0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.EbKymHcSUe true 0.13/0.34 % Computer : n010.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 : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 02:03:20 EDT 2022 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 960 s 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.34 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.54/0.62 % Total configuration time : 828 0.54/0.62 % Estimated wc time : 1656 0.54/0.62 % Estimated cpu time (8 cpus) : 207.0 0.55/0.70 % /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 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.55/0.75 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.55/0.75 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.55/0.75 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.55/0.75 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 50.41/7.01 % Solved by lams/20_acsne_simpl.sh. 50.41/7.01 % running E: timeout 13 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.EbKymHcSUe/e_inputa80546 --cpu-limit=11 --auto -s -p 50.41/7.01 % done 652 iterations in 6.154s 50.41/7.01 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 50.41/7.01 % SZS output start Refutation 50.41/7.01 thf(a_type, type, a: $tType). 50.41/7.01 thf('#form11_type', type, '#form11': $o). 50.41/7.01 thf('#sk12_type', type, '#sk12': a). 50.41/7.01 thf('#sk5_type', type, '#sk5': a > $o). 50.41/7.01 thf('#sk83_type', type, '#sk83': (a > $o) > a). 50.41/7.01 thf('#sk267_type', type, '#sk267': (a > $o) > a). 50.41/7.01 thf('#sk122_type', type, '#sk122': (a > $o) > a). 50.41/7.01 thf('#sk73_type', type, '#sk73': (a > $o) > a). 50.41/7.01 thf('#sk27_type', type, '#sk27': (a > $o) > a). 50.41/7.01 thf('#sk4_type', type, '#sk4': a). 50.41/7.01 thf('#sk130_type', type, '#sk130': (a > $o) > a). 50.41/7.01 thf('#sk3_type', type, '#sk3': a). 50.41/7.01 thf('#sk50_type', type, '#sk50': (a > $o) > a). 50.41/7.01 thf('#sk140_type', type, '#sk140': (a > $o) > a). 50.41/7.01 thf('#form139_type', type, '#form139': (a > $o) > $o). 50.41/7.01 thf('#sk272_type', type, '#sk272': (a > $o) > a). 50.41/7.01 thf('#sk8_type', type, '#sk8': a). 50.41/7.01 thf('#sk10_type', type, '#sk10': a). 50.41/7.01 thf('#form46_type', type, '#form46': $o). 50.41/7.01 thf('#sk7_type', type, '#sk7': a). 50.41/7.01 thf('#form266_type', type, '#form266': (a > $o) > $o). 50.41/7.01 thf('#sk2_type', type, '#sk2': a > a > $o). 50.41/7.01 thf('#sk6_type', type, '#sk6': a). 50.41/7.01 thf('#sk20_type', type, '#sk20': a > $o). 50.41/7.01 thf('#sk169_type', type, '#sk169': (a > $o) > a). 50.41/7.01 thf('#sk174_type', type, '#sk174': (a > $o) > a). 50.41/7.01 thf('#sk16_type', type, '#sk16': a > $o). 50.41/7.01 thf('#sk1_type', type, '#sk1': a > a > $o). 50.41/7.01 thf('#sk221_type', type, '#sk221': (a > $o) > a). 50.41/7.01 thf('#sk39_type', type, '#sk39': (a > $o) > a). 50.41/7.01 thf('#form9_type', type, '#form9': $o). 50.41/7.01 thf('#sk126_type', type, '#sk126': (a > $o) > a). 50.41/7.01 thf('#form82_type', type, '#form82': (a > $o) > $o). 50.41/7.01 thf('#sk61_type', type, '#sk61': (a > $o) > a). 50.41/7.01 thf(cTHM251G_pme, conjecture, 50.41/7.01 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 50.41/7.01 ( ( ~( ( ( ![Xx0:a,Xy0:a,Xz:a]: 50.41/7.01 ( ( ( ![Xq:( a > $o )]: 50.41/7.01 ( ( ( ![Xu:a,Xv:a]: 50.41/7.01 ( ( ( Xq @ Xu ) & 50.41/7.01 ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 50.41/7.01 ( Xq @ Xv ) ) ) & 50.41/7.01 ( ![Xw:a]: 50.41/7.01 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 50.41/7.01 ( Xq @ Xw ) ) ) ) => 50.41/7.01 ( Xq @ Xy0 ) ) ) & 50.41/7.01 ( ![Xq:( a > $o )]: 50.41/7.01 ( ( ( ![Xw:a]: 50.41/7.01 ( ( ( R @ Xy0 @ Xw ) | ( S @ Xy0 @ Xw ) ) => 50.41/7.01 ( Xq @ Xw ) ) ) & 50.41/7.01 ( ![Xu:a,Xv:a]: 50.41/7.01 ( ( ( Xq @ Xu ) & 50.41/7.01 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 50.41/7.01 ( Xq @ Xv ) ) ) ) => 50.41/7.01 ( Xq @ Xz ) ) ) ) => 50.41/7.01 ( ![Xq:( a > $o )]: 50.41/7.01 ( ( ( ![Xu:a,Xv:a]: 50.41/7.01 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & 50.41/7.01 ( Xq @ Xu ) ) => 50.41/7.01 ( Xq @ Xv ) ) ) & 50.41/7.01 ( ![Xw:a]: 50.41/7.01 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 50.41/7.01 ( Xq @ Xw ) ) ) ) => 50.41/7.01 ( Xq @ Xz ) ) ) ) ) & 50.41/7.01 ( ![Xx0:a,Xy0:a]: 50.41/7.01 ( ( ( ![Xq:( a > $o )]: 50.41/7.01 ( ( ( ![Xu:a,Xv:a]: 50.41/7.01 ( ( ( S @ Xu @ Xv ) & ( Xq @ Xu ) ) => ( Xq @ Xv ) ) ) & 50.41/7.01 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 50.41/7.01 ( Xq @ Xy0 ) ) ) | 50.41/7.01 ( ![Xq:( a > $o )]: 50.41/7.01 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 50.41/7.01 ( ![Xu:a,Xv:a]: 50.41/7.01 ( ( ( Xq @ Xu ) & ( R @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) ) => 50.41/7.01 ( Xq @ Xy0 ) ) ) ) => 50.41/7.01 ( ![Xq:( a > $o )]: 50.41/7.01 ( ( ( ![Xw:a]: 50.41/7.01 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 50.41/7.01 ( Xq @ Xw ) ) ) & 50.41/7.01 ( ![Xu:a,Xv:a]: 50.41/7.01 ( ( ( Xq @ Xu ) & 50.41/7.01 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 50.41/7.01 ( Xq @ Xv ) ) ) ) => 50.41/7.01 ( Xq @ Xy0 ) ) ) ) ) ) => 50.41/7.01 ( ![Xq:( a > $o )]: 50.41/7.01 ( ( ( ![Xu:a,Xv:a]: 50.41/7.01 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 50.41/7.01 ( Xq @ Xv ) ) ) & 50.41/7.01 ( ![Xw:a]: 50.41/7.01 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 50.41/7.01 ( Xq @ Xy ) ) ) ) ) | 50.41/7.01 ( ![Xq:( a > $o )]: 50.41/7.01 ( ( ( ![Xw:a]: 50.41/7.01 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 50.41/7.01 ( ![Xu:a,Xv:a]: 50.41/7.01 ( ( ( Xq @ Xu ) & ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 50.41/7.01 ( Xq @ Xv ) ) ) ) => 50.41/7.01 ( Xq @ Xy ) ) ) ))). 50.41/7.01 thf(zf_stmt_0, negated_conjecture, 50.41/7.01 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 50.41/7.01 ( ( ~( ( ( ![Xx0:a,Xy0:a,Xz:a]: 50.41/7.01 ( ( ( ![Xq:( a > $o )]: 50.41/7.01 ( ( ( ![Xu:a,Xv:a]: 50.41/7.01 ( ( ( Xq @ Xu ) & 50.41/7.01 ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 50.41/7.01 ( Xq @ Xv ) ) ) & 50.41/7.01 ( ![Xw:a]: 50.41/7.01 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 50.41/7.01 ( Xq @ Xw ) ) ) ) => 50.41/7.01 ( Xq @ Xy0 ) ) ) & 50.41/7.01 ( ![Xq:( a > $o )]: 50.41/7.01 ( ( ( ![Xw:a]: 50.41/7.01 ( ( ( R @ Xy0 @ Xw ) | ( S @ Xy0 @ Xw ) ) => 50.41/7.01 ( Xq @ Xw ) ) ) & 50.41/7.01 ( ![Xu:a,Xv:a]: 50.41/7.01 ( ( ( Xq @ Xu ) & 50.41/7.01 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 50.41/7.01 ( Xq @ Xv ) ) ) ) => 50.41/7.01 ( Xq @ Xz ) ) ) ) => 50.41/7.01 ( ![Xq:( a > $o )]: 50.41/7.01 ( ( ( ![Xu:a,Xv:a]: 50.41/7.01 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & 50.41/7.01 ( Xq @ Xu ) ) => 50.41/7.01 ( Xq @ Xv ) ) ) & 50.41/7.01 ( ![Xw:a]: 50.41/7.01 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 50.41/7.01 ( Xq @ Xw ) ) ) ) => 50.41/7.01 ( Xq @ Xz ) ) ) ) ) & 50.41/7.01 ( ![Xx0:a,Xy0:a]: 50.41/7.01 ( ( ( ![Xq:( a > $o )]: 50.41/7.01 ( ( ( ![Xu:a,Xv:a]: 50.41/7.01 ( ( ( S @ Xu @ Xv ) & ( Xq @ Xu ) ) => 50.41/7.01 ( Xq @ Xv ) ) ) & 50.41/7.01 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 50.41/7.01 ( Xq @ Xy0 ) ) ) | 50.41/7.01 ( ![Xq:( a > $o )]: 50.41/7.01 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 50.41/7.01 ( ![Xu:a,Xv:a]: 50.41/7.01 ( ( ( Xq @ Xu ) & ( R @ Xu @ Xv ) ) => 50.41/7.01 ( Xq @ Xv ) ) ) ) => 50.41/7.01 ( Xq @ Xy0 ) ) ) ) => 50.41/7.01 ( ![Xq:( a > $o )]: 50.41/7.01 ( ( ( ![Xw:a]: 50.41/7.01 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 50.41/7.01 ( Xq @ Xw ) ) ) & 50.41/7.01 ( ![Xu:a,Xv:a]: 50.41/7.01 ( ( ( Xq @ Xu ) & 50.41/7.01 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 50.41/7.01 ( Xq @ Xv ) ) ) ) => 50.41/7.01 ( Xq @ Xy0 ) ) ) ) ) ) => 50.41/7.01 ( ![Xq:( a > $o )]: 50.41/7.01 ( ( ( ![Xu:a,Xv:a]: 50.41/7.01 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 50.41/7.01 ( Xq @ Xv ) ) ) & 50.41/7.01 ( ![Xw:a]: 50.41/7.01 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 50.41/7.01 ( Xq @ Xy ) ) ) ) ) | 50.41/7.01 ( ![Xq:( a > $o )]: 50.41/7.01 ( ( ( ![Xw:a]: 50.41/7.01 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 50.41/7.01 ( ![Xu:a,Xv:a]: 50.41/7.01 ( ( ( Xq @ Xu ) & ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 50.41/7.01 ( Xq @ Xv ) ) ) ) => 50.41/7.01 ( Xq @ Xy ) ) ) ) )), 50.41/7.01 inference('cnf.neg', [status(esa)], [cTHM251G_pme])). 50.41/7.01 thf(zip_derived_cl0, plain, 50.41/7.01 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.41/7.01 (((!!) @ (^[Y1 : a > a > $o]: 50.41/7.01 (((!!) @ (^[Y2 : a]: 50.41/7.01 (((!!) @ (^[Y3 : a]: 50.41/7.01 (((((~) @ (((( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y8 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y9 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y7 @ 50.41/7.01 Y8) & 50.41/7.01 (( 50.41/7.01 (Y1 @ 50.41/7.01 Y8 @ 50.41/7.01 Y9) | 50.41/7.01 (Y0 @ 50.41/7.01 Y8 @ Y9))))) => 50.41/7.01 (Y7 @ Y9))))))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y8 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y1 @ 50.41/7.01 Y4 @ 50.41/7.01 Y8) | 50.41/7.01 (Y0 @ 50.41/7.01 Y4 @ Y8))) => 50.41/7.01 (Y7 @ Y8)))))))) => 50.41/7.01 (Y7 @ Y5)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y8 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y0 @ 50.41/7.01 Y5 @ 50.41/7.01 Y8) | 50.41/7.01 (Y1 @ 50.41/7.01 Y5 @ Y8))) => 50.41/7.01 (Y7 @ Y8)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y8 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y9 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y7 @ 50.41/7.01 Y8) & 50.41/7.01 (( 50.41/7.01 (Y0 @ 50.41/7.01 Y8 @ 50.41/7.01 Y9) | 50.41/7.01 (Y1 @ 50.41/7.01 Y8 @ Y9))))) => 50.41/7.01 (Y7 @ Y9))))))))))) => 50.41/7.01 (Y7 @ Y6)))))))) => 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y8 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y9 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y0 @ 50.41/7.01 Y8 @ 50.41/7.01 Y9) | 50.41/7.01 (Y1 @ 50.41/7.01 Y8 @ Y9))) & 50.41/7.01 (Y7 @ Y8))) => 50.41/7.01 (Y7 @ Y9))))))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y8 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y1 @ 50.41/7.01 Y4 @ 50.41/7.01 Y8) | 50.41/7.01 (Y0 @ 50.41/7.01 Y4 @ Y8))) => 50.41/7.01 (Y7 @ Y8)))))))) => 50.41/7.01 (Y7 @ Y6))))))))))))))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y8 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y1 @ 50.41/7.01 Y7 @ 50.41/7.01 Y8) & 50.41/7.01 (Y6 @ Y7))) => 50.41/7.01 (Y6 @ Y8))))))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (Y1 @ 50.41/7.01 Y4 @ 50.41/7.01 Y7) => 50.41/7.01 (Y6 @ Y7)))))))) => 50.41/7.01 (Y6 @ Y5)))))) | 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (Y0 @ 50.41/7.01 Y4 @ 50.41/7.01 Y7) => 50.41/7.01 (Y6 @ Y7)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y8 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y6 @ 50.41/7.01 Y7) & 50.41/7.01 (Y0 @ 50.41/7.01 Y7 @ Y8))) => 50.41/7.01 (Y6 @ Y8))))))))))) => 50.41/7.01 (Y6 @ Y5)))))))) => 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y1 @ 50.41/7.01 Y4 @ 50.41/7.01 Y7) | 50.41/7.01 (Y0 @ 50.41/7.01 Y4 @ Y7))) => 50.41/7.01 (Y6 @ Y7)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y8 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y6 @ 50.41/7.01 Y7) & 50.41/7.01 (( 50.41/7.01 (Y0 @ 50.41/7.01 Y7 @ 50.41/7.01 Y8) | 50.41/7.01 (Y1 @ 50.41/7.01 Y7 @ Y8))))) => 50.41/7.01 (Y6 @ Y8))))))))))) => 50.41/7.01 (Y6 @ Y5)))))))))))))))) => 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y0 @ 50.41/7.01 Y5 @ 50.41/7.01 Y6) | 50.41/7.01 (Y1 @ 50.41/7.01 Y5 @ Y6))) & 50.41/7.01 (Y4 @ Y5))) => 50.41/7.01 (Y4 @ Y6))))))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y1 @ 50.41/7.01 Y2 @ 50.41/7.01 Y5) | 50.41/7.01 (Y0 @ 50.41/7.01 Y2 @ Y5))) => 50.41/7.01 (Y4 @ Y5)))))))) => 50.41/7.01 (Y4 @ Y3)))))))))) | 50.41/7.01 (((!!) @ (^[Y4 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y0 @ 50.41/7.01 Y2 @ 50.41/7.01 Y5) | 50.41/7.01 (Y1 @ 50.41/7.01 Y2 @ Y5))) => 50.41/7.01 (Y4 @ Y5)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y4 @ 50.41/7.01 Y5) & 50.41/7.01 (( 50.41/7.01 (Y0 @ 50.41/7.01 Y5 @ 50.41/7.01 Y6) | 50.41/7.01 (Y1 @ 50.41/7.01 Y5 @ Y6))))) => 50.41/7.01 (Y4 @ Y6))))))))))) => 50.41/7.01 (Y4 @ Y3))))))))))))))))))))), 50.41/7.01 inference('cnf', [status(esa)], [zf_stmt_0])). 50.41/7.01 thf(zip_derived_cl1, plain, 50.41/7.01 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.41/7.01 (((!!) @ (^[Y1 : a]: 50.41/7.01 (((!!) @ (^[Y2 : a]: 50.41/7.01 (((((~) @ (((((((!!) @ (^[Y3 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y8 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y6 @ 50.41/7.01 Y7) & 50.41/7.01 (( 50.41/7.01 (Y0 @ 50.41/7.01 Y7 @ 50.41/7.01 Y8) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y7 @ Y8))))) => 50.41/7.01 (Y6 @ Y8))))))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y0 @ 50.41/7.01 Y3 @ 50.41/7.01 Y7) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y3 @ Y7))) => 50.41/7.01 (Y6 @ Y7)))))))) => 50.41/7.01 (Y6 @ Y4)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y4 @ 50.41/7.01 Y7) | 50.41/7.01 (Y0 @ 50.41/7.01 Y4 @ Y7))) => 50.41/7.01 (Y6 @ Y7)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y8 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y6 @ 50.41/7.01 Y7) & 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y7 @ 50.41/7.01 Y8) | 50.41/7.01 (Y0 @ 50.41/7.01 Y7 @ Y8))))) => 50.41/7.01 (Y6 @ Y8))))))))))) => 50.41/7.01 (Y6 @ Y5)))))))) => 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y8 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y7 @ 50.41/7.01 Y8) | 50.41/7.01 (Y0 @ 50.41/7.01 Y7 @ Y8))) & 50.41/7.01 (Y6 @ Y7))) => 50.41/7.01 (Y6 @ Y8))))))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y0 @ 50.41/7.01 Y3 @ 50.41/7.01 Y7) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y3 @ Y7))) => 50.41/7.01 (Y6 @ Y7)))))))) => 50.41/7.01 (Y6 @ Y5))))))))))))))))) & 50.41/7.01 (((!!) @ (^[Y3 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y0 @ 50.41/7.01 Y6 @ 50.41/7.01 Y7) & 50.41/7.01 (Y5 @ Y6))) => 50.41/7.01 (Y5 @ Y7))))))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (Y0 @ 50.41/7.01 Y3 @ 50.41/7.01 Y6) => 50.41/7.01 (Y5 @ Y6)))))))) => 50.41/7.01 (Y5 @ Y4)))))) | 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y3 @ 50.41/7.01 Y6) => 50.41/7.01 (Y5 @ Y6)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y5 @ 50.41/7.01 Y6) & 50.41/7.01 ('#sk1' @ 50.41/7.01 Y6 @ Y7))) => 50.41/7.01 (Y5 @ Y7))))))))))) => 50.41/7.01 (Y5 @ Y4)))))))) => 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y0 @ 50.41/7.01 Y3 @ 50.41/7.01 Y6) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y3 @ Y6))) => 50.41/7.01 (Y5 @ Y6)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y5 @ 50.41/7.01 Y6) & 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y6 @ 50.41/7.01 Y7) | 50.41/7.01 (Y0 @ 50.41/7.01 Y6 @ Y7))))) => 50.41/7.01 (Y5 @ Y7))))))))))) => 50.41/7.01 (Y5 @ Y4)))))))))))))))) => 50.41/7.01 (((!!) @ (^[Y3 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y4 @ 50.41/7.01 Y5) | 50.41/7.01 (Y0 @ 50.41/7.01 Y4 @ Y5))) & 50.41/7.01 (Y3 @ Y4))) => 50.41/7.01 (Y3 @ Y5))))))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y0 @ 50.41/7.01 Y1 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y1 @ Y4))) => 50.41/7.01 (Y3 @ Y4)))))))) => 50.41/7.01 (Y3 @ Y2)))))))))) | 50.41/7.01 (((!!) @ (^[Y3 : a > $o]: 50.41/7.01 (((((((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (((( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y1 @ Y4) | 50.41/7.01 (Y0 @ 50.41/7.01 Y1 @ Y4))) => 50.41/7.01 (Y3 @ Y4)))))) & 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y3 @ 50.41/7.01 Y4) & 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y4 @ 50.41/7.01 Y5) | 50.41/7.01 (Y0 @ 50.41/7.01 Y4 @ Y5))))) => 50.41/7.01 (Y3 @ Y5))))))))))) => 50.41/7.01 (Y3 @ Y2)))))))))))))))))), 50.41/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 50.41/7.01 thf(zip_derived_cl2, plain, 50.41/7.01 (~ (((!!) @ (^[Y0 : a]: 50.41/7.01 (((!!) @ (^[Y1 : a]: 50.41/7.01 (((((~) @ (((((((!!) @ (^[Y2 : a]: 50.41/7.01 (((!!) @ (^[Y3 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y5 @ 50.41/7.01 Y6) & 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y6 @ 50.41/7.01 Y7) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y6 @ Y7))))) => 50.41/7.01 (Y5 @ Y7))))))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y2 @ 50.41/7.01 Y6) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y2 @ Y6))) => 50.41/7.01 (Y5 @ Y6)))))))) => 50.41/7.01 (Y5 @ Y3)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y3 @ 50.41/7.01 Y6) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y3 @ Y6))) => 50.41/7.01 (Y5 @ Y6)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y5 @ 50.41/7.01 Y6) & 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y6 @ 50.41/7.01 Y7) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y6 @ Y7))))) => 50.41/7.01 (Y5 @ Y7))))))))))) => 50.41/7.01 (Y5 @ Y4)))))))) => 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y7 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y6 @ 50.41/7.01 Y7) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y6 @ Y7))) & 50.41/7.01 (Y5 @ Y6))) => 50.41/7.01 (Y5 @ Y7))))))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y2 @ 50.41/7.01 Y6) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y2 @ Y6))) => 50.41/7.01 (Y5 @ Y6)))))))) => 50.41/7.01 (Y5 @ Y4))))))))))))))))) & 50.41/7.01 (((!!) @ (^[Y2 : a]: 50.41/7.01 (((!!) @ (^[Y3 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y5 @ 50.41/7.01 Y6) & 50.41/7.01 (Y4 @ Y5))) => 50.41/7.01 (Y4 @ Y6))))))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y2 @ 50.41/7.01 Y5) => 50.41/7.01 (Y4 @ Y5)))))))) => 50.41/7.01 (Y4 @ Y3)))))) | 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y2 @ 50.41/7.01 Y5) => 50.41/7.01 (Y4 @ Y5)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y4 @ 50.41/7.01 Y5) & 50.41/7.01 ('#sk1' @ 50.41/7.01 Y5 @ Y6))) => 50.41/7.01 (Y4 @ Y6))))))))))) => 50.41/7.01 (Y4 @ Y3)))))))) => 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y2 @ 50.41/7.01 Y5) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y2 @ Y5))) => 50.41/7.01 (Y4 @ Y5)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y4 @ 50.41/7.01 Y5) & 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y5 @ 50.41/7.01 Y6) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y5 @ Y6))))) => 50.41/7.01 (Y4 @ Y6))))))))))) => 50.41/7.01 (Y4 @ Y3)))))))))))))))) => 50.41/7.01 (((!!) @ (^[Y2 : a > $o]: 50.41/7.01 (((((((!!) @ ( 50.41/7.01 ^[Y3 : a]: 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y3 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y3 @ Y4))) & 50.41/7.01 (Y2 @ Y3))) => 50.41/7.01 (Y2 @ Y4))))))))) & 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y3 : a]: 50.41/7.01 ((((('#sk2' @ 50.41/7.01 Y0 @ Y3) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y0 @ Y3))) => 50.41/7.01 (Y2 @ Y3)))))))) => 50.41/7.01 (Y2 @ Y1)))))))))) | 50.41/7.01 (((!!) @ (^[Y2 : a > $o]: 50.41/7.01 (((((((!!) @ (^[Y3 : a]: 50.41/7.01 ((((('#sk1' @ 50.41/7.01 Y0 @ Y3) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y0 @ Y3))) => 50.41/7.01 (Y2 @ Y3)))))) & 50.41/7.01 (((!!) @ (^[Y3 : a]: 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (((( 50.41/7.01 (Y2 @ 50.41/7.01 Y3) & 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y3 @ Y4) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y3 @ Y4))))) => 50.41/7.01 (Y2 @ Y4))))))))))) => 50.41/7.01 (Y2 @ Y1))))))))))))))), 50.41/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 50.41/7.01 thf(zip_derived_cl3, plain, 50.41/7.01 (~ (((!!) @ (^[Y0 : a]: 50.41/7.01 (((((~) @ (((((((!!) @ (^[Y1 : a]: 50.41/7.01 (((!!) @ (^[Y2 : a]: 50.41/7.01 (((!!) @ (^[Y3 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y4 @ 50.41/7.01 Y5) & 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y5 @ 50.41/7.01 Y6) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y5 @ Y6))))) => 50.41/7.01 (Y4 @ Y6))))))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y1 @ 50.41/7.01 Y5) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y1 @ Y5))) => 50.41/7.01 (Y4 @ Y5)))))))) => 50.41/7.01 (Y4 @ Y2)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y2 @ 50.41/7.01 Y5) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y2 @ Y5))) => 50.41/7.01 (Y4 @ Y5)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y4 @ 50.41/7.01 Y5) & 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y5 @ 50.41/7.01 Y6) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y5 @ Y6))))) => 50.41/7.01 (Y4 @ Y6))))))))))) => 50.41/7.01 (Y4 @ Y3)))))))) => 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a > $o]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y6 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y5 @ 50.41/7.01 Y6) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y5 @ Y6))) & 50.41/7.01 (Y4 @ Y5))) => 50.41/7.01 (Y4 @ Y6))))))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y1 @ 50.41/7.01 Y5) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y1 @ Y5))) => 50.41/7.01 (Y4 @ Y5)))))))) => 50.41/7.01 (Y4 @ Y3))))))))))))))))) & 50.41/7.01 (((!!) @ (^[Y1 : a]: 50.41/7.01 (((!!) @ (^[Y2 : a]: 50.41/7.01 (((((((!!) @ ( 50.41/7.01 ^[Y3 : a > $o]: 50.41/7.01 (((( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y4 @ 50.41/7.01 Y5) & 50.41/7.01 (Y3 @ Y4))) => 50.41/7.01 (Y3 @ Y5))))))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y1 @ 50.41/7.01 Y4) => 50.41/7.01 (Y3 @ Y4)))))))) => 50.41/7.01 (Y3 @ Y2)))))) | 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y3 : a > $o]: 50.41/7.01 (((( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y1 @ 50.41/7.01 Y4) => 50.41/7.01 (Y3 @ Y4)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y3 @ 50.41/7.01 Y4) & 50.41/7.01 ('#sk1' @ 50.41/7.01 Y4 @ Y5))) => 50.41/7.01 (Y3 @ Y5))))))))))) => 50.41/7.01 (Y3 @ Y2)))))))) => 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y3 : a > $o]: 50.41/7.01 (((((( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y1 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y1 @ Y4))) => 50.41/7.01 (Y3 @ Y4)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y3 @ 50.41/7.01 Y4) & 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y4 @ 50.41/7.01 Y5) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y4 @ Y5))))) => 50.41/7.01 (Y3 @ Y5))))))))))) => 50.41/7.01 (Y3 @ Y2)))))))))))))))) => 50.41/7.01 (((!!) @ (^[Y1 : a > $o]: 50.41/7.01 (((((((!!) @ (^[Y2 : a]: 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y3 : a]: 50.41/7.01 (((((( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y2 @ Y3) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y2 @ Y3))) & 50.41/7.01 (Y1 @ Y2))) => 50.41/7.01 (Y1 @ Y3))))))))) & 50.41/7.01 (((!!) @ (^[Y2 : a]: 50.41/7.01 ((((('#sk2' @ 50.41/7.01 '#sk3' @ Y2) | 50.41/7.01 ('#sk1' @ 50.41/7.01 '#sk3' @ Y2))) => 50.41/7.01 (Y1 @ Y2)))))))) => 50.41/7.01 (Y1 @ Y0)))))))))) | 50.41/7.01 (((!!) @ (^[Y1 : a > $o]: 50.41/7.01 (((((((!!) @ (^[Y2 : a]: 50.41/7.01 ((((('#sk1' @ '#sk3' @ Y2) | 50.41/7.01 ('#sk2' @ '#sk3' @ Y2))) => 50.41/7.01 (Y1 @ Y2)))))) & 50.41/7.01 (((!!) @ (^[Y2 : a]: 50.41/7.01 (((!!) @ (^[Y3 : a]: 50.41/7.01 (((((Y1 @ Y2) & 50.41/7.01 ((('#sk1' @ 50.41/7.01 Y2 @ Y3) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y2 @ Y3))))) => 50.41/7.01 (Y1 @ Y3))))))))))) => 50.41/7.01 (Y1 @ Y0)))))))))))), 50.41/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 50.41/7.01 thf(zip_derived_cl4, plain, 50.41/7.01 (~ (((((~) @ (((((((!!) @ (^[Y0 : a]: 50.41/7.01 (((!!) @ (^[Y1 : a]: 50.41/7.01 (((!!) @ (^[Y2 : a]: 50.41/7.01 (((((((!!) @ ( 50.41/7.01 ^[Y3 : a > $o]: 50.41/7.01 (((( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y3 @ 50.41/7.01 Y4) & 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y4 @ 50.41/7.01 Y5) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y4 @ Y5))))) => 50.41/7.01 (Y3 @ Y5))))))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y0 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y0 @ Y4))) => 50.41/7.01 (Y3 @ Y4)))))))) => 50.41/7.01 (Y3 @ Y1)))))) & 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y3 : a > $o]: 50.41/7.01 (((( 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y1 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y1 @ Y4))) => 50.41/7.01 (Y3 @ Y4)))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y3 @ 50.41/7.01 Y4) & 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y4 @ 50.41/7.01 Y5) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y4 @ Y5))))) => 50.41/7.01 (Y3 @ Y5))))))))))) => 50.41/7.01 (Y3 @ Y2)))))))) => 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y3 : a > $o]: 50.41/7.01 (((((( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y4 @ 50.41/7.01 Y5) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y4 @ Y5))) & 50.41/7.01 (Y3 @ Y4))) => 50.41/7.01 (Y3 @ Y5))))))))) & 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y0 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y0 @ Y4))) => 50.41/7.01 (Y3 @ Y4)))))))) => 50.41/7.01 (Y3 @ Y2))))))))))))))))) & 50.41/7.01 (((!!) @ (^[Y0 : a]: 50.41/7.01 (((!!) @ (^[Y1 : a]: 50.41/7.01 (((((((!!) @ (^[Y2 : a > $o]: 50.41/7.01 (((((((!!) @ ( 50.41/7.01 ^[Y3 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y3 @ 50.41/7.01 Y4) & 50.41/7.01 (Y2 @ Y3))) => 50.41/7.01 (Y2 @ Y4))))))))) & 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y3 : a]: 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y0 @ 50.41/7.01 Y3) => 50.41/7.01 (Y2 @ Y3)))))))) => 50.41/7.01 (Y2 @ Y1)))))) | 50.41/7.01 (((!!) @ (^[Y2 : a > $o]: 50.41/7.01 (((((((!!) @ ( 50.41/7.01 ^[Y3 : a]: 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y0 @ 50.41/7.01 Y3) => 50.41/7.01 (Y2 @ Y3)))))) & 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y3 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y2 @ 50.41/7.01 Y3) & 50.41/7.01 ('#sk1' @ 50.41/7.01 Y3 @ Y4))) => 50.41/7.01 (Y2 @ Y4))))))))))) => 50.41/7.01 (Y2 @ Y1)))))))) => 50.41/7.01 (((!!) @ (^[Y2 : a > $o]: 50.41/7.01 (((((((!!) @ ( 50.41/7.01 ^[Y3 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y0 @ 50.41/7.01 Y3) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y0 @ Y3))) => 50.41/7.01 (Y2 @ Y3)))))) & 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y3 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y2 @ 50.41/7.01 Y3) & 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y3 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y3 @ Y4))))) => 50.41/7.01 (Y2 @ Y4))))))))))) => 50.41/7.01 (Y2 @ Y1)))))))))))))))) => 50.41/7.01 (((!!) @ (^[Y0 : a > $o]: 50.41/7.01 (((((((!!) @ (^[Y1 : a]: 50.41/7.01 (((!!) @ (^[Y2 : a]: 50.41/7.01 ((((((('#sk1' @ 50.41/7.01 Y1 @ Y2) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y1 @ Y2))) & 50.41/7.01 (Y0 @ Y1))) => 50.41/7.01 (Y0 @ Y2))))))))) & 50.41/7.01 (((!!) @ (^[Y1 : a]: 50.41/7.01 ((((('#sk2' @ '#sk3' @ Y1) | 50.41/7.01 ('#sk1' @ '#sk3' @ Y1))) => 50.41/7.01 (Y0 @ Y1)))))))) => 50.41/7.01 (Y0 @ '#sk4')))))))))) | 50.41/7.01 (((!!) @ (^[Y0 : a > $o]: 50.41/7.01 (((((((!!) @ (^[Y1 : a]: 50.41/7.01 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 50.41/7.01 '#sk3' @ Y1))) => 50.41/7.01 (Y0 @ Y1)))))) & 50.41/7.01 (((!!) @ (^[Y1 : a]: 50.41/7.01 (((!!) @ (^[Y2 : a]: 50.41/7.01 (((((Y0 @ Y1) & 50.41/7.01 ((('#sk1' @ Y1 @ Y2) | 50.41/7.01 ('#sk2' @ Y1 @ Y2))))) => 50.41/7.01 (Y0 @ Y2))))))))))) => 50.41/7.01 (Y0 @ '#sk4'))))))))), 50.41/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 50.41/7.01 thf(zip_derived_cl5, plain, 50.41/7.01 ( (((((((!!) @ (^[Y0 : a]: 50.41/7.01 (((!!) @ (^[Y1 : a]: 50.41/7.01 (((!!) @ (^[Y2 : a]: 50.41/7.01 (((((((!!) @ (^[Y3 : a > $o]: 50.41/7.01 (((((((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y3 @ 50.41/7.01 Y4) & 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y4 @ 50.41/7.01 Y5) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y4 @ Y5))))) => 50.41/7.01 (Y3 @ Y5))))))))) & 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y0 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y0 @ Y4))) => 50.41/7.01 (Y3 @ Y4)))))))) => 50.41/7.01 (Y3 @ Y1)))))) & 50.41/7.01 (((!!) @ (^[Y3 : a > $o]: 50.41/7.01 (((((((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y1 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y1 @ Y4))) => 50.41/7.01 (Y3 @ Y4)))))) & 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y3 @ 50.41/7.01 Y4) & 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y4 @ 50.41/7.01 Y5) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y4 @ Y5))))) => 50.41/7.01 (Y3 @ Y5))))))))))) => 50.41/7.01 (Y3 @ Y2)))))))) => 50.41/7.01 (((!!) @ (^[Y3 : a > $o]: 50.41/7.01 (((((((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 ( 50.41/7.01 ( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y4 @ 50.41/7.01 Y5) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y4 @ Y5))) & 50.41/7.01 (Y3 @ Y4))) => 50.41/7.01 (Y3 @ Y5))))))))) & 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 ( 50.41/7.01 ( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y0 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y0 @ Y4))) => 50.41/7.01 (Y3 @ Y4)))))))) => 50.41/7.01 (Y3 @ Y2))))))))))))))))) & 50.41/7.01 (((!!) @ (^[Y0 : a]: 50.41/7.01 (((!!) @ (^[Y1 : a]: 50.41/7.01 (((((((!!) @ (^[Y2 : a > $o]: 50.41/7.01 (((((((!!) @ (^[Y3 : a]: 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y3 @ 50.41/7.01 Y4) & 50.41/7.01 (Y2 @ Y3))) => 50.41/7.01 (Y2 @ Y4))))))))) & 50.41/7.01 (((!!) @ (^[Y3 : a]: 50.41/7.01 ((('#sk2' @ 50.41/7.01 Y0 @ 50.41/7.01 Y3) => 50.41/7.01 (Y2 @ Y3)))))))) => 50.41/7.01 (Y2 @ Y1)))))) | 50.41/7.01 (((!!) @ (^[Y2 : a > $o]: 50.41/7.01 (((((((!!) @ (^[Y3 : a]: 50.41/7.01 ((('#sk1' @ 50.41/7.01 Y0 @ 50.41/7.01 Y3) => 50.41/7.01 (Y2 @ Y3)))))) & 50.41/7.01 (((!!) @ (^[Y3 : a]: 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y2 @ 50.41/7.01 Y3) & 50.41/7.01 ('#sk1' @ 50.41/7.01 Y3 @ Y4))) => 50.41/7.01 (Y2 @ Y4))))))))))) => 50.41/7.01 (Y2 @ Y1)))))))) => 50.41/7.01 (((!!) @ (^[Y2 : a > $o]: 50.41/7.01 (((((((!!) @ (^[Y3 : a]: 50.41/7.01 ((((('#sk2' @ 50.41/7.01 Y0 @ 50.41/7.01 Y3) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y0 @ Y3))) => 50.41/7.01 (Y2 @ Y3)))))) & 50.41/7.01 (((!!) @ (^[Y3 : a]: 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 ( 50.41/7.01 ( 50.41/7.01 (( 50.41/7.01 (Y2 @ 50.41/7.01 Y3) & 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y3 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y3 @ Y4))))) => 50.41/7.01 (Y2 @ Y4))))))))))) => 50.41/7.01 (Y2 @ Y1)))))))))))))))) => 50.41/7.01 (((!!) @ (^[Y0 : a > $o]: 50.41/7.01 (((((((!!) @ (^[Y1 : a]: 50.41/7.01 (((!!) @ (^[Y2 : a]: 50.41/7.01 ((((((('#sk1' @ Y1 @ Y2) | 50.41/7.01 ('#sk2' @ Y1 @ Y2))) & 50.41/7.01 (Y0 @ Y1))) => 50.41/7.01 (Y0 @ Y2))))))))) & 50.41/7.01 (((!!) @ (^[Y1 : a]: 50.41/7.01 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.41/7.01 '#sk3' @ Y1))) => 50.41/7.01 (Y0 @ Y1)))))))) => 50.41/7.01 (Y0 @ '#sk4'))))))))), 50.41/7.01 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 50.41/7.01 thf(zip_derived_cl7, plain, 50.41/7.01 ((~ (((((!!) @ (^[Y0 : a]: 50.41/7.01 (((!!) @ (^[Y1 : a]: 50.41/7.01 (((!!) @ (^[Y2 : a]: 50.41/7.01 (((((((!!) @ (^[Y3 : a > $o]: 50.41/7.01 (((((((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y3 @ 50.41/7.01 Y4) & 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y4 @ 50.41/7.01 Y5) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y4 @ Y5))))) => 50.41/7.01 (Y3 @ Y5))))))))) & 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y0 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y0 @ Y4))) => 50.41/7.01 (Y3 @ Y4)))))))) => 50.41/7.01 (Y3 @ Y1)))))) & 50.41/7.01 (((!!) @ (^[Y3 : a > $o]: 50.41/7.01 (((((((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y1 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y1 @ Y4))) => 50.41/7.01 (Y3 @ Y4)))))) & 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y3 @ 50.41/7.01 Y4) & 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y4 @ 50.41/7.01 Y5) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y4 @ Y5))))) => 50.41/7.01 (Y3 @ Y5))))))))))) => 50.41/7.01 (Y3 @ Y2)))))))) => 50.41/7.01 (((!!) @ (^[Y3 : a > $o]: 50.41/7.01 (((((((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 ( 50.41/7.01 ( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y4 @ 50.41/7.01 Y5) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y4 @ Y5))) & 50.41/7.01 (Y3 @ Y4))) => 50.41/7.01 (Y3 @ Y5))))))))) & 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 ( 50.41/7.01 ( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y0 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y0 @ Y4))) => 50.41/7.01 (Y3 @ Y4)))))))) => 50.41/7.01 (Y3 @ Y2))))))))))))))))) & 50.41/7.01 (((!!) @ (^[Y0 : a]: 50.41/7.01 (((!!) @ (^[Y1 : a]: 50.41/7.01 (((((((!!) @ (^[Y2 : a > $o]: 50.41/7.01 (((((((!!) @ (^[Y3 : a]: 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y3 @ 50.41/7.01 Y4) & 50.41/7.01 (Y2 @ Y3))) => 50.41/7.01 (Y2 @ Y4))))))))) & 50.41/7.01 (((!!) @ (^[Y3 : a]: 50.41/7.01 ((('#sk2' @ 50.41/7.01 Y0 @ 50.41/7.01 Y3) => 50.41/7.01 (Y2 @ Y3)))))))) => 50.41/7.01 (Y2 @ Y1)))))) | 50.41/7.01 (((!!) @ (^[Y2 : a > $o]: 50.41/7.01 (((((((!!) @ (^[Y3 : a]: 50.41/7.01 ((('#sk1' @ 50.41/7.01 Y0 @ 50.41/7.01 Y3) => 50.41/7.01 (Y2 @ Y3)))))) & 50.41/7.01 (((!!) @ (^[Y3 : a]: 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y2 @ 50.41/7.01 Y3) & 50.41/7.01 ('#sk1' @ 50.41/7.01 Y3 @ Y4))) => 50.41/7.01 (Y2 @ Y4))))))))))) => 50.41/7.01 (Y2 @ Y1)))))))) => 50.41/7.01 (((!!) @ (^[Y2 : a > $o]: 50.41/7.01 (((((((!!) @ (^[Y3 : a]: 50.41/7.01 ((((('#sk2' @ 50.41/7.01 Y0 @ 50.41/7.01 Y3) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y0 @ Y3))) => 50.41/7.01 (Y2 @ Y3)))))) & 50.41/7.01 (((!!) @ (^[Y3 : a]: 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 ( 50.41/7.01 ( 50.41/7.01 (( 50.41/7.01 (Y2 @ 50.41/7.01 Y3) & 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y3 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y3 @ Y4))))) => 50.41/7.01 (Y2 @ Y4))))))))))) => 50.41/7.01 (Y2 @ Y1)))))))))))))))) 50.41/7.01 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.01 (((((((!!) @ (^[Y1 : a]: 50.41/7.01 (((!!) @ (^[Y2 : a]: 50.41/7.01 ((((((('#sk1' @ Y1 @ Y2) | 50.41/7.01 ('#sk2' @ Y1 @ Y2))) & 50.41/7.01 (Y0 @ Y1))) => 50.41/7.01 (Y0 @ Y2))))))))) & 50.41/7.01 (((!!) @ (^[Y1 : a]: 50.41/7.01 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.41/7.01 '#sk3' @ Y1))) => 50.41/7.01 (Y0 @ Y1)))))))) => 50.41/7.01 (Y0 @ '#sk4')))))))), 50.41/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 50.41/7.01 thf(zip_derived_cl9, plain, 50.41/7.01 ((~ (((!!) @ (^[Y0 : a]: 50.41/7.01 (((!!) @ (^[Y1 : a]: 50.41/7.01 (((!!) @ (^[Y2 : a]: 50.41/7.01 (((((((!!) @ (^[Y3 : a > $o]: 50.41/7.01 (((((((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 ( 50.41/7.01 ( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y3 @ 50.41/7.01 Y4) & 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y4 @ 50.41/7.01 Y5) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y4 @ Y5))))) => 50.41/7.01 (Y3 @ Y5))))))))) & 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 ( 50.41/7.01 ( 50.41/7.01 (( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y0 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y0 @ Y4))) => 50.41/7.01 (Y3 @ Y4)))))))) => 50.41/7.01 (Y3 @ Y1)))))) & 50.41/7.01 (((!!) @ (^[Y3 : a > $o]: 50.41/7.01 (((((((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 ( 50.41/7.01 ( 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y1 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y1 @ Y4))) => 50.41/7.01 (Y3 @ Y4)))))) & 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 ( 50.41/7.01 ( 50.41/7.01 (!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (Y3 @ 50.41/7.01 Y4) & 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y4 @ 50.41/7.01 Y5) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y4 @ Y5))))) => 50.41/7.01 (Y3 @ Y5))))))))))) => 50.41/7.01 (Y3 @ Y2)))))))) => 50.41/7.01 (((!!) @ (^[Y3 : a > $o]: 50.41/7.01 (((((((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y5 : a]: 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 (( 50.41/7.01 ('#sk1' @ 50.41/7.01 Y4 @ 50.41/7.01 Y5) | 50.41/7.01 ('#sk2' @ 50.41/7.01 Y4 @ Y5))) & 50.41/7.01 (Y3 @ Y4))) => 50.41/7.01 (Y3 @ Y5))))))))) & 50.41/7.01 (((!!) @ ( 50.41/7.01 ^[Y4 : a]: 50.41/7.01 (((( 50.41/7.01 ('#sk2' @ 50.41/7.01 Y0 @ 50.41/7.01 Y4) | 50.41/7.01 ('#sk1' @ 50.41/7.01 Y0 @ Y4))) => 50.41/7.02 (Y3 @ Y4)))))))) => 50.41/7.02 (Y3 @ Y2))))))))))))))))) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) & 50.41/7.02 (Y2 @ Y3))) => 50.41/7.02 (Y2 @ Y4))))))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ((('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))))) => 50.41/7.02 (Y2 @ Y1)))))) | 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ((('#sk1' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ Y4))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))) => 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ((((('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) | 50.41/7.02 ('#sk1' @ 50.41/7.02 Y0 @ Y3))) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) | 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4))))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))))))))) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((((('#sk1' @ Y1 @ Y2) | 50.41/7.02 ('#sk2' @ Y1 @ Y2))) & 50.41/7.02 (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.41/7.02 '#sk3' @ Y1))) => 50.41/7.02 (Y0 @ Y1)))))))) => 50.41/7.02 (Y0 @ '#sk4')))))))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl7])). 50.41/7.02 thf(zip_derived_cl12, plain, 50.41/7.02 ((~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) | 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ Y4))))) => 50.41/7.02 (Y2 @ Y4))))))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ((((('#sk2' @ 50.41/7.02 '#sk6' @ 50.41/7.02 Y3) | 50.41/7.02 ('#sk1' @ 50.41/7.02 '#sk6' @ 50.41/7.02 Y3))) => 50.41/7.02 (Y2 @ Y3)))))))) => 50.41/7.02 (Y2 @ Y0)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ((((('#sk1' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) | 50.41/7.02 ('#sk2' @ 50.41/7.02 Y0 @ Y3))) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) | 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4))))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))) => 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (((( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) | 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4))) & 50.41/7.02 (Y2 @ Y3))) => 50.41/7.02 (Y2 @ Y4))))))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ((((('#sk2' @ 50.41/7.02 '#sk6' @ 50.41/7.02 Y3) | 50.41/7.02 ('#sk1' @ 50.41/7.02 '#sk6' @ 50.41/7.02 Y3))) => 50.41/7.02 (Y2 @ Y3)))))))) => 50.41/7.02 (Y2 @ Y1)))))))))))))) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((((('#sk1' @ Y1 @ Y2) | 50.41/7.02 ('#sk2' @ Y1 @ Y2))) & 50.41/7.02 (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.41/7.02 '#sk3' @ Y1))) => 50.41/7.02 (Y0 @ Y1)))))))) => 50.41/7.02 (Y0 @ '#sk4')))))) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) & 50.41/7.02 (Y2 @ Y3))) => 50.41/7.02 (Y2 @ Y4))))))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ((('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))))) => 50.41/7.02 (Y2 @ Y1)))))) | 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ((('#sk1' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ Y4))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))) => 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ((((('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) | 50.41/7.02 ('#sk1' @ 50.41/7.02 Y0 @ Y3))) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ 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(((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((((('#sk1' @ '#sk7' @ 50.41/7.02 Y2) | ('#sk2' @ 50.41/7.02 '#sk7' @ Y2))) => 50.41/7.02 (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((((Y1 @ 50.41/7.02 Y2) & 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) | 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ((((((('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) | 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((('#sk2' @ '#sk6' @ 50.41/7.02 Y2) | ('#sk1' @ 50.41/7.02 '#sk6' @ Y2))) => 50.41/7.02 (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0))))))))))) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) & 50.41/7.02 (Y2 @ Y3))) => 50.41/7.02 (Y2 @ Y4))))))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ((('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))))) => 50.41/7.02 (Y2 @ Y1)))))) | 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ((('#sk1' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ Y4))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))) => 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ((((('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) | 50.41/7.02 ('#sk1' @ 50.41/7.02 Y0 @ Y3))) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) | 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4))))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))))))))) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((((('#sk1' @ Y1 @ Y2) | 50.41/7.02 ('#sk2' @ Y1 @ Y2))) & 50.41/7.02 (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.41/7.02 '#sk3' @ Y1))) => 50.41/7.02 (Y0 @ Y1)))))))) => 50.41/7.02 (Y0 @ '#sk4')))))))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 50.41/7.02 thf(zip_derived_cl18, plain, 50.41/7.02 ((~ (((((((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & 50.41/7.02 ((('#sk2' @ Y1 @ 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(^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ((('#sk1' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ Y4))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))) => 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ((((('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) | 50.41/7.02 ('#sk1' @ 50.41/7.02 Y0 @ Y3))) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) | 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4))))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))))))))))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])). 50.41/7.02 thf(zip_derived_cl22, plain, 50.41/7.02 ((~ (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((((('#sk1' @ Y1 @ Y2) | 50.41/7.02 ('#sk2' @ Y1 @ Y2))) & 50.41/7.02 (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 50.41/7.02 '#sk6' @ Y1))) => 50.41/7.02 (Y0 @ Y1)))))))) => 50.41/7.02 (Y0 @ '#sk8')))))) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) & 51.22/7.02 (Y2 @ Y3))) => 51.22/7.02 (Y2 @ Y4))))))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))))) => 51.22/7.02 (Y2 @ Y1)))))) | 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk1' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ Y4))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))) => 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) | 51.22/7.02 ('#sk1' @ 51.22/7.02 Y0 @ Y3))) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 ( 51.22/7.02 ( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 (( 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) | 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ Y4))))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))))))))) 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : 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51.22/7.02 ((('#sk1' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ Y4))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))) => 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) | 51.22/7.02 ('#sk1' @ 51.22/7.02 Y0 @ Y3))) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 ( 51.22/7.02 ( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 (( 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) | 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ Y4))))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))))))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl29, plain, 51.22/7.02 ((~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((((((!!) @ (^[Y1 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y2 : a]: 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 ((((('#sk2' @ 51.22/7.02 Y2 @ 51.22/7.02 Y3) & 51.22/7.02 (Y1 @ Y2))) => 51.22/7.02 (Y1 @ Y3))))))))) & 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 ((('#sk2' @ '#sk10' @ 51.22/7.02 Y2) => (Y1 @ Y2)))))))) => 51.22/7.02 (Y1 @ Y0)))))) | 51.22/7.02 (((!!) @ (^[Y1 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y2 : a]: 51.22/7.02 ((('#sk1' @ '#sk10' @ 51.22/7.02 Y2) => (Y1 @ Y2)))))) & 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((((Y1 @ 51.22/7.02 Y2) & 51.22/7.02 ('#sk1' @ 51.22/7.02 Y2 @ Y3))) => 51.22/7.02 (Y1 @ Y3))))))))))) => 51.22/7.02 (Y1 @ Y0)))))))) => 51.22/7.02 (((!!) @ (^[Y1 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y2 : a]: 51.22/7.02 ((((('#sk2' @ '#sk10' @ 51.22/7.02 Y2) | ('#sk1' @ 51.22/7.02 '#sk10' @ Y2))) => 51.22/7.02 (Y1 @ Y2)))))) & 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((((Y1 @ Y2) & 51.22/7.02 ((('#sk1' @ 51.22/7.02 Y2 @ 51.22/7.02 Y3) | 51.22/7.02 ('#sk2' @ 51.22/7.02 Y2 @ Y3))))) => 51.22/7.02 (Y1 @ Y3))))))))))) => 51.22/7.02 (Y1 @ Y0))))))))))) 51.22/7.02 | ('#form9'))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl28])). 51.22/7.02 thf(zip_derived_cl38, plain, 51.22/7.02 ((~ (((((((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 ((((('#sk2' @ Y1 @ Y2) & 51.22/7.02 (Y0 @ Y1))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ 51.22/7.02 Y1)))))))) => 51.22/7.02 (Y0 @ '#sk12')))))) | 51.22/7.02 (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ 51.22/7.02 Y1)))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & 51.22/7.02 ('#sk1' @ Y1 @ Y2))) => 51.22/7.02 (Y0 @ Y2))))))))))) => 51.22/7.02 (Y0 @ '#sk12')))))))) => 51.22/7.02 (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk10' @ Y1) | 51.22/7.02 ('#sk1' @ '#sk10' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & 51.22/7.02 ((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))))) => 51.22/7.02 (Y0 @ Y2))))))))))) => 51.22/7.02 (Y0 @ '#sk12')))))))) 51.22/7.02 | ('#form9'))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl29])). 51.22/7.02 thf(zip_derived_cl47, plain, 51.22/7.02 ((~ (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk10' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk10' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & 51.22/7.02 ((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))))) => 51.22/7.02 (Y0 @ Y2))))))))))) => 51.22/7.02 (Y0 @ '#sk12')))))) 51.22/7.02 | ('#form9'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 51.22/7.02 thf(zip_derived_cl61, plain, 51.22/7.02 ((~ (((((((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 51.22/7.02 ('#sk20' @ Y0)))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk20' @ Y0) & 51.22/7.02 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 51.22/7.02 Y0 @ Y1))))) => 51.22/7.02 ('#sk20' @ Y1))))))))))) => 51.22/7.02 ('#sk20' @ '#sk12'))) 51.22/7.02 | ('#form9'))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 51.22/7.02 thf(zip_derived_cl72, plain, ((~ ('#sk20' @ '#sk12') | ('#form9'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 51.22/7.02 thf(zip_derived_cl46, plain, 51.22/7.02 (( (((((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 ((((('#sk2' @ Y1 @ Y2) & 51.22/7.02 (Y0 @ Y1))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk12')))))) | 51.22/7.02 (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & ('#sk1' @ 51.22/7.02 Y1 @ Y2))) => 51.22/7.02 (Y0 @ Y2))))))))))) => 51.22/7.02 (Y0 @ '#sk12')))))))) 51.22/7.02 | ('#form9'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 51.22/7.02 thf(zip_derived_cl57, plain, 51.22/7.02 (( (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 ((((('#sk2' @ Y1 @ Y2) & 51.22/7.02 (Y0 @ Y1))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk12')))))) 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & ('#sk1' @ 51.22/7.02 Y1 @ Y2))) => 51.22/7.02 (Y0 @ Y2))))))))))) => 51.22/7.02 (Y0 @ '#sk12')))))) 51.22/7.02 | ('#form9'))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl46])). 51.22/7.02 thf(zip_derived_cl67, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( (((((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 51.22/7.02 (X2 @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 51.22/7.02 (X2 @ '#sk12'))) 51.22/7.02 | ('#form9') 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & ('#sk1' @ 51.22/7.02 Y1 @ Y2))) => 51.22/7.02 (Y0 @ Y2))))))))))) => 51.22/7.02 (Y0 @ '#sk12')))))))), 51.22/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 51.22/7.02 thf(zip_derived_cl78, plain, 51.22/7.02 ((~ ('#form46') 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & ('#sk1' @ 51.22/7.02 Y1 @ Y2))) => 51.22/7.02 (Y0 @ Y2))))))))))) => 51.22/7.02 (Y0 @ '#sk12')))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl79, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.22/7.02 (X2 @ Y1))))))))))) => 51.22/7.02 (X2 @ '#sk12'))) 51.22/7.02 | ~ ('#form46'))), 51.22/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl78])). 51.22/7.02 thf(zip_derived_cl93, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.22/7.02 (X2 @ Y1))))))))))) 51.22/7.02 | (X2 @ '#sk12') 51.22/7.02 | ~ ('#form46'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])). 51.22/7.02 thf(zip_derived_cl108, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.22/7.02 (X2 @ Y1))))))))) 51.22/7.02 | ~ ('#form46') 51.22/7.02 | (X2 @ '#sk12'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl93])). 51.22/7.02 thf(zip_derived_cl121, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ ((('#sk1' @ '#sk10' @ ('#sk130' @ X2)) => (X2 @ ('#sk130' @ X2)))) 51.22/7.02 | (X2 @ '#sk12') 51.22/7.02 | ~ ('#form46') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.22/7.02 (X2 @ Y1))))))))))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl108])). 51.22/7.02 thf(zip_derived_cl140, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (X2 @ ('#sk130' @ X2)) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.22/7.02 (X2 @ Y1))))))))) 51.22/7.02 | ~ ('#form46') 51.22/7.02 | (X2 @ '#sk12'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl121])). 51.22/7.02 thf(zip_derived_cl152, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((((X2 @ ('#sk221' @ X2)) & ('#sk1' @ 51.22/7.02 ('#sk221' @ X2) @ Y0))) => 51.22/7.02 (X2 @ Y0)))))) 51.22/7.02 | (X2 @ '#sk12') 51.22/7.02 | ~ ('#form46') 51.22/7.02 | ~ (X2 @ ('#sk130' @ X2)))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl140])). 51.22/7.02 thf(zip_derived_cl169, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (((((X2 @ ('#sk221' @ X2)) & ('#sk1' @ ('#sk221' @ X2) @ 51.22/7.02 ('#sk272' @ X2)))) => 51.22/7.02 (X2 @ ('#sk272' @ X2)))) 51.22/7.02 | ~ (X2 @ ('#sk130' @ X2)) 51.22/7.02 | ~ ('#form46') 51.22/7.02 | (X2 @ '#sk12'))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl152])). 51.22/7.02 thf(zip_derived_cl180, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (X2 @ ('#sk272' @ X2)) 51.22/7.02 | (X2 @ '#sk12') 51.22/7.02 | ~ ('#form46') 51.22/7.02 | ~ (X2 @ ('#sk130' @ X2)))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl169])). 51.22/7.02 thf(zip_derived_cl179, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( (((X2 @ ('#sk221' @ X2)) & ('#sk1' @ ('#sk221' @ X2) @ 51.22/7.02 ('#sk272' @ X2)))) 51.22/7.02 | (X2 @ '#sk12') 51.22/7.02 | ~ ('#form46') 51.22/7.02 | ~ (X2 @ ('#sk130' @ X2)))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl169])). 51.22/7.02 thf(zip_derived_cl187, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ('#sk1' @ ('#sk221' @ X2) @ ('#sk272' @ X2)) 51.22/7.02 | ~ (X2 @ ('#sk130' @ X2)) 51.22/7.02 | ~ ('#form46') 51.22/7.02 | (X2 @ '#sk12'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl179])). 51.22/7.02 thf(zip_derived_cl139, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ('#sk1' @ '#sk10' @ ('#sk130' @ X2)) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.22/7.02 (X2 @ Y1))))))))) 51.22/7.02 | ~ ('#form46') 51.22/7.02 | (X2 @ '#sk12'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl121])). 51.22/7.02 thf(zip_derived_cl151, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((((X2 @ ('#sk221' @ X2)) & ('#sk1' @ 51.22/7.02 ('#sk221' @ X2) @ Y0))) => 51.22/7.02 (X2 @ Y0)))))) 51.22/7.02 | (X2 @ '#sk12') 51.22/7.02 | ~ ('#form46') 51.22/7.02 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl139])). 51.22/7.02 thf(zip_derived_cl168, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (((((X2 @ ('#sk221' @ X2)) & ('#sk1' @ ('#sk221' @ X2) @ 51.22/7.02 ('#sk272' @ X2)))) => 51.22/7.02 (X2 @ ('#sk272' @ X2)))) 51.22/7.02 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)) 51.22/7.02 | ~ ('#form46') 51.22/7.02 | (X2 @ '#sk12'))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl151])). 51.22/7.02 thf(zip_derived_cl178, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (X2 @ ('#sk272' @ X2)) 51.22/7.02 | (X2 @ '#sk12') 51.22/7.02 | ~ ('#form46') 51.22/7.02 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl168])). 51.22/7.02 thf(zip_derived_cl71, plain, 51.22/7.02 (( (((((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 51.22/7.02 ('#sk20' @ Y0)))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk20' @ Y0) & 51.22/7.02 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 51.22/7.02 Y1))))) => 51.22/7.02 ('#sk20' @ Y1))))))))))) 51.22/7.02 | ('#form9'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 51.22/7.02 thf(zip_derived_cl84, plain, 51.22/7.02 (( (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 51.22/7.02 ('#sk20' @ Y0)))))) 51.22/7.02 | ('#form9'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl71])). 51.22/7.02 thf(zip_derived_cl94, plain, 51.22/7.02 (![X2 : a]: 51.22/7.02 ( ((((('#sk2' @ '#sk10' @ X2) | ('#sk1' @ '#sk10' @ X2))) => 51.22/7.02 ('#sk20' @ X2))) 51.22/7.02 | ('#form9'))), 51.22/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl84])). 51.22/7.02 thf(zip_derived_cl109, plain, 51.22/7.02 (![X2 : a]: 51.22/7.02 (~ ((('#sk2' @ '#sk10' @ X2) | ('#sk1' @ '#sk10' @ X2))) 51.22/7.02 | ('#sk20' @ X2) 51.22/7.02 | ('#form9'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl94])). 51.22/7.02 thf(zip_derived_cl123, plain, 51.22/7.02 (![X2 : a]: (~ ('#sk1' @ '#sk10' @ X2) | ('#form9') | ('#sk20' @ X2))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl109])). 51.22/7.02 thf(zip_derived_cl186, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( (X2 @ ('#sk221' @ X2)) 51.22/7.02 | ~ (X2 @ ('#sk130' @ X2)) 51.22/7.02 | ~ ('#form46') 51.22/7.02 | (X2 @ '#sk12'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl179])). 51.22/7.02 thf(zip_derived_cl85, plain, 51.22/7.02 (( (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk20' @ Y0) & 51.22/7.02 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 51.22/7.02 ('#sk20' @ Y1))))))))) 51.22/7.02 | ('#form9'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl71])). 51.22/7.02 thf(zip_derived_cl95, plain, 51.22/7.02 (![X2 : a]: 51.22/7.02 ( (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk20' @ X2) & 51.22/7.02 ((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))))) => 51.22/7.02 ('#sk20' @ Y0)))))) 51.22/7.02 | ('#form9'))), 51.22/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 51.22/7.02 thf(zip_derived_cl110, plain, 51.22/7.02 (![X2 : a, X4 : a]: 51.22/7.02 ( ((((('#sk20' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) => 51.22/7.02 ('#sk20' @ X4))) 51.22/7.02 | ('#form9'))), 51.22/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl95])). 51.22/7.02 thf(zip_derived_cl124, plain, 51.22/7.02 (![X2 : a, X4 : a]: 51.22/7.02 (~ ((('#sk20' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) 51.22/7.02 | ('#sk20' @ X4) 51.22/7.02 | ('#form9'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl110])). 51.22/7.02 thf(zip_derived_cl141, plain, 51.22/7.02 (![X2 : a, X4 : a]: 51.22/7.02 (~ ('#sk20' @ X2) 51.22/7.02 | ~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 51.22/7.02 | ('#form9') 51.22/7.02 | ('#sk20' @ X4))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl124])). 51.22/7.02 thf(zip_derived_cl153, plain, 51.22/7.02 (![X2 : a, X4 : a]: 51.22/7.02 (~ ('#sk1' @ X2 @ X4) 51.22/7.02 | ('#sk20' @ X4) 51.22/7.02 | ('#form9') 51.22/7.02 | ~ ('#sk20' @ X2))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl141])). 51.22/7.02 thf(zip_derived_cl177, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( (((X2 @ ('#sk221' @ X2)) & ('#sk1' @ ('#sk221' @ X2) @ 51.22/7.02 ('#sk272' @ X2)))) 51.22/7.02 | (X2 @ '#sk12') 51.22/7.02 | ~ ('#form46') 51.22/7.02 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl168])). 51.22/7.02 thf(zip_derived_cl185, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ('#sk1' @ ('#sk221' @ X2) @ ('#sk272' @ X2)) 51.22/7.02 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)) 51.22/7.02 | ~ ('#form46') 51.22/7.02 | (X2 @ '#sk12'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl177])). 51.22/7.02 thf(zip_derived_cl184, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( (X2 @ ('#sk221' @ X2)) 51.22/7.02 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)) 51.22/7.02 | ~ ('#form46') 51.22/7.02 | (X2 @ '#sk12'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl177])). 51.22/7.02 thf(zip_derived_cl67, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( (((((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 51.22/7.02 (X2 @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 51.22/7.02 (X2 @ '#sk12'))) 51.22/7.02 | ('#form9') 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & ('#sk1' @ 51.22/7.02 Y1 @ Y2))) => 51.22/7.02 (Y0 @ Y2))))))))))) => 51.22/7.02 (Y0 @ '#sk12')))))))), 51.22/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 51.22/7.02 thf(zip_derived_cl68, plain, 51.22/7.02 (( (((((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 51.22/7.02 ('#sk20' @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))) => 51.22/7.02 ('#sk20' @ '#sk12'))) 51.22/7.02 | ('#form9') 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & ('#sk1' @ 51.22/7.02 Y1 @ Y2))) => 51.22/7.02 (Y0 @ Y2))))))))))) => 51.22/7.02 (Y0 @ '#sk12')))))))), 51.22/7.02 inference('triggered_bool_instantiation', [status(thm)], 51.22/7.02 [zip_derived_cl67])). 51.22/7.02 thf(zip_derived_cl78, plain, 51.22/7.02 ((~ ('#form46') 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & ('#sk1' @ 51.22/7.02 Y1 @ Y2))) => 51.22/7.02 (Y0 @ Y2))))))))))) => 51.22/7.02 (Y0 @ '#sk12')))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl271, plain, 51.22/7.02 (( ('#form46') 51.22/7.02 | ('#form9') 51.22/7.02 | (((((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 51.22/7.02 ('#sk20' @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))) => 51.22/7.02 ('#sk20' @ '#sk12'))))), 51.22/7.02 inference('renaming', [status(thm)], [zip_derived_cl68, zip_derived_cl78])). 51.22/7.02 thf(zip_derived_cl272, plain, 51.22/7.02 ((~ (((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 51.22/7.02 ('#sk20' @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))) 51.22/7.02 | ('#sk20' @ '#sk12') 51.22/7.02 | ('#form9') 51.22/7.02 | ('#form46'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl271])). 51.22/7.02 thf(zip_derived_cl72, plain, ((~ ('#sk20' @ '#sk12') | ('#form9'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 51.22/7.02 thf(zip_derived_cl273, plain, 51.22/7.02 (( ('#form46') 51.22/7.02 | ('#form9') 51.22/7.02 | ~ (((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 51.22/7.02 ('#sk20' @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))))), 51.22/7.02 inference('clc', [status(thm)], [zip_derived_cl272, zip_derived_cl72])). 51.22/7.02 thf(zip_derived_cl274, plain, 51.22/7.02 ((~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 51.22/7.02 ('#sk20' @ Y1))))))))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))) 51.22/7.02 | ('#form9') 51.22/7.02 | ('#form46'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl273])). 51.22/7.02 thf(zip_derived_cl67, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( (((((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 51.22/7.02 (X2 @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 51.22/7.02 (X2 @ '#sk12'))) 51.22/7.02 | ('#form9') 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & ('#sk1' @ 51.22/7.02 Y1 @ Y2))) => 51.22/7.02 (Y0 @ Y2))))))))))) => 51.22/7.02 (Y0 @ '#sk12')))))))), 51.22/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 51.22/7.02 thf(zip_derived_cl78, plain, 51.22/7.02 ((~ ('#form46') 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & ('#sk1' @ 51.22/7.02 Y1 @ Y2))) => 51.22/7.02 (Y0 @ Y2))))))))))) => 51.22/7.02 (Y0 @ '#sk12')))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl83, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ('#form46') 51.22/7.02 | ('#form9') 51.22/7.02 | (((((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 51.22/7.02 (X2 @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 51.22/7.02 (X2 @ '#sk12'))))), 51.22/7.02 inference('renaming', [status(thm)], [zip_derived_cl67, zip_derived_cl78])). 51.22/7.02 thf(zip_derived_cl92, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 51.22/7.02 (X2 @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) 51.22/7.02 | (X2 @ '#sk12') 51.22/7.02 | ('#form9') 51.22/7.02 | ('#form46'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl83])). 51.22/7.02 thf(zip_derived_cl107, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 51.22/7.02 (X2 @ Y1))))))))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 51.22/7.02 | ('#form46') 51.22/7.02 | ('#form9') 51.22/7.02 | (X2 @ '#sk12'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl92])). 51.22/7.02 thf(zip_derived_cl120, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ ('#sk126' @ X2) @ Y0) & (X2 @ 51.22/7.02 ('#sk126' @ X2)))) => 51.22/7.02 (X2 @ Y0)))))) 51.22/7.02 | (X2 @ '#sk12') 51.22/7.02 | ('#form9') 51.22/7.02 | ('#form46') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl107])). 51.22/7.02 thf(zip_derived_cl138, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ ((((('#sk2' @ ('#sk126' @ X2) @ ('#sk174' @ X2)) & (X2 @ 51.22/7.02 ('#sk126' @ X2)))) => 51.22/7.02 (X2 @ ('#sk174' @ X2)))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 51.22/7.02 | ('#form46') 51.22/7.02 | ('#form9') 51.22/7.02 | (X2 @ '#sk12'))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl120])). 51.22/7.02 thf(zip_derived_cl150, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (X2 @ ('#sk174' @ X2)) 51.22/7.02 | (X2 @ '#sk12') 51.22/7.02 | ('#form9') 51.22/7.02 | ('#form46') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl138])). 51.22/7.02 thf(zip_derived_cl165, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ('#form266' @ X2) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl275, plain, 51.22/7.02 ((~ ('#form266' @ '#sk20') 51.22/7.02 | ('#form46') 51.22/7.02 | ('#form9') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 51.22/7.02 ('#sk20' @ Y1))))))))))), 51.22/7.02 inference('renaming', [status(thm)], 51.22/7.02 [zip_derived_cl274, zip_derived_cl165])). 51.22/7.02 thf(zip_derived_cl276, plain, 51.22/7.02 ((~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ ('#sk126' @ '#sk20') @ Y0) & ('#sk20' @ 51.22/7.02 ('#sk126' @ '#sk20')))) => 51.22/7.02 ('#sk20' @ Y0)))))) 51.22/7.02 | ('#form9') 51.22/7.02 | ('#form46') 51.22/7.02 | ~ ('#form266' @ '#sk20'))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl275])). 51.22/7.02 thf(zip_derived_cl277, plain, 51.22/7.02 ((~ ((((('#sk2' @ ('#sk126' @ '#sk20') @ ('#sk174' @ '#sk20')) & 51.22/7.02 ('#sk20' @ ('#sk126' @ '#sk20')))) => 51.22/7.02 ('#sk20' @ ('#sk174' @ '#sk20')))) 51.22/7.02 | ~ ('#form266' @ '#sk20') 51.22/7.02 | ('#form46') 51.22/7.02 | ('#form9'))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl276])). 51.22/7.02 thf(zip_derived_cl278, plain, 51.22/7.02 (( ((('#sk2' @ ('#sk126' @ '#sk20') @ ('#sk174' @ '#sk20')) & ('#sk20' @ 51.22/7.02 ('#sk126' @ '#sk20')))) 51.22/7.02 | ('#form9') 51.22/7.02 | ('#form46') 51.22/7.02 | ~ ('#form266' @ '#sk20'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl277])). 51.22/7.02 thf(zip_derived_cl281, plain, 51.22/7.02 (( ('#sk20' @ ('#sk126' @ '#sk20')) 51.22/7.02 | ~ ('#form266' @ '#sk20') 51.22/7.02 | ('#form46') 51.22/7.02 | ('#form9'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl278])). 51.22/7.02 thf(zip_derived_cl279, plain, 51.22/7.02 ((~ ('#sk20' @ ('#sk174' @ '#sk20')) 51.22/7.02 | ('#form9') 51.22/7.02 | ('#form46') 51.22/7.02 | ~ ('#form266' @ '#sk20'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl277])). 51.22/7.02 thf(zip_derived_cl21, plain, 51.22/7.02 (( (((((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & 51.22/7.02 ((('#sk2' @ Y1 @ Y2) | 51.22/7.02 ('#sk1' @ Y1 @ Y2))))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk6' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk7')))))) & 51.22/7.02 (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk1' @ '#sk7' @ Y1) | ('#sk2' @ 51.22/7.02 '#sk7' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & 51.22/7.02 ((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))))) => 51.22/7.02 (Y0 @ Y2))))))))))) => 51.22/7.02 (Y0 @ '#sk8')))))))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) & 51.22/7.02 (Y2 @ Y3))) => 51.22/7.02 (Y2 @ Y4))))))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))))) => 51.22/7.02 (Y2 @ Y1)))))) | 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk1' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ Y4))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))) => 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) | 51.22/7.02 ('#sk1' @ 51.22/7.02 Y0 @ Y3))) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 ( 51.22/7.02 ( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 (( 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) | 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ Y4))))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))))))))) 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 ((((((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))) & 51.22/7.02 (Y0 @ Y1))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk3' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk4')))))))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 51.22/7.02 thf(zip_derived_cl26, plain, 51.22/7.02 (( (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & 51.22/7.02 ((('#sk2' @ Y1 @ Y2) | 51.22/7.02 ('#sk1' @ Y1 @ Y2))))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk6' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk7')))))) 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 ((((((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))) & 51.22/7.02 (Y0 @ Y1))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk3' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk4')))))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) & 51.22/7.02 (Y2 @ Y3))) => 51.22/7.02 (Y2 @ Y4))))))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))))) => 51.22/7.02 (Y2 @ Y1)))))) | 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk1' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ Y4))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))) => 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) | 51.22/7.02 ('#sk1' @ 51.22/7.02 Y0 @ Y3))) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 ( 51.22/7.02 ( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 (( 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) | 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ Y4))))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))))))))))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 51.22/7.02 thf(zip_derived_cl26, plain, 51.22/7.02 (( (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & 51.22/7.02 ((('#sk2' @ Y1 @ Y2) | 51.22/7.02 ('#sk1' @ Y1 @ Y2))))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk6' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk7')))))) 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 ((((((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))) & 51.22/7.02 (Y0 @ Y1))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk3' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk4')))))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) & 51.22/7.02 (Y2 @ Y3))) => 51.22/7.02 (Y2 @ Y4))))))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))))) => 51.22/7.02 (Y2 @ Y1)))))) | 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk1' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ Y4))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))) => 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) | 51.22/7.02 ('#sk1' @ 51.22/7.02 Y0 @ Y3))) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 ( 51.22/7.02 ( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 (( 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) | 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ Y4))))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))))))))))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 51.22/7.02 thf(zip_derived_cl32, plain, 51.22/7.02 ((~ ('#form11') 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 ((((((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))) & 51.22/7.02 (Y0 @ Y1))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk3' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk4')))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl35, plain, 51.22/7.02 (( ('#form11') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) & 51.22/7.02 (Y2 @ Y3))) => 51.22/7.02 (Y2 @ Y4))))))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))))) => 51.22/7.02 (Y2 @ Y1)))))) | 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk1' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ Y4))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))) => 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) | 51.22/7.02 ('#sk1' @ 51.22/7.02 Y0 @ Y3))) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 ( 51.22/7.02 ( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 (( 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) | 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ Y4))))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))))))))) 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & 51.22/7.02 ((('#sk2' @ Y1 @ Y2) | 51.22/7.02 ('#sk1' @ Y1 @ Y2))))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk6' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk7')))))))), 51.22/7.02 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl32])). 51.22/7.02 thf(zip_derived_cl28, plain, 51.22/7.02 (( ('#form9') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) & 51.22/7.02 (Y2 @ Y3))) => 51.22/7.02 (Y2 @ Y4))))))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))))) => 51.22/7.02 (Y2 @ Y1)))))) | 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk1' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ Y4))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))) => 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) | 51.22/7.02 ('#sk1' @ 51.22/7.02 Y0 @ Y3))) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 ( 51.22/7.02 ( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 (( 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) | 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ Y4))))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))))))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl41, plain, 51.22/7.02 ((~ ('#form9') 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & 51.22/7.02 ((('#sk2' @ Y1 @ Y2) | 51.22/7.02 ('#sk1' @ Y1 @ Y2))))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk6' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk7')))))) 51.22/7.02 | ('#form11'))), 51.22/7.02 inference('renaming', [status(thm)], [zip_derived_cl35, zip_derived_cl28])). 51.22/7.02 thf(zip_derived_cl48, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( (((((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((X2 @ Y0) & 51.22/7.02 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 51.22/7.02 Y0 @ Y1))))) => 51.22/7.02 (X2 @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))))) => 51.22/7.02 (X2 @ '#sk7'))) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9'))), 51.22/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 51.22/7.02 thf(zip_derived_cl62, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((X2 @ Y0) & 51.22/7.02 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 51.22/7.02 Y0 @ Y1))))) => 51.22/7.02 (X2 @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))))) 51.22/7.02 | (X2 @ '#sk7') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 51.22/7.02 thf(zip_derived_cl73, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((X2 @ Y0) & 51.22/7.02 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 51.22/7.02 Y1))))) => 51.22/7.02 (X2 @ Y1))))))))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | (X2 @ '#sk7'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl62])). 51.22/7.02 thf(zip_derived_cl86, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((((X2 @ ('#sk50' @ X2)) & 51.22/7.02 ((('#sk2' @ ('#sk50' @ X2) @ Y0) | ('#sk1' @ 51.22/7.02 ('#sk50' @ X2) @ Y0))))) => 51.22/7.02 (X2 @ Y0)))))) 51.22/7.02 | (X2 @ '#sk7') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl73])). 51.22/7.02 thf(zip_derived_cl96, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (((((X2 @ ('#sk50' @ X2)) & 51.22/7.02 ((('#sk2' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) | ('#sk1' @ 51.22/7.02 ('#sk50' @ X2) @ ('#sk73' @ X2)))))) => 51.22/7.02 (X2 @ ('#sk73' @ X2)))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | (X2 @ '#sk7'))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl86])). 51.22/7.02 thf(zip_derived_cl111, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( (((X2 @ ('#sk50' @ X2)) & 51.22/7.02 ((('#sk2' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) | ('#sk1' @ 51.22/7.02 ('#sk50' @ X2) @ ('#sk73' @ X2)))))) 51.22/7.02 | (X2 @ '#sk7') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 51.22/7.02 thf(zip_derived_cl125, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( (X2 @ ('#sk50' @ X2)) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | (X2 @ '#sk7'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl111])). 51.22/7.02 thf(zip_derived_cl112, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (X2 @ ('#sk73' @ X2)) 51.22/7.02 | (X2 @ '#sk7') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 51.22/7.02 thf(zip_derived_cl127, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ('#form139' @ X2) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl142, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ ('#form139' @ (^[Y0 : a]: (X2 @ Y0))) 51.22/7.02 | (X2 @ '#sk7') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11') 51.22/7.02 | (X2 @ ('#sk50' @ X2)))), 51.22/7.02 inference('renaming', [status(thm)], 51.22/7.02 [zip_derived_cl125, zip_derived_cl127])). 51.22/7.02 thf(zip_derived_cl155, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ ('#form139' @ X2) 51.22/7.02 | (X2 @ '#sk7') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11') 51.22/7.02 | (X2 @ ('#sk50' @ X2)))), 51.22/7.02 inference('ho_norm', [status(thm)], [zip_derived_cl142])). 51.22/7.02 thf(zip_derived_cl280, plain, 51.22/7.02 (( ('#sk2' @ ('#sk126' @ '#sk20') @ ('#sk174' @ '#sk20')) 51.22/7.02 | ~ ('#form266' @ '#sk20') 51.22/7.02 | ('#form46') 51.22/7.02 | ('#form9'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl278])). 51.22/7.02 thf(zip_derived_cl112, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (X2 @ ('#sk73' @ X2)) 51.22/7.02 | (X2 @ '#sk7') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 51.22/7.02 thf(zip_derived_cl127, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ('#form139' @ X2) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl129, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ ('#form139' @ X2) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | (X2 @ '#sk7') 51.22/7.02 | ~ (X2 @ ('#sk73' @ X2)))), 51.22/7.02 inference('renaming', [status(thm)], 51.22/7.02 [zip_derived_cl112, zip_derived_cl127])). 51.22/7.02 thf(zip_derived_cl154, plain, 51.22/7.02 (![X2 : a, X4 : a]: 51.22/7.02 (~ ('#sk2' @ X2 @ X4) 51.22/7.02 | ('#sk20' @ X4) 51.22/7.02 | ('#form9') 51.22/7.02 | ~ ('#sk20' @ X2))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl141])). 51.22/7.02 thf(zip_derived_cl127, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ('#form139' @ X2) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl128, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ ((((('#sk2' @ '#sk6' @ ('#sk140' @ X2)) | ('#sk1' @ '#sk6' @ 51.22/7.02 ('#sk140' @ X2)))) => 51.22/7.02 (X2 @ ('#sk140' @ X2)))) 51.22/7.02 | ('#form139' @ X2))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl127])). 51.22/7.02 thf(zip_derived_cl145, plain, 51.22/7.02 (![X2 : a > $o]: (~ (X2 @ ('#sk140' @ X2)) | ('#form139' @ X2))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl128])). 51.22/7.02 thf(zip_derived_cl27, plain, 51.22/7.02 (( (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk1' @ '#sk7' @ Y1) | ('#sk2' @ 51.22/7.02 '#sk7' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & 51.22/7.02 ((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))))) => 51.22/7.02 (Y0 @ Y2))))))))))) => 51.22/7.02 (Y0 @ '#sk8')))))) 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 ((((((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))) & 51.22/7.02 (Y0 @ Y1))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk3' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk4')))))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) & 51.22/7.02 (Y2 @ Y3))) => 51.22/7.02 (Y2 @ Y4))))))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))))) => 51.22/7.02 (Y2 @ Y1)))))) | 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk1' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ Y4))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))) => 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) | 51.22/7.02 ('#sk1' @ 51.22/7.02 Y0 @ Y3))) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 ( 51.22/7.02 ( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 (( 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) | 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ Y4))))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))))))))))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 51.22/7.02 thf(zip_derived_cl32, plain, 51.22/7.02 ((~ ('#form11') 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 ((((((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))) & 51.22/7.02 (Y0 @ Y1))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk3' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk4')))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl36, plain, 51.22/7.02 (( ('#form11') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) & 51.22/7.02 (Y2 @ Y3))) => 51.22/7.02 (Y2 @ Y4))))))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))))) => 51.22/7.02 (Y2 @ Y1)))))) | 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk1' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ Y4))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))) => 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) | 51.22/7.02 ('#sk1' @ 51.22/7.02 Y0 @ Y3))) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 ( 51.22/7.02 ( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 (( 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) | 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ Y4))))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))))))))) 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk1' @ '#sk7' @ Y1) | ('#sk2' @ 51.22/7.02 '#sk7' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & 51.22/7.02 ((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))))) => 51.22/7.02 (Y0 @ Y2))))))))))) => 51.22/7.02 (Y0 @ '#sk8')))))))), 51.22/7.02 inference('renaming', [status(thm)], [zip_derived_cl27, zip_derived_cl32])). 51.22/7.02 thf(zip_derived_cl28, plain, 51.22/7.02 (( ('#form9') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) & 51.22/7.02 (Y2 @ Y3))) => 51.22/7.02 (Y2 @ Y4))))))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))))) => 51.22/7.02 (Y2 @ Y1)))))) | 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk1' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ Y4))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))) => 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) | 51.22/7.02 ('#sk1' @ 51.22/7.02 Y0 @ Y3))) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 ( 51.22/7.02 ( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 (( 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) | 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ Y4))))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))))))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl43, plain, 51.22/7.02 ((~ ('#form9') 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk1' @ '#sk7' @ Y1) | ('#sk2' @ 51.22/7.02 '#sk7' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & 51.22/7.02 ((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))))) => 51.22/7.02 (Y0 @ Y2))))))))))) => 51.22/7.02 (Y0 @ '#sk8')))))) 51.22/7.02 | ('#form11'))), 51.22/7.02 inference('renaming', [status(thm)], [zip_derived_cl36, zip_derived_cl28])). 51.22/7.02 thf(zip_derived_cl52, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( (((((((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk1' @ '#sk7' @ Y0) | ('#sk2' @ '#sk7' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((X2 @ Y0) & 51.22/7.02 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 51.22/7.02 Y0 @ Y1))))) => 51.22/7.02 (X2 @ Y1))))))))))) => 51.22/7.02 (X2 @ '#sk8'))) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9'))), 51.22/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 51.22/7.02 thf(zip_derived_cl53, plain, 51.22/7.02 (( (((((((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk1' @ '#sk7' @ Y0) | ('#sk2' @ '#sk7' @ Y0))) => 51.22/7.02 ('#sk16' @ Y0)))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk16' @ Y0) & 51.22/7.02 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 51.22/7.02 Y1))))) => 51.22/7.02 ('#sk16' @ Y1))))))))))) => 51.22/7.02 ('#sk16' @ '#sk8'))) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9'))), 51.22/7.02 inference('triggered_bool_instantiation', [status(thm)], 51.22/7.02 [zip_derived_cl52])). 51.22/7.02 thf(zip_derived_cl322, plain, 51.22/7.02 ((~ (((((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk1' @ '#sk7' @ Y0) | ('#sk2' @ '#sk7' @ Y0))) => 51.22/7.02 ('#sk16' @ Y0)))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk16' @ Y0) & 51.22/7.02 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 51.22/7.02 Y1))))) => 51.22/7.02 ('#sk16' @ Y1))))))))))) 51.22/7.02 | ('#sk16' @ '#sk8') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 51.22/7.02 thf(zip_derived_cl22, plain, 51.22/7.02 ((~ (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 ((((((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))) & 51.22/7.02 (Y0 @ Y1))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk6' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk8')))))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) & 51.22/7.02 (Y2 @ Y3))) => 51.22/7.02 (Y2 @ Y4))))))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))))) => 51.22/7.02 (Y2 @ Y1)))))) | 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk1' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ Y4))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))) => 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) | 51.22/7.02 ('#sk1' @ 51.22/7.02 Y0 @ Y3))) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 ( 51.22/7.02 ( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 (( 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) | 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ Y4))))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))))))))) 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 ((((((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))) & 51.22/7.02 (Y0 @ Y1))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk3' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk4')))))))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 51.22/7.02 thf(zip_derived_cl28, plain, 51.22/7.02 (( ('#form9') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((((((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) & 51.22/7.02 (Y2 @ Y3))) => 51.22/7.02 (Y2 @ Y4))))))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))))) => 51.22/7.02 (Y2 @ Y1)))))) | 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((('#sk1' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 (( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ Y4))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))) => 51.22/7.02 (((!!) @ (^[Y2 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y3 : a]: 51.22/7.02 ((((('#sk2' @ 51.22/7.02 Y0 @ 51.22/7.02 Y3) | 51.22/7.02 ('#sk1' @ 51.22/7.02 Y0 @ Y3))) => 51.22/7.02 (Y2 @ Y3)))))) & 51.22/7.02 (((!!) @ (^[Y3 : a]: 51.22/7.02 (((!!) @ ( 51.22/7.02 ^[Y4 : a]: 51.22/7.02 ( 51.22/7.02 ( 51.22/7.02 (( 51.22/7.02 (Y2 @ 51.22/7.02 Y3) & 51.22/7.02 (( 51.22/7.02 ('#sk1' @ 51.22/7.02 Y3 @ 51.22/7.02 Y4) | 51.22/7.02 ('#sk2' @ 51.22/7.02 Y3 @ Y4))))) => 51.22/7.02 (Y2 @ Y4))))))))))) => 51.22/7.02 (Y2 @ Y1)))))))))))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl30, plain, 51.22/7.02 ((~ ('#form9') 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 ((((((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))) & 51.22/7.02 (Y0 @ Y1))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk3' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk4')))))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 ((((((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))) & 51.22/7.02 (Y0 @ Y1))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk6' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk8')))))))), 51.22/7.02 inference('renaming', [status(thm)], [zip_derived_cl22, zip_derived_cl28])). 51.22/7.02 thf(zip_derived_cl32, plain, 51.22/7.02 ((~ ('#form11') 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 ((((((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))) & 51.22/7.02 (Y0 @ Y1))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk3' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk4')))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl37, plain, 51.22/7.02 (( ('#form11') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 ((((((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))) & 51.22/7.02 (Y0 @ Y1))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk6' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk8')))))) 51.22/7.02 | ~ ('#form9'))), 51.22/7.02 inference('renaming', [status(thm)], [zip_derived_cl30, zip_derived_cl32])). 51.22/7.02 thf(zip_derived_cl45, plain, 51.22/7.02 ((~ (((((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 51.22/7.02 Y0 @ Y1))) & 51.22/7.02 ('#sk16' @ Y0))) => 51.22/7.02 ('#sk16' @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.22/7.02 ('#sk16' @ Y0)))))))) => 51.22/7.02 ('#sk16' @ '#sk8'))) 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11'))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl37])). 51.22/7.02 thf(zip_derived_cl56, plain, 51.22/7.02 ((~ ('#sk16' @ '#sk8') | ('#form11') | ~ ('#form9'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 51.22/7.02 thf(zip_derived_cl323, plain, 51.22/7.02 (( ('#form11') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ~ (((((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk1' @ '#sk7' @ Y0) | ('#sk2' @ '#sk7' @ Y0))) => 51.22/7.02 ('#sk16' @ Y0)))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk16' @ Y0) & 51.22/7.02 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 51.22/7.02 Y0 @ Y1))))) => 51.22/7.02 ('#sk16' @ Y1))))))))))))), 51.22/7.02 inference('clc', [status(thm)], [zip_derived_cl322, zip_derived_cl56])). 51.22/7.02 thf(zip_derived_cl324, plain, 51.22/7.02 ((~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk1' @ '#sk7' @ Y0) | ('#sk2' @ '#sk7' @ Y0))) => 51.22/7.02 ('#sk16' @ Y0)))))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk16' @ Y0) & 51.22/7.02 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 51.22/7.02 Y1))))) => 51.22/7.02 ('#sk16' @ Y1))))))))) 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl323])). 51.22/7.02 thf(zip_derived_cl325, plain, 51.22/7.02 ((~ ((((('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) | ('#sk2' @ '#sk7' @ 51.22/7.02 ('#sk61' @ '#sk16')))) => 51.22/7.02 ('#sk16' @ ('#sk61' @ '#sk16')))) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk16' @ Y0) & 51.22/7.02 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 51.22/7.02 Y1))))) => 51.22/7.02 ('#sk16' @ Y1))))))))))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl324])). 51.22/7.02 thf(zip_derived_cl327, plain, 51.22/7.02 ((~ ('#sk16' @ ('#sk61' @ '#sk16')) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk16' @ Y0) & 51.22/7.02 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 51.22/7.02 Y1))))) => 51.22/7.02 ('#sk16' @ Y1))))))))) 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl325])). 51.22/7.02 thf(zip_derived_cl329, plain, 51.22/7.02 ((~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk16' @ ('#sk122' @ '#sk16')) & 51.22/7.02 ((('#sk1' @ ('#sk122' @ '#sk16') @ Y0) | ('#sk2' @ 51.22/7.02 ('#sk122' @ '#sk16') @ Y0))))) => 51.22/7.02 ('#sk16' @ Y0)))))) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ~ ('#sk16' @ ('#sk61' @ '#sk16')))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl327])). 51.22/7.02 thf(zip_derived_cl331, plain, 51.22/7.02 ((~ ((((('#sk16' @ ('#sk122' @ '#sk16')) & 51.22/7.02 ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) | 51.22/7.02 ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')))))) => 51.22/7.02 ('#sk16' @ ('#sk169' @ '#sk16')))) 51.22/7.02 | ~ ('#sk16' @ ('#sk61' @ '#sk16')) 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11'))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl329])). 51.22/7.02 thf(zip_derived_cl334, plain, 51.22/7.02 ((~ ('#sk16' @ ('#sk169' @ '#sk16')) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ~ ('#sk16' @ ('#sk61' @ '#sk16')))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl331])). 51.22/7.02 thf(zip_derived_cl333, plain, 51.22/7.02 (( ((('#sk16' @ ('#sk122' @ '#sk16')) & 51.22/7.02 ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) | 51.22/7.02 ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')))))) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ~ ('#sk16' @ ('#sk61' @ '#sk16')))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl331])). 51.22/7.02 thf(zip_derived_cl337, plain, 51.22/7.02 (( ('#sk16' @ ('#sk122' @ '#sk16')) 51.22/7.02 | ~ ('#sk16' @ ('#sk61' @ '#sk16')) 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl333])). 51.22/7.02 thf(zip_derived_cl338, plain, 51.22/7.02 (( ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) | ('#sk2' @ 51.22/7.02 ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')))) 51.22/7.02 | ~ ('#sk16' @ ('#sk61' @ '#sk16')) 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl333])). 51.22/7.02 thf(zip_derived_cl341, plain, 51.22/7.02 (( ('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) 51.22/7.02 | ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ~ ('#sk16' @ ('#sk61' @ '#sk16')))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl338])). 51.22/7.02 thf(zip_derived_cl326, plain, 51.22/7.02 (( ((('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) | ('#sk2' @ '#sk7' @ 51.22/7.02 ('#sk61' @ '#sk16')))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk16' @ Y0) & 51.22/7.02 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 51.22/7.02 Y1))))) => 51.22/7.02 ('#sk16' @ Y1))))))))) 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl325])). 51.22/7.02 thf(zip_derived_cl328, plain, 51.22/7.02 (( ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) 51.22/7.02 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk16' @ Y0) & 51.22/7.02 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 51.22/7.02 Y1))))) => 51.22/7.02 ('#sk16' @ Y1))))))))))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl326])). 51.22/7.02 thf(zip_derived_cl330, plain, 51.22/7.02 ((~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk16' @ ('#sk122' @ '#sk16')) & 51.22/7.02 ((('#sk1' @ ('#sk122' @ '#sk16') @ Y0) | ('#sk2' @ 51.22/7.02 ('#sk122' @ '#sk16') @ Y0))))) => 51.22/7.02 ('#sk16' @ Y0)))))) 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11') 51.22/7.02 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 51.22/7.02 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl328])). 51.22/7.02 thf(zip_derived_cl332, plain, 51.22/7.02 ((~ ((((('#sk16' @ ('#sk122' @ '#sk16')) & 51.22/7.02 ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) | 51.22/7.02 ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')))))) => 51.22/7.02 ('#sk16' @ ('#sk169' @ '#sk16')))) 51.22/7.02 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) 51.22/7.02 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9'))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl330])). 51.22/7.02 thf(zip_derived_cl336, plain, 51.22/7.02 ((~ ('#sk16' @ ('#sk169' @ '#sk16')) 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11') 51.22/7.02 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 51.22/7.02 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl332])). 51.22/7.02 thf(zip_derived_cl335, plain, 51.22/7.02 (( ((('#sk16' @ ('#sk122' @ '#sk16')) & 51.22/7.02 ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) | 51.22/7.02 ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')))))) 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11') 51.22/7.02 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 51.22/7.02 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl332])). 51.22/7.02 thf(zip_derived_cl339, plain, 51.22/7.02 (( ('#sk16' @ ('#sk122' @ '#sk16')) 51.22/7.02 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) 51.22/7.02 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl335])). 51.22/7.02 thf(zip_derived_cl340, plain, 51.22/7.02 (( ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) | ('#sk2' @ 51.22/7.02 ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')))) 51.22/7.02 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) 51.22/7.02 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl335])). 51.22/7.02 thf(zip_derived_cl342, plain, 51.22/7.02 (( ('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) 51.22/7.02 | ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11') 51.22/7.02 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 51.22/7.02 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl340])). 51.22/7.02 thf(zip_derived_cl55, plain, 51.22/7.02 (( (((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 51.22/7.02 Y1))) & 51.22/7.02 ('#sk16' @ Y0))) => 51.22/7.02 ('#sk16' @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.22/7.02 ('#sk16' @ Y0)))))))) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 51.22/7.02 thf(zip_derived_cl65, plain, 51.22/7.02 (( (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 51.22/7.02 ('#sk16' @ Y0))) => 51.22/7.02 ('#sk16' @ Y1))))))))) 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 51.22/7.02 thf(zip_derived_cl76, plain, 51.22/7.02 (![X2 : a]: 51.22/7.02 ( (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) & 51.22/7.02 ('#sk16' @ X2))) => 51.22/7.02 ('#sk16' @ Y0)))))) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9'))), 51.22/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl65])). 51.22/7.02 thf(zip_derived_cl90, plain, 51.22/7.02 (![X2 : a, X4 : a]: 51.22/7.02 ( ((((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk16' @ X2))) => 51.22/7.02 ('#sk16' @ X4))) 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11'))), 51.22/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl76])). 51.22/7.02 thf(zip_derived_cl104, plain, 51.22/7.02 (![X2 : a, X4 : a]: 51.22/7.02 (~ ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk16' @ X2))) 51.22/7.02 | ('#sk16' @ X4) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl90])). 51.22/7.02 thf(zip_derived_cl119, plain, 51.22/7.02 (![X2 : a, X4 : a]: 51.22/7.02 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 51.22/7.02 | ~ ('#sk16' @ X2) 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11') 51.22/7.02 | ('#sk16' @ X4))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl104])). 51.22/7.02 thf(zip_derived_cl137, plain, 51.22/7.02 (![X2 : a, X4 : a]: 51.22/7.02 (~ ('#sk2' @ X2 @ X4) 51.22/7.02 | ('#sk16' @ X4) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ~ ('#sk16' @ X2))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl119])). 51.22/7.02 thf(zip_derived_cl165, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ('#form266' @ X2) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl166, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ ((('#sk2' @ '#sk10' @ ('#sk267' @ X2)) => (X2 @ ('#sk267' @ X2)))) 51.22/7.02 | ('#form266' @ X2))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl165])). 51.22/7.02 thf(zip_derived_cl175, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ('#sk2' @ '#sk10' @ ('#sk267' @ X2)) | ('#form266' @ X2))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl166])). 51.22/7.02 thf(zip_derived_cl176, plain, 51.22/7.02 (![X2 : a > $o]: (~ (X2 @ ('#sk267' @ X2)) | ('#form266' @ X2))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl166])). 51.22/7.02 thf(zip_derived_cl144, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ((('#sk2' @ '#sk6' @ ('#sk140' @ X2)) | ('#sk1' @ '#sk6' @ 51.22/7.02 ('#sk140' @ X2)))) 51.22/7.02 | ('#form139' @ X2))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl128])). 51.22/7.02 thf(zip_derived_cl158, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ('#sk2' @ '#sk6' @ ('#sk140' @ X2)) 51.22/7.02 | ('#sk1' @ '#sk6' @ ('#sk140' @ X2)) 51.22/7.02 | ('#form139' @ X2))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl144])). 51.22/7.02 thf(zip_derived_cl66, plain, 51.22/7.02 (( (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.22/7.02 ('#sk16' @ Y0)))))) 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 51.22/7.02 thf(zip_derived_cl77, plain, 51.22/7.02 (![X2 : a]: 51.22/7.02 ( ((((('#sk2' @ '#sk6' @ X2) | ('#sk1' @ '#sk6' @ X2))) => ('#sk16' @ 51.22/7.02 X2))) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9'))), 51.22/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl66])). 51.22/7.02 thf(zip_derived_cl91, plain, 51.22/7.02 (![X2 : a]: 51.22/7.02 (~ ((('#sk2' @ '#sk6' @ X2) | ('#sk1' @ '#sk6' @ X2))) 51.22/7.02 | ('#sk16' @ X2) 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl77])). 51.22/7.02 thf(zip_derived_cl105, plain, 51.22/7.02 (![X2 : a]: 51.22/7.02 (~ ('#sk2' @ '#sk6' @ X2) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#sk16' @ X2))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl91])). 51.22/7.02 thf(zip_derived_cl126, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ((('#sk2' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) | ('#sk1' @ 51.22/7.02 ('#sk50' @ X2) @ ('#sk73' @ X2)))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | (X2 @ '#sk7'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl111])). 51.22/7.02 thf(zip_derived_cl127, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ('#form139' @ X2) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl143, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ ('#form139' @ (^[Y0 : a]: (X2 @ Y0))) 51.22/7.02 | (X2 @ '#sk7') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11') 51.22/7.02 | ((('#sk2' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) | ('#sk1' @ 51.22/7.02 ('#sk50' @ X2) @ ('#sk73' @ X2)))))), 51.22/7.02 inference('renaming', [status(thm)], 51.22/7.02 [zip_derived_cl126, zip_derived_cl127])). 51.22/7.02 thf(zip_derived_cl156, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ ('#form139' @ X2) 51.22/7.02 | (X2 @ '#sk7') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#form11') 51.22/7.02 | ((('#sk2' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) | ('#sk1' @ 51.22/7.02 ('#sk50' @ X2) @ ('#sk73' @ X2)))))), 51.22/7.02 inference('ho_norm', [status(thm)], [zip_derived_cl143])). 51.22/7.02 thf(zip_derived_cl157, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ('#sk2' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) 51.22/7.02 | ('#sk1' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | (X2 @ '#sk7') 51.22/7.02 | ~ ('#form139' @ X2))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl156])). 51.22/7.02 thf(zip_derived_cl136, plain, 51.22/7.02 (![X2 : a, X4 : a]: 51.22/7.02 (~ ('#sk1' @ X2 @ X4) 51.22/7.02 | ('#sk16' @ X4) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ~ ('#sk16' @ X2))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl119])). 51.22/7.02 thf(zip_derived_cl122, plain, 51.22/7.02 (![X2 : a]: (~ ('#sk2' @ '#sk10' @ X2) | ('#form9') | ('#sk20' @ X2))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl109])). 51.22/7.02 thf(zip_derived_cl106, plain, 51.22/7.02 (![X2 : a]: 51.22/7.02 (~ ('#sk1' @ '#sk6' @ X2) 51.22/7.02 | ('#form11') 51.22/7.02 | ~ ('#form9') 51.22/7.02 | ('#sk16' @ X2))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl91])). 51.22/7.02 thf(zip_derived_cl32, plain, 51.22/7.02 ((~ ('#form11') 51.22/7.02 | (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 ((((((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))) & 51.22/7.02 (Y0 @ Y1))) => 51.22/7.02 (Y0 @ Y2))))))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.22/7.02 '#sk3' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))))) => 51.22/7.02 (Y0 @ '#sk4')))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl33, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( (((((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 51.22/7.02 Y0 @ Y1))) & 51.22/7.02 (X2 @ Y0))) => 51.22/7.02 (X2 @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))))) => 51.22/7.02 (X2 @ '#sk4'))) 51.22/7.02 | ~ ('#form11'))), 51.22/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 51.22/7.02 thf(zip_derived_cl42, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 51.22/7.02 Y0 @ Y1))) & 51.22/7.02 (X2 @ Y0))) => 51.22/7.02 (X2 @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))))) 51.22/7.02 | (X2 @ '#sk4') 51.22/7.02 | ~ ('#form11'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])). 51.22/7.02 thf(zip_derived_cl51, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 51.22/7.02 Y1))) & 51.22/7.02 (X2 @ Y0))) => 51.22/7.02 (X2 @ Y1))))))))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))) 51.22/7.02 | ~ ('#form11') 51.22/7.02 | (X2 @ '#sk4'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl42])). 51.22/7.02 thf(zip_derived_cl63, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((((('#sk1' @ ('#sk27' @ X2) @ Y0) | ('#sk2' @ 51.22/7.02 ('#sk27' @ X2) @ Y0))) & 51.22/7.02 (X2 @ ('#sk27' @ X2)))) => 51.22/7.02 (X2 @ Y0)))))) 51.22/7.02 | (X2 @ '#sk4') 51.22/7.02 | ~ ('#form11') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl51])). 51.22/7.02 thf(zip_derived_cl74, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ ((((((('#sk1' @ ('#sk27' @ X2) @ ('#sk39' @ X2)) | ('#sk2' @ 51.22/7.02 ('#sk27' @ X2) @ ('#sk39' @ X2)))) & 51.22/7.02 (X2 @ ('#sk27' @ X2)))) => 51.22/7.02 (X2 @ ('#sk39' @ X2)))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))) 51.22/7.02 | ~ ('#form11') 51.22/7.02 | (X2 @ '#sk4'))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl63])). 51.22/7.02 thf(zip_derived_cl88, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ (X2 @ ('#sk39' @ X2)) 51.22/7.02 | (X2 @ '#sk4') 51.22/7.02 | ~ ('#form11') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])). 51.22/7.02 thf(zip_derived_cl99, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ('#form82' @ X2) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl100, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 (~ ((((('#sk2' @ '#sk3' @ ('#sk83' @ X2)) | ('#sk1' @ '#sk3' @ 51.22/7.02 ('#sk83' @ X2)))) => 51.22/7.02 (X2 @ ('#sk83' @ X2)))) 51.22/7.02 | ('#form82' @ X2))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl99])). 51.22/7.02 thf(zip_derived_cl115, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ((('#sk2' @ '#sk3' @ ('#sk83' @ X2)) | ('#sk1' @ '#sk3' @ 51.22/7.02 ('#sk83' @ X2)))) 51.22/7.02 | ('#form82' @ X2))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 51.22/7.02 thf(zip_derived_cl133, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ('#sk2' @ '#sk3' @ ('#sk83' @ X2)) 51.22/7.02 | ('#sk1' @ '#sk3' @ ('#sk83' @ X2)) 51.22/7.02 | ('#form82' @ X2))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl115])). 51.22/7.02 thf(zip_derived_cl116, plain, 51.22/7.02 (![X2 : a > $o]: (~ (X2 @ ('#sk83' @ X2)) | ('#form82' @ X2))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 51.22/7.02 thf(zip_derived_cl33, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( (((((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 51.22/7.02 Y0 @ Y1))) & 51.22/7.02 (X2 @ Y0))) => 51.22/7.02 (X2 @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))))) => 51.22/7.02 (X2 @ '#sk4'))) 51.22/7.02 | ~ ('#form11'))), 51.22/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 51.22/7.02 thf(zip_derived_cl34, plain, 51.22/7.02 (( (((((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 51.22/7.02 Y1))) & 51.22/7.02 ('#sk5' @ Y0))) => 51.22/7.02 ('#sk5' @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.22/7.02 ('#sk5' @ Y0)))))))) => 51.22/7.02 ('#sk5' @ '#sk4'))) 51.22/7.02 | ~ ('#form11'))), 51.22/7.02 inference('triggered_bool_instantiation', [status(thm)], 51.22/7.02 [zip_derived_cl33])). 51.22/7.02 thf(zip_derived_cl6, plain, 51.22/7.02 (~ (((!!) @ (^[Y0 : a > $o]: 51.22/7.02 (((((((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 51.22/7.02 '#sk3' @ Y1))) => 51.22/7.02 (Y0 @ Y1)))))) & 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 (((!!) @ (^[Y2 : a]: 51.22/7.02 (((((Y0 @ Y1) & 51.22/7.02 ((('#sk1' @ Y1 @ Y2) | 51.22/7.02 ('#sk2' @ Y1 @ Y2))))) => 51.22/7.02 (Y0 @ Y2))))))))))) => 51.22/7.02 (Y0 @ '#sk4'))))))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 51.22/7.02 thf(zip_derived_cl8, plain, 51.22/7.02 (~ (((((((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 51.22/7.02 ('#sk5' @ Y0)))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk5' @ Y0) & 51.22/7.02 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 51.22/7.02 Y1))))) => 51.22/7.02 ('#sk5' @ Y1))))))))))) => 51.22/7.02 ('#sk5' @ '#sk4')))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 51.22/7.02 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk4')), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 51.22/7.02 thf(zip_derived_cl205, plain, 51.22/7.02 (( (((((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 51.22/7.02 Y1))) & 51.22/7.02 ('#sk5' @ Y0))) => 51.22/7.02 ('#sk5' @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.22/7.02 ('#sk5' @ Y0)))))))) => 51.22/7.02 ($false))) 51.22/7.02 | ~ ('#form11'))), 51.22/7.02 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl11])). 51.22/7.02 thf(zip_derived_cl206, plain, 51.22/7.02 (( (((~) @ (((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((((('#sk1' @ Y0 @ Y1) | 51.22/7.02 ('#sk2' @ Y0 @ Y1))) & 51.22/7.02 ('#sk5' @ Y0))) => 51.22/7.02 ('#sk5' @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ 51.22/7.02 Y0))) => 51.22/7.02 ('#sk5' @ Y0)))))))))) 51.22/7.02 | ~ ('#form11'))), 51.22/7.02 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl205])). 51.22/7.02 thf(zip_derived_cl207, plain, 51.22/7.02 ((~ (((((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 51.22/7.02 Y1))) & 51.22/7.02 ('#sk5' @ Y0))) => 51.22/7.02 ('#sk5' @ Y1))))))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.22/7.02 ('#sk5' @ Y0)))))))) 51.22/7.02 | ~ ('#form11'))), 51.22/7.02 inference('simplify nested equalities', [status(thm)], 51.22/7.02 [zip_derived_cl206])). 51.22/7.02 thf(zip_derived_cl208, plain, 51.22/7.02 ((~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 51.22/7.02 ('#sk5' @ Y0))) => 51.22/7.02 ('#sk5' @ Y1))))))))) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.22/7.02 ('#sk5' @ Y0)))))) 51.22/7.02 | ~ ('#form11'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl207])). 51.22/7.02 thf(zip_derived_cl99, plain, 51.22/7.02 (![X2 : a > $o]: 51.22/7.02 ( ('#form82' @ X2) 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.22/7.02 (X2 @ Y0)))))))), 51.22/7.02 define([status(thm)])). 51.22/7.02 thf(zip_derived_cl209, plain, 51.22/7.02 ((~ ('#form82' @ '#sk5') 51.22/7.02 | ~ ('#form11') 51.22/7.02 | ~ (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 51.22/7.02 Y1))) & 51.22/7.02 ('#sk5' @ Y0))) => 51.22/7.02 ('#sk5' @ Y1))))))))))), 51.22/7.02 inference('renaming', [status(thm)], 51.22/7.02 [zip_derived_cl208, zip_derived_cl99])). 51.22/7.02 thf(zip_derived_cl210, plain, 51.22/7.02 ((~ (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((((('#sk1' @ ('#sk27' @ '#sk5') @ Y0) | ('#sk2' @ 51.22/7.02 ('#sk27' @ '#sk5') @ Y0))) & 51.22/7.02 ('#sk5' @ ('#sk27' @ '#sk5')))) => 51.22/7.02 ('#sk5' @ Y0)))))) 51.22/7.02 | ~ ('#form11') 51.22/7.02 | ~ ('#form82' @ '#sk5'))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl209])). 51.22/7.02 thf(zip_derived_cl211, plain, 51.22/7.02 ((~ ((((((('#sk1' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) | ('#sk2' @ 51.22/7.02 ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')))) & 51.22/7.02 ('#sk5' @ ('#sk27' @ '#sk5')))) => 51.22/7.02 ('#sk5' @ ('#sk39' @ '#sk5')))) 51.22/7.02 | ~ ('#form82' @ '#sk5') 51.22/7.02 | ~ ('#form11'))), 51.22/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl210])). 51.22/7.02 thf(zip_derived_cl213, plain, 51.22/7.02 ((~ ('#sk5' @ ('#sk39' @ '#sk5')) 51.22/7.02 | ~ ('#form11') 51.22/7.02 | ~ ('#form82' @ '#sk5'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl211])). 51.22/7.02 thf(zip_derived_cl212, plain, 51.22/7.02 (( ((((('#sk1' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) | ('#sk2' @ 51.22/7.02 ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')))) & 51.22/7.02 ('#sk5' @ ('#sk27' @ '#sk5')))) 51.22/7.02 | ~ ('#form11') 51.22/7.02 | ~ ('#form82' @ '#sk5'))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl211])). 51.22/7.02 thf(zip_derived_cl215, plain, 51.22/7.02 (( ('#sk5' @ ('#sk27' @ '#sk5')) | ~ ('#form82' @ '#sk5') | ~ ('#form11'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl212])). 51.22/7.02 thf(zip_derived_cl214, plain, 51.22/7.02 (( ((('#sk1' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) | ('#sk2' @ 51.22/7.02 ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')))) 51.22/7.02 | ~ ('#form82' @ '#sk5') 51.22/7.02 | ~ ('#form11'))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl212])). 51.22/7.02 thf(zip_derived_cl216, plain, 51.22/7.02 (( ('#sk1' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) 51.22/7.02 | ('#sk2' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) 51.22/7.02 | ~ ('#form11') 51.22/7.02 | ~ ('#form82' @ '#sk5'))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl214])). 51.22/7.02 thf(zip_derived_cl10, plain, 51.22/7.02 ( (((((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 51.22/7.02 ('#sk5' @ Y0)))))) & 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk5' @ Y0) & 51.22/7.02 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 51.22/7.02 ('#sk5' @ Y1)))))))))))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 51.22/7.02 thf(zip_derived_cl14, plain, 51.22/7.02 ( (((!!) @ (^[Y0 : a]: 51.22/7.02 (((!!) @ (^[Y1 : a]: 51.22/7.02 ((((('#sk5' @ Y0) & 51.22/7.02 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 51.22/7.02 ('#sk5' @ Y1)))))))))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 51.22/7.02 thf(zip_derived_cl17, plain, 51.22/7.02 (![X2 : a]: 51.22/7.02 (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk5' @ X2) & 51.22/7.02 ((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))))) => 51.22/7.02 ('#sk5' @ Y0))))))), 51.22/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 51.22/7.02 thf(zip_derived_cl20, plain, 51.22/7.02 (![X2 : a, X4 : a]: 51.22/7.02 ((((('#sk5' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) => 51.22/7.02 ('#sk5' @ X4)))), 51.22/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 51.22/7.02 thf(zip_derived_cl25, plain, 51.22/7.02 (![X2 : a, X4 : a]: 51.22/7.02 (~ ((('#sk5' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) 51.22/7.02 | ('#sk5' @ X4))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 51.22/7.02 thf(zip_derived_cl31, plain, 51.22/7.02 (![X2 : a, X4 : a]: 51.22/7.02 (~ ('#sk5' @ X2) 51.22/7.02 | ~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 51.22/7.02 | ('#sk5' @ X4))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl25])). 51.22/7.02 thf(zip_derived_cl40, plain, 51.22/7.02 (![X2 : a, X4 : a]: 51.22/7.02 (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 51.22/7.02 thf(zip_derived_cl13, plain, 51.22/7.02 ( (((!!) @ (^[Y0 : a]: 51.22/7.02 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 51.22/7.02 ('#sk5' @ Y0))))))), 51.22/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 51.22/7.02 thf(zip_derived_cl16, plain, 51.22/7.02 (![X2 : a]: 51.22/7.02 ((((('#sk1' @ '#sk3' @ X2) | ('#sk2' @ '#sk3' @ X2))) => ('#sk5' @ 51.22/7.02 X2)))), 51.22/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 51.22/7.02 thf(zip_derived_cl19, plain, 51.22/7.02 (![X2 : a]: 51.22/7.02 (~ ((('#sk1' @ '#sk3' @ X2) | ('#sk2' @ '#sk3' @ X2))) 51.22/7.02 | ('#sk5' @ X2))), 51.22/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 51.22/7.02 thf(zip_derived_cl24, plain, 51.22/7.02 (![X2 : a]: (~ ('#sk2' @ '#sk3' @ X2) | ('#sk5' @ X2))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 51.22/7.02 thf(zip_derived_cl23, plain, 51.22/7.02 (![X2 : a]: (~ ('#sk1' @ '#sk3' @ X2) | ('#sk5' @ X2))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 51.22/7.02 thf(zip_derived_cl39, plain, 51.22/7.02 (![X2 : a, X4 : a]: 51.22/7.02 (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 51.22/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 51.22/7.02 thf(zip_derived_cl9489, plain, ($false), 51.22/7.02 inference('eprover', [status(thm)], 51.22/7.02 [zip_derived_cl72, zip_derived_cl180, zip_derived_cl187, 51.22/7.02 zip_derived_cl178, zip_derived_cl123, zip_derived_cl186, 51.22/7.02 zip_derived_cl153, zip_derived_cl185, zip_derived_cl184, 51.22/7.02 zip_derived_cl281, zip_derived_cl279, zip_derived_cl155, 51.22/7.02 zip_derived_cl280, zip_derived_cl129, zip_derived_cl154, 51.22/7.02 zip_derived_cl145, zip_derived_cl334, zip_derived_cl337, 51.22/7.02 zip_derived_cl341, zip_derived_cl336, zip_derived_cl339, 51.22/7.02 zip_derived_cl342, zip_derived_cl137, zip_derived_cl175, 51.22/7.02 zip_derived_cl176, zip_derived_cl158, zip_derived_cl105, 51.22/7.02 zip_derived_cl157, zip_derived_cl136, zip_derived_cl122, 51.22/7.02 zip_derived_cl106, zip_derived_cl133, zip_derived_cl116, 51.22/7.02 zip_derived_cl213, zip_derived_cl215, zip_derived_cl216, 51.22/7.02 zip_derived_cl40, zip_derived_cl24, zip_derived_cl23, 51.22/7.02 zip_derived_cl39])). 51.22/7.02 51.22/7.02 % SZS output end Refutation 51.22/7.02 51.22/7.02 51.22/7.02 % Terminating... 51.22/7.07 % Runner terminated. 51.22/7.08 % Zipperpin 1.5 exiting 51.22/7.08 EOF