0.10/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.m50tcFouGP true 0.13/0.34 % Computer : n024.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1440 0.13/0.34 % WCLimit : 180 0.13/0.34 % DateTime : Mon Jul 3 04:32:53 EDT 2023 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 1440 s 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.54/0.66 % Total configuration time : 828 0.54/0.66 % Estimated wc time : 1656 0.54/0.66 % Estimated cpu time (8 cpus) : 207.0 0.55/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.55/0.72 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.55/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.55/0.73 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 50.23/6.99 % Solved by lams/20_acsne_simpl.sh. 50.23/6.99 % done 735 iterations in 6.101s 50.23/6.99 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 50.23/6.99 % SZS output start Refutation 50.23/6.99 thf(a_type, type, a: $tType). 50.23/6.99 thf('#sk12_type', type, '#sk12': a). 50.23/6.99 thf('#sk20_type', type, '#sk20': a > $o). 50.23/6.99 thf('#form46_type', type, '#form46': $o). 50.23/6.99 thf('#sk16_type', type, '#sk16': a > $o). 50.23/6.99 thf('#sk6_type', type, '#sk6': a). 50.23/6.99 thf('#sk174_type', type, '#sk174': (a > $o) > a). 50.23/6.99 thf('#sk39_type', type, '#sk39': (a > $o) > a). 50.23/6.99 thf('#form82_type', type, '#form82': (a > $o) > $o). 50.23/6.99 thf('#sk73_type', type, '#sk73': (a > $o) > a). 50.23/6.99 thf('#form269_type', type, '#form269': (a > $o) > $o). 50.23/6.99 thf('#form168_type', type, '#form168': (a > $o) > $o). 50.23/6.99 thf('#sk275_type', type, '#sk275': (a > $o) > a). 50.23/6.99 thf('#sk5_type', type, '#sk5': a > $o). 50.23/6.99 thf('#sk4_type', type, '#sk4': a). 50.23/6.99 thf('#sk89_type', type, '#sk89': (a > $o) > a). 50.23/6.99 thf('#form139_type', type, '#form139': (a > $o) > $o). 50.23/6.99 thf('#sk270_type', type, '#sk270': (a > $o) > a). 50.23/6.99 thf('#sk140_type', type, '#sk140': (a > $o) > a). 50.23/6.99 thf('#sk61_type', type, '#sk61': (a > $o) > a). 50.23/6.99 thf('#form9_type', type, '#form9': $o). 50.23/6.99 thf('#sk169_type', type, '#sk169': (a > $o) > a). 50.23/6.99 thf('#form11_type', type, '#form11': $o). 50.23/6.99 thf('#sk8_type', type, '#sk8': a). 50.23/6.99 thf('#sk3_type', type, '#sk3': a). 50.23/6.99 thf('#sk7_type', type, '#sk7': a). 50.23/6.99 thf('#sk27_type', type, '#sk27': (a > $o) > a). 50.23/6.99 thf('#sk1_type', type, '#sk1': a > a > $o). 50.23/6.99 thf('#sk50_type', type, '#sk50': (a > $o) > a). 50.23/6.99 thf('#sk2_type', type, '#sk2': a > a > $o). 50.23/6.99 thf('#sk126_type', type, '#sk126': (a > $o) > a). 50.23/6.99 thf('#sk221_type', type, '#sk221': (a > $o) > a). 50.23/6.99 thf('#sk130_type', type, '#sk130': (a > $o) > a). 50.23/6.99 thf('#sk10_type', type, '#sk10': a). 50.23/6.99 thf('#sk83_type', type, '#sk83': (a > $o) > a). 50.23/6.99 thf(cTHM251D_pme, conjecture, 50.23/6.99 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 50.23/6.99 ( ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 50.23/6.99 ( ( ( ![Xq:( a > $o )]: 50.23/6.99 ( ( ( ![Xu:a,Xv:a]: 50.23/6.99 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & 50.23/6.99 ( Xq @ Xu ) ) => 50.23/6.99 ( Xq @ Xv ) ) ) & 50.23/6.99 ( ![Xw:a]: 50.23/6.99 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 50.23/6.99 ( Xq @ Xw ) ) ) ) => 50.23/6.99 ( Xq @ Xy0 ) ) ) & 50.23/6.99 ( ![Xq:( a > $o )]: 50.23/6.99 ( ( ( ![Xu:a,Xv:a]: 50.23/6.99 ( ( ( Xq @ Xu ) & 50.23/6.99 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 50.23/6.99 ( Xq @ Xv ) ) ) & 50.23/6.99 ( ![Xw:a]: 50.23/6.99 ( ( ( S @ Xy0 @ Xw ) | ( R @ Xy0 @ Xw ) ) => 50.23/6.99 ( Xq @ Xw ) ) ) ) => 50.23/6.99 ( Xq @ Xz ) ) ) ) => 50.23/6.99 ( ![Xq:( a > $o )]: 50.23/6.99 ( ( ( ![Xw:a]: 50.23/6.99 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => ( Xq @ Xw ) ) ) & 50.23/6.99 ( ![Xu:a,Xv:a]: 50.23/6.99 ( ( ( Xq @ Xu ) & ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 50.23/6.99 ( Xq @ Xv ) ) ) ) => 50.23/6.99 ( Xq @ Xz ) ) ) ) ) & 50.23/6.99 ( ![Xx0:a,Xy0:a]: 50.23/6.99 ( ( ( ![Xq:( a > $o )]: 50.23/6.99 ( ( ( ![Xu:a,Xv:a]: 50.23/6.99 ( ( ( Xq @ Xu ) & ( S @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) & 50.23/6.99 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 50.23/6.99 ( Xq @ Xy0 ) ) ) | 50.23/6.99 ( ![Xq:( a > $o )]: 50.23/6.99 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 50.23/6.99 ( ![Xu:a,Xv:a]: 50.23/6.99 ( ( ( Xq @ Xu ) & ( R @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) ) => 50.23/6.99 ( Xq @ Xy0 ) ) ) ) => 50.23/6.99 ( ![Xq:( a > $o )]: 50.23/6.99 ( ( ( ![Xu:a,Xv:a]: 50.23/6.99 ( ( ( Xq @ Xu ) & ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 50.23/6.99 ( Xq @ Xv ) ) ) & 50.23/6.99 ( ![Xw:a]: 50.23/6.99 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 50.23/6.99 ( Xq @ Xy0 ) ) ) ) ) ) => 50.23/6.99 ( ![Xq:( a > $o )]: 50.23/6.99 ( ( ( ![Xu:a,Xv:a]: 50.23/6.99 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 50.23/6.99 ( Xq @ Xv ) ) ) & 50.23/6.99 ( ![Xw:a]: 50.23/6.99 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 50.23/6.99 ( Xq @ Xy ) ) ) ) => 50.23/6.99 ( ![Xq:( a > $o )]: 50.23/6.99 ( ( ( ![Xw:a]: 50.23/6.99 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 50.23/6.99 ( ![Xu:a,Xv:a]: 50.23/6.99 ( ( ( Xq @ Xu ) & ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 50.23/6.99 ( Xq @ Xv ) ) ) ) => 50.23/6.99 ( Xq @ Xy ) ) ) ))). 50.23/6.99 thf(zf_stmt_0, negated_conjecture, 50.23/6.99 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 50.23/6.99 ( ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 50.23/6.99 ( ( ( ![Xq:( a > $o )]: 50.23/6.99 ( ( ( ![Xu:a,Xv:a]: 50.23/6.99 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & 50.23/6.99 ( Xq @ Xu ) ) => 50.23/6.99 ( Xq @ Xv ) ) ) & 50.23/6.99 ( ![Xw:a]: 50.23/6.99 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 50.23/6.99 ( Xq @ Xw ) ) ) ) => 50.23/6.99 ( Xq @ Xy0 ) ) ) & 50.23/6.99 ( ![Xq:( a > $o )]: 50.23/6.99 ( ( ( ![Xu:a,Xv:a]: 50.23/6.99 ( ( ( Xq @ Xu ) & 50.23/6.99 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 50.23/6.99 ( Xq @ Xv ) ) ) & 50.23/6.99 ( ![Xw:a]: 50.23/6.99 ( ( ( S @ Xy0 @ Xw ) | ( R @ Xy0 @ Xw ) ) => 50.23/6.99 ( Xq @ Xw ) ) ) ) => 50.23/6.99 ( Xq @ Xz ) ) ) ) => 50.23/6.99 ( ![Xq:( a > $o )]: 50.23/6.99 ( ( ( ![Xw:a]: 50.23/6.99 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 50.23/6.99 ( Xq @ Xw ) ) ) & 50.23/6.99 ( ![Xu:a,Xv:a]: 50.23/6.99 ( ( ( Xq @ Xu ) & 50.23/6.99 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 50.23/6.99 ( Xq @ Xv ) ) ) ) => 50.23/6.99 ( Xq @ Xz ) ) ) ) ) & 50.23/6.99 ( ![Xx0:a,Xy0:a]: 50.23/6.99 ( ( ( ![Xq:( a > $o )]: 50.23/6.99 ( ( ( ![Xu:a,Xv:a]: 50.23/6.99 ( ( ( Xq @ Xu ) & ( S @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) & 50.23/6.99 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 50.23/6.99 ( Xq @ Xy0 ) ) ) | 50.23/6.99 ( ![Xq:( a > $o )]: 50.23/6.99 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 50.23/6.99 ( ![Xu:a,Xv:a]: 50.23/6.99 ( ( ( Xq @ Xu ) & ( R @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) ) => 50.23/6.99 ( Xq @ Xy0 ) ) ) ) => 50.23/6.99 ( ![Xq:( a > $o )]: 50.23/6.99 ( ( ( ![Xu:a,Xv:a]: 50.23/6.99 ( ( ( Xq @ Xu ) & 50.23/6.99 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 50.23/6.99 ( Xq @ Xv ) ) ) & 50.23/6.99 ( ![Xw:a]: 50.23/6.99 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 50.23/6.99 ( Xq @ Xw ) ) ) ) => 50.23/6.99 ( Xq @ Xy0 ) ) ) ) ) ) => 50.23/6.99 ( ![Xq:( a > $o )]: 50.23/6.99 ( ( ( ![Xu:a,Xv:a]: 50.23/6.99 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 50.23/6.99 ( Xq @ Xv ) ) ) & 50.23/6.99 ( ![Xw:a]: 50.23/6.99 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 50.23/6.99 ( Xq @ Xy ) ) ) ) => 50.23/6.99 ( ![Xq:( a > $o )]: 50.23/6.99 ( ( ( ![Xw:a]: 50.23/6.99 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 50.23/6.99 ( ![Xu:a,Xv:a]: 50.23/6.99 ( ( ( Xq @ Xu ) & ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 50.23/6.99 ( Xq @ Xv ) ) ) ) => 50.23/6.99 ( Xq @ Xy ) ) ) ) )), 50.23/6.99 inference('cnf.neg', [status(esa)], [cTHM251D_pme])). 50.23/6.99 thf(zip_derived_cl0, plain, 50.23/6.99 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.23/6.99 (((!!) @ (^[Y1 : a > a > $o]: 50.23/6.99 (((!!) @ (^[Y2 : a]: 50.23/6.99 (((!!) @ (^[Y3 : a]: 50.23/6.99 (((((((((!!) @ ( 50.23/6.99 ^[Y4 : a]: 50.23/6.99 (((!!) @ ( 50.23/6.99 ^[Y5 : a]: 50.23/6.99 (( 50.23/6.99 (!!) @ ( 50.23/6.99 ^[Y6 : a]: 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (!!) @ ( 50.23/6.99 ^[Y7 : a > $o]: 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (!!) @ ( 50.23/6.99 ^[Y8 : a]: 50.23/6.99 (( 50.23/6.99 (!!) @ ( 50.23/6.99 ^[Y9 : a]: 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (Y0 @ 50.23/6.99 Y8 @ 50.23/6.99 Y9) | 50.23/6.99 (Y1 @ 50.23/6.99 Y8 @ Y9))) & 50.23/6.99 (Y7 @ Y8))) => 50.23/6.99 (Y7 @ Y9))))))))) & 50.23/6.99 (( 50.23/6.99 (!!) @ ( 50.23/6.99 ^[Y8 : a]: 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (Y1 @ 50.23/6.99 Y4 @ 50.23/6.99 Y8) | 50.23/6.99 (Y0 @ 50.23/6.99 Y4 @ Y8))) => 50.23/6.99 (Y7 @ Y8)))))))) => 50.23/6.99 (Y7 @ Y5)))))) & 50.23/6.99 (( 50.23/6.99 (!!) @ ( 50.23/6.99 ^[Y7 : a > $o]: 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (!!) @ ( 50.23/6.99 ^[Y8 : a]: 50.23/6.99 (( 50.23/6.99 (!!) @ ( 50.23/6.99 ^[Y9 : a]: 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (Y7 @ 50.23/6.99 Y8) & 50.23/6.99 (( 50.23/6.99 (Y0 @ 50.23/6.99 Y8 @ 50.23/6.99 Y9) | 50.23/6.99 (Y1 @ 50.23/6.99 Y8 @ Y9))))) => 50.23/6.99 (Y7 @ Y9))))))))) & 50.23/6.99 (( 50.23/6.99 (!!) @ ( 50.23/6.99 ^[Y8 : a]: 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (Y1 @ 50.23/6.99 Y5 @ 50.23/6.99 Y8) | 50.23/6.99 (Y0 @ 50.23/6.99 Y5 @ Y8))) => 50.23/6.99 (Y7 @ Y8)))))))) => 50.23/6.99 (Y7 @ Y6)))))))) => 50.23/6.99 (( 50.23/6.99 (!!) @ ( 50.23/6.99 ^[Y7 : a > $o]: 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (!!) @ ( 50.23/6.99 ^[Y8 : a]: 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (Y1 @ 50.23/6.99 Y4 @ 50.23/6.99 Y8) | 50.23/6.99 (Y0 @ 50.23/6.99 Y4 @ Y8))) => 50.23/6.99 (Y7 @ Y8)))))) & 50.23/6.99 (( 50.23/6.99 (!!) @ ( 50.23/6.99 ^[Y8 : a]: 50.23/6.99 (( 50.23/6.99 (!!) @ ( 50.23/6.99 ^[Y9 : a]: 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (Y7 @ 50.23/6.99 Y8) & 50.23/6.99 (( 50.23/6.99 (Y0 @ 50.23/6.99 Y8 @ 50.23/6.99 Y9) | 50.23/6.99 (Y1 @ 50.23/6.99 Y8 @ Y9))))) => 50.23/6.99 (Y7 @ Y9))))))))))) => 50.23/6.99 (Y7 @ Y6))))))))))))))))) & 50.23/6.99 (((!!) @ ( 50.23/6.99 ^[Y4 : a]: 50.23/6.99 (((!!) @ ( 50.23/6.99 ^[Y5 : a]: 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (!!) @ ( 50.23/6.99 ^[Y6 : a > $o]: 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (( 50.23/6.99 (!!) @ ( 50.23/6.99 ^[Y7 : a]: 50.23/6.99 (( 50.23/6.99 (!!) @ ( 50.23/7.00 ^[Y8 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y6 @ 50.23/7.00 Y7) & 50.23/7.00 (Y1 @ 50.23/7.00 Y7 @ Y8))) => 50.23/7.00 (Y6 @ Y8))))))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y7 : a]: 50.23/7.00 (( 50.23/7.00 (Y1 @ 50.23/7.00 Y4 @ 50.23/7.00 Y7) => 50.23/7.00 (Y6 @ Y7)))))))) => 50.23/7.00 (Y6 @ Y5)))))) | 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y7 : a]: 50.23/7.00 (( 50.23/7.00 (Y0 @ 50.23/7.00 Y4 @ 50.23/7.00 Y7) => 50.23/7.00 (Y6 @ Y7)))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y7 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y8 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y6 @ 50.23/7.00 Y7) & 50.23/7.00 (Y0 @ 50.23/7.00 Y7 @ Y8))) => 50.23/7.00 (Y6 @ Y8))))))))))) => 50.23/7.00 (Y6 @ Y5)))))))) => 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y7 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y8 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y6 @ 50.23/7.00 Y7) & 50.23/7.00 (( 50.23/7.00 (Y0 @ 50.23/7.00 Y7 @ 50.23/7.00 Y8) | 50.23/7.00 (Y1 @ 50.23/7.00 Y7 @ Y8))))) => 50.23/7.00 (Y6 @ Y8))))))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y7 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y0 @ 50.23/7.00 Y4 @ 50.23/7.00 Y7) | 50.23/7.00 (Y1 @ 50.23/7.00 Y4 @ Y7))) => 50.23/7.00 (Y6 @ Y7)))))))) => 50.23/7.00 (Y6 @ Y5)))))))))))))))) => 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a > $o]: 50.23/7.00 (((((( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y1 @ 50.23/7.00 Y5 @ 50.23/7.00 Y6) | 50.23/7.00 (Y0 @ 50.23/7.00 Y5 @ Y6))) & 50.23/7.00 (Y4 @ Y5))) => 50.23/7.00 (Y4 @ Y6))))))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y1 @ 50.23/7.00 Y2 @ 50.23/7.00 Y5) | 50.23/7.00 (Y0 @ 50.23/7.00 Y2 @ Y5))) => 50.23/7.00 (Y4 @ Y5)))))))) => 50.23/7.00 (Y4 @ Y3)))))))) => 50.23/7.00 (((!!) @ (^[Y4 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y0 @ 50.23/7.00 Y2 @ 50.23/7.00 Y5) | 50.23/7.00 (Y1 @ 50.23/7.00 Y2 @ Y5))) => 50.23/7.00 (Y4 @ Y5)))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y4 @ 50.23/7.00 Y5) & 50.23/7.00 (( 50.23/7.00 (Y0 @ 50.23/7.00 Y5 @ 50.23/7.00 Y6) | 50.23/7.00 (Y1 @ 50.23/7.00 Y5 @ Y6))))) => 50.23/7.00 (Y4 @ Y6))))))))))) => 50.23/7.00 (Y4 @ Y3))))))))))))))))))))), 50.23/7.00 inference('cnf', [status(esa)], [zf_stmt_0])). 50.23/7.00 thf(zip_derived_cl1, plain, 50.23/7.00 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y7 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y8 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y7 @ 50.23/7.00 Y8) | 50.23/7.00 (Y0 @ 50.23/7.00 Y7 @ Y8))) & 50.23/7.00 (Y6 @ Y7))) => 50.23/7.00 (Y6 @ Y8))))))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y7 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y0 @ 50.23/7.00 Y3 @ 50.23/7.00 Y7) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y7))) => 50.23/7.00 (Y6 @ Y7)))))))) => 50.23/7.00 (Y6 @ Y4)))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y7 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y8 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y6 @ 50.23/7.00 Y7) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y7 @ 50.23/7.00 Y8) | 50.23/7.00 (Y0 @ 50.23/7.00 Y7 @ Y8))))) => 50.23/7.00 (Y6 @ Y8))))))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y7 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y0 @ 50.23/7.00 Y4 @ 50.23/7.00 Y7) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y4 @ Y7))) => 50.23/7.00 (Y6 @ Y7)))))))) => 50.23/7.00 (Y6 @ Y5)))))))) => 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y7 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y0 @ 50.23/7.00 Y3 @ 50.23/7.00 Y7) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y7))) => 50.23/7.00 (Y6 @ Y7)))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y7 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y8 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y6 @ 50.23/7.00 Y7) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y7 @ 50.23/7.00 Y8) | 50.23/7.00 (Y0 @ 50.23/7.00 Y7 @ Y8))))) => 50.23/7.00 (Y6 @ Y8))))))))))) => 50.23/7.00 (Y6 @ Y5))))))))))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (((( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y7 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y5 @ 50.23/7.00 Y6) & 50.23/7.00 (Y0 @ 50.23/7.00 Y6 @ Y7))) => 50.23/7.00 (Y5 @ Y7))))))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (Y0 @ 50.23/7.00 Y3 @ 50.23/7.00 Y6) => 50.23/7.00 (Y5 @ Y6)))))))) => 50.23/7.00 (Y5 @ Y4)))))) | 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y6) => 50.23/7.00 (Y5 @ Y6)))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y7 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y5 @ 50.23/7.00 Y6) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y6 @ Y7))) => 50.23/7.00 (Y5 @ Y7))))))))))) => 50.23/7.00 (Y5 @ Y4)))))))) => 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y7 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y5 @ 50.23/7.00 Y6) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y6 @ 50.23/7.00 Y7) | 50.23/7.00 (Y0 @ 50.23/7.00 Y6 @ Y7))))) => 50.23/7.00 (Y5 @ Y7))))))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y6) | 50.23/7.00 (Y0 @ 50.23/7.00 Y3 @ Y6))) => 50.23/7.00 (Y5 @ Y6)))))))) => 50.23/7.00 (Y5 @ Y4)))))))))))))))) => 50.23/7.00 (((!!) @ (^[Y3 : a > $o]: 50.23/7.00 (((((((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y0 @ 50.23/7.00 Y4 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y4 @ Y5))) & 50.23/7.00 (Y3 @ Y4))) => 50.23/7.00 (Y3 @ Y5))))))))) & 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y0 @ 50.23/7.00 Y1 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y1 @ Y4))) => 50.23/7.00 (Y3 @ Y4)))))))) => 50.23/7.00 (Y3 @ Y2)))))))) => 50.23/7.00 (((!!) @ (^[Y3 : a > $o]: 50.23/7.00 (((((((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (((( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y1 @ Y4) | 50.23/7.00 (Y0 @ 50.23/7.00 Y1 @ Y4))) => 50.23/7.00 (Y3 @ Y4)))))) & 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y3 @ 50.23/7.00 Y4) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y4 @ 50.23/7.00 Y5) | 50.23/7.00 (Y0 @ 50.23/7.00 Y4 @ Y5))))) => 50.23/7.00 (Y3 @ Y5))))))))))) => 50.23/7.00 (Y3 @ Y2)))))))))))))))))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 50.23/7.00 thf(zip_derived_cl2, plain, 50.23/7.00 (~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((((!!) @ (^[Y2 : a]: 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (((( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y7 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y6 @ 50.23/7.00 Y7) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y6 @ Y7))) & 50.23/7.00 (Y5 @ Y6))) => 50.23/7.00 (Y5 @ Y7))))))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y2 @ 50.23/7.00 Y6) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y2 @ Y6))) => 50.23/7.00 (Y5 @ Y6)))))))) => 50.23/7.00 (Y5 @ Y3)))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y7 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y5 @ 50.23/7.00 Y6) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y6 @ 50.23/7.00 Y7) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y6 @ Y7))))) => 50.23/7.00 (Y5 @ Y7))))))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ 50.23/7.00 Y6) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y6))) => 50.23/7.00 (Y5 @ Y6)))))))) => 50.23/7.00 (Y5 @ Y4)))))))) => 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y2 @ 50.23/7.00 Y6) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y2 @ Y6))) => 50.23/7.00 (Y5 @ Y6)))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y7 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y5 @ 50.23/7.00 Y6) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y6 @ 50.23/7.00 Y7) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y6 @ Y7))))) => 50.23/7.00 (Y5 @ Y7))))))))))) => 50.23/7.00 (Y5 @ Y4))))))))))))))))) & 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((((((!!) @ ( 50.23/7.00 ^[Y4 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y4 @ 50.23/7.00 Y5) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y5 @ Y6))) => 50.23/7.00 (Y4 @ Y6))))))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y2 @ 50.23/7.00 Y5) => 50.23/7.00 (Y4 @ Y5)))))))) => 50.23/7.00 (Y4 @ Y3)))))) | 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y2 @ 50.23/7.00 Y5) => 50.23/7.00 (Y4 @ Y5)))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y4 @ 50.23/7.00 Y5) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y5 @ Y6))) => 50.23/7.00 (Y4 @ Y6))))))))))) => 50.23/7.00 (Y4 @ Y3)))))))) => 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y4 @ 50.23/7.00 Y5) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y5 @ 50.23/7.00 Y6) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y5 @ Y6))))) => 50.23/7.00 (Y4 @ Y6))))))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y2 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y2 @ Y5))) => 50.23/7.00 (Y4 @ Y5)))))))) => 50.23/7.00 (Y4 @ Y3)))))))))))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) & 50.23/7.00 (Y2 @ Y3))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk2' @ 50.23/7.00 Y0 @ Y3) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (((( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1))))))))))))))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 50.23/7.00 thf(zip_derived_cl3, plain, 50.23/7.00 (~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((((((!!) @ ( 50.23/7.00 ^[Y4 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y5 @ 50.23/7.00 Y6) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y5 @ Y6))) & 50.23/7.00 (Y4 @ Y5))) => 50.23/7.00 (Y4 @ Y6))))))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y1 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y1 @ Y5))) => 50.23/7.00 (Y4 @ Y5)))))))) => 50.23/7.00 (Y4 @ Y2)))))) & 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y4 @ 50.23/7.00 Y5) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y5 @ 50.23/7.00 Y6) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y5 @ Y6))))) => 50.23/7.00 (Y4 @ Y6))))))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y2 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y2 @ Y5))) => 50.23/7.00 (Y4 @ Y5)))))))) => 50.23/7.00 (Y4 @ Y3)))))))) => 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a > $o]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y1 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y1 @ Y5))) => 50.23/7.00 (Y4 @ Y5)))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y6 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y4 @ 50.23/7.00 Y5) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y5 @ 50.23/7.00 Y6) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y5 @ Y6))))) => 50.23/7.00 (Y4 @ Y6))))))))))) => 50.23/7.00 (Y4 @ Y3))))))))))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((((!!) @ (^[Y3 : a > $o]: 50.23/7.00 (((( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y3 @ 50.23/7.00 Y4) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y4 @ Y5))) => 50.23/7.00 (Y3 @ Y5))))))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y1 @ 50.23/7.00 Y4) => 50.23/7.00 (Y3 @ Y4)))))))) => 50.23/7.00 (Y3 @ Y2)))))) | 50.23/7.00 (((!!) @ (^[Y3 : a > $o]: 50.23/7.00 (((( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y1 @ 50.23/7.00 Y4) => 50.23/7.00 (Y3 @ Y4)))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y3 @ 50.23/7.00 Y4) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y4 @ Y5))) => 50.23/7.00 (Y3 @ Y5))))))))))) => 50.23/7.00 (Y3 @ Y2)))))))) => 50.23/7.00 (((!!) @ (^[Y3 : a > $o]: 50.23/7.00 (((((( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y3 @ 50.23/7.00 Y4) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y4 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y4 @ Y5))))) => 50.23/7.00 (Y3 @ Y5))))))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y1 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y1 @ Y4))) => 50.23/7.00 (Y3 @ Y4)))))))) => 50.23/7.00 (Y3 @ Y2)))))))))))))))) => 50.23/7.00 (((!!) @ (^[Y1 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y2 : a]: 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((((( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y2 @ Y3) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y2 @ Y3))) & 50.23/7.00 (Y1 @ Y2))) => 50.23/7.00 (Y1 @ Y3))))))))) & 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ 50.23/7.00 Y2) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y2))) => 50.23/7.00 (Y1 @ Y2)))))))) => 50.23/7.00 (Y1 @ Y0)))))))) => 50.23/7.00 (((!!) @ (^[Y1 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y2 : a]: 50.23/7.00 ((((('#sk1' @ '#sk3' @ Y2) | 50.23/7.00 ('#sk2' @ '#sk3' @ Y2))) => 50.23/7.00 (Y1 @ Y2)))))) & 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((((Y1 @ Y2) & 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y2 @ Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y2 @ Y3))))) => 50.23/7.00 (Y1 @ Y3))))))))))) => 50.23/7.00 (Y1 @ Y0)))))))))))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 50.23/7.00 thf(zip_derived_cl4, plain, 50.23/7.00 (~ (((((((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((((!!) @ (^[Y3 : a > $o]: 50.23/7.00 (((( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y4 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y4 @ Y5))) & 50.23/7.00 (Y3 @ Y4))) => 50.23/7.00 (Y3 @ Y5))))))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y0 @ Y4))) => 50.23/7.00 (Y3 @ Y4)))))))) => 50.23/7.00 (Y3 @ Y1)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a > $o]: 50.23/7.00 (((( 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y3 @ 50.23/7.00 Y4) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y4 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y4 @ Y5))))) => 50.23/7.00 (Y3 @ Y5))))))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y1 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y1 @ Y4))) => 50.23/7.00 (Y3 @ Y4)))))))) => 50.23/7.00 (Y3 @ Y2)))))))) => 50.23/7.00 (((!!) @ (^[Y3 : a > $o]: 50.23/7.00 (((((( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y0 @ Y4))) => 50.23/7.00 (Y3 @ Y4)))))) & 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y3 @ 50.23/7.00 Y4) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y4 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y4 @ Y5))))) => 50.23/7.00 (Y3 @ Y5))))))))))) => 50.23/7.00 (Y3 @ Y2))))))))))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))))) => 50.23/7.00 (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | 50.23/7.00 ('#sk1' @ '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4')))))))) => 50.23/7.00 (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((Y0 @ Y1) & 50.23/7.00 ((('#sk1' @ Y1 @ Y2) | 50.23/7.00 ('#sk2' @ Y1 @ Y2))))) => 50.23/7.00 (Y0 @ Y2))))))))))) => 50.23/7.00 (Y0 @ '#sk4'))))))))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 50.23/7.00 thf(zip_derived_cl6, plain, 50.23/7.00 (~ (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((Y0 @ Y1) & 50.23/7.00 ((('#sk1' @ Y1 @ Y2) | 50.23/7.00 ('#sk2' @ Y1 @ Y2))))) => 50.23/7.00 (Y0 @ Y2))))))))))) => 50.23/7.00 (Y0 @ '#sk4'))))))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 50.23/7.00 thf(zip_derived_cl8, plain, 50.23/7.00 (~ (((((((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 50.23/7.00 ('#sk5' @ Y0)))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk5' @ Y0) & 50.23/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.23/7.00 Y1))))) => 50.23/7.00 ('#sk5' @ Y1))))))))))) => 50.23/7.00 ('#sk5' @ '#sk4')))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 50.23/7.00 thf(zip_derived_cl10, plain, 50.23/7.00 ( (((((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 50.23/7.00 ('#sk5' @ Y0)))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk5' @ Y0) & 50.23/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 50.23/7.00 ('#sk5' @ Y1)))))))))))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 50.23/7.00 thf(zip_derived_cl14, plain, 50.23/7.00 ( (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk5' @ Y0) & 50.23/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 50.23/7.00 ('#sk5' @ Y1)))))))))), 50.23/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 50.23/7.00 thf(zip_derived_cl17, plain, 50.23/7.00 (![X2 : a]: 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk5' @ X2) & 50.23/7.00 ((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))))) => 50.23/7.00 ('#sk5' @ Y0))))))), 50.23/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 50.23/7.00 thf(zip_derived_cl20, plain, 50.23/7.00 (![X2 : a, X4 : a]: 50.23/7.00 ((((('#sk5' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) => 50.23/7.00 ('#sk5' @ X4)))), 50.23/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 50.23/7.00 thf(zip_derived_cl25, plain, 50.23/7.00 (![X2 : a, X4 : a]: 50.23/7.00 (~ ((('#sk5' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) 50.23/7.00 | ('#sk5' @ X4))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 50.23/7.00 thf(zip_derived_cl31, plain, 50.23/7.00 (![X2 : a, X4 : a]: 50.23/7.00 (~ ('#sk5' @ X2) 50.23/7.00 | ~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 50.23/7.00 | ('#sk5' @ X4))), 50.23/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl25])). 50.23/7.00 thf(zip_derived_cl39, plain, 50.23/7.00 (![X2 : a, X4 : a]: 50.23/7.00 (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 50.23/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 50.23/7.00 thf(zip_derived_cl40, plain, 50.23/7.00 (![X2 : a, X4 : a]: 50.23/7.00 (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 50.23/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 50.23/7.00 thf(zip_derived_cl5, plain, 50.23/7.00 ( (((((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((((!!) @ (^[Y3 : a > $o]: 50.23/7.00 (((((((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y4 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y4 @ Y5))) & 50.23/7.00 (Y3 @ Y4))) => 50.23/7.00 (Y3 @ Y5))))))))) & 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y0 @ Y4))) => 50.23/7.00 (Y3 @ Y4)))))))) => 50.23/7.00 (Y3 @ Y1)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a > $o]: 50.23/7.00 (((((((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y3 @ 50.23/7.00 Y4) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y4 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y4 @ Y5))))) => 50.23/7.00 (Y3 @ Y5))))))))) & 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y1 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y1 @ Y4))) => 50.23/7.00 (Y3 @ Y4)))))))) => 50.23/7.00 (Y3 @ Y2)))))))) => 50.23/7.00 (((!!) @ (^[Y3 : a > $o]: 50.23/7.00 (((((((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y0 @ Y4))) => 50.23/7.00 (Y3 @ Y4)))))) & 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y3 @ 50.23/7.00 Y4) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y4 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y4 @ Y5))))) => 50.23/7.00 (Y3 @ Y5))))))))))) => 50.23/7.00 (Y3 @ Y2))))))))))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))))) => 50.23/7.00 (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4'))))))))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 50.23/7.00 thf(zip_derived_cl7, plain, 50.23/7.00 ((~ (((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((((!!) @ (^[Y3 : a > $o]: 50.23/7.00 (((((((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y4 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y4 @ Y5))) & 50.23/7.00 (Y3 @ Y4))) => 50.23/7.00 (Y3 @ Y5))))))))) & 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y0 @ Y4))) => 50.23/7.00 (Y3 @ Y4)))))))) => 50.23/7.00 (Y3 @ Y1)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a > $o]: 50.23/7.00 (((((((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y3 @ 50.23/7.00 Y4) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y4 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y4 @ Y5))))) => 50.23/7.00 (Y3 @ Y5))))))))) & 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y1 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y1 @ Y4))) => 50.23/7.00 (Y3 @ Y4)))))))) => 50.23/7.00 (Y3 @ Y2)))))))) => 50.23/7.00 (((!!) @ (^[Y3 : a > $o]: 50.23/7.00 (((((((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y0 @ Y4))) => 50.23/7.00 (Y3 @ Y4)))))) & 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y3 @ 50.23/7.00 Y4) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y4 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y4 @ Y5))))) => 50.23/7.00 (Y3 @ Y5))))))))))) => 50.23/7.00 (Y3 @ Y2))))))))))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))))) 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4')))))))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 50.23/7.00 thf(zip_derived_cl9, plain, 50.23/7.00 ((~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((((!!) @ (^[Y3 : a > $o]: 50.23/7.00 (((((((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y4 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y4 @ Y5))) & 50.23/7.00 (Y3 @ Y4))) => 50.23/7.00 (Y3 @ Y5))))))))) & 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y0 @ Y4))) => 50.23/7.00 (Y3 @ Y4)))))))) => 50.23/7.00 (Y3 @ Y1)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a > $o]: 50.23/7.00 (((((((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y3 @ 50.23/7.00 Y4) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y4 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y4 @ Y5))))) => 50.23/7.00 (Y3 @ Y5))))))))) & 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y1 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y1 @ Y4))) => 50.23/7.00 (Y3 @ Y4)))))))) => 50.23/7.00 (Y3 @ Y2)))))))) => 50.23/7.00 (((!!) @ (^[Y3 : a > $o]: 50.23/7.00 (((((((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (((( 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y0 @ Y4))) => 50.23/7.00 (Y3 @ Y4)))))) & 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y5 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y3 @ 50.23/7.00 Y4) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y4 @ 50.23/7.00 Y5) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y4 @ Y5))))) => 50.23/7.00 (Y3 @ Y5))))))))))) => 50.23/7.00 (Y3 @ Y2))))))))))))))))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))) 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4')))))))), 50.23/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl7])). 50.23/7.00 thf(zip_derived_cl12, plain, 50.23/7.00 ((~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) & 50.23/7.00 (Y2 @ Y3))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk2' @ 50.23/7.00 '#sk6' @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk1' @ 50.23/7.00 '#sk6' @ 50.23/7.00 Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y0)))))) & 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk1' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk2' @ 50.23/7.00 '#sk6' @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk1' @ 50.23/7.00 '#sk6' @ 50.23/7.00 Y3))) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (((( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))) 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4')))))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl9])). 50.23/7.00 thf(zip_derived_cl15, plain, 50.23/7.00 ((~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((((((!!) @ (^[Y1 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y2 : a]: 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((((( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y2 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y2 @ Y3))) & 50.23/7.00 (Y1 @ Y2))) => 50.23/7.00 (Y1 @ Y3))))))))) & 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ 50.23/7.00 Y2) | ('#sk1' @ 50.23/7.00 '#sk6' @ Y2))) => 50.23/7.00 (Y1 @ Y2)))))))) => 50.23/7.00 (Y1 @ '#sk7')))))) & 50.23/7.00 (((!!) @ (^[Y1 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y2 : a]: 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((((Y1 @ 50.23/7.00 Y2) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y2 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y2 @ Y3))))) => 50.23/7.00 (Y1 @ Y3))))))))) & 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ 50.23/7.00 Y2) | ('#sk1' @ 50.23/7.00 '#sk7' @ Y2))) => 50.23/7.00 (Y1 @ Y2)))))))) => 50.23/7.00 (Y1 @ Y0)))))))) => 50.23/7.00 (((!!) @ (^[Y1 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y2 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ 50.23/7.00 Y2) | ('#sk1' @ 50.23/7.00 '#sk6' @ Y2))) => 50.23/7.00 (Y1 @ Y2)))))) & 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((((Y1 @ Y2) & 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y2 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y2 @ Y3))))) => 50.23/7.00 (Y1 @ Y3))))))))))) => 50.23/7.00 (Y1 @ Y0))))))))))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))) 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4')))))))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 50.23/7.00 thf(zip_derived_cl18, plain, 50.23/7.00 ((~ (((((((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk1' @ Y1 @ 50.23/7.00 Y2) | ('#sk2' @ 50.23/7.00 Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y1) | 50.23/7.00 ('#sk1' @ '#sk6' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk7')))))) & 50.23/7.00 (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((Y0 @ Y1) & 50.23/7.00 ((('#sk1' @ Y1 @ 50.23/7.00 Y2) | ('#sk2' @ 50.23/7.00 Y1 @ Y2))))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y1) | 50.23/7.00 ('#sk1' @ '#sk7' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk8')))))))) => 50.23/7.00 (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk6' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((Y0 @ Y1) & 50.23/7.00 ((('#sk1' @ Y1 @ Y2) | 50.23/7.00 ('#sk2' @ Y1 @ Y2))))) => 50.23/7.00 (Y0 @ Y2))))))))))) => 50.23/7.00 (Y0 @ '#sk8')))))))) 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4')))))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])). 50.23/7.00 thf(zip_derived_cl21, plain, 50.23/7.00 (( (((((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk1' @ Y1 @ Y2) | 50.23/7.00 ('#sk2' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk6' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk7')))))) & 50.23/7.00 (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((Y0 @ Y1) & 50.23/7.00 ((('#sk1' @ Y1 @ Y2) | 50.23/7.00 ('#sk2' @ Y1 @ Y2))))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk7' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk8')))))))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))) 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4')))))))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 50.23/7.00 thf(zip_derived_cl26, plain, 50.23/7.00 (( (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk1' @ Y1 @ Y2) | 50.23/7.00 ('#sk2' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk6' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk7')))))) 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4')))))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))))), 50.23/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 50.23/7.00 thf(zip_derived_cl32, plain, 50.23/7.00 ((~ ('#form11') 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4')))))))), 50.23/7.00 define([status(thm)])). 50.23/7.00 thf(zip_derived_cl33, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 ( (((((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.23/7.00 Y0 @ Y1))) & 50.23/7.00 (X2 @ Y0))) => 50.23/7.00 (X2 @ Y1))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))) => 50.23/7.00 (X2 @ '#sk4'))) 50.23/7.00 | ~ ('#form11'))), 50.23/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 50.23/7.00 thf(zip_derived_cl34, plain, 50.23/7.00 (( (((((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.23/7.00 Y1))) & 50.23/7.00 ('#sk5' @ Y0))) => 50.23/7.00 ('#sk5' @ Y1))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.23/7.00 ('#sk5' @ Y0)))))))) => 50.23/7.00 ('#sk5' @ '#sk4'))) 50.23/7.00 | ~ ('#form11'))), 50.23/7.00 inference('triggered_bool_instantiation', [status(thm)], 50.23/7.00 [zip_derived_cl33])). 50.23/7.00 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk4')), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 50.23/7.00 thf(zip_derived_cl204, plain, 50.23/7.00 (( (((((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.23/7.00 Y1))) & 50.23/7.00 ('#sk5' @ Y0))) => 50.23/7.00 ('#sk5' @ Y1))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.23/7.00 ('#sk5' @ Y0)))))))) => 50.23/7.00 ($false))) 50.23/7.00 | ~ ('#form11'))), 50.23/7.00 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl11])). 50.23/7.00 thf(zip_derived_cl205, plain, 50.23/7.00 (( (((~) @ (((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((((('#sk2' @ Y0 @ Y1) | 50.23/7.00 ('#sk1' @ Y0 @ Y1))) & 50.23/7.00 ('#sk5' @ Y0))) => 50.23/7.00 ('#sk5' @ Y1))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ 50.23/7.00 Y0))) => 50.23/7.00 ('#sk5' @ Y0)))))))))) 50.23/7.00 | ~ ('#form11'))), 50.23/7.00 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl204])). 50.23/7.00 thf(zip_derived_cl206, plain, 50.23/7.00 ((~ (((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.23/7.00 Y1))) & 50.23/7.00 ('#sk5' @ Y0))) => 50.23/7.00 ('#sk5' @ Y1))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.23/7.00 ('#sk5' @ Y0)))))))) 50.23/7.00 | ~ ('#form11'))), 50.23/7.00 inference('simplify nested equalities', [status(thm)], 50.23/7.00 [zip_derived_cl205])). 50.23/7.00 thf(zip_derived_cl207, plain, 50.23/7.00 ((~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 50.23/7.00 ('#sk5' @ Y0))) => 50.23/7.00 ('#sk5' @ Y1))))))))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.23/7.00 ('#sk5' @ Y0)))))) 50.23/7.00 | ~ ('#form11'))), 50.23/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl206])). 50.23/7.00 thf(zip_derived_cl33, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 ( (((((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.23/7.00 Y0 @ Y1))) & 50.23/7.00 (X2 @ Y0))) => 50.23/7.00 (X2 @ Y1))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))) => 50.23/7.00 (X2 @ '#sk4'))) 50.23/7.00 | ~ ('#form11'))), 50.23/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 50.23/7.00 thf(zip_derived_cl42, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ (((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.23/7.00 Y0 @ Y1))) & 50.23/7.00 (X2 @ Y0))) => 50.23/7.00 (X2 @ Y1))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))) 50.23/7.00 | (X2 @ '#sk4') 50.23/7.00 | ~ ('#form11'))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])). 50.23/7.00 thf(zip_derived_cl51, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.23/7.00 Y1))) & 50.23/7.00 (X2 @ Y0))) => 50.23/7.00 (X2 @ Y1))))))))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))) 50.23/7.00 | ~ ('#form11') 50.23/7.00 | (X2 @ '#sk4'))), 50.23/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl42])). 50.23/7.00 thf(zip_derived_cl63, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((((('#sk2' @ ('#sk27' @ X2) @ Y0) | ('#sk1' @ 50.23/7.00 ('#sk27' @ X2) @ Y0))) & 50.23/7.00 (X2 @ ('#sk27' @ X2)))) => 50.23/7.00 (X2 @ Y0)))))) 50.23/7.00 | (X2 @ '#sk4') 50.23/7.00 | ~ ('#form11') 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl51])). 50.23/7.00 thf(zip_derived_cl74, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ ((((((('#sk2' @ ('#sk27' @ X2) @ ('#sk39' @ X2)) | ('#sk1' @ 50.23/7.00 ('#sk27' @ X2) @ ('#sk39' @ X2)))) & 50.23/7.00 (X2 @ ('#sk27' @ X2)))) => 50.23/7.00 (X2 @ ('#sk39' @ X2)))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))) 50.23/7.00 | ~ ('#form11') 50.23/7.00 | (X2 @ '#sk4'))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl63])). 50.23/7.00 thf(zip_derived_cl88, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ (X2 @ ('#sk39' @ X2)) 50.23/7.00 | (X2 @ '#sk4') 50.23/7.00 | ~ ('#form11') 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])). 50.23/7.00 thf(zip_derived_cl99, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 ( ('#form82' @ X2) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))), 50.23/7.00 define([status(thm)])). 50.23/7.00 thf(zip_derived_cl208, plain, 50.23/7.00 ((~ ('#form82' @ '#sk5') 50.23/7.00 | ~ ('#form11') 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.23/7.00 Y1))) & 50.23/7.00 ('#sk5' @ Y0))) => 50.23/7.00 ('#sk5' @ Y1))))))))))), 50.23/7.00 inference('renaming', [status(thm)], 50.23/7.00 [zip_derived_cl207, zip_derived_cl99])). 50.23/7.00 thf(zip_derived_cl209, plain, 50.23/7.00 ((~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((((('#sk2' @ ('#sk27' @ '#sk5') @ Y0) | ('#sk1' @ 50.23/7.00 ('#sk27' @ '#sk5') @ Y0))) & 50.23/7.00 ('#sk5' @ ('#sk27' @ '#sk5')))) => 50.23/7.00 ('#sk5' @ Y0)))))) 50.23/7.00 | ~ ('#form11') 50.23/7.00 | ~ ('#form82' @ '#sk5'))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl208])). 50.23/7.00 thf(zip_derived_cl210, plain, 50.23/7.00 ((~ ((((((('#sk2' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) | ('#sk1' @ 50.23/7.00 ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')))) & 50.23/7.00 ('#sk5' @ ('#sk27' @ '#sk5')))) => 50.23/7.00 ('#sk5' @ ('#sk39' @ '#sk5')))) 50.23/7.00 | ~ ('#form82' @ '#sk5') 50.23/7.00 | ~ ('#form11'))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl209])). 50.23/7.00 thf(zip_derived_cl212, plain, 50.23/7.00 ((~ ('#sk5' @ ('#sk39' @ '#sk5')) 50.23/7.00 | ~ ('#form11') 50.23/7.00 | ~ ('#form82' @ '#sk5'))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl210])). 50.23/7.00 thf(zip_derived_cl211, plain, 50.23/7.00 (( ((((('#sk2' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) | ('#sk1' @ 50.23/7.00 ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')))) & 50.23/7.00 ('#sk5' @ ('#sk27' @ '#sk5')))) 50.23/7.00 | ~ ('#form11') 50.23/7.00 | ~ ('#form82' @ '#sk5'))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl210])). 50.23/7.00 thf(zip_derived_cl214, plain, 50.23/7.00 (( ('#sk5' @ ('#sk27' @ '#sk5')) | ~ ('#form82' @ '#sk5') | ~ ('#form11'))), 50.23/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl211])). 50.23/7.00 thf(zip_derived_cl213, plain, 50.23/7.00 (( ((('#sk2' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) | ('#sk1' @ 50.23/7.00 ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')))) 50.23/7.00 | ~ ('#form82' @ '#sk5') 50.23/7.00 | ~ ('#form11'))), 50.23/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl211])). 50.23/7.00 thf(zip_derived_cl215, plain, 50.23/7.00 (( ('#sk2' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) 50.23/7.00 | ('#sk1' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) 50.23/7.00 | ~ ('#form11') 50.23/7.00 | ~ ('#form82' @ '#sk5'))), 50.23/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl213])). 50.23/7.00 thf(zip_derived_cl27, plain, 50.23/7.00 (( (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((Y0 @ Y1) & 50.23/7.00 ((('#sk1' @ Y1 @ Y2) | 50.23/7.00 ('#sk2' @ Y1 @ Y2))))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk7' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk8')))))) 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4')))))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))))), 50.23/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 50.23/7.00 thf(zip_derived_cl32, plain, 50.23/7.00 ((~ ('#form11') 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4')))))))), 50.23/7.00 define([status(thm)])). 50.23/7.00 thf(zip_derived_cl36, plain, 50.23/7.00 (( ('#form11') 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))) 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((Y0 @ Y1) & 50.23/7.00 ((('#sk1' @ Y1 @ Y2) | 50.23/7.00 ('#sk2' @ Y1 @ Y2))))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk7' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk8')))))))), 50.23/7.00 inference('renaming', [status(thm)], [zip_derived_cl27, zip_derived_cl32])). 50.23/7.00 thf(zip_derived_cl22, plain, 50.23/7.00 ((~ (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk6' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((Y0 @ Y1) & 50.23/7.00 ((('#sk1' @ Y1 @ Y2) | 50.23/7.00 ('#sk2' @ Y1 @ Y2))))) => 50.23/7.00 (Y0 @ Y2))))))))))) => 50.23/7.00 (Y0 @ '#sk8')))))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))) 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4')))))))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 50.23/7.00 thf(zip_derived_cl28, plain, 50.23/7.00 (( ('#form9') 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))))), 50.23/7.00 define([status(thm)])). 50.23/7.00 thf(zip_derived_cl43, plain, 50.23/7.00 ((~ ('#form9') 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((Y0 @ Y1) & 50.23/7.00 ((('#sk1' @ Y1 @ Y2) | 50.23/7.00 ('#sk2' @ Y1 @ Y2))))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk7' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk8')))))) 50.23/7.00 | ('#form11'))), 50.23/7.00 inference('renaming', [status(thm)], [zip_derived_cl36, zip_derived_cl28])). 50.23/7.00 thf(zip_derived_cl52, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 ( (((((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((X2 @ Y0) & 50.23/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 50.23/7.00 Y0 @ Y1))))) => 50.23/7.00 (X2 @ Y1))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))) => 50.23/7.00 (X2 @ '#sk8'))) 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form9'))), 50.23/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 50.23/7.00 thf(zip_derived_cl53, plain, 50.23/7.00 (( (((((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk16' @ Y0) & 50.23/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.23/7.00 Y1))))) => 50.23/7.00 ('#sk16' @ Y1))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 50.23/7.00 ('#sk16' @ Y0)))))))) => 50.23/7.00 ('#sk16' @ '#sk8'))) 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form9'))), 50.23/7.00 inference('triggered_bool_instantiation', [status(thm)], 50.23/7.00 [zip_derived_cl52])). 50.23/7.00 thf(zip_derived_cl321, plain, 50.23/7.00 ((~ (((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk16' @ Y0) & 50.23/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.23/7.00 Y1))))) => 50.23/7.00 ('#sk16' @ Y1))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 50.23/7.00 ('#sk16' @ Y0)))))))) 50.23/7.00 | ('#sk16' @ '#sk8') 50.23/7.00 | ~ ('#form9') 50.23/7.00 | ('#form11'))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 50.23/7.00 thf(zip_derived_cl22, plain, 50.23/7.00 ((~ (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk6' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((Y0 @ Y1) & 50.23/7.00 ((('#sk1' @ Y1 @ Y2) | 50.23/7.00 ('#sk2' @ Y1 @ Y2))))) => 50.23/7.00 (Y0 @ Y2))))))))))) => 50.23/7.00 (Y0 @ '#sk8')))))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))) 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4')))))))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 50.23/7.00 thf(zip_derived_cl28, plain, 50.23/7.00 (( ('#form9') 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))))), 50.23/7.00 define([status(thm)])). 50.23/7.00 thf(zip_derived_cl30, plain, 50.23/7.00 ((~ ('#form9') 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4')))))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk6' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((Y0 @ Y1) & 50.23/7.00 ((('#sk1' @ Y1 @ Y2) | 50.23/7.00 ('#sk2' @ Y1 @ Y2))))) => 50.23/7.00 (Y0 @ Y2))))))))))) => 50.23/7.00 (Y0 @ '#sk8')))))))), 50.23/7.00 inference('renaming', [status(thm)], [zip_derived_cl22, zip_derived_cl28])). 50.23/7.00 thf(zip_derived_cl32, plain, 50.23/7.00 ((~ ('#form11') 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4')))))))), 50.23/7.00 define([status(thm)])). 50.23/7.00 thf(zip_derived_cl37, plain, 50.23/7.00 (( ('#form11') 50.23/7.00 | ~ (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk6' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 (((((Y0 @ Y1) & 50.23/7.00 ((('#sk1' @ Y1 @ Y2) | 50.23/7.00 ('#sk2' @ Y1 @ Y2))))) => 50.23/7.00 (Y0 @ Y2))))))))))) => 50.23/7.00 (Y0 @ '#sk8')))))) 50.23/7.00 | ~ ('#form9'))), 50.23/7.00 inference('renaming', [status(thm)], [zip_derived_cl30, zip_derived_cl32])). 50.23/7.00 thf(zip_derived_cl45, plain, 50.23/7.00 ((~ (((((((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.23/7.00 ('#sk16' @ Y0)))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk16' @ Y0) & 50.23/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 50.23/7.00 Y0 @ Y1))))) => 50.23/7.00 ('#sk16' @ Y1))))))))))) => 50.23/7.00 ('#sk16' @ '#sk8'))) 50.23/7.00 | ~ ('#form9') 50.23/7.00 | ('#form11'))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl37])). 50.23/7.00 thf(zip_derived_cl56, plain, 50.23/7.00 ((~ ('#sk16' @ '#sk8') | ('#form11') | ~ ('#form9'))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 50.23/7.00 thf(zip_derived_cl322, plain, 50.23/7.00 (( ('#form11') 50.23/7.00 | ~ ('#form9') 50.23/7.00 | ~ (((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk16' @ Y0) & 50.23/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 50.23/7.00 Y0 @ Y1))))) => 50.23/7.00 ('#sk16' @ Y1))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 50.23/7.00 ('#sk16' @ Y0)))))))))), 50.23/7.00 inference('clc', [status(thm)], [zip_derived_cl321, zip_derived_cl56])). 50.23/7.00 thf(zip_derived_cl323, plain, 50.23/7.00 ((~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk16' @ Y0) & 50.23/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 50.23/7.00 ('#sk16' @ Y1))))))))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 50.23/7.00 ('#sk16' @ Y0)))))) 50.23/7.00 | ~ ('#form9') 50.23/7.00 | ('#form11'))), 50.23/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl322])). 50.23/7.00 thf(zip_derived_cl52, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 ( (((((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((X2 @ Y0) & 50.23/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 50.23/7.00 Y0 @ Y1))))) => 50.23/7.00 (X2 @ Y1))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))) => 50.23/7.00 (X2 @ '#sk8'))) 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form9'))), 50.23/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 50.23/7.00 thf(zip_derived_cl64, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ (((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((X2 @ Y0) & 50.23/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 50.23/7.00 Y0 @ Y1))))) => 50.23/7.00 (X2 @ Y1))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))) 50.23/7.00 | (X2 @ '#sk8') 50.23/7.00 | ~ ('#form9') 50.23/7.00 | ('#form11'))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 50.23/7.00 thf(zip_derived_cl75, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((X2 @ Y0) & 50.23/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.23/7.00 Y1))))) => 50.23/7.00 (X2 @ Y1))))))))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))) 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form9') 50.23/7.00 | (X2 @ '#sk8'))), 50.23/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl64])). 50.23/7.00 thf(zip_derived_cl89, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((((X2 @ ('#sk61' @ X2)) & 50.23/7.00 ((('#sk1' @ ('#sk61' @ X2) @ Y0) | ('#sk2' @ 50.23/7.00 ('#sk61' @ X2) @ Y0))))) => 50.23/7.00 (X2 @ Y0)))))) 50.23/7.00 | (X2 @ '#sk8') 50.23/7.00 | ~ ('#form9') 50.23/7.00 | ('#form11') 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl75])). 50.23/7.00 thf(zip_derived_cl102, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ (((((X2 @ ('#sk61' @ X2)) & 50.23/7.00 ((('#sk1' @ ('#sk61' @ X2) @ ('#sk89' @ X2)) | ('#sk2' @ 50.23/7.00 ('#sk61' @ X2) @ ('#sk89' @ X2)))))) => 50.23/7.00 (X2 @ ('#sk89' @ X2)))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))) 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form9') 50.23/7.00 | (X2 @ '#sk8'))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl89])). 50.23/7.00 thf(zip_derived_cl117, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ (X2 @ ('#sk89' @ X2)) 50.23/7.00 | (X2 @ '#sk8') 50.23/7.00 | ~ ('#form9') 50.23/7.00 | ('#form11') 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])). 50.23/7.00 thf(zip_derived_cl135, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 ( ('#form168' @ X2) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))), 50.23/7.00 define([status(thm)])). 50.23/7.00 thf(zip_derived_cl324, plain, 50.23/7.00 ((~ ('#form168' @ '#sk16') 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form9') 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk16' @ Y0) & 50.23/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.23/7.00 Y1))))) => 50.23/7.00 ('#sk16' @ Y1))))))))))), 50.23/7.00 inference('renaming', [status(thm)], 50.23/7.00 [zip_derived_cl323, zip_derived_cl135])). 50.23/7.00 thf(zip_derived_cl325, plain, 50.23/7.00 ((~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk16' @ ('#sk61' @ '#sk16')) & 50.23/7.00 ((('#sk1' @ ('#sk61' @ '#sk16') @ Y0) | ('#sk2' @ 50.23/7.00 ('#sk61' @ '#sk16') @ Y0))))) => 50.23/7.00 ('#sk16' @ Y0)))))) 50.23/7.00 | ~ ('#form9') 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form168' @ '#sk16'))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl324])). 50.23/7.00 thf(zip_derived_cl326, plain, 50.23/7.00 ((~ ((((('#sk16' @ ('#sk61' @ '#sk16')) & 50.23/7.00 ((('#sk1' @ ('#sk61' @ '#sk16') @ ('#sk89' @ '#sk16')) | 50.23/7.00 ('#sk2' @ ('#sk61' @ '#sk16') @ ('#sk89' @ '#sk16')))))) => 50.23/7.00 ('#sk16' @ ('#sk89' @ '#sk16')))) 50.23/7.00 | ~ ('#form168' @ '#sk16') 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form9'))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl325])). 50.23/7.00 thf(zip_derived_cl328, plain, 50.23/7.00 ((~ ('#sk16' @ ('#sk89' @ '#sk16')) 50.23/7.00 | ~ ('#form9') 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form168' @ '#sk16'))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl326])). 50.23/7.00 thf(zip_derived_cl99, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 ( ('#form82' @ X2) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))), 50.23/7.00 define([status(thm)])). 50.23/7.00 thf(zip_derived_cl100, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ ((((('#sk2' @ '#sk3' @ ('#sk83' @ X2)) | ('#sk1' @ '#sk3' @ 50.23/7.00 ('#sk83' @ X2)))) => 50.23/7.00 (X2 @ ('#sk83' @ X2)))) 50.23/7.00 | ('#form82' @ X2))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl99])). 50.23/7.00 thf(zip_derived_cl114, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 ( ((('#sk2' @ '#sk3' @ ('#sk83' @ X2)) | ('#sk1' @ '#sk3' @ 50.23/7.00 ('#sk83' @ X2)))) 50.23/7.00 | ('#form82' @ X2))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 50.23/7.00 thf(zip_derived_cl132, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 ( ('#sk2' @ '#sk3' @ ('#sk83' @ X2)) 50.23/7.00 | ('#sk1' @ '#sk3' @ ('#sk83' @ X2)) 50.23/7.00 | ('#form82' @ X2))), 50.23/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl114])). 50.23/7.00 thf(zip_derived_cl115, plain, 50.23/7.00 (![X2 : a > $o]: (~ (X2 @ ('#sk83' @ X2)) | ('#form82' @ X2))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 50.23/7.00 thf(zip_derived_cl13, plain, 50.23/7.00 ( (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 50.23/7.00 ('#sk5' @ Y0))))))), 50.23/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 50.23/7.00 thf(zip_derived_cl16, plain, 50.23/7.00 (![X2 : a]: 50.23/7.00 ((((('#sk1' @ '#sk3' @ X2) | ('#sk2' @ '#sk3' @ X2))) => ('#sk5' @ 50.23/7.00 X2)))), 50.23/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 50.23/7.00 thf(zip_derived_cl19, plain, 50.23/7.00 (![X2 : a]: 50.23/7.00 (~ ((('#sk1' @ '#sk3' @ X2) | ('#sk2' @ '#sk3' @ X2))) 50.23/7.00 | ('#sk5' @ X2))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 50.23/7.00 thf(zip_derived_cl23, plain, 50.23/7.00 (![X2 : a]: (~ ('#sk1' @ '#sk3' @ X2) | ('#sk5' @ X2))), 50.23/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 50.23/7.00 thf(zip_derived_cl24, plain, 50.23/7.00 (![X2 : a]: (~ ('#sk2' @ '#sk3' @ X2) | ('#sk5' @ X2))), 50.23/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 50.23/7.00 thf(zip_derived_cl327, plain, 50.23/7.00 (( ((('#sk16' @ ('#sk61' @ '#sk16')) & 50.23/7.00 ((('#sk1' @ ('#sk61' @ '#sk16') @ ('#sk89' @ '#sk16')) | ('#sk2' @ 50.23/7.00 ('#sk61' @ '#sk16') @ ('#sk89' @ '#sk16')))))) 50.23/7.00 | ~ ('#form9') 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form168' @ '#sk16'))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl326])). 50.23/7.00 thf(zip_derived_cl329, plain, 50.23/7.00 (( ('#sk16' @ ('#sk61' @ '#sk16')) 50.23/7.00 | ~ ('#form168' @ '#sk16') 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form9'))), 50.23/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl327])). 50.23/7.00 thf(zip_derived_cl330, plain, 50.23/7.00 (( ((('#sk1' @ ('#sk61' @ '#sk16') @ ('#sk89' @ '#sk16')) | ('#sk2' @ 50.23/7.00 ('#sk61' @ '#sk16') @ ('#sk89' @ '#sk16')))) 50.23/7.00 | ~ ('#form168' @ '#sk16') 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form9'))), 50.23/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl327])). 50.23/7.00 thf(zip_derived_cl331, plain, 50.23/7.00 (( ('#sk1' @ ('#sk61' @ '#sk16') @ ('#sk89' @ '#sk16')) 50.23/7.00 | ('#sk2' @ ('#sk61' @ '#sk16') @ ('#sk89' @ '#sk16')) 50.23/7.00 | ~ ('#form9') 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form168' @ '#sk16'))), 50.23/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl330])). 50.23/7.00 thf(zip_derived_cl135, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 ( ('#form168' @ X2) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))), 50.23/7.00 define([status(thm)])). 50.23/7.00 thf(zip_derived_cl136, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ ((((('#sk2' @ '#sk7' @ ('#sk169' @ X2)) | ('#sk1' @ '#sk7' @ 50.23/7.00 ('#sk169' @ X2)))) => 50.23/7.00 (X2 @ ('#sk169' @ X2)))) 50.23/7.00 | ('#form168' @ X2))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl135])). 50.23/7.00 thf(zip_derived_cl151, plain, 50.23/7.00 (![X2 : a > $o]: (~ (X2 @ ('#sk169' @ X2)) | ('#form168' @ X2))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl136])). 50.23/7.00 thf(zip_derived_cl150, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 ( ((('#sk2' @ '#sk7' @ ('#sk169' @ X2)) | ('#sk1' @ '#sk7' @ 50.23/7.00 ('#sk169' @ X2)))) 50.23/7.00 | ('#form168' @ X2))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl136])). 50.23/7.00 thf(zip_derived_cl165, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 ( ('#sk2' @ '#sk7' @ ('#sk169' @ X2)) 50.23/7.00 | ('#sk1' @ '#sk7' @ ('#sk169' @ X2)) 50.23/7.00 | ('#form168' @ X2))), 50.23/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl150])). 50.23/7.00 thf(zip_derived_cl26, plain, 50.23/7.00 (( (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk1' @ Y1 @ Y2) | 50.23/7.00 ('#sk2' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk6' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk7')))))) 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4')))))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))))), 50.23/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 50.23/7.00 thf(zip_derived_cl32, plain, 50.23/7.00 ((~ ('#form11') 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk2' @ Y1 @ Y2) | 50.23/7.00 ('#sk1' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk3' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk4')))))))), 50.23/7.00 define([status(thm)])). 50.23/7.00 thf(zip_derived_cl35, plain, 50.23/7.00 (( ('#form11') 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))) 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk1' @ Y1 @ Y2) | 50.23/7.00 ('#sk2' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk6' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk7')))))))), 50.23/7.00 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl32])). 50.23/7.00 thf(zip_derived_cl28, plain, 50.23/7.00 (( ('#form9') 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk2' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))) | 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 ((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) => 50.23/7.00 (Y2 @ Y3)))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 (( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ Y4))) => 50.23/7.00 (Y2 @ Y4))))))))))) => 50.23/7.00 (Y2 @ Y1)))))))) => 50.23/7.00 (((!!) @ (^[Y2 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y3 : a]: 50.23/7.00 (((!!) @ ( 50.23/7.00 ^[Y4 : a]: 50.23/7.00 ( 50.23/7.00 ( 50.23/7.00 (( 50.23/7.00 (Y2 @ 50.23/7.00 Y3) & 50.23/7.00 (( 50.23/7.00 ('#sk1' @ 50.23/7.00 Y3 @ 50.23/7.00 Y4) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y3 @ Y4))))) => 50.23/7.00 (Y2 @ Y4))))))))) & 50.23/7.00 (((!!) @ (^[Y3 : a]: 50.23/7.00 ((((('#sk1' @ 50.23/7.00 Y0 @ 50.23/7.00 Y3) | 50.23/7.00 ('#sk2' @ 50.23/7.00 Y0 @ Y3))) => 50.23/7.00 (Y2 @ Y3)))))))) => 50.23/7.00 (Y2 @ Y1)))))))))))))))), 50.23/7.00 define([status(thm)])). 50.23/7.00 thf(zip_derived_cl41, plain, 50.23/7.00 ((~ ('#form9') 50.23/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.23/7.00 (((((((!!) @ (^[Y1 : a]: 50.23/7.00 (((!!) @ (^[Y2 : a]: 50.23/7.00 ((((((('#sk1' @ Y1 @ Y2) | 50.23/7.00 ('#sk2' @ Y1 @ Y2))) & 50.23/7.00 (Y0 @ Y1))) => 50.23/7.00 (Y0 @ Y2))))))))) & 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 50.23/7.00 '#sk6' @ Y1))) => 50.23/7.00 (Y0 @ Y1)))))))) => 50.23/7.00 (Y0 @ '#sk7')))))) 50.23/7.00 | ('#form11'))), 50.23/7.00 inference('renaming', [status(thm)], [zip_derived_cl35, zip_derived_cl28])). 50.23/7.00 thf(zip_derived_cl48, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 ( (((((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 50.23/7.00 Y0 @ Y1))) & 50.23/7.00 (X2 @ Y0))) => 50.23/7.00 (X2 @ Y1))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))) => 50.23/7.00 (X2 @ '#sk7'))) 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form9'))), 50.23/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 50.23/7.00 thf(zip_derived_cl62, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ (((((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 50.23/7.00 Y0 @ Y1))) & 50.23/7.00 (X2 @ Y0))) => 50.23/7.00 (X2 @ Y1))))))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))) 50.23/7.00 | (X2 @ '#sk7') 50.23/7.00 | ~ ('#form9') 50.23/7.00 | ('#form11'))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 50.23/7.00 thf(zip_derived_cl73, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.23/7.00 Y1))) & 50.23/7.00 (X2 @ Y0))) => 50.23/7.00 (X2 @ Y1))))))))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))) 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form9') 50.23/7.00 | (X2 @ '#sk7'))), 50.23/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl62])). 50.23/7.00 thf(zip_derived_cl86, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((((('#sk1' @ ('#sk50' @ X2) @ Y0) | ('#sk2' @ 50.23/7.00 ('#sk50' @ X2) @ Y0))) & 50.23/7.00 (X2 @ ('#sk50' @ X2)))) => 50.23/7.00 (X2 @ Y0)))))) 50.23/7.00 | (X2 @ '#sk7') 50.23/7.00 | ~ ('#form9') 50.23/7.00 | ('#form11') 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl73])). 50.23/7.00 thf(zip_derived_cl96, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ ((((((('#sk1' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) | ('#sk2' @ 50.23/7.00 ('#sk50' @ X2) @ ('#sk73' @ X2)))) & 50.23/7.00 (X2 @ ('#sk50' @ X2)))) => 50.23/7.00 (X2 @ ('#sk73' @ X2)))) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))) 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form9') 50.23/7.00 | (X2 @ '#sk7'))), 50.23/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl86])). 50.23/7.00 thf(zip_derived_cl111, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ (X2 @ ('#sk73' @ X2)) 50.23/7.00 | (X2 @ '#sk7') 50.23/7.00 | ~ ('#form9') 50.23/7.00 | ('#form11') 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 50.23/7.00 thf(zip_derived_cl111, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ (X2 @ ('#sk73' @ X2)) 50.23/7.00 | (X2 @ '#sk7') 50.23/7.00 | ~ ('#form9') 50.23/7.00 | ('#form11') 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 50.23/7.00 thf(zip_derived_cl126, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 ( ('#form139' @ X2) 50.23/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.23/7.00 (X2 @ Y0)))))))), 50.23/7.00 define([status(thm)])). 50.23/7.00 thf(zip_derived_cl128, plain, 50.23/7.00 (![X2 : a > $o]: 50.23/7.00 (~ ('#form139' @ X2) 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form9') 50.23/7.00 | (X2 @ '#sk7') 50.23/7.00 | ~ (X2 @ ('#sk73' @ X2)))), 50.23/7.00 inference('renaming', [status(thm)], 50.23/7.00 [zip_derived_cl111, zip_derived_cl126])). 50.23/7.00 thf(zip_derived_cl55, plain, 50.23/7.00 (( (((((!!) @ (^[Y0 : a]: 50.23/7.00 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.23/7.00 ('#sk16' @ Y0)))))) & 50.23/7.00 (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk16' @ Y0) & 50.23/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.23/7.00 Y1))))) => 50.23/7.00 ('#sk16' @ Y1))))))))))) 50.23/7.00 | ('#form11') 50.23/7.00 | ~ ('#form9'))), 50.23/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 50.23/7.00 thf(zip_derived_cl66, plain, 50.23/7.00 (( (((!!) @ (^[Y0 : a]: 50.23/7.00 (((!!) @ (^[Y1 : a]: 50.23/7.00 ((((('#sk16' @ Y0) & 50.23/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 50.23/7.00 ('#sk16' @ Y1))))))))) 50.23/7.00 | ~ ('#form9') 50.23/7.00 | ('#form11'))), 50.23/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 50.82/7.00 thf(zip_derived_cl77, plain, 50.82/7.00 (![X2 : a]: 50.82/7.00 ( (((!!) @ (^[Y0 : a]: 50.82/7.00 ((((('#sk16' @ X2) & 50.82/7.00 ((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))))) => 50.82/7.00 ('#sk16' @ Y0)))))) 50.82/7.00 | ('#form11') 50.82/7.00 | ~ ('#form9'))), 50.82/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl66])). 50.82/7.00 thf(zip_derived_cl91, plain, 50.82/7.00 (![X2 : a, X4 : a]: 50.82/7.00 ( ((((('#sk16' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) => 50.82/7.00 ('#sk16' @ X4))) 50.82/7.00 | ~ ('#form9') 50.82/7.00 | ('#form11'))), 50.82/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl77])). 50.82/7.00 thf(zip_derived_cl105, plain, 50.82/7.00 (![X2 : a, X4 : a]: 50.82/7.00 (~ ((('#sk16' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) 50.82/7.00 | ('#sk16' @ X4) 50.82/7.00 | ('#form11') 50.82/7.00 | ~ ('#form9'))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl91])). 50.82/7.00 thf(zip_derived_cl118, plain, 50.82/7.00 (![X2 : a, X4 : a]: 50.82/7.00 (~ ('#sk16' @ X2) 50.82/7.00 | ~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 50.82/7.00 | ~ ('#form9') 50.82/7.00 | ('#form11') 50.82/7.00 | ('#sk16' @ X4))), 50.82/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl105])). 50.82/7.00 thf(zip_derived_cl138, plain, 50.82/7.00 (![X2 : a, X4 : a]: 50.82/7.00 (~ ('#sk1' @ X2 @ X4) 50.82/7.00 | ('#sk16' @ X4) 50.82/7.00 | ('#form11') 50.82/7.00 | ~ ('#form9') 50.82/7.00 | ~ ('#sk16' @ X2))), 50.82/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl118])). 50.82/7.00 thf(zip_derived_cl139, plain, 50.82/7.00 (![X2 : a, X4 : a]: 50.82/7.00 (~ ('#sk2' @ X2 @ X4) 50.82/7.00 | ('#sk16' @ X4) 50.82/7.00 | ('#form11') 50.82/7.00 | ~ ('#form9') 50.82/7.00 | ~ ('#sk16' @ X2))), 50.82/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl118])). 50.82/7.00 thf(zip_derived_cl110, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( ((((('#sk1' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) | ('#sk2' @ 50.82/7.00 ('#sk50' @ X2) @ ('#sk73' @ X2)))) & 50.82/7.00 (X2 @ ('#sk50' @ X2)))) 50.82/7.00 | (X2 @ '#sk7') 50.82/7.00 | ~ ('#form9') 50.82/7.00 | ('#form11') 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.82/7.00 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.82/7.00 (X2 @ Y0)))))))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 50.82/7.00 thf(zip_derived_cl125, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( (X2 @ ('#sk50' @ X2)) 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.82/7.00 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.82/7.00 (X2 @ Y0)))))) 50.82/7.00 | ('#form11') 50.82/7.00 | ~ ('#form9') 50.82/7.00 | (X2 @ '#sk7'))), 50.82/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl110])). 50.82/7.00 thf(zip_derived_cl126, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( ('#form139' @ X2) 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.82/7.00 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.82/7.00 (X2 @ Y0)))))))), 50.82/7.00 define([status(thm)])). 50.82/7.00 thf(zip_derived_cl145, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ ('#form139' @ (^[Y0 : a]: (X2 @ Y0))) 50.82/7.00 | (X2 @ '#sk7') 50.82/7.00 | ~ ('#form9') 50.82/7.00 | ('#form11') 50.82/7.00 | (X2 @ ('#sk50' @ X2)))), 50.82/7.00 inference('renaming', [status(thm)], 50.82/7.00 [zip_derived_cl125, zip_derived_cl126])). 50.82/7.00 thf(zip_derived_cl160, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ ('#form139' @ X2) 50.82/7.00 | (X2 @ '#sk7') 50.82/7.00 | ~ ('#form9') 50.82/7.00 | ('#form11') 50.82/7.00 | (X2 @ ('#sk50' @ X2)))), 50.82/7.00 inference('ho_norm', [status(thm)], [zip_derived_cl145])). 50.82/7.00 thf(zip_derived_cl126, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( ('#form139' @ X2) 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.82/7.00 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.82/7.00 (X2 @ Y0)))))))), 50.82/7.00 define([status(thm)])). 50.82/7.00 thf(zip_derived_cl127, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ ((((('#sk2' @ '#sk6' @ ('#sk140' @ X2)) | ('#sk1' @ '#sk6' @ 50.82/7.00 ('#sk140' @ X2)))) => 50.82/7.00 (X2 @ ('#sk140' @ X2)))) 50.82/7.00 | ('#form139' @ X2))), 50.82/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl126])). 50.82/7.00 thf(zip_derived_cl146, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( ((('#sk2' @ '#sk6' @ ('#sk140' @ X2)) | ('#sk1' @ '#sk6' @ 50.82/7.00 ('#sk140' @ X2)))) 50.82/7.00 | ('#form139' @ X2))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 50.82/7.00 thf(zip_derived_cl161, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( ('#sk2' @ '#sk6' @ ('#sk140' @ X2)) 50.82/7.00 | ('#sk1' @ '#sk6' @ ('#sk140' @ X2)) 50.82/7.00 | ('#form139' @ X2))), 50.82/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl146])). 50.82/7.00 thf(zip_derived_cl147, plain, 50.82/7.00 (![X2 : a > $o]: (~ (X2 @ ('#sk140' @ X2)) | ('#form139' @ X2))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 50.82/7.00 thf(zip_derived_cl124, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( ((('#sk1' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) | ('#sk2' @ 50.82/7.00 ('#sk50' @ X2) @ ('#sk73' @ X2)))) 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.82/7.00 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.82/7.00 (X2 @ Y0)))))) 50.82/7.00 | ('#form11') 50.82/7.00 | ~ ('#form9') 50.82/7.00 | (X2 @ '#sk7'))), 50.82/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl110])). 50.82/7.00 thf(zip_derived_cl126, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( ('#form139' @ X2) 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.82/7.00 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.82/7.00 (X2 @ Y0)))))))), 50.82/7.00 define([status(thm)])). 50.82/7.00 thf(zip_derived_cl144, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ ('#form139' @ (^[Y0 : a]: (X2 @ Y0))) 50.82/7.00 | (X2 @ '#sk7') 50.82/7.00 | ~ ('#form9') 50.82/7.00 | ('#form11') 50.82/7.00 | ((('#sk1' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) | ('#sk2' @ 50.82/7.00 ('#sk50' @ X2) @ ('#sk73' @ X2)))))), 50.82/7.00 inference('renaming', [status(thm)], 50.82/7.00 [zip_derived_cl124, zip_derived_cl126])). 50.82/7.00 thf(zip_derived_cl158, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ ('#form139' @ X2) 50.82/7.00 | (X2 @ '#sk7') 50.82/7.00 | ~ ('#form9') 50.82/7.00 | ('#form11') 50.82/7.00 | ((('#sk1' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) | ('#sk2' @ 50.82/7.00 ('#sk50' @ X2) @ ('#sk73' @ X2)))))), 50.82/7.00 inference('ho_norm', [status(thm)], [zip_derived_cl144])). 50.82/7.00 thf(zip_derived_cl159, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( ('#sk1' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) 50.82/7.00 | ('#sk2' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) 50.82/7.00 | ('#form11') 50.82/7.00 | ~ ('#form9') 50.82/7.00 | (X2 @ '#sk7') 50.82/7.00 | ~ ('#form139' @ X2))), 50.82/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl158])). 50.82/7.00 thf(zip_derived_cl65, plain, 50.82/7.00 (( (((!!) @ (^[Y0 : a]: 50.82/7.00 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.82/7.00 ('#sk16' @ Y0)))))) 50.82/7.00 | ~ ('#form9') 50.82/7.00 | ('#form11'))), 50.82/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 50.82/7.00 thf(zip_derived_cl76, plain, 50.82/7.00 (![X2 : a]: 50.82/7.00 ( ((((('#sk2' @ '#sk6' @ X2) | ('#sk1' @ '#sk6' @ X2))) => ('#sk16' @ 50.82/7.00 X2))) 50.82/7.00 | ('#form11') 50.82/7.00 | ~ ('#form9'))), 50.82/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl65])). 50.82/7.00 thf(zip_derived_cl90, plain, 50.82/7.00 (![X2 : a]: 50.82/7.00 (~ ((('#sk2' @ '#sk6' @ X2) | ('#sk1' @ '#sk6' @ X2))) 50.82/7.00 | ('#sk16' @ X2) 50.82/7.00 | ~ ('#form9') 50.82/7.00 | ('#form11'))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl76])). 50.82/7.00 thf(zip_derived_cl104, plain, 50.82/7.00 (![X2 : a]: 50.82/7.00 (~ ('#sk1' @ '#sk6' @ X2) 50.82/7.00 | ('#form11') 50.82/7.00 | ~ ('#form9') 50.82/7.00 | ('#sk16' @ X2))), 50.82/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl90])). 50.82/7.00 thf(zip_derived_cl103, plain, 50.82/7.00 (![X2 : a]: 50.82/7.00 (~ ('#sk2' @ '#sk6' @ X2) 50.82/7.00 | ('#form11') 50.82/7.00 | ~ ('#form9') 50.82/7.00 | ('#sk16' @ X2))), 50.82/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl90])). 50.82/7.00 thf(zip_derived_cl28, plain, 50.82/7.00 (( ('#form9') 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((((((!!) @ (^[Y2 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y3 : a]: 50.82/7.00 (((!!) @ ( 50.82/7.00 ^[Y4 : a]: 50.82/7.00 (( 50.82/7.00 (( 50.82/7.00 (Y2 @ 50.82/7.00 Y3) & 50.82/7.00 ('#sk2' @ 50.82/7.00 Y3 @ Y4))) => 50.82/7.00 (Y2 @ Y4))))))))) & 50.82/7.00 (((!!) @ (^[Y3 : a]: 50.82/7.00 ((('#sk2' @ 50.82/7.00 Y0 @ 50.82/7.00 Y3) => 50.82/7.00 (Y2 @ Y3)))))))) => 50.82/7.00 (Y2 @ Y1)))))) | 50.82/7.00 (((!!) @ (^[Y2 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y3 : a]: 50.82/7.00 ((('#sk1' @ 50.82/7.00 Y0 @ 50.82/7.00 Y3) => 50.82/7.00 (Y2 @ Y3)))))) & 50.82/7.00 (((!!) @ (^[Y3 : a]: 50.82/7.00 (((!!) @ ( 50.82/7.00 ^[Y4 : a]: 50.82/7.00 (( 50.82/7.00 (( 50.82/7.00 (Y2 @ 50.82/7.00 Y3) & 50.82/7.00 ('#sk1' @ 50.82/7.00 Y3 @ Y4))) => 50.82/7.00 (Y2 @ Y4))))))))))) => 50.82/7.00 (Y2 @ Y1)))))))) => 50.82/7.00 (((!!) @ (^[Y2 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y3 : a]: 50.82/7.00 (((!!) @ ( 50.82/7.00 ^[Y4 : a]: 50.82/7.00 ( 50.82/7.00 ( 50.82/7.00 (( 50.82/7.00 (Y2 @ 50.82/7.00 Y3) & 50.82/7.00 (( 50.82/7.00 ('#sk1' @ 50.82/7.00 Y3 @ 50.82/7.00 Y4) | 50.82/7.00 ('#sk2' @ 50.82/7.00 Y3 @ Y4))))) => 50.82/7.00 (Y2 @ Y4))))))))) & 50.82/7.00 (((!!) @ (^[Y3 : a]: 50.82/7.00 ((((('#sk1' @ 50.82/7.00 Y0 @ 50.82/7.00 Y3) | 50.82/7.00 ('#sk2' @ 50.82/7.00 Y0 @ Y3))) => 50.82/7.00 (Y2 @ Y3)))))))) => 50.82/7.00 (Y2 @ Y1)))))))))))))))), 50.82/7.00 define([status(thm)])). 50.82/7.00 thf(zip_derived_cl29, plain, 50.82/7.00 ((~ (((!!) @ (^[Y0 : a]: 50.82/7.00 (((((((!!) @ (^[Y1 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y2 : a]: 50.82/7.00 (((!!) @ (^[Y3 : a]: 50.82/7.00 (((((Y1 @ 50.82/7.00 Y2) & 50.82/7.00 ('#sk2' @ 50.82/7.00 Y2 @ Y3))) => 50.82/7.00 (Y1 @ Y3))))))))) & 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 ((('#sk2' @ '#sk10' @ 50.82/7.00 Y2) => (Y1 @ Y2)))))))) => 50.82/7.00 (Y1 @ Y0)))))) | 50.82/7.00 (((!!) @ (^[Y1 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y2 : a]: 50.82/7.00 ((('#sk1' @ '#sk10' @ 50.82/7.00 Y2) => (Y1 @ Y2)))))) & 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 (((!!) @ (^[Y3 : a]: 50.82/7.00 (((((Y1 @ 50.82/7.00 Y2) & 50.82/7.00 ('#sk1' @ 50.82/7.00 Y2 @ Y3))) => 50.82/7.00 (Y1 @ Y3))))))))))) => 50.82/7.00 (Y1 @ Y0)))))))) => 50.82/7.00 (((!!) @ (^[Y1 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y2 : a]: 50.82/7.00 (((!!) @ (^[Y3 : a]: 50.82/7.00 (((((Y1 @ Y2) & 50.82/7.00 ((('#sk1' @ 50.82/7.00 Y2 @ 50.82/7.00 Y3) | 50.82/7.00 ('#sk2' @ 50.82/7.00 Y2 @ Y3))))) => 50.82/7.00 (Y1 @ Y3))))))))) & 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 ((((('#sk1' @ '#sk10' @ 50.82/7.00 Y2) | ('#sk2' @ 50.82/7.00 '#sk10' @ Y2))) => 50.82/7.00 (Y1 @ Y2)))))))) => 50.82/7.00 (Y1 @ Y0))))))))))) 50.82/7.00 | ('#form9'))), 50.82/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl28])). 50.82/7.00 thf(zip_derived_cl38, plain, 50.82/7.00 ((~ (((((((!!) @ (^[Y0 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y1 : a]: 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 (((((Y0 @ Y1) & 50.82/7.00 ('#sk2' @ Y1 @ Y2))) => 50.82/7.00 (Y0 @ Y2))))))))) & 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ 50.82/7.00 Y1)))))))) => 50.82/7.00 (Y0 @ '#sk12')))))) | 50.82/7.00 (((!!) @ (^[Y0 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y1 : a]: 50.82/7.00 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ 50.82/7.00 Y1)))))) & 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 (((((Y0 @ Y1) & 50.82/7.00 ('#sk1' @ Y1 @ Y2))) => 50.82/7.00 (Y0 @ Y2))))))))))) => 50.82/7.00 (Y0 @ '#sk12')))))))) => 50.82/7.00 (((!!) @ (^[Y0 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y1 : a]: 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 (((((Y0 @ Y1) & 50.82/7.00 ((('#sk1' @ Y1 @ Y2) | 50.82/7.00 ('#sk2' @ Y1 @ Y2))))) => 50.82/7.00 (Y0 @ Y2))))))))) & 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 ((((('#sk1' @ '#sk10' @ Y1) | 50.82/7.00 ('#sk2' @ '#sk10' @ Y1))) => 50.82/7.00 (Y0 @ Y1)))))))) => 50.82/7.00 (Y0 @ '#sk12')))))))) 50.82/7.00 | ('#form9'))), 50.82/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl29])). 50.82/7.00 thf(zip_derived_cl46, plain, 50.82/7.00 (( (((((!!) @ (^[Y0 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y1 : a]: 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 (((((Y0 @ Y1) & ('#sk2' @ 50.82/7.00 Y1 @ Y2))) => 50.82/7.00 (Y0 @ Y2))))))))) & 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))))) => 50.82/7.00 (Y0 @ '#sk12')))))) | 50.82/7.00 (((!!) @ (^[Y0 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y1 : a]: 50.82/7.00 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 (((((Y0 @ Y1) & ('#sk1' @ 50.82/7.00 Y1 @ Y2))) => 50.82/7.00 (Y0 @ Y2))))))))))) => 50.82/7.00 (Y0 @ '#sk12')))))))) 50.82/7.00 | ('#form9'))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 50.82/7.00 thf(zip_derived_cl57, plain, 50.82/7.00 (( (((!!) @ (^[Y0 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y1 : a]: 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 (((((Y0 @ Y1) & ('#sk2' @ 50.82/7.00 Y1 @ Y2))) => 50.82/7.00 (Y0 @ Y2))))))))) & 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))))) => 50.82/7.00 (Y0 @ '#sk12')))))) 50.82/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y1 : a]: 50.82/7.00 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 (((((Y0 @ Y1) & ('#sk1' @ 50.82/7.00 Y1 @ Y2))) => 50.82/7.00 (Y0 @ Y2))))))))))) => 50.82/7.00 (Y0 @ '#sk12')))))) 50.82/7.00 | ('#form9'))), 50.82/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl46])). 50.82/7.00 thf(zip_derived_cl67, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( (((((((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.82/7.00 (X2 @ Y1))))))))) & 50.82/7.00 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 50.82/7.00 (X2 @ '#sk12'))) 50.82/7.00 | ('#form9') 50.82/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y1 : a]: 50.82/7.00 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 (((((Y0 @ Y1) & ('#sk1' @ 50.82/7.00 Y1 @ Y2))) => 50.82/7.00 (Y0 @ Y2))))))))))) => 50.82/7.00 (Y0 @ '#sk12')))))))), 50.82/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 50.82/7.00 thf(zip_derived_cl78, plain, 50.82/7.00 ((~ ('#form46') 50.82/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y1 : a]: 50.82/7.00 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 (((((Y0 @ Y1) & ('#sk1' @ 50.82/7.00 Y1 @ Y2))) => 50.82/7.00 (Y0 @ Y2))))))))))) => 50.82/7.00 (Y0 @ '#sk12')))))))), 50.82/7.00 define([status(thm)])). 50.82/7.00 thf(zip_derived_cl79, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) & 50.82/7.00 (((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.82/7.00 (X2 @ Y1))))))))))) => 50.82/7.00 (X2 @ '#sk12'))) 50.82/7.00 | ~ ('#form46'))), 50.82/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl78])). 50.82/7.00 thf(zip_derived_cl93, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ (((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) & 50.82/7.00 (((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.82/7.00 (X2 @ Y1))))))))))) 50.82/7.00 | (X2 @ '#sk12') 50.82/7.00 | ~ ('#form46'))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])). 50.82/7.00 thf(zip_derived_cl107, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.82/7.00 (X2 @ Y1))))))))) 50.82/7.00 | ~ ('#form46') 50.82/7.00 | (X2 @ '#sk12'))), 50.82/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl93])). 50.82/7.00 thf(zip_derived_cl120, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ ((('#sk1' @ '#sk10' @ ('#sk130' @ X2)) => (X2 @ ('#sk130' @ X2)))) 50.82/7.00 | (X2 @ '#sk12') 50.82/7.00 | ~ ('#form46') 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.82/7.00 (X2 @ Y1))))))))))), 50.82/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl107])). 50.82/7.00 thf(zip_derived_cl142, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ (X2 @ ('#sk130' @ X2)) 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.82/7.00 (X2 @ Y1))))))))) 50.82/7.00 | ~ ('#form46') 50.82/7.00 | (X2 @ '#sk12'))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl120])). 50.82/7.00 thf(zip_derived_cl155, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ (((!!) @ (^[Y0 : a]: 50.82/7.00 (((((X2 @ ('#sk221' @ X2)) & ('#sk1' @ 50.82/7.00 ('#sk221' @ X2) @ Y0))) => 50.82/7.00 (X2 @ Y0)))))) 50.82/7.00 | (X2 @ '#sk12') 50.82/7.00 | ~ ('#form46') 50.82/7.00 | ~ (X2 @ ('#sk130' @ X2)))), 50.82/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl142])). 50.82/7.00 thf(zip_derived_cl172, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ (((((X2 @ ('#sk221' @ X2)) & ('#sk1' @ ('#sk221' @ X2) @ 50.82/7.00 ('#sk275' @ X2)))) => 50.82/7.00 (X2 @ ('#sk275' @ X2)))) 50.82/7.00 | ~ (X2 @ ('#sk130' @ X2)) 50.82/7.00 | ~ ('#form46') 50.82/7.00 | (X2 @ '#sk12'))), 50.82/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl155])). 50.82/7.00 thf(zip_derived_cl180, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ (X2 @ ('#sk275' @ X2)) 50.82/7.00 | (X2 @ '#sk12') 50.82/7.00 | ~ ('#form46') 50.82/7.00 | ~ (X2 @ ('#sk130' @ X2)))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl172])). 50.82/7.00 thf(zip_derived_cl179, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( (((X2 @ ('#sk221' @ X2)) & ('#sk1' @ ('#sk221' @ X2) @ 50.82/7.00 ('#sk275' @ X2)))) 50.82/7.00 | (X2 @ '#sk12') 50.82/7.00 | ~ ('#form46') 50.82/7.00 | ~ (X2 @ ('#sk130' @ X2)))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl172])). 50.82/7.00 thf(zip_derived_cl185, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( (X2 @ ('#sk221' @ X2)) 50.82/7.00 | ~ (X2 @ ('#sk130' @ X2)) 50.82/7.00 | ~ ('#form46') 50.82/7.00 | (X2 @ '#sk12'))), 50.82/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl179])). 50.82/7.00 thf(zip_derived_cl47, plain, 50.82/7.00 ((~ (((!!) @ (^[Y0 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y1 : a]: 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 (((((Y0 @ Y1) & 50.82/7.00 ((('#sk1' @ Y1 @ Y2) | 50.82/7.00 ('#sk2' @ Y1 @ Y2))))) => 50.82/7.00 (Y0 @ Y2))))))))) & 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 ((((('#sk1' @ '#sk10' @ Y1) | ('#sk2' @ 50.82/7.00 '#sk10' @ Y1))) => 50.82/7.00 (Y0 @ Y1)))))))) => 50.82/7.00 (Y0 @ '#sk12')))))) 50.82/7.00 | ('#form9'))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 50.82/7.00 thf(zip_derived_cl61, plain, 50.82/7.00 ((~ (((((((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 ((((('#sk20' @ Y0) & 50.82/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 50.82/7.00 Y0 @ Y1))))) => 50.82/7.00 ('#sk20' @ Y1))))))))) & 50.82/7.00 (((!!) @ (^[Y0 : a]: 50.82/7.00 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.82/7.00 ('#sk20' @ Y0)))))))) => 50.82/7.00 ('#sk20' @ '#sk12'))) 50.82/7.00 | ('#form9'))), 50.82/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 50.82/7.00 thf(zip_derived_cl71, plain, 50.82/7.00 (( (((((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 ((((('#sk20' @ Y0) & 50.82/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.82/7.00 Y1))))) => 50.82/7.00 ('#sk20' @ Y1))))))))) & 50.82/7.00 (((!!) @ (^[Y0 : a]: 50.82/7.00 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.82/7.00 ('#sk20' @ Y0)))))))) 50.82/7.00 | ('#form9'))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 50.82/7.00 thf(zip_derived_cl85, plain, 50.82/7.00 (( (((!!) @ (^[Y0 : a]: 50.82/7.00 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.82/7.00 ('#sk20' @ Y0)))))) 50.82/7.00 | ('#form9'))), 50.82/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl71])). 50.82/7.00 thf(zip_derived_cl95, plain, 50.82/7.00 (![X2 : a]: 50.82/7.00 ( ((((('#sk1' @ '#sk10' @ X2) | ('#sk2' @ '#sk10' @ X2))) => 50.82/7.00 ('#sk20' @ X2))) 50.82/7.00 | ('#form9'))), 50.82/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 50.82/7.00 thf(zip_derived_cl109, plain, 50.82/7.00 (![X2 : a]: 50.82/7.00 (~ ((('#sk1' @ '#sk10' @ X2) | ('#sk2' @ '#sk10' @ X2))) 50.82/7.00 | ('#sk20' @ X2) 50.82/7.00 | ('#form9'))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])). 50.82/7.00 thf(zip_derived_cl122, plain, 50.82/7.00 (![X2 : a]: (~ ('#sk1' @ '#sk10' @ X2) | ('#form9') | ('#sk20' @ X2))), 50.82/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl109])). 50.82/7.00 thf(zip_derived_cl186, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( ('#sk1' @ ('#sk221' @ X2) @ ('#sk275' @ X2)) 50.82/7.00 | ~ (X2 @ ('#sk130' @ X2)) 50.82/7.00 | ~ ('#form46') 50.82/7.00 | (X2 @ '#sk12'))), 50.82/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl179])). 50.82/7.00 thf(zip_derived_cl72, plain, ((~ ('#sk20' @ '#sk12') | ('#form9'))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 50.82/7.00 thf(zip_derived_cl141, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( ('#sk1' @ '#sk10' @ ('#sk130' @ X2)) 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.82/7.00 (X2 @ Y1))))))))) 50.82/7.00 | ~ ('#form46') 50.82/7.00 | (X2 @ '#sk12'))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl120])). 50.82/7.00 thf(zip_derived_cl154, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ (((!!) @ (^[Y0 : a]: 50.82/7.00 (((((X2 @ ('#sk221' @ X2)) & ('#sk1' @ 50.82/7.00 ('#sk221' @ X2) @ Y0))) => 50.82/7.00 (X2 @ Y0)))))) 50.82/7.00 | (X2 @ '#sk12') 50.82/7.00 | ~ ('#form46') 50.82/7.00 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)))), 50.82/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl141])). 50.82/7.00 thf(zip_derived_cl171, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ (((((X2 @ ('#sk221' @ X2)) & ('#sk1' @ ('#sk221' @ X2) @ 50.82/7.00 ('#sk275' @ X2)))) => 50.82/7.00 (X2 @ ('#sk275' @ X2)))) 50.82/7.00 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)) 50.82/7.00 | ~ ('#form46') 50.82/7.00 | (X2 @ '#sk12'))), 50.82/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl154])). 50.82/7.00 thf(zip_derived_cl178, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ (X2 @ ('#sk275' @ X2)) 50.82/7.00 | (X2 @ '#sk12') 50.82/7.00 | ~ ('#form46') 50.82/7.00 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl171])). 50.82/7.00 thf(zip_derived_cl177, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( (((X2 @ ('#sk221' @ X2)) & ('#sk1' @ ('#sk221' @ X2) @ 50.82/7.00 ('#sk275' @ X2)))) 50.82/7.00 | (X2 @ '#sk12') 50.82/7.00 | ~ ('#form46') 50.82/7.00 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl171])). 50.82/7.00 thf(zip_derived_cl183, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( (X2 @ ('#sk221' @ X2)) 50.82/7.00 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)) 50.82/7.00 | ~ ('#form46') 50.82/7.00 | (X2 @ '#sk12'))), 50.82/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl177])). 50.82/7.00 thf(zip_derived_cl84, plain, 50.82/7.00 (( (((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 ((((('#sk20' @ Y0) & 50.82/7.00 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 50.82/7.00 ('#sk20' @ Y1))))))))) 50.82/7.00 | ('#form9'))), 50.82/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl71])). 50.82/7.00 thf(zip_derived_cl94, plain, 50.82/7.00 (![X2 : a]: 50.82/7.00 ( (((!!) @ (^[Y0 : a]: 50.82/7.00 ((((('#sk20' @ X2) & 50.82/7.00 ((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))))) => 50.82/7.00 ('#sk20' @ Y0)))))) 50.82/7.00 | ('#form9'))), 50.82/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl84])). 50.82/7.00 thf(zip_derived_cl108, plain, 50.82/7.00 (![X2 : a, X4 : a]: 50.82/7.00 ( ((((('#sk20' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) => 50.82/7.00 ('#sk20' @ X4))) 50.82/7.00 | ('#form9'))), 50.82/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])). 50.82/7.00 thf(zip_derived_cl121, plain, 50.82/7.00 (![X2 : a, X4 : a]: 50.82/7.00 (~ ((('#sk20' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) 50.82/7.00 | ('#sk20' @ X4) 50.82/7.00 | ('#form9'))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 50.82/7.00 thf(zip_derived_cl143, plain, 50.82/7.00 (![X2 : a, X4 : a]: 50.82/7.00 (~ ('#sk20' @ X2) 50.82/7.00 | ~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 50.82/7.00 | ('#form9') 50.82/7.00 | ('#sk20' @ X4))), 50.82/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl121])). 50.82/7.00 thf(zip_derived_cl156, plain, 50.82/7.00 (![X2 : a, X4 : a]: 50.82/7.00 (~ ('#sk1' @ X2 @ X4) 50.82/7.00 | ('#sk20' @ X4) 50.82/7.00 | ('#form9') 50.82/7.00 | ~ ('#sk20' @ X2))), 50.82/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl143])). 50.82/7.00 thf(zip_derived_cl184, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( ('#sk1' @ ('#sk221' @ X2) @ ('#sk275' @ X2)) 50.82/7.00 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)) 50.82/7.00 | ~ ('#form46') 50.82/7.00 | (X2 @ '#sk12'))), 50.82/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl177])). 50.82/7.00 thf(zip_derived_cl67, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( (((((((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.82/7.00 (X2 @ Y1))))))))) & 50.82/7.00 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 50.82/7.00 (X2 @ '#sk12'))) 50.82/7.00 | ('#form9') 50.82/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y1 : a]: 50.82/7.00 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 (((((Y0 @ Y1) & ('#sk1' @ 50.82/7.00 Y1 @ Y2))) => 50.82/7.00 (Y0 @ Y2))))))))))) => 50.82/7.00 (Y0 @ '#sk12')))))))), 50.82/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 50.82/7.00 thf(zip_derived_cl68, plain, 50.82/7.00 (( (((((((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 ((((('#sk20' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.82/7.00 ('#sk20' @ Y1))))))))) & 50.82/7.00 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))) => 50.82/7.00 ('#sk20' @ '#sk12'))) 50.82/7.00 | ('#form9') 50.82/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y1 : a]: 50.82/7.00 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 (((((Y0 @ Y1) & ('#sk1' @ 50.82/7.00 Y1 @ Y2))) => 50.82/7.00 (Y0 @ Y2))))))))))) => 50.82/7.00 (Y0 @ '#sk12')))))))), 50.82/7.00 inference('triggered_bool_instantiation', [status(thm)], 50.82/7.00 [zip_derived_cl67])). 50.82/7.00 thf(zip_derived_cl78, plain, 50.82/7.00 ((~ ('#form46') 50.82/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y1 : a]: 50.82/7.00 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 (((((Y0 @ Y1) & ('#sk1' @ 50.82/7.00 Y1 @ Y2))) => 50.82/7.00 (Y0 @ Y2))))))))))) => 50.82/7.00 (Y0 @ '#sk12')))))))), 50.82/7.00 define([status(thm)])). 50.82/7.00 thf(zip_derived_cl270, plain, 50.82/7.00 (( ('#form46') 50.82/7.00 | ('#form9') 50.82/7.00 | (((((((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 ((((('#sk20' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.82/7.00 ('#sk20' @ Y1))))))))) & 50.82/7.00 (((!!) @ (^[Y0 : a]: 50.82/7.00 ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))) => 50.82/7.00 ('#sk20' @ '#sk12'))))), 50.82/7.00 inference('renaming', [status(thm)], [zip_derived_cl68, zip_derived_cl78])). 50.82/7.00 thf(zip_derived_cl271, plain, 50.82/7.00 ((~ (((((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 ((((('#sk20' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.82/7.00 ('#sk20' @ Y1))))))))) & 50.82/7.00 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))) 50.82/7.00 | ('#sk20' @ '#sk12') 50.82/7.00 | ('#form9') 50.82/7.00 | ('#form46'))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl270])). 50.82/7.00 thf(zip_derived_cl72, plain, ((~ ('#sk20' @ '#sk12') | ('#form9'))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 50.82/7.00 thf(zip_derived_cl272, plain, 50.82/7.00 (( ('#form46') 50.82/7.00 | ('#form9') 50.82/7.00 | ~ (((((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 ((((('#sk20' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.82/7.00 ('#sk20' @ Y1))))))))) & 50.82/7.00 (((!!) @ (^[Y0 : a]: 50.82/7.00 ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))))), 50.82/7.00 inference('clc', [status(thm)], [zip_derived_cl271, zip_derived_cl72])). 50.82/7.00 thf(zip_derived_cl273, plain, 50.82/7.00 ((~ (((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 ((((('#sk20' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.82/7.00 ('#sk20' @ Y1))))))))) 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))) 50.82/7.00 | ('#form9') 50.82/7.00 | ('#form46'))), 50.82/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl272])). 50.82/7.00 thf(zip_derived_cl67, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( (((((((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.82/7.00 (X2 @ Y1))))))))) & 50.82/7.00 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 50.82/7.00 (X2 @ '#sk12'))) 50.82/7.00 | ('#form9') 50.82/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y1 : a]: 50.82/7.00 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 (((((Y0 @ Y1) & ('#sk1' @ 50.82/7.00 Y1 @ Y2))) => 50.82/7.00 (Y0 @ Y2))))))))))) => 50.82/7.00 (Y0 @ '#sk12')))))))), 50.82/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 50.82/7.00 thf(zip_derived_cl78, plain, 50.82/7.00 ((~ ('#form46') 50.82/7.00 | (((!!) @ (^[Y0 : a > $o]: 50.82/7.00 (((((((!!) @ (^[Y1 : a]: 50.82/7.00 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((!!) @ (^[Y2 : a]: 50.82/7.00 (((((Y0 @ Y1) & ('#sk1' @ 50.82/7.00 Y1 @ Y2))) => 50.82/7.00 (Y0 @ Y2))))))))))) => 50.82/7.00 (Y0 @ '#sk12')))))))), 50.82/7.00 define([status(thm)])). 50.82/7.00 thf(zip_derived_cl83, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( ('#form46') 50.82/7.00 | ('#form9') 50.82/7.00 | (((((((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.82/7.00 (X2 @ Y1))))))))) & 50.82/7.00 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 50.82/7.00 (X2 @ '#sk12'))))), 50.82/7.00 inference('renaming', [status(thm)], [zip_derived_cl67, zip_derived_cl78])). 50.82/7.00 thf(zip_derived_cl92, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ (((((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.82/7.00 (X2 @ Y1))))))))) & 50.82/7.00 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) 50.82/7.00 | (X2 @ '#sk12') 50.82/7.00 | ('#form9') 50.82/7.00 | ('#form46'))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl83])). 50.82/7.00 thf(zip_derived_cl106, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ (((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.82/7.00 (X2 @ Y1))))))))) 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 50.82/7.00 | ('#form46') 50.82/7.00 | ('#form9') 50.82/7.00 | (X2 @ '#sk12'))), 50.82/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl92])). 50.82/7.00 thf(zip_derived_cl119, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ (((!!) @ (^[Y0 : a]: 50.82/7.00 (((((X2 @ ('#sk126' @ X2)) & ('#sk2' @ 50.82/7.00 ('#sk126' @ X2) @ Y0))) => 50.82/7.00 (X2 @ Y0)))))) 50.82/7.00 | (X2 @ '#sk12') 50.82/7.00 | ('#form9') 50.82/7.00 | ('#form46') 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 50.82/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl106])). 50.82/7.00 thf(zip_derived_cl140, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ (((((X2 @ ('#sk126' @ X2)) & ('#sk2' @ ('#sk126' @ X2) @ 50.82/7.00 ('#sk174' @ X2)))) => 50.82/7.00 (X2 @ ('#sk174' @ X2)))) 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 50.82/7.00 | ('#form46') 50.82/7.00 | ('#form9') 50.82/7.00 | (X2 @ '#sk12'))), 50.82/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl119])). 50.82/7.00 thf(zip_derived_cl153, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ (X2 @ ('#sk174' @ X2)) 50.82/7.00 | (X2 @ '#sk12') 50.82/7.00 | ('#form9') 50.82/7.00 | ('#form46') 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl140])). 50.82/7.00 thf(zip_derived_cl168, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( ('#form269' @ X2) 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 50.82/7.00 define([status(thm)])). 50.82/7.00 thf(zip_derived_cl274, plain, 50.82/7.00 ((~ ('#form269' @ '#sk20') 50.82/7.00 | ('#form46') 50.82/7.00 | ('#form9') 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: 50.82/7.00 (((!!) @ (^[Y1 : a]: 50.82/7.00 ((((('#sk20' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.82/7.00 ('#sk20' @ Y1))))))))))), 50.82/7.00 inference('renaming', [status(thm)], 50.82/7.00 [zip_derived_cl273, zip_derived_cl168])). 50.82/7.00 thf(zip_derived_cl275, plain, 50.82/7.00 ((~ (((!!) @ (^[Y0 : a]: 50.82/7.00 ((((('#sk20' @ ('#sk126' @ '#sk20')) & ('#sk2' @ 50.82/7.00 ('#sk126' @ '#sk20') @ Y0))) => 50.82/7.00 ('#sk20' @ Y0)))))) 50.82/7.00 | ('#form9') 50.82/7.00 | ('#form46') 50.82/7.00 | ~ ('#form269' @ '#sk20'))), 50.82/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl274])). 50.82/7.00 thf(zip_derived_cl276, plain, 50.82/7.00 ((~ ((((('#sk20' @ ('#sk126' @ '#sk20')) & ('#sk2' @ 50.82/7.00 ('#sk126' @ '#sk20') @ ('#sk174' @ '#sk20')))) => 50.82/7.00 ('#sk20' @ ('#sk174' @ '#sk20')))) 50.82/7.00 | ~ ('#form269' @ '#sk20') 50.82/7.00 | ('#form46') 50.82/7.00 | ('#form9'))), 50.82/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl275])). 50.82/7.00 thf(zip_derived_cl278, plain, 50.82/7.00 ((~ ('#sk20' @ ('#sk174' @ '#sk20')) 50.82/7.00 | ('#form9') 50.82/7.00 | ('#form46') 50.82/7.00 | ~ ('#form269' @ '#sk20'))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl276])). 50.82/7.00 thf(zip_derived_cl277, plain, 50.82/7.00 (( ((('#sk20' @ ('#sk126' @ '#sk20')) & ('#sk2' @ ('#sk126' @ '#sk20') @ 50.82/7.00 ('#sk174' @ '#sk20')))) 50.82/7.00 | ('#form9') 50.82/7.00 | ('#form46') 50.82/7.00 | ~ ('#form269' @ '#sk20'))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl276])). 50.82/7.00 thf(zip_derived_cl279, plain, 50.82/7.00 (( ('#sk20' @ ('#sk126' @ '#sk20')) 50.82/7.00 | ~ ('#form269' @ '#sk20') 50.82/7.00 | ('#form46') 50.82/7.00 | ('#form9'))), 50.82/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl277])). 50.82/7.00 thf(zip_derived_cl280, plain, 50.82/7.00 (( ('#sk2' @ ('#sk126' @ '#sk20') @ ('#sk174' @ '#sk20')) 50.82/7.00 | ~ ('#form269' @ '#sk20') 50.82/7.00 | ('#form46') 50.82/7.00 | ('#form9'))), 50.82/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl277])). 50.82/7.00 thf(zip_derived_cl157, plain, 50.82/7.00 (![X2 : a, X4 : a]: 50.82/7.00 (~ ('#sk2' @ X2 @ X4) 50.82/7.00 | ('#sk20' @ X4) 50.82/7.00 | ('#form9') 50.82/7.00 | ~ ('#sk20' @ X2))), 50.82/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl143])). 50.82/7.00 thf(zip_derived_cl168, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( ('#form269' @ X2) 50.82/7.00 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 50.82/7.00 define([status(thm)])). 50.82/7.00 thf(zip_derived_cl169, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 (~ ((('#sk2' @ '#sk10' @ ('#sk270' @ X2)) => (X2 @ ('#sk270' @ X2)))) 50.82/7.00 | ('#form269' @ X2))), 50.82/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl168])). 50.82/7.00 thf(zip_derived_cl175, plain, 50.82/7.00 (![X2 : a > $o]: 50.82/7.00 ( ('#sk2' @ '#sk10' @ ('#sk270' @ X2)) | ('#form269' @ X2))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl169])). 50.82/7.00 thf(zip_derived_cl176, plain, 50.82/7.00 (![X2 : a > $o]: (~ (X2 @ ('#sk270' @ X2)) | ('#form269' @ X2))), 50.82/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl169])). 50.82/7.00 thf(zip_derived_cl123, plain, 50.82/7.00 (![X2 : a]: (~ ('#sk2' @ '#sk10' @ X2) | ('#form9') | ('#sk20' @ X2))), 50.82/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl109])). 50.82/7.00 thf(zip_derived_cl9159, plain, ($false), 50.82/7.00 inference('eprover', [status(thm)], 50.82/7.00 [zip_derived_cl39, zip_derived_cl40, zip_derived_cl212, 50.82/7.00 zip_derived_cl214, zip_derived_cl215, zip_derived_cl328, 50.82/7.00 zip_derived_cl132, zip_derived_cl115, zip_derived_cl23, 50.82/7.00 zip_derived_cl24, zip_derived_cl329, zip_derived_cl331, 50.82/7.00 zip_derived_cl151, zip_derived_cl165, zip_derived_cl128, 50.82/7.00 zip_derived_cl138, zip_derived_cl139, zip_derived_cl160, 50.82/7.00 zip_derived_cl161, zip_derived_cl147, zip_derived_cl159, 50.82/7.00 zip_derived_cl104, zip_derived_cl103, zip_derived_cl180, 50.82/7.00 zip_derived_cl185, zip_derived_cl122, zip_derived_cl186, 50.82/7.00 zip_derived_cl72, zip_derived_cl178, zip_derived_cl183, 50.82/7.00 zip_derived_cl156, zip_derived_cl184, zip_derived_cl278, 50.82/7.00 zip_derived_cl279, zip_derived_cl280, zip_derived_cl157, 50.82/7.00 zip_derived_cl175, zip_derived_cl176, zip_derived_cl123])). 50.82/7.00 50.82/7.00 % SZS output end Refutation 50.82/7.00 50.82/7.00 50.82/7.00 % Terminating... 50.82/7.06 % Runner terminated. 50.82/7.08 % Zipperpin 1.5 exiting 50.82/7.08 EOF