0.02/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.dB17S7B3Qn true 0.07/0.34 % Computer : n025.cluster.edu 0.07/0.34 % Model : x86_64 x86_64 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.07/0.34 % Memory : 8042.1875MB 0.07/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.07/0.34 % CPULimit : 960 0.07/0.34 % WCLimit : 120 0.07/0.34 % DateTime : Tue Aug 9 02:19:11 EDT 2022 0.07/0.34 % CPUTime : 0.07/0.34 % Running portfolio for 960 s 0.07/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.07/0.34 % Number of cores: 8 0.07/0.35 % Python version: Python 3.6.8 0.07/0.35 % Running in HO mode 0.33/0.57 % Total configuration time : 828 0.33/0.57 % Estimated wc time : 1656 0.33/0.57 % Estimated cpu time (8 cpus) : 207.0 0.57/0.68 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.57/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.57/0.70 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.57/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.66/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.66/0.78 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.66/0.82 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.67/0.84 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 31.35/7.55 % Solved by lams/20_acsne_simpl.sh. 31.35/7.55 % done 414 iterations in 6.390s 31.35/7.55 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 31.35/7.55 % SZS output start Refutation 31.35/7.55 thf(a_type, type, a: $tType). 31.35/7.55 thf('#form266_type', type, '#form266': (a > $o) > $o). 31.35/7.55 thf('#sk12_type', type, '#sk12': a). 31.35/7.55 thf('#sk20_type', type, '#sk20': a > $o). 31.35/7.55 thf('#form46_type', type, '#form46': $o). 31.35/7.55 thf('#sk16_type', type, '#sk16': a > $o). 31.35/7.55 thf('#sk6_type', type, '#sk6': a). 31.35/7.55 thf('#sk174_type', type, '#sk174': (a > $o) > a). 31.35/7.55 thf('#sk39_type', type, '#sk39': (a > $o) > a). 31.35/7.55 thf('#form82_type', type, '#form82': (a > $o) > $o). 31.35/7.55 thf('#sk73_type', type, '#sk73': (a > $o) > a). 31.35/7.55 thf('#sk5_type', type, '#sk5': a > $o). 31.35/7.55 thf('#sk4_type', type, '#sk4': a). 31.35/7.55 thf('#form139_type', type, '#form139': (a > $o) > $o). 31.35/7.55 thf('#sk272_type', type, '#sk272': (a > $o) > a). 31.35/7.55 thf('#sk140_type', type, '#sk140': (a > $o) > a). 31.35/7.55 thf('#sk61_type', type, '#sk61': (a > $o) > a). 31.35/7.55 thf('#form9_type', type, '#form9': $o). 31.35/7.55 thf('#sk169_type', type, '#sk169': (a > $o) > a). 31.35/7.55 thf('#form11_type', type, '#form11': $o). 31.35/7.55 thf('#sk8_type', type, '#sk8': a). 31.35/7.55 thf('#sk267_type', type, '#sk267': (a > $o) > a). 31.35/7.55 thf('#sk3_type', type, '#sk3': a). 31.35/7.55 thf('#sk7_type', type, '#sk7': a). 31.35/7.55 thf('#sk27_type', type, '#sk27': (a > $o) > a). 31.35/7.55 thf('#sk1_type', type, '#sk1': a > a > $o). 31.35/7.55 thf('#sk122_type', type, '#sk122': (a > $o) > a). 31.35/7.55 thf('#sk50_type', type, '#sk50': (a > $o) > a). 31.35/7.55 thf('#sk2_type', type, '#sk2': a > a > $o). 31.35/7.55 thf('#sk126_type', type, '#sk126': (a > $o) > a). 31.35/7.55 thf('#sk221_type', type, '#sk221': (a > $o) > a). 31.35/7.55 thf('#sk130_type', type, '#sk130': (a > $o) > a). 31.35/7.55 thf('#sk10_type', type, '#sk10': a). 31.35/7.55 thf('#sk83_type', type, '#sk83': (a > $o) > a). 31.35/7.55 thf(cTHM251G_pme, conjecture, 31.35/7.55 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 31.35/7.55 ( ( ~( ( ( ![Xx0:a,Xy0:a,Xz:a]: 31.35/7.55 ( ( ( ![Xq:( a > $o )]: 31.35/7.55 ( ( ( ![Xu:a,Xv:a]: 31.35/7.55 ( ( ( Xq @ Xu ) & 31.35/7.55 ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 31.35/7.55 ( Xq @ Xv ) ) ) & 31.35/7.55 ( ![Xw:a]: 31.35/7.55 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 31.35/7.55 ( Xq @ Xw ) ) ) ) => 31.35/7.55 ( Xq @ Xy0 ) ) ) & 31.35/7.55 ( ![Xq:( a > $o )]: 31.35/7.55 ( ( ( ![Xw:a]: 31.35/7.55 ( ( ( R @ Xy0 @ Xw ) | ( S @ Xy0 @ Xw ) ) => 31.35/7.55 ( Xq @ Xw ) ) ) & 31.35/7.55 ( ![Xu:a,Xv:a]: 31.35/7.55 ( ( ( Xq @ Xu ) & 31.35/7.55 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 31.35/7.55 ( Xq @ Xv ) ) ) ) => 31.35/7.55 ( Xq @ Xz ) ) ) ) => 31.35/7.55 ( ![Xq:( a > $o )]: 31.35/7.55 ( ( ( ![Xu:a,Xv:a]: 31.35/7.55 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & 31.35/7.55 ( Xq @ Xu ) ) => 31.35/7.55 ( Xq @ Xv ) ) ) & 31.35/7.55 ( ![Xw:a]: 31.35/7.55 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 31.35/7.55 ( Xq @ Xw ) ) ) ) => 31.35/7.55 ( Xq @ Xz ) ) ) ) ) & 31.35/7.55 ( ![Xx0:a,Xy0:a]: 31.35/7.55 ( ( ( ![Xq:( a > $o )]: 31.35/7.55 ( ( ( ![Xu:a,Xv:a]: 31.35/7.55 ( ( ( S @ Xu @ Xv ) & ( Xq @ Xu ) ) => ( Xq @ Xv ) ) ) & 31.35/7.55 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 31.35/7.55 ( Xq @ Xy0 ) ) ) | 31.35/7.55 ( ![Xq:( a > $o )]: 31.35/7.55 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 31.35/7.55 ( ![Xu:a,Xv:a]: 31.35/7.55 ( ( ( Xq @ Xu ) & ( R @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) ) => 31.35/7.55 ( Xq @ Xy0 ) ) ) ) => 31.35/7.55 ( ![Xq:( a > $o )]: 31.35/7.55 ( ( ( ![Xw:a]: 31.35/7.55 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 31.35/7.55 ( Xq @ Xw ) ) ) & 31.35/7.55 ( ![Xu:a,Xv:a]: 31.35/7.55 ( ( ( Xq @ Xu ) & 31.35/7.55 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 31.35/7.55 ( Xq @ Xv ) ) ) ) => 31.35/7.55 ( Xq @ Xy0 ) ) ) ) ) ) => 31.35/7.55 ( ![Xq:( a > $o )]: 31.35/7.55 ( ( ( ![Xu:a,Xv:a]: 31.35/7.55 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 31.35/7.55 ( Xq @ Xv ) ) ) & 31.35/7.55 ( ![Xw:a]: 31.35/7.55 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 31.35/7.55 ( Xq @ Xy ) ) ) ) ) | 31.35/7.55 ( ![Xq:( a > $o )]: 31.35/7.55 ( ( ( ![Xw:a]: 31.35/7.55 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 31.35/7.55 ( ![Xu:a,Xv:a]: 31.35/7.55 ( ( ( Xq @ Xu ) & ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 31.35/7.55 ( Xq @ Xv ) ) ) ) => 31.35/7.55 ( Xq @ Xy ) ) ) ))). 31.35/7.55 thf(zf_stmt_0, negated_conjecture, 31.35/7.55 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 31.35/7.55 ( ( ~( ( ( ![Xx0:a,Xy0:a,Xz:a]: 31.35/7.55 ( ( ( ![Xq:( a > $o )]: 31.35/7.55 ( ( ( ![Xu:a,Xv:a]: 31.35/7.55 ( ( ( Xq @ Xu ) & 31.35/7.55 ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 31.35/7.55 ( Xq @ Xv ) ) ) & 31.35/7.55 ( ![Xw:a]: 31.35/7.55 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 31.35/7.55 ( Xq @ Xw ) ) ) ) => 31.35/7.55 ( Xq @ Xy0 ) ) ) & 31.35/7.55 ( ![Xq:( a > $o )]: 31.35/7.55 ( ( ( ![Xw:a]: 31.35/7.55 ( ( ( R @ Xy0 @ Xw ) | ( S @ Xy0 @ Xw ) ) => 31.35/7.55 ( Xq @ Xw ) ) ) & 31.35/7.55 ( ![Xu:a,Xv:a]: 31.35/7.55 ( ( ( Xq @ Xu ) & 31.35/7.55 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 31.35/7.55 ( Xq @ Xv ) ) ) ) => 31.35/7.55 ( Xq @ Xz ) ) ) ) => 31.35/7.55 ( ![Xq:( a > $o )]: 31.35/7.55 ( ( ( ![Xu:a,Xv:a]: 31.35/7.55 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & 31.35/7.55 ( Xq @ Xu ) ) => 31.35/7.55 ( Xq @ Xv ) ) ) & 31.35/7.55 ( ![Xw:a]: 31.35/7.55 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 31.35/7.55 ( Xq @ Xw ) ) ) ) => 31.35/7.55 ( Xq @ Xz ) ) ) ) ) & 31.35/7.55 ( ![Xx0:a,Xy0:a]: 31.35/7.55 ( ( ( ![Xq:( a > $o )]: 31.35/7.55 ( ( ( ![Xu:a,Xv:a]: 31.35/7.55 ( ( ( S @ Xu @ Xv ) & ( Xq @ Xu ) ) => 31.35/7.55 ( Xq @ Xv ) ) ) & 31.35/7.55 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 31.35/7.55 ( Xq @ Xy0 ) ) ) | 31.35/7.55 ( ![Xq:( a > $o )]: 31.35/7.55 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 31.35/7.55 ( ![Xu:a,Xv:a]: 31.35/7.55 ( ( ( Xq @ Xu ) & ( R @ Xu @ Xv ) ) => 31.35/7.55 ( Xq @ Xv ) ) ) ) => 31.35/7.55 ( Xq @ Xy0 ) ) ) ) => 31.35/7.55 ( ![Xq:( a > $o )]: 31.35/7.55 ( ( ( ![Xw:a]: 31.35/7.55 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 31.35/7.55 ( Xq @ Xw ) ) ) & 31.35/7.55 ( ![Xu:a,Xv:a]: 31.35/7.55 ( ( ( Xq @ Xu ) & 31.35/7.55 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 31.35/7.55 ( Xq @ Xv ) ) ) ) => 31.35/7.55 ( Xq @ Xy0 ) ) ) ) ) ) => 31.35/7.55 ( ![Xq:( a > $o )]: 31.35/7.55 ( ( ( ![Xu:a,Xv:a]: 31.35/7.55 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 31.35/7.55 ( Xq @ Xv ) ) ) & 31.35/7.55 ( ![Xw:a]: 31.35/7.55 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 31.35/7.55 ( Xq @ Xy ) ) ) ) ) | 31.35/7.55 ( ![Xq:( a > $o )]: 31.35/7.55 ( ( ( ![Xw:a]: 31.35/7.55 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 31.35/7.55 ( ![Xu:a,Xv:a]: 31.35/7.55 ( ( ( Xq @ Xu ) & ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 31.35/7.55 ( Xq @ Xv ) ) ) ) => 31.35/7.55 ( Xq @ Xy ) ) ) ) )), 31.35/7.55 inference('cnf.neg', [status(esa)], [cTHM251G_pme])). 31.35/7.55 thf(zip_derived_cl0, plain, 31.35/7.55 (~ (((!!) @ (^[Y0 : a > a > $o]: 31.35/7.55 (((!!) @ (^[Y1 : a > a > $o]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((((~) @ (((( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y8 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y9 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y7 @ 31.35/7.55 Y8) & 31.35/7.55 (( 31.35/7.55 (Y1 @ 31.35/7.55 Y8 @ 31.35/7.55 Y9) | 31.35/7.55 (Y0 @ 31.35/7.55 Y8 @ Y9))))) => 31.35/7.55 (Y7 @ Y9))))))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y8 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y1 @ 31.35/7.55 Y4 @ 31.35/7.55 Y8) | 31.35/7.55 (Y0 @ 31.35/7.55 Y4 @ Y8))) => 31.35/7.55 (Y7 @ Y8)))))))) => 31.35/7.55 (Y7 @ Y5)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y8 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y0 @ 31.35/7.55 Y5 @ 31.35/7.55 Y8) | 31.35/7.55 (Y1 @ 31.35/7.55 Y5 @ Y8))) => 31.35/7.55 (Y7 @ Y8)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y8 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y9 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y7 @ 31.35/7.55 Y8) & 31.35/7.55 (( 31.35/7.55 (Y0 @ 31.35/7.55 Y8 @ 31.35/7.55 Y9) | 31.35/7.55 (Y1 @ 31.35/7.55 Y8 @ Y9))))) => 31.35/7.55 (Y7 @ Y9))))))))))) => 31.35/7.55 (Y7 @ Y6)))))))) => 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y8 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y9 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y0 @ 31.35/7.55 Y8 @ 31.35/7.55 Y9) | 31.35/7.55 (Y1 @ 31.35/7.55 Y8 @ Y9))) & 31.35/7.55 (Y7 @ Y8))) => 31.35/7.55 (Y7 @ Y9))))))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y8 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y1 @ 31.35/7.55 Y4 @ 31.35/7.55 Y8) | 31.35/7.55 (Y0 @ 31.35/7.55 Y4 @ Y8))) => 31.35/7.55 (Y7 @ Y8)))))))) => 31.35/7.55 (Y7 @ Y6))))))))))))))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y8 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y1 @ 31.35/7.55 Y7 @ 31.35/7.55 Y8) & 31.35/7.55 (Y6 @ Y7))) => 31.35/7.55 (Y6 @ Y8))))))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (Y1 @ 31.35/7.55 Y4 @ 31.35/7.55 Y7) => 31.35/7.55 (Y6 @ Y7)))))))) => 31.35/7.55 (Y6 @ Y5)))))) | 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (Y0 @ 31.35/7.55 Y4 @ 31.35/7.55 Y7) => 31.35/7.55 (Y6 @ Y7)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y8 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y6 @ 31.35/7.55 Y7) & 31.35/7.55 (Y0 @ 31.35/7.55 Y7 @ Y8))) => 31.35/7.55 (Y6 @ Y8))))))))))) => 31.35/7.55 (Y6 @ Y5)))))))) => 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y1 @ 31.35/7.55 Y4 @ 31.35/7.55 Y7) | 31.35/7.55 (Y0 @ 31.35/7.55 Y4 @ Y7))) => 31.35/7.55 (Y6 @ Y7)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y8 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y6 @ 31.35/7.55 Y7) & 31.35/7.55 (( 31.35/7.55 (Y0 @ 31.35/7.55 Y7 @ 31.35/7.55 Y8) | 31.35/7.55 (Y1 @ 31.35/7.55 Y7 @ Y8))))) => 31.35/7.55 (Y6 @ Y8))))))))))) => 31.35/7.55 (Y6 @ Y5)))))))))))))))) => 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y0 @ 31.35/7.55 Y5 @ 31.35/7.55 Y6) | 31.35/7.55 (Y1 @ 31.35/7.55 Y5 @ Y6))) & 31.35/7.55 (Y4 @ Y5))) => 31.35/7.55 (Y4 @ Y6))))))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y1 @ 31.35/7.55 Y2 @ 31.35/7.55 Y5) | 31.35/7.55 (Y0 @ 31.35/7.55 Y2 @ Y5))) => 31.35/7.55 (Y4 @ Y5)))))))) => 31.35/7.55 (Y4 @ Y3)))))))))) | 31.35/7.55 (((!!) @ (^[Y4 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y0 @ 31.35/7.55 Y2 @ 31.35/7.55 Y5) | 31.35/7.55 (Y1 @ 31.35/7.55 Y2 @ Y5))) => 31.35/7.55 (Y4 @ Y5)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y4 @ 31.35/7.55 Y5) & 31.35/7.55 (( 31.35/7.55 (Y0 @ 31.35/7.55 Y5 @ 31.35/7.55 Y6) | 31.35/7.55 (Y1 @ 31.35/7.55 Y5 @ Y6))))) => 31.35/7.55 (Y4 @ Y6))))))))))) => 31.35/7.55 (Y4 @ Y3))))))))))))))))))))), 31.35/7.55 inference('cnf', [status(esa)], [zf_stmt_0])). 31.35/7.55 thf(zip_derived_cl1, plain, 31.35/7.55 (~ (((!!) @ (^[Y0 : a > a > $o]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((~) @ (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y8 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y6 @ 31.35/7.55 Y7) & 31.35/7.55 (( 31.35/7.55 (Y0 @ 31.35/7.55 Y7 @ 31.35/7.55 Y8) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y7 @ Y8))))) => 31.35/7.55 (Y6 @ Y8))))))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y0 @ 31.35/7.55 Y3 @ 31.35/7.55 Y7) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y7))) => 31.35/7.55 (Y6 @ Y7)))))))) => 31.35/7.55 (Y6 @ Y4)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y4 @ 31.35/7.55 Y7) | 31.35/7.55 (Y0 @ 31.35/7.55 Y4 @ Y7))) => 31.35/7.55 (Y6 @ Y7)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y8 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y6 @ 31.35/7.55 Y7) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y7 @ 31.35/7.55 Y8) | 31.35/7.55 (Y0 @ 31.35/7.55 Y7 @ Y8))))) => 31.35/7.55 (Y6 @ Y8))))))))))) => 31.35/7.55 (Y6 @ Y5)))))))) => 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y8 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y7 @ 31.35/7.55 Y8) | 31.35/7.55 (Y0 @ 31.35/7.55 Y7 @ Y8))) & 31.35/7.55 (Y6 @ Y7))) => 31.35/7.55 (Y6 @ Y8))))))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y0 @ 31.35/7.55 Y3 @ 31.35/7.55 Y7) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y7))) => 31.35/7.55 (Y6 @ Y7)))))))) => 31.35/7.55 (Y6 @ Y5))))))))))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y0 @ 31.35/7.55 Y6 @ 31.35/7.55 Y7) & 31.35/7.55 (Y5 @ Y6))) => 31.35/7.55 (Y5 @ Y7))))))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (Y0 @ 31.35/7.55 Y3 @ 31.35/7.55 Y6) => 31.35/7.55 (Y5 @ Y6)))))))) => 31.35/7.55 (Y5 @ Y4)))))) | 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y6) => 31.35/7.55 (Y5 @ Y6)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y5 @ 31.35/7.55 Y6) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y6 @ Y7))) => 31.35/7.55 (Y5 @ Y7))))))))))) => 31.35/7.55 (Y5 @ Y4)))))))) => 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y0 @ 31.35/7.55 Y3 @ 31.35/7.55 Y6) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y6))) => 31.35/7.55 (Y5 @ Y6)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y5 @ 31.35/7.55 Y6) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y6 @ 31.35/7.55 Y7) | 31.35/7.55 (Y0 @ 31.35/7.55 Y6 @ Y7))))) => 31.35/7.55 (Y5 @ Y7))))))))))) => 31.35/7.55 (Y5 @ Y4)))))))))))))))) => 31.35/7.55 (((!!) @ (^[Y3 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y4 @ 31.35/7.55 Y5) | 31.35/7.55 (Y0 @ 31.35/7.55 Y4 @ Y5))) & 31.35/7.55 (Y3 @ Y4))) => 31.35/7.55 (Y3 @ Y5))))))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y0 @ 31.35/7.55 Y1 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y1 @ Y4))) => 31.35/7.55 (Y3 @ Y4)))))))) => 31.35/7.55 (Y3 @ Y2)))))))))) | 31.35/7.55 (((!!) @ (^[Y3 : a > $o]: 31.35/7.55 (((((((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (((( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y1 @ Y4) | 31.35/7.55 (Y0 @ 31.35/7.55 Y1 @ Y4))) => 31.35/7.55 (Y3 @ Y4)))))) & 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y4 @ 31.35/7.55 Y5) | 31.35/7.55 (Y0 @ 31.35/7.55 Y4 @ Y5))))) => 31.35/7.55 (Y3 @ Y5))))))))))) => 31.35/7.55 (Y3 @ Y2)))))))))))))))))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 31.35/7.55 thf(zip_derived_cl2, plain, 31.35/7.55 (~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((~) @ (((((((!!) @ (^[Y2 : a]: 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y5 @ 31.35/7.55 Y6) & 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y6 @ 31.35/7.55 Y7) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y6 @ Y7))))) => 31.35/7.55 (Y5 @ Y7))))))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y2 @ 31.35/7.55 Y6) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y2 @ Y6))) => 31.35/7.55 (Y5 @ Y6)))))))) => 31.35/7.55 (Y5 @ Y3)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y6) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y6))) => 31.35/7.55 (Y5 @ Y6)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y5 @ 31.35/7.55 Y6) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y6 @ 31.35/7.55 Y7) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y6 @ Y7))))) => 31.35/7.55 (Y5 @ Y7))))))))))) => 31.35/7.55 (Y5 @ Y4)))))))) => 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y7 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y6 @ 31.35/7.55 Y7) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y6 @ Y7))) & 31.35/7.55 (Y5 @ Y6))) => 31.35/7.55 (Y5 @ Y7))))))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y2 @ 31.35/7.55 Y6) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y2 @ Y6))) => 31.35/7.55 (Y5 @ Y6)))))))) => 31.35/7.55 (Y5 @ Y4))))))))))))))))) & 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y5 @ 31.35/7.55 Y6) & 31.35/7.55 (Y4 @ Y5))) => 31.35/7.55 (Y4 @ Y6))))))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y2 @ 31.35/7.55 Y5) => 31.35/7.55 (Y4 @ Y5)))))))) => 31.35/7.55 (Y4 @ Y3)))))) | 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y2 @ 31.35/7.55 Y5) => 31.35/7.55 (Y4 @ Y5)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y4 @ 31.35/7.55 Y5) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y5 @ Y6))) => 31.35/7.55 (Y4 @ Y6))))))))))) => 31.35/7.55 (Y4 @ Y3)))))))) => 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y2 @ 31.35/7.55 Y5) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y2 @ Y5))) => 31.35/7.55 (Y4 @ Y5)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y4 @ 31.35/7.55 Y5) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y5 @ 31.35/7.55 Y6) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y5 @ Y6))))) => 31.35/7.55 (Y4 @ Y6))))))))))) => 31.35/7.55 (Y4 @ Y3)))))))))))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ ( 31.35/7.55 ^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk1' @ 31.35/7.55 Y0 @ Y3) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (((( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1))))))))))))))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 31.35/7.55 thf(zip_derived_cl3, plain, 31.35/7.55 (~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((((~) @ (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y4 @ 31.35/7.55 Y5) & 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y5 @ 31.35/7.55 Y6) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y5 @ Y6))))) => 31.35/7.55 (Y4 @ Y6))))))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y1 @ 31.35/7.55 Y5) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y1 @ Y5))) => 31.35/7.55 (Y4 @ Y5)))))))) => 31.35/7.55 (Y4 @ Y2)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y2 @ 31.35/7.55 Y5) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y2 @ Y5))) => 31.35/7.55 (Y4 @ Y5)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y4 @ 31.35/7.55 Y5) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y5 @ 31.35/7.55 Y6) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y5 @ Y6))))) => 31.35/7.55 (Y4 @ Y6))))))))))) => 31.35/7.55 (Y4 @ Y3)))))))) => 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a > $o]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y6 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y5 @ 31.35/7.55 Y6) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y5 @ Y6))) & 31.35/7.55 (Y4 @ Y5))) => 31.35/7.55 (Y4 @ Y6))))))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y1 @ 31.35/7.55 Y5) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y1 @ Y5))) => 31.35/7.55 (Y4 @ Y5)))))))) => 31.35/7.55 (Y4 @ Y3))))))))))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((((!!) @ ( 31.35/7.55 ^[Y3 : a > $o]: 31.35/7.55 (((( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y4 @ 31.35/7.55 Y5) & 31.35/7.55 (Y3 @ Y4))) => 31.35/7.55 (Y3 @ Y5))))))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y1 @ 31.35/7.55 Y4) => 31.35/7.55 (Y3 @ Y4)))))))) => 31.35/7.55 (Y3 @ Y2)))))) | 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y3 : a > $o]: 31.35/7.55 (((( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y1 @ 31.35/7.55 Y4) => 31.35/7.55 (Y3 @ Y4)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y3 @ 31.35/7.55 Y4) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y4 @ Y5))) => 31.35/7.55 (Y3 @ Y5))))))))))) => 31.35/7.55 (Y3 @ Y2)))))))) => 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y3 : a > $o]: 31.35/7.55 (((((( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y1 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y1 @ Y4))) => 31.35/7.55 (Y3 @ Y4)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y4 @ 31.35/7.55 Y5) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y4 @ Y5))))) => 31.35/7.55 (Y3 @ Y5))))))))))) => 31.35/7.55 (Y3 @ Y2)))))))))))))))) => 31.35/7.55 (((!!) @ (^[Y1 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y2 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y3 : a]: 31.35/7.55 (((((( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y2 @ Y3) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y2 @ Y3))) & 31.35/7.55 (Y1 @ Y2))) => 31.35/7.55 (Y1 @ Y3))))))))) & 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 '#sk3' @ Y2) | 31.35/7.55 ('#sk1' @ 31.35/7.55 '#sk3' @ Y2))) => 31.35/7.55 (Y1 @ Y2)))))))) => 31.35/7.55 (Y1 @ Y0)))))))))) | 31.35/7.55 (((!!) @ (^[Y1 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y2 : a]: 31.35/7.55 ((((('#sk1' @ '#sk3' @ Y2) | 31.35/7.55 ('#sk2' @ '#sk3' @ Y2))) => 31.35/7.55 (Y1 @ Y2)))))) & 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((((Y1 @ Y2) & 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y2 @ Y3) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y2 @ Y3))))) => 31.35/7.55 (Y1 @ Y3))))))))))) => 31.35/7.55 (Y1 @ Y0)))))))))))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 31.35/7.55 thf(zip_derived_cl4, plain, 31.35/7.55 (~ (((((~) @ (((((((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((((!!) @ ( 31.35/7.55 ^[Y3 : a > $o]: 31.35/7.55 (((( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y4 @ 31.35/7.55 Y5) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y4 @ Y5))))) => 31.35/7.55 (Y3 @ Y5))))))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y4))) => 31.35/7.55 (Y3 @ Y4)))))))) => 31.35/7.55 (Y3 @ Y1)))))) & 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y3 : a > $o]: 31.35/7.55 (((( 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y1 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y1 @ Y4))) => 31.35/7.55 (Y3 @ Y4)))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y4 @ 31.35/7.55 Y5) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y4 @ Y5))))) => 31.35/7.55 (Y3 @ Y5))))))))))) => 31.35/7.55 (Y3 @ Y2)))))))) => 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y3 : a > $o]: 31.35/7.55 (((((( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y4 @ 31.35/7.55 Y5) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y4 @ Y5))) & 31.35/7.55 (Y3 @ Y4))) => 31.35/7.55 (Y3 @ Y5))))))))) & 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y4))) => 31.35/7.55 (Y3 @ Y4)))))))) => 31.35/7.55 (Y3 @ Y2))))))))))))))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ ( 31.35/7.55 ^[Y3 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y3 : a]: 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ ( 31.35/7.55 ^[Y3 : a]: 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y3 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ ( 31.35/7.55 ^[Y3 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y3 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))))) => 31.35/7.55 (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ 31.35/7.55 Y1 @ Y2) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | 31.35/7.55 ('#sk1' @ '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4')))))))))) | 31.35/7.55 (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((Y0 @ Y1) & 31.35/7.55 ((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))))) => 31.35/7.55 (Y0 @ Y2))))))))))) => 31.35/7.55 (Y0 @ '#sk4'))))))))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 31.35/7.55 thf(zip_derived_cl6, plain, 31.35/7.55 (~ (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((Y0 @ Y1) & 31.35/7.55 ((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))))) => 31.35/7.55 (Y0 @ Y2))))))))))) => 31.35/7.55 (Y0 @ '#sk4'))))))), 31.35/7.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 31.35/7.55 thf(zip_derived_cl8, plain, 31.35/7.55 (~ (((((((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.35/7.55 ('#sk5' @ Y0)))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk5' @ Y0) & 31.35/7.55 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.35/7.55 Y1))))) => 31.35/7.55 ('#sk5' @ Y1))))))))))) => 31.35/7.55 ('#sk5' @ '#sk4')))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 31.35/7.55 thf(zip_derived_cl10, plain, 31.35/7.55 ( (((((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.35/7.55 ('#sk5' @ Y0)))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk5' @ Y0) & 31.35/7.55 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 31.35/7.55 ('#sk5' @ Y1)))))))))))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 31.35/7.55 thf(zip_derived_cl14, plain, 31.35/7.55 ( (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk5' @ Y0) & 31.35/7.55 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 31.35/7.55 ('#sk5' @ Y1)))))))))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 31.35/7.55 thf(zip_derived_cl17, plain, 31.35/7.55 (![X2 : a]: 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk5' @ X2) & 31.35/7.55 ((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))))) => 31.35/7.55 ('#sk5' @ Y0))))))), 31.35/7.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 31.35/7.55 thf(zip_derived_cl20, plain, 31.35/7.55 (![X2 : a, X4 : a]: 31.35/7.55 ((((('#sk5' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) => 31.35/7.55 ('#sk5' @ X4)))), 31.35/7.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 31.35/7.55 thf(zip_derived_cl25, plain, 31.35/7.55 (![X2 : a, X4 : a]: 31.35/7.55 (~ ((('#sk5' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) 31.35/7.55 | ('#sk5' @ X4))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 31.35/7.55 thf(zip_derived_cl31, plain, 31.35/7.55 (![X2 : a, X4 : a]: 31.35/7.55 (~ ('#sk5' @ X2) 31.35/7.55 | ~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 31.35/7.55 | ('#sk5' @ X4))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl25])). 31.35/7.55 thf(zip_derived_cl39, plain, 31.35/7.55 (![X2 : a, X4 : a]: 31.35/7.55 (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 31.35/7.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 31.35/7.55 thf(zip_derived_cl40, plain, 31.35/7.55 (![X2 : a, X4 : a]: 31.35/7.55 (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 31.35/7.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 31.35/7.55 thf(zip_derived_cl5, plain, 31.35/7.55 ( (((((((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((((!!) @ (^[Y3 : a > $o]: 31.35/7.55 (((((((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y4 @ 31.35/7.55 Y5) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y4 @ Y5))))) => 31.35/7.55 (Y3 @ Y5))))))))) & 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y4))) => 31.35/7.55 (Y3 @ Y4)))))))) => 31.35/7.55 (Y3 @ Y1)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a > $o]: 31.35/7.55 (((((((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y1 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y1 @ Y4))) => 31.35/7.55 (Y3 @ Y4)))))) & 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y4 @ 31.35/7.55 Y5) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y4 @ Y5))))) => 31.35/7.55 (Y3 @ Y5))))))))))) => 31.35/7.55 (Y3 @ Y2)))))))) => 31.35/7.55 (((!!) @ (^[Y3 : a > $o]: 31.35/7.55 (((((((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y4 @ 31.35/7.55 Y5) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y4 @ Y5))) & 31.35/7.55 (Y3 @ Y4))) => 31.35/7.55 (Y3 @ Y5))))))))) & 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y4))) => 31.35/7.55 (Y3 @ Y4)))))))) => 31.35/7.55 (Y3 @ Y2))))))))))))))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))))) => 31.35/7.55 (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4'))))))))), 31.35/7.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 31.35/7.55 thf(zip_derived_cl7, plain, 31.35/7.55 ((~ (((((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((((!!) @ (^[Y3 : a > $o]: 31.35/7.55 (((((((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y4 @ 31.35/7.55 Y5) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y4 @ Y5))))) => 31.35/7.55 (Y3 @ Y5))))))))) & 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y4))) => 31.35/7.55 (Y3 @ Y4)))))))) => 31.35/7.55 (Y3 @ Y1)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a > $o]: 31.35/7.55 (((((((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y1 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y1 @ Y4))) => 31.35/7.55 (Y3 @ Y4)))))) & 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y4 @ 31.35/7.55 Y5) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y4 @ Y5))))) => 31.35/7.55 (Y3 @ Y5))))))))))) => 31.35/7.55 (Y3 @ Y2)))))))) => 31.35/7.55 (((!!) @ (^[Y3 : a > $o]: 31.35/7.55 (((((((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y4 @ 31.35/7.55 Y5) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y4 @ Y5))) & 31.35/7.55 (Y3 @ Y4))) => 31.35/7.55 (Y3 @ Y5))))))))) & 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y4))) => 31.35/7.55 (Y3 @ Y4)))))))) => 31.35/7.55 (Y3 @ Y2))))))))))))))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))))) 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4')))))))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 31.35/7.55 thf(zip_derived_cl9, plain, 31.35/7.55 ((~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((((!!) @ (^[Y3 : a > $o]: 31.35/7.55 (((((((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y4 @ 31.35/7.55 Y5) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y4 @ Y5))))) => 31.35/7.55 (Y3 @ Y5))))))))) & 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y4))) => 31.35/7.55 (Y3 @ Y4)))))))) => 31.35/7.55 (Y3 @ Y1)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a > $o]: 31.35/7.55 (((((((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y1 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y1 @ Y4))) => 31.35/7.55 (Y3 @ Y4)))))) & 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y4 @ 31.35/7.55 Y5) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y4 @ Y5))))) => 31.35/7.55 (Y3 @ Y5))))))))))) => 31.35/7.55 (Y3 @ Y2)))))))) => 31.35/7.55 (((!!) @ (^[Y3 : a > $o]: 31.35/7.55 (((((((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y5 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y4 @ 31.35/7.55 Y5) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y4 @ Y5))) & 31.35/7.55 (Y3 @ Y4))) => 31.35/7.55 (Y3 @ Y5))))))))) & 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (((( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y4))) => 31.35/7.55 (Y3 @ Y4)))))))) => 31.35/7.55 (Y3 @ Y2))))))))))))))))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))) 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4')))))))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl7])). 31.35/7.55 thf(zip_derived_cl12, plain, 31.35/7.55 ((~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 '#sk6' @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 '#sk6' @ 31.35/7.55 Y3))) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y0)))))) & 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (((( 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 '#sk6' @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 '#sk6' @ 31.35/7.55 Y3))) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))) 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4')))))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl9])). 31.35/7.55 thf(zip_derived_cl15, plain, 31.35/7.55 ((~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((((((!!) @ (^[Y1 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y2 : a]: 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((((Y1 @ 31.35/7.55 Y2) & 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y2 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y2 @ Y3))))) => 31.35/7.55 (Y1 @ Y3))))))))) & 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ 31.35/7.55 Y2) | ('#sk1' @ 31.35/7.55 '#sk6' @ Y2))) => 31.35/7.55 (Y1 @ Y2)))))))) => 31.35/7.55 (Y1 @ '#sk7')))))) & 31.35/7.55 (((!!) @ (^[Y1 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y2 : a]: 31.35/7.55 ((((('#sk1' @ '#sk7' @ 31.35/7.55 Y2) | ('#sk2' @ 31.35/7.55 '#sk7' @ Y2))) => 31.35/7.55 (Y1 @ Y2)))))) & 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((((Y1 @ 31.35/7.55 Y2) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y2 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y2 @ Y3))))) => 31.35/7.55 (Y1 @ Y3))))))))))) => 31.35/7.55 (Y1 @ Y0)))))))) => 31.35/7.55 (((!!) @ (^[Y1 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y2 : a]: 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((((((('#sk1' @ 31.35/7.55 Y2 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y2 @ Y3))) & 31.35/7.55 (Y1 @ Y2))) => 31.35/7.55 (Y1 @ Y3))))))))) & 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ 31.35/7.55 Y2) | ('#sk1' @ 31.35/7.55 '#sk6' @ Y2))) => 31.35/7.55 (Y1 @ Y2)))))))) => 31.35/7.55 (Y1 @ Y0))))))))))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))) 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4')))))))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 31.35/7.55 thf(zip_derived_cl18, plain, 31.35/7.55 ((~ (((((((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((Y0 @ Y1) & 31.35/7.55 ((('#sk2' @ Y1 @ 31.35/7.55 Y2) | ('#sk1' @ 31.35/7.55 Y1 @ Y2))))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y1) | 31.35/7.55 ('#sk1' @ '#sk6' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk7')))))) & 31.35/7.55 (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk1' @ '#sk7' @ Y1) | 31.35/7.55 ('#sk2' @ '#sk7' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((Y0 @ Y1) & 31.35/7.55 ((('#sk1' @ Y1 @ 31.35/7.55 Y2) | ('#sk2' @ 31.35/7.55 Y1 @ Y2))))) => 31.35/7.55 (Y0 @ Y2))))))))))) => 31.35/7.55 (Y0 @ '#sk8')))))))) => 31.35/7.55 (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk6' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk8')))))))) 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4')))))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])). 31.35/7.55 thf(zip_derived_cl21, plain, 31.35/7.55 (( (((((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((Y0 @ Y1) & 31.35/7.55 ((('#sk2' @ Y1 @ Y2) | 31.35/7.55 ('#sk1' @ Y1 @ Y2))))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk6' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk7')))))) & 31.35/7.55 (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk1' @ '#sk7' @ Y1) | ('#sk2' @ 31.35/7.55 '#sk7' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((Y0 @ Y1) & 31.35/7.55 ((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))))) => 31.35/7.55 (Y0 @ Y2))))))))))) => 31.35/7.55 (Y0 @ '#sk8')))))))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))) 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4')))))))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 31.35/7.55 thf(zip_derived_cl26, plain, 31.35/7.55 (( (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((Y0 @ Y1) & 31.35/7.55 ((('#sk2' @ Y1 @ Y2) | 31.35/7.55 ('#sk1' @ Y1 @ Y2))))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk6' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk7')))))) 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4')))))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 31.35/7.55 thf(zip_derived_cl32, plain, 31.35/7.55 ((~ ('#form11') 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4')))))))), 31.35/7.55 define([status(thm)])). 31.35/7.55 thf(zip_derived_cl33, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( (((((((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.35/7.55 Y0 @ Y1))) & 31.35/7.55 (X2 @ Y0))) => 31.35/7.55 (X2 @ Y1))))))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))))) => 31.35/7.55 (X2 @ '#sk4'))) 31.35/7.55 | ~ ('#form11'))), 31.35/7.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 31.35/7.55 thf(zip_derived_cl34, plain, 31.35/7.55 (( (((((((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.35/7.55 Y1))) & 31.35/7.55 ('#sk5' @ Y0))) => 31.35/7.55 ('#sk5' @ Y1))))))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 31.35/7.55 ('#sk5' @ Y0)))))))) => 31.35/7.55 ('#sk5' @ '#sk4'))) 31.35/7.55 | ~ ('#form11'))), 31.35/7.55 inference('triggered_bool_instantiation', [status(thm)], 31.35/7.55 [zip_derived_cl33])). 31.35/7.55 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk4')), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 31.35/7.55 thf(zip_derived_cl205, plain, 31.35/7.55 (( (((((((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.35/7.55 Y1))) & 31.35/7.55 ('#sk5' @ Y0))) => 31.35/7.55 ('#sk5' @ Y1))))))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 31.35/7.55 ('#sk5' @ Y0)))))))) => 31.35/7.55 ($false))) 31.35/7.55 | ~ ('#form11'))), 31.35/7.55 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl11])). 31.35/7.55 thf(zip_derived_cl206, plain, 31.35/7.55 (( (((~) @ (((((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((((('#sk1' @ Y0 @ Y1) | 31.35/7.55 ('#sk2' @ Y0 @ Y1))) & 31.35/7.55 ('#sk5' @ Y0))) => 31.35/7.55 ('#sk5' @ Y1))))))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ 31.35/7.55 Y0))) => 31.35/7.55 ('#sk5' @ Y0)))))))))) 31.35/7.55 | ~ ('#form11'))), 31.35/7.55 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl205])). 31.35/7.55 thf(zip_derived_cl207, plain, 31.35/7.55 ((~ (((((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.35/7.55 Y1))) & 31.35/7.55 ('#sk5' @ Y0))) => 31.35/7.55 ('#sk5' @ Y1))))))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 31.35/7.55 ('#sk5' @ Y0)))))))) 31.35/7.55 | ~ ('#form11'))), 31.35/7.55 inference('simplify nested equalities', [status(thm)], 31.35/7.55 [zip_derived_cl206])). 31.35/7.55 thf(zip_derived_cl208, plain, 31.35/7.55 ((~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 31.35/7.55 ('#sk5' @ Y0))) => 31.35/7.55 ('#sk5' @ Y1))))))))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 31.35/7.55 ('#sk5' @ Y0)))))) 31.35/7.55 | ~ ('#form11'))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl207])). 31.35/7.55 thf(zip_derived_cl33, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( (((((((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.35/7.55 Y0 @ Y1))) & 31.35/7.55 (X2 @ Y0))) => 31.35/7.55 (X2 @ Y1))))))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))))) => 31.35/7.55 (X2 @ '#sk4'))) 31.35/7.55 | ~ ('#form11'))), 31.35/7.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 31.35/7.55 thf(zip_derived_cl42, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ (((((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.35/7.55 Y0 @ Y1))) & 31.35/7.55 (X2 @ Y0))) => 31.35/7.55 (X2 @ Y1))))))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))))) 31.35/7.55 | (X2 @ '#sk4') 31.35/7.55 | ~ ('#form11'))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])). 31.35/7.55 thf(zip_derived_cl51, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.35/7.55 Y1))) & 31.35/7.55 (X2 @ Y0))) => 31.35/7.55 (X2 @ Y1))))))))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))) 31.35/7.55 | ~ ('#form11') 31.35/7.55 | (X2 @ '#sk4'))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl42])). 31.35/7.55 thf(zip_derived_cl63, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((((('#sk1' @ ('#sk27' @ X2) @ Y0) | ('#sk2' @ 31.35/7.55 ('#sk27' @ X2) @ Y0))) & 31.35/7.55 (X2 @ ('#sk27' @ X2)))) => 31.35/7.55 (X2 @ Y0)))))) 31.35/7.55 | (X2 @ '#sk4') 31.35/7.55 | ~ ('#form11') 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl51])). 31.35/7.55 thf(zip_derived_cl74, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ ((((((('#sk1' @ ('#sk27' @ X2) @ ('#sk39' @ X2)) | ('#sk2' @ 31.35/7.55 ('#sk27' @ X2) @ ('#sk39' @ X2)))) & 31.35/7.55 (X2 @ ('#sk27' @ X2)))) => 31.35/7.55 (X2 @ ('#sk39' @ X2)))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))) 31.35/7.55 | ~ ('#form11') 31.35/7.55 | (X2 @ '#sk4'))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl63])). 31.35/7.55 thf(zip_derived_cl88, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ (X2 @ ('#sk39' @ X2)) 31.35/7.55 | (X2 @ '#sk4') 31.35/7.55 | ~ ('#form11') 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])). 31.35/7.55 thf(zip_derived_cl99, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( ('#form82' @ X2) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))))), 31.35/7.55 define([status(thm)])). 31.35/7.55 thf(zip_derived_cl209, plain, 31.35/7.55 ((~ ('#form82' @ '#sk5') 31.35/7.55 | ~ ('#form11') 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.35/7.55 Y1))) & 31.35/7.55 ('#sk5' @ Y0))) => 31.35/7.55 ('#sk5' @ Y1))))))))))), 31.35/7.55 inference('renaming', [status(thm)], 31.35/7.55 [zip_derived_cl208, zip_derived_cl99])). 31.35/7.55 thf(zip_derived_cl210, plain, 31.35/7.55 ((~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((((('#sk1' @ ('#sk27' @ '#sk5') @ Y0) | ('#sk2' @ 31.35/7.55 ('#sk27' @ '#sk5') @ Y0))) & 31.35/7.55 ('#sk5' @ ('#sk27' @ '#sk5')))) => 31.35/7.55 ('#sk5' @ Y0)))))) 31.35/7.55 | ~ ('#form11') 31.35/7.55 | ~ ('#form82' @ '#sk5'))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl209])). 31.35/7.55 thf(zip_derived_cl211, plain, 31.35/7.55 ((~ ((((((('#sk1' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) | ('#sk2' @ 31.35/7.55 ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')))) & 31.35/7.55 ('#sk5' @ ('#sk27' @ '#sk5')))) => 31.35/7.55 ('#sk5' @ ('#sk39' @ '#sk5')))) 31.35/7.55 | ~ ('#form82' @ '#sk5') 31.35/7.55 | ~ ('#form11'))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl210])). 31.35/7.55 thf(zip_derived_cl213, plain, 31.35/7.55 ((~ ('#sk5' @ ('#sk39' @ '#sk5')) 31.35/7.55 | ~ ('#form11') 31.35/7.55 | ~ ('#form82' @ '#sk5'))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl211])). 31.35/7.55 thf(zip_derived_cl212, plain, 31.35/7.55 (( ((((('#sk1' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) | ('#sk2' @ 31.35/7.55 ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')))) & 31.35/7.55 ('#sk5' @ ('#sk27' @ '#sk5')))) 31.35/7.55 | ~ ('#form11') 31.35/7.55 | ~ ('#form82' @ '#sk5'))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl211])). 31.35/7.55 thf(zip_derived_cl215, plain, 31.35/7.55 (( ('#sk5' @ ('#sk27' @ '#sk5')) | ~ ('#form82' @ '#sk5') | ~ ('#form11'))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl212])). 31.35/7.55 thf(zip_derived_cl214, plain, 31.35/7.55 (( ((('#sk1' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) | ('#sk2' @ 31.35/7.55 ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')))) 31.35/7.55 | ~ ('#form82' @ '#sk5') 31.35/7.55 | ~ ('#form11'))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl212])). 31.35/7.55 thf(zip_derived_cl216, plain, 31.35/7.55 (( ('#sk1' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) 31.35/7.55 | ('#sk2' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) 31.35/7.55 | ~ ('#form11') 31.35/7.55 | ~ ('#form82' @ '#sk5'))), 31.35/7.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl214])). 31.35/7.55 thf(zip_derived_cl99, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( ('#form82' @ X2) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))))), 31.35/7.55 define([status(thm)])). 31.35/7.55 thf(zip_derived_cl100, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ ((((('#sk2' @ '#sk3' @ ('#sk83' @ X2)) | ('#sk1' @ '#sk3' @ 31.35/7.55 ('#sk83' @ X2)))) => 31.35/7.55 (X2 @ ('#sk83' @ X2)))) 31.35/7.55 | ('#form82' @ X2))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl99])). 31.35/7.55 thf(zip_derived_cl115, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( ((('#sk2' @ '#sk3' @ ('#sk83' @ X2)) | ('#sk1' @ '#sk3' @ 31.35/7.55 ('#sk83' @ X2)))) 31.35/7.55 | ('#form82' @ X2))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 31.35/7.55 thf(zip_derived_cl133, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( ('#sk2' @ '#sk3' @ ('#sk83' @ X2)) 31.35/7.55 | ('#sk1' @ '#sk3' @ ('#sk83' @ X2)) 31.35/7.55 | ('#form82' @ X2))), 31.35/7.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl115])). 31.35/7.55 thf(zip_derived_cl22, plain, 31.35/7.55 ((~ (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk6' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk8')))))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))) 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4')))))))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 31.35/7.55 thf(zip_derived_cl22, plain, 31.35/7.55 ((~ (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk6' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk8')))))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))) 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4')))))))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 31.35/7.55 thf(zip_derived_cl28, plain, 31.35/7.55 (( ('#form9') 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))))), 31.35/7.55 define([status(thm)])). 31.35/7.55 thf(zip_derived_cl30, plain, 31.35/7.55 ((~ ('#form9') 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4')))))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk6' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk8')))))))), 31.35/7.55 inference('renaming', [status(thm)], [zip_derived_cl22, zip_derived_cl28])). 31.35/7.55 thf(zip_derived_cl32, plain, 31.35/7.55 ((~ ('#form11') 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4')))))))), 31.35/7.55 define([status(thm)])). 31.35/7.55 thf(zip_derived_cl37, plain, 31.35/7.55 (( ('#form11') 31.35/7.55 | ~ (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk6' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk8')))))) 31.35/7.55 | ~ ('#form9'))), 31.35/7.55 inference('renaming', [status(thm)], [zip_derived_cl30, zip_derived_cl32])). 31.35/7.55 thf(zip_derived_cl45, plain, 31.35/7.55 ((~ (((((((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.35/7.55 Y0 @ Y1))) & 31.35/7.55 ('#sk16' @ Y0))) => 31.35/7.55 ('#sk16' @ Y1))))))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.35/7.55 ('#sk16' @ Y0)))))))) => 31.35/7.55 ('#sk16' @ '#sk8'))) 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11'))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl37])). 31.35/7.55 thf(zip_derived_cl56, plain, 31.35/7.55 ((~ ('#sk16' @ '#sk8') | ('#form11') | ~ ('#form9'))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 31.35/7.55 thf(zip_derived_cl27, plain, 31.35/7.55 (( (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk1' @ '#sk7' @ Y1) | ('#sk2' @ 31.35/7.55 '#sk7' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((Y0 @ Y1) & 31.35/7.55 ((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))))) => 31.35/7.55 (Y0 @ Y2))))))))))) => 31.35/7.55 (Y0 @ '#sk8')))))) 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4')))))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 31.35/7.55 thf(zip_derived_cl32, plain, 31.35/7.55 ((~ ('#form11') 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4')))))))), 31.35/7.55 define([status(thm)])). 31.35/7.55 thf(zip_derived_cl36, plain, 31.35/7.55 (( ('#form11') 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))) 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk1' @ '#sk7' @ Y1) | ('#sk2' @ 31.35/7.55 '#sk7' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((Y0 @ Y1) & 31.35/7.55 ((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))))) => 31.35/7.55 (Y0 @ Y2))))))))))) => 31.35/7.55 (Y0 @ '#sk8')))))))), 31.35/7.55 inference('renaming', [status(thm)], [zip_derived_cl27, zip_derived_cl32])). 31.35/7.55 thf(zip_derived_cl28, plain, 31.35/7.55 (( ('#form9') 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))))), 31.35/7.55 define([status(thm)])). 31.35/7.55 thf(zip_derived_cl43, plain, 31.35/7.55 ((~ ('#form9') 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk1' @ '#sk7' @ Y1) | ('#sk2' @ 31.35/7.55 '#sk7' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((Y0 @ Y1) & 31.35/7.55 ((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))))) => 31.35/7.55 (Y0 @ Y2))))))))))) => 31.35/7.55 (Y0 @ '#sk8')))))) 31.35/7.55 | ('#form11'))), 31.35/7.55 inference('renaming', [status(thm)], [zip_derived_cl36, zip_derived_cl28])). 31.35/7.55 thf(zip_derived_cl52, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( (((((((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk1' @ '#sk7' @ Y0) | ('#sk2' @ '#sk7' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((X2 @ Y0) & 31.35/7.55 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.35/7.55 Y0 @ Y1))))) => 31.35/7.55 (X2 @ Y1))))))))))) => 31.35/7.55 (X2 @ '#sk8'))) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9'))), 31.35/7.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 31.35/7.55 thf(zip_derived_cl53, plain, 31.35/7.55 (( (((((((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk1' @ '#sk7' @ Y0) | ('#sk2' @ '#sk7' @ Y0))) => 31.35/7.55 ('#sk16' @ Y0)))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk16' @ Y0) & 31.35/7.55 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.35/7.55 Y1))))) => 31.35/7.55 ('#sk16' @ Y1))))))))))) => 31.35/7.55 ('#sk16' @ '#sk8'))) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9'))), 31.35/7.55 inference('triggered_bool_instantiation', [status(thm)], 31.35/7.55 [zip_derived_cl52])). 31.35/7.55 thf(zip_derived_cl322, plain, 31.35/7.55 ((~ (((((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk1' @ '#sk7' @ Y0) | ('#sk2' @ '#sk7' @ Y0))) => 31.35/7.55 ('#sk16' @ Y0)))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk16' @ Y0) & 31.35/7.55 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.35/7.55 Y1))))) => 31.35/7.55 ('#sk16' @ Y1))))))))))) 31.35/7.55 | ('#sk16' @ '#sk8') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11'))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 31.35/7.55 thf(zip_derived_cl56, plain, 31.35/7.55 ((~ ('#sk16' @ '#sk8') | ('#form11') | ~ ('#form9'))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 31.35/7.55 thf(zip_derived_cl323, plain, 31.35/7.55 (( ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ~ (((((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk1' @ '#sk7' @ Y0) | ('#sk2' @ '#sk7' @ Y0))) => 31.35/7.55 ('#sk16' @ Y0)))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk16' @ Y0) & 31.35/7.55 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.35/7.55 Y0 @ Y1))))) => 31.35/7.55 ('#sk16' @ Y1))))))))))))), 31.35/7.55 inference('clc', [status(thm)], [zip_derived_cl322, zip_derived_cl56])). 31.35/7.55 thf(zip_derived_cl324, plain, 31.35/7.55 ((~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk1' @ '#sk7' @ Y0) | ('#sk2' @ '#sk7' @ Y0))) => 31.35/7.55 ('#sk16' @ Y0)))))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk16' @ Y0) & 31.35/7.55 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.35/7.55 Y1))))) => 31.35/7.55 ('#sk16' @ Y1))))))))) 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11'))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl323])). 31.35/7.55 thf(zip_derived_cl325, plain, 31.35/7.55 ((~ ((((('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) | ('#sk2' @ '#sk7' @ 31.35/7.55 ('#sk61' @ '#sk16')))) => 31.35/7.55 ('#sk16' @ ('#sk61' @ '#sk16')))) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk16' @ Y0) & 31.35/7.55 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.35/7.55 Y1))))) => 31.35/7.55 ('#sk16' @ Y1))))))))))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl324])). 31.35/7.55 thf(zip_derived_cl327, plain, 31.35/7.55 ((~ ('#sk16' @ ('#sk61' @ '#sk16')) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk16' @ Y0) & 31.35/7.55 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.35/7.55 Y1))))) => 31.35/7.55 ('#sk16' @ Y1))))))))) 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11'))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl325])). 31.35/7.55 thf(zip_derived_cl329, plain, 31.35/7.55 ((~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk16' @ ('#sk122' @ '#sk16')) & 31.35/7.55 ((('#sk1' @ ('#sk122' @ '#sk16') @ Y0) | ('#sk2' @ 31.35/7.55 ('#sk122' @ '#sk16') @ Y0))))) => 31.35/7.55 ('#sk16' @ Y0)))))) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ~ ('#sk16' @ ('#sk61' @ '#sk16')))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl327])). 31.35/7.55 thf(zip_derived_cl331, plain, 31.35/7.55 ((~ ((((('#sk16' @ ('#sk122' @ '#sk16')) & 31.35/7.55 ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) | 31.35/7.55 ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')))))) => 31.35/7.55 ('#sk16' @ ('#sk169' @ '#sk16')))) 31.35/7.55 | ~ ('#sk16' @ ('#sk61' @ '#sk16')) 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11'))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl329])). 31.35/7.55 thf(zip_derived_cl333, plain, 31.35/7.55 (( ((('#sk16' @ ('#sk122' @ '#sk16')) & 31.35/7.55 ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) | 31.35/7.55 ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')))))) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ~ ('#sk16' @ ('#sk61' @ '#sk16')))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl331])). 31.35/7.55 thf(zip_derived_cl337, plain, 31.35/7.55 (( ('#sk16' @ ('#sk122' @ '#sk16')) 31.35/7.55 | ~ ('#sk16' @ ('#sk61' @ '#sk16')) 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11'))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl333])). 31.35/7.55 thf(zip_derived_cl338, plain, 31.35/7.55 (( ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) | ('#sk2' @ 31.35/7.55 ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')))) 31.35/7.55 | ~ ('#sk16' @ ('#sk61' @ '#sk16')) 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11'))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl333])). 31.35/7.55 thf(zip_derived_cl341, plain, 31.35/7.55 (( ('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) 31.35/7.55 | ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ~ ('#sk16' @ ('#sk61' @ '#sk16')))), 31.35/7.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl338])). 31.35/7.55 thf(zip_derived_cl13, plain, 31.35/7.55 ( (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.35/7.55 ('#sk5' @ Y0))))))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 31.35/7.55 thf(zip_derived_cl16, plain, 31.35/7.55 (![X2 : a]: 31.35/7.55 ((((('#sk1' @ '#sk3' @ X2) | ('#sk2' @ '#sk3' @ X2))) => ('#sk5' @ 31.35/7.55 X2)))), 31.35/7.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 31.35/7.55 thf(zip_derived_cl19, plain, 31.35/7.55 (![X2 : a]: 31.35/7.55 (~ ((('#sk1' @ '#sk3' @ X2) | ('#sk2' @ '#sk3' @ X2))) 31.35/7.55 | ('#sk5' @ X2))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 31.35/7.55 thf(zip_derived_cl23, plain, 31.35/7.55 (![X2 : a]: (~ ('#sk1' @ '#sk3' @ X2) | ('#sk5' @ X2))), 31.35/7.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 31.35/7.55 thf(zip_derived_cl24, plain, 31.35/7.55 (![X2 : a]: (~ ('#sk2' @ '#sk3' @ X2) | ('#sk5' @ X2))), 31.35/7.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 31.35/7.55 thf(zip_derived_cl116, plain, 31.35/7.55 (![X2 : a > $o]: (~ (X2 @ ('#sk83' @ X2)) | ('#form82' @ X2))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 31.35/7.55 thf(zip_derived_cl52, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( (((((((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk1' @ '#sk7' @ Y0) | ('#sk2' @ '#sk7' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((X2 @ Y0) & 31.35/7.55 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.35/7.55 Y0 @ Y1))))) => 31.35/7.55 (X2 @ Y1))))))))))) => 31.35/7.55 (X2 @ '#sk8'))) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9'))), 31.35/7.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 31.35/7.55 thf(zip_derived_cl64, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ (((((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk1' @ '#sk7' @ Y0) | ('#sk2' @ '#sk7' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((X2 @ Y0) & 31.35/7.55 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.35/7.55 Y0 @ Y1))))) => 31.35/7.55 (X2 @ Y1))))))))))) 31.35/7.55 | (X2 @ '#sk8') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11'))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 31.35/7.55 thf(zip_derived_cl75, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk1' @ '#sk7' @ Y0) | ('#sk2' @ '#sk7' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((X2 @ Y0) & 31.35/7.55 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.35/7.55 Y0 @ Y1))))) => 31.35/7.55 (X2 @ Y1))))))))) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | (X2 @ '#sk8'))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl64])). 31.35/7.55 thf(zip_derived_cl89, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ ((((('#sk1' @ '#sk7' @ ('#sk61' @ X2)) | ('#sk2' @ '#sk7' @ 31.35/7.55 ('#sk61' @ X2)))) => 31.35/7.55 (X2 @ ('#sk61' @ X2)))) 31.35/7.55 | (X2 @ '#sk8') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11') 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((X2 @ Y0) & 31.35/7.55 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.35/7.55 Y0 @ Y1))))) => 31.35/7.55 (X2 @ Y1))))))))))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl75])). 31.35/7.55 thf(zip_derived_cl103, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ (X2 @ ('#sk61' @ X2)) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((X2 @ Y0) & 31.35/7.55 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.35/7.55 Y0 @ Y1))))) => 31.35/7.55 (X2 @ Y1))))))))) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | (X2 @ '#sk8'))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl89])). 31.35/7.55 thf(zip_derived_cl118, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((((X2 @ ('#sk122' @ X2)) & 31.35/7.55 ((('#sk1' @ ('#sk122' @ X2) @ Y0) | ('#sk2' @ 31.35/7.55 ('#sk122' @ X2) @ Y0))))) => 31.35/7.55 (X2 @ Y0)))))) 31.35/7.55 | (X2 @ '#sk8') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11') 31.35/7.55 | ~ (X2 @ ('#sk61' @ X2)))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl103])). 31.35/7.55 thf(zip_derived_cl135, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ (((((X2 @ ('#sk122' @ X2)) & 31.35/7.55 ((('#sk1' @ ('#sk122' @ X2) @ ('#sk169' @ X2)) | ('#sk2' @ 31.35/7.55 ('#sk122' @ X2) @ ('#sk169' @ X2)))))) => 31.35/7.55 (X2 @ ('#sk169' @ X2)))) 31.35/7.55 | ~ (X2 @ ('#sk61' @ X2)) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | (X2 @ '#sk8'))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl118])). 31.35/7.55 thf(zip_derived_cl148, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ (X2 @ ('#sk169' @ X2)) 31.35/7.55 | (X2 @ '#sk8') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11') 31.35/7.55 | ~ (X2 @ ('#sk61' @ X2)))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl135])). 31.35/7.55 thf(zip_derived_cl26, plain, 31.35/7.55 (( (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((Y0 @ Y1) & 31.35/7.55 ((('#sk2' @ Y1 @ Y2) | 31.35/7.55 ('#sk1' @ Y1 @ Y2))))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk6' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk7')))))) 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4')))))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 31.35/7.55 thf(zip_derived_cl32, plain, 31.35/7.55 ((~ ('#form11') 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 ((((((('#sk1' @ Y1 @ Y2) | 31.35/7.55 ('#sk2' @ Y1 @ Y2))) & 31.35/7.55 (Y0 @ Y1))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk3' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk4')))))))), 31.35/7.55 define([status(thm)])). 31.35/7.55 thf(zip_derived_cl35, plain, 31.35/7.55 (( ('#form11') 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))) 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((Y0 @ Y1) & 31.35/7.55 ((('#sk2' @ Y1 @ Y2) | 31.35/7.55 ('#sk1' @ Y1 @ Y2))))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk6' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk7')))))))), 31.35/7.55 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl32])). 31.35/7.55 thf(zip_derived_cl28, plain, 31.35/7.55 (( ('#form9') 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 (( 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) | 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ Y4))))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))))))))))), 31.35/7.55 define([status(thm)])). 31.35/7.55 thf(zip_derived_cl41, plain, 31.35/7.55 ((~ ('#form9') 31.35/7.55 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y1 : a]: 31.35/7.55 (((!!) @ (^[Y2 : a]: 31.35/7.55 (((((Y0 @ Y1) & 31.35/7.55 ((('#sk2' @ Y1 @ Y2) | 31.35/7.55 ('#sk1' @ Y1 @ Y2))))) => 31.35/7.55 (Y0 @ Y2))))))))) & 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 31.35/7.55 '#sk6' @ Y1))) => 31.35/7.55 (Y0 @ Y1)))))))) => 31.35/7.55 (Y0 @ '#sk7')))))) 31.35/7.55 | ('#form11'))), 31.35/7.55 inference('renaming', [status(thm)], [zip_derived_cl35, zip_derived_cl28])). 31.35/7.55 thf(zip_derived_cl48, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( (((((((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((X2 @ Y0) & 31.35/7.55 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 31.35/7.55 Y0 @ Y1))))) => 31.35/7.55 (X2 @ Y1))))))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))))) => 31.35/7.55 (X2 @ '#sk7'))) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9'))), 31.35/7.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 31.35/7.55 thf(zip_derived_cl62, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ (((((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((X2 @ Y0) & 31.35/7.55 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 31.35/7.55 Y0 @ Y1))))) => 31.35/7.55 (X2 @ Y1))))))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))))) 31.35/7.55 | (X2 @ '#sk7') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11'))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 31.35/7.55 thf(zip_derived_cl73, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((X2 @ Y0) & 31.35/7.55 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.35/7.55 Y1))))) => 31.35/7.55 (X2 @ Y1))))))))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | (X2 @ '#sk7'))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl62])). 31.35/7.55 thf(zip_derived_cl86, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((((X2 @ ('#sk50' @ X2)) & 31.35/7.55 ((('#sk2' @ ('#sk50' @ X2) @ Y0) | ('#sk1' @ 31.35/7.55 ('#sk50' @ X2) @ Y0))))) => 31.35/7.55 (X2 @ Y0)))))) 31.35/7.55 | (X2 @ '#sk7') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11') 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl73])). 31.35/7.55 thf(zip_derived_cl96, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ (((((X2 @ ('#sk50' @ X2)) & 31.35/7.55 ((('#sk2' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) | ('#sk1' @ 31.35/7.55 ('#sk50' @ X2) @ ('#sk73' @ X2)))))) => 31.35/7.55 (X2 @ ('#sk73' @ X2)))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | (X2 @ '#sk7'))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl86])). 31.35/7.55 thf(zip_derived_cl112, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ (X2 @ ('#sk73' @ X2)) 31.35/7.55 | (X2 @ '#sk7') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11') 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 31.35/7.55 thf(zip_derived_cl112, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ (X2 @ ('#sk73' @ X2)) 31.35/7.55 | (X2 @ '#sk7') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11') 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 31.35/7.55 thf(zip_derived_cl127, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( ('#form139' @ X2) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))))), 31.35/7.55 define([status(thm)])). 31.35/7.55 thf(zip_derived_cl129, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ ('#form139' @ X2) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | (X2 @ '#sk7') 31.35/7.55 | ~ (X2 @ ('#sk73' @ X2)))), 31.35/7.55 inference('renaming', [status(thm)], 31.35/7.55 [zip_derived_cl112, zip_derived_cl127])). 31.35/7.55 thf(zip_derived_cl326, plain, 31.35/7.55 (( ((('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) | ('#sk2' @ '#sk7' @ 31.35/7.55 ('#sk61' @ '#sk16')))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk16' @ Y0) & 31.35/7.55 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.35/7.55 Y1))))) => 31.35/7.55 ('#sk16' @ Y1))))))))) 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11'))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl325])). 31.35/7.55 thf(zip_derived_cl328, plain, 31.35/7.55 (( ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) 31.35/7.55 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((('#sk16' @ Y0) & 31.35/7.55 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.35/7.55 Y1))))) => 31.35/7.55 ('#sk16' @ Y1))))))))))), 31.35/7.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl326])). 31.35/7.55 thf(zip_derived_cl330, plain, 31.35/7.55 ((~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk16' @ ('#sk122' @ '#sk16')) & 31.35/7.55 ((('#sk1' @ ('#sk122' @ '#sk16') @ Y0) | ('#sk2' @ 31.35/7.55 ('#sk122' @ '#sk16') @ Y0))))) => 31.35/7.55 ('#sk16' @ Y0)))))) 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11') 31.35/7.55 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 31.35/7.55 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl328])). 31.35/7.55 thf(zip_derived_cl332, plain, 31.35/7.55 ((~ ((((('#sk16' @ ('#sk122' @ '#sk16')) & 31.35/7.55 ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) | 31.35/7.55 ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')))))) => 31.35/7.55 ('#sk16' @ ('#sk169' @ '#sk16')))) 31.35/7.55 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) 31.35/7.55 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9'))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl330])). 31.35/7.55 thf(zip_derived_cl336, plain, 31.35/7.55 ((~ ('#sk16' @ ('#sk169' @ '#sk16')) 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11') 31.35/7.55 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 31.35/7.55 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl332])). 31.35/7.55 thf(zip_derived_cl335, plain, 31.35/7.55 (( ((('#sk16' @ ('#sk122' @ '#sk16')) & 31.35/7.55 ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) | 31.35/7.55 ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')))))) 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11') 31.35/7.55 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 31.35/7.55 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl332])). 31.35/7.55 thf(zip_derived_cl339, plain, 31.35/7.55 (( ('#sk16' @ ('#sk122' @ '#sk16')) 31.35/7.55 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) 31.35/7.55 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9'))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl335])). 31.35/7.55 thf(zip_derived_cl340, plain, 31.35/7.55 (( ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) | ('#sk2' @ 31.35/7.55 ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')))) 31.35/7.55 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) 31.35/7.55 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9'))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl335])). 31.35/7.55 thf(zip_derived_cl342, plain, 31.35/7.55 (( ('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) 31.35/7.55 | ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk169' @ '#sk16')) 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11') 31.35/7.55 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 31.35/7.55 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')))), 31.35/7.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl340])). 31.35/7.55 thf(zip_derived_cl55, plain, 31.35/7.55 (( (((((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.35/7.55 Y1))) & 31.35/7.55 ('#sk16' @ Y0))) => 31.35/7.55 ('#sk16' @ Y1))))))))) & 31.35/7.55 (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.35/7.55 ('#sk16' @ Y0)))))))) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9'))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 31.35/7.55 thf(zip_derived_cl65, plain, 31.35/7.55 (( (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 31.35/7.55 ('#sk16' @ Y0))) => 31.35/7.55 ('#sk16' @ Y1))))))))) 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11'))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 31.35/7.55 thf(zip_derived_cl76, plain, 31.35/7.55 (![X2 : a]: 31.35/7.55 ( (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) & 31.35/7.55 ('#sk16' @ X2))) => 31.35/7.55 ('#sk16' @ Y0)))))) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9'))), 31.35/7.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl65])). 31.35/7.55 thf(zip_derived_cl90, plain, 31.35/7.55 (![X2 : a, X4 : a]: 31.35/7.55 ( ((((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk16' @ X2))) => 31.35/7.55 ('#sk16' @ X4))) 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11'))), 31.35/7.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl76])). 31.35/7.55 thf(zip_derived_cl104, plain, 31.35/7.55 (![X2 : a, X4 : a]: 31.35/7.55 (~ ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk16' @ X2))) 31.35/7.55 | ('#sk16' @ X4) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9'))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl90])). 31.35/7.55 thf(zip_derived_cl119, plain, 31.35/7.55 (![X2 : a, X4 : a]: 31.35/7.55 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 31.35/7.55 | ~ ('#sk16' @ X2) 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11') 31.35/7.55 | ('#sk16' @ X4))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl104])). 31.35/7.55 thf(zip_derived_cl136, plain, 31.35/7.55 (![X2 : a, X4 : a]: 31.35/7.55 (~ ('#sk1' @ X2 @ X4) 31.35/7.55 | ('#sk16' @ X4) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ~ ('#sk16' @ X2))), 31.35/7.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl119])). 31.35/7.55 thf(zip_derived_cl137, plain, 31.35/7.55 (![X2 : a, X4 : a]: 31.35/7.55 (~ ('#sk2' @ X2 @ X4) 31.35/7.55 | ('#sk16' @ X4) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ~ ('#sk16' @ X2))), 31.35/7.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl119])). 31.35/7.55 thf(zip_derived_cl111, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( (((X2 @ ('#sk50' @ X2)) & 31.35/7.55 ((('#sk2' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) | ('#sk1' @ 31.35/7.55 ('#sk50' @ X2) @ ('#sk73' @ X2)))))) 31.35/7.55 | (X2 @ '#sk7') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11') 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 31.35/7.55 thf(zip_derived_cl125, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( (X2 @ ('#sk50' @ X2)) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | (X2 @ '#sk7'))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl111])). 31.35/7.55 thf(zip_derived_cl127, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( ('#form139' @ X2) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))))), 31.35/7.55 define([status(thm)])). 31.35/7.55 thf(zip_derived_cl142, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ ('#form139' @ (^[Y0 : a]: (X2 @ Y0))) 31.35/7.55 | (X2 @ '#sk7') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11') 31.35/7.55 | (X2 @ ('#sk50' @ X2)))), 31.35/7.55 inference('renaming', [status(thm)], 31.35/7.55 [zip_derived_cl125, zip_derived_cl127])). 31.35/7.55 thf(zip_derived_cl155, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ ('#form139' @ X2) 31.35/7.55 | (X2 @ '#sk7') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11') 31.35/7.55 | (X2 @ ('#sk50' @ X2)))), 31.35/7.55 inference('ho_norm', [status(thm)], [zip_derived_cl142])). 31.35/7.55 thf(zip_derived_cl127, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( ('#form139' @ X2) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))))), 31.35/7.55 define([status(thm)])). 31.35/7.55 thf(zip_derived_cl128, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ ((((('#sk2' @ '#sk6' @ ('#sk140' @ X2)) | ('#sk1' @ '#sk6' @ 31.35/7.55 ('#sk140' @ X2)))) => 31.35/7.55 (X2 @ ('#sk140' @ X2)))) 31.35/7.55 | ('#form139' @ X2))), 31.35/7.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl127])). 31.35/7.55 thf(zip_derived_cl144, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( ((('#sk2' @ '#sk6' @ ('#sk140' @ X2)) | ('#sk1' @ '#sk6' @ 31.35/7.55 ('#sk140' @ X2)))) 31.35/7.55 | ('#form139' @ X2))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl128])). 31.35/7.55 thf(zip_derived_cl158, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( ('#sk2' @ '#sk6' @ ('#sk140' @ X2)) 31.35/7.55 | ('#sk1' @ '#sk6' @ ('#sk140' @ X2)) 31.35/7.55 | ('#form139' @ X2))), 31.35/7.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl144])). 31.35/7.55 thf(zip_derived_cl145, plain, 31.35/7.55 (![X2 : a > $o]: (~ (X2 @ ('#sk140' @ X2)) | ('#form139' @ X2))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl128])). 31.35/7.55 thf(zip_derived_cl126, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( ((('#sk2' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) | ('#sk1' @ 31.35/7.55 ('#sk50' @ X2) @ ('#sk73' @ X2)))) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | (X2 @ '#sk7'))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl111])). 31.35/7.55 thf(zip_derived_cl127, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( ('#form139' @ X2) 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.35/7.55 (X2 @ Y0)))))))), 31.35/7.55 define([status(thm)])). 31.35/7.55 thf(zip_derived_cl143, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ ('#form139' @ (^[Y0 : a]: (X2 @ Y0))) 31.35/7.55 | (X2 @ '#sk7') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11') 31.35/7.55 | ((('#sk2' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) | ('#sk1' @ 31.35/7.55 ('#sk50' @ X2) @ ('#sk73' @ X2)))))), 31.35/7.55 inference('renaming', [status(thm)], 31.35/7.55 [zip_derived_cl126, zip_derived_cl127])). 31.35/7.55 thf(zip_derived_cl156, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 (~ ('#form139' @ X2) 31.35/7.55 | (X2 @ '#sk7') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11') 31.35/7.55 | ((('#sk2' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) | ('#sk1' @ 31.35/7.55 ('#sk50' @ X2) @ ('#sk73' @ X2)))))), 31.35/7.55 inference('ho_norm', [status(thm)], [zip_derived_cl143])). 31.35/7.55 thf(zip_derived_cl157, plain, 31.35/7.55 (![X2 : a > $o]: 31.35/7.55 ( ('#sk2' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) 31.35/7.55 | ('#sk1' @ ('#sk50' @ X2) @ ('#sk73' @ X2)) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | (X2 @ '#sk7') 31.35/7.55 | ~ ('#form139' @ X2))), 31.35/7.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl156])). 31.35/7.55 thf(zip_derived_cl66, plain, 31.35/7.55 (( (((!!) @ (^[Y0 : a]: 31.35/7.55 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.35/7.55 ('#sk16' @ Y0)))))) 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11'))), 31.35/7.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 31.35/7.55 thf(zip_derived_cl77, plain, 31.35/7.55 (![X2 : a]: 31.35/7.55 ( ((((('#sk2' @ '#sk6' @ X2) | ('#sk1' @ '#sk6' @ X2))) => ('#sk16' @ 31.35/7.55 X2))) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9'))), 31.35/7.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl66])). 31.35/7.55 thf(zip_derived_cl91, plain, 31.35/7.55 (![X2 : a]: 31.35/7.55 (~ ((('#sk2' @ '#sk6' @ X2) | ('#sk1' @ '#sk6' @ X2))) 31.35/7.55 | ('#sk16' @ X2) 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#form11'))), 31.35/7.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl77])). 31.35/7.55 thf(zip_derived_cl106, plain, 31.35/7.55 (![X2 : a]: 31.35/7.55 (~ ('#sk1' @ '#sk6' @ X2) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#sk16' @ X2))), 31.35/7.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl91])). 31.35/7.55 thf(zip_derived_cl105, plain, 31.35/7.55 (![X2 : a]: 31.35/7.55 (~ ('#sk2' @ '#sk6' @ X2) 31.35/7.55 | ('#form11') 31.35/7.55 | ~ ('#form9') 31.35/7.55 | ('#sk16' @ X2))), 31.35/7.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl91])). 31.35/7.55 thf(zip_derived_cl28, plain, 31.35/7.55 (( ('#form9') 31.35/7.55 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.55 (((!!) @ (^[Y1 : a]: 31.35/7.55 (((((((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 ('#sk2' @ 31.35/7.55 Y3 @ 31.35/7.55 Y4) & 31.35/7.55 (Y2 @ Y3))) => 31.35/7.55 (Y2 @ Y4))))))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))))) => 31.35/7.55 (Y2 @ Y1)))))) | 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((('#sk1' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 (( 31.35/7.55 (( 31.35/7.55 (Y2 @ 31.35/7.55 Y3) & 31.35/7.55 ('#sk1' @ 31.35/7.55 Y3 @ Y4))) => 31.35/7.55 (Y2 @ Y4))))))))))) => 31.35/7.55 (Y2 @ Y1)))))))) => 31.35/7.55 (((!!) @ (^[Y2 : a > $o]: 31.35/7.55 (((((((!!) @ (^[Y3 : a]: 31.35/7.55 ((((('#sk2' @ 31.35/7.55 Y0 @ 31.35/7.55 Y3) | 31.35/7.55 ('#sk1' @ 31.35/7.55 Y0 @ Y3))) => 31.35/7.55 (Y2 @ Y3)))))) & 31.35/7.55 (((!!) @ (^[Y3 : a]: 31.35/7.55 (((!!) @ ( 31.35/7.55 ^[Y4 : a]: 31.35/7.55 ( 31.35/7.55 ( 31.35/7.56 (( 31.35/7.56 (Y2 @ 31.35/7.56 Y3) & 31.35/7.56 (( 31.35/7.56 ('#sk1' @ 31.35/7.56 Y3 @ 31.35/7.56 Y4) | 31.35/7.56 ('#sk2' @ 31.35/7.56 Y3 @ Y4))))) => 31.35/7.56 (Y2 @ Y4))))))))))) => 31.35/7.56 (Y2 @ Y1)))))))))))))))), 31.35/7.56 define([status(thm)])). 31.35/7.56 thf(zip_derived_cl29, plain, 31.35/7.56 ((~ (((!!) @ (^[Y0 : a]: 31.35/7.56 (((((((!!) @ (^[Y1 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y2 : a]: 31.35/7.56 (((!!) @ (^[Y3 : a]: 31.35/7.56 ((((('#sk2' @ 31.35/7.56 Y2 @ 31.35/7.56 Y3) & 31.35/7.56 (Y1 @ Y2))) => 31.35/7.56 (Y1 @ Y3))))))))) & 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 ((('#sk2' @ '#sk10' @ 31.35/7.56 Y2) => (Y1 @ Y2)))))))) => 31.35/7.56 (Y1 @ Y0)))))) | 31.35/7.56 (((!!) @ (^[Y1 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y2 : a]: 31.35/7.56 ((('#sk1' @ '#sk10' @ 31.35/7.56 Y2) => (Y1 @ Y2)))))) & 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 (((!!) @ (^[Y3 : a]: 31.35/7.56 (((((Y1 @ 31.35/7.56 Y2) & 31.35/7.56 ('#sk1' @ 31.35/7.56 Y2 @ Y3))) => 31.35/7.56 (Y1 @ Y3))))))))))) => 31.35/7.56 (Y1 @ Y0)))))))) => 31.35/7.56 (((!!) @ (^[Y1 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y2 : a]: 31.35/7.56 ((((('#sk2' @ '#sk10' @ 31.35/7.56 Y2) | ('#sk1' @ 31.35/7.56 '#sk10' @ Y2))) => 31.35/7.56 (Y1 @ Y2)))))) & 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 (((!!) @ (^[Y3 : a]: 31.35/7.56 (((((Y1 @ Y2) & 31.35/7.56 ((('#sk1' @ 31.35/7.56 Y2 @ 31.35/7.56 Y3) | 31.35/7.56 ('#sk2' @ 31.35/7.56 Y2 @ Y3))))) => 31.35/7.56 (Y1 @ Y3))))))))))) => 31.35/7.56 (Y1 @ Y0))))))))))) 31.35/7.56 | ('#form9'))), 31.35/7.56 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl28])). 31.35/7.56 thf(zip_derived_cl38, plain, 31.35/7.56 ((~ (((((((!!) @ (^[Y0 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y1 : a]: 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 ((((('#sk2' @ Y1 @ Y2) & 31.35/7.56 (Y0 @ Y1))) => 31.35/7.56 (Y0 @ Y2))))))))) & 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ 31.35/7.56 Y1)))))))) => 31.35/7.56 (Y0 @ '#sk12')))))) | 31.35/7.56 (((!!) @ (^[Y0 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y1 : a]: 31.35/7.56 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ 31.35/7.56 Y1)))))) & 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 (((((Y0 @ Y1) & 31.35/7.56 ('#sk1' @ Y1 @ Y2))) => 31.35/7.56 (Y0 @ Y2))))))))))) => 31.35/7.56 (Y0 @ '#sk12')))))))) => 31.35/7.56 (((!!) @ (^[Y0 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y1 : a]: 31.35/7.56 ((((('#sk2' @ '#sk10' @ Y1) | 31.35/7.56 ('#sk1' @ '#sk10' @ Y1))) => 31.35/7.56 (Y0 @ Y1)))))) & 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 (((((Y0 @ Y1) & 31.35/7.56 ((('#sk1' @ Y1 @ Y2) | 31.35/7.56 ('#sk2' @ Y1 @ Y2))))) => 31.35/7.56 (Y0 @ Y2))))))))))) => 31.35/7.56 (Y0 @ '#sk12')))))))) 31.35/7.56 | ('#form9'))), 31.35/7.56 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl29])). 31.35/7.56 thf(zip_derived_cl46, plain, 31.35/7.56 (( (((((!!) @ (^[Y0 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y1 : a]: 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 ((((('#sk2' @ Y1 @ Y2) & 31.35/7.56 (Y0 @ Y1))) => 31.35/7.56 (Y0 @ Y2))))))))) & 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))))) => 31.35/7.56 (Y0 @ '#sk12')))))) | 31.35/7.56 (((!!) @ (^[Y0 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y1 : a]: 31.35/7.56 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 (((((Y0 @ Y1) & ('#sk1' @ 31.35/7.56 Y1 @ Y2))) => 31.35/7.56 (Y0 @ Y2))))))))))) => 31.35/7.56 (Y0 @ '#sk12')))))))) 31.35/7.56 | ('#form9'))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 31.35/7.56 thf(zip_derived_cl57, plain, 31.35/7.56 (( (((!!) @ (^[Y0 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y1 : a]: 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 ((((('#sk2' @ Y1 @ Y2) & 31.35/7.56 (Y0 @ Y1))) => 31.35/7.56 (Y0 @ Y2))))))))) & 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))))) => 31.35/7.56 (Y0 @ '#sk12')))))) 31.35/7.56 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y1 : a]: 31.35/7.56 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 (((((Y0 @ Y1) & ('#sk1' @ 31.35/7.56 Y1 @ Y2))) => 31.35/7.56 (Y0 @ Y2))))))))))) => 31.35/7.56 (Y0 @ '#sk12')))))) 31.35/7.56 | ('#form9'))), 31.35/7.56 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl46])). 31.35/7.56 thf(zip_derived_cl67, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 ( (((((((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 31.35/7.56 (X2 @ Y1))))))))) & 31.35/7.56 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 31.35/7.56 (X2 @ '#sk12'))) 31.35/7.56 | ('#form9') 31.35/7.56 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y1 : a]: 31.35/7.56 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 (((((Y0 @ Y1) & ('#sk1' @ 31.35/7.56 Y1 @ Y2))) => 31.35/7.56 (Y0 @ Y2))))))))))) => 31.35/7.56 (Y0 @ '#sk12')))))))), 31.35/7.56 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 31.35/7.56 thf(zip_derived_cl78, plain, 31.35/7.56 ((~ ('#form46') 31.35/7.56 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y1 : a]: 31.35/7.56 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 (((((Y0 @ Y1) & ('#sk1' @ 31.35/7.56 Y1 @ Y2))) => 31.35/7.56 (Y0 @ Y2))))))))))) => 31.35/7.56 (Y0 @ '#sk12')))))))), 31.35/7.56 define([status(thm)])). 31.35/7.56 thf(zip_derived_cl79, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 ( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) & 31.35/7.56 (((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 31.35/7.56 (X2 @ Y1))))))))))) => 31.35/7.56 (X2 @ '#sk12'))) 31.35/7.56 | ~ ('#form46'))), 31.35/7.56 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl78])). 31.35/7.56 thf(zip_derived_cl93, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 (~ (((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) & 31.35/7.56 (((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 31.35/7.56 (X2 @ Y1))))))))))) 31.35/7.56 | (X2 @ '#sk12') 31.35/7.56 | ~ ('#form46'))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])). 31.35/7.56 thf(zip_derived_cl108, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 (~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 31.35/7.56 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 31.35/7.56 (X2 @ Y1))))))))) 31.35/7.56 | ~ ('#form46') 31.35/7.56 | (X2 @ '#sk12'))), 31.35/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl93])). 31.35/7.56 thf(zip_derived_cl121, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 (~ ((('#sk1' @ '#sk10' @ ('#sk130' @ X2)) => (X2 @ ('#sk130' @ X2)))) 31.35/7.56 | (X2 @ '#sk12') 31.35/7.56 | ~ ('#form46') 31.35/7.56 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 31.35/7.56 (X2 @ Y1))))))))))), 31.35/7.56 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl108])). 31.35/7.56 thf(zip_derived_cl140, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 (~ (X2 @ ('#sk130' @ X2)) 31.35/7.56 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 31.35/7.56 (X2 @ Y1))))))))) 31.35/7.56 | ~ ('#form46') 31.35/7.56 | (X2 @ '#sk12'))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl121])). 31.35/7.56 thf(zip_derived_cl152, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 (~ (((!!) @ (^[Y0 : a]: 31.35/7.56 (((((X2 @ ('#sk221' @ X2)) & ('#sk1' @ 31.35/7.56 ('#sk221' @ X2) @ Y0))) => 31.35/7.56 (X2 @ Y0)))))) 31.35/7.56 | (X2 @ '#sk12') 31.35/7.56 | ~ ('#form46') 31.35/7.56 | ~ (X2 @ ('#sk130' @ X2)))), 31.35/7.56 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl140])). 31.35/7.56 thf(zip_derived_cl169, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 (~ (((((X2 @ ('#sk221' @ X2)) & ('#sk1' @ ('#sk221' @ X2) @ 31.35/7.56 ('#sk272' @ X2)))) => 31.35/7.56 (X2 @ ('#sk272' @ X2)))) 31.35/7.56 | ~ (X2 @ ('#sk130' @ X2)) 31.35/7.56 | ~ ('#form46') 31.35/7.56 | (X2 @ '#sk12'))), 31.35/7.56 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl152])). 31.35/7.56 thf(zip_derived_cl180, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 (~ (X2 @ ('#sk272' @ X2)) 31.35/7.56 | (X2 @ '#sk12') 31.35/7.56 | ~ ('#form46') 31.35/7.56 | ~ (X2 @ ('#sk130' @ X2)))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl169])). 31.35/7.56 thf(zip_derived_cl179, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 ( (((X2 @ ('#sk221' @ X2)) & ('#sk1' @ ('#sk221' @ X2) @ 31.35/7.56 ('#sk272' @ X2)))) 31.35/7.56 | (X2 @ '#sk12') 31.35/7.56 | ~ ('#form46') 31.35/7.56 | ~ (X2 @ ('#sk130' @ X2)))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl169])). 31.35/7.56 thf(zip_derived_cl186, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 ( (X2 @ ('#sk221' @ X2)) 31.35/7.56 | ~ (X2 @ ('#sk130' @ X2)) 31.35/7.56 | ~ ('#form46') 31.35/7.56 | (X2 @ '#sk12'))), 31.35/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl179])). 31.35/7.56 thf(zip_derived_cl47, plain, 31.35/7.56 ((~ (((!!) @ (^[Y0 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y1 : a]: 31.35/7.56 ((((('#sk2' @ '#sk10' @ Y1) | ('#sk1' @ 31.35/7.56 '#sk10' @ Y1))) => 31.35/7.56 (Y0 @ Y1)))))) & 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 (((((Y0 @ Y1) & 31.35/7.56 ((('#sk1' @ Y1 @ Y2) | 31.35/7.56 ('#sk2' @ Y1 @ Y2))))) => 31.35/7.56 (Y0 @ Y2))))))))))) => 31.35/7.56 (Y0 @ '#sk12')))))) 31.35/7.56 | ('#form9'))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 31.35/7.56 thf(zip_derived_cl61, plain, 31.35/7.56 ((~ (((((((!!) @ (^[Y0 : a]: 31.35/7.56 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 31.35/7.56 ('#sk20' @ Y0)))))) & 31.35/7.56 (((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((((('#sk20' @ Y0) & 31.35/7.56 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.35/7.56 Y0 @ Y1))))) => 31.35/7.56 ('#sk20' @ Y1))))))))))) => 31.35/7.56 ('#sk20' @ '#sk12'))) 31.35/7.56 | ('#form9'))), 31.35/7.56 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 31.35/7.56 thf(zip_derived_cl71, plain, 31.35/7.56 (( (((((!!) @ (^[Y0 : a]: 31.35/7.56 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 31.35/7.56 ('#sk20' @ Y0)))))) & 31.35/7.56 (((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((((('#sk20' @ Y0) & 31.35/7.56 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.35/7.56 Y1))))) => 31.35/7.56 ('#sk20' @ Y1))))))))))) 31.35/7.56 | ('#form9'))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 31.35/7.56 thf(zip_derived_cl84, plain, 31.35/7.56 (( (((!!) @ (^[Y0 : a]: 31.35/7.56 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 31.35/7.56 ('#sk20' @ Y0)))))) 31.35/7.56 | ('#form9'))), 31.35/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl71])). 31.35/7.56 thf(zip_derived_cl94, plain, 31.35/7.56 (![X2 : a]: 31.35/7.56 ( ((((('#sk2' @ '#sk10' @ X2) | ('#sk1' @ '#sk10' @ X2))) => 31.35/7.56 ('#sk20' @ X2))) 31.35/7.56 | ('#form9'))), 31.35/7.56 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl84])). 31.35/7.56 thf(zip_derived_cl109, plain, 31.35/7.56 (![X2 : a]: 31.35/7.56 (~ ((('#sk2' @ '#sk10' @ X2) | ('#sk1' @ '#sk10' @ X2))) 31.35/7.56 | ('#sk20' @ X2) 31.35/7.56 | ('#form9'))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl94])). 31.35/7.56 thf(zip_derived_cl123, plain, 31.35/7.56 (![X2 : a]: (~ ('#sk1' @ '#sk10' @ X2) | ('#form9') | ('#sk20' @ X2))), 31.35/7.56 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl109])). 31.35/7.56 thf(zip_derived_cl187, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 ( ('#sk1' @ ('#sk221' @ X2) @ ('#sk272' @ X2)) 31.35/7.56 | ~ (X2 @ ('#sk130' @ X2)) 31.35/7.56 | ~ ('#form46') 31.35/7.56 | (X2 @ '#sk12'))), 31.35/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl179])). 31.35/7.56 thf(zip_derived_cl72, plain, ((~ ('#sk20' @ '#sk12') | ('#form9'))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 31.35/7.56 thf(zip_derived_cl139, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 ( ('#sk1' @ '#sk10' @ ('#sk130' @ X2)) 31.35/7.56 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 31.35/7.56 (X2 @ Y1))))))))) 31.35/7.56 | ~ ('#form46') 31.35/7.56 | (X2 @ '#sk12'))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl121])). 31.35/7.56 thf(zip_derived_cl151, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 (~ (((!!) @ (^[Y0 : a]: 31.35/7.56 (((((X2 @ ('#sk221' @ X2)) & ('#sk1' @ 31.35/7.56 ('#sk221' @ X2) @ Y0))) => 31.35/7.56 (X2 @ Y0)))))) 31.35/7.56 | (X2 @ '#sk12') 31.35/7.56 | ~ ('#form46') 31.35/7.56 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)))), 31.35/7.56 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl139])). 31.35/7.56 thf(zip_derived_cl168, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 (~ (((((X2 @ ('#sk221' @ X2)) & ('#sk1' @ ('#sk221' @ X2) @ 31.35/7.56 ('#sk272' @ X2)))) => 31.35/7.56 (X2 @ ('#sk272' @ X2)))) 31.35/7.56 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)) 31.35/7.56 | ~ ('#form46') 31.35/7.56 | (X2 @ '#sk12'))), 31.35/7.56 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl151])). 31.35/7.56 thf(zip_derived_cl178, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 (~ (X2 @ ('#sk272' @ X2)) 31.35/7.56 | (X2 @ '#sk12') 31.35/7.56 | ~ ('#form46') 31.35/7.56 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl168])). 31.35/7.56 thf(zip_derived_cl177, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 ( (((X2 @ ('#sk221' @ X2)) & ('#sk1' @ ('#sk221' @ X2) @ 31.35/7.56 ('#sk272' @ X2)))) 31.35/7.56 | (X2 @ '#sk12') 31.35/7.56 | ~ ('#form46') 31.35/7.56 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl168])). 31.35/7.56 thf(zip_derived_cl184, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 ( (X2 @ ('#sk221' @ X2)) 31.35/7.56 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)) 31.35/7.56 | ~ ('#form46') 31.35/7.56 | (X2 @ '#sk12'))), 31.35/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl177])). 31.35/7.56 thf(zip_derived_cl85, plain, 31.35/7.56 (( (((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((((('#sk20' @ Y0) & 31.35/7.56 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 31.35/7.56 ('#sk20' @ Y1))))))))) 31.35/7.56 | ('#form9'))), 31.35/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl71])). 31.35/7.56 thf(zip_derived_cl95, plain, 31.35/7.56 (![X2 : a]: 31.35/7.56 ( (((!!) @ (^[Y0 : a]: 31.35/7.56 ((((('#sk20' @ X2) & 31.35/7.56 ((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))))) => 31.35/7.56 ('#sk20' @ Y0)))))) 31.35/7.56 | ('#form9'))), 31.35/7.56 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 31.35/7.56 thf(zip_derived_cl110, plain, 31.35/7.56 (![X2 : a, X4 : a]: 31.35/7.56 ( ((((('#sk20' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) => 31.35/7.56 ('#sk20' @ X4))) 31.35/7.56 | ('#form9'))), 31.35/7.56 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl95])). 31.35/7.56 thf(zip_derived_cl124, plain, 31.35/7.56 (![X2 : a, X4 : a]: 31.35/7.56 (~ ((('#sk20' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) 31.35/7.56 | ('#sk20' @ X4) 31.35/7.56 | ('#form9'))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl110])). 31.35/7.56 thf(zip_derived_cl141, plain, 31.35/7.56 (![X2 : a, X4 : a]: 31.35/7.56 (~ ('#sk20' @ X2) 31.35/7.56 | ~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 31.35/7.56 | ('#form9') 31.35/7.56 | ('#sk20' @ X4))), 31.35/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl124])). 31.35/7.56 thf(zip_derived_cl153, plain, 31.35/7.56 (![X2 : a, X4 : a]: 31.35/7.56 (~ ('#sk1' @ X2 @ X4) 31.35/7.56 | ('#sk20' @ X4) 31.35/7.56 | ('#form9') 31.35/7.56 | ~ ('#sk20' @ X2))), 31.35/7.56 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl141])). 31.35/7.56 thf(zip_derived_cl185, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 ( ('#sk1' @ ('#sk221' @ X2) @ ('#sk272' @ X2)) 31.35/7.56 | ('#sk1' @ '#sk10' @ ('#sk130' @ X2)) 31.35/7.56 | ~ ('#form46') 31.35/7.56 | (X2 @ '#sk12'))), 31.35/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl177])). 31.35/7.56 thf(zip_derived_cl67, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 ( (((((((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 31.35/7.56 (X2 @ Y1))))))))) & 31.35/7.56 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 31.35/7.56 (X2 @ '#sk12'))) 31.35/7.56 | ('#form9') 31.35/7.56 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y1 : a]: 31.35/7.56 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 (((((Y0 @ Y1) & ('#sk1' @ 31.35/7.56 Y1 @ Y2))) => 31.35/7.56 (Y0 @ Y2))))))))))) => 31.35/7.56 (Y0 @ '#sk12')))))))), 31.35/7.56 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 31.35/7.56 thf(zip_derived_cl68, plain, 31.35/7.56 (( (((((((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 31.35/7.56 ('#sk20' @ Y1))))))))) & 31.35/7.56 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))) => 31.35/7.56 ('#sk20' @ '#sk12'))) 31.35/7.56 | ('#form9') 31.35/7.56 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y1 : a]: 31.35/7.56 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 (((((Y0 @ Y1) & ('#sk1' @ 31.35/7.56 Y1 @ Y2))) => 31.35/7.56 (Y0 @ Y2))))))))))) => 31.35/7.56 (Y0 @ '#sk12')))))))), 31.35/7.56 inference('triggered_bool_instantiation', [status(thm)], 31.35/7.56 [zip_derived_cl67])). 31.35/7.56 thf(zip_derived_cl78, plain, 31.35/7.56 ((~ ('#form46') 31.35/7.56 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y1 : a]: 31.35/7.56 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 (((((Y0 @ Y1) & ('#sk1' @ 31.35/7.56 Y1 @ Y2))) => 31.35/7.56 (Y0 @ Y2))))))))))) => 31.35/7.56 (Y0 @ '#sk12')))))))), 31.35/7.56 define([status(thm)])). 31.35/7.56 thf(zip_derived_cl271, plain, 31.35/7.56 (( ('#form46') 31.35/7.56 | ('#form9') 31.35/7.56 | (((((((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 31.35/7.56 ('#sk20' @ Y1))))))))) & 31.35/7.56 (((!!) @ (^[Y0 : a]: 31.35/7.56 ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))) => 31.35/7.56 ('#sk20' @ '#sk12'))))), 31.35/7.56 inference('renaming', [status(thm)], [zip_derived_cl68, zip_derived_cl78])). 31.35/7.56 thf(zip_derived_cl272, plain, 31.35/7.56 ((~ (((((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 31.35/7.56 ('#sk20' @ Y1))))))))) & 31.35/7.56 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))) 31.35/7.56 | ('#sk20' @ '#sk12') 31.35/7.56 | ('#form9') 31.35/7.56 | ('#form46'))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl271])). 31.35/7.56 thf(zip_derived_cl72, plain, ((~ ('#sk20' @ '#sk12') | ('#form9'))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 31.35/7.56 thf(zip_derived_cl273, plain, 31.35/7.56 (( ('#form46') 31.35/7.56 | ('#form9') 31.35/7.56 | ~ (((((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 31.35/7.56 ('#sk20' @ Y1))))))))) & 31.35/7.56 (((!!) @ (^[Y0 : a]: 31.35/7.56 ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))))), 31.35/7.56 inference('clc', [status(thm)], [zip_derived_cl272, zip_derived_cl72])). 31.35/7.56 thf(zip_derived_cl274, plain, 31.35/7.56 ((~ (((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 31.35/7.56 ('#sk20' @ Y1))))))))) 31.35/7.56 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))) 31.35/7.56 | ('#form9') 31.35/7.56 | ('#form46'))), 31.35/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl273])). 31.35/7.56 thf(zip_derived_cl67, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 ( (((((((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 31.35/7.56 (X2 @ Y1))))))))) & 31.35/7.56 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 31.35/7.56 (X2 @ '#sk12'))) 31.35/7.56 | ('#form9') 31.35/7.56 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y1 : a]: 31.35/7.56 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 (((((Y0 @ Y1) & ('#sk1' @ 31.35/7.56 Y1 @ Y2))) => 31.35/7.56 (Y0 @ Y2))))))))))) => 31.35/7.56 (Y0 @ '#sk12')))))))), 31.35/7.56 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 31.35/7.56 thf(zip_derived_cl78, plain, 31.35/7.56 ((~ ('#form46') 31.35/7.56 | (((!!) @ (^[Y0 : a > $o]: 31.35/7.56 (((((((!!) @ (^[Y1 : a]: 31.35/7.56 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 (((!!) @ (^[Y2 : a]: 31.35/7.56 (((((Y0 @ Y1) & ('#sk1' @ 31.35/7.56 Y1 @ Y2))) => 31.35/7.56 (Y0 @ Y2))))))))))) => 31.35/7.56 (Y0 @ '#sk12')))))))), 31.35/7.56 define([status(thm)])). 31.35/7.56 thf(zip_derived_cl83, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 ( ('#form46') 31.35/7.56 | ('#form9') 31.35/7.56 | (((((((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 31.35/7.56 (X2 @ Y1))))))))) & 31.35/7.56 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 31.35/7.56 (X2 @ '#sk12'))))), 31.35/7.56 inference('renaming', [status(thm)], [zip_derived_cl67, zip_derived_cl78])). 31.35/7.56 thf(zip_derived_cl92, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 (~ (((((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 31.35/7.56 (X2 @ Y1))))))))) & 31.35/7.56 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) 31.35/7.56 | (X2 @ '#sk12') 31.35/7.56 | ('#form9') 31.35/7.56 | ('#form46'))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl83])). 31.35/7.56 thf(zip_derived_cl107, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 (~ (((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 31.35/7.56 (X2 @ Y1))))))))) 31.35/7.56 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 31.35/7.56 | ('#form46') 31.35/7.56 | ('#form9') 31.35/7.56 | (X2 @ '#sk12'))), 31.35/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl92])). 31.35/7.56 thf(zip_derived_cl120, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 (~ (((!!) @ (^[Y0 : a]: 31.35/7.56 ((((('#sk2' @ ('#sk126' @ X2) @ Y0) & (X2 @ 31.35/7.56 ('#sk126' @ X2)))) => 31.35/7.56 (X2 @ Y0)))))) 31.35/7.56 | (X2 @ '#sk12') 31.35/7.56 | ('#form9') 31.35/7.56 | ('#form46') 31.35/7.56 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 31.35/7.56 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl107])). 31.35/7.56 thf(zip_derived_cl138, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 (~ ((((('#sk2' @ ('#sk126' @ X2) @ ('#sk174' @ X2)) & (X2 @ 31.35/7.56 ('#sk126' @ X2)))) => 31.35/7.56 (X2 @ ('#sk174' @ X2)))) 31.35/7.56 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 31.35/7.56 | ('#form46') 31.35/7.56 | ('#form9') 31.35/7.56 | (X2 @ '#sk12'))), 31.35/7.56 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl120])). 31.35/7.56 thf(zip_derived_cl150, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 (~ (X2 @ ('#sk174' @ X2)) 31.35/7.56 | (X2 @ '#sk12') 31.35/7.56 | ('#form9') 31.35/7.56 | ('#form46') 31.35/7.56 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl138])). 31.35/7.56 thf(zip_derived_cl165, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 ( ('#form266' @ X2) 31.35/7.56 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 31.35/7.56 define([status(thm)])). 31.35/7.56 thf(zip_derived_cl275, plain, 31.35/7.56 ((~ ('#form266' @ '#sk20') 31.35/7.56 | ('#form46') 31.35/7.56 | ('#form9') 31.35/7.56 | ~ (((!!) @ (^[Y0 : a]: 31.35/7.56 (((!!) @ (^[Y1 : a]: 31.35/7.56 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 31.35/7.56 ('#sk20' @ Y1))))))))))), 31.35/7.56 inference('renaming', [status(thm)], 31.35/7.56 [zip_derived_cl274, zip_derived_cl165])). 31.35/7.56 thf(zip_derived_cl276, plain, 31.35/7.56 ((~ (((!!) @ (^[Y0 : a]: 31.35/7.56 ((((('#sk2' @ ('#sk126' @ '#sk20') @ Y0) & ('#sk20' @ 31.35/7.56 ('#sk126' @ '#sk20')))) => 31.35/7.56 ('#sk20' @ Y0)))))) 31.35/7.56 | ('#form9') 31.35/7.56 | ('#form46') 31.35/7.56 | ~ ('#form266' @ '#sk20'))), 31.35/7.56 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl275])). 31.35/7.56 thf(zip_derived_cl277, plain, 31.35/7.56 ((~ ((((('#sk2' @ ('#sk126' @ '#sk20') @ ('#sk174' @ '#sk20')) & 31.35/7.56 ('#sk20' @ ('#sk126' @ '#sk20')))) => 31.35/7.56 ('#sk20' @ ('#sk174' @ '#sk20')))) 31.35/7.56 | ~ ('#form266' @ '#sk20') 31.35/7.56 | ('#form46') 31.35/7.56 | ('#form9'))), 31.35/7.56 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl276])). 31.35/7.56 thf(zip_derived_cl279, plain, 31.35/7.56 ((~ ('#sk20' @ ('#sk174' @ '#sk20')) 31.35/7.56 | ('#form9') 31.35/7.56 | ('#form46') 31.35/7.56 | ~ ('#form266' @ '#sk20'))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl277])). 31.35/7.56 thf(zip_derived_cl278, plain, 31.35/7.56 (( ((('#sk2' @ ('#sk126' @ '#sk20') @ ('#sk174' @ '#sk20')) & ('#sk20' @ 31.35/7.56 ('#sk126' @ '#sk20')))) 31.35/7.56 | ('#form9') 31.35/7.56 | ('#form46') 31.35/7.56 | ~ ('#form266' @ '#sk20'))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl277])). 31.35/7.56 thf(zip_derived_cl281, plain, 31.35/7.56 (( ('#sk20' @ ('#sk126' @ '#sk20')) 31.35/7.56 | ~ ('#form266' @ '#sk20') 31.35/7.56 | ('#form46') 31.35/7.56 | ('#form9'))), 31.35/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl278])). 31.35/7.56 thf(zip_derived_cl280, plain, 31.35/7.56 (( ('#sk2' @ ('#sk126' @ '#sk20') @ ('#sk174' @ '#sk20')) 31.35/7.56 | ~ ('#form266' @ '#sk20') 31.35/7.56 | ('#form46') 31.35/7.56 | ('#form9'))), 31.35/7.56 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl278])). 31.35/7.56 thf(zip_derived_cl154, plain, 31.35/7.56 (![X2 : a, X4 : a]: 31.35/7.56 (~ ('#sk2' @ X2 @ X4) 31.35/7.56 | ('#sk20' @ X4) 31.35/7.56 | ('#form9') 31.35/7.56 | ~ ('#sk20' @ X2))), 31.35/7.56 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl141])). 31.35/7.56 thf(zip_derived_cl165, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 ( ('#form266' @ X2) 31.35/7.56 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 31.35/7.56 define([status(thm)])). 31.35/7.56 thf(zip_derived_cl166, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 (~ ((('#sk2' @ '#sk10' @ ('#sk267' @ X2)) => (X2 @ ('#sk267' @ X2)))) 31.35/7.56 | ('#form266' @ X2))), 31.35/7.56 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl165])). 31.35/7.56 thf(zip_derived_cl175, plain, 31.35/7.56 (![X2 : a > $o]: 31.35/7.56 ( ('#sk2' @ '#sk10' @ ('#sk267' @ X2)) | ('#form266' @ X2))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl166])). 31.35/7.56 thf(zip_derived_cl176, plain, 31.35/7.56 (![X2 : a > $o]: (~ (X2 @ ('#sk267' @ X2)) | ('#form266' @ X2))), 31.35/7.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl166])). 31.35/7.56 thf(zip_derived_cl122, plain, 31.35/7.56 (![X2 : a]: (~ ('#sk2' @ '#sk10' @ X2) | ('#form9') | ('#sk20' @ X2))), 31.35/7.56 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl109])). 31.35/7.56 thf(zip_derived_cl6671, plain, ($false), 31.35/7.56 inference('eprover', [status(thm)], 31.35/7.56 [zip_derived_cl39, zip_derived_cl40, zip_derived_cl213, 31.35/7.56 zip_derived_cl215, zip_derived_cl216, zip_derived_cl133, 31.35/7.56 zip_derived_cl56, zip_derived_cl337, zip_derived_cl341, 31.35/7.56 zip_derived_cl23, zip_derived_cl24, zip_derived_cl116, 31.35/7.56 zip_derived_cl148, zip_derived_cl129, zip_derived_cl336, 31.35/7.56 zip_derived_cl339, zip_derived_cl342, zip_derived_cl136, 31.35/7.56 zip_derived_cl137, zip_derived_cl155, zip_derived_cl158, 31.35/7.56 zip_derived_cl145, zip_derived_cl157, zip_derived_cl106, 31.35/7.56 zip_derived_cl105, zip_derived_cl180, zip_derived_cl186, 31.35/7.56 zip_derived_cl123, zip_derived_cl187, zip_derived_cl72, 31.35/7.56 zip_derived_cl178, zip_derived_cl184, zip_derived_cl153, 31.35/7.56 zip_derived_cl185, zip_derived_cl279, zip_derived_cl281, 31.35/7.56 zip_derived_cl280, zip_derived_cl154, zip_derived_cl175, 31.35/7.56 zip_derived_cl176, zip_derived_cl122])). 31.35/7.56 31.35/7.56 % SZS output end Refutation 31.35/7.56 31.35/7.56 31.35/7.56 % Terminating... 31.84/7.76 % Runner terminated. 31.84/7.76 % Zipperpin 1.5 exiting 31.84/7.77 EOF