0.05/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.10 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.0wCchU4H4L true 0.11/0.30 % Computer : n021.cluster.edu 0.11/0.30 % Model : x86_64 x86_64 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.30 % Memory : 8042.1875MB 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.30 % CPULimit : 1440 0.11/0.30 % WCLimit : 180 0.11/0.30 % DateTime : Thu Jul 4 06:20:54 EDT 2024 0.11/0.30 % CPUTime : 0.11/0.30 % Running portfolio for 1440 s 0.11/0.30 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.11/0.30 % Number of cores: 8 0.11/0.31 % Python version: Python 3.6.8 0.11/0.31 % Running in HO mode 0.47/0.59 % Total configuration time : 828 0.47/0.59 % Estimated wc time : 1656 0.47/0.59 % Estimated cpu time (8 cpus) : 207.0 0.47/0.67 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.47/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.47/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.47/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.47/0.67 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.47/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.47/0.67 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.47/0.68 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 53.28/7.25 % Solved by lams/20_acsne_simpl.sh. 53.28/7.25 % done 379 iterations in 6.341s 53.28/7.25 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 53.28/7.25 % SZS output start Refutation 53.28/7.25 thf(a_type, type, a: $tType). 53.28/7.25 thf('#sk180_type', type, '#sk180': (a > $o) > a). 53.28/7.25 thf('#sk6_type', type, '#sk6': a). 53.28/7.25 thf('#form19_type', type, '#form19': $o). 53.28/7.25 thf('#sk82_type', type, '#sk82': (a > $o) > a). 53.28/7.25 thf('#sk115_type', type, '#sk115': (a > $o) > a). 53.28/7.25 thf('#sk5_type', type, '#sk5': a > $o). 53.28/7.25 thf('#form14_type', type, '#form14': $o). 53.28/7.25 thf('#sk4_type', type, '#sk4': a). 53.28/7.25 thf('#sk140_type', type, '#sk140': (a > $o) > a). 53.28/7.25 thf('#sk15_type', type, '#sk15': a). 53.28/7.25 thf('#form9_type', type, '#form9': $o). 53.28/7.25 thf('#form285_type', type, '#form285': (a > $o) > $o). 53.28/7.25 thf('#sk99_type', type, '#sk99': (a > $o) > a). 53.28/7.25 thf('#sk23_type', type, '#sk23': a). 53.28/7.25 thf('#sk8_type', type, '#sk8': a > $o). 53.28/7.25 thf('#sk59_type', type, '#sk59': (a > $o) > a). 53.28/7.25 thf('#sk136_type', type, '#sk136': (a > $o) > a). 53.28/7.25 thf('#sk43_type', type, '#sk43': a > $o). 53.28/7.25 thf('#sk86_type', type, '#sk86': (a > $o) > a). 53.28/7.25 thf('#sk3_type', type, '#sk3': a). 53.28/7.25 thf('#sk7_type', type, '#sk7': a). 53.28/7.25 thf('#sk1_type', type, '#sk1': a > a > $o). 53.28/7.25 thf('#sk42_type', type, '#sk42': (a > $o) > a). 53.28/7.25 thf('#sk50_type', type, '#sk50': (a > $o) > a). 53.28/7.25 thf('#sk2_type', type, '#sk2': a > a > $o). 53.28/7.25 thf('#form147_type', type, '#form147': (a > $o) > $o). 53.28/7.25 thf('#sk71_type', type, '#sk71': (a > $o) > a). 53.28/7.25 thf('#sk148_type', type, '#sk148': (a > $o) > a). 53.28/7.25 thf('#sk10_type', type, '#sk10': a). 53.28/7.25 thf('#sk286_type', type, '#sk286': (a > $o) > a). 53.28/7.25 thf(cTHM251G_pme, conjecture, 53.28/7.25 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 53.28/7.25 ( ( ![Xq:( a > $o )]: 53.28/7.25 ( ( ( ![Xu:a,Xv:a]: 53.28/7.25 ( ( ( Xq @ Xu ) & ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 53.28/7.25 ( Xq @ Xv ) ) ) & 53.28/7.25 ( ![Xw:a]: 53.28/7.25 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 53.28/7.25 ( Xq @ Xy ) ) ) | 53.28/7.25 ( ~( ( ( ![Xx0:a,Xy0:a]: 53.28/7.25 ( ( ( ![Xq:( a > $o )]: 53.28/7.25 ( ( ( ![Xu:a,Xv:a]: 53.28/7.25 ( ( ( Xq @ Xu ) & ( S @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) & 53.28/7.25 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 53.28/7.25 ( Xq @ Xy0 ) ) ) | 53.28/7.25 ( ![Xq:( a > $o )]: 53.28/7.25 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 53.28/7.25 ( ![Xu:a,Xv:a]: 53.28/7.25 ( ( ( R @ Xu @ Xv ) & ( Xq @ Xu ) ) => ( Xq @ Xv ) ) ) ) => 53.28/7.25 ( Xq @ Xy0 ) ) ) ) => 53.28/7.25 ( ![Xq:( a > $o )]: 53.28/7.25 ( ( ( ![Xw:a]: 53.28/7.25 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 53.28/7.25 ( Xq @ Xw ) ) ) & 53.28/7.25 ( ![Xu:a,Xv:a]: 53.28/7.25 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & 53.28/7.25 ( Xq @ Xu ) ) => 53.28/7.25 ( Xq @ Xv ) ) ) ) => 53.28/7.25 ( Xq @ Xy0 ) ) ) ) ) & 53.28/7.25 ( ![Xx0:a,Xy0:a,Xz:a]: 53.28/7.25 ( ( ( ![Xq:( a > $o )]: 53.28/7.25 ( ( ( ![Xu:a,Xv:a]: 53.28/7.25 ( ( ( Xq @ Xu ) & 53.28/7.25 ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 53.28/7.25 ( Xq @ Xv ) ) ) & 53.28/7.25 ( ![Xw:a]: 53.28/7.25 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 53.28/7.25 ( Xq @ Xw ) ) ) ) => 53.28/7.25 ( Xq @ Xy0 ) ) ) & 53.28/7.25 ( ![Xq:( a > $o )]: 53.28/7.25 ( ( ( ![Xw:a]: 53.28/7.25 ( ( ( R @ Xy0 @ Xw ) | ( S @ Xy0 @ Xw ) ) => 53.28/7.25 ( Xq @ Xw ) ) ) & 53.28/7.25 ( ![Xu:a,Xv:a]: 53.28/7.25 ( ( ( Xq @ Xu ) & 53.28/7.25 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 53.28/7.25 ( Xq @ Xv ) ) ) ) => 53.28/7.25 ( Xq @ Xz ) ) ) ) => 53.28/7.25 ( ![Xq:( a > $o )]: 53.28/7.25 ( ( ( ![Xu:a,Xv:a]: 53.28/7.25 ( ( ( Xq @ Xu ) & 53.28/7.25 ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 53.28/7.25 ( Xq @ Xv ) ) ) & 53.28/7.25 ( ![Xw:a]: 53.28/7.25 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 53.28/7.25 ( Xq @ Xw ) ) ) ) => 53.28/7.25 ( Xq @ Xz ) ) ) ) ) ) => 53.28/7.25 ( ![Xq:( a > $o )]: 53.28/7.25 ( ( ( ![Xw:a]: 53.28/7.25 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 53.28/7.25 ( ![Xu:a,Xv:a]: 53.28/7.25 ( ( ( Xq @ Xu ) & ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 53.28/7.25 ( Xq @ Xv ) ) ) ) => 53.28/7.25 ( Xq @ Xy ) ) ) ) ) ))). 53.28/7.25 thf(zf_stmt_0, negated_conjecture, 53.28/7.25 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 53.28/7.25 ( ( ![Xq:( a > $o )]: 53.28/7.25 ( ( ( ![Xu:a,Xv:a]: 53.28/7.25 ( ( ( Xq @ Xu ) & ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 53.28/7.25 ( Xq @ Xv ) ) ) & 53.28/7.25 ( ![Xw:a]: 53.28/7.25 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 53.28/7.25 ( Xq @ Xy ) ) ) | 53.28/7.25 ( ~( ( ( ![Xx0:a,Xy0:a]: 53.28/7.25 ( ( ( ![Xq:( a > $o )]: 53.28/7.25 ( ( ( ![Xu:a,Xv:a]: 53.28/7.25 ( ( ( Xq @ Xu ) & ( S @ Xu @ Xv ) ) => 53.28/7.25 ( Xq @ Xv ) ) ) & 53.28/7.25 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 53.28/7.25 ( Xq @ Xy0 ) ) ) | 53.28/7.25 ( ![Xq:( a > $o )]: 53.28/7.25 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 53.28/7.25 ( ![Xu:a,Xv:a]: 53.28/7.25 ( ( ( R @ Xu @ Xv ) & ( Xq @ Xu ) ) => 53.28/7.25 ( Xq @ Xv ) ) ) ) => 53.28/7.25 ( Xq @ Xy0 ) ) ) ) => 53.28/7.25 ( ![Xq:( a > $o )]: 53.28/7.25 ( ( ( ![Xw:a]: 53.28/7.25 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 53.28/7.25 ( Xq @ Xw ) ) ) & 53.28/7.25 ( ![Xu:a,Xv:a]: 53.28/7.25 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & 53.28/7.25 ( Xq @ Xu ) ) => 53.28/7.25 ( Xq @ Xv ) ) ) ) => 53.28/7.25 ( Xq @ Xy0 ) ) ) ) ) & 53.28/7.25 ( ![Xx0:a,Xy0:a,Xz:a]: 53.28/7.25 ( ( ( ![Xq:( a > $o )]: 53.28/7.25 ( ( ( ![Xu:a,Xv:a]: 53.28/7.25 ( ( ( Xq @ Xu ) & 53.28/7.25 ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 53.28/7.25 ( Xq @ Xv ) ) ) & 53.28/7.25 ( ![Xw:a]: 53.28/7.25 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 53.28/7.25 ( Xq @ Xw ) ) ) ) => 53.28/7.25 ( Xq @ Xy0 ) ) ) & 53.28/7.25 ( ![Xq:( a > $o )]: 53.28/7.25 ( ( ( ![Xw:a]: 53.28/7.25 ( ( ( R @ Xy0 @ Xw ) | ( S @ Xy0 @ Xw ) ) => 53.28/7.25 ( Xq @ Xw ) ) ) & 53.28/7.25 ( ![Xu:a,Xv:a]: 53.28/7.25 ( ( ( Xq @ Xu ) & 53.28/7.25 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 53.28/7.25 ( Xq @ Xv ) ) ) ) => 53.28/7.25 ( Xq @ Xz ) ) ) ) => 53.28/7.25 ( ![Xq:( a > $o )]: 53.28/7.25 ( ( ( ![Xu:a,Xv:a]: 53.28/7.25 ( ( ( Xq @ Xu ) & 53.28/7.25 ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 53.28/7.25 ( Xq @ Xv ) ) ) & 53.28/7.25 ( ![Xw:a]: 53.28/7.25 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 53.28/7.25 ( Xq @ Xw ) ) ) ) => 53.28/7.25 ( Xq @ Xz ) ) ) ) ) ) => 53.28/7.25 ( ![Xq:( a > $o )]: 53.28/7.25 ( ( ( ![Xw:a]: 53.28/7.25 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 53.28/7.25 ( ![Xu:a,Xv:a]: 53.28/7.25 ( ( ( Xq @ Xu ) & ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 53.28/7.25 ( Xq @ Xv ) ) ) ) => 53.28/7.25 ( Xq @ Xy ) ) ) ) ) ) )), 53.28/7.25 inference('cnf.neg', [status(esa)], [cTHM251G_pme])). 53.28/7.25 thf(zip_derived_cl0, plain, 53.28/7.25 (~ (((!!) @ (^[Y0 : a > a > $o]: 53.28/7.25 (((!!) @ (^[Y1 : a > a > $o]: 53.28/7.25 (((!!) @ (^[Y2 : a]: 53.28/7.25 (((!!) @ (^[Y3 : a]: 53.28/7.25 (((((!!) @ (^[Y4 : a > $o]: 53.28/7.25 (( 53.28/7.25 (( 53.28/7.25 (( 53.28/7.25 (!!) @ ( 53.28/7.25 ^[Y5 : a]: 53.28/7.25 (( 53.28/7.25 (!!) @ ( 53.28/7.25 ^[Y6 : a]: 53.28/7.25 (( 53.28/7.25 (( 53.28/7.25 (Y4 @ 53.28/7.25 Y5) & 53.28/7.25 (( 53.28/7.25 (Y1 @ 53.28/7.25 Y5 @ 53.28/7.25 Y6) | 53.28/7.25 (Y0 @ 53.28/7.25 Y5 @ Y6))))) => 53.28/7.25 (Y4 @ Y6))))))))) & 53.28/7.25 (( 53.28/7.25 (!!) @ ( 53.28/7.25 ^[Y5 : a]: 53.28/7.25 (( 53.28/7.25 (( 53.28/7.25 (Y0 @ 53.28/7.25 Y2 @ 53.28/7.25 Y5) | 53.28/7.25 (Y1 @ 53.28/7.25 Y2 @ Y5))) => 53.28/7.25 (Y4 @ Y5)))))))) => 53.28/7.25 (Y4 @ Y3)))))) | 53.28/7.25 (((~) @ (((( 53.28/7.25 (( 53.28/7.25 (!!) @ ( 53.28/7.25 ^[Y4 : a]: 53.28/7.25 (( 53.28/7.25 (!!) @ ( 53.28/7.25 ^[Y5 : a]: 53.28/7.25 (( 53.28/7.25 (( 53.28/7.25 (( 53.28/7.25 (!!) @ ( 53.28/7.25 ^[Y6 : a > $o]: 53.28/7.25 (( 53.28/7.25 (( 53.28/7.25 (( 53.28/7.25 (!!) @ ( 53.28/7.25 ^[Y7 : a]: 53.28/7.25 (( 53.28/7.25 (!!) @ ( 53.28/7.25 ^[Y8 : a]: 53.28/7.25 (( 53.28/7.25 (( 53.28/7.25 (Y6 @ 53.28/7.25 Y7) & 53.28/7.25 (Y1 @ 53.28/7.25 Y7 @ Y8))) => 53.28/7.25 (Y6 @ Y8))))))))) & 53.28/7.25 (( 53.28/7.25 (!!) @ ( 53.28/7.25 ^[Y7 : a]: 53.28/7.25 (( 53.28/7.25 (Y1 @ 53.28/7.25 Y4 @ 53.28/7.25 Y7) => 53.28/7.25 (Y6 @ Y7)))))))) => 53.28/7.25 (Y6 @ Y5)))))) | 53.28/7.25 (( 53.28/7.25 (!!) @ ( 53.28/7.25 ^[Y6 : a > $o]: 53.28/7.25 (( 53.28/7.25 (( 53.28/7.25 (( 53.28/7.25 (!!) @ ( 53.28/7.25 ^[Y7 : a]: 53.28/7.25 (( 53.28/7.25 (Y0 @ 53.28/7.25 Y4 @ 53.28/7.25 Y7) => 53.28/7.25 (Y6 @ Y7)))))) & 53.28/7.25 (( 53.28/7.25 (!!) @ ( 53.28/7.25 ^[Y7 : a]: 53.28/7.25 (( 53.28/7.25 (!!) @ ( 53.28/7.25 ^[Y8 : a]: 53.28/7.25 (( 53.28/7.25 (( 53.28/7.25 (Y0 @ 53.28/7.25 Y7 @ 53.28/7.25 Y8) & 53.28/7.25 (Y6 @ Y7))) => 53.28/7.25 (Y6 @ Y8))))))))))) => 53.28/7.25 (Y6 @ Y5)))))))) => 53.28/7.25 (( 53.28/7.25 (!!) @ ( 53.28/7.25 ^[Y6 : a > $o]: 53.28/7.25 (( 53.28/7.25 (( 53.28/7.25 (( 53.28/7.25 (!!) @ ( 53.28/7.25 ^[Y7 : a]: 53.28/7.25 (( 53.28/7.25 (( 53.28/7.25 (Y1 @ 53.28/7.25 Y4 @ 53.28/7.25 Y7) | 53.28/7.25 (Y0 @ 53.28/7.25 Y4 @ Y7))) => 53.28/7.25 (Y6 @ Y7)))))) & 53.28/7.25 (( 53.28/7.25 (!!) @ ( 53.28/7.25 ^[Y7 : a]: 53.28/7.25 (( 53.28/7.25 (!!) @ ( 53.28/7.25 ^[Y8 : a]: 53.28/7.25 (( 53.28/7.25 (( 53.28/7.25 (( 53.28/7.25 (Y1 @ 53.28/7.25 Y7 @ 53.28/7.26 Y8) | 53.28/7.26 (Y0 @ 53.28/7.26 Y7 @ Y8))) & 53.28/7.26 (Y6 @ Y7))) => 53.28/7.26 (Y6 @ Y8))))))))))) => 53.28/7.26 (Y6 @ Y5)))))))))))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y7 : a > $o]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y8 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y9 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y7 @ 53.28/7.26 Y8) & 53.28/7.26 (( 53.28/7.26 (Y1 @ 53.28/7.26 Y8 @ 53.28/7.26 Y9) | 53.28/7.26 (Y0 @ 53.28/7.26 Y8 @ Y9))))) => 53.28/7.26 (Y7 @ Y9))))))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y8 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y1 @ 53.28/7.26 Y4 @ 53.28/7.26 Y8) | 53.28/7.26 (Y0 @ 53.28/7.26 Y4 @ Y8))) => 53.28/7.26 (Y7 @ Y8)))))))) => 53.28/7.26 (Y7 @ Y5)))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y7 : a > $o]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y8 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y0 @ 53.28/7.26 Y5 @ 53.28/7.26 Y8) | 53.28/7.26 (Y1 @ 53.28/7.26 Y5 @ Y8))) => 53.28/7.26 (Y7 @ Y8)))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y8 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y9 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y7 @ 53.28/7.26 Y8) & 53.28/7.26 (( 53.28/7.26 (Y0 @ 53.28/7.26 Y8 @ 53.28/7.26 Y9) | 53.28/7.26 (Y1 @ 53.28/7.26 Y8 @ Y9))))) => 53.28/7.26 (Y7 @ Y9))))))))))) => 53.28/7.26 (Y7 @ Y6)))))))) => 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y7 : a > $o]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y8 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y9 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y7 @ 53.28/7.26 Y8) & 53.28/7.26 (( 53.28/7.26 (Y1 @ 53.28/7.26 Y8 @ 53.28/7.26 Y9) | 53.28/7.26 (Y0 @ 53.28/7.26 Y8 @ Y9))))) => 53.28/7.26 (Y7 @ Y9))))))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y8 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y1 @ 53.28/7.26 Y4 @ 53.28/7.26 Y8) | 53.28/7.26 (Y0 @ 53.28/7.26 Y4 @ Y8))) => 53.28/7.26 (Y7 @ Y8)))))))) => 53.28/7.26 (Y7 @ Y6))))))))))))))))))) => 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a > $o]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y1 @ 53.28/7.26 Y2 @ 53.28/7.26 Y5) | 53.28/7.26 (Y0 @ 53.28/7.26 Y2 @ Y5))) => 53.28/7.26 (Y4 @ Y5)))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y4 @ 53.28/7.26 Y5) & 53.28/7.26 (( 53.28/7.26 (Y0 @ 53.28/7.26 Y5 @ 53.28/7.26 Y6) | 53.28/7.26 (Y1 @ 53.28/7.26 Y5 @ Y6))))) => 53.28/7.26 (Y4 @ Y6))))))))))) => 53.28/7.26 (Y4 @ Y3))))))))))))))))))))))))), 53.28/7.26 inference('cnf', [status(esa)], [zf_stmt_0])). 53.28/7.26 thf(zip_derived_cl1, plain, 53.28/7.26 (~ (((!!) @ (^[Y0 : a > a > $o]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 (Y0 @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (((( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y1 @ Y4) | 53.28/7.26 (Y0 @ 53.28/7.26 Y1 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y2)))))) | 53.28/7.26 (((~) @ (((((((!!) @ (^[Y3 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a > $o]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y7 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y5 @ 53.28/7.26 Y6) & 53.28/7.26 (Y0 @ 53.28/7.26 Y6 @ Y7))) => 53.28/7.26 (Y5 @ Y7))))))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a]: 53.28/7.26 (( 53.28/7.26 (Y0 @ 53.28/7.26 Y3 @ 53.28/7.26 Y6) => 53.28/7.26 (Y5 @ Y6)))))))) => 53.28/7.26 (Y5 @ Y4)))))) | 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a > $o]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a]: 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y3 @ 53.28/7.26 Y6) => 53.28/7.26 (Y5 @ Y6)))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y7 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y6 @ 53.28/7.26 Y7) & 53.28/7.26 (Y5 @ Y6))) => 53.28/7.26 (Y5 @ Y7))))))))))) => 53.28/7.26 (Y5 @ Y4)))))))) => 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a > $o]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y0 @ 53.28/7.26 Y3 @ 53.28/7.26 Y6) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y3 @ Y6))) => 53.28/7.26 (Y5 @ Y6)))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y7 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y0 @ 53.28/7.26 Y6 @ 53.28/7.26 Y7) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y6 @ Y7))) & 53.28/7.26 (Y5 @ Y6))) => 53.28/7.26 (Y5 @ Y7))))))))))) => 53.28/7.26 (Y5 @ Y4)))))))))))))) & 53.28/7.26 (((!!) @ (^[Y3 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a > $o]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y7 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y8 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y6 @ 53.28/7.26 Y7) & 53.28/7.26 (( 53.28/7.26 (Y0 @ 53.28/7.26 Y7 @ 53.28/7.26 Y8) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y7 @ Y8))))) => 53.28/7.26 (Y6 @ Y8))))))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y7 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y0 @ 53.28/7.26 Y3 @ 53.28/7.26 Y7) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y3 @ Y7))) => 53.28/7.26 (Y6 @ Y7)))))))) => 53.28/7.26 (Y6 @ Y4)))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a > $o]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y7 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ 53.28/7.26 Y7) | 53.28/7.26 (Y0 @ 53.28/7.26 Y4 @ Y7))) => 53.28/7.26 (Y6 @ Y7)))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y7 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y8 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y6 @ 53.28/7.26 Y7) & 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y7 @ 53.28/7.26 Y8) | 53.28/7.26 (Y0 @ 53.28/7.26 Y7 @ Y8))))) => 53.28/7.26 (Y6 @ Y8))))))))))) => 53.28/7.26 (Y6 @ Y5)))))))) => 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a > $o]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y7 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y8 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y6 @ 53.28/7.26 Y7) & 53.28/7.26 (( 53.28/7.26 (Y0 @ 53.28/7.26 Y7 @ 53.28/7.26 Y8) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y7 @ Y8))))) => 53.28/7.26 (Y6 @ Y8))))))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y7 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y0 @ 53.28/7.26 Y3 @ 53.28/7.26 Y7) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y3 @ Y7))) => 53.28/7.26 (Y6 @ Y7)))))))) => 53.28/7.26 (Y6 @ Y5))))))))))))))))))) => 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y0 @ 53.28/7.26 Y1 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y1 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 (Y0 @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))))) => 53.28/7.26 (Y3 @ Y2)))))))))))))))))))))), 53.28/7.26 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 53.28/7.26 thf(zip_derived_cl2, plain, 53.28/7.26 (~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((((!!) @ (^[Y2 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y3 : a]: 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (((( 53.28/7.26 (Y2 @ 53.28/7.26 Y3) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y3 @ Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y3 @ Y4))))) => 53.28/7.26 (Y2 @ Y4))))))))) & 53.28/7.26 (((!!) @ (^[Y3 : a]: 53.28/7.26 ((((('#sk1' @ 53.28/7.26 Y0 @ Y3) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ Y3))) => 53.28/7.26 (Y2 @ Y3)))))))) => 53.28/7.26 (Y2 @ Y1)))))) | 53.28/7.26 (((~) @ (((((((!!) @ (^[Y2 : a]: 53.28/7.26 (((!!) @ (^[Y3 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a > $o]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y4 @ 53.28/7.26 Y5) & 53.28/7.26 ('#sk2' @ 53.28/7.26 Y5 @ Y6))) => 53.28/7.26 (Y4 @ Y6))))))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y2 @ 53.28/7.26 Y5) => 53.28/7.26 (Y4 @ Y5)))))))) => 53.28/7.26 (Y4 @ Y3)))))) | 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a > $o]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y2 @ 53.28/7.26 Y5) => 53.28/7.26 (Y4 @ Y5)))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y5 @ 53.28/7.26 Y6) & 53.28/7.26 (Y4 @ Y5))) => 53.28/7.26 (Y4 @ Y6))))))))))) => 53.28/7.26 (Y4 @ Y3)))))))) => 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a > $o]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y2 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y2 @ Y5))) => 53.28/7.26 (Y4 @ Y5)))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y5 @ 53.28/7.26 Y6) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y5 @ Y6))) & 53.28/7.26 (Y4 @ Y5))) => 53.28/7.26 (Y4 @ Y6))))))))))) => 53.28/7.26 (Y4 @ Y3)))))))))))))) & 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((!!) @ (^[Y3 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a > $o]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y7 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y5 @ 53.28/7.26 Y6) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y6 @ 53.28/7.26 Y7) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y6 @ Y7))))) => 53.28/7.26 (Y5 @ Y7))))))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y2 @ 53.28/7.26 Y6) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y2 @ Y6))) => 53.28/7.26 (Y5 @ Y6)))))))) => 53.28/7.26 (Y5 @ Y3)))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a > $o]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y3 @ 53.28/7.26 Y6) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y3 @ Y6))) => 53.28/7.26 (Y5 @ Y6)))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y6 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y7 : a]: 53.28/7.26 (( 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53.28/7.26 ((('#sk2' @ 53.28/7.26 Y0 @ Y3) => 53.28/7.26 (Y2 @ Y3)))))))) => 53.28/7.26 (Y2 @ Y1)))))) | 53.28/7.26 (((!!) @ (^[Y2 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y3 : a]: 53.28/7.26 ((('#sk1' @ 53.28/7.26 Y0 @ Y3) => 53.28/7.26 (Y2 @ Y3)))))) & 53.28/7.26 (((!!) @ (^[Y3 : a]: 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 ( 53.28/7.26 ( 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (Y2 @ Y3))) => 53.28/7.26 (Y2 @ Y4))))))))))) => 53.28/7.26 (Y2 @ Y1)))))))) => 53.28/7.26 (((!!) @ (^[Y2 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y3 : a]: 53.28/7.26 ((((('#sk2' @ 53.28/7.26 Y0 @ Y3) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y3))) => 53.28/7.26 (Y2 @ Y3)))))) & 53.28/7.26 (((!!) @ (^[Y3 : a]: 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (((( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y3 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y3 @ Y4))) & 53.28/7.26 (Y2 @ Y3))) => 53.28/7.26 (Y2 @ Y4))))))))))) => 53.28/7.26 (Y2 @ Y1)))))))))))))) 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y1 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y1 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 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'#sk3' @ Y1) | ('#sk1' @ 53.28/7.26 '#sk3' @ Y1))) => 53.28/7.26 (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((Y0 @ Y1) & 53.28/7.26 ((('#sk1' @ Y1 @ Y2) | 53.28/7.26 ('#sk2' @ Y1 @ Y2))))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk4')))))))), 53.28/7.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl8])). 53.28/7.26 thf(zip_derived_cl14, plain, 53.28/7.26 ((~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((((((!!) @ (^[Y1 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y2 : a]: 53.28/7.26 (((!!) @ (^[Y3 : a]: 53.28/7.26 (((((Y1 @ 53.28/7.26 Y2) & 53.28/7.26 ('#sk2' @ 53.28/7.26 Y2 @ Y3))) => 53.28/7.26 (Y1 @ Y3))))))))) & 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 ((('#sk2' @ '#sk6' @ 53.28/7.26 Y2) => (Y1 @ Y2)))))))) => 53.28/7.26 (Y1 @ Y0)))))) | 53.28/7.26 (((!!) @ (^[Y1 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y2 : a]: 53.28/7.26 ((('#sk1' @ '#sk6' @ 53.28/7.26 Y2) => (Y1 @ Y2)))))) & 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((!!) @ (^[Y3 : a]: 53.28/7.26 ((((('#sk1' @ 53.28/7.26 Y2 @ 53.28/7.26 Y3) & 53.28/7.26 (Y1 @ Y2))) => 53.28/7.26 (Y1 @ Y3))))))))))) => 53.28/7.26 (Y1 @ Y0)))))))) => 53.28/7.26 (((!!) @ (^[Y1 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y2 : a]: 53.28/7.26 ((((('#sk2' @ '#sk6' @ 53.28/7.26 Y2) | ('#sk1' @ 53.28/7.26 '#sk6' @ Y2))) => 53.28/7.26 (Y1 @ Y2)))))) & 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((!!) @ (^[Y3 : a]: 53.28/7.26 ((((((('#sk2' @ 53.28/7.26 Y2 @ 53.28/7.26 Y3) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y2 @ Y3))) & 53.28/7.26 (Y1 @ Y2))) => 53.28/7.26 (Y1 @ Y3))))))))))) => 53.28/7.26 (Y1 @ Y0))))))))))) 53.28/7.26 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 53.28/7.26 '#sk3' @ Y1))) => 53.28/7.26 (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((Y0 @ Y1) & 53.28/7.26 ((('#sk1' @ Y1 @ Y2) | 53.28/7.26 ('#sk2' @ Y1 @ Y2))))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 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53.28/7.26 ((((('#sk2' @ '#sk3' @ Y1) | 53.28/7.26 ('#sk1' @ '#sk3' @ Y1))) => 53.28/7.26 (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((Y0 @ Y1) & 53.28/7.26 ((('#sk1' @ Y1 @ Y2) | 53.28/7.26 ('#sk2' @ Y1 @ Y2))))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk4')))))) 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y1 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y1 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))))) => 53.28/7.26 (Y3 @ Y2)))))))) => 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y2))))))))))))))))) 53.28/7.26 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 ((((('#sk1' @ Y1 @ Y2) & 53.28/7.26 (Y0 @ Y1))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk7')))))))), 53.28/7.26 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl25])). 53.28/7.26 thf(zip_derived_cl36, plain, 53.28/7.26 ((~ ('#form14') 53.28/7.26 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 53.28/7.26 '#sk3' @ Y1))) => 53.28/7.26 (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((Y0 @ Y1) & 53.28/7.26 ((('#sk1' @ Y1 @ Y2) | 53.28/7.26 ('#sk2' @ Y1 @ Y2))))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk4')))))))), 53.28/7.26 define([status(thm)])). 53.28/7.26 thf(zip_derived_cl37, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 ( (((((((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 53.28/7.26 (X2 @ Y0)))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((((X2 @ Y0) & 53.28/7.26 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 53.28/7.26 Y0 @ Y1))))) => 53.28/7.26 (X2 @ Y1))))))))))) => 53.28/7.26 (X2 @ '#sk4'))) 53.28/7.26 | ~ ('#form14'))), 53.28/7.26 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl36])). 53.28/7.26 thf(zip_derived_cl39, plain, 53.28/7.26 (( (((((((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 53.28/7.26 ('#sk5' @ Y0)))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk5' @ Y0) & 53.28/7.26 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 53.28/7.26 Y1))))) => 53.28/7.26 ('#sk5' @ Y1))))))))))) => 53.28/7.26 ('#sk5' @ '#sk4'))) 53.28/7.26 | ~ ('#form14'))), 53.28/7.26 inference('triggered_bool_instantiation', [status(thm)], 53.28/7.26 [zip_derived_cl37])). 53.28/7.26 thf(zip_derived_cl5, plain, 53.28/7.26 (~ (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((Y0 @ Y1) & 53.28/7.26 ((('#sk2' @ Y1 @ Y2) | 53.28/7.26 ('#sk1' @ Y1 @ Y2))))) => 53.28/7.26 (Y0 @ Y2))))))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 53.28/7.26 '#sk3' @ Y1))) => 53.28/7.26 (Y0 @ Y1)))))))) => 53.28/7.26 (Y0 @ '#sk4'))))))), 53.28/7.26 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 53.28/7.26 thf(zip_derived_cl7, plain, 53.28/7.26 (~ (((((((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk5' @ Y0) & 53.28/7.26 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 53.28/7.26 Y1))))) => 53.28/7.26 ('#sk5' @ Y1))))))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 53.28/7.26 ('#sk5' @ Y0)))))))) => 53.28/7.26 ('#sk5' @ '#sk4')))), 53.28/7.26 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl5])). 53.28/7.26 thf(zip_derived_cl10, plain, (~ ('#sk5' @ '#sk4')), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 53.28/7.26 thf(zip_derived_cl283, plain, 53.28/7.26 (( (((((((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 53.28/7.26 ('#sk5' @ Y0)))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk5' @ Y0) & 53.28/7.26 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 53.28/7.26 Y1))))) => 53.28/7.26 ('#sk5' @ Y1))))))))))) => 53.28/7.26 ($false))) 53.28/7.26 | ~ ('#form14'))), 53.28/7.26 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl10])). 53.28/7.26 thf(zip_derived_cl284, plain, 53.28/7.26 (( (((~) @ (((((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ 53.28/7.26 Y0))) => 53.28/7.26 ('#sk5' @ Y0)))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk5' @ Y0) & 53.28/7.26 ((('#sk1' @ Y0 @ Y1) | 53.28/7.26 ('#sk2' @ Y0 @ Y1))))) => 53.28/7.26 ('#sk5' @ Y1))))))))))))) 53.28/7.26 | ~ ('#form14'))), 53.28/7.26 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl283])). 53.28/7.26 thf(zip_derived_cl285, plain, 53.28/7.26 ((~ (((((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 53.28/7.26 ('#sk5' @ Y0)))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk5' @ Y0) & 53.28/7.26 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 53.28/7.26 Y1))))) => 53.28/7.26 ('#sk5' @ Y1))))))))))) 53.28/7.26 | ~ ('#form14'))), 53.28/7.26 inference('simplify nested equalities', [status(thm)], 53.28/7.26 [zip_derived_cl284])). 53.28/7.26 thf(zip_derived_cl286, plain, 53.28/7.26 ((~ (((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 53.28/7.26 ('#sk5' @ Y0)))))) 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk5' @ Y0) & 53.28/7.26 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 53.28/7.26 Y1))))) => 53.28/7.26 ('#sk5' @ Y1))))))))) 53.28/7.26 | ~ ('#form14'))), 53.28/7.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl285])). 53.28/7.26 thf(zip_derived_cl287, plain, 53.28/7.26 ((~ ((((('#sk2' @ '#sk3' @ ('#sk42' @ '#sk5')) | ('#sk1' @ '#sk3' @ 53.28/7.26 ('#sk42' @ '#sk5')))) => 53.28/7.26 ('#sk5' @ ('#sk42' @ '#sk5')))) 53.28/7.26 | ~ ('#form14') 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk5' @ Y0) & 53.28/7.26 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 53.28/7.26 Y1))))) => 53.28/7.26 ('#sk5' @ Y1))))))))))), 53.28/7.26 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl286])). 53.28/7.26 thf(zip_derived_cl289, plain, 53.28/7.26 ((~ ('#sk5' @ ('#sk42' @ '#sk5')) 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk5' @ Y0) & 53.28/7.26 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 53.28/7.26 Y1))))) => 53.28/7.26 ('#sk5' @ Y1))))))))) 53.28/7.26 | ~ ('#form14'))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl287])). 53.28/7.26 thf(zip_derived_cl291, plain, 53.28/7.26 ((~ (((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk5' @ ('#sk71' @ '#sk5')) & 53.28/7.26 ((('#sk1' @ ('#sk71' @ '#sk5') @ Y0) | ('#sk2' @ 53.28/7.26 ('#sk71' @ '#sk5') @ Y0))))) => 53.28/7.26 ('#sk5' @ Y0)))))) 53.28/7.26 | ~ ('#form14') 53.28/7.26 | ~ ('#sk5' @ ('#sk42' @ '#sk5')))), 53.28/7.26 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl289])). 53.28/7.26 thf(zip_derived_cl293, plain, 53.28/7.26 ((~ ((((('#sk5' @ ('#sk71' @ '#sk5')) & 53.28/7.26 ((('#sk1' @ ('#sk71' @ '#sk5') @ ('#sk99' @ '#sk5')) | ('#sk2' @ 53.28/7.26 ('#sk71' @ '#sk5') @ ('#sk99' @ '#sk5')))))) => 53.28/7.26 ('#sk5' @ ('#sk99' @ '#sk5')))) 53.28/7.26 | ~ ('#sk5' @ ('#sk42' @ '#sk5')) 53.28/7.26 | ~ ('#form14'))), 53.28/7.26 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl291])). 53.28/7.26 thf(zip_derived_cl296, plain, 53.28/7.26 ((~ ('#sk5' @ ('#sk99' @ '#sk5')) 53.28/7.26 | ~ ('#form14') 53.28/7.26 | ~ ('#sk5' @ ('#sk42' @ '#sk5')))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl293])). 53.28/7.26 thf(zip_derived_cl288, plain, 53.28/7.26 (( ((('#sk2' @ '#sk3' @ ('#sk42' @ '#sk5')) | ('#sk1' @ '#sk3' @ 53.28/7.26 ('#sk42' @ '#sk5')))) 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk5' @ Y0) & 53.28/7.26 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 53.28/7.26 Y1))))) => 53.28/7.26 ('#sk5' @ Y1))))))))) 53.28/7.26 | ~ ('#form14'))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl287])). 53.28/7.26 thf(zip_derived_cl290, plain, 53.28/7.26 (( ('#sk2' @ '#sk3' @ ('#sk42' @ '#sk5')) 53.28/7.26 | ('#sk1' @ '#sk3' @ ('#sk42' @ '#sk5')) 53.28/7.26 | ~ ('#form14') 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk5' @ Y0) & 53.28/7.26 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 53.28/7.26 Y1))))) => 53.28/7.26 ('#sk5' @ Y1))))))))))), 53.28/7.26 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl288])). 53.28/7.26 thf(zip_derived_cl292, plain, 53.28/7.26 ((~ (((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk5' @ ('#sk71' @ '#sk5')) & 53.28/7.26 ((('#sk1' @ ('#sk71' @ '#sk5') @ Y0) | ('#sk2' @ 53.28/7.26 ('#sk71' @ '#sk5') @ Y0))))) => 53.28/7.26 ('#sk5' @ Y0)))))) 53.28/7.26 | ~ ('#form14') 53.28/7.26 | ('#sk1' @ '#sk3' @ ('#sk42' @ '#sk5')) 53.28/7.26 | ('#sk2' @ '#sk3' @ ('#sk42' @ '#sk5')))), 53.28/7.26 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl290])). 53.28/7.26 thf(zip_derived_cl294, plain, 53.28/7.26 ((~ ((((('#sk5' @ ('#sk71' @ '#sk5')) & 53.28/7.26 ((('#sk1' @ ('#sk71' @ '#sk5') @ ('#sk99' @ '#sk5')) | ('#sk2' @ 53.28/7.26 ('#sk71' @ '#sk5') @ ('#sk99' @ '#sk5')))))) => 53.28/7.26 ('#sk5' @ ('#sk99' @ '#sk5')))) 53.28/7.26 | ('#sk2' @ '#sk3' @ ('#sk42' @ '#sk5')) 53.28/7.26 | ('#sk1' @ '#sk3' @ ('#sk42' @ '#sk5')) 53.28/7.26 | ~ ('#form14'))), 53.28/7.26 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl292])). 53.28/7.26 thf(zip_derived_cl298, plain, 53.28/7.26 ((~ ('#sk5' @ ('#sk99' @ '#sk5')) 53.28/7.26 | ~ ('#form14') 53.28/7.26 | ('#sk1' @ '#sk3' @ ('#sk42' @ '#sk5')) 53.28/7.26 | ('#sk2' @ '#sk3' @ ('#sk42' @ '#sk5')))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl294])). 53.28/7.26 thf(zip_derived_cl9, plain, 53.28/7.26 ( (((((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk5' @ Y0) & 53.28/7.26 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))))) => 53.28/7.26 ('#sk5' @ Y1))))))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 53.28/7.26 ('#sk5' @ Y0))))))))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 53.28/7.26 thf(zip_derived_cl12, plain, 53.28/7.26 ( (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk5' @ Y0) & 53.28/7.26 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))))) => 53.28/7.26 ('#sk5' @ Y1)))))))))), 53.28/7.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl9])). 53.28/7.26 thf(zip_derived_cl15, plain, 53.28/7.26 (![X2 : a]: 53.28/7.26 (((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk5' @ X2) & 53.28/7.26 ((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))))) => 53.28/7.26 ('#sk5' @ Y0))))))), 53.28/7.26 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])). 53.28/7.26 thf(zip_derived_cl18, plain, 53.28/7.26 (![X2 : a, X4 : a]: 53.28/7.26 ((((('#sk5' @ X2) & ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))))) => 53.28/7.26 ('#sk5' @ X4)))), 53.28/7.26 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 53.28/7.26 thf(zip_derived_cl22, plain, 53.28/7.26 (![X2 : a, X4 : a]: 53.28/7.26 (~ ((('#sk5' @ X2) & ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))))) 53.28/7.26 | ('#sk5' @ X4))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 53.28/7.26 thf(zip_derived_cl27, plain, 53.28/7.26 (![X2 : a, X4 : a]: 53.28/7.26 (~ ('#sk5' @ X2) 53.28/7.26 | ~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 53.28/7.26 | ('#sk5' @ X4))), 53.28/7.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl22])). 53.28/7.26 thf(zip_derived_cl35, plain, 53.28/7.26 (![X2 : a, X4 : a]: 53.28/7.26 (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 53.28/7.26 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl27])). 53.28/7.26 thf(zip_derived_cl34, plain, 53.28/7.26 (![X2 : a, X4 : a]: 53.28/7.26 (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 53.28/7.26 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl27])). 53.28/7.26 thf(zip_derived_cl13, plain, 53.28/7.26 ( (((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 53.28/7.26 ('#sk5' @ Y0))))))), 53.28/7.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl9])). 53.28/7.26 thf(zip_derived_cl16, plain, 53.28/7.26 (![X2 : a]: 53.28/7.26 ((((('#sk1' @ '#sk3' @ X2) | ('#sk2' @ '#sk3' @ X2))) => ('#sk5' @ 53.28/7.26 X2)))), 53.28/7.26 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 53.28/7.26 thf(zip_derived_cl19, plain, 53.28/7.26 (![X2 : a]: 53.28/7.26 (~ ((('#sk1' @ '#sk3' @ X2) | ('#sk2' @ '#sk3' @ X2))) 53.28/7.26 | ('#sk5' @ X2))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 53.28/7.26 thf(zip_derived_cl23, plain, 53.28/7.26 (![X2 : a]: (~ ('#sk1' @ '#sk3' @ X2) | ('#sk5' @ X2))), 53.28/7.26 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 53.28/7.26 thf(zip_derived_cl295, plain, 53.28/7.26 (( ((('#sk5' @ ('#sk71' @ '#sk5')) & 53.28/7.26 ((('#sk1' @ ('#sk71' @ '#sk5') @ ('#sk99' @ '#sk5')) | ('#sk2' @ 53.28/7.26 ('#sk71' @ '#sk5') @ ('#sk99' @ '#sk5')))))) 53.28/7.26 | ~ ('#form14') 53.28/7.26 | ~ ('#sk5' @ ('#sk42' @ '#sk5')))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl293])). 53.28/7.26 thf(zip_derived_cl299, plain, 53.28/7.26 (( ('#sk5' @ ('#sk71' @ '#sk5')) 53.28/7.26 | ~ ('#sk5' @ ('#sk42' @ '#sk5')) 53.28/7.26 | ~ ('#form14'))), 53.28/7.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl295])). 53.28/7.26 thf(zip_derived_cl297, plain, 53.28/7.26 (( ((('#sk5' @ ('#sk71' @ '#sk5')) & 53.28/7.26 ((('#sk1' @ ('#sk71' @ '#sk5') @ ('#sk99' @ '#sk5')) | ('#sk2' @ 53.28/7.26 ('#sk71' @ '#sk5') @ ('#sk99' @ '#sk5')))))) 53.28/7.26 | ~ ('#form14') 53.28/7.26 | ('#sk1' @ '#sk3' @ ('#sk42' @ '#sk5')) 53.28/7.26 | ('#sk2' @ '#sk3' @ ('#sk42' @ '#sk5')))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl294])). 53.28/7.26 thf(zip_derived_cl301, plain, 53.28/7.26 (( ('#sk5' @ ('#sk71' @ '#sk5')) 53.28/7.26 | ('#sk2' @ '#sk3' @ ('#sk42' @ '#sk5')) 53.28/7.26 | ('#sk1' @ '#sk3' @ ('#sk42' @ '#sk5')) 53.28/7.26 | ~ ('#form14'))), 53.28/7.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl297])). 53.28/7.26 thf(zip_derived_cl300, plain, 53.28/7.26 (( ((('#sk1' @ ('#sk71' @ '#sk5') @ ('#sk99' @ '#sk5')) | ('#sk2' @ 53.28/7.26 ('#sk71' @ '#sk5') @ ('#sk99' @ '#sk5')))) 53.28/7.26 | ~ ('#sk5' @ ('#sk42' @ '#sk5')) 53.28/7.26 | ~ ('#form14'))), 53.28/7.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl295])). 53.28/7.26 thf(zip_derived_cl303, plain, 53.28/7.26 (( ('#sk1' @ ('#sk71' @ '#sk5') @ ('#sk99' @ '#sk5')) 53.28/7.26 | ('#sk2' @ ('#sk71' @ '#sk5') @ ('#sk99' @ '#sk5')) 53.28/7.26 | ~ ('#form14') 53.28/7.26 | ~ ('#sk5' @ ('#sk42' @ '#sk5')))), 53.28/7.26 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl300])). 53.28/7.26 thf(zip_derived_cl302, plain, 53.28/7.26 (( ((('#sk1' @ ('#sk71' @ '#sk5') @ ('#sk99' @ '#sk5')) | ('#sk2' @ 53.28/7.26 ('#sk71' @ '#sk5') @ ('#sk99' @ '#sk5')))) 53.28/7.26 | ('#sk2' @ '#sk3' @ ('#sk42' @ '#sk5')) 53.28/7.26 | ('#sk1' @ '#sk3' @ ('#sk42' @ '#sk5')) 53.28/7.26 | ~ ('#form14'))), 53.28/7.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl297])). 53.28/7.26 thf(zip_derived_cl304, plain, 53.28/7.26 (( ('#sk1' @ ('#sk71' @ '#sk5') @ ('#sk99' @ '#sk5')) 53.28/7.26 | ('#sk2' @ ('#sk71' @ '#sk5') @ ('#sk99' @ '#sk5')) 53.28/7.26 | ~ ('#form14') 53.28/7.26 | ('#sk1' @ '#sk3' @ ('#sk42' @ '#sk5')) 53.28/7.26 | ('#sk2' @ '#sk3' @ ('#sk42' @ '#sk5')))), 53.28/7.26 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl302])). 53.28/7.26 thf(zip_derived_cl24, plain, 53.28/7.26 (![X2 : a]: (~ ('#sk2' @ '#sk3' @ X2) | ('#sk5' @ X2))), 53.28/7.26 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 53.28/7.26 thf(zip_derived_cl28, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 ( (((((((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 53.28/7.26 (X2 @ Y1))))))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) => 53.28/7.26 (X2 @ '#sk7'))) 53.28/7.26 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk2' @ '#sk3' @ Y1) | 53.28/7.26 ('#sk1' @ '#sk3' @ Y1))) => 53.28/7.26 (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((Y0 @ Y1) & 53.28/7.26 ((('#sk1' @ Y1 @ Y2) | 53.28/7.26 ('#sk2' @ Y1 @ Y2))))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk4')))))) 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y1 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y1 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))))) => 53.28/7.26 (Y3 @ Y2)))))))) => 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y2))))))))))))))))) 53.28/7.26 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 ((((('#sk1' @ Y1 @ Y2) & 53.28/7.26 (Y0 @ Y1))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk7')))))))), 53.28/7.26 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl25])). 53.28/7.26 thf(zip_derived_cl36, plain, 53.28/7.26 ((~ ('#form14') 53.28/7.26 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 53.28/7.26 '#sk3' @ Y1))) => 53.28/7.26 (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((Y0 @ Y1) & 53.28/7.26 ((('#sk1' @ Y1 @ Y2) | 53.28/7.26 ('#sk2' @ Y1 @ Y2))))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk4')))))))), 53.28/7.26 define([status(thm)])). 53.28/7.26 thf(zip_derived_cl40, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 ( ('#form14') 53.28/7.26 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 ((((('#sk1' @ Y1 @ Y2) & 53.28/7.26 (Y0 @ Y1))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk7')))))) 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y1 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y1 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))))) => 53.28/7.26 (Y3 @ Y2)))))))) => 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y2))))))))))))))))) 53.28/7.26 | (((((((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 53.28/7.26 (X2 @ Y1))))))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) => 53.28/7.26 (X2 @ '#sk7'))))), 53.28/7.26 inference('renaming', [status(thm)], [zip_derived_cl28, zip_derived_cl36])). 53.28/7.26 thf(zip_derived_cl43, plain, 53.28/7.26 ((~ ('#form19') 53.28/7.26 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 ((((('#sk1' @ Y1 @ Y2) & 53.28/7.26 (Y0 @ Y1))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk7')))))))), 53.28/7.26 define([status(thm)])). 53.28/7.26 thf(zip_derived_cl44, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 ( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 53.28/7.26 (X2 @ Y1))))))))))) => 53.28/7.26 (X2 @ '#sk7'))) 53.28/7.26 | ~ ('#form19'))), 53.28/7.26 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 53.28/7.26 thf(zip_derived_cl53, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 (~ (((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 53.28/7.26 (X2 @ Y1))))))))))) 53.28/7.26 | (X2 @ '#sk7') 53.28/7.26 | ~ ('#form19'))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 53.28/7.26 thf(zip_derived_cl60, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 (~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 53.28/7.26 (X2 @ Y1))))))))) 53.28/7.26 | ~ ('#form19') 53.28/7.26 | (X2 @ '#sk7'))), 53.28/7.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl53])). 53.28/7.26 thf(zip_derived_cl71, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 (~ ((('#sk1' @ '#sk6' @ ('#sk50' @ X2)) => (X2 @ ('#sk50' @ X2)))) 53.28/7.26 | (X2 @ '#sk7') 53.28/7.26 | ~ ('#form19') 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 53.28/7.26 (X2 @ Y1))))))))))), 53.28/7.26 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl60])). 53.28/7.26 thf(zip_derived_cl88, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 (~ (X2 @ ('#sk50' @ X2)) 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 53.28/7.26 (X2 @ Y1))))))))) 53.28/7.26 | ~ ('#form19') 53.28/7.26 | (X2 @ '#sk7'))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 53.28/7.26 thf(zip_derived_cl100, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 (~ (((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk1' @ ('#sk86' @ X2) @ Y0) & (X2 @ 53.28/7.26 ('#sk86' @ X2)))) => 53.28/7.26 (X2 @ Y0)))))) 53.28/7.26 | (X2 @ '#sk7') 53.28/7.26 | ~ ('#form19') 53.28/7.26 | ~ (X2 @ ('#sk50' @ X2)))), 53.28/7.26 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl88])). 53.28/7.26 thf(zip_derived_cl111, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 (~ ((((('#sk1' @ ('#sk86' @ X2) @ ('#sk115' @ X2)) & (X2 @ 53.28/7.26 ('#sk86' @ X2)))) => 53.28/7.26 (X2 @ ('#sk115' @ X2)))) 53.28/7.26 | ~ (X2 @ ('#sk50' @ X2)) 53.28/7.26 | ~ ('#form19') 53.28/7.26 | (X2 @ '#sk7'))), 53.28/7.26 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl100])). 53.28/7.26 thf(zip_derived_cl129, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 (~ (X2 @ ('#sk115' @ X2)) 53.28/7.26 | (X2 @ '#sk7') 53.28/7.26 | ~ ('#form19') 53.28/7.26 | ~ (X2 @ ('#sk50' @ X2)))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl111])). 53.28/7.26 thf(zip_derived_cl128, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 ( ((('#sk1' @ ('#sk86' @ X2) @ ('#sk115' @ X2)) & (X2 @ 53.28/7.26 ('#sk86' @ X2)))) 53.28/7.26 | (X2 @ '#sk7') 53.28/7.26 | ~ ('#form19') 53.28/7.26 | ~ (X2 @ ('#sk50' @ X2)))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl111])). 53.28/7.26 thf(zip_derived_cl147, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 ( (X2 @ ('#sk86' @ X2)) 53.28/7.26 | ~ (X2 @ ('#sk50' @ X2)) 53.28/7.26 | ~ ('#form19') 53.28/7.26 | (X2 @ '#sk7'))), 53.28/7.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl128])). 53.28/7.26 thf(zip_derived_cl146, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 ( ('#sk1' @ ('#sk86' @ X2) @ ('#sk115' @ X2)) 53.28/7.26 | ~ (X2 @ ('#sk50' @ X2)) 53.28/7.26 | ~ ('#form19') 53.28/7.26 | (X2 @ '#sk7'))), 53.28/7.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl128])). 53.28/7.26 thf(zip_derived_cl21, plain, 53.28/7.26 ((~ (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 53.28/7.26 '#sk6' @ Y1))) => 53.28/7.26 (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 ((((((('#sk2' @ Y1 @ Y2) | 53.28/7.26 ('#sk1' @ Y1 @ Y2))) & 53.28/7.26 (Y0 @ Y1))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk7')))))) 53.28/7.26 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 53.28/7.26 '#sk3' @ Y1))) => 53.28/7.26 (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((Y0 @ Y1) & 53.28/7.26 ((('#sk1' @ Y1 @ Y2) | 53.28/7.26 ('#sk2' @ Y1 @ Y2))))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk4')))))) 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y1 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y1 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))))) => 53.28/7.26 (Y3 @ Y2)))))))) => 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 ( 53.28/7.26 ( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 ( 53.28/7.26 ( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y2))))))))))))))))))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 53.28/7.26 thf(zip_derived_cl26, plain, 53.28/7.26 ((~ (((((((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 53.28/7.26 ('#sk8' @ Y0)))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 53.28/7.26 Y0 @ Y1))) & 53.28/7.26 ('#sk8' @ Y0))) => 53.28/7.26 ('#sk8' @ Y1))))))))))) => 53.28/7.26 ('#sk8' @ '#sk7'))) 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y1 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y1 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))))) => 53.28/7.26 (Y3 @ Y2)))))))) => 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 ( 53.28/7.26 ( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 ( 53.28/7.26 ( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y2))))))))))))))))) 53.28/7.26 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 53.28/7.26 '#sk3' @ Y1))) => 53.28/7.26 (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((Y0 @ Y1) & 53.28/7.26 ((('#sk1' @ Y1 @ Y2) | 53.28/7.26 ('#sk2' @ Y1 @ Y2))))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk4')))))))), 53.28/7.26 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl21])). 53.28/7.26 thf(zip_derived_cl26, plain, 53.28/7.26 ((~ (((((((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 53.28/7.26 ('#sk8' @ Y0)))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 53.28/7.26 Y0 @ Y1))) & 53.28/7.26 ('#sk8' @ Y0))) => 53.28/7.26 ('#sk8' @ Y1))))))))))) => 53.28/7.26 ('#sk8' @ '#sk7'))) 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y1 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y1 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))))) => 53.28/7.26 (Y3 @ Y2)))))))) => 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 ( 53.28/7.26 ( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 ( 53.28/7.26 ( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y2))))))))))))))))) 53.28/7.26 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 53.28/7.26 '#sk3' @ Y1))) => 53.28/7.26 (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((Y0 @ Y1) & 53.28/7.26 ((('#sk1' @ Y1 @ Y2) | 53.28/7.26 ('#sk2' @ Y1 @ Y2))))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk4')))))))), 53.28/7.26 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl21])). 53.28/7.26 thf(zip_derived_cl31, plain, 53.28/7.26 (( ('#form9') 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y1 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y1 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))))) => 53.28/7.26 (Y3 @ Y2)))))))) => 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 ( 53.28/7.26 ( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 ( 53.28/7.26 ( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y2))))))))))))))))))), 53.28/7.26 define([status(thm)])). 53.28/7.26 thf(zip_derived_cl33, plain, 53.28/7.26 ((~ ('#form9') 53.28/7.26 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 53.28/7.26 '#sk3' @ Y1))) => 53.28/7.26 (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((Y0 @ Y1) & 53.28/7.26 ((('#sk1' @ Y1 @ Y2) | 53.28/7.26 ('#sk2' @ Y1 @ Y2))))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk4')))))) 53.28/7.26 | ~ (((((((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 53.28/7.26 ('#sk8' @ Y0)))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 53.28/7.26 Y0 @ Y1))) & 53.28/7.26 ('#sk8' @ Y0))) => 53.28/7.26 ('#sk8' @ Y1))))))))))) => 53.28/7.26 ('#sk8' @ '#sk7'))))), 53.28/7.26 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl31])). 53.28/7.26 thf(zip_derived_cl36, plain, 53.28/7.26 ((~ ('#form14') 53.28/7.26 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 53.28/7.26 '#sk3' @ Y1))) => 53.28/7.26 (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((Y0 @ Y1) & 53.28/7.26 ((('#sk1' @ Y1 @ Y2) | 53.28/7.26 ('#sk2' @ Y1 @ Y2))))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk4')))))))), 53.28/7.26 define([status(thm)])). 53.28/7.26 thf(zip_derived_cl41, plain, 53.28/7.26 (( ('#form14') 53.28/7.26 | ~ (((((((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 53.28/7.26 ('#sk8' @ Y0)))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 53.28/7.26 Y0 @ Y1))) & 53.28/7.26 ('#sk8' @ Y0))) => 53.28/7.26 ('#sk8' @ Y1))))))))))) => 53.28/7.26 ('#sk8' @ '#sk7'))) 53.28/7.26 | ~ ('#form9'))), 53.28/7.26 inference('renaming', [status(thm)], [zip_derived_cl33, zip_derived_cl36])). 53.28/7.26 thf(zip_derived_cl50, plain, 53.28/7.26 ((~ ('#sk8' @ '#sk7') | ~ ('#form9') | ('#form14'))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])). 53.28/7.26 thf(zip_derived_cl87, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 ( ('#sk1' @ '#sk6' @ ('#sk50' @ X2)) 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 53.28/7.26 (X2 @ Y1))))))))) 53.28/7.26 | ~ ('#form19') 53.28/7.26 | (X2 @ '#sk7'))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 53.28/7.26 thf(zip_derived_cl99, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 (~ (((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk1' @ ('#sk86' @ X2) @ Y0) & (X2 @ 53.28/7.26 ('#sk86' @ X2)))) => 53.28/7.26 (X2 @ Y0)))))) 53.28/7.26 | (X2 @ '#sk7') 53.28/7.26 | ~ ('#form19') 53.28/7.26 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)))), 53.28/7.26 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl87])). 53.28/7.26 thf(zip_derived_cl110, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 (~ ((((('#sk1' @ ('#sk86' @ X2) @ ('#sk115' @ X2)) & (X2 @ 53.28/7.26 ('#sk86' @ X2)))) => 53.28/7.26 (X2 @ ('#sk115' @ X2)))) 53.28/7.26 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)) 53.28/7.26 | ~ ('#form19') 53.28/7.26 | (X2 @ '#sk7'))), 53.28/7.26 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl99])). 53.28/7.26 thf(zip_derived_cl127, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 (~ (X2 @ ('#sk115' @ X2)) 53.28/7.26 | (X2 @ '#sk7') 53.28/7.26 | ~ ('#form19') 53.28/7.26 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl110])). 53.28/7.26 thf(zip_derived_cl126, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 ( ((('#sk1' @ ('#sk86' @ X2) @ ('#sk115' @ X2)) & (X2 @ 53.28/7.26 ('#sk86' @ X2)))) 53.28/7.26 | (X2 @ '#sk7') 53.28/7.26 | ~ ('#form19') 53.28/7.26 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl110])). 53.28/7.26 thf(zip_derived_cl145, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 ( (X2 @ ('#sk86' @ X2)) 53.28/7.26 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)) 53.28/7.26 | ~ ('#form19') 53.28/7.26 | (X2 @ '#sk7'))), 53.28/7.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl126])). 53.28/7.26 thf(zip_derived_cl49, plain, 53.28/7.26 (( (((((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 53.28/7.26 ('#sk8' @ Y0)))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 53.28/7.26 Y1))) & 53.28/7.26 ('#sk8' @ Y0))) => 53.28/7.26 ('#sk8' @ Y1))))))))))) 53.28/7.26 | ~ ('#form9') 53.28/7.26 | ('#form14'))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])). 53.28/7.26 thf(zip_derived_cl55, plain, 53.28/7.26 (( (((!!) @ (^[Y0 : a]: 53.28/7.26 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 53.28/7.26 ('#sk8' @ Y0)))))) 53.28/7.26 | ('#form14') 53.28/7.26 | ~ ('#form9'))), 53.28/7.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl49])). 53.28/7.26 thf(zip_derived_cl62, plain, 53.28/7.26 (![X2 : a]: 53.28/7.26 ( ((((('#sk2' @ '#sk6' @ X2) | ('#sk1' @ '#sk6' @ X2))) => ('#sk8' @ 53.28/7.26 X2))) 53.28/7.26 | ~ ('#form9') 53.28/7.26 | ('#form14'))), 53.28/7.26 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl55])). 53.28/7.26 thf(zip_derived_cl74, plain, 53.28/7.26 (![X2 : a]: 53.28/7.26 (~ ((('#sk2' @ '#sk6' @ X2) | ('#sk1' @ '#sk6' @ X2))) 53.28/7.26 | ('#sk8' @ X2) 53.28/7.26 | ('#form14') 53.28/7.26 | ~ ('#form9'))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 53.28/7.26 thf(zip_derived_cl92, plain, 53.28/7.26 (![X2 : a]: 53.28/7.26 (~ ('#sk1' @ '#sk6' @ X2) 53.28/7.26 | ~ ('#form9') 53.28/7.26 | ('#form14') 53.28/7.26 | ('#sk8' @ X2))), 53.28/7.26 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl74])). 53.28/7.26 thf(zip_derived_cl144, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 ( ('#sk1' @ ('#sk86' @ X2) @ ('#sk115' @ X2)) 53.28/7.26 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)) 53.28/7.26 | ~ ('#form19') 53.28/7.26 | (X2 @ '#sk7'))), 53.28/7.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl126])). 53.28/7.26 thf(zip_derived_cl56, plain, 53.28/7.26 (( (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 53.28/7.26 ('#sk8' @ Y0))) => 53.28/7.26 ('#sk8' @ Y1))))))))) 53.28/7.26 | ('#form14') 53.28/7.26 | ~ ('#form9'))), 53.28/7.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl49])). 53.28/7.26 thf(zip_derived_cl63, plain, 53.28/7.26 (![X2 : a]: 53.28/7.26 ( (((!!) @ (^[Y0 : a]: 53.28/7.26 ((((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) & 53.28/7.26 ('#sk8' @ X2))) => 53.28/7.26 ('#sk8' @ Y0)))))) 53.28/7.26 | ~ ('#form9') 53.28/7.26 | ('#form14'))), 53.28/7.26 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl56])). 53.28/7.26 thf(zip_derived_cl75, plain, 53.28/7.26 (![X2 : a, X4 : a]: 53.28/7.26 ( ((((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk8' @ X2))) => 53.28/7.26 ('#sk8' @ X4))) 53.28/7.26 | ('#form14') 53.28/7.26 | ~ ('#form9'))), 53.28/7.26 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 53.28/7.26 thf(zip_derived_cl93, plain, 53.28/7.26 (![X2 : a, X4 : a]: 53.28/7.26 (~ ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk8' @ X2))) 53.28/7.26 | ('#sk8' @ X4) 53.28/7.26 | ~ ('#form9') 53.28/7.26 | ('#form14'))), 53.28/7.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 53.28/7.26 thf(zip_derived_cl103, plain, 53.28/7.26 (![X2 : a, X4 : a]: 53.28/7.26 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 53.28/7.26 | ~ ('#sk8' @ X2) 53.28/7.26 | ('#form14') 53.28/7.26 | ~ ('#form9') 53.28/7.26 | ('#sk8' @ X4))), 53.28/7.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl93])). 53.28/7.26 thf(zip_derived_cl116, plain, 53.28/7.26 (![X2 : a, X4 : a]: 53.28/7.26 (~ ('#sk1' @ X2 @ X4) 53.28/7.26 | ('#sk8' @ X4) 53.28/7.26 | ~ ('#form9') 53.28/7.26 | ('#form14') 53.28/7.26 | ~ ('#sk8' @ X2))), 53.28/7.26 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl103])). 53.28/7.26 thf(zip_derived_cl28, plain, 53.28/7.26 (![X2 : a > $o]: 53.28/7.26 ( (((((((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 53.28/7.26 (X2 @ Y1))))))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) => 53.28/7.26 (X2 @ '#sk7'))) 53.28/7.26 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk2' @ '#sk3' @ Y1) | 53.28/7.26 ('#sk1' @ '#sk3' @ Y1))) => 53.28/7.26 (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((Y0 @ Y1) & 53.28/7.26 ((('#sk1' @ Y1 @ Y2) | 53.28/7.26 ('#sk2' @ Y1 @ Y2))))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk4')))))) 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y1 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y1 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))) & 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))))) => 53.28/7.26 (Y3 @ Y2)))))))) => 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y2))))))))))))))))) 53.28/7.26 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 ((((('#sk1' @ Y1 @ Y2) & 53.28/7.26 (Y0 @ Y1))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk7')))))))), 53.28/7.26 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl25])). 53.28/7.26 thf(zip_derived_cl29, plain, 53.28/7.26 (( (((((((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk8' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 53.28/7.26 ('#sk8' @ Y1))))))))) & 53.28/7.26 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))))) => 53.28/7.26 ('#sk8' @ '#sk7'))) 53.28/7.26 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.26 (((((((!!) @ (^[Y1 : a]: 53.28/7.26 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 53.28/7.26 '#sk3' @ Y1))) => 53.28/7.26 (Y0 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((Y0 @ Y1) & 53.28/7.26 ((('#sk1' @ Y1 @ Y2) | 53.28/7.26 ('#sk2' @ Y1 @ Y2))))) => 53.28/7.26 (Y0 @ Y2))))))))))) => 53.28/7.26 (Y0 @ '#sk4')))))) 53.28/7.26 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.26 (((!!) @ (^[Y1 : a]: 53.28/7.26 (((!!) @ (^[Y2 : a]: 53.28/7.26 (((((((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (!!) @ ( 53.28/7.26 ^[Y5 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 (Y3 @ 53.28/7.26 Y4) & 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y4 @ 53.28/7.26 Y5) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y4 @ Y5))))) => 53.28/7.26 (Y3 @ Y5))))))))) & 53.28/7.26 (((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk2' @ 53.28/7.26 Y0 @ 53.28/7.26 Y4) | 53.28/7.26 ('#sk1' @ 53.28/7.26 Y0 @ Y4))) => 53.28/7.26 (Y3 @ Y4)))))))) => 53.28/7.26 (Y3 @ Y1)))))) & 53.28/7.26 (((!!) @ (^[Y3 : a > $o]: 53.28/7.26 (((((((!!) @ ( 53.28/7.26 ^[Y4 : a]: 53.28/7.26 (( 53.28/7.26 (( 53.28/7.26 ('#sk1' @ 53.28/7.26 Y1 @ 53.28/7.27 Y4) | 53.28/7.27 ('#sk2' @ 53.28/7.27 Y1 @ Y4))) => 53.28/7.27 (Y3 @ Y4)))))) & 53.28/7.27 (((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y5 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 (Y3 @ 53.28/7.27 Y4) & 53.28/7.27 (( 53.28/7.27 ('#sk1' @ 53.28/7.27 Y4 @ 53.28/7.27 Y5) | 53.28/7.27 ('#sk2' @ 53.28/7.27 Y4 @ Y5))))) => 53.28/7.27 (Y3 @ Y5))))))))))) => 53.28/7.27 (Y3 @ Y2)))))))) => 53.28/7.27 (((!!) @ (^[Y3 : a > $o]: 53.28/7.27 (((((((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 ( 53.28/7.27 ( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y5 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 (Y3 @ 53.28/7.27 Y4) & 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y4 @ 53.28/7.27 Y5) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y4 @ Y5))))) => 53.28/7.27 (Y3 @ Y5))))))))) & 53.28/7.27 (((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 ( 53.28/7.27 ( 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y0 @ 53.28/7.27 Y4) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y0 @ Y4))) => 53.28/7.27 (Y3 @ Y4)))))))) => 53.28/7.27 (Y3 @ Y2))))))))))))))))) 53.28/7.27 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.27 (((((((!!) @ (^[Y1 : a]: 53.28/7.27 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 (((!!) @ (^[Y2 : a]: 53.28/7.27 ((((('#sk1' @ Y1 @ Y2) & 53.28/7.27 (Y0 @ Y1))) => 53.28/7.27 (Y0 @ Y2))))))))))) => 53.28/7.27 (Y0 @ '#sk7')))))))), 53.28/7.27 inference('triggered_bool_instantiation', [status(thm)], 53.28/7.27 [zip_derived_cl28])). 53.28/7.27 thf(zip_derived_cl36, plain, 53.28/7.27 ((~ ('#form14') 53.28/7.27 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.27 (((((((!!) @ (^[Y1 : a]: 53.28/7.27 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 53.28/7.27 '#sk3' @ Y1))) => 53.28/7.27 (Y0 @ Y1)))))) & 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 (((!!) @ (^[Y2 : a]: 53.28/7.27 (((((Y0 @ Y1) & 53.28/7.27 ((('#sk1' @ Y1 @ Y2) | 53.28/7.27 ('#sk2' @ Y1 @ Y2))))) => 53.28/7.27 (Y0 @ Y2))))))))))) => 53.28/7.27 (Y0 @ '#sk4')))))))), 53.28/7.27 define([status(thm)])). 53.28/7.27 thf(zip_derived_cl204, plain, 53.28/7.27 (( ('#form14') 53.28/7.27 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.27 (((((((!!) @ (^[Y1 : a]: 53.28/7.27 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 (((!!) @ (^[Y2 : a]: 53.28/7.27 ((((('#sk1' @ Y1 @ Y2) & 53.28/7.27 (Y0 @ Y1))) => 53.28/7.27 (Y0 @ Y2))))))))))) => 53.28/7.27 (Y0 @ '#sk7')))))) 53.28/7.27 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 (((!!) @ (^[Y2 : a]: 53.28/7.27 (((((((!!) @ (^[Y3 : a > $o]: 53.28/7.27 (((((((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y5 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 (Y3 @ 53.28/7.27 Y4) & 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y4 @ 53.28/7.27 Y5) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y4 @ Y5))))) => 53.28/7.27 (Y3 @ Y5))))))))) & 53.28/7.27 (((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y0 @ 53.28/7.27 Y4) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y0 @ Y4))) => 53.28/7.27 (Y3 @ Y4)))))))) => 53.28/7.27 (Y3 @ Y1)))))) & 53.28/7.27 (((!!) @ (^[Y3 : a > $o]: 53.28/7.27 (((((((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 ('#sk1' @ 53.28/7.27 Y1 @ 53.28/7.27 Y4) | 53.28/7.27 ('#sk2' @ 53.28/7.27 Y1 @ Y4))) => 53.28/7.27 (Y3 @ Y4)))))) & 53.28/7.27 (((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y5 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 (Y3 @ 53.28/7.27 Y4) & 53.28/7.27 (( 53.28/7.27 ('#sk1' @ 53.28/7.27 Y4 @ 53.28/7.27 Y5) | 53.28/7.27 ('#sk2' @ 53.28/7.27 Y4 @ Y5))))) => 53.28/7.27 (Y3 @ Y5))))))))))) => 53.28/7.27 (Y3 @ Y2)))))))) => 53.28/7.27 (((!!) @ (^[Y3 : a > $o]: 53.28/7.27 (((((((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 ( 53.28/7.27 ( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y5 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 (Y3 @ 53.28/7.27 Y4) & 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y4 @ 53.28/7.27 Y5) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y4 @ Y5))))) => 53.28/7.27 (Y3 @ Y5))))))))) & 53.28/7.27 (((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 ( 53.28/7.27 ( 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y0 @ 53.28/7.27 Y4) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y0 @ Y4))) => 53.28/7.27 (Y3 @ Y4)))))))) => 53.28/7.27 (Y3 @ Y2))))))))))))))))) 53.28/7.27 | (((((((!!) @ (^[Y0 : a]: 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 ((((('#sk8' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 53.28/7.27 ('#sk8' @ Y1))))))))) & 53.28/7.27 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))))) => 53.28/7.27 ('#sk8' @ '#sk7'))))), 53.28/7.27 inference('renaming', [status(thm)], [zip_derived_cl29, zip_derived_cl36])). 53.28/7.27 thf(zip_derived_cl43, plain, 53.28/7.27 ((~ ('#form19') 53.28/7.27 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.27 (((((((!!) @ (^[Y1 : a]: 53.28/7.27 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 (((!!) @ (^[Y2 : a]: 53.28/7.27 ((((('#sk1' @ Y1 @ Y2) & 53.28/7.27 (Y0 @ Y1))) => 53.28/7.27 (Y0 @ Y2))))))))))) => 53.28/7.27 (Y0 @ '#sk7')))))))), 53.28/7.27 define([status(thm)])). 53.28/7.27 thf(zip_derived_cl205, plain, 53.28/7.27 (( ('#form19') 53.28/7.27 | (((((((!!) @ (^[Y0 : a]: 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 ((((('#sk8' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 53.28/7.27 ('#sk8' @ Y1))))))))) & 53.28/7.27 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))))) => 53.28/7.27 ('#sk8' @ '#sk7'))) 53.28/7.27 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 (((!!) @ (^[Y2 : a]: 53.28/7.27 (((((((!!) @ (^[Y3 : a > $o]: 53.28/7.27 (((((((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y5 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 (Y3 @ 53.28/7.27 Y4) & 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y4 @ 53.28/7.27 Y5) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y4 @ Y5))))) => 53.28/7.27 (Y3 @ Y5))))))))) & 53.28/7.27 (((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y0 @ 53.28/7.27 Y4) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y0 @ Y4))) => 53.28/7.27 (Y3 @ Y4)))))))) => 53.28/7.27 (Y3 @ Y1)))))) & 53.28/7.27 (((!!) @ (^[Y3 : a > $o]: 53.28/7.27 (((((((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 ('#sk1' @ 53.28/7.27 Y1 @ 53.28/7.27 Y4) | 53.28/7.27 ('#sk2' @ 53.28/7.27 Y1 @ Y4))) => 53.28/7.27 (Y3 @ Y4)))))) & 53.28/7.27 (((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y5 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 (Y3 @ 53.28/7.27 Y4) & 53.28/7.27 (( 53.28/7.27 ('#sk1' @ 53.28/7.27 Y4 @ 53.28/7.27 Y5) | 53.28/7.27 ('#sk2' @ 53.28/7.27 Y4 @ Y5))))) => 53.28/7.27 (Y3 @ Y5))))))))))) => 53.28/7.27 (Y3 @ Y2)))))))) => 53.28/7.27 (((!!) @ (^[Y3 : a > $o]: 53.28/7.27 (((((((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 ( 53.28/7.27 ( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y5 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 (Y3 @ 53.28/7.27 Y4) & 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y4 @ 53.28/7.27 Y5) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y4 @ Y5))))) => 53.28/7.27 (Y3 @ Y5))))))))) & 53.28/7.27 (((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 ( 53.28/7.27 ( 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y0 @ 53.28/7.27 Y4) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y0 @ Y4))) => 53.28/7.27 (Y3 @ Y4)))))))) => 53.28/7.27 (Y3 @ Y2))))))))))))))))) 53.28/7.27 | ('#form14'))), 53.28/7.27 inference('renaming', [status(thm)], 53.28/7.27 [zip_derived_cl204, zip_derived_cl43])). 53.28/7.27 thf(zip_derived_cl31, plain, 53.28/7.27 (( ('#form9') 53.28/7.27 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 (((!!) @ (^[Y2 : a]: 53.28/7.27 (((((((!!) @ (^[Y3 : a > $o]: 53.28/7.27 (((((((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y5 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 (Y3 @ 53.28/7.27 Y4) & 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y4 @ 53.28/7.27 Y5) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y4 @ Y5))))) => 53.28/7.27 (Y3 @ Y5))))))))) & 53.28/7.27 (((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y0 @ 53.28/7.27 Y4) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y0 @ Y4))) => 53.28/7.27 (Y3 @ Y4)))))))) => 53.28/7.27 (Y3 @ Y1)))))) & 53.28/7.27 (((!!) @ (^[Y3 : a > $o]: 53.28/7.27 (((((((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 ('#sk1' @ 53.28/7.27 Y1 @ 53.28/7.27 Y4) | 53.28/7.27 ('#sk2' @ 53.28/7.27 Y1 @ Y4))) => 53.28/7.27 (Y3 @ Y4)))))) & 53.28/7.27 (((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y5 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 (Y3 @ 53.28/7.27 Y4) & 53.28/7.27 (( 53.28/7.27 ('#sk1' @ 53.28/7.27 Y4 @ 53.28/7.27 Y5) | 53.28/7.27 ('#sk2' @ 53.28/7.27 Y4 @ Y5))))) => 53.28/7.27 (Y3 @ Y5))))))))))) => 53.28/7.27 (Y3 @ Y2)))))))) => 53.28/7.27 (((!!) @ (^[Y3 : a > $o]: 53.28/7.27 (((((((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 ( 53.28/7.27 ( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y5 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 (Y3 @ 53.28/7.27 Y4) & 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y4 @ 53.28/7.27 Y5) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y4 @ Y5))))) => 53.28/7.27 (Y3 @ Y5))))))))) & 53.28/7.27 (((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 ( 53.28/7.27 ( 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y0 @ 53.28/7.27 Y4) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y0 @ Y4))) => 53.28/7.27 (Y3 @ Y4)))))))) => 53.28/7.27 (Y3 @ Y2))))))))))))))))))), 53.28/7.27 define([status(thm)])). 53.28/7.27 thf(zip_derived_cl206, plain, 53.28/7.27 ((~ ('#form9') 53.28/7.27 | ('#form14') 53.28/7.27 | (((((((!!) @ (^[Y0 : a]: 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 ((((('#sk8' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 53.28/7.27 ('#sk8' @ Y1))))))))) & 53.28/7.27 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))))) => 53.28/7.27 ('#sk8' @ '#sk7'))) 53.28/7.27 | ('#form19'))), 53.28/7.27 inference('renaming', [status(thm)], 53.28/7.27 [zip_derived_cl205, zip_derived_cl31])). 53.28/7.27 thf(zip_derived_cl207, plain, 53.28/7.27 ((~ (((((!!) @ (^[Y0 : a]: 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 ((((('#sk8' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 53.28/7.27 ('#sk8' @ Y1))))))))) & 53.28/7.27 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))))) 53.28/7.27 | ('#sk8' @ '#sk7') 53.28/7.27 | ('#form19') 53.28/7.27 | ('#form14') 53.28/7.27 | ~ ('#form9'))), 53.28/7.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])). 53.28/7.27 thf(zip_derived_cl50, plain, 53.28/7.27 ((~ ('#sk8' @ '#sk7') | ~ ('#form9') | ('#form14'))), 53.28/7.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])). 53.28/7.27 thf(zip_derived_cl208, plain, 53.28/7.27 ((~ ('#form9') 53.28/7.27 | ('#form14') 53.28/7.27 | ('#form19') 53.28/7.27 | ~ (((((!!) @ (^[Y0 : a]: 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 ((((('#sk8' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 53.28/7.27 ('#sk8' @ Y1))))))))) & 53.28/7.27 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))))))), 53.28/7.27 inference('clc', [status(thm)], [zip_derived_cl207, zip_derived_cl50])). 53.28/7.27 thf(zip_derived_cl209, plain, 53.28/7.27 ((~ (((!!) @ (^[Y0 : a]: 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 ((((('#sk8' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 53.28/7.27 ('#sk8' @ Y1))))))))) 53.28/7.27 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) 53.28/7.27 | ('#form19') 53.28/7.27 | ('#form14') 53.28/7.27 | ~ ('#form9'))), 53.28/7.27 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl208])). 53.28/7.27 thf(zip_derived_cl40, plain, 53.28/7.27 (![X2 : a > $o]: 53.28/7.27 ( ('#form14') 53.28/7.27 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.27 (((((((!!) @ (^[Y1 : a]: 53.28/7.27 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 (((!!) @ (^[Y2 : a]: 53.28/7.27 ((((('#sk1' @ Y1 @ Y2) & 53.28/7.27 (Y0 @ Y1))) => 53.28/7.27 (Y0 @ Y2))))))))))) => 53.28/7.27 (Y0 @ '#sk7')))))) 53.28/7.27 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 (((!!) @ (^[Y2 : a]: 53.28/7.27 (((((((!!) @ (^[Y3 : a > $o]: 53.28/7.27 (((((( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y5 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 (Y3 @ 53.28/7.27 Y4) & 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y4 @ 53.28/7.27 Y5) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y4 @ Y5))))) => 53.28/7.27 (Y3 @ Y5))))))))) & 53.28/7.27 (( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y0 @ 53.28/7.27 Y4) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y0 @ Y4))) => 53.28/7.27 (Y3 @ Y4)))))))) => 53.28/7.27 (Y3 @ Y1)))))) & 53.28/7.27 (((!!) @ (^[Y3 : a > $o]: 53.28/7.27 (((((( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 ('#sk1' @ 53.28/7.27 Y1 @ 53.28/7.27 Y4) | 53.28/7.27 ('#sk2' @ 53.28/7.27 Y1 @ Y4))) => 53.28/7.27 (Y3 @ Y4)))))) & 53.28/7.27 (( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y5 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 (Y3 @ 53.28/7.27 Y4) & 53.28/7.27 (( 53.28/7.27 ('#sk1' @ 53.28/7.27 Y4 @ 53.28/7.27 Y5) | 53.28/7.27 ('#sk2' @ 53.28/7.27 Y4 @ Y5))))) => 53.28/7.27 (Y3 @ Y5))))))))))) => 53.28/7.27 (Y3 @ Y2)))))))) => 53.28/7.27 (((!!) @ (^[Y3 : a > $o]: 53.28/7.27 (((((((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y5 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 (Y3 @ 53.28/7.27 Y4) & 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y4 @ 53.28/7.27 Y5) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y4 @ Y5))))) => 53.28/7.27 (Y3 @ Y5))))))))) & 53.28/7.27 (((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y0 @ 53.28/7.27 Y4) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y0 @ Y4))) => 53.28/7.27 (Y3 @ Y4)))))))) => 53.28/7.27 (Y3 @ Y2))))))))))))))))) 53.28/7.27 | (((((((!!) @ (^[Y0 : a]: 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 53.28/7.27 (X2 @ Y1))))))))) & 53.28/7.27 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) => 53.28/7.27 (X2 @ '#sk7'))))), 53.28/7.27 inference('renaming', [status(thm)], [zip_derived_cl28, zip_derived_cl36])). 53.28/7.27 thf(zip_derived_cl43, plain, 53.28/7.27 ((~ ('#form19') 53.28/7.27 | (((!!) @ (^[Y0 : a > $o]: 53.28/7.27 (((((((!!) @ (^[Y1 : a]: 53.28/7.27 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 (((!!) @ (^[Y2 : a]: 53.28/7.27 ((((('#sk1' @ Y1 @ Y2) & 53.28/7.27 (Y0 @ Y1))) => 53.28/7.27 (Y0 @ Y2))))))))))) => 53.28/7.27 (Y0 @ '#sk7')))))))), 53.28/7.27 define([status(thm)])). 53.28/7.27 thf(zip_derived_cl47, plain, 53.28/7.27 (![X2 : a > $o]: 53.28/7.27 ( ('#form19') 53.28/7.27 | (((((((!!) @ (^[Y0 : a]: 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 53.28/7.27 (X2 @ Y1))))))))) & 53.28/7.27 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) => 53.28/7.27 (X2 @ '#sk7'))) 53.28/7.27 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.27 (((!!) @ (^[Y1 : a]: 53.28/7.27 (((!!) @ (^[Y2 : a]: 53.28/7.27 (((((((!!) @ (^[Y3 : a > $o]: 53.28/7.27 (((((( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y5 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 (Y3 @ 53.28/7.27 Y4) & 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y4 @ 53.28/7.27 Y5) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y4 @ Y5))))) => 53.28/7.27 (Y3 @ Y5))))))))) & 53.28/7.27 (( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y0 @ 53.28/7.27 Y4) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y0 @ Y4))) => 53.28/7.27 (Y3 @ Y4)))))))) => 53.28/7.27 (Y3 @ Y1)))))) & 53.28/7.27 (((!!) @ (^[Y3 : a > $o]: 53.28/7.27 (((((( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 ('#sk1' @ 53.28/7.27 Y1 @ 53.28/7.27 Y4) | 53.28/7.27 ('#sk2' @ 53.28/7.27 Y1 @ Y4))) => 53.28/7.27 (Y3 @ Y4)))))) & 53.28/7.27 (( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y5 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 (Y3 @ 53.28/7.27 Y4) & 53.28/7.27 (( 53.28/7.27 ('#sk1' @ 53.28/7.27 Y4 @ 53.28/7.27 Y5) | 53.28/7.27 ('#sk2' @ 53.28/7.27 Y4 @ Y5))))) => 53.28/7.27 (Y3 @ Y5))))))))))) => 53.28/7.27 (Y3 @ Y2)))))))) => 53.28/7.27 (((!!) @ (^[Y3 : a > $o]: 53.28/7.27 (((((((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (!!) @ ( 53.28/7.27 ^[Y5 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.27 (Y3 @ 53.28/7.27 Y4) & 53.28/7.27 (( 53.28/7.27 ('#sk2' @ 53.28/7.27 Y4 @ 53.28/7.27 Y5) | 53.28/7.27 ('#sk1' @ 53.28/7.27 Y4 @ Y5))))) => 53.28/7.27 (Y3 @ Y5))))))))) & 53.28/7.27 (((!!) @ ( 53.28/7.27 ^[Y4 : a]: 53.28/7.27 (( 53.28/7.27 (( 53.28/7.28 ('#sk2' @ 53.28/7.28 Y0 @ 53.28/7.28 Y4) | 53.28/7.28 ('#sk1' @ 53.28/7.28 Y0 @ Y4))) => 53.28/7.28 (Y3 @ Y4)))))))) => 53.28/7.28 (Y3 @ Y2))))))))))))))))) 53.28/7.28 | ('#form14'))), 53.28/7.28 inference('renaming', [status(thm)], [zip_derived_cl40, zip_derived_cl43])). 53.28/7.28 thf(zip_derived_cl31, plain, 53.28/7.28 (( ('#form9') 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((!!) @ (^[Y2 : a]: 53.28/7.28 (((((((!!) @ (^[Y3 : a > $o]: 53.28/7.28 (((((((!!) @ ( 53.28/7.28 ^[Y4 : a]: 53.28/7.28 (( 53.28/7.28 (!!) @ ( 53.28/7.28 ^[Y5 : a]: 53.28/7.28 (( 53.28/7.28 (( 53.28/7.28 (Y3 @ 53.28/7.28 Y4) & 53.28/7.28 (( 53.28/7.28 ('#sk2' @ 53.28/7.28 Y4 @ 53.28/7.28 Y5) | 53.28/7.28 ('#sk1' @ 53.28/7.28 Y4 @ Y5))))) => 53.28/7.28 (Y3 @ Y5))))))))) & 53.28/7.28 (((!!) @ ( 53.28/7.28 ^[Y4 : a]: 53.28/7.28 (( 53.28/7.28 (( 53.28/7.28 ('#sk2' @ 53.28/7.28 Y0 @ 53.28/7.28 Y4) | 53.28/7.28 ('#sk1' @ 53.28/7.28 Y0 @ Y4))) => 53.28/7.28 (Y3 @ Y4)))))))) => 53.28/7.28 (Y3 @ Y1)))))) & 53.28/7.28 (((!!) @ (^[Y3 : a > $o]: 53.28/7.28 (((((((!!) @ ( 53.28/7.28 ^[Y4 : a]: 53.28/7.28 (( 53.28/7.28 (( 53.28/7.28 ('#sk1' @ 53.28/7.28 Y1 @ 53.28/7.28 Y4) | 53.28/7.28 ('#sk2' @ 53.28/7.28 Y1 @ Y4))) => 53.28/7.28 (Y3 @ Y4)))))) & 53.28/7.28 (((!!) @ ( 53.28/7.28 ^[Y4 : a]: 53.28/7.28 (( 53.28/7.28 (!!) @ ( 53.28/7.28 ^[Y5 : a]: 53.28/7.28 (( 53.28/7.28 (( 53.28/7.28 (Y3 @ 53.28/7.28 Y4) & 53.28/7.28 (( 53.28/7.28 ('#sk1' @ 53.28/7.28 Y4 @ 53.28/7.28 Y5) | 53.28/7.28 ('#sk2' @ 53.28/7.28 Y4 @ Y5))))) => 53.28/7.28 (Y3 @ Y5))))))))))) => 53.28/7.28 (Y3 @ Y2)))))))) => 53.28/7.28 (((!!) @ (^[Y3 : a > $o]: 53.28/7.28 (((((((!!) @ ( 53.28/7.28 ^[Y4 : a]: 53.28/7.28 ( 53.28/7.28 ( 53.28/7.28 (!!) @ ( 53.28/7.28 ^[Y5 : a]: 53.28/7.28 (( 53.28/7.28 (( 53.28/7.28 (Y3 @ 53.28/7.28 Y4) & 53.28/7.28 (( 53.28/7.28 ('#sk2' @ 53.28/7.28 Y4 @ 53.28/7.28 Y5) | 53.28/7.28 ('#sk1' @ 53.28/7.28 Y4 @ Y5))))) => 53.28/7.28 (Y3 @ Y5))))))))) & 53.28/7.28 (((!!) @ ( 53.28/7.28 ^[Y4 : a]: 53.28/7.28 ( 53.28/7.28 ( 53.28/7.28 (( 53.28/7.28 ('#sk2' @ 53.28/7.28 Y0 @ 53.28/7.28 Y4) | 53.28/7.28 ('#sk1' @ 53.28/7.28 Y0 @ Y4))) => 53.28/7.28 (Y3 @ Y4)))))))) => 53.28/7.28 (Y3 @ Y2))))))))))))))))))), 53.28/7.28 define([status(thm)])). 53.28/7.28 thf(zip_derived_cl52, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ ('#form9') 53.28/7.28 | ('#form14') 53.28/7.28 | (((((((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 53.28/7.28 (X2 @ Y1))))))))) & 53.28/7.28 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) => 53.28/7.28 (X2 @ '#sk7'))) 53.28/7.28 | ('#form19'))), 53.28/7.28 inference('renaming', [status(thm)], [zip_derived_cl47, zip_derived_cl31])). 53.28/7.28 thf(zip_derived_cl59, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ (((((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 53.28/7.28 (X2 @ Y1))))))))) & 53.28/7.28 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) 53.28/7.28 | (X2 @ '#sk7') 53.28/7.28 | ('#form19') 53.28/7.28 | ('#form14') 53.28/7.28 | ~ ('#form9'))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 53.28/7.28 thf(zip_derived_cl70, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 53.28/7.28 (X2 @ Y1))))))))) 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 53.28/7.28 | ~ ('#form9') 53.28/7.28 | ('#form14') 53.28/7.28 | ('#form19') 53.28/7.28 | (X2 @ '#sk7'))), 53.28/7.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl59])). 53.28/7.28 thf(zip_derived_cl86, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((((X2 @ ('#sk59' @ X2)) & ('#sk2' @ ('#sk59' @ X2) @ 53.28/7.28 Y0))) => 53.28/7.28 (X2 @ Y0)))))) 53.28/7.28 | (X2 @ '#sk7') 53.28/7.28 | ('#form19') 53.28/7.28 | ('#form14') 53.28/7.28 | ~ ('#form9') 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl70])). 53.28/7.28 thf(zip_derived_cl98, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ (((((X2 @ ('#sk59' @ X2)) & ('#sk2' @ ('#sk59' @ X2) @ 53.28/7.28 ('#sk82' @ X2)))) => 53.28/7.28 (X2 @ ('#sk82' @ X2)))) 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 53.28/7.28 | ~ ('#form9') 53.28/7.28 | ('#form14') 53.28/7.28 | ('#form19') 53.28/7.28 | (X2 @ '#sk7'))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl86])). 53.28/7.28 thf(zip_derived_cl109, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ (X2 @ ('#sk82' @ X2)) 53.28/7.28 | (X2 @ '#sk7') 53.28/7.28 | ('#form19') 53.28/7.28 | ('#form14') 53.28/7.28 | ~ ('#form9') 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl98])). 53.28/7.28 thf(zip_derived_cl123, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 ( ('#form147' @ X2) 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 53.28/7.28 define([status(thm)])). 53.28/7.28 thf(zip_derived_cl210, plain, 53.28/7.28 ((~ ('#form147' @ '#sk8') 53.28/7.28 | ~ ('#form9') 53.28/7.28 | ('#form14') 53.28/7.28 | ('#form19') 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk8' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 53.28/7.28 ('#sk8' @ Y1))))))))))), 53.28/7.28 inference('renaming', [status(thm)], 53.28/7.28 [zip_derived_cl209, zip_derived_cl123])). 53.28/7.28 thf(zip_derived_cl211, plain, 53.28/7.28 ((~ (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk8' @ ('#sk59' @ '#sk8')) & ('#sk2' @ 53.28/7.28 ('#sk59' @ '#sk8') @ Y0))) => 53.28/7.28 ('#sk8' @ Y0)))))) 53.28/7.28 | ('#form19') 53.28/7.28 | ('#form14') 53.28/7.28 | ~ ('#form9') 53.28/7.28 | ~ ('#form147' @ '#sk8'))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl210])). 53.28/7.28 thf(zip_derived_cl212, plain, 53.28/7.28 ((~ ((((('#sk8' @ ('#sk59' @ '#sk8')) & ('#sk2' @ ('#sk59' @ '#sk8') @ 53.28/7.28 ('#sk82' @ '#sk8')))) => 53.28/7.28 ('#sk8' @ ('#sk82' @ '#sk8')))) 53.28/7.28 | ~ ('#form147' @ '#sk8') 53.28/7.28 | ~ ('#form9') 53.28/7.28 | ('#form14') 53.28/7.28 | ('#form19'))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl211])). 53.28/7.28 thf(zip_derived_cl214, plain, 53.28/7.28 ((~ ('#sk8' @ ('#sk82' @ '#sk8')) 53.28/7.28 | ('#form19') 53.28/7.28 | ('#form14') 53.28/7.28 | ~ ('#form9') 53.28/7.28 | ~ ('#form147' @ '#sk8'))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl212])). 53.28/7.28 thf(zip_derived_cl213, plain, 53.28/7.28 (( ((('#sk8' @ ('#sk59' @ '#sk8')) & ('#sk2' @ ('#sk59' @ '#sk8') @ 53.28/7.28 ('#sk82' @ '#sk8')))) 53.28/7.28 | ('#form19') 53.28/7.28 | ('#form14') 53.28/7.28 | ~ ('#form9') 53.28/7.28 | ~ ('#form147' @ '#sk8'))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl212])). 53.28/7.28 thf(zip_derived_cl215, plain, 53.28/7.28 (( ('#sk8' @ ('#sk59' @ '#sk8')) 53.28/7.28 | ~ ('#form147' @ '#sk8') 53.28/7.28 | ~ ('#form9') 53.28/7.28 | ('#form14') 53.28/7.28 | ('#form19'))), 53.28/7.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl213])). 53.28/7.28 thf(zip_derived_cl216, plain, 53.28/7.28 (( ('#sk2' @ ('#sk59' @ '#sk8') @ ('#sk82' @ '#sk8')) 53.28/7.28 | ~ ('#form147' @ '#sk8') 53.28/7.28 | ~ ('#form9') 53.28/7.28 | ('#form14') 53.28/7.28 | ('#form19'))), 53.28/7.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl213])). 53.28/7.28 thf(zip_derived_cl115, plain, 53.28/7.28 (![X2 : a, X4 : a]: 53.28/7.28 (~ ('#sk2' @ X2 @ X4) 53.28/7.28 | ('#sk8' @ X4) 53.28/7.28 | ~ ('#form9') 53.28/7.28 | ('#form14') 53.28/7.28 | ~ ('#sk8' @ X2))), 53.28/7.28 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl103])). 53.28/7.28 thf(zip_derived_cl123, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 ( ('#form147' @ X2) 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 53.28/7.28 define([status(thm)])). 53.28/7.28 thf(zip_derived_cl124, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ ((('#sk2' @ '#sk6' @ ('#sk148' @ X2)) => (X2 @ ('#sk148' @ X2)))) 53.28/7.28 | ('#form147' @ X2))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl123])). 53.28/7.28 thf(zip_derived_cl142, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 ( ('#sk2' @ '#sk6' @ ('#sk148' @ X2)) | ('#form147' @ X2))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl124])). 53.28/7.28 thf(zip_derived_cl143, plain, 53.28/7.28 (![X2 : a > $o]: (~ (X2 @ ('#sk148' @ X2)) | ('#form147' @ X2))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl124])). 53.28/7.28 thf(zip_derived_cl91, plain, 53.28/7.28 (![X2 : a]: 53.28/7.28 (~ ('#sk2' @ '#sk6' @ X2) 53.28/7.28 | ~ ('#form9') 53.28/7.28 | ('#form14') 53.28/7.28 | ('#sk8' @ X2))), 53.28/7.28 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl74])). 53.28/7.28 thf(zip_derived_cl31, plain, 53.28/7.28 (( ('#form9') 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((!!) @ (^[Y2 : a]: 53.28/7.28 (((((((!!) @ (^[Y3 : a > $o]: 53.28/7.28 (((((((!!) @ ( 53.28/7.28 ^[Y4 : a]: 53.28/7.28 (( 53.28/7.28 (!!) @ ( 53.28/7.28 ^[Y5 : a]: 53.28/7.28 (( 53.28/7.28 (( 53.28/7.28 (Y3 @ 53.28/7.28 Y4) & 53.28/7.28 (( 53.28/7.28 ('#sk2' @ 53.28/7.28 Y4 @ 53.28/7.28 Y5) | 53.28/7.28 ('#sk1' @ 53.28/7.28 Y4 @ Y5))))) => 53.28/7.28 (Y3 @ Y5))))))))) & 53.28/7.28 (((!!) @ ( 53.28/7.28 ^[Y4 : a]: 53.28/7.28 (( 53.28/7.28 (( 53.28/7.28 ('#sk2' @ 53.28/7.28 Y0 @ 53.28/7.28 Y4) | 53.28/7.28 ('#sk1' @ 53.28/7.28 Y0 @ Y4))) => 53.28/7.28 (Y3 @ Y4)))))))) => 53.28/7.28 (Y3 @ Y1)))))) & 53.28/7.28 (((!!) @ (^[Y3 : a > $o]: 53.28/7.28 (((((((!!) @ ( 53.28/7.28 ^[Y4 : a]: 53.28/7.28 (( 53.28/7.28 (( 53.28/7.28 ('#sk1' @ 53.28/7.28 Y1 @ 53.28/7.28 Y4) | 53.28/7.28 ('#sk2' @ 53.28/7.28 Y1 @ Y4))) => 53.28/7.28 (Y3 @ Y4)))))) & 53.28/7.28 (((!!) @ ( 53.28/7.28 ^[Y4 : a]: 53.28/7.28 (( 53.28/7.28 (!!) @ ( 53.28/7.28 ^[Y5 : a]: 53.28/7.28 (( 53.28/7.28 (( 53.28/7.28 (Y3 @ 53.28/7.28 Y4) & 53.28/7.28 (( 53.28/7.28 ('#sk1' @ 53.28/7.28 Y4 @ 53.28/7.28 Y5) | 53.28/7.28 ('#sk2' @ 53.28/7.28 Y4 @ Y5))))) => 53.28/7.28 (Y3 @ Y5))))))))))) => 53.28/7.28 (Y3 @ Y2)))))))) => 53.28/7.28 (((!!) @ (^[Y3 : a > $o]: 53.28/7.28 (((((((!!) @ ( 53.28/7.28 ^[Y4 : a]: 53.28/7.28 ( 53.28/7.28 ( 53.28/7.28 (!!) @ ( 53.28/7.28 ^[Y5 : a]: 53.28/7.28 (( 53.28/7.28 (( 53.28/7.28 (Y3 @ 53.28/7.28 Y4) & 53.28/7.28 (( 53.28/7.28 ('#sk2' @ 53.28/7.28 Y4 @ 53.28/7.28 Y5) | 53.28/7.28 ('#sk1' @ 53.28/7.28 Y4 @ Y5))))) => 53.28/7.28 (Y3 @ Y5))))))))) & 53.28/7.28 (((!!) @ ( 53.28/7.28 ^[Y4 : a]: 53.28/7.28 ( 53.28/7.28 ( 53.28/7.28 (( 53.28/7.28 ('#sk2' @ 53.28/7.28 Y0 @ 53.28/7.28 Y4) | 53.28/7.28 ('#sk1' @ 53.28/7.28 Y0 @ Y4))) => 53.28/7.28 (Y3 @ Y4)))))))) => 53.28/7.28 (Y3 @ Y2))))))))))))))))))), 53.28/7.28 define([status(thm)])). 53.28/7.28 thf(zip_derived_cl32, plain, 53.28/7.28 ((~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((((((!!) @ (^[Y2 : a > $o]: 53.28/7.28 (((((((!!) @ (^[Y3 : a]: 53.28/7.28 (((!!) @ ( 53.28/7.28 ^[Y4 : a]: 53.28/7.28 ( 53.28/7.28 ( 53.28/7.28 (( 53.28/7.28 (Y2 @ 53.28/7.28 Y3) & 53.28/7.28 (( 53.28/7.28 ('#sk2' @ 53.28/7.28 Y3 @ 53.28/7.28 Y4) | 53.28/7.28 ('#sk1' @ 53.28/7.28 Y3 @ Y4))))) => 53.28/7.28 (Y2 @ Y4))))))))) & 53.28/7.28 (((!!) @ (^[Y3 : a]: 53.28/7.28 ((((('#sk2' @ 53.28/7.28 '#sk10' @ 53.28/7.28 Y3) | 53.28/7.28 ('#sk1' @ 53.28/7.28 '#sk10' @ 53.28/7.28 Y3))) => 53.28/7.28 (Y2 @ Y3)))))))) => 53.28/7.28 (Y2 @ Y0)))))) & 53.28/7.28 (((!!) @ (^[Y2 : a > $o]: 53.28/7.28 (((((((!!) @ (^[Y3 : a]: 53.28/7.28 ((((('#sk1' @ 53.28/7.28 Y0 @ 53.28/7.28 Y3) | 53.28/7.28 ('#sk2' @ 53.28/7.28 Y0 @ Y3))) => 53.28/7.28 (Y2 @ Y3)))))) & 53.28/7.28 (((!!) @ (^[Y3 : a]: 53.28/7.28 (((!!) @ ( 53.28/7.28 ^[Y4 : a]: 53.28/7.28 ( 53.28/7.28 ( 53.28/7.28 (( 53.28/7.28 (Y2 @ 53.28/7.28 Y3) & 53.28/7.28 (( 53.28/7.28 ('#sk1' @ 53.28/7.28 Y3 @ 53.28/7.28 Y4) | 53.28/7.28 ('#sk2' @ 53.28/7.28 Y3 @ Y4))))) => 53.28/7.28 (Y2 @ Y4))))))))))) => 53.28/7.28 (Y2 @ Y1)))))))) => 53.28/7.28 (((!!) @ (^[Y2 : a > $o]: 53.28/7.28 (((((((!!) @ (^[Y3 : a]: 53.28/7.28 (((!!) @ ( 53.28/7.28 ^[Y4 : a]: 53.28/7.28 (((( 53.28/7.28 (Y2 @ 53.28/7.28 Y3) & 53.28/7.28 (( 53.28/7.28 ('#sk2' @ 53.28/7.28 Y3 @ 53.28/7.28 Y4) | 53.28/7.28 ('#sk1' @ 53.28/7.28 Y3 @ Y4))))) => 53.28/7.28 (Y2 @ Y4))))))))) & 53.28/7.28 (((!!) @ (^[Y3 : a]: 53.28/7.28 ((((('#sk2' @ 53.28/7.28 '#sk10' @ 53.28/7.28 Y3) | 53.28/7.28 ('#sk1' @ 53.28/7.28 '#sk10' @ 53.28/7.28 Y3))) => 53.28/7.28 (Y2 @ Y3)))))))) => 53.28/7.28 (Y2 @ Y1)))))))))))))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl31])). 53.28/7.28 thf(zip_derived_cl42, plain, 53.28/7.28 ((~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((((((!!) @ (^[Y1 : a > $o]: 53.28/7.28 (((((((!!) @ (^[Y2 : a]: 53.28/7.28 (((!!) @ (^[Y3 : a]: 53.28/7.28 (((((Y1 @ 53.28/7.28 Y2) & 53.28/7.28 (( 53.28/7.28 ('#sk2' @ 53.28/7.28 Y2 @ 53.28/7.28 Y3) | 53.28/7.28 ('#sk1' @ 53.28/7.28 Y2 @ Y3))))) => 53.28/7.28 (Y1 @ Y3))))))))) & 53.28/7.28 (((!!) @ (^[Y2 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ 53.28/7.28 Y2) | ('#sk1' @ 53.28/7.28 '#sk10' @ Y2))) => 53.28/7.28 (Y1 @ Y2)))))))) => 53.28/7.28 (Y1 @ '#sk15')))))) & 53.28/7.28 (((!!) @ (^[Y1 : a > $o]: 53.28/7.28 (((((((!!) @ (^[Y2 : a]: 53.28/7.28 ((((('#sk1' @ '#sk15' @ 53.28/7.28 Y2) | ('#sk2' @ 53.28/7.28 '#sk15' @ Y2))) => 53.28/7.28 (Y1 @ Y2)))))) & 53.28/7.28 (((!!) @ (^[Y2 : a]: 53.28/7.28 (((!!) @ (^[Y3 : a]: 53.28/7.28 (((((Y1 @ 53.28/7.28 Y2) & 53.28/7.28 (( 53.28/7.28 ('#sk1' @ 53.28/7.28 Y2 @ 53.28/7.28 Y3) | 53.28/7.28 ('#sk2' @ 53.28/7.28 Y2 @ Y3))))) => 53.28/7.28 (Y1 @ Y3))))))))))) => 53.28/7.28 (Y1 @ Y0)))))))) => 53.28/7.28 (((!!) @ (^[Y1 : a > $o]: 53.28/7.28 (((((((!!) @ (^[Y2 : a]: 53.28/7.28 (((!!) @ (^[Y3 : a]: 53.28/7.28 (((((Y1 @ Y2) & 53.28/7.28 ((('#sk2' @ 53.28/7.28 Y2 @ 53.28/7.28 Y3) | 53.28/7.28 ('#sk1' @ 53.28/7.28 Y2 @ Y3))))) => 53.28/7.28 (Y1 @ Y3))))))))) & 53.28/7.28 (((!!) @ (^[Y2 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ 53.28/7.28 Y2) | ('#sk1' @ 53.28/7.28 '#sk10' @ Y2))) => 53.28/7.28 (Y1 @ Y2)))))))) => 53.28/7.28 (Y1 @ Y0))))))))))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl32])). 53.28/7.28 thf(zip_derived_cl51, plain, 53.28/7.28 ((~ (((((((!!) @ (^[Y0 : a > $o]: 53.28/7.28 (((((((!!) @ (^[Y1 : a]: 53.28/7.28 (((!!) @ (^[Y2 : a]: 53.28/7.28 (((((Y0 @ Y1) & 53.28/7.28 ((('#sk2' @ Y1 @ 53.28/7.28 Y2) | ('#sk1' @ 53.28/7.28 Y1 @ Y2))))) => 53.28/7.28 (Y0 @ Y2))))))))) & 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y1) | 53.28/7.28 ('#sk1' @ '#sk10' @ Y1))) => 53.28/7.28 (Y0 @ Y1)))))))) => 53.28/7.28 (Y0 @ '#sk15')))))) & 53.28/7.28 (((!!) @ (^[Y0 : a > $o]: 53.28/7.28 (((((((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk1' @ '#sk15' @ Y1) | 53.28/7.28 ('#sk2' @ '#sk15' @ Y1))) => 53.28/7.28 (Y0 @ Y1)))))) & 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((!!) @ (^[Y2 : a]: 53.28/7.28 (((((Y0 @ Y1) & 53.28/7.28 ((('#sk1' @ Y1 @ 53.28/7.28 Y2) | ('#sk2' @ 53.28/7.28 Y1 @ Y2))))) => 53.28/7.28 (Y0 @ Y2))))))))))) => 53.28/7.28 (Y0 @ '#sk23')))))))) => 53.28/7.28 (((!!) @ (^[Y0 : a > $o]: 53.28/7.28 (((((((!!) @ (^[Y1 : a]: 53.28/7.28 (((!!) @ (^[Y2 : a]: 53.28/7.28 (((((Y0 @ Y1) & 53.28/7.28 ((('#sk2' @ Y1 @ Y2) | 53.28/7.28 ('#sk1' @ Y1 @ Y2))))) => 53.28/7.28 (Y0 @ Y2))))))))) & 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y1) | 53.28/7.28 ('#sk1' @ '#sk10' @ Y1))) => 53.28/7.28 (Y0 @ Y1)))))))) => 53.28/7.28 (Y0 @ '#sk23')))))))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl42])). 53.28/7.28 thf(zip_derived_cl58, plain, 53.28/7.28 ((~ (((!!) @ (^[Y0 : a > $o]: 53.28/7.28 (((((((!!) @ (^[Y1 : a]: 53.28/7.28 (((!!) @ (^[Y2 : a]: 53.28/7.28 (((((Y0 @ Y1) & 53.28/7.28 ((('#sk2' @ Y1 @ Y2) | 53.28/7.28 ('#sk1' @ Y1 @ Y2))))) => 53.28/7.28 (Y0 @ Y2))))))))) & 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y1) | ('#sk1' @ 53.28/7.28 '#sk10' @ Y1))) => 53.28/7.28 (Y0 @ Y1)))))))) => 53.28/7.28 (Y0 @ '#sk23')))))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 53.28/7.28 thf(zip_derived_cl69, plain, 53.28/7.28 ((~ (((((((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk43' @ Y0) & 53.28/7.28 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 53.28/7.28 Y0 @ Y1))))) => 53.28/7.28 ('#sk43' @ Y1))))))))) & 53.28/7.28 (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 53.28/7.28 ('#sk43' @ Y0)))))))) => 53.28/7.28 ('#sk43' @ '#sk23'))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl58])). 53.28/7.28 thf(zip_derived_cl85, plain, ((~ ('#sk43' @ '#sk23') | ('#form9'))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl69])). 53.28/7.28 thf(zip_derived_cl57, plain, 53.28/7.28 (( (((((!!) @ (^[Y0 : a > $o]: 53.28/7.28 (((((((!!) @ (^[Y1 : a]: 53.28/7.28 (((!!) @ (^[Y2 : a]: 53.28/7.28 (((((Y0 @ Y1) & 53.28/7.28 ((('#sk2' @ Y1 @ Y2) | 53.28/7.28 ('#sk1' @ Y1 @ Y2))))) => 53.28/7.28 (Y0 @ Y2))))))))) & 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y1) | ('#sk1' @ 53.28/7.28 '#sk10' @ Y1))) => 53.28/7.28 (Y0 @ Y1)))))))) => 53.28/7.28 (Y0 @ '#sk15')))))) & 53.28/7.28 (((!!) @ (^[Y0 : a > $o]: 53.28/7.28 (((((((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk1' @ '#sk15' @ Y1) | ('#sk2' @ 53.28/7.28 '#sk15' @ Y1))) => 53.28/7.28 (Y0 @ Y1)))))) & 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((!!) @ (^[Y2 : a]: 53.28/7.28 (((((Y0 @ Y1) & 53.28/7.28 ((('#sk1' @ Y1 @ Y2) | 53.28/7.28 ('#sk2' @ Y1 @ Y2))))) => 53.28/7.28 (Y0 @ Y2))))))))))) => 53.28/7.28 (Y0 @ '#sk23')))))))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 53.28/7.28 thf(zip_derived_cl65, plain, 53.28/7.28 (( (((!!) @ (^[Y0 : a > $o]: 53.28/7.28 (((((((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk1' @ '#sk15' @ Y1) | ('#sk2' @ 53.28/7.28 '#sk15' @ Y1))) => 53.28/7.28 (Y0 @ Y1)))))) & 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((!!) @ (^[Y2 : a]: 53.28/7.28 (((((Y0 @ Y1) & 53.28/7.28 ((('#sk1' @ Y1 @ Y2) | 53.28/7.28 ('#sk2' @ Y1 @ Y2))))) => 53.28/7.28 (Y0 @ Y2))))))))))) => 53.28/7.28 (Y0 @ '#sk23')))))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl57])). 53.28/7.28 thf(zip_derived_cl80, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 ( (((((((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ 53.28/7.28 Y0))) => 53.28/7.28 (X2 @ Y0)))))) & 53.28/7.28 (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((((X2 @ Y0) & 53.28/7.28 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 53.28/7.28 Y0 @ Y1))))) => 53.28/7.28 (X2 @ Y1))))))))))) => 53.28/7.28 (X2 @ '#sk23'))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl65])). 53.28/7.28 thf(zip_derived_cl81, plain, 53.28/7.28 (( (((((((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ Y0))) => 53.28/7.28 ('#sk43' @ Y0)))))) & 53.28/7.28 (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk43' @ Y0) & 53.28/7.28 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 53.28/7.28 Y1))))) => 53.28/7.28 ('#sk43' @ Y1))))))))))) => 53.28/7.28 ('#sk43' @ '#sk23'))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('triggered_bool_instantiation', [status(thm)], 53.28/7.28 [zip_derived_cl80])). 53.28/7.28 thf(zip_derived_cl367, plain, 53.28/7.28 ((~ (((((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ Y0))) => 53.28/7.28 ('#sk43' @ Y0)))))) & 53.28/7.28 (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk43' @ Y0) & 53.28/7.28 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 53.28/7.28 Y1))))) => 53.28/7.28 ('#sk43' @ Y1))))))))))) 53.28/7.28 | ('#sk43' @ '#sk23') 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 53.28/7.28 thf(zip_derived_cl85, plain, ((~ ('#sk43' @ '#sk23') | ('#form9'))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl69])). 53.28/7.28 thf(zip_derived_cl368, plain, 53.28/7.28 (( ('#form9') 53.28/7.28 | ~ (((((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ Y0))) => 53.28/7.28 ('#sk43' @ Y0)))))) & 53.28/7.28 (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk43' @ Y0) & 53.28/7.28 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 53.28/7.28 Y0 @ Y1))))) => 53.28/7.28 ('#sk43' @ Y1))))))))))))), 53.28/7.28 inference('clc', [status(thm)], [zip_derived_cl367, zip_derived_cl85])). 53.28/7.28 thf(zip_derived_cl369, plain, 53.28/7.28 ((~ (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ Y0))) => 53.28/7.28 ('#sk43' @ Y0)))))) 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk43' @ Y0) & 53.28/7.28 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 53.28/7.28 Y1))))) => 53.28/7.28 ('#sk43' @ Y1))))))))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl368])). 53.28/7.28 thf(zip_derived_cl370, plain, 53.28/7.28 ((~ ((((('#sk1' @ '#sk15' @ ('#sk140' @ '#sk43')) | ('#sk2' @ '#sk15' @ 53.28/7.28 ('#sk140' @ '#sk43')))) => 53.28/7.28 ('#sk43' @ ('#sk140' @ '#sk43')))) 53.28/7.28 | ('#form9') 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk43' @ Y0) & 53.28/7.28 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 53.28/7.28 Y1))))) => 53.28/7.28 ('#sk43' @ Y1))))))))))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl369])). 53.28/7.28 thf(zip_derived_cl371, plain, 53.28/7.28 (( ((('#sk1' @ '#sk15' @ ('#sk140' @ '#sk43')) | ('#sk2' @ '#sk15' @ 53.28/7.28 ('#sk140' @ '#sk43')))) 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk43' @ Y0) & 53.28/7.28 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 53.28/7.28 Y1))))) => 53.28/7.28 ('#sk43' @ Y1))))))))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl370])). 53.28/7.28 thf(zip_derived_cl373, plain, 53.28/7.28 (( ('#sk1' @ '#sk15' @ ('#sk140' @ '#sk43')) 53.28/7.28 | ('#sk2' @ '#sk15' @ ('#sk140' @ '#sk43')) 53.28/7.28 | ('#form9') 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk43' @ Y0) & 53.28/7.28 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 53.28/7.28 Y1))))) => 53.28/7.28 ('#sk43' @ Y1))))))))))), 53.28/7.28 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl371])). 53.28/7.28 thf(zip_derived_cl375, plain, 53.28/7.28 ((~ (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk43' @ ('#sk71' @ '#sk43')) & 53.28/7.28 ((('#sk1' @ ('#sk71' @ '#sk43') @ Y0) | ('#sk2' @ 53.28/7.28 ('#sk71' @ '#sk43') @ Y0))))) => 53.28/7.28 ('#sk43' @ Y0)))))) 53.28/7.28 | ('#form9') 53.28/7.28 | ('#sk2' @ '#sk15' @ ('#sk140' @ '#sk43')) 53.28/7.28 | ('#sk1' @ '#sk15' @ ('#sk140' @ '#sk43')))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl373])). 53.28/7.28 thf(zip_derived_cl377, plain, 53.28/7.28 ((~ ((((('#sk43' @ ('#sk71' @ '#sk43')) & 53.28/7.28 ((('#sk1' @ ('#sk71' @ '#sk43') @ ('#sk99' @ '#sk43')) | 53.28/7.28 ('#sk2' @ ('#sk71' @ '#sk43') @ ('#sk99' @ '#sk43')))))) => 53.28/7.28 ('#sk43' @ ('#sk99' @ '#sk43')))) 53.28/7.28 | ('#sk1' @ '#sk15' @ ('#sk140' @ '#sk43')) 53.28/7.28 | ('#sk2' @ '#sk15' @ ('#sk140' @ '#sk43')) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl375])). 53.28/7.28 thf(zip_derived_cl381, plain, 53.28/7.28 ((~ ('#sk43' @ ('#sk99' @ '#sk43')) 53.28/7.28 | ('#form9') 53.28/7.28 | ('#sk2' @ '#sk15' @ ('#sk140' @ '#sk43')) 53.28/7.28 | ('#sk1' @ '#sk15' @ ('#sk140' @ '#sk43')))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl377])). 53.28/7.28 thf(zip_derived_cl80, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 ( (((((((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ 53.28/7.28 Y0))) => 53.28/7.28 (X2 @ Y0)))))) & 53.28/7.28 (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((((X2 @ Y0) & 53.28/7.28 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 53.28/7.28 Y0 @ Y1))))) => 53.28/7.28 (X2 @ Y1))))))))))) => 53.28/7.28 (X2 @ '#sk23'))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl65])). 53.28/7.28 thf(zip_derived_cl95, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ (((((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ Y0))) => 53.28/7.28 (X2 @ Y0)))))) & 53.28/7.28 (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((((X2 @ Y0) & 53.28/7.28 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 53.28/7.28 Y0 @ Y1))))) => 53.28/7.28 (X2 @ Y1))))))))))) 53.28/7.28 | (X2 @ '#sk23') 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])). 53.28/7.28 thf(zip_derived_cl105, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ Y0))) => 53.28/7.28 (X2 @ Y0)))))) 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((((X2 @ Y0) & 53.28/7.28 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 53.28/7.28 Y0 @ Y1))))) => 53.28/7.28 (X2 @ Y1))))))))) 53.28/7.28 | ('#form9') 53.28/7.28 | (X2 @ '#sk23'))), 53.28/7.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl95])). 53.28/7.28 thf(zip_derived_cl118, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ ((((('#sk1' @ '#sk15' @ ('#sk140' @ X2)) | ('#sk2' @ '#sk15' @ 53.28/7.28 ('#sk140' @ X2)))) => 53.28/7.28 (X2 @ ('#sk140' @ X2)))) 53.28/7.28 | (X2 @ '#sk23') 53.28/7.28 | ('#form9') 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((((X2 @ Y0) & 53.28/7.28 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 53.28/7.28 Y0 @ Y1))))) => 53.28/7.28 (X2 @ Y1))))))))))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl105])). 53.28/7.28 thf(zip_derived_cl136, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ (X2 @ ('#sk140' @ X2)) 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((((X2 @ Y0) & 53.28/7.28 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 53.28/7.28 Y0 @ Y1))))) => 53.28/7.28 (X2 @ Y1))))))))) 53.28/7.28 | ('#form9') 53.28/7.28 | (X2 @ '#sk23'))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl118])). 53.28/7.28 thf(zip_derived_cl154, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((((X2 @ ('#sk71' @ X2)) & 53.28/7.28 ((('#sk1' @ ('#sk71' @ X2) @ Y0) | ('#sk2' @ 53.28/7.28 ('#sk71' @ X2) @ Y0))))) => 53.28/7.28 (X2 @ Y0)))))) 53.28/7.28 | (X2 @ '#sk23') 53.28/7.28 | ('#form9') 53.28/7.28 | ~ (X2 @ ('#sk140' @ X2)))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl136])). 53.28/7.28 thf(zip_derived_cl165, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ (((((X2 @ ('#sk71' @ X2)) & 53.28/7.28 ((('#sk1' @ ('#sk71' @ X2) @ ('#sk99' @ X2)) | ('#sk2' @ 53.28/7.28 ('#sk71' @ X2) @ ('#sk99' @ X2)))))) => 53.28/7.28 (X2 @ ('#sk99' @ X2)))) 53.28/7.28 | ~ (X2 @ ('#sk140' @ X2)) 53.28/7.28 | ('#form9') 53.28/7.28 | (X2 @ '#sk23'))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl154])). 53.28/7.28 thf(zip_derived_cl174, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ (X2 @ ('#sk99' @ X2)) 53.28/7.28 | (X2 @ '#sk23') 53.28/7.28 | ('#form9') 53.28/7.28 | ~ (X2 @ ('#sk140' @ X2)))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl165])). 53.28/7.28 thf(zip_derived_cl380, plain, 53.28/7.28 (( ((('#sk43' @ ('#sk71' @ '#sk43')) & 53.28/7.28 ((('#sk1' @ ('#sk71' @ '#sk43') @ ('#sk99' @ '#sk43')) | ('#sk2' @ 53.28/7.28 ('#sk71' @ '#sk43') @ ('#sk99' @ '#sk43')))))) 53.28/7.28 | ('#form9') 53.28/7.28 | ('#sk2' @ '#sk15' @ ('#sk140' @ '#sk43')) 53.28/7.28 | ('#sk1' @ '#sk15' @ ('#sk140' @ '#sk43')))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl377])). 53.28/7.28 thf(zip_derived_cl385, plain, 53.28/7.28 (( ((('#sk1' @ ('#sk71' @ '#sk43') @ ('#sk99' @ '#sk43')) | ('#sk2' @ 53.28/7.28 ('#sk71' @ '#sk43') @ ('#sk99' @ '#sk43')))) 53.28/7.28 | ('#sk1' @ '#sk15' @ ('#sk140' @ '#sk43')) 53.28/7.28 | ('#sk2' @ '#sk15' @ ('#sk140' @ '#sk43')) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl380])). 53.28/7.28 thf(zip_derived_cl387, plain, 53.28/7.28 (( ('#sk1' @ ('#sk71' @ '#sk43') @ ('#sk99' @ '#sk43')) 53.28/7.28 | ('#sk2' @ ('#sk71' @ '#sk43') @ ('#sk99' @ '#sk43')) 53.28/7.28 | ('#form9') 53.28/7.28 | ('#sk2' @ '#sk15' @ ('#sk140' @ '#sk43')) 53.28/7.28 | ('#sk1' @ '#sk15' @ ('#sk140' @ '#sk43')))), 53.28/7.28 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl385])). 53.28/7.28 thf(zip_derived_cl384, plain, 53.28/7.28 (( ('#sk43' @ ('#sk71' @ '#sk43')) 53.28/7.28 | ('#sk1' @ '#sk15' @ ('#sk140' @ '#sk43')) 53.28/7.28 | ('#sk2' @ '#sk15' @ ('#sk140' @ '#sk43')) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl380])). 53.28/7.28 thf(zip_derived_cl372, plain, 53.28/7.28 ((~ ('#sk43' @ ('#sk140' @ '#sk43')) 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk43' @ Y0) & 53.28/7.28 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 53.28/7.28 Y1))))) => 53.28/7.28 ('#sk43' @ Y1))))))))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl370])). 53.28/7.28 thf(zip_derived_cl374, plain, 53.28/7.28 ((~ (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk43' @ ('#sk71' @ '#sk43')) & 53.28/7.28 ((('#sk1' @ ('#sk71' @ '#sk43') @ Y0) | ('#sk2' @ 53.28/7.28 ('#sk71' @ '#sk43') @ Y0))))) => 53.28/7.28 ('#sk43' @ Y0)))))) 53.28/7.28 | ('#form9') 53.28/7.28 | ~ ('#sk43' @ ('#sk140' @ '#sk43')))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl372])). 53.28/7.28 thf(zip_derived_cl376, plain, 53.28/7.28 ((~ ((((('#sk43' @ ('#sk71' @ '#sk43')) & 53.28/7.28 ((('#sk1' @ ('#sk71' @ '#sk43') @ ('#sk99' @ '#sk43')) | 53.28/7.28 ('#sk2' @ ('#sk71' @ '#sk43') @ ('#sk99' @ '#sk43')))))) => 53.28/7.28 ('#sk43' @ ('#sk99' @ '#sk43')))) 53.28/7.28 | ~ ('#sk43' @ ('#sk140' @ '#sk43')) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl374])). 53.28/7.28 thf(zip_derived_cl378, plain, 53.28/7.28 (( ((('#sk43' @ ('#sk71' @ '#sk43')) & 53.28/7.28 ((('#sk1' @ ('#sk71' @ '#sk43') @ ('#sk99' @ '#sk43')) | ('#sk2' @ 53.28/7.28 ('#sk71' @ '#sk43') @ ('#sk99' @ '#sk43')))))) 53.28/7.28 | ('#form9') 53.28/7.28 | ~ ('#sk43' @ ('#sk140' @ '#sk43')))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl376])). 53.28/7.28 thf(zip_derived_cl383, plain, 53.28/7.28 (( ((('#sk1' @ ('#sk71' @ '#sk43') @ ('#sk99' @ '#sk43')) | ('#sk2' @ 53.28/7.28 ('#sk71' @ '#sk43') @ ('#sk99' @ '#sk43')))) 53.28/7.28 | ~ ('#sk43' @ ('#sk140' @ '#sk43')) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl378])). 53.28/7.28 thf(zip_derived_cl386, plain, 53.28/7.28 (( ('#sk1' @ ('#sk71' @ '#sk43') @ ('#sk99' @ '#sk43')) 53.28/7.28 | ('#sk2' @ ('#sk71' @ '#sk43') @ ('#sk99' @ '#sk43')) 53.28/7.28 | ('#form9') 53.28/7.28 | ~ ('#sk43' @ ('#sk140' @ '#sk43')))), 53.28/7.28 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl383])). 53.28/7.28 thf(zip_derived_cl382, plain, 53.28/7.28 (( ('#sk43' @ ('#sk71' @ '#sk43')) 53.28/7.28 | ~ ('#sk43' @ ('#sk140' @ '#sk43')) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl378])). 53.28/7.28 thf(zip_derived_cl64, plain, 53.28/7.28 (( (((!!) @ (^[Y0 : a > $o]: 53.28/7.28 (((((((!!) @ (^[Y1 : a]: 53.28/7.28 (((!!) @ (^[Y2 : a]: 53.28/7.28 (((((Y0 @ Y1) & 53.28/7.28 ((('#sk2' @ Y1 @ Y2) | 53.28/7.28 ('#sk1' @ Y1 @ Y2))))) => 53.28/7.28 (Y0 @ Y2))))))))) & 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y1) | ('#sk1' @ 53.28/7.28 '#sk10' @ Y1))) => 53.28/7.28 (Y0 @ Y1)))))))) => 53.28/7.28 (Y0 @ '#sk15')))))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl57])). 53.28/7.28 thf(zip_derived_cl76, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 ( (((((((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((((X2 @ Y0) & 53.28/7.28 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 53.28/7.28 Y0 @ Y1))))) => 53.28/7.28 (X2 @ Y1))))))))) & 53.28/7.28 (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ 53.28/7.28 Y0))) => 53.28/7.28 (X2 @ Y0)))))))) => 53.28/7.28 (X2 @ '#sk15'))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl64])). 53.28/7.28 thf(zip_derived_cl94, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ (((((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((((X2 @ Y0) & 53.28/7.28 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 53.28/7.28 Y0 @ Y1))))) => 53.28/7.28 (X2 @ Y1))))))))) & 53.28/7.28 (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 53.28/7.28 (X2 @ Y0)))))))) 53.28/7.28 | (X2 @ '#sk15') 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl76])). 53.28/7.28 thf(zip_derived_cl104, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 (((((X2 @ Y0) & 53.28/7.28 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 53.28/7.28 Y1))))) => 53.28/7.28 (X2 @ Y1))))))))) 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 53.28/7.28 (X2 @ Y0)))))) 53.28/7.28 | ('#form9') 53.28/7.28 | (X2 @ '#sk15'))), 53.28/7.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl94])). 53.28/7.28 thf(zip_derived_cl117, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ (((!!) @ (^[Y0 : a]: 53.28/7.28 (((((X2 @ ('#sk136' @ X2)) & 53.28/7.28 ((('#sk2' @ ('#sk136' @ X2) @ Y0) | ('#sk1' @ 53.28/7.28 ('#sk136' @ X2) @ Y0))))) => 53.28/7.28 (X2 @ Y0)))))) 53.28/7.28 | (X2 @ '#sk15') 53.28/7.28 | ('#form9') 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 53.28/7.28 (X2 @ Y0)))))))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl104])). 53.28/7.28 thf(zip_derived_cl134, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ (((((X2 @ ('#sk136' @ X2)) & 53.28/7.28 ((('#sk2' @ ('#sk136' @ X2) @ ('#sk180' @ X2)) | ('#sk1' @ 53.28/7.28 ('#sk136' @ X2) @ ('#sk180' @ X2)))))) => 53.28/7.28 (X2 @ ('#sk180' @ X2)))) 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 53.28/7.28 (X2 @ Y0)))))) 53.28/7.28 | ('#form9') 53.28/7.28 | (X2 @ '#sk15'))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl117])). 53.28/7.28 thf(zip_derived_cl152, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ (X2 @ ('#sk180' @ X2)) 53.28/7.28 | (X2 @ '#sk15') 53.28/7.28 | ('#form9') 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 53.28/7.28 (X2 @ Y0)))))))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl134])). 53.28/7.28 thf(zip_derived_cl152, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ (X2 @ ('#sk180' @ X2)) 53.28/7.28 | (X2 @ '#sk15') 53.28/7.28 | ('#form9') 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 53.28/7.28 (X2 @ Y0)))))))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl134])). 53.28/7.28 thf(zip_derived_cl161, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 ( ('#form285' @ X2) 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 53.28/7.28 (X2 @ Y0)))))))), 53.28/7.28 define([status(thm)])). 53.28/7.28 thf(zip_derived_cl163, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ ('#form285' @ X2) 53.28/7.28 | ('#form9') 53.28/7.28 | (X2 @ '#sk15') 53.28/7.28 | ~ (X2 @ ('#sk180' @ X2)))), 53.28/7.28 inference('renaming', [status(thm)], 53.28/7.28 [zip_derived_cl152, zip_derived_cl161])). 53.28/7.28 thf(zip_derived_cl84, plain, 53.28/7.28 (( (((((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk43' @ Y0) & 53.28/7.28 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 53.28/7.28 Y1))))) => 53.28/7.28 ('#sk43' @ Y1))))))))) & 53.28/7.28 (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 53.28/7.28 ('#sk43' @ Y0)))))))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl69])). 53.28/7.28 thf(zip_derived_cl96, plain, 53.28/7.28 (( (((!!) @ (^[Y0 : a]: 53.28/7.28 (((!!) @ (^[Y1 : a]: 53.28/7.28 ((((('#sk43' @ Y0) & 53.28/7.28 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))))) => 53.28/7.28 ('#sk43' @ Y1))))))))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl84])). 53.28/7.28 thf(zip_derived_cl106, plain, 53.28/7.28 (![X2 : a]: 53.28/7.28 ( (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk43' @ X2) & 53.28/7.28 ((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))))) => 53.28/7.28 ('#sk43' @ Y0)))))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl96])). 53.28/7.28 thf(zip_derived_cl119, plain, 53.28/7.28 (![X2 : a, X4 : a]: 53.28/7.28 ( ((((('#sk43' @ X2) & ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))))) => 53.28/7.28 ('#sk43' @ X4))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl106])). 53.28/7.28 thf(zip_derived_cl137, plain, 53.28/7.28 (![X2 : a, X4 : a]: 53.28/7.28 (~ ((('#sk43' @ X2) & ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))))) 53.28/7.28 | ('#sk43' @ X4) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl119])). 53.28/7.28 thf(zip_derived_cl155, plain, 53.28/7.28 (![X2 : a, X4 : a]: 53.28/7.28 (~ ('#sk43' @ X2) 53.28/7.28 | ~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 53.28/7.28 | ('#form9') 53.28/7.28 | ('#sk43' @ X4))), 53.28/7.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl137])). 53.28/7.28 thf(zip_derived_cl167, plain, 53.28/7.28 (![X2 : a, X4 : a]: 53.28/7.28 (~ ('#sk1' @ X2 @ X4) 53.28/7.28 | ('#sk43' @ X4) 53.28/7.28 | ('#form9') 53.28/7.28 | ~ ('#sk43' @ X2))), 53.28/7.28 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl155])). 53.28/7.28 thf(zip_derived_cl166, plain, 53.28/7.28 (![X2 : a, X4 : a]: 53.28/7.28 (~ ('#sk2' @ X2 @ X4) 53.28/7.28 | ('#sk43' @ X4) 53.28/7.28 | ('#form9') 53.28/7.28 | ~ ('#sk43' @ X2))), 53.28/7.28 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl155])). 53.28/7.28 thf(zip_derived_cl151, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 ( (((X2 @ ('#sk136' @ X2)) & 53.28/7.28 ((('#sk2' @ ('#sk136' @ X2) @ ('#sk180' @ X2)) | ('#sk1' @ 53.28/7.28 ('#sk136' @ X2) @ ('#sk180' @ X2)))))) 53.28/7.28 | (X2 @ '#sk15') 53.28/7.28 | ('#form9') 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 53.28/7.28 (X2 @ Y0)))))))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl134])). 53.28/7.28 thf(zip_derived_cl159, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 ( (X2 @ ('#sk136' @ X2)) 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 53.28/7.28 (X2 @ Y0)))))) 53.28/7.28 | ('#form9') 53.28/7.28 | (X2 @ '#sk15'))), 53.28/7.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl151])). 53.28/7.28 thf(zip_derived_cl161, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 ( ('#form285' @ X2) 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 53.28/7.28 (X2 @ Y0)))))))), 53.28/7.28 define([status(thm)])). 53.28/7.28 thf(zip_derived_cl168, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ ('#form285' @ (^[Y0 : a]: (X2 @ Y0))) 53.28/7.28 | (X2 @ '#sk15') 53.28/7.28 | ('#form9') 53.28/7.28 | (X2 @ ('#sk136' @ X2)))), 53.28/7.28 inference('renaming', [status(thm)], 53.28/7.28 [zip_derived_cl159, zip_derived_cl161])). 53.28/7.28 thf(zip_derived_cl175, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ ('#form285' @ X2) 53.28/7.28 | (X2 @ '#sk15') 53.28/7.28 | ('#form9') 53.28/7.28 | (X2 @ ('#sk136' @ X2)))), 53.28/7.28 inference('ho_norm', [status(thm)], [zip_derived_cl168])). 53.28/7.28 thf(zip_derived_cl160, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 ( ((('#sk2' @ ('#sk136' @ X2) @ ('#sk180' @ X2)) | ('#sk1' @ 53.28/7.28 ('#sk136' @ X2) @ ('#sk180' @ X2)))) 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 53.28/7.28 (X2 @ Y0)))))) 53.28/7.28 | ('#form9') 53.28/7.28 | (X2 @ '#sk15'))), 53.28/7.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl151])). 53.28/7.28 thf(zip_derived_cl161, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 ( ('#form285' @ X2) 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 53.28/7.28 (X2 @ Y0)))))))), 53.28/7.28 define([status(thm)])). 53.28/7.28 thf(zip_derived_cl169, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ ('#form285' @ (^[Y0 : a]: (X2 @ Y0))) 53.28/7.28 | (X2 @ '#sk15') 53.28/7.28 | ('#form9') 53.28/7.28 | ((('#sk2' @ ('#sk136' @ X2) @ ('#sk180' @ X2)) | ('#sk1' @ 53.28/7.28 ('#sk136' @ X2) @ ('#sk180' @ X2)))))), 53.28/7.28 inference('renaming', [status(thm)], 53.28/7.28 [zip_derived_cl160, zip_derived_cl161])). 53.28/7.28 thf(zip_derived_cl176, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ ('#form285' @ X2) 53.28/7.28 | (X2 @ '#sk15') 53.28/7.28 | ('#form9') 53.28/7.28 | ((('#sk2' @ ('#sk136' @ X2) @ ('#sk180' @ X2)) | ('#sk1' @ 53.28/7.28 ('#sk136' @ X2) @ ('#sk180' @ X2)))))), 53.28/7.28 inference('ho_norm', [status(thm)], [zip_derived_cl169])). 53.28/7.28 thf(zip_derived_cl177, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 ( ('#sk2' @ ('#sk136' @ X2) @ ('#sk180' @ X2)) 53.28/7.28 | ('#sk1' @ ('#sk136' @ X2) @ ('#sk180' @ X2)) 53.28/7.28 | ('#form9') 53.28/7.28 | (X2 @ '#sk15') 53.28/7.28 | ~ ('#form285' @ X2))), 53.28/7.28 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl176])). 53.28/7.28 thf(zip_derived_cl161, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 ( ('#form285' @ X2) 53.28/7.28 | ~ (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 53.28/7.28 (X2 @ Y0)))))))), 53.28/7.28 define([status(thm)])). 53.28/7.28 thf(zip_derived_cl162, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 (~ ((((('#sk2' @ '#sk10' @ ('#sk286' @ X2)) | ('#sk1' @ '#sk10' @ 53.28/7.28 ('#sk286' @ X2)))) => 53.28/7.28 (X2 @ ('#sk286' @ X2)))) 53.28/7.28 | ('#form285' @ X2))), 53.28/7.28 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl161])). 53.28/7.28 thf(zip_derived_cl170, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 ( ((('#sk2' @ '#sk10' @ ('#sk286' @ X2)) | ('#sk1' @ '#sk10' @ 53.28/7.28 ('#sk286' @ X2)))) 53.28/7.28 | ('#form285' @ X2))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl162])). 53.28/7.28 thf(zip_derived_cl178, plain, 53.28/7.28 (![X2 : a > $o]: 53.28/7.28 ( ('#sk2' @ '#sk10' @ ('#sk286' @ X2)) 53.28/7.28 | ('#sk1' @ '#sk10' @ ('#sk286' @ X2)) 53.28/7.28 | ('#form285' @ X2))), 53.28/7.28 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl170])). 53.28/7.28 thf(zip_derived_cl171, plain, 53.28/7.28 (![X2 : a > $o]: (~ (X2 @ ('#sk286' @ X2)) | ('#form285' @ X2))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl162])). 53.28/7.28 thf(zip_derived_cl97, plain, 53.28/7.28 (( (((!!) @ (^[Y0 : a]: 53.28/7.28 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 53.28/7.28 ('#sk43' @ Y0)))))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl84])). 53.28/7.28 thf(zip_derived_cl107, plain, 53.28/7.28 (![X2 : a]: 53.28/7.28 ( ((((('#sk2' @ '#sk10' @ X2) | ('#sk1' @ '#sk10' @ X2))) => 53.28/7.28 ('#sk43' @ X2))) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl97])). 53.28/7.28 thf(zip_derived_cl120, plain, 53.28/7.28 (![X2 : a]: 53.28/7.28 (~ ((('#sk2' @ '#sk10' @ X2) | ('#sk1' @ '#sk10' @ X2))) 53.28/7.28 | ('#sk43' @ X2) 53.28/7.28 | ('#form9'))), 53.28/7.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])). 53.28/7.28 thf(zip_derived_cl139, plain, 53.28/7.28 (![X2 : a]: (~ ('#sk1' @ '#sk10' @ X2) | ('#form9') | ('#sk43' @ X2))), 53.28/7.28 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl120])). 53.28/7.28 thf(zip_derived_cl138, plain, 53.28/7.28 (![X2 : a]: (~ ('#sk2' @ '#sk10' @ X2) | ('#form9') | ('#sk43' @ X2))), 53.28/7.28 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl120])). 53.28/7.28 thf(zip_derived_cl7301, plain, ($false), 53.28/7.28 inference('eprover', [status(thm)], 53.28/7.28 [zip_derived_cl296, zip_derived_cl298, zip_derived_cl35, 53.28/7.28 zip_derived_cl34, zip_derived_cl23, zip_derived_cl299, 53.28/7.28 zip_derived_cl301, zip_derived_cl303, zip_derived_cl304, 53.28/7.28 zip_derived_cl24, zip_derived_cl129, zip_derived_cl147, 53.28/7.28 zip_derived_cl146, zip_derived_cl50, zip_derived_cl127, 53.28/7.28 zip_derived_cl145, zip_derived_cl92, zip_derived_cl144, 53.28/7.28 zip_derived_cl116, zip_derived_cl214, zip_derived_cl215, 53.28/7.28 zip_derived_cl216, zip_derived_cl115, zip_derived_cl142, 53.28/7.28 zip_derived_cl143, zip_derived_cl91, zip_derived_cl85, 53.28/7.28 zip_derived_cl381, zip_derived_cl174, zip_derived_cl387, 53.28/7.28 zip_derived_cl384, zip_derived_cl386, zip_derived_cl382, 53.28/7.28 zip_derived_cl163, zip_derived_cl167, zip_derived_cl166, 53.28/7.28 zip_derived_cl175, zip_derived_cl177, zip_derived_cl178, 53.28/7.28 zip_derived_cl171, zip_derived_cl139, zip_derived_cl138])). 53.28/7.28 53.28/7.28 % SZS output end Refutation 53.28/7.28 53.28/7.28 53.28/7.28 % Terminating... 53.53/7.33 % Runner terminated. 53.53/7.34 % Zipperpin 1.5 exiting 53.53/7.35 EOF