0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.FRpByjMCPw true 0.13/0.34 % Computer : n005.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1440 0.13/0.34 % WCLimit : 180 0.13/0.34 % DateTime : Thu Jul 4 06:33:24 EDT 2024 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 1440 s 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.58/0.68 % Total configuration time : 828 0.58/0.68 % Estimated wc time : 1656 0.58/0.68 % Estimated cpu time (8 cpus) : 207.0 0.58/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.58/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.58/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.58/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 52.90/7.30 % Solved by lams/20_acsne_simpl.sh. 52.90/7.30 % done 752 iterations in 6.374s 52.90/7.30 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 52.90/7.30 % SZS output start Refutation 52.90/7.30 thf(a_type, type, a: $tType). 52.90/7.30 thf('#sk60_type', type, '#sk60': (a > $o) > a). 52.90/7.30 thf('#sk266_type', type, '#sk266': (a > $o) > a). 52.90/7.30 thf('#sk6_type', type, '#sk6': a). 52.90/7.30 thf('#form19_type', type, '#form19': $o). 52.90/7.30 thf('#form97_type', type, '#form97': (a > $o) > $o). 52.90/7.30 thf('#sk5_type', type, '#sk5': a > $o). 52.90/7.30 thf('#form14_type', type, '#form14': $o). 52.90/7.30 thf('#sk4_type', type, '#sk4': a). 52.90/7.30 thf('#sk116_type', type, '#sk116': (a > $o) > a). 52.90/7.30 thf('#sk56_type', type, '#sk56': (a > $o) > a). 52.90/7.30 thf('#sk141_type', type, '#sk141': (a > $o) > a). 52.90/7.30 thf('#sk137_type', type, '#sk137': (a > $o) > a). 52.90/7.30 thf('#sk15_type', type, '#sk15': a). 52.90/7.30 thf('#sk146_type', type, '#sk146': (a > $o) > a). 52.90/7.30 thf('#form9_type', type, '#form9': $o). 52.90/7.30 thf('#sk98_type', type, '#sk98': (a > $o) > a). 52.90/7.30 thf('#sk108_type', type, '#sk108': (a > $o) > a). 52.90/7.30 thf('#sk23_type', type, '#sk23': a). 52.90/7.30 thf('#sk8_type', type, '#sk8': a > $o). 52.90/7.30 thf('#sk43_type', type, '#sk43': a > $o). 52.90/7.30 thf('#form265_type', type, '#form265': (a > $o) > $o). 52.90/7.30 thf('#sk3_type', type, '#sk3': a). 52.90/7.30 thf('#sk7_type', type, '#sk7': a). 52.90/7.30 thf('#sk1_type', type, '#sk1': a > a > $o). 52.90/7.30 thf('#sk42_type', type, '#sk42': (a > $o) > a). 52.90/7.30 thf('#sk50_type', type, '#sk50': (a > $o) > a). 52.90/7.30 thf('#sk185_type', type, '#sk185': (a > $o) > a). 52.90/7.30 thf('#sk2_type', type, '#sk2': a > a > $o). 52.90/7.30 thf('#sk10_type', type, '#sk10': a). 52.90/7.30 thf('#form420_type', type, '#form420': $o). 52.90/7.30 thf('#sk85_type', type, '#sk85': (a > $o) > a). 52.90/7.30 thf(cTHM251D_pme, conjecture, 52.90/7.30 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 52.90/7.30 ( ( ( ( ![Xx0:a,Xy0:a]: 52.90/7.30 ( ( ( ![Xq:( a > $o )]: 52.90/7.30 ( ( ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 52.90/7.30 ( ![Xu:a,Xv:a]: 52.90/7.30 ( ( ( S @ Xu @ Xv ) & ( Xq @ Xu ) ) => ( Xq @ Xv ) ) ) ) => 52.90/7.30 ( Xq @ Xy0 ) ) ) | 52.90/7.30 ( ![Xq:( a > $o )]: 52.90/7.30 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 52.90/7.30 ( ![Xu:a,Xv:a]: 52.90/7.30 ( ( ( R @ Xu @ Xv ) & ( Xq @ Xu ) ) => ( Xq @ Xv ) ) ) ) => 52.90/7.30 ( Xq @ Xy0 ) ) ) ) => 52.90/7.30 ( ![Xq:( a > $o )]: 52.90/7.30 ( ( ( ![Xw:a]: 52.90/7.30 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => ( Xq @ Xw ) ) ) & 52.90/7.30 ( ![Xu:a,Xv:a]: 52.90/7.30 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 52.90/7.30 ( Xq @ Xv ) ) ) ) => 52.90/7.30 ( Xq @ Xy0 ) ) ) ) ) & 52.90/7.30 ( ![Xx0:a,Xy0:a,Xz:a]: 52.90/7.30 ( ( ( ![Xq:( a > $o )]: 52.90/7.30 ( ( ( ![Xu:a,Xv:a]: 52.90/7.30 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & 52.90/7.30 ( Xq @ Xu ) ) => 52.90/7.30 ( Xq @ Xv ) ) ) & 52.90/7.30 ( ![Xw:a]: 52.90/7.30 ( ( ( R @ Xy0 @ Xw ) | ( S @ Xy0 @ Xw ) ) => 52.90/7.30 ( Xq @ Xw ) ) ) ) => 52.90/7.30 ( Xq @ Xz ) ) ) & 52.90/7.30 ( ![Xq:( a > $o )]: 52.90/7.30 ( ( ( ![Xw:a]: 52.90/7.30 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 52.90/7.30 ( Xq @ Xw ) ) ) & 52.90/7.30 ( ![Xu:a,Xv:a]: 52.90/7.30 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & 52.90/7.30 ( Xq @ Xu ) ) => 52.90/7.30 ( Xq @ Xv ) ) ) ) => 52.90/7.30 ( Xq @ Xy0 ) ) ) ) => 52.90/7.30 ( ![Xq:( a > $o )]: 52.90/7.30 ( ( ( ![Xw:a]: 52.90/7.30 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => ( Xq @ Xw ) ) ) & 52.90/7.30 ( ![Xu:a,Xv:a]: 52.90/7.30 ( ( ( Xq @ Xu ) & ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 52.90/7.30 ( Xq @ Xv ) ) ) ) => 52.90/7.30 ( Xq @ Xz ) ) ) ) ) ) => 52.90/7.30 ( ![Xq:( a > $o )]: 52.90/7.30 ( ( ( ![Xu:a,Xv:a]: 52.90/7.30 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 52.90/7.30 ( Xq @ Xv ) ) ) & 52.90/7.30 ( ![Xw:a]: 52.90/7.30 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 52.90/7.30 ( Xq @ Xy ) ) ) ) => 52.90/7.30 ( ![Xq:( a > $o )]: 52.90/7.30 ( ( ( ![Xw:a]: 52.90/7.30 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 52.90/7.30 ( ![Xu:a,Xv:a]: 52.90/7.30 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 52.90/7.30 ( Xq @ Xv ) ) ) ) => 52.90/7.30 ( Xq @ Xy ) ) ) ))). 52.90/7.30 thf(zf_stmt_0, negated_conjecture, 52.90/7.30 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 52.90/7.30 ( ( ( ( ![Xx0:a,Xy0:a]: 52.90/7.30 ( ( ( ![Xq:( a > $o )]: 52.90/7.30 ( ( ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 52.90/7.30 ( ![Xu:a,Xv:a]: 52.90/7.30 ( ( ( S @ Xu @ Xv ) & ( Xq @ Xu ) ) => ( Xq @ Xv ) ) ) ) => 52.90/7.30 ( Xq @ Xy0 ) ) ) | 52.90/7.30 ( ![Xq:( a > $o )]: 52.90/7.30 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 52.90/7.30 ( ![Xu:a,Xv:a]: 52.90/7.30 ( ( ( R @ Xu @ Xv ) & ( Xq @ Xu ) ) => ( Xq @ Xv ) ) ) ) => 52.90/7.30 ( Xq @ Xy0 ) ) ) ) => 52.90/7.30 ( ![Xq:( a > $o )]: 52.90/7.30 ( ( ( ![Xw:a]: 52.90/7.30 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 52.90/7.30 ( Xq @ Xw ) ) ) & 52.90/7.30 ( ![Xu:a,Xv:a]: 52.90/7.30 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & 52.90/7.30 ( Xq @ Xu ) ) => 52.90/7.30 ( Xq @ Xv ) ) ) ) => 52.90/7.30 ( Xq @ Xy0 ) ) ) ) ) & 52.90/7.30 ( ![Xx0:a,Xy0:a,Xz:a]: 52.90/7.30 ( ( ( ![Xq:( a > $o )]: 52.90/7.30 ( ( ( ![Xu:a,Xv:a]: 52.90/7.30 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & 52.90/7.30 ( Xq @ Xu ) ) => 52.90/7.30 ( Xq @ Xv ) ) ) & 52.90/7.30 ( ![Xw:a]: 52.90/7.30 ( ( ( R @ Xy0 @ Xw ) | ( S @ Xy0 @ Xw ) ) => 52.90/7.30 ( Xq @ Xw ) ) ) ) => 52.90/7.30 ( Xq @ Xz ) ) ) & 52.90/7.30 ( ![Xq:( a > $o )]: 52.90/7.30 ( ( ( ![Xw:a]: 52.90/7.30 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 52.90/7.30 ( Xq @ Xw ) ) ) & 52.90/7.30 ( ![Xu:a,Xv:a]: 52.90/7.30 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & 52.90/7.30 ( Xq @ Xu ) ) => 52.90/7.30 ( Xq @ Xv ) ) ) ) => 52.90/7.30 ( Xq @ Xy0 ) ) ) ) => 52.90/7.30 ( ![Xq:( a > $o )]: 52.90/7.30 ( ( ( ![Xw:a]: 52.90/7.30 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 52.90/7.30 ( Xq @ Xw ) ) ) & 52.90/7.30 ( ![Xu:a,Xv:a]: 52.90/7.30 ( ( ( Xq @ Xu ) & 52.90/7.30 ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 52.90/7.30 ( Xq @ Xv ) ) ) ) => 52.90/7.30 ( Xq @ Xz ) ) ) ) ) ) => 52.90/7.30 ( ![Xq:( a > $o )]: 52.90/7.30 ( ( ( ![Xu:a,Xv:a]: 52.90/7.30 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 52.90/7.30 ( Xq @ Xv ) ) ) & 52.90/7.30 ( ![Xw:a]: 52.90/7.30 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 52.90/7.30 ( Xq @ Xy ) ) ) ) => 52.90/7.30 ( ![Xq:( a > $o )]: 52.90/7.30 ( ( ( ![Xw:a]: 52.90/7.30 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 52.90/7.30 ( ![Xu:a,Xv:a]: 52.90/7.30 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 52.90/7.30 ( Xq @ Xv ) ) ) ) => 52.90/7.30 ( Xq @ Xy ) ) ) ) )), 52.90/7.30 inference('cnf.neg', [status(esa)], [cTHM251D_pme])). 52.90/7.30 thf(zip_derived_cl0, plain, 52.90/7.30 (~ (((!!) @ (^[Y0 : a > a > $o]: 52.90/7.30 (((!!) @ (^[Y1 : a > a > $o]: 52.90/7.30 (((!!) @ (^[Y2 : a]: 52.90/7.30 (((!!) @ (^[Y3 : a]: 52.90/7.30 (((((((((!!) @ ( 52.90/7.30 ^[Y4 : a]: 52.90/7.30 (((!!) @ ( 52.90/7.30 ^[Y5 : a]: 52.90/7.30 (( 52.90/7.30 (( 52.90/7.30 (( 52.90/7.30 (!!) @ ( 52.90/7.30 ^[Y6 : a > $o]: 52.90/7.30 (( 52.90/7.30 (( 52.90/7.30 (( 52.90/7.30 (!!) @ ( 52.90/7.30 ^[Y7 : a]: 52.90/7.30 (( 52.90/7.30 (Y1 @ 52.90/7.30 Y4 @ 52.90/7.30 Y7) => 52.90/7.30 (Y6 @ Y7)))))) & 52.90/7.30 (( 52.90/7.30 (!!) @ ( 52.90/7.30 ^[Y7 : a]: 52.90/7.30 (( 52.90/7.30 (!!) @ ( 52.90/7.30 ^[Y8 : a]: 52.90/7.30 (( 52.90/7.30 (( 52.90/7.30 (Y1 @ 52.90/7.30 Y7 @ 52.90/7.30 Y8) & 52.90/7.30 (Y6 @ Y7))) => 52.90/7.30 (Y6 @ Y8))))))))))) => 52.90/7.30 (Y6 @ Y5)))))) | 52.90/7.30 (( 52.90/7.30 (!!) @ ( 52.90/7.30 ^[Y6 : a > $o]: 52.90/7.30 (( 52.90/7.30 (( 52.90/7.30 (( 52.90/7.30 (!!) @ ( 52.90/7.30 ^[Y7 : a]: 52.90/7.30 (( 52.90/7.30 (Y0 @ 52.90/7.30 Y4 @ 52.90/7.30 Y7) => 52.90/7.30 (Y6 @ Y7)))))) & 52.90/7.30 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y8 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y0 @ 52.90/7.31 Y7 @ 52.90/7.31 Y8) & 52.90/7.31 (Y6 @ Y7))) => 52.90/7.31 (Y6 @ Y8))))))))))) => 52.90/7.31 (Y6 @ Y5)))))))) => 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y0 @ 52.90/7.31 Y4 @ 52.90/7.31 Y7) | 52.90/7.31 (Y1 @ 52.90/7.31 Y4 @ Y7))) => 52.90/7.31 (Y6 @ Y7)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y8 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y0 @ 52.90/7.31 Y7 @ 52.90/7.31 Y8) | 52.90/7.31 (Y1 @ 52.90/7.31 Y7 @ Y8))) & 52.90/7.31 (Y6 @ Y7))) => 52.90/7.31 (Y6 @ Y8))))))))))) => 52.90/7.31 (Y6 @ Y5)))))))))))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y8 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y9 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y1 @ 52.90/7.31 Y8 @ 52.90/7.31 Y9) | 52.90/7.31 (Y0 @ 52.90/7.31 Y8 @ Y9))) & 52.90/7.31 (Y7 @ Y8))) => 52.90/7.31 (Y7 @ Y9))))))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y8 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y0 @ 52.90/7.31 Y5 @ 52.90/7.31 Y8) | 52.90/7.31 (Y1 @ 52.90/7.31 Y5 @ Y8))) => 52.90/7.31 (Y7 @ Y8)))))))) => 52.90/7.31 (Y7 @ Y6)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y8 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y0 @ 52.90/7.31 Y4 @ 52.90/7.31 Y8) | 52.90/7.31 (Y1 @ 52.90/7.31 Y4 @ Y8))) => 52.90/7.31 (Y7 @ Y8)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y8 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y9 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y1 @ 52.90/7.31 Y8 @ 52.90/7.31 Y9) | 52.90/7.31 (Y0 @ 52.90/7.31 Y8 @ Y9))) & 52.90/7.31 (Y7 @ Y8))) => 52.90/7.31 (Y7 @ Y9))))))))))) => 52.90/7.31 (Y7 @ Y5)))))))) => 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y8 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y0 @ 52.90/7.31 Y4 @ 52.90/7.31 Y8) | 52.90/7.31 (Y1 @ 52.90/7.31 Y4 @ Y8))) => 52.90/7.31 (Y7 @ Y8)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y8 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y9 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y7 @ 52.90/7.31 Y8) & 52.90/7.31 (( 52.90/7.31 (Y1 @ 52.90/7.31 Y8 @ 52.90/7.31 Y9) | 52.90/7.31 (Y0 @ 52.90/7.31 Y8 @ Y9))))) => 52.90/7.31 (Y7 @ Y9))))))))))) => 52.90/7.31 (Y7 @ Y6))))))))))))))))))) => 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a > $o]: 52.90/7.31 (((((( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y0 @ 52.90/7.31 Y5 @ 52.90/7.31 Y6) | 52.90/7.31 (Y1 @ 52.90/7.31 Y5 @ Y6))) & 52.90/7.31 (Y4 @ Y5))) => 52.90/7.31 (Y4 @ Y6))))))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y0 @ 52.90/7.31 Y2 @ 52.90/7.31 Y5) | 52.90/7.31 (Y1 @ 52.90/7.31 Y2 @ Y5))) => 52.90/7.31 (Y4 @ Y5)))))))) => 52.90/7.31 (Y4 @ Y3)))))))) => 52.90/7.31 (((!!) @ (^[Y4 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y0 @ 52.90/7.31 Y2 @ 52.90/7.31 Y5) | 52.90/7.31 (Y1 @ 52.90/7.31 Y2 @ Y5))) => 52.90/7.31 (Y4 @ Y5)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y1 @ 52.90/7.31 Y5 @ 52.90/7.31 Y6) | 52.90/7.31 (Y0 @ 52.90/7.31 Y5 @ Y6))) & 52.90/7.31 (Y4 @ Y5))) => 52.90/7.31 (Y4 @ Y6))))))))))) => 52.90/7.31 (Y4 @ Y3))))))))))))))))))))), 52.90/7.31 inference('cnf', [status(esa)], [zf_stmt_0])). 52.90/7.31 thf(zip_derived_cl1, plain, 52.90/7.31 (~ (((!!) @ (^[Y0 : a > a > $o]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((((!!) @ (^[Y3 : a]: 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (((( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (Y0 @ 52.90/7.31 Y3 @ 52.90/7.31 Y6) => 52.90/7.31 (Y5 @ Y6)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y0 @ 52.90/7.31 Y6 @ 52.90/7.31 Y7) & 52.90/7.31 (Y5 @ Y6))) => 52.90/7.31 (Y5 @ Y7))))))))))) => 52.90/7.31 (Y5 @ Y4)))))) | 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y3 @ 52.90/7.31 Y6) => 52.90/7.31 (Y5 @ Y6)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y6 @ 52.90/7.31 Y7) & 52.90/7.31 (Y5 @ Y6))) => 52.90/7.31 (Y5 @ Y7))))))))))) => 52.90/7.31 (Y5 @ Y4)))))))) => 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y3 @ 52.90/7.31 Y6) | 52.90/7.31 (Y0 @ 52.90/7.31 Y3 @ Y6))) => 52.90/7.31 (Y5 @ Y6)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y6 @ 52.90/7.31 Y7) | 52.90/7.31 (Y0 @ 52.90/7.31 Y6 @ Y7))) & 52.90/7.31 (Y5 @ Y6))) => 52.90/7.31 (Y5 @ Y7))))))))))) => 52.90/7.31 (Y5 @ Y4)))))))))))))) & 52.90/7.31 (((!!) @ (^[Y3 : a]: 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y8 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y0 @ 52.90/7.31 Y7 @ 52.90/7.31 Y8) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y7 @ Y8))) & 52.90/7.31 (Y6 @ Y7))) => 52.90/7.31 (Y6 @ Y8))))))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ 52.90/7.31 Y7) | 52.90/7.31 (Y0 @ 52.90/7.31 Y4 @ Y7))) => 52.90/7.31 (Y6 @ Y7)))))))) => 52.90/7.31 (Y6 @ Y5)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y3 @ 52.90/7.31 Y7) | 52.90/7.31 (Y0 @ 52.90/7.31 Y3 @ Y7))) => 52.90/7.31 (Y6 @ Y7)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y8 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y0 @ 52.90/7.31 Y7 @ 52.90/7.31 Y8) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y7 @ Y8))) & 52.90/7.31 (Y6 @ Y7))) => 52.90/7.31 (Y6 @ Y8))))))))))) => 52.90/7.31 (Y6 @ Y4)))))))) => 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y3 @ 52.90/7.31 Y7) | 52.90/7.31 (Y0 @ 52.90/7.31 Y3 @ Y7))) => 52.90/7.31 (Y6 @ Y7)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y8 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y6 @ 52.90/7.31 Y7) & 52.90/7.31 (( 52.90/7.31 (Y0 @ 52.90/7.31 Y7 @ 52.90/7.31 Y8) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y7 @ Y8))))) => 52.90/7.31 (Y6 @ Y8))))))))))) => 52.90/7.31 (Y6 @ Y5))))))))))))))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 (Y0 @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 (Y0 @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))))) => 52.90/7.31 (Y3 @ Y2)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (((( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ Y4) | 52.90/7.31 (Y0 @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y0 @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2)))))))))))))))))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 52.90/7.31 thf(zip_derived_cl2, plain, 52.90/7.31 (~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((((((((!!) @ (^[Y2 : a]: 52.90/7.31 (((!!) @ (^[Y3 : a]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y2 @ 52.90/7.31 Y5) => 52.90/7.31 (Y4 @ Y5)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y5 @ 52.90/7.31 Y6) & 52.90/7.31 (Y4 @ Y5))) => 52.90/7.31 (Y4 @ Y6))))))))))) => 52.90/7.31 (Y4 @ Y3)))))) | 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y2 @ 52.90/7.31 Y5) => 52.90/7.31 (Y4 @ Y5)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y5 @ 52.90/7.31 Y6) & 52.90/7.31 (Y4 @ Y5))) => 52.90/7.31 (Y4 @ Y6))))))))))) => 52.90/7.31 (Y4 @ Y3)))))))) => 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y2 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y2 @ Y5))) => 52.90/7.31 (Y4 @ Y5)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y5 @ 52.90/7.31 Y6) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y5 @ Y6))) & 52.90/7.31 (Y4 @ Y5))) => 52.90/7.31 (Y4 @ Y6))))))))))) => 52.90/7.31 (Y4 @ Y3)))))))))))))) & 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((!!) @ (^[Y3 : a]: 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (((( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y6 @ 52.90/7.31 Y7) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y6 @ Y7))) & 52.90/7.31 (Y5 @ Y6))) => 52.90/7.31 (Y5 @ Y7))))))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y3 @ 52.90/7.31 Y6) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y3 @ Y6))) => 52.90/7.31 (Y5 @ Y6)))))))) => 52.90/7.31 (Y5 @ Y4)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y2 @ 52.90/7.31 Y6) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y2 @ Y6))) => 52.90/7.31 (Y5 @ Y6)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y6 @ 52.90/7.31 Y7) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y6 @ Y7))) & 52.90/7.31 (Y5 @ Y6))) => 52.90/7.31 (Y5 @ Y7))))))))))) => 52.90/7.31 (Y5 @ Y3)))))))) => 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y2 @ 52.90/7.31 Y6) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y2 @ Y6))) => 52.90/7.31 (Y5 @ Y6)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y7 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y5 @ 52.90/7.31 Y6) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y6 @ 52.90/7.31 Y7) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y6 @ Y7))))) => 52.90/7.31 (Y5 @ Y7))))))))))) => 52.90/7.31 (Y5 @ Y4))))))))))))))))))) => 52.90/7.31 (((!!) @ (^[Y2 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y3 : a]: 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y3 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y3 @ Y4))) & 52.90/7.31 (Y2 @ Y3))) => 52.90/7.31 (Y2 @ Y4))))))))) & 52.90/7.31 (((!!) @ (^[Y3 : a]: 52.90/7.31 ((((('#sk1' @ 52.90/7.31 Y0 @ Y3) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y3))) => 52.90/7.31 (Y2 @ Y3)))))))) => 52.90/7.31 (Y2 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y2 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y3 : a]: 52.90/7.31 ((((('#sk1' @ 52.90/7.31 Y0 @ Y3) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y3))) => 52.90/7.31 (Y2 @ Y3)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a]: 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (((( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y3 @ Y4) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y3 @ Y4))) & 52.90/7.31 (Y2 @ Y3))) => 52.90/7.31 (Y2 @ Y4))))))))))) => 52.90/7.31 (Y2 @ Y1))))))))))))))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 52.90/7.31 thf(zip_derived_cl3, plain, 52.90/7.31 (~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2)))))) | 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2)))))))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((!!) @ (^[Y3 : a]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y5 @ 52.90/7.31 Y6) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y5 @ Y6))) & 52.90/7.31 (Y4 @ Y5))) => 52.90/7.31 (Y4 @ Y6))))))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y2 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y2 @ Y5))) => 52.90/7.31 (Y4 @ Y5)))))))) => 52.90/7.31 (Y4 @ Y3)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y5))) => 52.90/7.31 (Y4 @ Y5)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y5 @ 52.90/7.31 Y6) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y5 @ Y6))) & 52.90/7.31 (Y4 @ Y5))) => 52.90/7.31 (Y4 @ Y6))))))))))) => 52.90/7.31 (Y4 @ Y2)))))))) => 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a > $o]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y5))) => 52.90/7.31 (Y4 @ Y5)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y6 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y4 @ 52.90/7.31 Y5) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y5 @ 52.90/7.31 Y6) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y5 @ Y6))))) => 52.90/7.31 (Y4 @ Y6))))))))))) => 52.90/7.31 (Y4 @ Y3))))))))))))))))))) => 52.90/7.31 (((!!) @ (^[Y1 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y2 : a]: 52.90/7.31 (((!!) @ (^[Y3 : a]: 52.90/7.31 (((((( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y2 @ Y3) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y2 @ Y3))) & 52.90/7.31 (Y1 @ Y2))) => 52.90/7.31 (Y1 @ Y3))))))))) & 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ 52.90/7.31 Y2) | ('#sk2' @ 52.90/7.31 '#sk3' @ Y2))) => 52.90/7.31 (Y1 @ Y2)))))))) => 52.90/7.31 (Y1 @ Y0)))))))) => 52.90/7.31 (((!!) @ (^[Y1 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y2 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y2) | 52.90/7.31 ('#sk2' @ '#sk3' @ Y2))) => 52.90/7.31 (Y1 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((!!) @ (^[Y3 : a]: 52.90/7.31 ((((((('#sk2' @ 52.90/7.31 Y2 @ Y3) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y2 @ Y3))) & 52.90/7.31 (Y1 @ Y2))) => 52.90/7.31 (Y1 @ Y3))))))))))) => 52.90/7.31 (Y1 @ Y0)))))))))))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 52.90/7.31 thf(zip_derived_cl4, plain, 52.90/7.31 (~ (((((((((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((((((!!) @ (^[Y2 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y3 : a]: 52.90/7.31 (( 52.90/7.31 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(((!!) @ (^[Y3 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y3 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y3 @ Y4))) & 52.90/7.31 (Y2 @ Y3))) => 52.90/7.31 (Y2 @ Y4))))))))))) => 52.90/7.31 (Y2 @ Y1)))))))))))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))))) => 52.90/7.31 (Y3 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((( 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : 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@ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk4'))))))))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 52.90/7.31 thf(zip_derived_cl5, plain, 52.90/7.31 ( (((((((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((((((!!) @ (^[Y2 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y3 : a]: 52.90/7.31 ((('#sk2' @ 52.90/7.31 Y0 @ 52.90/7.31 Y3) => 52.90/7.31 (Y2 @ Y3)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a]: 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y3 @ 52.90/7.31 Y4) & 52.90/7.31 (Y2 @ Y3))) => 52.90/7.31 (Y2 @ Y4))))))))))) => 52.90/7.31 (Y2 @ Y1)))))) | 52.90/7.31 (((!!) @ (^[Y2 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y3 : a]: 52.90/7.31 ((('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y3) => 52.90/7.31 (Y2 @ Y3)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a]: 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y3 @ 52.90/7.31 Y4) & 52.90/7.31 (Y2 @ Y3))) => 52.90/7.31 (Y2 @ Y4))))))))))) => 52.90/7.31 (Y2 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y2 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y3 : a]: 52.90/7.31 ((((('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y3) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y3))) => 52.90/7.31 (Y2 @ Y3)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a]: 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y3 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y3 @ Y4))) & 52.90/7.31 (Y2 @ Y3))) => 52.90/7.31 (Y2 @ Y4))))))))))) => 52.90/7.31 (Y2 @ Y1)))))))))))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 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52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y3 @ 52.90/7.31 Y4) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2))))))))))))))))) 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk1' @ Y1 @ Y2) | 52.90/7.31 ('#sk2' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk3' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))))) => 52.90/7.31 (Y0 @ '#sk4')))))))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 52.90/7.31 thf(zip_derived_cl18, plain, 52.90/7.31 (( (((((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((('#sk2' @ Y1 @ Y2) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk7')))))) | 52.90/7.31 (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((('#sk1' @ Y1 @ Y2) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk7')))))))) 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk1' @ Y1 @ Y2) | 52.90/7.31 ('#sk2' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk3' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))))) => 52.90/7.31 (Y0 @ '#sk4')))))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))))) => 52.90/7.31 (Y3 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y3 @ 52.90/7.31 Y4) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2))))))))))))))))))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 52.90/7.31 thf(zip_derived_cl22, plain, 52.90/7.31 (( (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((('#sk2' @ Y1 @ Y2) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk7')))))) 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((('#sk1' @ Y1 @ Y2) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk7')))))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))))) => 52.90/7.31 (Y3 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y3 @ 52.90/7.31 Y4) & 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52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk1' @ Y1 @ Y2) | 52.90/7.31 ('#sk2' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y1) | 52.90/7.31 ('#sk2' @ '#sk3' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))))) => 52.90/7.31 (Y0 @ '#sk4')))))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))))) => 52.90/7.31 (Y3 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y3 @ 52.90/7.31 Y4) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2))))))))))))))))) 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((('#sk1' @ Y1 @ Y2) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk7')))))))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 52.90/7.31 thf(zip_derived_cl27, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( (((((((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))))) => 52.90/7.31 (X2 @ '#sk7'))) 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk1' @ Y1 @ Y2) | 52.90/7.31 ('#sk2' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y1) | 52.90/7.31 ('#sk2' @ '#sk3' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))))) => 52.90/7.31 (Y0 @ '#sk4')))))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))))) => 52.90/7.31 (Y3 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y3 @ 52.90/7.31 Y4) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2))))))))))))))))) 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((('#sk1' @ Y1 @ Y2) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk7')))))))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 52.90/7.31 thf(zip_derived_cl34, plain, 52.90/7.31 ((~ ('#form14') 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk1' @ Y1 @ Y2) | 52.90/7.31 ('#sk2' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk3' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))))) => 52.90/7.31 (Y0 @ '#sk4')))))))), 52.90/7.31 define([status(thm)])). 52.90/7.31 thf(zip_derived_cl38, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( ('#form14') 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((('#sk1' @ Y1 @ Y2) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk7')))))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))))) => 52.90/7.31 (Y3 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y3 @ 52.90/7.31 Y4) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2))))))))))))))))) 52.90/7.31 | (((((((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))))) => 52.90/7.31 (X2 @ '#sk7'))))), 52.90/7.31 inference('renaming', [status(thm)], [zip_derived_cl27, zip_derived_cl34])). 52.90/7.31 thf(zip_derived_cl43, plain, 52.90/7.31 ((~ ('#form19') 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((('#sk1' @ Y1 @ Y2) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk7')))))))), 52.90/7.31 define([status(thm)])). 52.90/7.31 thf(zip_derived_cl44, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))))) => 52.90/7.31 (X2 @ '#sk7'))) 52.90/7.31 | ~ ('#form19'))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 52.90/7.31 thf(zip_derived_cl53, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ (((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))))) 52.90/7.31 | (X2 @ '#sk7') 52.90/7.31 | ~ ('#form19'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 52.90/7.31 thf(zip_derived_cl60, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))) 52.90/7.31 | ~ ('#form19') 52.90/7.31 | (X2 @ '#sk7'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl53])). 52.90/7.31 thf(zip_derived_cl71, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ ((('#sk1' @ '#sk6' @ ('#sk50' @ X2)) => (X2 @ ('#sk50' @ X2)))) 52.90/7.31 | (X2 @ '#sk7') 52.90/7.31 | ~ ('#form19') 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl60])). 52.90/7.31 thf(zip_derived_cl87, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ (X2 @ ('#sk50' @ X2)) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))) 52.90/7.31 | ~ ('#form19') 52.90/7.31 | (X2 @ '#sk7'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 52.90/7.31 thf(zip_derived_cl100, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ ('#sk85' @ X2) @ Y0) & (X2 @ 52.90/7.31 ('#sk85' @ X2)))) => 52.90/7.31 (X2 @ Y0)))))) 52.90/7.31 | (X2 @ '#sk7') 52.90/7.31 | ~ ('#form19') 52.90/7.31 | ~ (X2 @ ('#sk50' @ X2)))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl87])). 52.90/7.31 thf(zip_derived_cl114, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ ((((('#sk1' @ ('#sk85' @ X2) @ ('#sk116' @ X2)) & (X2 @ 52.90/7.31 ('#sk85' @ X2)))) => 52.90/7.31 (X2 @ ('#sk116' @ X2)))) 52.90/7.31 | ~ (X2 @ ('#sk50' @ X2)) 52.90/7.31 | ~ ('#form19') 52.90/7.31 | (X2 @ '#sk7'))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl100])). 52.90/7.31 thf(zip_derived_cl129, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( ((('#sk1' @ ('#sk85' @ X2) @ ('#sk116' @ X2)) & (X2 @ 52.90/7.31 ('#sk85' @ X2)))) 52.90/7.31 | (X2 @ '#sk7') 52.90/7.31 | ~ ('#form19') 52.90/7.31 | ~ (X2 @ ('#sk50' @ X2)))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl114])). 52.90/7.31 thf(zip_derived_cl148, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( (X2 @ ('#sk85' @ X2)) 52.90/7.31 | ~ (X2 @ ('#sk50' @ X2)) 52.90/7.31 | ~ ('#form19') 52.90/7.31 | (X2 @ '#sk7'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl129])). 52.90/7.31 thf(zip_derived_cl130, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ (X2 @ ('#sk116' @ X2)) 52.90/7.31 | (X2 @ '#sk7') 52.90/7.31 | ~ ('#form19') 52.90/7.31 | ~ (X2 @ ('#sk50' @ X2)))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl114])). 52.90/7.31 thf(zip_derived_cl19, plain, 52.90/7.31 ((~ (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk6' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk6' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk1' @ Y1 @ Y2) | 52.90/7.31 ('#sk2' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk7')))))) 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk1' @ Y1 @ Y2) | 52.90/7.31 ('#sk2' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk3' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))))) => 52.90/7.31 (Y0 @ '#sk4')))))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))))) => 52.90/7.31 (Y3 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y3 @ 52.90/7.31 Y4) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2))))))))))))))))))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 52.90/7.31 thf(zip_derived_cl23, plain, 52.90/7.31 ((~ (((((((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 52.90/7.31 ('#sk8' @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 52.90/7.31 Y0 @ Y1))) & 52.90/7.31 ('#sk8' @ Y0))) => 52.90/7.31 ('#sk8' @ Y1))))))))))) => 52.90/7.31 ('#sk8' @ '#sk7'))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))))) => 52.90/7.31 (Y3 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y3 @ 52.90/7.31 Y4) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2))))))))))))))))) 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk1' @ Y1 @ Y2) | 52.90/7.31 ('#sk2' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk3' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))))) => 52.90/7.31 (Y0 @ '#sk4')))))))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 52.90/7.31 thf(zip_derived_cl23, plain, 52.90/7.31 ((~ (((((((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 52.90/7.31 ('#sk8' @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 52.90/7.31 Y0 @ Y1))) & 52.90/7.31 ('#sk8' @ Y0))) => 52.90/7.31 ('#sk8' @ Y1))))))))))) => 52.90/7.31 ('#sk8' @ '#sk7'))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))))) => 52.90/7.31 (Y3 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y3 @ 52.90/7.31 Y4) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2))))))))))))))))) 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk1' @ Y1 @ Y2) | 52.90/7.31 ('#sk2' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk3' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))))) => 52.90/7.31 (Y0 @ '#sk4')))))))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 52.90/7.31 thf(zip_derived_cl30, plain, 52.90/7.31 (( ('#form9') 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))))) => 52.90/7.31 (Y3 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y3 @ 52.90/7.31 Y4) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2))))))))))))))))))), 52.90/7.31 define([status(thm)])). 52.90/7.31 thf(zip_derived_cl32, plain, 52.90/7.31 ((~ ('#form9') 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk1' @ Y1 @ Y2) | 52.90/7.31 ('#sk2' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk3' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))))) => 52.90/7.31 (Y0 @ '#sk4')))))) 52.90/7.31 | ~ (((((((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 52.90/7.31 ('#sk8' @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 52.90/7.31 Y0 @ Y1))) & 52.90/7.31 ('#sk8' @ Y0))) => 52.90/7.31 ('#sk8' @ Y1))))))))))) => 52.90/7.31 ('#sk8' @ '#sk7'))))), 52.90/7.31 inference('renaming', [status(thm)], [zip_derived_cl23, zip_derived_cl30])). 52.90/7.31 thf(zip_derived_cl34, plain, 52.90/7.31 ((~ ('#form14') 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk1' @ Y1 @ Y2) | 52.90/7.31 ('#sk2' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk3' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))))) => 52.90/7.31 (Y0 @ '#sk4')))))))), 52.90/7.31 define([status(thm)])). 52.90/7.31 thf(zip_derived_cl39, plain, 52.90/7.31 (( ('#form14') 52.90/7.31 | ~ (((((((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 52.90/7.31 ('#sk8' @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 52.90/7.31 Y0 @ Y1))) & 52.90/7.31 ('#sk8' @ Y0))) => 52.90/7.31 ('#sk8' @ Y1))))))))))) => 52.90/7.31 ('#sk8' @ '#sk7'))) 52.90/7.31 | ~ ('#form9'))), 52.90/7.31 inference('renaming', [status(thm)], [zip_derived_cl32, zip_derived_cl34])). 52.90/7.31 thf(zip_derived_cl50, plain, 52.90/7.31 ((~ ('#sk8' @ '#sk7') | ~ ('#form9') | ('#form14'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 52.90/7.31 thf(zip_derived_cl147, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( ('#sk1' @ ('#sk85' @ X2) @ ('#sk116' @ X2)) 52.90/7.31 | ~ (X2 @ ('#sk50' @ X2)) 52.90/7.31 | ~ ('#form19') 52.90/7.31 | (X2 @ '#sk7'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl129])). 52.90/7.31 thf(zip_derived_cl86, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( ('#sk1' @ '#sk6' @ ('#sk50' @ X2)) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))) 52.90/7.31 | ~ ('#form19') 52.90/7.31 | (X2 @ '#sk7'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 52.90/7.31 thf(zip_derived_cl99, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ ('#sk85' @ X2) @ Y0) & (X2 @ 52.90/7.31 ('#sk85' @ X2)))) => 52.90/7.31 (X2 @ Y0)))))) 52.90/7.31 | (X2 @ '#sk7') 52.90/7.31 | ~ ('#form19') 52.90/7.31 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl86])). 52.90/7.31 thf(zip_derived_cl113, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ ((((('#sk1' @ ('#sk85' @ X2) @ ('#sk116' @ X2)) & (X2 @ 52.90/7.31 ('#sk85' @ X2)))) => 52.90/7.31 (X2 @ ('#sk116' @ X2)))) 52.90/7.31 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)) 52.90/7.31 | ~ ('#form19') 52.90/7.31 | (X2 @ '#sk7'))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl99])). 52.90/7.31 thf(zip_derived_cl127, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( ((('#sk1' @ ('#sk85' @ X2) @ ('#sk116' @ X2)) & (X2 @ 52.90/7.31 ('#sk85' @ X2)))) 52.90/7.31 | (X2 @ '#sk7') 52.90/7.31 | ~ ('#form19') 52.90/7.31 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl113])). 52.90/7.31 thf(zip_derived_cl146, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( (X2 @ ('#sk85' @ X2)) 52.90/7.31 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)) 52.90/7.31 | ~ ('#form19') 52.90/7.31 | (X2 @ '#sk7'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl127])). 52.90/7.31 thf(zip_derived_cl128, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ (X2 @ ('#sk116' @ X2)) 52.90/7.31 | (X2 @ '#sk7') 52.90/7.31 | ~ ('#form19') 52.90/7.31 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl113])). 52.90/7.31 thf(zip_derived_cl49, plain, 52.90/7.31 (( (((((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 52.90/7.31 ('#sk8' @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk8' @ Y0))) => 52.90/7.31 ('#sk8' @ Y1))))))))))) 52.90/7.31 | ~ ('#form9') 52.90/7.31 | ('#form14'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 52.90/7.31 thf(zip_derived_cl55, plain, 52.90/7.31 (( (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 52.90/7.31 ('#sk8' @ Y0)))))) 52.90/7.31 | ('#form14') 52.90/7.31 | ~ ('#form9'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl49])). 52.90/7.31 thf(zip_derived_cl62, plain, 52.90/7.31 (![X2 : a]: 52.90/7.31 ( ((((('#sk1' @ '#sk6' @ X2) | ('#sk2' @ '#sk6' @ X2))) => ('#sk8' @ 52.90/7.31 X2))) 52.90/7.31 | ~ ('#form9') 52.90/7.31 | ('#form14'))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl55])). 52.90/7.31 thf(zip_derived_cl73, plain, 52.90/7.31 (![X2 : a]: 52.90/7.31 (~ ((('#sk1' @ '#sk6' @ X2) | ('#sk2' @ '#sk6' @ X2))) 52.90/7.31 | ('#sk8' @ X2) 52.90/7.31 | ('#form14') 52.90/7.31 | ~ ('#form9'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 52.90/7.31 thf(zip_derived_cl90, plain, 52.90/7.31 (![X2 : a]: 52.90/7.31 (~ ('#sk1' @ '#sk6' @ X2) 52.90/7.31 | ~ ('#form9') 52.90/7.31 | ('#form14') 52.90/7.31 | ('#sk8' @ X2))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl73])). 52.90/7.31 thf(zip_derived_cl145, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( ('#sk1' @ ('#sk85' @ X2) @ ('#sk116' @ X2)) 52.90/7.31 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)) 52.90/7.31 | ~ ('#form19') 52.90/7.31 | (X2 @ '#sk7'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl127])). 52.90/7.31 thf(zip_derived_cl56, plain, 52.90/7.31 (( (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 52.90/7.31 ('#sk8' @ Y0))) => 52.90/7.31 ('#sk8' @ Y1))))))))) 52.90/7.31 | ('#form14') 52.90/7.31 | ~ ('#form9'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl49])). 52.90/7.31 thf(zip_derived_cl63, plain, 52.90/7.31 (![X2 : a]: 52.90/7.31 ( (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) & 52.90/7.31 ('#sk8' @ X2))) => 52.90/7.31 ('#sk8' @ Y0)))))) 52.90/7.31 | ~ ('#form9') 52.90/7.31 | ('#form14'))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl56])). 52.90/7.31 thf(zip_derived_cl74, plain, 52.90/7.31 (![X2 : a, X4 : a]: 52.90/7.31 ( ((((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk8' @ X2))) => 52.90/7.31 ('#sk8' @ X4))) 52.90/7.31 | ('#form14') 52.90/7.31 | ~ ('#form9'))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 52.90/7.31 thf(zip_derived_cl92, plain, 52.90/7.31 (![X2 : a, X4 : a]: 52.90/7.31 (~ ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk8' @ X2))) 52.90/7.31 | ('#sk8' @ X4) 52.90/7.31 | ~ ('#form9') 52.90/7.31 | ('#form14'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])). 52.90/7.31 thf(zip_derived_cl106, plain, 52.90/7.31 (![X2 : a, X4 : a]: 52.90/7.31 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 52.90/7.31 | ~ ('#sk8' @ X2) 52.90/7.31 | ('#form14') 52.90/7.31 | ~ ('#form9') 52.90/7.31 | ('#sk8' @ X4))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl92])). 52.90/7.31 thf(zip_derived_cl119, plain, 52.90/7.31 (![X2 : a, X4 : a]: 52.90/7.31 (~ ('#sk1' @ X2 @ X4) 52.90/7.31 | ('#sk8' @ X4) 52.90/7.31 | ~ ('#form9') 52.90/7.31 | ('#form14') 52.90/7.31 | ~ ('#sk8' @ X2))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl106])). 52.90/7.31 thf(zip_derived_cl30, plain, 52.90/7.31 (( ('#form9') 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))))) => 52.90/7.31 (Y3 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y3 @ 52.90/7.31 Y4) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2))))))))))))))))))), 52.90/7.31 define([status(thm)])). 52.90/7.31 thf(zip_derived_cl31, plain, 52.90/7.31 ((~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((((((!!) @ (^[Y2 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y3 : a]: 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y3 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y3 @ Y4))) & 52.90/7.31 (Y2 @ Y3))) => 52.90/7.31 (Y2 @ Y4))))))))) & 52.90/7.31 (((!!) @ (^[Y3 : a]: 52.90/7.31 ((((('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y3) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y3))) => 52.90/7.31 (Y2 @ Y3)))))))) => 52.90/7.31 (Y2 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y2 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y3 : a]: 52.90/7.31 ((((('#sk1' @ 52.90/7.31 '#sk10' @ 52.90/7.31 Y3) | 52.90/7.31 ('#sk2' @ 52.90/7.31 '#sk10' @ 52.90/7.31 Y3))) => 52.90/7.31 (Y2 @ Y3)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a]: 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y3 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y3 @ Y4))) & 52.90/7.31 (Y2 @ Y3))) => 52.90/7.31 (Y2 @ Y4))))))))))) => 52.90/7.31 (Y2 @ Y0)))))))) => 52.90/7.31 (((!!) @ (^[Y2 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y3 : a]: 52.90/7.31 ((((('#sk1' @ 52.90/7.31 '#sk10' @ 52.90/7.31 Y3) | 52.90/7.31 ('#sk2' @ 52.90/7.31 '#sk10' @ 52.90/7.31 Y3))) => 52.90/7.31 (Y2 @ Y3)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a]: 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (((( 52.90/7.31 (Y2 @ 52.90/7.31 Y3) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y3 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y3 @ Y4))))) => 52.90/7.31 (Y2 @ Y4))))))))))) => 52.90/7.31 (Y2 @ Y1)))))))))))))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])). 52.90/7.31 thf(zip_derived_cl40, plain, 52.90/7.31 ((~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((((((!!) @ (^[Y1 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y2 : a]: 52.90/7.31 (((!!) @ (^[Y3 : a]: 52.90/7.31 (((((( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y2 @ 52.90/7.31 Y3) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y2 @ Y3))) & 52.90/7.31 (Y1 @ Y2))) => 52.90/7.31 (Y1 @ Y3))))))))) & 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((('#sk1' @ '#sk15' @ 52.90/7.31 Y2) | ('#sk2' @ 52.90/7.31 '#sk15' @ Y2))) => 52.90/7.31 (Y1 @ Y2)))))))) => 52.90/7.31 (Y1 @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y2 : a]: 52.90/7.31 ((((('#sk1' @ '#sk10' @ 52.90/7.31 Y2) | ('#sk2' @ 52.90/7.31 '#sk10' @ Y2))) => 52.90/7.31 (Y1 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((!!) @ (^[Y3 : a]: 52.90/7.31 (((((( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y2 @ 52.90/7.31 Y3) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y2 @ Y3))) & 52.90/7.31 (Y1 @ Y2))) => 52.90/7.31 (Y1 @ Y3))))))))))) => 52.90/7.31 (Y1 @ '#sk15')))))))) => 52.90/7.31 (((!!) @ (^[Y1 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y2 : a]: 52.90/7.31 ((((('#sk1' @ '#sk10' @ 52.90/7.31 Y2) | ('#sk2' @ 52.90/7.31 '#sk10' @ Y2))) => 52.90/7.31 (Y1 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((!!) @ (^[Y3 : a]: 52.90/7.31 (((((Y1 @ Y2) & 52.90/7.31 ((('#sk2' @ 52.90/7.31 Y2 @ 52.90/7.31 Y3) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y2 @ Y3))))) => 52.90/7.31 (Y1 @ Y3))))))))))) => 52.90/7.31 (Y1 @ Y0))))))))))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl31])). 52.90/7.31 thf(zip_derived_cl51, plain, 52.90/7.31 ((~ (((((((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk2' @ Y1 @ 52.90/7.31 Y2) | ('#sk1' @ 52.90/7.31 Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk15' @ Y1) | 52.90/7.31 ('#sk2' @ '#sk15' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))))) => 52.90/7.31 (Y0 @ '#sk23')))))) & 52.90/7.31 (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk10' @ Y1) | 52.90/7.31 ('#sk2' @ '#sk10' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk2' @ Y1 @ 52.90/7.31 Y2) | ('#sk1' @ 52.90/7.31 Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk15')))))))) => 52.90/7.31 (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk10' @ Y1) | 52.90/7.31 ('#sk2' @ '#sk10' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((Y0 @ Y1) & 52.90/7.31 ((('#sk2' @ Y1 @ Y2) | 52.90/7.31 ('#sk1' @ Y1 @ Y2))))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk23')))))))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl40])). 52.90/7.31 thf(zip_derived_cl57, plain, 52.90/7.31 (( (((((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk2' @ Y1 @ Y2) | 52.90/7.31 ('#sk1' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk15' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk15' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))))) => 52.90/7.31 (Y0 @ '#sk23')))))) & 52.90/7.31 (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk10' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk10' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk2' @ Y1 @ Y2) | 52.90/7.31 ('#sk1' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk15')))))))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 52.90/7.31 thf(zip_derived_cl65, plain, 52.90/7.31 (( (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk10' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk10' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk2' @ Y1 @ Y2) | 52.90/7.31 ('#sk1' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk15')))))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl57])). 52.90/7.31 thf(zip_derived_cl79, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( (((((((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ 52.90/7.31 Y0))) => 52.90/7.31 (X2 @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.90/7.31 Y0 @ Y1))) & 52.90/7.31 (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))))) => 52.90/7.31 (X2 @ '#sk15'))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl65])). 52.90/7.31 thf(zip_derived_cl80, plain, 52.90/7.31 (( (((((((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 52.90/7.31 ('#sk43' @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk43' @ Y0))) => 52.90/7.31 ('#sk43' @ Y1))))))))))) => 52.90/7.31 ('#sk43' @ '#sk15'))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('triggered_bool_instantiation', [status(thm)], 52.90/7.31 [zip_derived_cl79])). 52.90/7.31 thf(zip_derived_cl361, plain, 52.90/7.31 ((~ (((((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 52.90/7.31 ('#sk43' @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk43' @ Y0))) => 52.90/7.31 ('#sk43' @ Y1))))))))))) 52.90/7.31 | ('#sk43' @ '#sk15') 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])). 52.90/7.31 thf(zip_derived_cl362, plain, 52.90/7.31 ((~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 52.90/7.31 ('#sk43' @ Y0)))))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk43' @ Y0))) => 52.90/7.31 ('#sk43' @ Y1))))))))) 52.90/7.31 | ('#form9') 52.90/7.31 | ('#sk43' @ '#sk15'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl361])). 52.90/7.31 thf(zip_derived_cl363, plain, 52.90/7.31 ((~ ((((('#sk1' @ '#sk10' @ ('#sk141' @ '#sk43')) | ('#sk2' @ '#sk10' @ 52.90/7.31 ('#sk141' @ '#sk43')))) => 52.90/7.31 ('#sk43' @ ('#sk141' @ '#sk43')))) 52.90/7.31 | ('#sk43' @ '#sk15') 52.90/7.31 | ('#form9') 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk43' @ Y0))) => 52.90/7.31 ('#sk43' @ Y1))))))))))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl362])). 52.90/7.31 thf(zip_derived_cl364, plain, 52.90/7.31 (( ((('#sk1' @ '#sk10' @ ('#sk141' @ '#sk43')) | ('#sk2' @ '#sk10' @ 52.90/7.31 ('#sk141' @ '#sk43')))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk43' @ Y0))) => 52.90/7.31 ('#sk43' @ Y1))))))))) 52.90/7.31 | ('#form9') 52.90/7.31 | ('#sk43' @ '#sk15'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl363])). 52.90/7.31 thf(zip_derived_cl366, plain, 52.90/7.31 (( ('#form420') 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk43' @ Y0))) => 52.90/7.31 ('#sk43' @ Y1))))))))))), 52.90/7.31 define([status(thm)])). 52.90/7.31 thf(zip_derived_cl367, plain, 52.90/7.31 ((~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((((('#sk2' @ ('#sk137' @ '#sk43') @ Y0) | ('#sk1' @ 52.90/7.31 ('#sk137' @ '#sk43') @ Y0))) & 52.90/7.31 ('#sk43' @ ('#sk137' @ '#sk43')))) => 52.90/7.31 ('#sk43' @ Y0)))))) 52.90/7.31 | ('#form420'))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl366])). 52.90/7.31 thf(zip_derived_cl371, plain, 52.90/7.31 ((~ ((((((('#sk2' @ ('#sk137' @ '#sk43') @ ('#sk185' @ '#sk43')) | 52.90/7.31 ('#sk1' @ ('#sk137' @ '#sk43') @ ('#sk185' @ '#sk43')))) & 52.90/7.31 ('#sk43' @ ('#sk137' @ '#sk43')))) => 52.90/7.31 ('#sk43' @ ('#sk185' @ '#sk43')))) 52.90/7.31 | ('#form420'))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl367])). 52.90/7.31 thf(zip_derived_cl372, plain, 52.90/7.31 (( ((((('#sk2' @ ('#sk137' @ '#sk43') @ ('#sk185' @ '#sk43')) | 52.90/7.31 ('#sk1' @ ('#sk137' @ '#sk43') @ ('#sk185' @ '#sk43')))) & 52.90/7.31 ('#sk43' @ ('#sk137' @ '#sk43')))) 52.90/7.31 | ('#form420'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl371])). 52.90/7.31 thf(zip_derived_cl375, plain, 52.90/7.31 (( ('#sk43' @ ('#sk137' @ '#sk43')) | ('#form420'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl372])). 52.90/7.31 thf(zip_derived_cl374, plain, 52.90/7.31 (( ((('#sk2' @ ('#sk137' @ '#sk43') @ ('#sk185' @ '#sk43')) | ('#sk1' @ 52.90/7.31 ('#sk137' @ '#sk43') @ ('#sk185' @ '#sk43')))) 52.90/7.31 | ('#form420'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl372])). 52.90/7.31 thf(zip_derived_cl376, plain, 52.90/7.31 (( ('#sk2' @ ('#sk137' @ '#sk43') @ ('#sk185' @ '#sk43')) 52.90/7.31 | ('#sk1' @ ('#sk137' @ '#sk43') @ ('#sk185' @ '#sk43')) 52.90/7.31 | ('#form420'))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl374])). 52.90/7.31 thf(zip_derived_cl27, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( (((((((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))))) => 52.90/7.31 (X2 @ '#sk7'))) 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk1' @ Y1 @ Y2) | 52.90/7.31 ('#sk2' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y1) | 52.90/7.31 ('#sk2' @ '#sk3' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))))) => 52.90/7.31 (Y0 @ '#sk4')))))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))))) => 52.90/7.31 (Y3 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y3 @ 52.90/7.31 Y4) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2))))))))))))))))) 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((('#sk1' @ Y1 @ Y2) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk7')))))))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 52.90/7.31 thf(zip_derived_cl28, plain, 52.90/7.31 (( (((((((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 52.90/7.31 ('#sk8' @ Y1))))))))))) => 52.90/7.31 ('#sk8' @ '#sk7'))) 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk1' @ Y1 @ Y2) | 52.90/7.31 ('#sk2' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk3' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))))) => 52.90/7.31 (Y0 @ '#sk4')))))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))))) => 52.90/7.31 (Y3 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y3 @ 52.90/7.31 Y4) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2))))))))))))))))) 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((('#sk1' @ Y1 @ Y2) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk7')))))))), 52.90/7.31 inference('triggered_bool_instantiation', [status(thm)], 52.90/7.31 [zip_derived_cl27])). 52.90/7.31 thf(zip_derived_cl34, plain, 52.90/7.31 ((~ ('#form14') 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk1' @ Y1 @ Y2) | 52.90/7.31 ('#sk2' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk3' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))))) => 52.90/7.31 (Y0 @ '#sk4')))))))), 52.90/7.31 define([status(thm)])). 52.90/7.31 thf(zip_derived_cl203, plain, 52.90/7.31 (( ('#form14') 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((('#sk1' @ Y1 @ Y2) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk7')))))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))))) => 52.90/7.31 (Y3 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y3 @ 52.90/7.31 Y4) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2))))))))))))))))) 52.90/7.31 | (((((((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 52.90/7.31 ('#sk8' @ Y1))))))))))) => 52.90/7.31 ('#sk8' @ '#sk7'))))), 52.90/7.31 inference('renaming', [status(thm)], [zip_derived_cl28, zip_derived_cl34])). 52.90/7.31 thf(zip_derived_cl43, plain, 52.90/7.31 ((~ ('#form19') 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((('#sk1' @ Y1 @ Y2) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk7')))))))), 52.90/7.31 define([status(thm)])). 52.90/7.31 thf(zip_derived_cl204, plain, 52.90/7.31 (( ('#form19') 52.90/7.31 | (((((((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 52.90/7.31 ('#sk8' @ Y1))))))))))) => 52.90/7.31 ('#sk8' @ '#sk7'))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))))) => 52.90/7.31 (Y3 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y3 @ 52.90/7.31 Y4) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2))))))))))))))))) 52.90/7.31 | ('#form14'))), 52.90/7.31 inference('renaming', [status(thm)], 52.90/7.31 [zip_derived_cl203, zip_derived_cl43])). 52.90/7.31 thf(zip_derived_cl30, plain, 52.90/7.31 (( ('#form9') 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y1 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y1 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))))) => 52.90/7.31 (Y3 @ Y2)))))) & 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 (( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))) & 52.90/7.31 (Y3 @ Y4))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y1)))))))) => 52.90/7.31 (((!!) @ (^[Y3 : a > $o]: 52.90/7.31 (((((((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (( 52.90/7.31 ('#sk1' @ 52.90/7.31 Y0 @ 52.90/7.31 Y4) | 52.90/7.31 ('#sk2' @ 52.90/7.31 Y0 @ Y4))) => 52.90/7.31 (Y3 @ Y4)))))) & 52.90/7.31 (((!!) @ ( 52.90/7.31 ^[Y4 : a]: 52.90/7.31 ( 52.90/7.31 ( 52.90/7.31 (!!) @ ( 52.90/7.31 ^[Y5 : a]: 52.90/7.31 (( 52.90/7.31 (( 52.90/7.31 (Y3 @ 52.90/7.31 Y4) & 52.90/7.31 (( 52.90/7.31 ('#sk2' @ 52.90/7.31 Y4 @ 52.90/7.31 Y5) | 52.90/7.31 ('#sk1' @ 52.90/7.31 Y4 @ Y5))))) => 52.90/7.31 (Y3 @ Y5))))))))))) => 52.90/7.31 (Y3 @ Y2))))))))))))))))))), 52.90/7.31 define([status(thm)])). 52.90/7.31 thf(zip_derived_cl205, plain, 52.90/7.31 ((~ ('#form9') 52.90/7.31 | ('#form14') 52.90/7.31 | (((((((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 52.90/7.31 ('#sk8' @ Y1))))))))))) => 52.90/7.31 ('#sk8' @ '#sk7'))) 52.90/7.31 | ('#form19'))), 52.90/7.31 inference('renaming', [status(thm)], 52.90/7.31 [zip_derived_cl204, zip_derived_cl30])). 52.90/7.31 thf(zip_derived_cl206, plain, 52.90/7.31 ((~ (((((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 52.90/7.31 ('#sk8' @ Y1))))))))))) 52.90/7.31 | ('#sk8' @ '#sk7') 52.90/7.31 | ('#form19') 52.90/7.31 | ('#form14') 52.90/7.31 | ~ ('#form9'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl205])). 52.90/7.31 thf(zip_derived_cl50, plain, 52.90/7.31 ((~ ('#sk8' @ '#sk7') | ~ ('#form9') | ('#form14'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 52.90/7.31 thf(zip_derived_cl207, plain, 52.90/7.31 ((~ ('#form9') 52.90/7.31 | ('#form14') 52.90/7.31 | ('#form19') 52.90/7.31 | ~ (((((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 52.90/7.31 ('#sk8' @ Y1))))))))))))), 52.90/7.31 inference('clc', [status(thm)], [zip_derived_cl206, zip_derived_cl50])). 52.90/7.31 thf(zip_derived_cl208, plain, 52.90/7.31 ((~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 52.90/7.31 ('#sk8' @ Y1))))))))) 52.90/7.31 | ('#form19') 52.90/7.31 | ('#form14') 52.90/7.31 | ~ ('#form9'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl207])). 52.90/7.31 thf(zip_derived_cl209, plain, 52.90/7.31 ((~ ((('#sk2' @ '#sk6' @ ('#sk60' @ '#sk8')) => ('#sk8' @ 52.90/7.31 ('#sk60' @ '#sk8')))) 52.90/7.31 | ~ ('#form9') 52.90/7.31 | ('#form14') 52.90/7.31 | ('#form19') 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 52.90/7.31 ('#sk8' @ Y1))))))))))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl208])). 52.90/7.31 thf(zip_derived_cl211, plain, 52.90/7.31 ((~ ('#sk8' @ ('#sk60' @ '#sk8')) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 52.90/7.31 ('#sk8' @ Y1))))))))) 52.90/7.31 | ('#form19') 52.90/7.31 | ('#form14') 52.90/7.31 | ~ ('#form9'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl209])). 52.90/7.31 thf(zip_derived_cl213, plain, 52.90/7.31 ((~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk2' @ ('#sk108' @ '#sk8') @ Y0) & ('#sk8' @ 52.90/7.31 ('#sk108' @ '#sk8')))) => 52.90/7.31 ('#sk8' @ Y0)))))) 52.90/7.31 | ~ ('#form9') 52.90/7.31 | ('#form14') 52.90/7.31 | ('#form19') 52.90/7.31 | ~ ('#sk8' @ ('#sk60' @ '#sk8')))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl211])). 52.90/7.31 thf(zip_derived_cl215, plain, 52.90/7.31 ((~ ((((('#sk2' @ ('#sk108' @ '#sk8') @ ('#sk146' @ '#sk8')) & ('#sk8' @ 52.90/7.31 ('#sk108' @ '#sk8')))) => 52.90/7.31 ('#sk8' @ ('#sk146' @ '#sk8')))) 52.90/7.31 | ~ ('#sk8' @ ('#sk60' @ '#sk8')) 52.90/7.31 | ('#form19') 52.90/7.31 | ('#form14') 52.90/7.31 | ~ ('#form9'))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl213])). 52.90/7.31 thf(zip_derived_cl218, plain, 52.90/7.31 (( ((('#sk2' @ ('#sk108' @ '#sk8') @ ('#sk146' @ '#sk8')) & ('#sk8' @ 52.90/7.31 ('#sk108' @ '#sk8')))) 52.90/7.31 | ~ ('#form9') 52.90/7.31 | ('#form14') 52.90/7.31 | ('#form19') 52.90/7.31 | ~ ('#sk8' @ ('#sk60' @ '#sk8')))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl215])). 52.90/7.31 thf(zip_derived_cl222, plain, 52.90/7.31 (( ('#sk2' @ ('#sk108' @ '#sk8') @ ('#sk146' @ '#sk8')) 52.90/7.31 | ~ ('#sk8' @ ('#sk60' @ '#sk8')) 52.90/7.31 | ('#form19') 52.90/7.31 | ('#form14') 52.90/7.31 | ~ ('#form9'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl218])). 52.90/7.31 thf(zip_derived_cl210, plain, 52.90/7.31 (( ('#sk2' @ '#sk6' @ ('#sk60' @ '#sk8')) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 52.90/7.31 ('#sk8' @ Y1))))))))) 52.90/7.31 | ('#form19') 52.90/7.31 | ('#form14') 52.90/7.31 | ~ ('#form9'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl209])). 52.90/7.31 thf(zip_derived_cl212, plain, 52.90/7.31 ((~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk2' @ ('#sk108' @ '#sk8') @ Y0) & ('#sk8' @ 52.90/7.31 ('#sk108' @ '#sk8')))) => 52.90/7.31 ('#sk8' @ Y0)))))) 52.90/7.31 | ~ ('#form9') 52.90/7.31 | ('#form14') 52.90/7.31 | ('#form19') 52.90/7.31 | ('#sk2' @ '#sk6' @ ('#sk60' @ '#sk8')))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl210])). 52.90/7.31 thf(zip_derived_cl214, plain, 52.90/7.31 ((~ ((((('#sk2' @ ('#sk108' @ '#sk8') @ ('#sk146' @ '#sk8')) & ('#sk8' @ 52.90/7.31 ('#sk108' @ '#sk8')))) => 52.90/7.31 ('#sk8' @ ('#sk146' @ '#sk8')))) 52.90/7.31 | ('#sk2' @ '#sk6' @ ('#sk60' @ '#sk8')) 52.90/7.31 | ('#form19') 52.90/7.31 | ('#form14') 52.90/7.31 | ~ ('#form9'))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl212])). 52.90/7.31 thf(zip_derived_cl216, plain, 52.90/7.31 (( ((('#sk2' @ ('#sk108' @ '#sk8') @ ('#sk146' @ '#sk8')) & ('#sk8' @ 52.90/7.31 ('#sk108' @ '#sk8')))) 52.90/7.31 | ~ ('#form9') 52.90/7.31 | ('#form14') 52.90/7.31 | ('#form19') 52.90/7.31 | ('#sk2' @ '#sk6' @ ('#sk60' @ '#sk8')))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl214])). 52.90/7.31 thf(zip_derived_cl220, plain, 52.90/7.31 (( ('#sk2' @ ('#sk108' @ '#sk8') @ ('#sk146' @ '#sk8')) 52.90/7.31 | ('#sk2' @ '#sk6' @ ('#sk60' @ '#sk8')) 52.90/7.31 | ('#form19') 52.90/7.31 | ('#form14') 52.90/7.31 | ~ ('#form9'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl216])). 52.90/7.31 thf(zip_derived_cl373, plain, 52.90/7.31 ((~ ('#sk43' @ ('#sk185' @ '#sk43')) | ('#form420'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl371])). 52.90/7.31 thf(zip_derived_cl219, plain, 52.90/7.31 ((~ ('#sk8' @ ('#sk146' @ '#sk8')) 52.90/7.31 | ~ ('#form9') 52.90/7.31 | ('#form14') 52.90/7.31 | ('#form19') 52.90/7.31 | ~ ('#sk8' @ ('#sk60' @ '#sk8')))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl215])). 52.90/7.31 thf(zip_derived_cl217, plain, 52.90/7.31 ((~ ('#sk8' @ ('#sk146' @ '#sk8')) 52.90/7.31 | ~ ('#form9') 52.90/7.31 | ('#form14') 52.90/7.31 | ('#form19') 52.90/7.31 | ('#sk2' @ '#sk6' @ ('#sk60' @ '#sk8')))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl214])). 52.90/7.31 thf(zip_derived_cl223, plain, 52.90/7.31 (( ('#sk8' @ ('#sk108' @ '#sk8')) 52.90/7.31 | ~ ('#sk8' @ ('#sk60' @ '#sk8')) 52.90/7.31 | ('#form19') 52.90/7.31 | ('#form14') 52.90/7.31 | ~ ('#form9'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl218])). 52.90/7.31 thf(zip_derived_cl221, plain, 52.90/7.31 (( ('#sk8' @ ('#sk108' @ '#sk8')) 52.90/7.31 | ('#sk2' @ '#sk6' @ ('#sk60' @ '#sk8')) 52.90/7.31 | ('#form19') 52.90/7.31 | ('#form14') 52.90/7.31 | ~ ('#form9'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl216])). 52.90/7.31 thf(zip_derived_cl120, plain, 52.90/7.31 (![X2 : a, X4 : a]: 52.90/7.31 (~ ('#sk2' @ X2 @ X4) 52.90/7.31 | ('#sk8' @ X4) 52.90/7.31 | ~ ('#form9') 52.90/7.31 | ('#form14') 52.90/7.31 | ~ ('#sk8' @ X2))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl106])). 52.90/7.31 thf(zip_derived_cl34, plain, 52.90/7.31 ((~ ('#form14') 52.90/7.31 | (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk1' @ Y1 @ Y2) | 52.90/7.31 ('#sk2' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk3' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))))) => 52.90/7.31 (Y0 @ '#sk4')))))))), 52.90/7.31 define([status(thm)])). 52.90/7.31 thf(zip_derived_cl35, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( (((((((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 52.90/7.31 Y0 @ Y1))) & 52.90/7.31 (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 52.90/7.31 (X2 @ Y0)))))))) => 52.90/7.31 (X2 @ '#sk4'))) 52.90/7.31 | ~ ('#form14'))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 52.90/7.31 thf(zip_derived_cl48, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ (((((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 52.90/7.31 Y0 @ Y1))) & 52.90/7.31 (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 52.90/7.31 (X2 @ Y0)))))))) 52.90/7.31 | (X2 @ '#sk4') 52.90/7.31 | ~ ('#form14'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 52.90/7.31 thf(zip_derived_cl54, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 52.90/7.31 (X2 @ Y0)))))) 52.90/7.31 | ~ ('#form14') 52.90/7.31 | (X2 @ '#sk4'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl48])). 52.90/7.31 thf(zip_derived_cl61, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((((('#sk1' @ ('#sk42' @ X2) @ Y0) | ('#sk2' @ 52.90/7.31 ('#sk42' @ X2) @ Y0))) & 52.90/7.31 (X2 @ ('#sk42' @ X2)))) => 52.90/7.31 (X2 @ Y0)))))) 52.90/7.31 | (X2 @ '#sk4') 52.90/7.31 | ~ ('#form14') 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 52.90/7.31 (X2 @ Y0)))))))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl54])). 52.90/7.31 thf(zip_derived_cl72, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ ((((((('#sk1' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) | ('#sk2' @ 52.90/7.31 ('#sk42' @ X2) @ ('#sk56' @ X2)))) & 52.90/7.31 (X2 @ ('#sk42' @ X2)))) => 52.90/7.31 (X2 @ ('#sk56' @ X2)))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 52.90/7.31 (X2 @ Y0)))))) 52.90/7.31 | ~ ('#form14') 52.90/7.31 | (X2 @ '#sk4'))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl61])). 52.90/7.31 thf(zip_derived_cl89, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ (X2 @ ('#sk56' @ X2)) 52.90/7.31 | (X2 @ '#sk4') 52.90/7.31 | ~ ('#form14') 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 52.90/7.31 (X2 @ Y0)))))))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl72])). 52.90/7.31 thf(zip_derived_cl103, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( ('#form97' @ X2) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 52.90/7.31 (X2 @ Y0)))))))), 52.90/7.31 define([status(thm)])). 52.90/7.31 thf(zip_derived_cl104, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ ((((('#sk1' @ '#sk3' @ ('#sk98' @ X2)) | ('#sk2' @ '#sk3' @ 52.90/7.31 ('#sk98' @ X2)))) => 52.90/7.31 (X2 @ ('#sk98' @ X2)))) 52.90/7.31 | ('#form97' @ X2))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl103])). 52.90/7.31 thf(zip_derived_cl117, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( ((('#sk1' @ '#sk3' @ ('#sk98' @ X2)) | ('#sk2' @ '#sk3' @ 52.90/7.31 ('#sk98' @ X2)))) 52.90/7.31 | ('#form97' @ X2))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl104])). 52.90/7.31 thf(zip_derived_cl134, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( ('#sk1' @ '#sk3' @ ('#sk98' @ X2)) 52.90/7.31 | ('#sk2' @ '#sk3' @ ('#sk98' @ X2)) 52.90/7.31 | ('#form97' @ X2))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl117])). 52.90/7.31 thf(zip_derived_cl118, plain, 52.90/7.31 (![X2 : a > $o]: (~ (X2 @ ('#sk98' @ X2)) | ('#form97' @ X2))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl104])). 52.90/7.31 thf(zip_derived_cl35, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( (((((((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 52.90/7.31 Y0 @ Y1))) & 52.90/7.31 (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 52.90/7.31 (X2 @ Y0)))))))) => 52.90/7.31 (X2 @ '#sk4'))) 52.90/7.31 | ~ ('#form14'))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 52.90/7.31 thf(zip_derived_cl37, plain, 52.90/7.31 (( (((((((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk5' @ Y0))) => 52.90/7.31 ('#sk5' @ Y1))))))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 52.90/7.31 ('#sk5' @ Y0)))))))) => 52.90/7.31 ('#sk5' @ '#sk4'))) 52.90/7.31 | ~ ('#form14'))), 52.90/7.31 inference('triggered_bool_instantiation', [status(thm)], 52.90/7.31 [zip_derived_cl35])). 52.90/7.31 thf(zip_derived_cl6, plain, 52.90/7.31 (~ (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk3' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk2' @ Y1 @ Y2) | 52.90/7.31 ('#sk1' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk4'))))))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 52.90/7.31 thf(zip_derived_cl8, plain, 52.90/7.31 (~ (((((((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 52.90/7.31 ('#sk5' @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk5' @ Y0))) => 52.90/7.31 ('#sk5' @ Y1))))))))))) => 52.90/7.31 ('#sk5' @ '#sk4')))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 52.90/7.31 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk4')), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 52.90/7.31 thf(zip_derived_cl288, plain, 52.90/7.31 (( (((((((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk5' @ Y0))) => 52.90/7.31 ('#sk5' @ Y1))))))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 52.90/7.31 ('#sk5' @ Y0)))))))) => 52.90/7.31 ($false))) 52.90/7.31 | ~ ('#form14'))), 52.90/7.31 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl11])). 52.90/7.31 thf(zip_derived_cl289, plain, 52.90/7.31 (( (((~) @ (((((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk1' @ Y0 @ Y1) | 52.90/7.31 ('#sk2' @ Y0 @ Y1))) & 52.90/7.31 ('#sk5' @ Y0))) => 52.90/7.31 ('#sk5' @ Y1))))))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ 52.90/7.31 Y0))) => 52.90/7.31 ('#sk5' @ Y0)))))))))) 52.90/7.31 | ~ ('#form14'))), 52.90/7.31 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl288])). 52.90/7.31 thf(zip_derived_cl290, plain, 52.90/7.31 ((~ (((((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk5' @ Y0))) => 52.90/7.31 ('#sk5' @ Y1))))))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 52.90/7.31 ('#sk5' @ Y0)))))))) 52.90/7.31 | ~ ('#form14'))), 52.90/7.31 inference('simplify nested equalities', [status(thm)], 52.90/7.31 [zip_derived_cl289])). 52.90/7.31 thf(zip_derived_cl291, plain, 52.90/7.31 ((~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 52.90/7.31 ('#sk5' @ Y0))) => 52.90/7.31 ('#sk5' @ Y1))))))))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 52.90/7.31 ('#sk5' @ Y0)))))) 52.90/7.31 | ~ ('#form14'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl290])). 52.90/7.31 thf(zip_derived_cl103, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( ('#form97' @ X2) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 52.90/7.31 (X2 @ Y0)))))))), 52.90/7.31 define([status(thm)])). 52.90/7.31 thf(zip_derived_cl292, plain, 52.90/7.31 ((~ ('#form97' @ '#sk5') 52.90/7.31 | ~ ('#form14') 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk5' @ Y0))) => 52.90/7.31 ('#sk5' @ Y1))))))))))), 52.90/7.31 inference('renaming', [status(thm)], 52.90/7.31 [zip_derived_cl291, zip_derived_cl103])). 52.90/7.31 thf(zip_derived_cl293, plain, 52.90/7.31 ((~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((((('#sk1' @ ('#sk42' @ '#sk5') @ Y0) | ('#sk2' @ 52.90/7.31 ('#sk42' @ '#sk5') @ Y0))) & 52.90/7.31 ('#sk5' @ ('#sk42' @ '#sk5')))) => 52.90/7.31 ('#sk5' @ Y0)))))) 52.90/7.31 | ~ ('#form14') 52.90/7.31 | ~ ('#form97' @ '#sk5'))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl292])). 52.90/7.31 thf(zip_derived_cl294, plain, 52.90/7.31 ((~ ((((((('#sk1' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) | ('#sk2' @ 52.90/7.31 ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')))) & 52.90/7.31 ('#sk5' @ ('#sk42' @ '#sk5')))) => 52.90/7.31 ('#sk5' @ ('#sk56' @ '#sk5')))) 52.90/7.31 | ~ ('#form97' @ '#sk5') 52.90/7.31 | ~ ('#form14'))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl293])). 52.90/7.31 thf(zip_derived_cl296, plain, 52.90/7.31 ((~ ('#sk5' @ ('#sk56' @ '#sk5')) 52.90/7.31 | ~ ('#form14') 52.90/7.31 | ~ ('#form97' @ '#sk5'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl294])). 52.90/7.31 thf(zip_derived_cl295, plain, 52.90/7.31 (( ((((('#sk1' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) | ('#sk2' @ 52.90/7.31 ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')))) & 52.90/7.31 ('#sk5' @ ('#sk42' @ '#sk5')))) 52.90/7.31 | ~ ('#form14') 52.90/7.31 | ~ ('#form97' @ '#sk5'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl294])). 52.90/7.31 thf(zip_derived_cl298, plain, 52.90/7.31 (( ('#sk5' @ ('#sk42' @ '#sk5')) | ~ ('#form97' @ '#sk5') | ~ ('#form14'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl295])). 52.90/7.31 thf(zip_derived_cl297, plain, 52.90/7.31 (( ((('#sk1' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) | ('#sk2' @ 52.90/7.31 ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')))) 52.90/7.31 | ~ ('#form97' @ '#sk5') 52.90/7.31 | ~ ('#form14'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl295])). 52.90/7.31 thf(zip_derived_cl299, plain, 52.90/7.31 (( ('#sk1' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) 52.90/7.31 | ('#sk2' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) 52.90/7.31 | ~ ('#form14') 52.90/7.31 | ~ ('#form97' @ '#sk5'))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl297])). 52.90/7.31 thf(zip_derived_cl10, plain, 52.90/7.31 ( (((((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 52.90/7.31 ('#sk5' @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 52.90/7.31 ('#sk5' @ Y0))) => 52.90/7.31 ('#sk5' @ Y1)))))))))))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 52.90/7.31 thf(zip_derived_cl14, plain, 52.90/7.31 ( (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 52.90/7.31 ('#sk5' @ Y0))) => 52.90/7.31 ('#sk5' @ Y1)))))))))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 52.90/7.31 thf(zip_derived_cl17, plain, 52.90/7.31 (![X2 : a]: 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) & 52.90/7.31 ('#sk5' @ X2))) => 52.90/7.31 ('#sk5' @ Y0))))))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 52.90/7.31 thf(zip_derived_cl21, plain, 52.90/7.31 (![X2 : a, X4 : a]: 52.90/7.31 ((((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk5' @ X2))) => 52.90/7.31 ('#sk5' @ X4)))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 52.90/7.31 thf(zip_derived_cl26, plain, 52.90/7.31 (![X2 : a, X4 : a]: 52.90/7.31 (~ ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk5' @ X2))) 52.90/7.31 | ('#sk5' @ X4))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 52.90/7.31 thf(zip_derived_cl33, plain, 52.90/7.31 (![X2 : a, X4 : a]: 52.90/7.31 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 52.90/7.31 | ~ ('#sk5' @ X2) 52.90/7.31 | ('#sk5' @ X4))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 52.90/7.31 thf(zip_derived_cl41, plain, 52.90/7.31 (![X2 : a, X4 : a]: 52.90/7.31 (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl33])). 52.90/7.31 thf(zip_derived_cl91, plain, 52.90/7.31 (![X2 : a]: 52.90/7.31 (~ ('#sk2' @ '#sk6' @ X2) 52.90/7.31 | ~ ('#form9') 52.90/7.31 | ('#form14') 52.90/7.31 | ('#sk8' @ X2))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl73])). 52.90/7.31 thf(zip_derived_cl13, plain, 52.90/7.31 ( (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 52.90/7.31 ('#sk5' @ Y0))))))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 52.90/7.31 thf(zip_derived_cl16, plain, 52.90/7.31 (![X2 : a]: 52.90/7.31 ((((('#sk1' @ '#sk3' @ X2) | ('#sk2' @ '#sk3' @ X2))) => ('#sk5' @ 52.90/7.31 X2)))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 52.90/7.31 thf(zip_derived_cl20, plain, 52.90/7.31 (![X2 : a]: 52.90/7.31 (~ ((('#sk1' @ '#sk3' @ X2) | ('#sk2' @ '#sk3' @ X2))) 52.90/7.31 | ('#sk5' @ X2))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 52.90/7.31 thf(zip_derived_cl25, plain, 52.90/7.31 (![X2 : a]: (~ ('#sk2' @ '#sk3' @ X2) | ('#sk5' @ X2))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 52.90/7.31 thf(zip_derived_cl24, plain, 52.90/7.31 (![X2 : a]: (~ ('#sk1' @ '#sk3' @ X2) | ('#sk5' @ X2))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 52.90/7.31 thf(zip_derived_cl42, plain, 52.90/7.31 (![X2 : a, X4 : a]: 52.90/7.31 (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl33])). 52.90/7.31 thf(zip_derived_cl365, plain, 52.90/7.31 ((~ ('#sk43' @ ('#sk141' @ '#sk43')) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk43' @ Y0))) => 52.90/7.31 ('#sk43' @ Y1))))))))) 52.90/7.31 | ('#form9') 52.90/7.31 | ('#sk43' @ '#sk15'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl363])). 52.90/7.31 thf(zip_derived_cl366, plain, 52.90/7.31 (( ('#form420') 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk43' @ Y0))) => 52.90/7.31 ('#sk43' @ Y1))))))))))), 52.90/7.31 define([status(thm)])). 52.90/7.31 thf(zip_derived_cl369, plain, 52.90/7.31 ((~ ('#form420') 52.90/7.31 | ('#sk43' @ '#sk15') 52.90/7.31 | ('#form9') 52.90/7.31 | ~ ('#sk43' @ ('#sk141' @ '#sk43')))), 52.90/7.31 inference('renaming', [status(thm)], 52.90/7.31 [zip_derived_cl365, zip_derived_cl366])). 52.90/7.31 thf(zip_derived_cl364, plain, 52.90/7.31 (( ((('#sk1' @ '#sk10' @ ('#sk141' @ '#sk43')) | ('#sk2' @ '#sk10' @ 52.90/7.31 ('#sk141' @ '#sk43')))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk43' @ Y0))) => 52.90/7.31 ('#sk43' @ Y1))))))))) 52.90/7.31 | ('#form9') 52.90/7.31 | ('#sk43' @ '#sk15'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl363])). 52.90/7.31 thf(zip_derived_cl366, plain, 52.90/7.31 (( ('#form420') 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk43' @ Y0))) => 52.90/7.31 ('#sk43' @ Y1))))))))))), 52.90/7.31 define([status(thm)])). 52.90/7.31 thf(zip_derived_cl368, plain, 52.90/7.31 ((~ ('#form420') 52.90/7.31 | ('#sk43' @ '#sk15') 52.90/7.31 | ('#form9') 52.90/7.31 | ((('#sk1' @ '#sk10' @ ('#sk141' @ '#sk43')) | ('#sk2' @ '#sk10' @ 52.90/7.31 ('#sk141' @ '#sk43')))))), 52.90/7.31 inference('renaming', [status(thm)], 52.90/7.31 [zip_derived_cl364, zip_derived_cl366])). 52.90/7.31 thf(zip_derived_cl370, plain, 52.90/7.31 (( ('#sk1' @ '#sk10' @ ('#sk141' @ '#sk43')) 52.90/7.31 | ('#sk2' @ '#sk10' @ ('#sk141' @ '#sk43')) 52.90/7.31 | ('#form9') 52.90/7.31 | ('#sk43' @ '#sk15') 52.90/7.31 | ~ ('#form420'))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl368])). 52.90/7.31 thf(zip_derived_cl58, plain, 52.90/7.31 ((~ (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk10' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk10' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 (((((Y0 @ Y1) & 52.90/7.31 ((('#sk2' @ Y1 @ Y2) | 52.90/7.31 ('#sk1' @ Y1 @ Y2))))) => 52.90/7.31 (Y0 @ Y2))))))))))) => 52.90/7.31 (Y0 @ '#sk23')))))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 52.90/7.31 thf(zip_derived_cl69, plain, 52.90/7.31 ((~ (((((((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 52.90/7.31 ('#sk43' @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk43' @ Y0) & 52.90/7.31 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.90/7.31 Y0 @ Y1))))) => 52.90/7.31 ('#sk43' @ Y1))))))))))) => 52.90/7.31 ('#sk43' @ '#sk23'))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl58])). 52.90/7.31 thf(zip_derived_cl83, plain, 52.90/7.31 (( (((((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 52.90/7.31 ('#sk43' @ Y0)))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk43' @ Y0) & 52.90/7.31 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.90/7.31 Y1))))) => 52.90/7.31 ('#sk43' @ Y1))))))))))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl69])). 52.90/7.31 thf(zip_derived_cl95, plain, 52.90/7.31 (( (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 52.90/7.31 ('#sk43' @ Y0)))))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl83])). 52.90/7.31 thf(zip_derived_cl109, plain, 52.90/7.31 (![X2 : a]: 52.90/7.31 ( ((((('#sk1' @ '#sk10' @ X2) | ('#sk2' @ '#sk10' @ X2))) => 52.90/7.31 ('#sk43' @ X2))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl95])). 52.90/7.31 thf(zip_derived_cl123, plain, 52.90/7.31 (![X2 : a]: 52.90/7.31 (~ ((('#sk1' @ '#sk10' @ X2) | ('#sk2' @ '#sk10' @ X2))) 52.90/7.31 | ('#sk43' @ X2) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl109])). 52.90/7.31 thf(zip_derived_cl139, plain, 52.90/7.31 (![X2 : a]: (~ ('#sk2' @ '#sk10' @ X2) | ('#form9') | ('#sk43' @ X2))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl123])). 52.90/7.31 thf(zip_derived_cl138, plain, 52.90/7.31 (![X2 : a]: (~ ('#sk1' @ '#sk10' @ X2) | ('#form9') | ('#sk43' @ X2))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl123])). 52.90/7.31 thf(zip_derived_cl64, plain, 52.90/7.31 (( (((!!) @ (^[Y0 : a > $o]: 52.90/7.31 (((((((!!) @ (^[Y1 : a]: 52.90/7.31 (((!!) @ (^[Y2 : a]: 52.90/7.31 ((((((('#sk2' @ Y1 @ Y2) | 52.90/7.31 ('#sk1' @ Y1 @ Y2))) & 52.90/7.31 (Y0 @ Y1))) => 52.90/7.31 (Y0 @ Y2))))))))) & 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk1' @ '#sk15' @ Y1) | ('#sk2' @ 52.90/7.31 '#sk15' @ Y1))) => 52.90/7.31 (Y0 @ Y1)))))))) => 52.90/7.31 (Y0 @ '#sk23')))))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl57])). 52.90/7.31 thf(zip_derived_cl75, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( (((((((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.90/7.31 Y0 @ Y1))) & 52.90/7.31 (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ 52.90/7.31 Y0))) => 52.90/7.31 (X2 @ Y0)))))))) => 52.90/7.31 (X2 @ '#sk23'))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl64])). 52.90/7.31 thf(zip_derived_cl93, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ (((((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.90/7.31 Y0 @ Y1))) & 52.90/7.31 (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ Y0))) => 52.90/7.31 (X2 @ Y0)))))))) 52.90/7.31 | (X2 @ '#sk23') 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 52.90/7.31 thf(zip_derived_cl107, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ Y0))) => 52.90/7.31 (X2 @ Y0)))))) 52.90/7.31 | ('#form9') 52.90/7.31 | (X2 @ '#sk23'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl93])). 52.90/7.31 thf(zip_derived_cl121, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((((('#sk2' @ ('#sk137' @ X2) @ Y0) | ('#sk1' @ 52.90/7.31 ('#sk137' @ X2) @ Y0))) & 52.90/7.31 (X2 @ ('#sk137' @ X2)))) => 52.90/7.31 (X2 @ Y0)))))) 52.90/7.31 | (X2 @ '#sk23') 52.90/7.31 | ('#form9') 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ Y0))) => 52.90/7.31 (X2 @ Y0)))))))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl107])). 52.90/7.31 thf(zip_derived_cl135, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ ((((((('#sk2' @ ('#sk137' @ X2) @ ('#sk185' @ X2)) | ('#sk1' @ 52.90/7.31 ('#sk137' @ X2) @ ('#sk185' @ X2)))) & 52.90/7.31 (X2 @ ('#sk137' @ X2)))) => 52.90/7.31 (X2 @ ('#sk185' @ X2)))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ Y0))) => 52.90/7.31 (X2 @ Y0)))))) 52.90/7.31 | ('#form9') 52.90/7.31 | (X2 @ '#sk23'))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl121])). 52.90/7.31 thf(zip_derived_cl150, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ (X2 @ ('#sk185' @ X2)) 52.90/7.31 | (X2 @ '#sk23') 52.90/7.31 | ('#form9') 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ Y0))) => 52.90/7.31 (X2 @ Y0)))))))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl135])). 52.90/7.31 thf(zip_derived_cl160, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( ('#form265' @ X2) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ Y0))) => 52.90/7.31 (X2 @ Y0)))))))), 52.90/7.31 define([status(thm)])). 52.90/7.31 thf(zip_derived_cl161, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 (~ ((((('#sk1' @ '#sk15' @ ('#sk266' @ X2)) | ('#sk2' @ '#sk15' @ 52.90/7.31 ('#sk266' @ X2)))) => 52.90/7.31 (X2 @ ('#sk266' @ X2)))) 52.90/7.31 | ('#form265' @ X2))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl160])). 52.90/7.31 thf(zip_derived_cl169, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( ((('#sk1' @ '#sk15' @ ('#sk266' @ X2)) | ('#sk2' @ '#sk15' @ 52.90/7.31 ('#sk266' @ X2)))) 52.90/7.31 | ('#form265' @ X2))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl161])). 52.90/7.31 thf(zip_derived_cl177, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( ('#sk1' @ '#sk15' @ ('#sk266' @ X2)) 52.90/7.31 | ('#sk2' @ '#sk15' @ ('#sk266' @ X2)) 52.90/7.31 | ('#form265' @ X2))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl169])). 52.90/7.31 thf(zip_derived_cl170, plain, 52.90/7.31 (![X2 : a > $o]: (~ (X2 @ ('#sk266' @ X2)) | ('#form265' @ X2))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl161])). 52.90/7.31 thf(zip_derived_cl75, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( (((((((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.90/7.31 Y0 @ Y1))) & 52.90/7.31 (X2 @ Y0))) => 52.90/7.31 (X2 @ Y1))))))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ 52.90/7.31 Y0))) => 52.90/7.31 (X2 @ Y0)))))))) => 52.90/7.31 (X2 @ '#sk23'))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl64])). 52.90/7.31 thf(zip_derived_cl76, plain, 52.90/7.31 (( (((((((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk43' @ Y0))) => 52.90/7.31 ('#sk43' @ Y1))))))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ Y0))) => 52.90/7.31 ('#sk43' @ Y0)))))))) => 52.90/7.31 ('#sk43' @ '#sk23'))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('triggered_bool_instantiation', [status(thm)], 52.90/7.31 [zip_derived_cl75])). 52.90/7.31 thf(zip_derived_cl330, plain, 52.90/7.31 ((~ (((((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk43' @ Y0))) => 52.90/7.31 ('#sk43' @ Y1))))))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ Y0))) => 52.90/7.31 ('#sk43' @ Y0)))))))) 52.90/7.31 | ('#sk43' @ '#sk23') 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl76])). 52.90/7.31 thf(zip_derived_cl84, plain, ((~ ('#sk43' @ '#sk23') | ('#form9'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl69])). 52.90/7.31 thf(zip_derived_cl331, plain, 52.90/7.31 (( ('#form9') 52.90/7.31 | ~ (((((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.90/7.31 Y0 @ Y1))) & 52.90/7.31 ('#sk43' @ Y0))) => 52.90/7.31 ('#sk43' @ Y1))))))))) & 52.90/7.31 (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ Y0))) => 52.90/7.31 ('#sk43' @ Y0)))))))))), 52.90/7.31 inference('clc', [status(thm)], [zip_derived_cl330, zip_derived_cl84])). 52.90/7.31 thf(zip_derived_cl332, plain, 52.90/7.31 ((~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 52.90/7.31 ('#sk43' @ Y0))) => 52.90/7.31 ('#sk43' @ Y1))))))))) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ Y0))) => 52.90/7.31 ('#sk43' @ Y0)))))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl331])). 52.90/7.31 thf(zip_derived_cl160, plain, 52.90/7.31 (![X2 : a > $o]: 52.90/7.31 ( ('#form265' @ X2) 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk1' @ '#sk15' @ Y0) | ('#sk2' @ '#sk15' @ Y0))) => 52.90/7.31 (X2 @ Y0)))))))), 52.90/7.31 define([status(thm)])). 52.90/7.31 thf(zip_derived_cl333, plain, 52.90/7.31 ((~ ('#form265' @ '#sk43') 52.90/7.31 | ('#form9') 52.90/7.31 | ~ (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.90/7.31 Y1))) & 52.90/7.31 ('#sk43' @ Y0))) => 52.90/7.31 ('#sk43' @ Y1))))))))))), 52.90/7.31 inference('renaming', [status(thm)], 52.90/7.31 [zip_derived_cl332, zip_derived_cl160])). 52.90/7.31 thf(zip_derived_cl334, plain, 52.90/7.31 ((~ (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((((('#sk2' @ ('#sk137' @ '#sk43') @ Y0) | ('#sk1' @ 52.90/7.31 ('#sk137' @ '#sk43') @ Y0))) & 52.90/7.31 ('#sk43' @ ('#sk137' @ '#sk43')))) => 52.90/7.31 ('#sk43' @ Y0)))))) 52.90/7.31 | ('#form9') 52.90/7.31 | ~ ('#form265' @ '#sk43'))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl333])). 52.90/7.31 thf(zip_derived_cl335, plain, 52.90/7.31 ((~ ((((((('#sk2' @ ('#sk137' @ '#sk43') @ ('#sk185' @ '#sk43')) | 52.90/7.31 ('#sk1' @ ('#sk137' @ '#sk43') @ ('#sk185' @ '#sk43')))) & 52.90/7.31 ('#sk43' @ ('#sk137' @ '#sk43')))) => 52.90/7.31 ('#sk43' @ ('#sk185' @ '#sk43')))) 52.90/7.31 | ~ ('#form265' @ '#sk43') 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl334])). 52.90/7.31 thf(zip_derived_cl337, plain, 52.90/7.31 ((~ ('#sk43' @ ('#sk185' @ '#sk43')) 52.90/7.31 | ('#form9') 52.90/7.31 | ~ ('#form265' @ '#sk43'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl335])). 52.90/7.31 thf(zip_derived_cl336, plain, 52.90/7.31 (( ((((('#sk2' @ ('#sk137' @ '#sk43') @ ('#sk185' @ '#sk43')) | 52.90/7.31 ('#sk1' @ ('#sk137' @ '#sk43') @ ('#sk185' @ '#sk43')))) & 52.90/7.31 ('#sk43' @ ('#sk137' @ '#sk43')))) 52.90/7.31 | ('#form9') 52.90/7.31 | ~ ('#form265' @ '#sk43'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl335])). 52.90/7.31 thf(zip_derived_cl339, plain, 52.90/7.31 (( ('#sk43' @ ('#sk137' @ '#sk43')) 52.90/7.31 | ~ ('#form265' @ '#sk43') 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl336])). 52.90/7.31 thf(zip_derived_cl338, plain, 52.90/7.31 (( ((('#sk2' @ ('#sk137' @ '#sk43') @ ('#sk185' @ '#sk43')) | ('#sk1' @ 52.90/7.31 ('#sk137' @ '#sk43') @ ('#sk185' @ '#sk43')))) 52.90/7.31 | ~ ('#form265' @ '#sk43') 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl336])). 52.90/7.31 thf(zip_derived_cl340, plain, 52.90/7.31 (( ('#sk2' @ ('#sk137' @ '#sk43') @ ('#sk185' @ '#sk43')) 52.90/7.31 | ('#sk1' @ ('#sk137' @ '#sk43') @ ('#sk185' @ '#sk43')) 52.90/7.31 | ('#form9') 52.90/7.31 | ~ ('#form265' @ '#sk43'))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl338])). 52.90/7.31 thf(zip_derived_cl96, plain, 52.90/7.31 (( (((!!) @ (^[Y0 : a]: 52.90/7.31 (((!!) @ (^[Y1 : a]: 52.90/7.31 ((((('#sk43' @ Y0) & 52.90/7.31 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))))) => 52.90/7.31 ('#sk43' @ Y1))))))))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl83])). 52.90/7.31 thf(zip_derived_cl110, plain, 52.90/7.31 (![X2 : a]: 52.90/7.31 ( (((!!) @ (^[Y0 : a]: 52.90/7.31 ((((('#sk43' @ X2) & 52.90/7.31 ((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))))) => 52.90/7.31 ('#sk43' @ Y0)))))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl96])). 52.90/7.31 thf(zip_derived_cl124, plain, 52.90/7.31 (![X2 : a, X4 : a]: 52.90/7.31 ( ((((('#sk43' @ X2) & ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))))) => 52.90/7.31 ('#sk43' @ X4))) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl110])). 52.90/7.31 thf(zip_derived_cl140, plain, 52.90/7.31 (![X2 : a, X4 : a]: 52.90/7.31 (~ ((('#sk43' @ X2) & ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))))) 52.90/7.31 | ('#sk43' @ X4) 52.90/7.31 | ('#form9'))), 52.90/7.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl124])). 52.90/7.31 thf(zip_derived_cl153, plain, 52.90/7.31 (![X2 : a, X4 : a]: 52.90/7.31 (~ ('#sk43' @ X2) 52.90/7.31 | ~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 52.90/7.31 | ('#form9') 52.90/7.31 | ('#sk43' @ X4))), 52.90/7.31 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl140])). 52.90/7.31 thf(zip_derived_cl165, plain, 52.90/7.31 (![X2 : a, X4 : a]: 52.90/7.31 (~ ('#sk2' @ X2 @ X4) 52.90/7.31 | ('#sk43' @ X4) 52.90/7.31 | ('#form9') 52.90/7.31 | ~ ('#sk43' @ X2))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl153])). 52.90/7.31 thf(zip_derived_cl166, plain, 52.90/7.31 (![X2 : a, X4 : a]: 52.90/7.31 (~ ('#sk1' @ X2 @ X4) 52.90/7.31 | ('#sk43' @ X4) 52.90/7.31 | ('#form9') 52.90/7.31 | ~ ('#sk43' @ X2))), 52.90/7.31 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl153])). 52.90/7.31 thf(zip_derived_cl13777, plain, ($false), 52.90/7.31 inference('eprover', [status(thm)], 52.90/7.31 [zip_derived_cl148, zip_derived_cl130, zip_derived_cl50, 52.90/7.31 zip_derived_cl147, zip_derived_cl146, zip_derived_cl128, 52.90/7.31 zip_derived_cl90, zip_derived_cl145, zip_derived_cl119, 52.90/7.31 zip_derived_cl375, zip_derived_cl376, zip_derived_cl222, 52.90/7.31 zip_derived_cl220, zip_derived_cl373, zip_derived_cl219, 52.90/7.31 zip_derived_cl217, zip_derived_cl223, zip_derived_cl221, 52.90/7.31 zip_derived_cl120, zip_derived_cl134, zip_derived_cl118, 52.90/7.31 zip_derived_cl296, zip_derived_cl298, zip_derived_cl299, 52.90/7.31 zip_derived_cl41, zip_derived_cl91, zip_derived_cl25, 52.90/7.31 zip_derived_cl24, zip_derived_cl42, zip_derived_cl369, 52.90/7.31 zip_derived_cl370, zip_derived_cl139, zip_derived_cl138, 52.90/7.31 zip_derived_cl177, zip_derived_cl170, zip_derived_cl337, 52.90/7.31 zip_derived_cl339, zip_derived_cl340, zip_derived_cl165, 52.90/7.31 zip_derived_cl166])). 52.90/7.31 52.90/7.31 % SZS output end Refutation 52.90/7.31 52.90/7.31 52.90/7.31 % Terminating... 53.51/7.40 % Runner terminated. 53.51/7.41 % Zipperpin 1.5 exiting 53.51/7.42 EOF