 inference('ho_norm', [status(thm)], [zip_derived_cl171])). 50.75/7.03 thf(zip_derived_cl104, plain, 50.75/7.03 (( (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk88' @ Y0 @ Y1) & 50.75/7.03 ('#sk88' @ Y1 @ Y2))) => 50.75/7.03 ('#sk88' @ Y0 @ Y2)))))))))))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl93])). 50.75/7.03 thf(zip_derived_cl117, plain, 50.75/7.03 (![X2 : a]: 50.75/7.03 ( (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk88' @ X2 @ Y0) & ('#sk88' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 ('#sk88' @ X2 @ Y1))))))))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl104])). 50.75/7.03 thf(zip_derived_cl129, plain, 50.75/7.03 (![X2 : a, X4 : a]: 50.75/7.03 ( (((!!) @ (^[Y0 : a]: 50.75/7.03 ((((('#sk88' @ X2 @ X4) & ('#sk88' @ X4 @ Y0))) => 50.75/7.03 ('#sk88' @ X2 @ Y0)))))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl117])). 50.75/7.03 thf(zip_derived_cl142, plain, 50.75/7.03 (![X2 : a, X4 : a, X6 : a]: 50.75/7.03 ( ((((('#sk88' @ X2 @ X4) & ('#sk88' @ X4 @ X6))) => ('#sk88' @ X2 @ 50.75/7.03 X6))) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl129])). 50.75/7.03 thf(zip_derived_cl152, plain, 50.75/7.03 (![X2 : a, X4 : a, X6 : a]: 50.75/7.03 (~ ((('#sk88' @ X2 @ X4) & ('#sk88' @ X4 @ X6))) 50.75/7.03 | ('#sk88' @ X2 @ X6) 50.75/7.03 | ('#form9'))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])). 50.75/7.03 thf(zip_derived_cl163, plain, 50.75/7.03 (![X2 : a, X4 : a, X6 : a]: 50.75/7.03 (~ ('#sk88' @ X2 @ X4) 50.75/7.03 | ~ ('#sk88' @ X4 @ X6) 50.75/7.03 | ('#form9') 50.75/7.03 | ('#sk88' @ X2 @ X6))), 50.75/7.03 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl152])). 50.75/7.03 thf(zip_derived_cl23, plain, 50.75/7.03 ((~ (((((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk8' @ Y1 @ Y2) & 50.75/7.03 ('#sk8' @ Y0 @ Y1))) => 50.75/7.03 ('#sk8' @ Y0 @ Y2)))))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.75/7.03 Y1))) => 50.75/7.03 ('#sk8' @ Y0 @ Y1))))))))))) => 50.75/7.03 ('#sk8' @ '#sk6' @ '#sk7'))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ Y2))))))))))))))))) 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4')))))))), 50.75/7.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 50.75/7.03 thf(zip_derived_cl31, plain, 50.75/7.03 (( ('#form9') 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y1 @ 50.75/7.03 Y2)))))) & 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ 50.75/7.03 Y6) & 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))))) => 50.75/7.03 (Y3 @ Y0 @ 50.75/7.03 Y1)))))))) => 50.75/7.03 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.03 (((((((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 ('#sk2' @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) | 50.75/7.03 ('#sk1' @ 50.75/7.03 Y4 @ Y5))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y5))))))))) & 50.75/7.03 (((!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 ( 50.75/7.03 ( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y6 : a]: 50.75/7.03 (( 50.75/7.03 (( 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ 50.75/7.03 Y5) & 50.75/7.03 (Y3 @ 50.75/7.03 Y5 @ Y6))) => 50.75/7.03 (Y3 @ 50.75/7.03 Y4 @ Y6)))))))))))))) => 50.75/7.03 (Y3 @ Y0 @ Y2))))))))))))))))))), 50.75/7.03 define([status(thm)])). 50.75/7.03 thf(zip_derived_cl33, plain, 50.75/7.03 ((~ ('#form9') 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4')))))) 50.75/7.03 | ~ (((((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk8' @ Y1 @ Y2) & 50.75/7.03 ('#sk8' @ Y0 @ Y1))) => 50.75/7.03 ('#sk8' @ Y0 @ Y2)))))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.75/7.03 Y0 @ Y1))) => 50.75/7.03 ('#sk8' @ Y0 @ Y1))))))))))) => 50.75/7.03 ('#sk8' @ '#sk6' @ '#sk7'))))), 50.75/7.03 inference('renaming', [status(thm)], [zip_derived_cl23, zip_derived_cl31])). 50.75/7.03 thf(zip_derived_cl37, plain, 50.75/7.03 ((~ ('#form19') 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ Y2 @ 50.75/7.03 Y3) & (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4')))))))), 50.75/7.03 define([status(thm)])). 50.75/7.03 thf(zip_derived_cl44, plain, 50.75/7.03 (( ('#form19') 50.75/7.03 | ~ (((((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk8' @ Y1 @ Y2) & 50.75/7.03 ('#sk8' @ Y0 @ Y1))) => 50.75/7.03 ('#sk8' @ Y0 @ Y2)))))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.75/7.03 Y0 @ Y1))) => 50.75/7.03 ('#sk8' @ Y0 @ Y1))))))))))) => 50.75/7.03 ('#sk8' @ '#sk6' @ '#sk7'))) 50.75/7.03 | ~ ('#form9'))), 50.75/7.03 inference('renaming', [status(thm)], [zip_derived_cl33, zip_derived_cl37])). 50.75/7.03 thf(zip_derived_cl56, plain, 50.75/7.03 ((~ ('#sk8' @ '#sk6' @ '#sk7') | ~ ('#form9') | ('#form19'))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 50.75/7.03 thf(zip_derived_cl151, plain, 50.75/7.03 (![X2 : a, X4 : a]: 50.75/7.03 (~ ('#sk1' @ X2 @ X4) | ('#form9') | ('#sk88' @ X2 @ X4))), 50.75/7.03 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl141])). 50.75/7.03 thf(zip_derived_cl176, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 (~ (X2 @ ('#sk582' @ X2) @ ('#sk626' @ X2)) | ('#form581' @ X2))), 50.75/7.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl172])). 50.75/7.03 thf(zip_derived_cl26, plain, 50.75/7.03 (![X2 : a > a > $o]: 50.75/7.03 ( (((((((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 50.75/7.03 (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((X2 @ Y1 @ Y2) & (X2 @ 50.75/7.03 Y0 @ Y1))) => 50.75/7.03 (X2 @ Y0 @ Y2)))))))))))))) => 50.75/7.03 (X2 @ '#sk6' @ '#sk7'))) 50.75/7.03 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.03 (((((((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.03 ('#sk1' @ Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((!!) @ (^[Y3 : a]: 50.75/7.03 (((((Y0 @ 50.75/7.03 Y2 @ Y3) & 50.75/7.03 (Y0 @ 50.75/7.03 Y1 @ Y2))) => 50.75/7.03 (Y0 @ Y1 @ 50.75/7.03 Y3)))))))))))))) => 50.75/7.03 (Y0 @ '#sk3' @ '#sk4')))))) 50.75/7.03 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.03 (((!!) @ (^[Y1 : a]: 50.75/7.03 (((!!) @ (^[Y2 : a]: 50.75/7.03 (((((((!!) @ (^[Y3 : 50.75/7.03 a > a > $o]: 50.75/7.03 (((((( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y4 : a]: 50.75/7.03 (( 50.75/7.03 (!!) @ ( 50.75/7.03 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y6 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) & 50.75/7.04 (Y3 @ 50.75/7.04 Y5 @ Y6))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y6)))))))))))) & 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 ('#sk1' @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) | 50.75/7.04 ('#sk2' @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))))))))))) => 50.75/7.04 (Y3 @ Y1 @ 50.75/7.04 Y2)))))) & 50.75/7.04 (((!!) @ (^[Y3 : 50.75/7.04 a > a > $o]: 50.75/7.04 (((((( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y6 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 (Y3 @ 50.75/7.04 Y5 @ 50.75/7.04 Y6) & 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y6)))))))))))) & 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 ('#sk2' @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) | 50.75/7.04 ('#sk1' @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))))))))))) => 50.75/7.04 (Y3 @ Y0 @ 50.75/7.04 Y1)))))))) => 50.75/7.04 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.04 (((((((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 ('#sk2' @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) | 50.75/7.04 ('#sk1' @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))))))))) & 50.75/7.04 (((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y6 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) & 50.75/7.04 (Y3 @ 50.75/7.04 Y5 @ Y6))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y6)))))))))))))) => 50.75/7.04 (Y3 @ Y0 @ 50.75/7.04 Y2))))))))))))))))) 50.75/7.04 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.04 (((((((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((!!) @ (^[Y3 : a]: 50.75/7.04 (((((Y0 @ 50.75/7.04 Y1 @ Y2) & 50.75/7.04 (Y0 @ 50.75/7.04 Y2 @ Y3))) => 50.75/7.04 (Y0 @ Y1 @ 50.75/7.04 Y3)))))))))))) & 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((('#sk2' @ Y1 @ Y2) => 50.75/7.04 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.04 (Y0 @ '#sk6' @ '#sk7')))))))), 50.75/7.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 50.75/7.04 thf(zip_derived_cl27, plain, 50.75/7.04 (( (((((((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk1' @ Y0 @ Y1) => ('#sk8' @ Y0 @ Y1))))))))) & 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk8' @ Y1 @ Y2) & 50.75/7.04 ('#sk8' @ Y0 @ Y1))) => 50.75/7.04 ('#sk8' @ Y0 @ Y2)))))))))))))) => 50.75/7.04 ('#sk8' @ '#sk6' @ '#sk7'))) 50.75/7.04 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.04 (((((((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.04 ('#sk1' @ Y1 @ Y2))) => 50.75/7.04 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((!!) @ (^[Y3 : a]: 50.75/7.04 (((((Y0 @ Y2 @ 50.75/7.04 Y3) & (Y0 @ 50.75/7.04 Y1 @ Y2))) => 50.75/7.04 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.04 (Y0 @ '#sk3' @ '#sk4')))))) 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((((((!!) @ (^[Y3 : a > a > $o]: 50.75/7.04 (((((((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y6 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) & 50.75/7.04 (Y3 @ 50.75/7.04 Y5 @ Y6))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y6)))))))))))) & 50.75/7.04 (((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 ('#sk1' @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) | 50.75/7.04 ('#sk2' @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))))))))))) => 50.75/7.04 (Y3 @ Y1 @ 50.75/7.04 Y2)))))) & 50.75/7.04 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.04 (((((((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y6 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 (Y3 @ 50.75/7.04 Y5 @ 50.75/7.04 Y6) & 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y6)))))))))))) & 50.75/7.04 (((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 ('#sk2' @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) | 50.75/7.04 ('#sk1' @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))))))))))) => 50.75/7.04 (Y3 @ Y0 @ 50.75/7.04 Y1)))))))) => 50.75/7.04 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.04 (((((((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 ( 50.75/7.04 ( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 ('#sk2' @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) | 50.75/7.04 ('#sk1' @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))))))))) & 50.75/7.04 (((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 ( 50.75/7.04 ( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y6 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) & 50.75/7.04 (Y3 @ 50.75/7.04 Y5 @ Y6))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y6)))))))))))))) => 50.75/7.04 (Y3 @ Y0 @ Y2))))))))))))))))) 50.75/7.04 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.04 (((((((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((!!) @ (^[Y3 : a]: 50.75/7.04 (((((Y0 @ Y1 @ 50.75/7.04 Y2) & (Y0 @ 50.75/7.04 Y2 @ Y3))) => 50.75/7.04 (Y0 @ Y1 @ Y3)))))))))))) & 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((('#sk2' @ Y1 @ Y2) => 50.75/7.04 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.04 (Y0 @ '#sk6' @ '#sk7')))))))), 50.75/7.04 inference('triggered_bool_instantiation', [status(thm)], 50.75/7.04 [zip_derived_cl26])). 50.75/7.04 thf(zip_derived_cl37, plain, 50.75/7.04 ((~ ('#form19') 50.75/7.04 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.04 (((((((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.04 ('#sk1' @ Y1 @ Y2))) => 50.75/7.04 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((!!) @ (^[Y3 : a]: 50.75/7.04 (((((Y0 @ Y2 @ 50.75/7.04 Y3) & (Y0 @ 50.75/7.04 Y1 @ Y2))) => 50.75/7.04 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.04 (Y0 @ '#sk3' @ '#sk4')))))))), 50.75/7.04 define([status(thm)])). 50.75/7.04 thf(zip_derived_cl198, plain, 50.75/7.04 (( ('#form19') 50.75/7.04 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.04 (((((((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((!!) @ (^[Y3 : a]: 50.75/7.04 (((((Y0 @ Y1 @ 50.75/7.04 Y2) & (Y0 @ 50.75/7.04 Y2 @ Y3))) => 50.75/7.04 (Y0 @ Y1 @ Y3)))))))))))) & 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((('#sk2' @ Y1 @ Y2) => 50.75/7.04 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.04 (Y0 @ '#sk6' @ '#sk7')))))) 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((((((!!) @ (^[Y3 : a > a > $o]: 50.75/7.04 (((((((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y6 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) & 50.75/7.04 (Y3 @ 50.75/7.04 Y5 @ Y6))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y6)))))))))))) & 50.75/7.04 (((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 ('#sk1' @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) | 50.75/7.04 ('#sk2' @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))))))))))) => 50.75/7.04 (Y3 @ Y1 @ 50.75/7.04 Y2)))))) & 50.75/7.04 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.04 (((((((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y6 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 (Y3 @ 50.75/7.04 Y5 @ 50.75/7.04 Y6) & 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y6)))))))))))) & 50.75/7.04 (((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 ('#sk2' @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) | 50.75/7.04 ('#sk1' @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))))))))))) => 50.75/7.04 (Y3 @ Y0 @ 50.75/7.04 Y1)))))))) => 50.75/7.04 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.04 (((((((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 ( 50.75/7.04 ( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 ('#sk2' @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) | 50.75/7.04 ('#sk1' @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))))))))) & 50.75/7.04 (((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 ( 50.75/7.04 ( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y6 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) & 50.75/7.04 (Y3 @ 50.75/7.04 Y5 @ Y6))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y6)))))))))))))) => 50.75/7.04 (Y3 @ Y0 @ Y2))))))))))))))))) 50.75/7.04 | (((((((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk1' @ Y0 @ Y1) => ('#sk8' @ Y0 @ 50.75/7.04 Y1))))))))) & 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk8' @ Y1 @ Y2) & 50.75/7.04 ('#sk8' @ Y0 @ Y1))) => 50.75/7.04 ('#sk8' @ Y0 @ Y2)))))))))))))) => 50.75/7.04 ('#sk8' @ '#sk6' @ '#sk7'))))), 50.75/7.04 inference('renaming', [status(thm)], [zip_derived_cl27, zip_derived_cl37])). 50.75/7.04 thf(zip_derived_cl47, plain, 50.75/7.04 ((~ ('#form29') 50.75/7.04 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.04 (((((((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((!!) @ (^[Y3 : a]: 50.75/7.04 (((((Y0 @ Y1 @ 50.75/7.04 Y2) & (Y0 @ 50.75/7.04 Y2 @ Y3))) => 50.75/7.04 (Y0 @ Y1 @ Y3)))))))))))) & 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((('#sk2' @ Y1 @ Y2) => 50.75/7.04 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.04 (Y0 @ '#sk6' @ '#sk7')))))))), 50.75/7.04 define([status(thm)])). 50.75/7.04 thf(zip_derived_cl199, plain, 50.75/7.04 (( ('#form29') 50.75/7.04 | (((((((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk1' @ Y0 @ Y1) => ('#sk8' @ Y0 @ 50.75/7.04 Y1))))))))) & 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk8' @ Y1 @ Y2) & 50.75/7.04 ('#sk8' @ Y0 @ Y1))) => 50.75/7.04 ('#sk8' @ Y0 @ Y2)))))))))))))) => 50.75/7.04 ('#sk8' @ '#sk6' @ '#sk7'))) 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((((((!!) @ (^[Y3 : a > a > $o]: 50.75/7.04 (((((((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y6 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) & 50.75/7.04 (Y3 @ 50.75/7.04 Y5 @ Y6))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y6)))))))))))) & 50.75/7.04 (((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 ('#sk1' @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) | 50.75/7.04 ('#sk2' @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))))))))))) => 50.75/7.04 (Y3 @ Y1 @ 50.75/7.04 Y2)))))) & 50.75/7.04 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.04 (((((((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y6 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 (Y3 @ 50.75/7.04 Y5 @ 50.75/7.04 Y6) & 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y6)))))))))))) & 50.75/7.04 (((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 ('#sk2' @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) | 50.75/7.04 ('#sk1' @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))))))))))) => 50.75/7.04 (Y3 @ Y0 @ 50.75/7.04 Y1)))))))) => 50.75/7.04 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.04 (((((((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 ( 50.75/7.04 ( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 ('#sk2' @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) | 50.75/7.04 ('#sk1' @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))))))))) & 50.75/7.04 (((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 ( 50.75/7.04 ( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y6 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) & 50.75/7.04 (Y3 @ 50.75/7.04 Y5 @ Y6))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y6)))))))))))))) => 50.75/7.04 (Y3 @ Y0 @ Y2))))))))))))))))) 50.75/7.04 | ('#form19'))), 50.75/7.04 inference('renaming', [status(thm)], 50.75/7.04 [zip_derived_cl198, zip_derived_cl47])). 50.75/7.04 thf(zip_derived_cl31, plain, 50.75/7.04 (( ('#form9') 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((((((!!) @ (^[Y3 : a > a > $o]: 50.75/7.04 (((((((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y6 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) & 50.75/7.04 (Y3 @ 50.75/7.04 Y5 @ Y6))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y6)))))))))))) & 50.75/7.04 (((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 ('#sk1' @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) | 50.75/7.04 ('#sk2' @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))))))))))) => 50.75/7.04 (Y3 @ Y1 @ 50.75/7.04 Y2)))))) & 50.75/7.04 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.04 (((((((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y6 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 (Y3 @ 50.75/7.04 Y5 @ 50.75/7.04 Y6) & 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y6)))))))))))) & 50.75/7.04 (((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 ('#sk2' @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) | 50.75/7.04 ('#sk1' @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))))))))))) => 50.75/7.04 (Y3 @ Y0 @ 50.75/7.04 Y1)))))))) => 50.75/7.04 (((!!) @ (^[Y3 : a > a > $o]: 50.75/7.04 (((((((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 ( 50.75/7.04 ( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 ('#sk2' @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) | 50.75/7.04 ('#sk1' @ 50.75/7.04 Y4 @ Y5))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y5))))))))) & 50.75/7.04 (((!!) @ ( 50.75/7.04 ^[Y4 : a]: 50.75/7.04 ( 50.75/7.04 ( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y5 : a]: 50.75/7.04 (( 50.75/7.04 (!!) @ ( 50.75/7.04 ^[Y6 : a]: 50.75/7.04 (( 50.75/7.04 (( 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ 50.75/7.04 Y5) & 50.75/7.04 (Y3 @ 50.75/7.04 Y5 @ Y6))) => 50.75/7.04 (Y3 @ 50.75/7.04 Y4 @ Y6)))))))))))))) => 50.75/7.04 (Y3 @ Y0 @ Y2))))))))))))))))))), 50.75/7.04 define([status(thm)])). 50.75/7.04 thf(zip_derived_cl200, plain, 50.75/7.04 ((~ ('#form9') 50.75/7.04 | ('#form19') 50.75/7.04 | (((((((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk1' @ Y0 @ Y1) => ('#sk8' @ Y0 @ 50.75/7.04 Y1))))))))) & 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk8' @ Y1 @ Y2) & 50.75/7.04 ('#sk8' @ Y0 @ Y1))) => 50.75/7.04 ('#sk8' @ Y0 @ Y2)))))))))))))) => 50.75/7.04 ('#sk8' @ '#sk6' @ '#sk7'))) 50.75/7.04 | ('#form29'))), 50.75/7.04 inference('renaming', [status(thm)], 50.75/7.04 [zip_derived_cl199, zip_derived_cl31])). 50.75/7.04 thf(zip_derived_cl201, plain, 50.75/7.04 ((~ (((((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk1' @ Y0 @ Y1) => ('#sk8' @ Y0 @ Y1))))))))) & 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk8' @ Y1 @ Y2) & 50.75/7.04 ('#sk8' @ Y0 @ Y1))) => 50.75/7.04 ('#sk8' @ Y0 @ Y2)))))))))))))) 50.75/7.04 | ('#sk8' @ '#sk6' @ '#sk7') 50.75/7.04 | ('#form29') 50.75/7.04 | ('#form19') 50.75/7.04 | ~ ('#form9'))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl200])). 50.75/7.04 thf(zip_derived_cl56, plain, 50.75/7.04 ((~ ('#sk8' @ '#sk6' @ '#sk7') | ~ ('#form9') | ('#form19'))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 50.75/7.04 thf(zip_derived_cl202, plain, 50.75/7.04 ((~ ('#form9') 50.75/7.04 | ('#form19') 50.75/7.04 | ('#form29') 50.75/7.04 | ~ (((((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk1' @ Y0 @ Y1) => ('#sk8' @ Y0 @ 50.75/7.04 Y1))))))))) & 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk8' @ Y1 @ Y2) & 50.75/7.04 ('#sk8' @ Y0 @ Y1))) => 50.75/7.04 ('#sk8' @ Y0 @ Y2)))))))))))))))), 50.75/7.04 inference('clc', [status(thm)], [zip_derived_cl201, zip_derived_cl56])). 50.75/7.04 thf(zip_derived_cl203, plain, 50.75/7.04 ((~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk1' @ Y0 @ Y1) => ('#sk8' @ Y0 @ Y1))))))))) 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk8' @ Y1 @ Y2) & 50.75/7.04 ('#sk8' @ Y0 @ Y1))) => 50.75/7.04 ('#sk8' @ Y0 @ Y2)))))))))))) 50.75/7.04 | ('#form29') 50.75/7.04 | ('#form19') 50.75/7.04 | ~ ('#form9'))), 50.75/7.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl202])). 50.75/7.04 thf(zip_derived_cl105, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 ( ('#form185' @ X2) 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((((X2 @ Y1 @ Y2) & (X2 @ 50.75/7.04 Y0 @ Y1))) => 50.75/7.04 (X2 @ Y0 @ Y2)))))))))))))), 50.75/7.04 define([status(thm)])). 50.75/7.04 thf(zip_derived_cl204, plain, 50.75/7.04 ((~ ('#form185' @ '#sk8') 50.75/7.04 | ~ ('#form9') 50.75/7.04 | ('#form19') 50.75/7.04 | ('#form29') 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk1' @ Y0 @ Y1) => ('#sk8' @ Y0 @ Y1))))))))))), 50.75/7.04 inference('renaming', [status(thm)], 50.75/7.04 [zip_derived_cl203, zip_derived_cl105])). 50.75/7.04 thf(zip_derived_cl205, plain, 50.75/7.04 ((~ (((!!) @ (^[Y0 : a]: 50.75/7.04 ((('#sk1' @ ('#sk128' @ '#sk8') @ Y0) => ('#sk8' @ 50.75/7.04 ('#sk128' @ '#sk8') @ Y0)))))) 50.75/7.04 | ('#form29') 50.75/7.04 | ('#form19') 50.75/7.04 | ~ ('#form9') 50.75/7.04 | ~ ('#form185' @ '#sk8'))), 50.75/7.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl204])). 50.75/7.04 thf(zip_derived_cl206, plain, 50.75/7.04 ((~ ((('#sk1' @ ('#sk128' @ '#sk8') @ ('#sk247' @ '#sk8')) => ('#sk8' @ 50.75/7.04 ('#sk128' @ '#sk8') @ ('#sk247' @ '#sk8')))) 50.75/7.04 | ~ ('#form185' @ '#sk8') 50.75/7.04 | ~ ('#form9') 50.75/7.04 | ('#form19') 50.75/7.04 | ('#form29'))), 50.75/7.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl205])). 50.75/7.04 thf(zip_derived_cl207, plain, 50.75/7.04 (( ('#sk1' @ ('#sk128' @ '#sk8') @ ('#sk247' @ '#sk8')) 50.75/7.04 | ('#form29') 50.75/7.04 | ('#form19') 50.75/7.04 | ~ ('#form9') 50.75/7.04 | ~ ('#form185' @ '#sk8'))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])). 50.75/7.04 thf(zip_derived_cl208, plain, 50.75/7.04 ((~ ('#sk8' @ ('#sk128' @ '#sk8') @ ('#sk247' @ '#sk8')) 50.75/7.04 | ('#form29') 50.75/7.04 | ('#form19') 50.75/7.04 | ~ ('#form9') 50.75/7.04 | ~ ('#form185' @ '#sk8'))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])). 50.75/7.04 thf(zip_derived_cl55, plain, 50.75/7.04 (( (((((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk8' @ Y1 @ Y2) & 50.75/7.04 ('#sk8' @ Y0 @ Y1))) => 50.75/7.04 ('#sk8' @ Y0 @ Y2)))))))))))) & 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 50.75/7.04 ('#sk8' @ Y0 @ Y1))))))))))) 50.75/7.04 | ~ ('#form9') 50.75/7.04 | ('#form19'))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 50.75/7.04 thf(zip_derived_cl62, plain, 50.75/7.04 (( (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 50.75/7.04 ('#sk8' @ Y0 @ Y1))))))))) 50.75/7.04 | ('#form19') 50.75/7.04 | ~ ('#form9'))), 50.75/7.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 50.75/7.04 thf(zip_derived_cl69, plain, 50.75/7.04 (![X2 : a]: 50.75/7.04 ( (((!!) @ (^[Y0 : a]: 50.75/7.04 ((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) => 50.75/7.04 ('#sk8' @ X2 @ Y0)))))) 50.75/7.04 | ~ ('#form9') 50.75/7.04 | ('#form19'))), 50.75/7.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl62])). 50.75/7.04 thf(zip_derived_cl80, plain, 50.75/7.04 (![X2 : a, X4 : a]: 50.75/7.04 ( ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) => ('#sk8' @ X2 @ X4))) 50.75/7.04 | ('#form19') 50.75/7.04 | ~ ('#form9'))), 50.75/7.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl69])). 50.75/7.04 thf(zip_derived_cl100, plain, 50.75/7.04 (![X2 : a, X4 : a]: 50.75/7.04 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 50.75/7.04 | ('#sk8' @ X2 @ X4) 50.75/7.04 | ~ ('#form9') 50.75/7.04 | ('#form19'))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])). 50.75/7.04 thf(zip_derived_cl113, plain, 50.75/7.04 (![X2 : a, X4 : a]: 50.75/7.04 (~ ('#sk1' @ X2 @ X4) 50.75/7.04 | ('#form19') 50.75/7.04 | ~ ('#form9') 50.75/7.04 | ('#sk8' @ X2 @ X4))), 50.75/7.04 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl100])). 50.75/7.04 thf(zip_derived_cl47, plain, 50.75/7.04 ((~ ('#form29') 50.75/7.04 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.04 (((((((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((!!) @ (^[Y3 : a]: 50.75/7.04 (((((Y0 @ Y1 @ 50.75/7.04 Y2) & (Y0 @ 50.75/7.04 Y2 @ Y3))) => 50.75/7.04 (Y0 @ Y1 @ Y3)))))))))))) & 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((('#sk2' @ Y1 @ Y2) => 50.75/7.04 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.04 (Y0 @ '#sk6' @ '#sk7')))))))), 50.75/7.04 define([status(thm)])). 50.75/7.04 thf(zip_derived_cl48, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 ( (((((((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((((X2 @ Y0 @ Y1) & (X2 @ 50.75/7.04 Y1 @ Y2))) => 50.75/7.04 (X2 @ Y0 @ Y2)))))))))))) & 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 50.75/7.04 (X2 @ '#sk6' @ '#sk7'))) 50.75/7.04 | ~ ('#form29'))), 50.75/7.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl47])). 50.75/7.04 thf(zip_derived_cl59, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ (((((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((((X2 @ Y0 @ Y1) & (X2 @ 50.75/7.04 Y1 @ Y2))) => 50.75/7.04 (X2 @ Y0 @ Y2)))))))))))) & 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) 50.75/7.04 | (X2 @ '#sk6' @ '#sk7') 50.75/7.04 | ~ ('#form29'))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 50.75/7.04 thf(zip_derived_cl66, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((((X2 @ Y0 @ Y1) & (X2 @ 50.75/7.04 Y1 @ Y2))) => 50.75/7.04 (X2 @ Y0 @ Y2)))))))))))) 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 50.75/7.04 | ~ ('#form29') 50.75/7.04 | (X2 @ '#sk6' @ '#sk7'))), 50.75/7.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl59])). 50.75/7.04 thf(zip_derived_cl77, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((((X2 @ ('#sk105' @ X2) @ Y0) & (X2 @ 50.75/7.04 Y0 @ Y1))) => 50.75/7.04 (X2 @ ('#sk105' @ X2) @ Y1))))))))) 50.75/7.04 | (X2 @ '#sk6' @ '#sk7') 50.75/7.04 | ~ ('#form29') 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.75/7.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl66])). 50.75/7.04 thf(zip_derived_cl96, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((((X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) & (X2 @ 50.75/7.04 ('#sk139' @ X2) @ Y0))) => 50.75/7.04 (X2 @ ('#sk105' @ X2) @ Y0)))))) 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 50.75/7.04 | ~ ('#form29') 50.75/7.04 | (X2 @ '#sk6' @ '#sk7'))), 50.75/7.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl77])). 50.75/7.04 thf(zip_derived_cl108, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ (((((X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) & (X2 @ 50.75/7.04 ('#sk139' @ X2) @ ('#sk199' @ X2)))) => 50.75/7.04 (X2 @ ('#sk105' @ X2) @ ('#sk199' @ X2)))) 50.75/7.04 | (X2 @ '#sk6' @ '#sk7') 50.75/7.04 | ~ ('#form29') 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.75/7.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 50.75/7.04 thf(zip_derived_cl121, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ (X2 @ ('#sk105' @ X2) @ ('#sk199' @ X2)) 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 50.75/7.04 | ~ ('#form29') 50.75/7.04 | (X2 @ '#sk6' @ '#sk7'))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 50.75/7.04 thf(zip_derived_cl135, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 ( ('#form360' @ X2) 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.75/7.04 define([status(thm)])). 50.75/7.04 thf(zip_derived_cl136, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ (((!!) @ (^[Y0 : a]: 50.75/7.04 ((('#sk2' @ ('#sk361' @ X2) @ Y0) => (X2 @ 50.75/7.04 ('#sk361' @ X2) @ Y0)))))) 50.75/7.04 | ('#form360' @ X2))), 50.75/7.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl135])). 50.75/7.04 thf(zip_derived_cl147, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ ((('#sk2' @ ('#sk361' @ X2) @ ('#sk441' @ X2)) => (X2 @ 50.75/7.04 ('#sk361' @ X2) @ ('#sk441' @ X2)))) 50.75/7.04 | ('#form360' @ X2))), 50.75/7.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl136])). 50.75/7.04 thf(zip_derived_cl157, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 ( ('#sk2' @ ('#sk361' @ X2) @ ('#sk441' @ X2)) | ('#form360' @ X2))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl147])). 50.75/7.04 thf(zip_derived_cl112, plain, 50.75/7.04 (![X2 : a, X4 : a]: 50.75/7.04 (~ ('#sk2' @ X2 @ X4) 50.75/7.04 | ('#form19') 50.75/7.04 | ~ ('#form9') 50.75/7.04 | ('#sk8' @ X2 @ X4))), 50.75/7.04 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl100])). 50.75/7.04 thf(zip_derived_cl158, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ (X2 @ ('#sk361' @ X2) @ ('#sk441' @ X2)) | ('#form360' @ X2))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl147])). 50.75/7.04 thf(zip_derived_cl120, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 ( (((X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) & (X2 @ 50.75/7.04 ('#sk139' @ X2) @ ('#sk199' @ X2)))) 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 50.75/7.04 | ~ ('#form29') 50.75/7.04 | (X2 @ '#sk6' @ '#sk7'))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 50.75/7.04 thf(zip_derived_cl134, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 ( (X2 @ ('#sk139' @ X2) @ ('#sk199' @ X2)) 50.75/7.04 | (X2 @ '#sk6' @ '#sk7') 50.75/7.04 | ~ ('#form29') 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.75/7.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl120])). 50.75/7.04 thf(zip_derived_cl135, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 ( ('#form360' @ X2) 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.75/7.04 define([status(thm)])). 50.75/7.04 thf(zip_derived_cl146, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ ('#form360' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 50.75/7.04 | ~ ('#form29') 50.75/7.04 | (X2 @ '#sk6' @ '#sk7') 50.75/7.04 | (X2 @ ('#sk139' @ X2) @ ('#sk199' @ X2)))), 50.75/7.04 inference('renaming', [status(thm)], 50.75/7.04 [zip_derived_cl134, zip_derived_cl135])). 50.75/7.04 thf(zip_derived_cl156, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ ('#form360' @ X2) 50.75/7.04 | ~ ('#form29') 50.75/7.04 | (X2 @ '#sk6' @ '#sk7') 50.75/7.04 | (X2 @ ('#sk139' @ X2) @ ('#sk199' @ X2)))), 50.75/7.04 inference('ho_norm', [status(thm)], [zip_derived_cl146])). 50.75/7.04 thf(zip_derived_cl121, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ (X2 @ ('#sk105' @ X2) @ ('#sk199' @ X2)) 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 50.75/7.04 | ~ ('#form29') 50.75/7.04 | (X2 @ '#sk6' @ '#sk7'))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 50.75/7.04 thf(zip_derived_cl135, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 ( ('#form360' @ X2) 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.75/7.04 define([status(thm)])). 50.75/7.04 thf(zip_derived_cl137, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ ('#form360' @ X2) 50.75/7.04 | (X2 @ '#sk6' @ '#sk7') 50.75/7.04 | ~ ('#form29') 50.75/7.04 | ~ (X2 @ ('#sk105' @ X2) @ ('#sk199' @ X2)))), 50.75/7.04 inference('renaming', [status(thm)], 50.75/7.04 [zip_derived_cl121, zip_derived_cl135])). 50.75/7.04 thf(zip_derived_cl133, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 ( (X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) 50.75/7.04 | (X2 @ '#sk6' @ '#sk7') 50.75/7.04 | ~ ('#form29') 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.75/7.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl120])). 50.75/7.04 thf(zip_derived_cl135, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 ( ('#form360' @ X2) 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.75/7.04 define([status(thm)])). 50.75/7.04 thf(zip_derived_cl145, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ ('#form360' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 50.75/7.04 | ~ ('#form29') 50.75/7.04 | (X2 @ '#sk6' @ '#sk7') 50.75/7.04 | (X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)))), 50.75/7.04 inference('renaming', [status(thm)], 50.75/7.04 [zip_derived_cl133, zip_derived_cl135])). 50.75/7.04 thf(zip_derived_cl155, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ ('#form360' @ X2) 50.75/7.04 | ~ ('#form29') 50.75/7.04 | (X2 @ '#sk6' @ '#sk7') 50.75/7.04 | (X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)))), 50.75/7.04 inference('ho_norm', [status(thm)], [zip_derived_cl145])). 50.75/7.04 thf(zip_derived_cl61, plain, 50.75/7.04 (( (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk8' @ Y1 @ Y2) & 50.75/7.04 ('#sk8' @ Y0 @ Y1))) => 50.75/7.04 ('#sk8' @ Y0 @ Y2)))))))))))) 50.75/7.04 | ('#form19') 50.75/7.04 | ~ ('#form9'))), 50.75/7.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 50.75/7.04 thf(zip_derived_cl68, plain, 50.75/7.04 (![X2 : a]: 50.75/7.04 ( (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((((('#sk8' @ Y0 @ Y1) & ('#sk8' @ X2 @ Y0))) => 50.75/7.04 ('#sk8' @ X2 @ Y1))))))))) 50.75/7.04 | ~ ('#form9') 50.75/7.04 | ('#form19'))), 50.75/7.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl61])). 50.75/7.04 thf(zip_derived_cl79, plain, 50.75/7.04 (![X2 : a, X4 : a]: 50.75/7.04 ( (((!!) @ (^[Y0 : a]: 50.75/7.04 ((((('#sk8' @ X4 @ Y0) & ('#sk8' @ X2 @ X4))) => 50.75/7.04 ('#sk8' @ X2 @ Y0)))))) 50.75/7.04 | ('#form19') 50.75/7.04 | ~ ('#form9'))), 50.75/7.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl68])). 50.75/7.04 thf(zip_derived_cl99, plain, 50.75/7.04 (![X2 : a, X4 : a, X6 : a]: 50.75/7.04 ( ((((('#sk8' @ X4 @ X6) & ('#sk8' @ X2 @ X4))) => ('#sk8' @ X2 @ X6))) 50.75/7.04 | ~ ('#form9') 50.75/7.04 | ('#form19'))), 50.75/7.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl79])). 50.75/7.04 thf(zip_derived_cl111, plain, 50.75/7.04 (![X2 : a, X4 : a, X6 : a]: 50.75/7.04 (~ ((('#sk8' @ X4 @ X6) & ('#sk8' @ X2 @ X4))) 50.75/7.04 | ('#sk8' @ X2 @ X6) 50.75/7.04 | ('#form19') 50.75/7.04 | ~ ('#form9'))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl99])). 50.75/7.04 thf(zip_derived_cl125, plain, 50.75/7.04 (![X2 : a, X4 : a, X6 : a]: 50.75/7.04 (~ ('#sk8' @ X4 @ X6) 50.75/7.04 | ~ ('#sk8' @ X2 @ X4) 50.75/7.04 | ~ ('#form9') 50.75/7.04 | ('#form19') 50.75/7.04 | ('#sk8' @ X2 @ X6))), 50.75/7.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl111])). 50.75/7.04 thf(zip_derived_cl105, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 ( ('#form185' @ X2) 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((((X2 @ Y1 @ Y2) & (X2 @ 50.75/7.04 Y0 @ Y1))) => 50.75/7.04 (X2 @ Y0 @ Y2)))))))))))))), 50.75/7.04 define([status(thm)])). 50.75/7.04 thf(zip_derived_cl106, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((((X2 @ Y0 @ Y1) & (X2 @ 50.75/7.04 ('#sk186' @ X2) @ Y0))) => 50.75/7.04 (X2 @ ('#sk186' @ X2) @ Y1))))))))) 50.75/7.04 | ('#form185' @ X2))), 50.75/7.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl105])). 50.75/7.04 thf(zip_derived_cl119, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((((X2 @ ('#sk258' @ X2) @ Y0) & (X2 @ 50.75/7.04 ('#sk186' @ X2) @ ('#sk258' @ X2)))) => 50.75/7.04 (X2 @ ('#sk186' @ X2) @ Y0)))))) 50.75/7.04 | ('#form185' @ X2))), 50.75/7.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl106])). 50.75/7.04 thf(zip_derived_cl132, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ (((((X2 @ ('#sk258' @ X2) @ ('#sk343' @ X2)) & (X2 @ 50.75/7.04 ('#sk186' @ X2) @ ('#sk258' @ X2)))) => 50.75/7.04 (X2 @ ('#sk186' @ X2) @ ('#sk343' @ X2)))) 50.75/7.04 | ('#form185' @ X2))), 50.75/7.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl119])). 50.75/7.04 thf(zip_derived_cl143, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 ( (((X2 @ ('#sk258' @ X2) @ ('#sk343' @ X2)) & (X2 @ 50.75/7.04 ('#sk186' @ X2) @ ('#sk258' @ X2)))) 50.75/7.04 | ('#form185' @ X2))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl132])). 50.75/7.04 thf(zip_derived_cl154, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 ( (X2 @ ('#sk186' @ X2) @ ('#sk258' @ X2)) | ('#form185' @ X2))), 50.75/7.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl143])). 50.75/7.04 thf(zip_derived_cl153, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 ( (X2 @ ('#sk258' @ X2) @ ('#sk343' @ X2)) | ('#form185' @ X2))), 50.75/7.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl143])). 50.75/7.04 thf(zip_derived_cl144, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 (~ (X2 @ ('#sk186' @ X2) @ ('#sk343' @ X2)) | ('#form185' @ X2))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl132])). 50.75/7.04 thf(zip_derived_cl37, plain, 50.75/7.04 ((~ ('#form19') 50.75/7.04 | (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.04 (((((((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk2' @ Y1 @ Y2) | 50.75/7.04 ('#sk1' @ Y1 @ Y2))) => 50.75/7.04 (Y0 @ Y1 @ Y2))))))))) & 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((!!) @ (^[Y3 : a]: 50.75/7.04 (((((Y0 @ Y2 @ 50.75/7.04 Y3) & (Y0 @ 50.75/7.04 Y1 @ Y2))) => 50.75/7.04 (Y0 @ Y1 @ Y3)))))))))))))) => 50.75/7.04 (Y0 @ '#sk3' @ '#sk4')))))))), 50.75/7.04 define([status(thm)])). 50.75/7.04 thf(zip_derived_cl38, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 ( (((((((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.75/7.04 Y1))) => 50.75/7.04 (X2 @ Y0 @ Y1))))))))) & 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((((X2 @ Y1 @ Y2) & (X2 @ 50.75/7.04 Y0 @ Y1))) => 50.75/7.04 (X2 @ Y0 @ Y2)))))))))))))) => 50.75/7.04 (X2 @ '#sk3' @ '#sk4'))) 50.75/7.04 | ~ ('#form19'))), 50.75/7.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 50.75/7.04 thf(zip_derived_cl40, plain, 50.75/7.04 (( (((((((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.75/7.04 Y1))) => 50.75/7.04 ('#sk5' @ Y0 @ Y1))))))))) & 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk5' @ Y1 @ Y2) & 50.75/7.04 ('#sk5' @ Y0 @ Y1))) => 50.75/7.04 ('#sk5' @ Y0 @ Y2)))))))))))))) => 50.75/7.04 ('#sk5' @ '#sk3' @ '#sk4'))) 50.75/7.04 | ~ ('#form19'))), 50.75/7.04 inference('triggered_bool_instantiation', [status(thm)], 50.75/7.04 [zip_derived_cl38])). 50.75/7.04 thf(zip_derived_cl6, plain, 50.75/7.04 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.75/7.04 (((((((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((!!) @ (^[Y3 : a]: 50.75/7.04 (((((Y0 @ Y1 @ 50.75/7.04 Y2) & (Y0 @ 50.75/7.04 Y2 @ Y3))) => 50.75/7.04 (Y0 @ Y1 @ Y3)))))))))))) & 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk1' @ Y1 @ Y2) | 50.75/7.04 ('#sk2' @ Y1 @ Y2))) => 50.75/7.04 (Y0 @ Y1 @ Y2))))))))))) => 50.75/7.04 (Y0 @ '#sk3' @ '#sk4'))))))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 50.75/7.04 thf(zip_derived_cl8, plain, 50.75/7.04 (~ (((((((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk5' @ Y0 @ Y1) & 50.75/7.04 ('#sk5' @ Y1 @ Y2))) => 50.75/7.04 ('#sk5' @ Y0 @ Y2)))))))))))) & 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.75/7.04 Y1))) => 50.75/7.04 ('#sk5' @ Y0 @ Y1))))))))))) => 50.75/7.04 ('#sk5' @ '#sk3' @ '#sk4')))), 50.75/7.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 50.75/7.04 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk3' @ '#sk4')), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 50.75/7.04 thf(zip_derived_cl256, plain, 50.75/7.04 (( (((((((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.75/7.04 Y1))) => 50.75/7.04 ('#sk5' @ Y0 @ Y1))))))))) & 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk5' @ Y1 @ Y2) & 50.75/7.04 ('#sk5' @ Y0 @ Y1))) => 50.75/7.04 ('#sk5' @ Y0 @ Y2)))))))))))))) => 50.75/7.04 ($false))) 50.75/7.04 | ~ ('#form19'))), 50.75/7.04 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl11])). 50.75/7.04 thf(zip_derived_cl257, plain, 50.75/7.04 (( (((~) @ (((((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.75/7.04 Y0 @ Y1))) => 50.75/7.04 ('#sk5' @ Y0 @ Y1))))))))) & 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk5' @ Y1 @ Y2) & 50.75/7.04 ('#sk5' @ Y0 @ Y1))) => 50.75/7.04 ('#sk5' @ Y0 @ Y2)))))))))))))))) 50.75/7.04 | ~ ('#form19'))), 50.75/7.04 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl256])). 50.75/7.04 thf(zip_derived_cl258, plain, 50.75/7.04 ((~ (((((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 50.75/7.04 ('#sk5' @ Y0 @ Y1))))))))) & 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk5' @ Y1 @ Y2) & 50.75/7.04 ('#sk5' @ Y0 @ Y1))) => 50.75/7.04 ('#sk5' @ Y0 @ Y2)))))))))))))) 50.75/7.04 | ~ ('#form19'))), 50.75/7.04 inference('simplify nested equalities', [status(thm)], 50.75/7.04 [zip_derived_cl257])). 50.75/7.04 thf(zip_derived_cl259, plain, 50.75/7.04 ((~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 50.75/7.04 ('#sk5' @ Y0 @ Y1))))))))) 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk5' @ Y1 @ Y2) & 50.75/7.04 ('#sk5' @ Y0 @ Y1))) => 50.75/7.04 ('#sk5' @ Y0 @ Y2)))))))))))) 50.75/7.04 | ~ ('#form19'))), 50.75/7.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl258])). 50.75/7.04 thf(zip_derived_cl105, plain, 50.75/7.04 (![X2 : a > a > $o]: 50.75/7.04 ( ('#form185' @ X2) 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 (((((X2 @ Y1 @ Y2) & (X2 @ 50.75/7.04 Y0 @ Y1))) => 50.75/7.04 (X2 @ Y0 @ Y2)))))))))))))), 50.75/7.04 define([status(thm)])). 50.75/7.04 thf(zip_derived_cl260, plain, 50.75/7.04 ((~ ('#form185' @ '#sk5') 50.75/7.04 | ~ ('#form19') 50.75/7.04 | ~ (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 50.75/7.04 ('#sk5' @ Y0 @ Y1))))))))))), 50.75/7.04 inference('renaming', [status(thm)], 50.75/7.04 [zip_derived_cl259, zip_derived_cl105])). 50.75/7.04 thf(zip_derived_cl261, plain, 50.75/7.04 ((~ (((!!) @ (^[Y0 : a]: 50.75/7.04 ((((('#sk2' @ ('#sk87' @ '#sk5') @ Y0) | ('#sk1' @ 50.75/7.04 ('#sk87' @ '#sk5') @ Y0))) => 50.75/7.04 ('#sk5' @ ('#sk87' @ '#sk5') @ Y0)))))) 50.75/7.04 | ~ ('#form19') 50.75/7.04 | ~ ('#form185' @ '#sk5'))), 50.75/7.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl260])). 50.75/7.04 thf(zip_derived_cl262, plain, 50.75/7.04 ((~ ((((('#sk2' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')) | ('#sk1' @ 50.75/7.04 ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')))) => 50.75/7.04 ('#sk5' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')))) 50.75/7.04 | ~ ('#form185' @ '#sk5') 50.75/7.04 | ~ ('#form19'))), 50.75/7.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl261])). 50.75/7.04 thf(zip_derived_cl263, plain, 50.75/7.04 (( ((('#sk2' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')) | ('#sk1' @ 50.75/7.04 ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')))) 50.75/7.04 | ~ ('#form19') 50.75/7.04 | ~ ('#form185' @ '#sk5'))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl262])). 50.75/7.04 thf(zip_derived_cl265, plain, 50.75/7.04 (( ('#sk2' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')) 50.75/7.04 | ('#sk1' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')) 50.75/7.04 | ~ ('#form185' @ '#sk5') 50.75/7.04 | ~ ('#form19'))), 50.75/7.04 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl263])). 50.75/7.04 thf(zip_derived_cl10, plain, 50.75/7.04 ( (((((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk5' @ Y0 @ Y1) & 50.75/7.04 ('#sk5' @ Y1 @ Y2))) => 50.75/7.04 ('#sk5' @ Y0 @ Y2)))))))))))) & 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 50.75/7.04 ('#sk5' @ Y0 @ Y1)))))))))))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 50.75/7.04 thf(zip_derived_cl14, plain, 50.75/7.04 ( (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 50.75/7.04 ('#sk5' @ Y0 @ Y1)))))))))), 50.75/7.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 50.75/7.04 thf(zip_derived_cl17, plain, 50.75/7.04 (![X2 : a]: 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 ((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) => 50.75/7.04 ('#sk5' @ X2 @ Y0))))))), 50.75/7.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 50.75/7.04 thf(zip_derived_cl21, plain, 50.75/7.04 (![X2 : a, X4 : a]: 50.75/7.04 ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) => ('#sk5' @ X2 @ X4)))), 50.75/7.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 50.75/7.04 thf(zip_derived_cl25, plain, 50.75/7.04 (![X2 : a, X4 : a]: 50.75/7.04 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) | ('#sk5' @ X2 @ X4))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 50.75/7.04 thf(zip_derived_cl36, plain, 50.75/7.04 (![X2 : a, X4 : a]: (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 50.75/7.04 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl25])). 50.75/7.04 thf(zip_derived_cl13, plain, 50.75/7.04 ( (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 (((!!) @ (^[Y2 : a]: 50.75/7.04 ((((('#sk5' @ Y0 @ Y1) & ('#sk5' @ 50.75/7.04 Y1 @ Y2))) => 50.75/7.04 ('#sk5' @ Y0 @ Y2))))))))))))), 50.75/7.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 50.75/7.04 thf(zip_derived_cl16, plain, 50.75/7.04 (![X2 : a]: 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 (((!!) @ (^[Y1 : a]: 50.75/7.04 ((((('#sk5' @ X2 @ Y0) & ('#sk5' @ Y0 @ Y1))) => 50.75/7.04 ('#sk5' @ X2 @ Y1)))))))))), 50.75/7.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 50.75/7.04 thf(zip_derived_cl20, plain, 50.75/7.04 (![X2 : a, X4 : a]: 50.75/7.04 (((!!) @ (^[Y0 : a]: 50.75/7.04 ((((('#sk5' @ X2 @ X4) & ('#sk5' @ X4 @ Y0))) => 50.75/7.04 ('#sk5' @ X2 @ Y0))))))), 50.75/7.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 50.75/7.04 thf(zip_derived_cl24, plain, 50.75/7.04 (![X2 : a, X4 : a, X6 : a]: 50.75/7.04 ((((('#sk5' @ X2 @ X4) & ('#sk5' @ X4 @ X6))) => ('#sk5' @ X2 @ X6)))), 50.75/7.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])). 50.75/7.04 thf(zip_derived_cl34, plain, 50.75/7.04 (![X2 : a, X4 : a, X6 : a]: 50.75/7.04 (~ ((('#sk5' @ X2 @ X4) & ('#sk5' @ X4 @ X6))) | ('#sk5' @ X2 @ X6))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl24])). 50.75/7.04 thf(zip_derived_cl46, plain, 50.75/7.04 (![X2 : a, X4 : a, X6 : a]: 50.75/7.04 (~ ('#sk5' @ X2 @ X4) | ~ ('#sk5' @ X4 @ X6) | ('#sk5' @ X2 @ X6))), 50.75/7.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl34])). 50.75/7.04 thf(zip_derived_cl264, plain, 50.75/7.04 ((~ ('#sk5' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')) 50.75/7.04 | ~ ('#form19') 50.75/7.04 | ~ ('#form185' @ '#sk5'))), 50.75/7.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl262])). 50.75/7.04 thf(zip_derived_cl35, plain, 50.75/7.04 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 50.75/7.04 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl25])). 50.75/7.04 thf(zip_derived_cl6760, plain, ($false), 50.75/7.04 inference('eprover', [status(thm)], 50.75/7.04 [zip_derived_cl94, zip_derived_cl169, zip_derived_cl173, 50.75/7.04 zip_derived_cl162, zip_derived_cl177, zip_derived_cl168, 50.75/7.04 zip_derived_cl150, zip_derived_cl174, zip_derived_cl163, 50.75/7.04 zip_derived_cl56, zip_derived_cl151, zip_derived_cl176, 50.75/7.04 zip_derived_cl207, zip_derived_cl208, zip_derived_cl113, 50.75/7.04 zip_derived_cl157, zip_derived_cl112, zip_derived_cl158, 50.75/7.04 zip_derived_cl156, zip_derived_cl137, zip_derived_cl155, 50.75/7.04 zip_derived_cl125, zip_derived_cl154, zip_derived_cl153, 50.75/7.04 zip_derived_cl144, zip_derived_cl265, zip_derived_cl36, 50.75/7.04 zip_derived_cl46, zip_derived_cl264, zip_derived_cl35])). 50.75/7.04 50.75/7.04 % SZS output end Refutation 50.75/7.04 50.75/7.04 50.75/7.04 % Terminating... 50.98/7.12 % Runner terminated. 50.98/7.12 % Zipperpin 1.5 exiting 50.98/7.13 EOF