0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.yAiOLJIwRh true 0.14/0.34 % Computer : n023.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 : Mon Jul 3 05:03:06 EDT 2023 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 0.14/0.34 % Number of cores: 8 0.14/0.35 % Python version: Python 3.6.8 0.14/0.35 % Running in HO mode 0.45/0.62 % Total configuration time : 828 0.45/0.62 % Estimated wc time : 1656 0.45/0.62 % Estimated cpu time (8 cpus) : 207.0 0.51/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.51/0.70 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.51/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.51/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.51/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.52/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.52/0.75 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.53/0.76 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 50.13/7.01 % Solved by lams/20_acsne_simpl.sh. 50.13/7.01 % done 869 iterations in 6.119s 50.13/7.01 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 50.13/7.01 % SZS output start Refutation 50.13/7.01 thf(a_type, type, a: $tType). 50.13/7.01 thf('#sk4_type', type, '#sk4': a). 50.13/7.01 thf('#sk30_type', type, '#sk30': a > a > $o). 50.13/7.01 thf('#sk103_type', type, '#sk103': (a > a > $o) > a). 50.13/7.01 thf('#form374_type', type, '#form374': (a > a > $o) > $o). 50.13/7.01 thf('#form235_type', type, '#form235': (a > a > $o) > $o). 50.13/7.01 thf('#sk3_type', type, '#sk3': a). 50.13/7.01 thf('#sk348_type', type, '#sk348': (a > a > $o) > a). 50.13/7.01 thf('#sk12_type', type, '#sk12': a). 50.13/7.01 thf('#sk21_type', type, '#sk21': a > a > $o). 50.13/7.01 thf('#sk47_type', type, '#sk47': (a > a > $o) > a). 50.13/7.01 thf('#sk420_type', type, '#sk420': (a > a > $o) > a). 50.13/7.01 thf('#sk77_type', type, '#sk77': (a > a > $o) > a). 50.13/7.01 thf('#sk6_type', type, '#sk6': a). 50.13/7.01 thf('#sk2_type', type, '#sk2': a > a > $o). 50.13/7.01 thf('#sk325_type', type, '#sk325': (a > a > $o) > a). 50.13/7.01 thf('#sk357_type', type, '#sk357': (a > a > $o) > a). 50.13/7.01 thf('#sk8_type', type, '#sk8': a). 50.13/7.01 thf('#sk10_type', type, '#sk10': a). 50.13/7.01 thf('#sk220_type', type, '#sk220': (a > a > $o) > a). 50.13/7.01 thf('#sk156_type', type, '#sk156': (a > a > $o) > a). 50.13/7.01 thf('#sk7_type', type, '#sk7': a). 50.13/7.01 thf('#form419_type', type, '#form419': (a > a > $o) > $o). 50.13/7.01 thf('#sk248_type', type, '#sk248': (a > a > $o) > a). 50.13/7.01 thf('#form9_type', type, '#form9': $o). 50.13/7.01 thf('#form11_type', type, '#form11': $o). 50.13/7.01 thf('#sk5_type', type, '#sk5': a > a > $o). 50.13/7.01 thf('#sk1_type', type, '#sk1': a > a > $o). 50.13/7.01 thf('#form94_type', type, '#form94': $o). 50.13/7.01 thf('#sk436_type', type, '#sk436': (a > a > $o) > a). 50.13/7.01 thf('#sk428_type', type, '#sk428': (a > a > $o) > a). 50.13/7.01 thf('#sk181_type', type, '#sk181': (a > a > $o) > a). 50.13/7.01 thf('#sk525_type', type, '#sk525': (a > a > $o) > a). 50.13/7.01 thf(cTHM250H_pme, conjecture, 50.13/7.01 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 50.13/7.01 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 50.13/7.01 ( ( ( ![Xp1:( a > a > $o )]: 50.13/7.01 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 50.13/7.01 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 50.13/7.01 ( ![Xx1:a,Xy1:a]: 50.13/7.01 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.13/7.01 ( Xp1 @ Xy0 @ Xz ) ) ) & 50.13/7.01 ( ![Xp1:( a > a > $o )]: 50.13/7.01 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 50.13/7.01 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 50.13/7.01 ( ![Xx1:a,Xy1:a]: 50.13/7.01 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 50.13/7.01 ( ![Xp1:( a > a > $o )]: 50.13/7.01 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 50.13/7.01 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 50.13/7.01 ( ![Xx1:a,Xy1:a]: 50.13/7.01 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) & 50.13/7.01 ( ![Xx0:a,Xy0:a]: 50.13/7.01 ( ( ( ![Xp1:( a > a > $o )]: 50.13/7.01 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 50.13/7.01 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xz ) ) ) & 50.13/7.01 ( ![Xx1:a,Xy1:a]: 50.13/7.01 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 50.13/7.01 ( ![Xp1:( a > a > $o )]: 50.13/7.01 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 50.13/7.01 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xz ) ) ) & 50.13/7.01 ( ![Xx1:a,Xy1:a]: 50.13/7.01 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 50.13/7.01 ( ![Xp1:( a > a > $o )]: 50.13/7.01 ( ( ( ![Xx1:a,Xy1:a]: 50.13/7.01 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 50.13/7.01 ( ![Xx1:a,Xy1:a,Xz:a]: 50.13/7.01 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) & 50.13/7.01 ( ~( ![Xp1:( a > a > $o )]: 50.13/7.01 ( ( ( ![Xx0:a,Xy0:a]: 50.13/7.01 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 50.13/7.01 ( ![Xx0:a,Xy0:a,Xz:a]: 50.13/7.01 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 50.13/7.01 ( Xp1 @ Xx @ Xy ) ) ) ) ) | 50.13/7.01 ( ![Xp1:( a > a > $o )]: 50.13/7.01 ( ( ( ![Xx0:a,Xy0:a]: 50.13/7.01 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 50.13/7.01 ( ![Xx0:a,Xy0:a,Xz:a]: 50.13/7.01 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 50.13/7.01 ( Xp1 @ Xx @ Xy ) ) ) ))). 50.13/7.01 thf(zf_stmt_0, negated_conjecture, 50.13/7.01 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 50.13/7.01 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 50.13/7.01 ( ( ( ![Xp1:( a > a > $o )]: 50.13/7.01 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 50.13/7.01 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 50.13/7.01 ( ![Xx1:a,Xy1:a]: 50.13/7.01 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.13/7.01 ( Xp1 @ Xy0 @ Xz ) ) ) & 50.13/7.01 ( ![Xp1:( a > a > $o )]: 50.13/7.01 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 50.13/7.01 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 50.13/7.01 ( ![Xx1:a,Xy1:a]: 50.13/7.01 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 50.13/7.01 ( ![Xp1:( a > a > $o )]: 50.13/7.01 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 50.13/7.01 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 50.13/7.01 ( ![Xx1:a,Xy1:a]: 50.13/7.01 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) & 50.13/7.01 ( ![Xx0:a,Xy0:a]: 50.13/7.01 ( ( ( ![Xp1:( a > a > $o )]: 50.13/7.01 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 50.13/7.01 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xz ) ) ) & 50.13/7.01 ( ![Xx1:a,Xy1:a]: 50.13/7.01 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 50.13/7.01 ( ![Xp1:( a > a > $o )]: 50.13/7.01 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 50.13/7.01 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xz ) ) ) & 50.13/7.01 ( ![Xx1:a,Xy1:a]: 50.13/7.01 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 50.13/7.01 ( ![Xp1:( a > a > $o )]: 50.13/7.01 ( ( ( ![Xx1:a,Xy1:a]: 50.13/7.01 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 50.13/7.01 ( ![Xx1:a,Xy1:a,Xz:a]: 50.13/7.01 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 50.13/7.01 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) & 50.13/7.01 ( ~( ![Xp1:( a > a > $o )]: 50.13/7.01 ( ( ( ![Xx0:a,Xy0:a]: 50.13/7.01 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 50.13/7.01 ( ![Xx0:a,Xy0:a,Xz:a]: 50.13/7.01 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 50.13/7.01 ( Xp1 @ Xx @ Xy ) ) ) ) ) | 50.13/7.01 ( ![Xp1:( a > a > $o )]: 50.13/7.01 ( ( ( ![Xx0:a,Xy0:a]: 50.13/7.01 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 50.13/7.01 ( ![Xx0:a,Xy0:a,Xz:a]: 50.13/7.01 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 50.13/7.01 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 50.13/7.01 ( Xp1 @ Xx @ Xy ) ) ) ) )), 50.13/7.01 inference('cnf.neg', [status(esa)], [cTHM250H_pme])). 50.13/7.01 thf(zip_derived_cl0, plain, 50.13/7.01 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.01 (((!!) @ (^[Y1 : a > a > $o]: 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (((((((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y9 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y10 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y7 @ 50.13/7.01 Y8 @ 50.13/7.01 Y9) & 50.13/7.01 (Y7 @ 50.13/7.01 Y9 @ Y10))) => 50.13/7.01 (Y7 @ 50.13/7.01 Y8 @ Y10)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y9 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y1 @ 50.13/7.01 Y8 @ 50.13/7.01 Y9) | 50.13/7.01 (Y0 @ 50.13/7.01 Y8 @ Y9))) => 50.13/7.01 (Y7 @ 50.13/7.01 Y8 @ Y9))))))))))) => 50.13/7.01 (Y7 @ 50.13/7.01 Y5 @ Y6)))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y9 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y10 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y7 @ 50.13/7.01 Y8 @ 50.13/7.01 Y9) & 50.13/7.01 (Y7 @ 50.13/7.01 Y9 @ Y10))) => 50.13/7.01 (Y7 @ 50.13/7.01 Y8 @ Y10)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y9 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y0 @ 50.13/7.01 Y8 @ 50.13/7.01 Y9) | 50.13/7.01 (Y1 @ 50.13/7.01 Y8 @ Y9))) => 50.13/7.01 (Y7 @ 50.13/7.01 Y8 @ Y9))))))))))) => 50.13/7.01 (Y7 @ 50.13/7.01 Y4 @ Y5)))))))) => 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y9 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y10 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y7 @ 50.13/7.01 Y9 @ 50.13/7.01 Y10) & 50.13/7.01 (Y7 @ 50.13/7.01 Y8 @ Y9))) => 50.13/7.01 (Y7 @ 50.13/7.01 Y8 @ Y10)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y9 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y0 @ 50.13/7.01 Y8 @ 50.13/7.01 Y9) | 50.13/7.01 (Y1 @ 50.13/7.01 Y8 @ Y9))) => 50.13/7.01 (Y7 @ 50.13/7.01 Y8 @ Y9))))))))))) => 50.13/7.01 (Y7 @ 50.13/7.01 Y4 @ Y6))))))))))))))))) & 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y9 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y6 @ 50.13/7.01 Y8 @ 50.13/7.01 Y9) & 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ Y8))) => 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ Y9)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (Y0 @ 50.13/7.01 Y7 @ 50.13/7.01 Y8) => 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ Y8))))))))))) => 50.13/7.01 (Y6 @ 50.13/7.01 Y4 @ Y5)))))) | 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y9 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y6 @ 50.13/7.01 Y8 @ 50.13/7.01 Y9) & 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ Y8))) => 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ Y9)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (Y1 @ 50.13/7.01 Y7 @ 50.13/7.01 Y8) => 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ Y8))))))))))) => 50.13/7.01 (Y6 @ 50.13/7.01 Y4 @ Y5)))))))) => 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y0 @ 50.13/7.01 Y7 @ 50.13/7.01 Y8) | 50.13/7.01 (Y1 @ 50.13/7.01 Y7 @ Y8))) => 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ Y8))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y9 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ 50.13/7.01 Y8) & 50.13/7.01 (Y6 @ 50.13/7.01 Y8 @ Y9))) => 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ Y9)))))))))))))) => 50.13/7.01 (Y6 @ 50.13/7.01 Y4 @ Y5)))))))))))))) & 50.13/7.01 (((~) @ (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y4 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y1 @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) | 50.13/7.01 (Y0 @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y6))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y4 @ 50.13/7.01 Y6 @ 50.13/7.01 Y7) & 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y7)))))))))))))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y2 @ Y3)))))))))) | 50.13/7.01 (((!!) @ (^[Y4 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y1 @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) | 50.13/7.01 (Y0 @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y6))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y4 @ 50.13/7.01 Y6 @ 50.13/7.01 Y7) & 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y7)))))))))))))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y2 @ Y3))))))))))))))))))))), 50.13/7.01 inference('cnf', [status(esa)], [zf_stmt_0])). 50.13/7.01 thf(zip_derived_cl1, plain, 50.13/7.01 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.01 (((!!) @ (^[Y1 : a]: 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 (((((((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y9 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ 50.13/7.01 Y8) & 50.13/7.01 (Y6 @ 50.13/7.01 Y8 @ Y9))) => 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ Y9)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y0 @ 50.13/7.01 Y7 @ 50.13/7.01 Y8) | 50.13/7.01 ('#sk1' @ 50.13/7.01 Y7 @ Y8))) => 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ Y8))))))))))) => 50.13/7.01 (Y6 @ 50.13/7.01 Y4 @ Y5)))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y9 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ 50.13/7.01 Y8) & 50.13/7.01 (Y6 @ 50.13/7.01 Y8 @ Y9))) => 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ Y9)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y7 @ 50.13/7.01 Y8) | 50.13/7.01 (Y0 @ 50.13/7.01 Y7 @ Y8))) => 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ Y8))))))))))) => 50.13/7.01 (Y6 @ 50.13/7.01 Y3 @ Y4)))))))) => 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y9 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y6 @ 50.13/7.01 Y8 @ 50.13/7.01 Y9) & 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ Y8))) => 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ Y9)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y7 @ 50.13/7.01 Y8) | 50.13/7.01 (Y0 @ 50.13/7.01 Y7 @ Y8))) => 50.13/7.01 (Y6 @ 50.13/7.01 Y7 @ Y8))))))))))) => 50.13/7.01 (Y6 @ 50.13/7.01 Y3 @ Y5))))))))))))))))) & 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (((((( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y5 @ 50.13/7.01 Y7 @ 50.13/7.01 Y8) & 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ Y7))) => 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ Y8)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y6 @ 50.13/7.01 Y7) => 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ Y7))))))))))) => 50.13/7.01 (Y5 @ 50.13/7.01 Y3 @ Y4)))))) | 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y5 @ 50.13/7.01 Y7 @ 50.13/7.01 Y8) & 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ Y7))) => 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ Y8)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (Y0 @ 50.13/7.01 Y6 @ 50.13/7.01 Y7) => 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ Y7))))))))))) => 50.13/7.01 (Y5 @ 50.13/7.01 Y3 @ Y4)))))))) => 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y5 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y6 @ 50.13/7.01 Y7) | 50.13/7.01 (Y0 @ 50.13/7.01 Y6 @ Y7))) => 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ Y7))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ 50.13/7.01 Y7) & 50.13/7.01 (Y5 @ 50.13/7.01 Y7 @ Y8))) => 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ Y8)))))))))))))) => 50.13/7.01 (Y5 @ 50.13/7.01 Y3 @ Y4)))))))))))))) & 50.13/7.01 (((~) @ (((!!) @ (^[Y3 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y0 @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) | 50.13/7.01 ('#sk1' @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y3 @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) & 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y6)))))))))))))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y1 @ Y2)))))))))) | 50.13/7.01 (((!!) @ (^[Y3 : a > a > $o]: 50.13/7.01 (((((((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y0 @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) | 50.13/7.01 ('#sk1' @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))))))))) & 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y3 @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) & 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y6)))))))))))))) => 50.13/7.01 (Y3 @ Y1 @ Y2)))))))))))))))))), 50.13/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 50.13/7.01 thf(zip_derived_cl2, plain, 50.13/7.01 (~ (((!!) @ (^[Y0 : a]: 50.13/7.01 (((!!) @ (^[Y1 : a]: 50.13/7.01 (((((((!!) @ (^[Y2 : a]: 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (((((( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ 50.13/7.01 Y7) & 50.13/7.01 (Y5 @ 50.13/7.01 Y7 @ Y8))) => 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ Y8)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk2' @ 50.13/7.01 Y6 @ 50.13/7.01 Y7) | 50.13/7.01 ('#sk1' @ 50.13/7.01 Y6 @ Y7))) => 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ Y7))))))))))) => 50.13/7.01 (Y5 @ 50.13/7.01 Y3 @ Y4)))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ 50.13/7.01 Y7) & 50.13/7.01 (Y5 @ 50.13/7.01 Y7 @ Y8))) => 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ Y8)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y6 @ 50.13/7.01 Y7) | 50.13/7.01 ('#sk2' @ 50.13/7.01 Y6 @ Y7))) => 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ Y7))))))))))) => 50.13/7.01 (Y5 @ 50.13/7.01 Y2 @ Y3)))))))) => 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y5 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y8 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y5 @ 50.13/7.01 Y7 @ 50.13/7.01 Y8) & 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ Y7))) => 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ Y8)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y6 @ 50.13/7.01 Y7) | 50.13/7.01 ('#sk2' @ 50.13/7.01 Y6 @ Y7))) => 50.13/7.01 (Y5 @ 50.13/7.01 Y6 @ Y7))))))))))) => 50.13/7.01 (Y5 @ 50.13/7.01 Y2 @ Y4))))))))))))))))) & 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (((((((!!) @ ( 50.13/7.01 ^[Y4 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y4 @ 50.13/7.01 Y6 @ 50.13/7.01 Y7) & 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y7)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) => 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y6))))))))))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y2 @ Y3)))))) | 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y4 @ 50.13/7.01 Y6 @ 50.13/7.01 Y7) & 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y7)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 ('#sk2' @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) => 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y6))))))))))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y2 @ Y3)))))))) => 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : 50.13/7.01 a > a > $o]: 50.13/7.01 (((( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) | 50.13/7.01 ('#sk2' @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y6))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) & 50.13/7.01 (Y4 @ 50.13/7.01 Y6 @ Y7))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y7)))))))))))))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y2 @ Y3)))))))))))))) & 50.13/7.01 (((~) @ (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.01 (((((((!!) @ ( 50.13/7.01 ^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk2' @ 50.13/7.01 Y3 @ 50.13/7.01 Y4) | 50.13/7.01 ('#sk1' @ 50.13/7.01 Y3 @ Y4))) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))))))))) & 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y2 @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) & 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y5)))))))))))))) => 50.13/7.01 (Y2 @ Y0 @ Y1)))))))))) | 50.13/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.01 (((((((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (((( 50.13/7.01 ('#sk2' @ 50.13/7.01 Y3 @ Y4) | 50.13/7.01 ('#sk1' @ 50.13/7.01 Y3 @ Y4))) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))))))))) & 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y2 @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) & 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y5)))))))))))))) => 50.13/7.01 (Y2 @ Y0 @ Y1))))))))))))))), 50.13/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 50.13/7.01 thf(zip_derived_cl3, plain, 50.13/7.01 (~ (((!!) @ (^[Y0 : a]: 50.13/7.01 (((((((!!) @ (^[Y1 : a]: 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (((((((!!) @ ( 50.13/7.01 ^[Y4 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) & 50.13/7.01 (Y4 @ 50.13/7.01 Y6 @ Y7))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y7)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk2' @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) | 50.13/7.01 ('#sk1' @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y6))))))))))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y2 @ Y3)))))) & 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : 50.13/7.01 a > a > $o]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) & 50.13/7.01 (Y4 @ 50.13/7.01 Y6 @ Y7))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y7)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) | 50.13/7.01 ('#sk2' @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y6))))))))))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y1 @ Y2)))))))) => 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : 50.13/7.01 a > a > $o]: 50.13/7.01 (((( 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y7 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y4 @ 50.13/7.01 Y6 @ 50.13/7.01 Y7) & 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y7)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) | 50.13/7.01 ('#sk2' @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y5 @ Y6))))))))))) => 50.13/7.01 (Y4 @ 50.13/7.01 Y1 @ Y3))))))))))))))))) & 50.13/7.01 (((!!) @ (^[Y1 : a]: 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 (((((((!!) @ (^[Y3 : a > a > $o]: 50.13/7.01 (((((( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y3 @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) & 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y6)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))))))))))) => 50.13/7.01 (Y3 @ Y1 @ 50.13/7.01 Y2)))))) | 50.13/7.01 (((!!) @ (^[Y3 : a > a > $o]: 50.13/7.01 (((((( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y3 @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) & 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y6)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 ('#sk2' @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))))))))))) => 50.13/7.01 (Y3 @ Y1 @ 50.13/7.01 Y2)))))))) => 50.13/7.01 (((!!) @ (^[Y3 : a > a > $o]: 50.13/7.01 (((((((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) | 50.13/7.01 ('#sk2' @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))))))))) & 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) & 50.13/7.01 (Y3 @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y6)))))))))))))) => 50.13/7.01 (Y3 @ Y1 @ Y2)))))))))))))) & 50.13/7.01 (((~) @ (((!!) @ (^[Y1 : a > a > $o]: 50.13/7.01 (((((((!!) @ (^[Y2 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y3 : a]: 50.13/7.01 ((((('#sk2' @ 50.13/7.01 Y2 @ Y3) | 50.13/7.01 ('#sk1' @ 50.13/7.01 Y2 @ Y3))) => 50.13/7.01 (Y1 @ Y2 @ 50.13/7.01 Y3))))))))) & 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y1 @ 50.13/7.01 Y3 @ 50.13/7.01 Y4) & 50.13/7.01 (Y1 @ 50.13/7.01 Y2 @ Y3))) => 50.13/7.01 (Y1 @ 50.13/7.01 Y2 @ Y4)))))))))))))) => 50.13/7.01 (Y1 @ '#sk3' @ Y0)))))))))) | 50.13/7.01 (((!!) @ (^[Y1 : a > a > $o]: 50.13/7.01 (((((((!!) @ (^[Y2 : a]: 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 ((((('#sk2' @ 50.13/7.01 Y2 @ Y3) | 50.13/7.01 ('#sk1' @ 50.13/7.01 Y2 @ Y3))) => 50.13/7.01 (Y1 @ Y2 @ Y3))))))))) & 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (((( 50.13/7.01 (Y1 @ 50.13/7.01 Y3 @ Y4) & 50.13/7.01 (Y1 @ 50.13/7.01 Y2 @ Y3))) => 50.13/7.01 (Y1 @ 50.13/7.01 Y2 @ Y4)))))))))))))) => 50.13/7.01 (Y1 @ '#sk3' @ Y0)))))))))))), 50.13/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 50.13/7.01 thf(zip_derived_cl4, plain, 50.13/7.01 (~ (((((((!!) @ (^[Y0 : a]: 50.13/7.01 (((!!) @ (^[Y1 : a]: 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 (((((((!!) @ (^[Y3 : a > a > $o]: 50.13/7.01 (((((( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) & 50.13/7.01 (Y3 @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y6)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk2' @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) | 50.13/7.01 ('#sk1' @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))))))))))) => 50.13/7.01 (Y3 @ Y1 @ 50.13/7.01 Y2)))))) & 50.13/7.01 (((!!) @ (^[Y3 : a > a > $o]: 50.13/7.01 (((((( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) & 50.13/7.01 (Y3 @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y6)))))))))))) & 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) | 50.13/7.01 ('#sk2' @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))))))))))) => 50.13/7.01 (Y3 @ Y0 @ 50.13/7.01 Y1)))))))) => 50.13/7.01 (((!!) @ (^[Y3 : a > a > $o]: 50.13/7.01 (((((((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y3 @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) & 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y6)))))))))))) & 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) | 50.13/7.01 ('#sk2' @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))))))))))) => 50.13/7.01 (Y3 @ Y0 @ Y2))))))))))))))))) & 50.13/7.01 (((!!) @ (^[Y0 : a]: 50.13/7.01 (((!!) @ (^[Y1 : a]: 50.13/7.01 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.01 (((((((!!) @ (^[Y3 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y2 @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) & 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y5)))))))))))) & 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y3 @ 50.13/7.01 Y4) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))))))))))) => 50.13/7.01 (Y2 @ Y0 @ Y1)))))) | 50.13/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.01 (((((((!!) @ (^[Y3 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y2 @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) & 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y5)))))))))))) & 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 ('#sk2' @ 50.13/7.01 Y3 @ 50.13/7.01 Y4) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))))))))))) => 50.13/7.01 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.01 (((((((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y3 @ 50.13/7.01 Y4) | 50.13/7.01 ('#sk2' @ 50.13/7.01 Y3 @ Y4))) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))))))))) & 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ 50.13/7.01 Y4) & 50.13/7.01 (Y2 @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y5)))))))))))))) => 50.13/7.01 (Y2 @ Y0 @ Y1)))))))))))))) & 50.13/7.01 (((~) @ (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.01 (((((((!!) @ (^[Y1 : a]: 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 ((((('#sk2' @ 50.13/7.01 Y1 @ Y2) | 50.13/7.01 ('#sk1' @ 50.13/7.01 Y1 @ Y2))) => 50.13/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.01 (((!!) @ (^[Y1 : a]: 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y3 : a]: 50.13/7.01 (((((Y0 @ 50.13/7.01 Y2 @ Y3) & 50.13/7.01 (Y0 @ 50.13/7.01 Y1 @ Y2))) => 50.13/7.01 (Y0 @ Y1 @ 50.13/7.01 Y3)))))))))))))) => 50.13/7.01 (Y0 @ '#sk3' @ '#sk4')))))))))) | 50.13/7.01 (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.01 (((((((!!) @ (^[Y1 : a]: 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.01 ('#sk1' @ Y1 @ Y2))) => 50.13/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.01 (((!!) @ (^[Y1 : a]: 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (((((Y0 @ Y2 @ 50.13/7.01 Y3) & (Y0 @ 50.13/7.01 Y1 @ Y2))) => 50.13/7.01 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.01 (Y0 @ '#sk3' @ '#sk4'))))))))), 50.13/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 50.13/7.01 thf(zip_derived_cl5, plain, 50.13/7.01 (~ (((((!!) @ (^[Y0 : a]: 50.13/7.01 (((!!) @ (^[Y1 : a]: 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 (((((((!!) @ (^[Y3 : a > a > $o]: 50.13/7.01 (((((((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) & 50.13/7.01 (Y3 @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y6)))))))))))) & 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk2' @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) | 50.13/7.01 ('#sk1' @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))))))))))) => 50.13/7.01 (Y3 @ Y1 @ Y2)))))) & 50.13/7.01 (((!!) @ (^[Y3 : a > a > $o]: 50.13/7.01 (((((((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) & 50.13/7.01 (Y3 @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y6)))))))))))) & 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) | 50.13/7.01 ('#sk2' @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))))))))))) => 50.13/7.01 (Y3 @ Y0 @ Y1)))))))) => 50.13/7.01 (((!!) @ (^[Y3 : a > a > $o]: 50.13/7.01 (((((((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y3 @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) & 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y6)))))))))))) & 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) | 50.13/7.01 ('#sk2' @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))))))))))) => 50.13/7.01 (Y3 @ Y0 @ Y2))))))))))))))))) & 50.13/7.01 (((!!) @ (^[Y0 : a]: 50.13/7.01 (((!!) @ (^[Y1 : a]: 50.13/7.01 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.01 (((((((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y2 @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) & 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y5)))))))))))) & 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y3 @ 50.13/7.01 Y4) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))))))))))) => 50.13/7.01 (Y2 @ Y0 @ Y1)))))) | 50.13/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.01 (((((((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y2 @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) & 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y5)))))))))))) & 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 ('#sk2' @ 50.13/7.01 Y3 @ 50.13/7.01 Y4) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))))))))))) => 50.13/7.01 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.01 (((((((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y3 @ 50.13/7.01 Y4) | 50.13/7.01 ('#sk2' @ 50.13/7.01 Y3 @ Y4))) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))))))))) & 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ 50.13/7.01 Y4) & 50.13/7.01 (Y2 @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y5)))))))))))))) => 50.13/7.01 (Y2 @ Y0 @ Y1)))))))))))))) & 50.13/7.01 (((~) @ (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.01 (((((((!!) @ (^[Y1 : a]: 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 ((((('#sk2' @ Y1 @ 50.13/7.01 Y2) | ('#sk1' @ 50.13/7.01 Y1 @ Y2))) => 50.13/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.01 (((!!) @ (^[Y1 : a]: 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y0 @ 50.13/7.01 Y2 @ 50.13/7.01 Y3) & 50.13/7.01 (Y0 @ 50.13/7.01 Y1 @ Y2))) => 50.13/7.01 (Y0 @ 50.13/7.01 Y1 @ Y3)))))))))))))) => 50.13/7.01 (Y0 @ '#sk3' @ '#sk4'))))))))))), 50.13/7.01 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 50.13/7.01 thf(zip_derived_cl7, plain, 50.13/7.01 ((~ (((!!) @ (^[Y0 : a]: 50.13/7.01 (((!!) @ (^[Y1 : a]: 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 (((((((!!) @ (^[Y3 : a > a > $o]: 50.13/7.01 (((((((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 ( 50.13/7.01 ( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) & 50.13/7.01 (Y3 @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y6)))))))))))) & 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 ( 50.13/7.01 ( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk2' @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) | 50.13/7.01 ('#sk1' @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))))))))))) => 50.13/7.01 (Y3 @ Y1 @ Y2)))))) & 50.13/7.01 (((!!) @ (^[Y3 : a > a > $o]: 50.13/7.01 (((((((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 ( 50.13/7.01 ( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) & 50.13/7.01 (Y3 @ 50.13/7.01 Y5 @ Y6))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y6)))))))))))) & 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 ( 50.13/7.01 ( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) | 50.13/7.01 ('#sk2' @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))))))))))) => 50.13/7.01 (Y3 @ Y0 @ Y1)))))))) => 50.13/7.01 (((!!) @ (^[Y3 : a > a > $o]: 50.13/7.01 (((((((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y6 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y3 @ 50.13/7.01 Y5 @ 50.13/7.01 Y6) & 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y6)))))))))))) & 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) | 50.13/7.01 ('#sk2' @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y3 @ 50.13/7.01 Y4 @ Y5))))))))))) => 50.13/7.01 (Y3 @ Y0 @ Y2))))))))))))))))) 50.13/7.01 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.01 (((!!) @ (^[Y1 : a]: 50.13/7.01 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.01 (((((((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y2 @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) & 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y5)))))))))))) & 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y3 @ 50.13/7.01 Y4) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))))))))))) => 50.13/7.01 (Y2 @ Y0 @ Y1)))))) | 50.13/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.01 (((((((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y2 @ 50.13/7.01 Y4 @ 50.13/7.01 Y5) & 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y5)))))))))))) & 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 (( 50.13/7.01 ('#sk2' @ 50.13/7.01 Y3 @ 50.13/7.01 Y4) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))))))))))) => 50.13/7.01 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.01 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.01 (((((((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 ( 50.13/7.01 ( 50.13/7.01 (( 50.13/7.01 ('#sk1' @ 50.13/7.01 Y3 @ 50.13/7.01 Y4) | 50.13/7.01 ('#sk2' @ 50.13/7.01 Y3 @ Y4))) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y4))))))))) & 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 ( 50.13/7.01 ( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ 50.13/7.01 Y4) & 50.13/7.01 (Y2 @ 50.13/7.01 Y4 @ Y5))) => 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ Y5)))))))))))))) => 50.13/7.01 (Y2 @ Y0 @ Y1)))))))))))))) 50.13/7.01 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.01 (((((((!!) @ (^[Y1 : a]: 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.01 ('#sk1' @ Y1 @ Y2))) => 50.13/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.01 (((!!) @ (^[Y1 : a]: 50.13/7.01 (((!!) @ (^[Y2 : a]: 50.13/7.01 (((!!) @ (^[Y3 : a]: 50.13/7.01 (((((Y0 @ Y2 @ 50.13/7.01 Y3) & (Y0 @ 50.13/7.01 Y1 @ Y2))) => 50.13/7.01 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.01 (Y0 @ '#sk3' @ '#sk4')))))))), 50.13/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl5])). 50.13/7.01 thf(zip_derived_cl9, plain, 50.13/7.01 ((~ (((!!) @ (^[Y0 : a]: 50.13/7.01 (((!!) @ (^[Y1 : a]: 50.13/7.01 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.01 (((((((!!) @ (^[Y3 : a]: 50.13/7.01 (((!!) @ ( 50.13/7.01 ^[Y4 : a]: 50.13/7.01 ( 50.13/7.01 ( 50.13/7.01 (!!) @ ( 50.13/7.01 ^[Y5 : a]: 50.13/7.01 (( 50.13/7.01 (( 50.13/7.01 (Y2 @ 50.13/7.01 Y3 @ 50.13/7.01 Y4) & 50.13/7.01 (Y2 @ 50.13/7.02 Y4 @ Y5))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))) & 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ Y5))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ '#sk6' @ Y0)))))))) => 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (((( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ '#sk6' @ Y1)))))))))))))) 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.02 (Y0 @ '#sk3' @ '#sk4')))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))) | 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ Y5))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))))))))))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl7])). 50.13/7.02 thf(zip_derived_cl12, plain, 50.13/7.02 ((~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((((((!!) @ (^[Y1 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 (Y1 @ 50.13/7.02 Y2 @ 50.13/7.02 Y3) & 50.13/7.02 (Y1 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y1 @ 50.13/7.02 Y2 @ Y4)))))))))))) & 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 ((((('#sk2' @ 50.13/7.02 Y2 @ 50.13/7.02 Y3) | 50.13/7.02 ('#sk1' @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y1 @ Y2 @ 50.13/7.02 Y3))))))))))) => 50.13/7.02 (Y1 @ '#sk7' @ Y0)))))) & 50.13/7.02 (((!!) @ (^[Y1 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 (Y1 @ 50.13/7.02 Y2 @ 50.13/7.02 Y3) & 50.13/7.02 (Y1 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y1 @ 50.13/7.02 Y2 @ Y4)))))))))))) & 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 ((((('#sk1' @ 50.13/7.02 Y2 @ 50.13/7.02 Y3) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y1 @ Y2 @ 50.13/7.02 Y3))))))))))) => 50.13/7.02 (Y1 @ '#sk6' @ '#sk7')))))))) => 50.13/7.02 (((!!) @ (^[Y1 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (((( 50.13/7.02 (Y1 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y1 @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y1 @ 50.13/7.02 Y2 @ Y4)))))))))))) & 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 ((((('#sk1' @ 50.13/7.02 Y2 @ Y3) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y1 @ Y2 @ 50.13/7.02 Y3))))))))))) => 50.13/7.02 (Y1 @ '#sk6' @ Y0))))))))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))) | 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ Y5))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))))))))) 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.02 (Y0 @ '#sk3' @ '#sk4')))))))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl9])). 50.13/7.02 thf(zip_derived_cl15, plain, 50.13/7.02 ((~ (((((((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ 50.13/7.02 Y1 @ 50.13/7.02 Y2) & 50.13/7.02 (Y0 @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y0 @ Y1 @ 50.13/7.02 Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk7' @ '#sk8')))))) & 50.13/7.02 (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ 50.13/7.02 Y1 @ 50.13/7.02 Y2) & 50.13/7.02 (Y0 @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y0 @ Y1 @ 50.13/7.02 Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk1' @ Y1 @ Y2) | 50.13/7.02 ('#sk2' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk6' @ '#sk7')))))))) => 50.13/7.02 (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & 50.13/7.02 (Y0 @ Y1 @ 50.13/7.02 Y2))) => 50.13/7.02 (Y0 @ Y1 @ 50.13/7.02 Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk1' @ Y1 @ Y2) | 50.13/7.02 ('#sk2' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk6' @ '#sk8')))))))) 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.02 (Y0 @ '#sk3' @ '#sk4')))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))) | 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ Y5))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))))))))))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 50.13/7.02 thf(zip_derived_cl19, plain, 50.13/7.02 ((~ (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk1' @ Y1 @ Y2) | 50.13/7.02 ('#sk2' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk6' @ '#sk8')))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))) | 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ Y5))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))))))))) 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.02 (Y0 @ '#sk3' @ '#sk4')))))))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 50.13/7.02 thf(zip_derived_cl24, plain, 50.13/7.02 (( ('#form9') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))) | 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ Y5))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl25, plain, 50.13/7.02 ((~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((((((!!) @ (^[Y1 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 (Y1 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y1 @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y1 @ 50.13/7.02 Y2 @ Y4)))))))))))) & 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 ((('#sk1' @ 50.13/7.02 Y2 @ Y3) => 50.13/7.02 (Y1 @ Y2 @ 50.13/7.02 Y3))))))))))) => 50.13/7.02 (Y1 @ '#sk10' @ Y0)))))) | 50.13/7.02 (((!!) @ (^[Y1 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 (Y1 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y1 @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y1 @ 50.13/7.02 Y2 @ Y4)))))))))))) & 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 ((('#sk2' @ 50.13/7.02 Y2 @ Y3) => 50.13/7.02 (Y1 @ Y2 @ 50.13/7.02 Y3))))))))))) => 50.13/7.02 (Y1 @ '#sk10' @ Y0)))))))) => 50.13/7.02 (((!!) @ (^[Y1 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 ((((('#sk1' @ 50.13/7.02 Y2 @ Y3) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y1 @ Y2 @ 50.13/7.02 Y3))))))))) & 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (((( 50.13/7.02 (Y1 @ 50.13/7.02 Y2 @ 50.13/7.02 Y3) & 50.13/7.02 (Y1 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y1 @ 50.13/7.02 Y2 @ Y4)))))))))))))) => 50.13/7.02 (Y1 @ '#sk10' @ Y0))))))))))) 50.13/7.02 | ('#form9'))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl24])). 50.13/7.02 thf(zip_derived_cl37, plain, 50.13/7.02 ((~ (((((((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ 50.13/7.02 Y2 @ 50.13/7.02 Y3) & 50.13/7.02 (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ 50.13/7.02 Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((('#sk1' @ Y1 @ Y2) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk10' @ '#sk12')))))) | 50.13/7.02 (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ 50.13/7.02 Y2 @ 50.13/7.02 Y3) & 50.13/7.02 (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ 50.13/7.02 Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((('#sk2' @ Y1 @ Y2) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk10' @ '#sk12')))))))) => 50.13/7.02 (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk1' @ Y1 @ Y2) | 50.13/7.02 ('#sk2' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y1 @ 50.13/7.02 Y2) & 50.13/7.02 (Y0 @ Y2 @ 50.13/7.02 Y3))) => 50.13/7.02 (Y0 @ Y1 @ 50.13/7.02 Y3)))))))))))))) => 50.13/7.02 (Y0 @ '#sk10' @ '#sk12')))))))) 50.13/7.02 | ('#form9'))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl25])). 50.13/7.02 thf(zip_derived_cl47, plain, 50.13/7.02 ((~ (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk1' @ Y1 @ Y2) | 50.13/7.02 ('#sk2' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y1 @ 50.13/7.02 Y2) & (Y0 @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.02 (Y0 @ '#sk10' @ '#sk12')))))) 50.13/7.02 | ('#form9'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 50.13/7.02 thf(zip_derived_cl66, plain, 50.13/7.02 ((~ (((((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 ('#sk30' @ Y0 @ Y1))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk30' @ Y0 @ Y1) & 50.13/7.02 ('#sk30' @ Y1 @ Y2))) => 50.13/7.02 ('#sk30' @ Y0 @ Y2)))))))))))))) => 50.13/7.02 ('#sk30' @ '#sk10' @ '#sk12'))) 50.13/7.02 | ('#form9'))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 50.13/7.02 thf(zip_derived_cl79, plain, 50.13/7.02 ((~ ('#sk30' @ '#sk10' @ '#sk12') | ('#form9'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl66])). 50.13/7.02 thf(zip_derived_cl46, plain, 50.13/7.02 (( (((((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((('#sk1' @ Y1 @ Y2) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk10' @ '#sk12')))))) | 50.13/7.02 (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((('#sk2' @ Y1 @ Y2) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk10' @ '#sk12')))))))) 50.13/7.02 | ('#form9'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 50.13/7.02 thf(zip_derived_cl62, plain, 50.13/7.02 (( (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 50.13/7.02 Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk10' @ '#sk12')))))) 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((('#sk2' @ Y1 @ Y2) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk10' @ '#sk12')))))) 50.13/7.02 | ('#form9'))), 50.13/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl46])). 50.13/7.02 thf(zip_derived_cl72, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( (((((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 50.13/7.02 (X2 @ '#sk10' @ '#sk12'))) 50.13/7.02 | ('#form9') 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ 50.13/7.02 Y2 @ Y3) & 50.13/7.02 (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ 50.13/7.02 Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((('#sk2' @ Y1 @ Y2) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk10' @ '#sk12')))))))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl62])). 50.13/7.02 thf(zip_derived_cl85, plain, 50.13/7.02 ((~ ('#form94') 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((('#sk2' @ Y1 @ Y2) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk10' @ '#sk12')))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl86, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( (((((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 50.13/7.02 (X2 @ '#sk10' @ '#sk12'))) 50.13/7.02 | ~ ('#form94'))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 50.13/7.02 thf(zip_derived_cl102, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) 50.13/7.02 | (X2 @ '#sk10' @ '#sk12') 50.13/7.02 | ~ ('#form94'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl86])). 50.13/7.02 thf(zip_derived_cl112, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 50.13/7.02 | ~ ('#form94') 50.13/7.02 | (X2 @ '#sk10' @ '#sk12'))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl102])). 50.13/7.02 thf(zip_derived_cl18, plain, 50.13/7.02 (( (((((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y1 @ 50.13/7.02 Y2) & (Y0 @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk7' @ '#sk8')))))) & 50.13/7.02 (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y1 @ 50.13/7.02 Y2) & (Y0 @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk1' @ Y1 @ Y2) | 50.13/7.02 ('#sk2' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk6' @ '#sk7')))))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))) | 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ Y5))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))))))))) 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.02 (Y0 @ '#sk3' @ '#sk4')))))))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 50.13/7.02 thf(zip_derived_cl22, plain, 50.13/7.02 (( (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y1 @ 50.13/7.02 Y2) & (Y0 @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk7' @ '#sk8')))))) 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.02 (Y0 @ '#sk3' @ '#sk4')))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))) | 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ Y5))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))))))))))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])). 50.13/7.02 thf(zip_derived_cl29, plain, 50.13/7.02 ((~ ('#form11') 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.02 (Y0 @ '#sk3' @ '#sk4')))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl30, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( (((((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))))) => 50.13/7.02 (X2 @ '#sk3' @ '#sk4'))) 50.13/7.02 | ~ ('#form11'))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl29])). 50.13/7.02 thf(zip_derived_cl42, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))))) 50.13/7.02 | (X2 @ '#sk3' @ '#sk4') 50.13/7.02 | ~ ('#form11'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl30])). 50.13/7.02 thf(zip_derived_cl54, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))) 50.13/7.02 | ~ ('#form11') 50.13/7.02 | (X2 @ '#sk3' @ '#sk4'))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl42])). 50.13/7.02 thf(zip_derived_cl68, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((!!) @ (^[Y0 : a]: 50.13/7.02 ((((('#sk2' @ ('#sk47' @ X2) @ Y0) | ('#sk1' @ 50.13/7.02 ('#sk47' @ X2) @ Y0))) => 50.13/7.02 (X2 @ ('#sk47' @ X2) @ Y0)))))) 50.13/7.02 | (X2 @ '#sk3' @ '#sk4') 50.13/7.02 | ~ ('#form11') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl54])). 50.13/7.02 thf(zip_derived_cl81, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ ((((('#sk2' @ ('#sk47' @ X2) @ ('#sk77' @ X2)) | ('#sk1' @ 50.13/7.02 ('#sk47' @ X2) @ ('#sk77' @ X2)))) => 50.13/7.02 (X2 @ ('#sk47' @ X2) @ ('#sk77' @ X2)))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))) 50.13/7.02 | ~ ('#form11') 50.13/7.02 | (X2 @ '#sk3' @ '#sk4'))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl68])). 50.13/7.02 thf(zip_derived_cl96, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ((('#sk2' @ ('#sk47' @ X2) @ ('#sk77' @ X2)) | ('#sk1' @ 50.13/7.02 ('#sk47' @ X2) @ ('#sk77' @ X2)))) 50.13/7.02 | (X2 @ '#sk3' @ '#sk4') 50.13/7.02 | ~ ('#form11') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 50.13/7.02 thf(zip_derived_cl106, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#sk2' @ ('#sk47' @ X2) @ ('#sk77' @ X2)) 50.13/7.02 | ('#sk1' @ ('#sk47' @ X2) @ ('#sk77' @ X2)) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))) 50.13/7.02 | ~ ('#form11') 50.13/7.02 | (X2 @ '#sk3' @ '#sk4'))), 50.13/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl96])). 50.13/7.02 thf(zip_derived_cl116, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#form235' @ X2) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl125, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ ('#form235' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 50.13/7.02 | (X2 @ '#sk10' @ '#sk12') 50.13/7.02 | ~ ('#form94') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 inference('renaming', [status(thm)], 50.13/7.02 [zip_derived_cl112, zip_derived_cl116])). 50.13/7.02 thf(zip_derived_cl137, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ ('#form235' @ X2) 50.13/7.02 | (X2 @ '#sk10' @ '#sk12') 50.13/7.02 | ~ ('#form94') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 inference('ho_norm', [status(thm)], [zip_derived_cl125])). 50.13/7.02 thf(zip_derived_cl138, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((!!) @ (^[Y0 : a]: 50.13/7.02 ((('#sk2' @ ('#sk357' @ X2) @ Y0) => (X2 @ 50.13/7.02 ('#sk357' @ X2) @ Y0)))))) 50.13/7.02 | ~ ('#form94') 50.13/7.02 | (X2 @ '#sk10' @ '#sk12') 50.13/7.02 | ~ ('#form235' @ X2))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl137])). 50.13/7.02 thf(zip_derived_cl156, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ ((('#sk2' @ ('#sk357' @ X2) @ ('#sk436' @ X2)) => (X2 @ 50.13/7.02 ('#sk357' @ X2) @ ('#sk436' @ X2)))) 50.13/7.02 | ~ ('#form235' @ X2) 50.13/7.02 | (X2 @ '#sk10' @ '#sk12') 50.13/7.02 | ~ ('#form94'))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl138])). 50.13/7.02 thf(zip_derived_cl170, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#sk2' @ ('#sk357' @ X2) @ ('#sk436' @ X2)) 50.13/7.02 | ~ ('#form94') 50.13/7.02 | (X2 @ '#sk10' @ '#sk12') 50.13/7.02 | ~ ('#form235' @ X2))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl156])). 50.13/7.02 thf(zip_derived_cl78, plain, 50.13/7.02 (( (((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 50.13/7.02 ('#sk30' @ Y0 @ Y1))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk30' @ Y0 @ Y1) & 50.13/7.02 ('#sk30' @ Y1 @ Y2))) => 50.13/7.02 ('#sk30' @ Y0 @ Y2)))))))))))))) 50.13/7.02 | ('#form9'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl66])). 50.13/7.02 thf(zip_derived_cl93, plain, 50.13/7.02 (( (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 50.13/7.02 ('#sk30' @ Y0 @ Y1))))))))) 50.13/7.02 | ('#form9'))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl78])). 50.13/7.02 thf(zip_derived_cl103, plain, 50.13/7.02 (![X2 : a]: 50.13/7.02 ( (((!!) @ (^[Y0 : a]: 50.13/7.02 ((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) => 50.13/7.02 ('#sk30' @ X2 @ Y0)))))) 50.13/7.02 | ('#form9'))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl93])). 50.13/7.02 thf(zip_derived_cl113, plain, 50.13/7.02 (![X2 : a, X4 : a]: 50.13/7.02 ( ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) => ('#sk30' @ X2 @ X4))) 50.13/7.02 | ('#form9'))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl103])). 50.13/7.02 thf(zip_derived_cl126, plain, 50.13/7.02 (![X2 : a, X4 : a]: 50.13/7.02 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 50.13/7.02 | ('#sk30' @ X2 @ X4) 50.13/7.02 | ('#form9'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl113])). 50.13/7.02 thf(zip_derived_cl140, plain, 50.13/7.02 (![X2 : a, X4 : a]: 50.13/7.02 (~ ('#sk2' @ X2 @ X4) | ('#form9') | ('#sk30' @ X2 @ X4))), 50.13/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl126])). 50.13/7.02 thf(zip_derived_cl171, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (X2 @ ('#sk357' @ X2) @ ('#sk436' @ X2)) 50.13/7.02 | ~ ('#form94') 50.13/7.02 | (X2 @ '#sk10' @ '#sk12') 50.13/7.02 | ~ ('#form235' @ X2))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl156])). 50.13/7.02 thf(zip_derived_cl72, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( (((((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 50.13/7.02 (X2 @ '#sk10' @ '#sk12'))) 50.13/7.02 | ('#form9') 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ 50.13/7.02 Y2 @ Y3) & 50.13/7.02 (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ 50.13/7.02 Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((('#sk2' @ Y1 @ Y2) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk10' @ '#sk12')))))))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl62])). 50.13/7.02 thf(zip_derived_cl73, plain, 50.13/7.02 (( (((((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk30' @ Y1 @ Y2) & 50.13/7.02 ('#sk30' @ Y0 @ Y1))) => 50.13/7.02 ('#sk30' @ Y0 @ Y2)))))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((('#sk1' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 50.13/7.02 Y1))))))))))) => 50.13/7.02 ('#sk30' @ '#sk10' @ '#sk12'))) 50.13/7.02 | ('#form9') 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((('#sk2' @ Y1 @ Y2) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk10' @ '#sk12')))))))), 50.13/7.02 inference('triggered_bool_instantiation', [status(thm)], 50.13/7.02 [zip_derived_cl72])). 50.13/7.02 thf(zip_derived_cl85, plain, 50.13/7.02 ((~ ('#form94') 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((('#sk2' @ Y1 @ Y2) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk10' @ '#sk12')))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl247, plain, 50.13/7.02 (( ('#form94') 50.13/7.02 | ('#form9') 50.13/7.02 | (((((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk30' @ Y1 @ Y2) & 50.13/7.02 ('#sk30' @ Y0 @ Y1))) => 50.13/7.02 ('#sk30' @ Y0 @ Y2)))))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((('#sk1' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 50.13/7.02 Y1))))))))))) => 50.13/7.02 ('#sk30' @ '#sk10' @ '#sk12'))))), 50.13/7.02 inference('renaming', [status(thm)], [zip_derived_cl73, zip_derived_cl85])). 50.13/7.02 thf(zip_derived_cl248, plain, 50.13/7.02 ((~ (((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk30' @ Y1 @ Y2) & 50.13/7.02 ('#sk30' @ Y0 @ Y1))) => 50.13/7.02 ('#sk30' @ Y0 @ Y2)))))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((('#sk1' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))))) 50.13/7.02 | ('#sk30' @ '#sk10' @ '#sk12') 50.13/7.02 | ('#form9') 50.13/7.02 | ('#form94'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl247])). 50.13/7.02 thf(zip_derived_cl79, plain, 50.13/7.02 ((~ ('#sk30' @ '#sk10' @ '#sk12') | ('#form9'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl66])). 50.13/7.02 thf(zip_derived_cl249, plain, 50.13/7.02 (( ('#form94') 50.13/7.02 | ('#form9') 50.13/7.02 | ~ (((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk30' @ Y1 @ Y2) & 50.13/7.02 ('#sk30' @ Y0 @ Y1))) => 50.13/7.02 ('#sk30' @ Y0 @ Y2)))))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((('#sk1' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 50.13/7.02 Y1))))))))))))), 50.13/7.02 inference('clc', [status(thm)], [zip_derived_cl248, zip_derived_cl79])). 50.13/7.02 thf(zip_derived_cl250, plain, 50.13/7.02 ((~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk30' @ Y1 @ Y2) & 50.13/7.02 ('#sk30' @ Y0 @ Y1))) => 50.13/7.02 ('#sk30' @ Y0 @ Y2)))))))))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((('#sk1' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))) 50.13/7.02 | ('#form9') 50.13/7.02 | ('#form94'))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl249])). 50.13/7.02 thf(zip_derived_cl116, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#form235' @ X2) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl251, plain, 50.13/7.02 ((~ ('#form235' @ '#sk30') 50.13/7.02 | ('#form94') 50.13/7.02 | ('#form9') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((('#sk1' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))))), 50.13/7.02 inference('renaming', [status(thm)], 50.13/7.02 [zip_derived_cl250, zip_derived_cl116])). 50.13/7.02 thf(zip_derived_cl252, plain, 50.13/7.02 ((~ (((!!) @ (^[Y0 : a]: 50.13/7.02 ((('#sk1' @ ('#sk348' @ '#sk30') @ Y0) => ('#sk30' @ 50.13/7.02 ('#sk348' @ '#sk30') @ Y0)))))) 50.13/7.02 | ('#form9') 50.13/7.02 | ('#form94') 50.13/7.02 | ~ ('#form235' @ '#sk30'))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl251])). 50.13/7.02 thf(zip_derived_cl253, plain, 50.13/7.02 ((~ ((('#sk1' @ ('#sk348' @ '#sk30') @ ('#sk428' @ '#sk30')) => 50.13/7.02 ('#sk30' @ ('#sk348' @ '#sk30') @ ('#sk428' @ '#sk30')))) 50.13/7.02 | ~ ('#form235' @ '#sk30') 50.13/7.02 | ('#form94') 50.13/7.02 | ('#form9'))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl252])). 50.13/7.02 thf(zip_derived_cl255, plain, 50.13/7.02 ((~ ('#sk30' @ ('#sk348' @ '#sk30') @ ('#sk428' @ '#sk30')) 50.13/7.02 | ('#form9') 50.13/7.02 | ('#form94') 50.13/7.02 | ~ ('#form235' @ '#sk30'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl253])). 50.13/7.02 thf(zip_derived_cl254, plain, 50.13/7.02 (( ('#sk1' @ ('#sk348' @ '#sk30') @ ('#sk428' @ '#sk30')) 50.13/7.02 | ('#form9') 50.13/7.02 | ('#form94') 50.13/7.02 | ~ ('#form235' @ '#sk30'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl253])). 50.13/7.02 thf(zip_derived_cl94, plain, 50.13/7.02 (( (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk30' @ Y0 @ Y1) & 50.13/7.02 ('#sk30' @ Y1 @ Y2))) => 50.13/7.02 ('#sk30' @ Y0 @ Y2)))))))))))) 50.13/7.02 | ('#form9'))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl78])). 50.13/7.02 thf(zip_derived_cl104, plain, 50.13/7.02 (![X2 : a]: 50.13/7.02 ( (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk30' @ X2 @ Y0) & ('#sk30' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 ('#sk30' @ X2 @ Y1))))))))) 50.13/7.02 | ('#form9'))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])). 50.13/7.02 thf(zip_derived_cl114, plain, 50.13/7.02 (![X2 : a, X4 : a]: 50.13/7.02 ( (((!!) @ (^[Y0 : a]: 50.13/7.02 ((((('#sk30' @ X2 @ X4) & ('#sk30' @ X4 @ Y0))) => 50.13/7.02 ('#sk30' @ X2 @ Y0)))))) 50.13/7.02 | ('#form9'))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl104])). 50.13/7.02 thf(zip_derived_cl127, plain, 50.13/7.02 (![X2 : a, X4 : a, X6 : a]: 50.13/7.02 ( ((((('#sk30' @ X2 @ X4) & ('#sk30' @ X4 @ X6))) => ('#sk30' @ X2 @ 50.13/7.02 X6))) 50.13/7.02 | ('#form9'))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl114])). 50.13/7.02 thf(zip_derived_cl141, plain, 50.13/7.02 (![X2 : a, X4 : a, X6 : a]: 50.13/7.02 (~ ((('#sk30' @ X2 @ X4) & ('#sk30' @ X4 @ X6))) 50.13/7.02 | ('#sk30' @ X2 @ X6) 50.13/7.02 | ('#form9'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 50.13/7.02 thf(zip_derived_cl157, plain, 50.13/7.02 (![X2 : a, X4 : a, X6 : a]: 50.13/7.02 (~ ('#sk30' @ X2 @ X4) 50.13/7.02 | ~ ('#sk30' @ X4 @ X6) 50.13/7.02 | ('#form9') 50.13/7.02 | ('#sk30' @ X2 @ X6))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl141])). 50.13/7.02 thf(zip_derived_cl139, plain, 50.13/7.02 (![X2 : a, X4 : a]: 50.13/7.02 (~ ('#sk1' @ X2 @ X4) | ('#form9') | ('#sk30' @ X2 @ X4))), 50.13/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl126])). 50.13/7.02 thf(zip_derived_cl19, plain, 50.13/7.02 ((~ (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk1' @ Y1 @ Y2) | 50.13/7.02 ('#sk2' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk6' @ '#sk8')))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))) | 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ Y5))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))))))))) 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.02 (Y0 @ '#sk3' @ '#sk4')))))))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 50.13/7.02 thf(zip_derived_cl24, plain, 50.13/7.02 (( ('#form9') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))) | 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ Y5))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl26, plain, 50.13/7.02 ((~ ('#form9') 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.02 (Y0 @ '#sk3' @ '#sk4')))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & 50.13/7.02 (Y0 @ Y1 @ 50.13/7.02 Y2))) => 50.13/7.02 (Y0 @ Y1 @ 50.13/7.02 Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk1' @ Y1 @ Y2) | 50.13/7.02 ('#sk2' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk6' @ '#sk8')))))))), 50.13/7.02 inference('renaming', [status(thm)], [zip_derived_cl19, zip_derived_cl24])). 50.13/7.02 thf(zip_derived_cl29, plain, 50.13/7.02 ((~ ('#form11') 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.02 (Y0 @ '#sk3' @ '#sk4')))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl36, plain, 50.13/7.02 (( ('#form11') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & 50.13/7.02 (Y0 @ Y1 @ 50.13/7.02 Y2))) => 50.13/7.02 (Y0 @ Y1 @ 50.13/7.02 Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk1' @ Y1 @ Y2) | 50.13/7.02 ('#sk2' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk6' @ '#sk8')))))) 50.13/7.02 | ~ ('#form9'))), 50.13/7.02 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl29])). 50.13/7.02 thf(zip_derived_cl45, plain, 50.13/7.02 ((~ (((((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk21' @ Y1 @ Y2) & 50.13/7.02 ('#sk21' @ Y0 @ Y1))) => 50.13/7.02 ('#sk21' @ Y0 @ Y2)))))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 ('#sk21' @ Y0 @ Y1))))))))))) => 50.13/7.02 ('#sk21' @ '#sk6' @ '#sk8'))) 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11'))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl36])). 50.13/7.02 thf(zip_derived_cl61, plain, 50.13/7.02 ((~ ('#sk21' @ '#sk6' @ '#sk8') | ('#form11') | ~ ('#form9'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 50.13/7.02 thf(zip_derived_cl116, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#form235' @ X2) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl117, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((X2 @ Y0 @ Y1) & (X2 @ 50.13/7.02 ('#sk181' @ X2) @ Y0))) => 50.13/7.02 (X2 @ ('#sk181' @ X2) @ Y1))))))))) 50.13/7.02 | ('#form235' @ X2))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl116])). 50.13/7.02 thf(zip_derived_cl130, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((((X2 @ ('#sk248' @ X2) @ Y0) & (X2 @ 50.13/7.02 ('#sk181' @ X2) @ ('#sk248' @ X2)))) => 50.13/7.02 (X2 @ ('#sk181' @ X2) @ Y0)))))) 50.13/7.02 | ('#form235' @ X2))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl117])). 50.13/7.02 thf(zip_derived_cl147, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((((X2 @ ('#sk248' @ X2) @ ('#sk325' @ X2)) & (X2 @ 50.13/7.02 ('#sk181' @ X2) @ ('#sk248' @ X2)))) => 50.13/7.02 (X2 @ ('#sk181' @ X2) @ ('#sk325' @ X2)))) 50.13/7.02 | ('#form235' @ X2))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl130])). 50.13/7.02 thf(zip_derived_cl161, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( (((X2 @ ('#sk248' @ X2) @ ('#sk325' @ X2)) & (X2 @ 50.13/7.02 ('#sk181' @ X2) @ ('#sk248' @ X2)))) 50.13/7.02 | ('#form235' @ X2))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl147])). 50.13/7.02 thf(zip_derived_cl176, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( (X2 @ ('#sk248' @ X2) @ ('#sk325' @ X2)) | ('#form235' @ X2))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl161])). 50.13/7.02 thf(zip_derived_cl22, plain, 50.13/7.02 (( (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y1 @ 50.13/7.02 Y2) & (Y0 @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk7' @ '#sk8')))))) 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.02 (Y0 @ '#sk3' @ '#sk4')))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))) | 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ Y5))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))))))))))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])). 50.13/7.02 thf(zip_derived_cl29, plain, 50.13/7.02 ((~ ('#form11') 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.02 (Y0 @ '#sk3' @ '#sk4')))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl34, plain, 50.13/7.02 (( ('#form11') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))) | 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ Y5))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))))))))) 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y1 @ 50.13/7.02 Y2) & (Y0 @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk7' @ '#sk8')))))))), 50.13/7.02 inference('renaming', [status(thm)], [zip_derived_cl22, zip_derived_cl29])). 50.13/7.02 thf(zip_derived_cl24, plain, 50.13/7.02 (( ('#form9') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))) | 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ Y5))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl41, plain, 50.13/7.02 ((~ ('#form9') 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y1 @ 50.13/7.02 Y2) & (Y0 @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk7' @ '#sk8')))))) 50.13/7.02 | ('#form11'))), 50.13/7.02 inference('renaming', [status(thm)], [zip_derived_cl34, zip_derived_cl24])). 50.13/7.02 thf(zip_derived_cl49, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( (((((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y0 @ Y1) & (X2 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))) => 50.13/7.02 (X2 @ '#sk7' @ '#sk8'))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9'))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 50.13/7.02 thf(zip_derived_cl67, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y0 @ Y1) & (X2 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))) 50.13/7.02 | (X2 @ '#sk7' @ '#sk8') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 50.13/7.02 thf(zip_derived_cl80, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y0 @ Y1) & (X2 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk7' @ '#sk8'))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl67])). 50.13/7.02 thf(zip_derived_cl95, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((X2 @ ('#sk103' @ X2) @ Y0) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ ('#sk103' @ X2) @ Y1))))))))) 50.13/7.02 | (X2 @ '#sk7' @ '#sk8') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl80])). 50.13/7.02 thf(zip_derived_cl105, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((((X2 @ ('#sk103' @ X2) @ ('#sk156' @ X2)) & (X2 @ 50.13/7.02 ('#sk156' @ X2) @ Y0))) => 50.13/7.02 (X2 @ ('#sk103' @ X2) @ Y0)))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk7' @ '#sk8'))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl95])). 50.13/7.02 thf(zip_derived_cl115, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((((X2 @ ('#sk103' @ X2) @ ('#sk156' @ X2)) & (X2 @ 50.13/7.02 ('#sk156' @ X2) @ ('#sk220' @ X2)))) => 50.13/7.02 (X2 @ ('#sk103' @ X2) @ ('#sk220' @ X2)))) 50.13/7.02 | (X2 @ '#sk7' @ '#sk8') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl105])). 50.13/7.02 thf(zip_derived_cl129, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (X2 @ ('#sk103' @ X2) @ ('#sk220' @ X2)) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk7' @ '#sk8'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl115])). 50.13/7.02 thf(zip_derived_cl144, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#form374' @ X2) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl145, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((!!) @ (^[Y0 : a]: 50.13/7.02 ((((('#sk2' @ ('#sk47' @ X2) @ Y0) | ('#sk1' @ 50.13/7.02 ('#sk47' @ X2) @ Y0))) => 50.13/7.02 (X2 @ ('#sk47' @ X2) @ Y0)))))) 50.13/7.02 | ('#form374' @ X2))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl144])). 50.13/7.02 thf(zip_derived_cl160, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ ((((('#sk2' @ ('#sk47' @ X2) @ ('#sk77' @ X2)) | ('#sk1' @ 50.13/7.02 ('#sk47' @ X2) @ ('#sk77' @ X2)))) => 50.13/7.02 (X2 @ ('#sk47' @ X2) @ ('#sk77' @ X2)))) 50.13/7.02 | ('#form374' @ X2))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl145])). 50.13/7.02 thf(zip_derived_cl174, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ((('#sk2' @ ('#sk47' @ X2) @ ('#sk77' @ X2)) | ('#sk1' @ 50.13/7.02 ('#sk47' @ X2) @ ('#sk77' @ X2)))) 50.13/7.02 | ('#form374' @ X2))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl160])). 50.13/7.02 thf(zip_derived_cl182, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#sk2' @ ('#sk47' @ X2) @ ('#sk77' @ X2)) 50.13/7.02 | ('#sk1' @ ('#sk47' @ X2) @ ('#sk77' @ X2)) 50.13/7.02 | ('#form374' @ X2))), 50.13/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl174])). 50.13/7.02 thf(zip_derived_cl177, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( (X2 @ ('#sk181' @ X2) @ ('#sk248' @ X2)) | ('#form235' @ X2))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl161])). 50.13/7.02 thf(zip_derived_cl162, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (X2 @ ('#sk181' @ X2) @ ('#sk325' @ X2)) | ('#form235' @ X2))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl147])). 50.13/7.02 thf(zip_derived_cl30, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( (((((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))))) => 50.13/7.02 (X2 @ '#sk3' @ '#sk4'))) 50.13/7.02 | ~ ('#form11'))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl29])). 50.13/7.02 thf(zip_derived_cl31, plain, 50.13/7.02 (( (((((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 ('#sk5' @ Y0 @ Y1))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk5' @ Y1 @ Y2) & 50.13/7.02 ('#sk5' @ Y0 @ Y1))) => 50.13/7.02 ('#sk5' @ Y0 @ Y2)))))))))))))) => 50.13/7.02 ('#sk5' @ '#sk3' @ '#sk4'))) 50.13/7.02 | ~ ('#form11'))), 50.13/7.02 inference('triggered_bool_instantiation', [status(thm)], 50.13/7.02 [zip_derived_cl30])). 50.13/7.02 thf(zip_derived_cl6, plain, 50.13/7.02 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.02 (Y0 @ '#sk3' @ '#sk4'))))))), 50.13/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 50.13/7.02 thf(zip_derived_cl8, plain, 50.13/7.02 (~ (((((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 ('#sk5' @ Y0 @ Y1))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk5' @ Y1 @ Y2) & 50.13/7.02 ('#sk5' @ Y0 @ Y1))) => 50.13/7.02 ('#sk5' @ Y0 @ Y2)))))))))))))) => 50.13/7.02 ('#sk5' @ '#sk3' @ '#sk4')))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 50.13/7.02 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk3' @ '#sk4')), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 50.13/7.02 thf(zip_derived_cl205, plain, 50.13/7.02 (( (((((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 ('#sk5' @ Y0 @ Y1))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk5' @ Y1 @ Y2) & 50.13/7.02 ('#sk5' @ Y0 @ Y1))) => 50.13/7.02 ('#sk5' @ Y0 @ Y2)))))))))))))) => 50.13/7.02 ($false))) 50.13/7.02 | ~ ('#form11'))), 50.13/7.02 inference('demod', [status(thm)], [zip_derived_cl31, zip_derived_cl11])). 50.13/7.02 thf(zip_derived_cl206, plain, 50.13/7.02 (( (((~) @ (((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 ('#sk5' @ Y0 @ Y1))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk5' @ Y1 @ Y2) & 50.13/7.02 ('#sk5' @ Y0 @ Y1))) => 50.13/7.02 ('#sk5' @ Y0 @ Y2)))))))))))))))) 50.13/7.02 | ~ ('#form11'))), 50.13/7.02 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl205])). 50.13/7.02 thf(zip_derived_cl207, plain, 50.13/7.02 ((~ (((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 50.13/7.02 ('#sk5' @ Y0 @ Y1))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk5' @ Y1 @ Y2) & 50.13/7.02 ('#sk5' @ Y0 @ Y1))) => 50.13/7.02 ('#sk5' @ Y0 @ Y2)))))))))))))) 50.13/7.02 | ~ ('#form11'))), 50.13/7.02 inference('simplify nested equalities', [status(thm)], 50.13/7.02 [zip_derived_cl206])). 50.13/7.02 thf(zip_derived_cl208, plain, 50.13/7.02 ((~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 50.13/7.02 ('#sk5' @ Y0 @ Y1))))))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk5' @ Y1 @ Y2) & 50.13/7.02 ('#sk5' @ Y0 @ Y1))) => 50.13/7.02 ('#sk5' @ Y0 @ Y2)))))))))))) 50.13/7.02 | ~ ('#form11'))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl207])). 50.13/7.02 thf(zip_derived_cl144, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#form374' @ X2) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl209, plain, 50.13/7.02 ((~ ('#form374' @ '#sk5') 50.13/7.02 | ~ ('#form11') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk5' @ Y1 @ Y2) & 50.13/7.02 ('#sk5' @ Y0 @ Y1))) => 50.13/7.02 ('#sk5' @ Y0 @ Y2)))))))))))))), 50.13/7.02 inference('renaming', [status(thm)], 50.13/7.02 [zip_derived_cl208, zip_derived_cl144])). 50.13/7.02 thf(zip_derived_cl116, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#form235' @ X2) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl210, plain, 50.13/7.02 ((~ ('#form235' @ '#sk5') | ~ ('#form11') | ~ ('#form374' @ '#sk5'))), 50.13/7.02 inference('renaming', [status(thm)], 50.13/7.02 [zip_derived_cl209, zip_derived_cl116])). 50.13/7.02 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk3' @ '#sk4')), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 50.13/7.02 thf(zip_derived_cl129, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (X2 @ ('#sk103' @ X2) @ ('#sk220' @ X2)) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk7' @ '#sk8'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl115])). 50.13/7.02 thf(zip_derived_cl144, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#form374' @ X2) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl146, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ ('#form374' @ X2) 50.13/7.02 | (X2 @ '#sk7' @ '#sk8') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11') 50.13/7.02 | ~ (X2 @ ('#sk103' @ X2) @ ('#sk220' @ X2)))), 50.13/7.02 inference('renaming', [status(thm)], 50.13/7.02 [zip_derived_cl129, zip_derived_cl144])). 50.13/7.02 thf(zip_derived_cl128, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( (((X2 @ ('#sk103' @ X2) @ ('#sk156' @ X2)) & (X2 @ 50.13/7.02 ('#sk156' @ X2) @ ('#sk220' @ X2)))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk7' @ '#sk8'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl115])). 50.13/7.02 thf(zip_derived_cl143, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( (X2 @ ('#sk156' @ X2) @ ('#sk220' @ X2)) 50.13/7.02 | (X2 @ '#sk7' @ '#sk8') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl128])). 50.13/7.02 thf(zip_derived_cl144, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#form374' @ X2) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl159, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ ('#form374' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk7' @ '#sk8') 50.13/7.02 | (X2 @ ('#sk156' @ X2) @ ('#sk220' @ X2)))), 50.13/7.02 inference('renaming', [status(thm)], 50.13/7.02 [zip_derived_cl143, zip_derived_cl144])). 50.13/7.02 thf(zip_derived_cl173, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ ('#form374' @ X2) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk7' @ '#sk8') 50.13/7.02 | (X2 @ ('#sk156' @ X2) @ ('#sk220' @ X2)))), 50.13/7.02 inference('ho_norm', [status(thm)], [zip_derived_cl159])). 50.13/7.02 thf(zip_derived_cl23, plain, 50.13/7.02 (( (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y1 @ 50.13/7.02 Y2) & (Y0 @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk1' @ Y1 @ Y2) | 50.13/7.02 ('#sk2' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk6' @ '#sk7')))))) 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.02 (Y0 @ '#sk3' @ '#sk4')))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))) | 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ Y5))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))))))))))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])). 50.13/7.02 thf(zip_derived_cl29, plain, 50.13/7.02 ((~ ('#form11') 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk2' @ Y1 @ Y2) | 50.13/7.02 ('#sk1' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y2 @ 50.13/7.02 Y3) & (Y0 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))))) => 50.13/7.02 (Y0 @ '#sk3' @ '#sk4')))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl35, plain, 50.13/7.02 (( ('#form11') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))) | 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ Y5))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))))))))) 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y1 @ 50.13/7.02 Y2) & (Y0 @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk1' @ Y1 @ Y2) | 50.13/7.02 ('#sk2' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk6' @ '#sk7')))))))), 50.13/7.02 inference('renaming', [status(thm)], [zip_derived_cl23, zip_derived_cl29])). 50.13/7.02 thf(zip_derived_cl24, plain, 50.13/7.02 (( ('#form9') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))) | 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ 50.13/7.02 Y5) & 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 (( 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))) => 50.13/7.02 (((!!) @ (^[Y2 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (( 50.13/7.02 ('#sk1' @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) | 50.13/7.02 ('#sk2' @ 50.13/7.02 Y3 @ Y4))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y4))))))))) & 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((!!) @ ( 50.13/7.02 ^[Y4 : a]: 50.13/7.02 ( 50.13/7.02 ( 50.13/7.02 (!!) @ ( 50.13/7.02 ^[Y5 : a]: 50.13/7.02 (( 50.13/7.02 (( 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ 50.13/7.02 Y4) & 50.13/7.02 (Y2 @ 50.13/7.02 Y4 @ Y5))) => 50.13/7.02 (Y2 @ 50.13/7.02 Y3 @ Y5)))))))))))))) => 50.13/7.02 (Y2 @ Y0 @ Y1)))))))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl43, plain, 50.13/7.02 ((~ ('#form9') 50.13/7.02 | (((!!) @ (^[Y0 : a > a > $o]: 50.13/7.02 (((((((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((!!) @ (^[Y3 : a]: 50.13/7.02 (((((Y0 @ Y1 @ 50.13/7.02 Y2) & (Y0 @ 50.13/7.02 Y2 @ Y3))) => 50.13/7.02 (Y0 @ Y1 @ Y3)))))))))))) & 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk1' @ Y1 @ Y2) | 50.13/7.02 ('#sk2' @ Y1 @ Y2))) => 50.13/7.02 (Y0 @ Y1 @ Y2))))))))))) => 50.13/7.02 (Y0 @ '#sk6' @ '#sk7')))))) 50.13/7.02 | ('#form11'))), 50.13/7.02 inference('renaming', [status(thm)], [zip_derived_cl35, zip_derived_cl24])). 50.13/7.02 thf(zip_derived_cl55, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( (((((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y0 @ Y1) & (X2 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))) => 50.13/7.02 (X2 @ '#sk6' @ '#sk7'))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9'))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 50.13/7.02 thf(zip_derived_cl69, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y0 @ Y1) & (X2 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))) 50.13/7.02 | (X2 @ '#sk6' @ '#sk7') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 50.13/7.02 thf(zip_derived_cl82, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y0 @ Y1) & (X2 @ 50.13/7.02 Y1 @ Y2))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk6' @ '#sk7'))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 50.13/7.02 thf(zip_derived_cl98, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((((X2 @ ('#sk103' @ X2) @ Y0) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ ('#sk103' @ X2) @ Y1))))))))) 50.13/7.02 | (X2 @ '#sk6' @ '#sk7') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl82])). 50.13/7.02 thf(zip_derived_cl108, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((((X2 @ ('#sk103' @ X2) @ ('#sk156' @ X2)) & (X2 @ 50.13/7.02 ('#sk156' @ X2) @ Y0))) => 50.13/7.02 (X2 @ ('#sk103' @ X2) @ Y0)))))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk6' @ '#sk7'))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl98])). 50.13/7.02 thf(zip_derived_cl120, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((((X2 @ ('#sk103' @ X2) @ ('#sk156' @ X2)) & (X2 @ 50.13/7.02 ('#sk156' @ X2) @ ('#sk220' @ X2)))) => 50.13/7.02 (X2 @ ('#sk103' @ X2) @ ('#sk220' @ X2)))) 50.13/7.02 | (X2 @ '#sk6' @ '#sk7') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl108])). 50.13/7.02 thf(zip_derived_cl133, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (X2 @ ('#sk103' @ X2) @ ('#sk220' @ X2)) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk6' @ '#sk7'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl120])). 50.13/7.02 thf(zip_derived_cl152, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#form419' @ X2) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl153, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (((!!) @ (^[Y0 : a]: 50.13/7.02 ((((('#sk1' @ ('#sk420' @ X2) @ Y0) | ('#sk2' @ 50.13/7.02 ('#sk420' @ X2) @ Y0))) => 50.13/7.02 (X2 @ ('#sk420' @ X2) @ Y0)))))) 50.13/7.02 | ('#form419' @ X2))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl152])). 50.13/7.02 thf(zip_derived_cl167, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ ((((('#sk1' @ ('#sk420' @ X2) @ ('#sk525' @ X2)) | ('#sk2' @ 50.13/7.02 ('#sk420' @ X2) @ ('#sk525' @ X2)))) => 50.13/7.02 (X2 @ ('#sk420' @ X2) @ ('#sk525' @ X2)))) 50.13/7.02 | ('#form419' @ X2))), 50.13/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl153])). 50.13/7.02 thf(zip_derived_cl180, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ((('#sk1' @ ('#sk420' @ X2) @ ('#sk525' @ X2)) | ('#sk2' @ 50.13/7.02 ('#sk420' @ X2) @ ('#sk525' @ X2)))) 50.13/7.02 | ('#form419' @ X2))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl167])). 50.13/7.02 thf(zip_derived_cl183, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#sk1' @ ('#sk420' @ X2) @ ('#sk525' @ X2)) 50.13/7.02 | ('#sk2' @ ('#sk420' @ X2) @ ('#sk525' @ X2)) 50.13/7.02 | ('#form419' @ X2))), 50.13/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl180])). 50.13/7.02 thf(zip_derived_cl10, plain, 50.13/7.02 ( (((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 50.13/7.02 ('#sk5' @ Y0 @ Y1))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk5' @ Y1 @ Y2) & 50.13/7.02 ('#sk5' @ Y0 @ Y1))) => 50.13/7.02 ('#sk5' @ Y0 @ Y2))))))))))))))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 50.13/7.02 thf(zip_derived_cl14, plain, 50.13/7.02 ( (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk5' @ Y1 @ Y2) & ('#sk5' @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 ('#sk5' @ Y0 @ Y2))))))))))))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 50.13/7.02 thf(zip_derived_cl17, plain, 50.13/7.02 (![X2 : a]: 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk5' @ Y0 @ Y1) & ('#sk5' @ X2 @ Y0))) => 50.13/7.02 ('#sk5' @ X2 @ Y1)))))))))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 50.13/7.02 thf(zip_derived_cl21, plain, 50.13/7.02 (![X2 : a, X4 : a]: 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 ((((('#sk5' @ X4 @ Y0) & ('#sk5' @ X2 @ X4))) => 50.13/7.02 ('#sk5' @ X2 @ Y0))))))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 50.13/7.02 thf(zip_derived_cl28, plain, 50.13/7.02 (![X2 : a, X4 : a, X6 : a]: 50.13/7.02 ((((('#sk5' @ X4 @ X6) & ('#sk5' @ X2 @ X4))) => ('#sk5' @ X2 @ X6)))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl21])). 50.13/7.02 thf(zip_derived_cl40, plain, 50.13/7.02 (![X2 : a, X4 : a, X6 : a]: 50.13/7.02 (~ ((('#sk5' @ X4 @ X6) & ('#sk5' @ X2 @ X4))) | ('#sk5' @ X2 @ X6))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl28])). 50.13/7.02 thf(zip_derived_cl48, plain, 50.13/7.02 (![X2 : a, X4 : a, X6 : a]: 50.13/7.02 (~ ('#sk5' @ X4 @ X6) | ~ ('#sk5' @ X2 @ X4) | ('#sk5' @ X2 @ X6))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl40])). 50.13/7.02 thf(zip_derived_cl106, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#sk2' @ ('#sk47' @ X2) @ ('#sk77' @ X2)) 50.13/7.02 | ('#sk1' @ ('#sk47' @ X2) @ ('#sk77' @ X2)) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))) 50.13/7.02 | ~ ('#form11') 50.13/7.02 | (X2 @ '#sk3' @ '#sk4'))), 50.13/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl96])). 50.13/7.02 thf(zip_derived_cl116, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#form235' @ X2) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 (((((X2 @ Y1 @ Y2) & (X2 @ 50.13/7.02 Y0 @ Y1))) => 50.13/7.02 (X2 @ Y0 @ Y2)))))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl118, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ ('#form235' @ X2) 50.13/7.02 | (X2 @ '#sk3' @ '#sk4') 50.13/7.02 | ~ ('#form11') 50.13/7.02 | ('#sk1' @ ('#sk47' @ X2) @ ('#sk77' @ X2)) 50.13/7.02 | ('#sk2' @ ('#sk47' @ X2) @ ('#sk77' @ X2)))), 50.13/7.02 inference('renaming', [status(thm)], 50.13/7.02 [zip_derived_cl106, zip_derived_cl116])). 50.13/7.02 thf(zip_derived_cl13, plain, 50.13/7.02 ( (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 50.13/7.02 ('#sk5' @ Y0 @ Y1)))))))))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 50.13/7.02 thf(zip_derived_cl16, plain, 50.13/7.02 (![X2 : a]: 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 ((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) => 50.13/7.02 ('#sk5' @ X2 @ Y0))))))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 50.13/7.02 thf(zip_derived_cl20, plain, 50.13/7.02 (![X2 : a, X4 : a]: 50.13/7.02 ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) => ('#sk5' @ X2 @ X4)))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 50.13/7.02 thf(zip_derived_cl27, plain, 50.13/7.02 (![X2 : a, X4 : a]: 50.13/7.02 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) | ('#sk5' @ X2 @ X4))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 50.13/7.02 thf(zip_derived_cl38, plain, 50.13/7.02 (![X2 : a, X4 : a]: (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 50.13/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl27])). 50.13/7.02 thf(zip_derived_cl142, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( (X2 @ ('#sk103' @ X2) @ ('#sk156' @ X2)) 50.13/7.02 | (X2 @ '#sk7' @ '#sk8') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl128])). 50.13/7.02 thf(zip_derived_cl144, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#form374' @ X2) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl158, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ ('#form374' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk7' @ '#sk8') 50.13/7.02 | (X2 @ ('#sk103' @ X2) @ ('#sk156' @ X2)))), 50.13/7.02 inference('renaming', [status(thm)], 50.13/7.02 [zip_derived_cl142, zip_derived_cl144])). 50.13/7.02 thf(zip_derived_cl172, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ ('#form374' @ X2) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk7' @ '#sk8') 50.13/7.02 | (X2 @ ('#sk103' @ X2) @ ('#sk156' @ X2)))), 50.13/7.02 inference('ho_norm', [status(thm)], [zip_derived_cl158])). 50.13/7.02 thf(zip_derived_cl133, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (X2 @ ('#sk103' @ X2) @ ('#sk220' @ X2)) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk6' @ '#sk7'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl120])). 50.13/7.02 thf(zip_derived_cl152, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#form419' @ X2) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl154, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ ('#form419' @ X2) 50.13/7.02 | (X2 @ '#sk6' @ '#sk7') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11') 50.13/7.02 | ~ (X2 @ ('#sk103' @ X2) @ ('#sk220' @ X2)))), 50.13/7.02 inference('renaming', [status(thm)], 50.13/7.02 [zip_derived_cl133, zip_derived_cl152])). 50.13/7.02 thf(zip_derived_cl132, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( (((X2 @ ('#sk103' @ X2) @ ('#sk156' @ X2)) & (X2 @ 50.13/7.02 ('#sk156' @ X2) @ ('#sk220' @ X2)))) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk6' @ '#sk7'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl120])). 50.13/7.02 thf(zip_derived_cl151, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( (X2 @ ('#sk156' @ X2) @ ('#sk220' @ X2)) 50.13/7.02 | (X2 @ '#sk6' @ '#sk7') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl132])). 50.13/7.02 thf(zip_derived_cl152, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#form419' @ X2) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl166, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ ('#form419' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk6' @ '#sk7') 50.13/7.02 | (X2 @ ('#sk156' @ X2) @ ('#sk220' @ X2)))), 50.13/7.02 inference('renaming', [status(thm)], 50.13/7.02 [zip_derived_cl151, zip_derived_cl152])). 50.13/7.02 thf(zip_derived_cl179, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ ('#form419' @ X2) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk6' @ '#sk7') 50.13/7.02 | (X2 @ ('#sk156' @ X2) @ ('#sk220' @ X2)))), 50.13/7.02 inference('ho_norm', [status(thm)], [zip_derived_cl166])). 50.13/7.02 thf(zip_derived_cl39, plain, 50.13/7.02 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 50.13/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl27])). 50.13/7.02 thf(zip_derived_cl175, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (X2 @ ('#sk47' @ X2) @ ('#sk77' @ X2)) | ('#form374' @ X2))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl160])). 50.13/7.02 thf(zip_derived_cl60, plain, 50.13/7.02 (( (((((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk21' @ Y1 @ Y2) & 50.13/7.02 ('#sk21' @ Y0 @ Y1))) => 50.13/7.02 ('#sk21' @ Y0 @ Y2)))))))))))) & 50.13/7.02 (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 50.13/7.02 ('#sk21' @ Y0 @ Y1))))))))))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 50.13/7.02 thf(zip_derived_cl71, plain, 50.13/7.02 (( (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 50.13/7.02 ('#sk21' @ Y0 @ Y1))))))))) 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11'))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl60])). 50.13/7.02 thf(zip_derived_cl84, plain, 50.13/7.02 (![X2 : a]: 50.13/7.02 ( (((!!) @ (^[Y0 : a]: 50.13/7.02 ((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) => 50.13/7.02 ('#sk21' @ X2 @ Y0)))))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9'))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl71])). 50.13/7.02 thf(zip_derived_cl100, plain, 50.13/7.02 (![X2 : a, X4 : a]: 50.13/7.02 ( ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) => ('#sk21' @ X2 @ X4))) 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11'))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl84])). 50.13/7.02 thf(zip_derived_cl110, plain, 50.13/7.02 (![X2 : a, X4 : a]: 50.13/7.02 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 50.13/7.02 | ('#sk21' @ X2 @ X4) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 50.13/7.02 thf(zip_derived_cl123, plain, 50.13/7.02 (![X2 : a, X4 : a]: 50.13/7.02 (~ ('#sk2' @ X2 @ X4) 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11') 50.13/7.02 | ('#sk21' @ X2 @ X4))), 50.13/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl110])). 50.13/7.02 thf(zip_derived_cl122, plain, 50.13/7.02 (![X2 : a, X4 : a]: 50.13/7.02 (~ ('#sk1' @ X2 @ X4) 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11') 50.13/7.02 | ('#sk21' @ X2 @ X4))), 50.13/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl110])). 50.13/7.02 thf(zip_derived_cl181, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ (X2 @ ('#sk420' @ X2) @ ('#sk525' @ X2)) | ('#form419' @ X2))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl167])). 50.13/7.02 thf(zip_derived_cl150, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( (X2 @ ('#sk103' @ X2) @ ('#sk156' @ X2)) 50.13/7.02 | (X2 @ '#sk6' @ '#sk7') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11') 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl132])). 50.13/7.02 thf(zip_derived_cl152, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 ( ('#form419' @ X2) 50.13/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.13/7.02 Y1))) => 50.13/7.02 (X2 @ Y0 @ Y1))))))))))), 50.13/7.02 define([status(thm)])). 50.13/7.02 thf(zip_derived_cl165, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ ('#form419' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk6' @ '#sk7') 50.13/7.02 | (X2 @ ('#sk103' @ X2) @ ('#sk156' @ X2)))), 50.13/7.02 inference('renaming', [status(thm)], 50.13/7.02 [zip_derived_cl150, zip_derived_cl152])). 50.13/7.02 thf(zip_derived_cl178, plain, 50.13/7.02 (![X2 : a > a > $o]: 50.13/7.02 (~ ('#form419' @ X2) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | (X2 @ '#sk6' @ '#sk7') 50.13/7.02 | (X2 @ ('#sk103' @ X2) @ ('#sk156' @ X2)))), 50.13/7.02 inference('ho_norm', [status(thm)], [zip_derived_cl165])). 50.13/7.02 thf(zip_derived_cl70, plain, 50.13/7.02 (( (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 (((!!) @ (^[Y2 : a]: 50.13/7.02 ((((('#sk21' @ Y1 @ Y2) & 50.13/7.02 ('#sk21' @ Y0 @ Y1))) => 50.13/7.02 ('#sk21' @ Y0 @ Y2)))))))))))) 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11'))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl60])). 50.13/7.02 thf(zip_derived_cl83, plain, 50.13/7.02 (![X2 : a]: 50.13/7.02 ( (((!!) @ (^[Y0 : a]: 50.13/7.02 (((!!) @ (^[Y1 : a]: 50.13/7.02 ((((('#sk21' @ Y0 @ Y1) & ('#sk21' @ X2 @ 50.13/7.02 Y0))) => 50.13/7.02 ('#sk21' @ X2 @ Y1))))))))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9'))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl70])). 50.13/7.02 thf(zip_derived_cl99, plain, 50.13/7.02 (![X2 : a, X4 : a]: 50.13/7.02 ( (((!!) @ (^[Y0 : a]: 50.13/7.02 ((((('#sk21' @ X4 @ Y0) & ('#sk21' @ X2 @ X4))) => 50.13/7.02 ('#sk21' @ X2 @ Y0)))))) 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11'))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl83])). 50.13/7.02 thf(zip_derived_cl109, plain, 50.13/7.02 (![X2 : a, X4 : a, X6 : a]: 50.13/7.02 ( ((((('#sk21' @ X4 @ X6) & ('#sk21' @ X2 @ X4))) => ('#sk21' @ X2 @ 50.13/7.02 X6))) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9'))), 50.13/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl99])). 50.13/7.02 thf(zip_derived_cl121, plain, 50.13/7.02 (![X2 : a, X4 : a, X6 : a]: 50.13/7.02 (~ ((('#sk21' @ X4 @ X6) & ('#sk21' @ X2 @ X4))) 50.13/7.02 | ('#sk21' @ X2 @ X6) 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#form11'))), 50.13/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl109])). 50.13/7.02 thf(zip_derived_cl134, plain, 50.13/7.02 (![X2 : a, X4 : a, X6 : a]: 50.13/7.02 (~ ('#sk21' @ X4 @ X6) 50.13/7.02 | ~ ('#sk21' @ X2 @ X4) 50.13/7.02 | ('#form11') 50.13/7.02 | ~ ('#form9') 50.13/7.02 | ('#sk21' @ X2 @ X6))), 50.13/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl121])). 50.13/7.02 thf(zip_derived_cl7493, plain, ($false), 50.13/7.02 inference('eprover', [status(thm)], 50.13/7.02 [zip_derived_cl79, zip_derived_cl170, zip_derived_cl140, 50.13/7.02 zip_derived_cl171, zip_derived_cl255, zip_derived_cl254, 50.13/7.02 zip_derived_cl157, zip_derived_cl139, zip_derived_cl61, 50.13/7.02 zip_derived_cl176, zip_derived_cl182, zip_derived_cl177, 50.13/7.02 zip_derived_cl162, zip_derived_cl210, zip_derived_cl11, 50.13/7.02 zip_derived_cl146, zip_derived_cl173, zip_derived_cl183, 50.13/7.02 zip_derived_cl48, zip_derived_cl118, zip_derived_cl38, 50.13/7.02 zip_derived_cl172, zip_derived_cl154, zip_derived_cl179, 50.13/7.02 zip_derived_cl39, zip_derived_cl175, zip_derived_cl123, 50.13/7.02 zip_derived_cl122, zip_derived_cl181, zip_derived_cl178, 50.13/7.02 zip_derived_cl134])). 50.13/7.02 50.13/7.02 % SZS output end Refutation 50.13/7.02 50.13/7.02 50.13/7.02 % Terminating... 50.13/7.06 % Runner terminated. 50.17/7.07 % Zipperpin 1.5 exiting 50.17/7.07 EOF