0.04/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.fAxACf1BG7 true 0.14/0.35 % Computer : n011.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 1440 0.14/0.35 % WCLimit : 180 0.14/0.35 % DateTime : Mon Jul 3 04:35:09 EDT 2023 0.14/0.35 % CPUTime : 0.14/0.35 % Running portfolio for 1440 s 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.35 % Number of cores: 8 0.14/0.35 % Python version: Python 3.6.8 0.14/0.36 % Running in HO mode 0.56/0.65 % Total configuration time : 828 0.56/0.65 % Estimated wc time : 1656 0.56/0.65 % Estimated cpu time (8 cpus) : 207.0 0.58/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.58/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.58/0.77 % /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/40_b.comb.sh running for 70s 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/30_sp5.sh running for 60s 234.44/30.60 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 316.34/41.07 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 343.88/44.57 % Solved by lams/30_b.l.sh. 343.88/44.57 % done 464 iterations in 13.840s 343.88/44.57 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 343.88/44.57 % SZS output start Refutation 343.88/44.57 thf(a_type, type, a: $tType). 343.88/44.57 thf('#form213_type', type, '#form213': (a > $o) > $o). 343.88/44.57 thf('#sk6_type', type, '#sk6': a). 343.88/44.57 thf('#sk249_type', type, '#sk249': (a > $o) > a). 343.88/44.57 thf('#sk279_type', type, '#sk279': (a > $o) > a). 343.88/44.57 thf('#sk19_type', type, '#sk19': a). 343.88/44.57 thf('#sk120_type', type, '#sk120': (a > $o) > a). 343.88/44.57 thf('#sk5_type', type, '#sk5': a > $o). 343.88/44.57 thf('#sk14_type', type, '#sk14': a). 343.88/44.57 thf('#sk4_type', type, '#sk4': a). 343.88/44.57 thf('#sk116_type', type, '#sk116': (a > $o) > a). 343.88/44.57 thf('#sk150_type', type, '#sk150': (a > $o) > a). 343.88/44.57 thf('#sk36_type', type, '#sk36': a > $o). 343.88/44.57 thf('#form9_type', type, '#form9': $o). 343.88/44.57 thf('#form169_type', type, '#form169': (a > $o) > $o). 343.88/44.57 thf('#sk18_type', type, '#sk18': a > $o). 343.88/44.57 thf('#form133_type', type, '#form133': (a > $o) > $o). 343.88/44.57 thf('#sk23_type', type, '#sk23': (a > $o) > a). 343.88/44.57 thf('#sk47_type', type, '#sk47': (a > $o) > a). 343.88/44.57 thf('#form8_type', type, '#form8': $o). 343.88/44.57 thf('#form248_type', type, '#form248': (a > $o) > $o). 343.88/44.57 thf('#form54_type', type, '#form54': (a > $o) > $o). 343.88/44.57 thf('#sk202_type', type, '#sk202': (a > $o) > a). 343.88/44.57 thf('#sk55_type', type, '#sk55': (a > $o) > a). 343.88/44.57 thf('#sk193_type', type, '#sk193': (a > $o) > a). 343.88/44.57 thf('#sk3_type', type, '#sk3': a). 343.88/44.57 thf('#sk7_type', type, '#sk7': a). 343.88/44.57 thf('#sk1_type', type, '#sk1': a > a > $o). 343.88/44.57 thf('#sk170_type', type, '#sk170': (a > $o) > a). 343.88/44.57 thf('#sk2_type', type, '#sk2': a > a > $o). 343.88/44.57 thf('#form110_type', type, '#form110': $o). 343.88/44.57 thf('#sk214_type', type, '#sk214': (a > $o) > a). 343.88/44.57 thf('#sk10_type', type, '#sk10': a). 343.88/44.57 thf('#sk32_type', type, '#sk32': (a > $o) > a). 343.88/44.57 thf('#sk62_type', type, '#sk62': (a > $o) > a). 343.88/44.57 thf('#sk134_type', type, '#sk134': (a > $o) > a). 343.88/44.57 thf(cTHM251G_pme, conjecture, 343.88/44.57 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 343.88/44.57 ( ( ~( ( ( ![Xx0:a,Xy0:a]: 343.88/44.57 ( ( ( ![Xq:( a > $o )]: 343.88/44.57 ( ( ( ![Xu:a,Xv:a]: 343.88/44.57 ( ( ( S @ Xu @ Xv ) & ( Xq @ Xu ) ) => ( Xq @ Xv ) ) ) & 343.88/44.57 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 343.88/44.57 ( Xq @ Xy0 ) ) ) | 343.88/44.57 ( ![Xq:( a > $o )]: 343.88/44.57 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 343.88/44.57 ( ![Xu:a,Xv:a]: 343.88/44.57 ( ( ( R @ Xu @ Xv ) & ( Xq @ Xu ) ) => ( Xq @ Xv ) ) ) ) => 343.88/44.57 ( Xq @ Xy0 ) ) ) ) => 343.88/44.57 ( ![Xq:( a > $o )]: 343.88/44.57 ( ( ( ![Xu:a,Xv:a]: 343.88/44.57 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & 343.88/44.57 ( Xq @ Xu ) ) => 343.88/44.57 ( Xq @ Xv ) ) ) & 343.88/44.57 ( ![Xw:a]: 343.88/44.57 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 343.88/44.57 ( Xq @ Xw ) ) ) ) => 343.88/44.57 ( Xq @ Xy0 ) ) ) ) ) & 343.88/44.57 ( ![Xx0:a,Xy0:a,Xz:a]: 343.88/44.57 ( ( ( ![Xq:( a > $o )]: 343.88/44.57 ( ( ( ![Xw:a]: 343.88/44.57 ( ( ( S @ Xy0 @ Xw ) | ( R @ Xy0 @ Xw ) ) => 343.88/44.57 ( Xq @ Xw ) ) ) & 343.88/44.57 ( ![Xu:a,Xv:a]: 343.88/44.57 ( ( ( Xq @ Xu ) & 343.88/44.57 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 343.88/44.57 ( Xq @ Xv ) ) ) ) => 343.88/44.57 ( Xq @ Xz ) ) ) & 343.88/44.57 ( ![Xq:( a > $o )]: 343.88/44.57 ( ( ( ![Xu:a,Xv:a]: 343.88/44.57 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & 343.88/44.57 ( Xq @ Xu ) ) => 343.88/44.57 ( Xq @ Xv ) ) ) & 343.88/44.57 ( ![Xw:a]: 343.88/44.57 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 343.88/44.57 ( Xq @ Xw ) ) ) ) => 343.88/44.57 ( Xq @ Xy0 ) ) ) ) => 343.88/44.57 ( ![Xq:( a > $o )]: 343.88/44.57 ( ( ( ![Xw:a]: 343.88/44.57 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 343.88/44.57 ( Xq @ Xw ) ) ) & 343.88/44.57 ( ![Xu:a,Xv:a]: 343.88/44.57 ( ( ( Xq @ Xu ) & 343.88/44.57 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 343.88/44.57 ( Xq @ Xv ) ) ) ) => 343.88/44.57 ( Xq @ Xz ) ) ) ) ) ) => 343.88/44.57 ( ![Xq:( a > $o )]: 343.88/44.57 ( ( ( ![Xu:a,Xv:a]: 343.88/44.57 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 343.88/44.57 ( Xq @ Xv ) ) ) & 343.88/44.57 ( ![Xw:a]: 343.88/44.57 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 343.88/44.57 ( Xq @ Xy ) ) ) ) ) | 343.88/44.57 ( ![Xq:( a > $o )]: 343.88/44.57 ( ( ( ![Xw:a]: 343.88/44.57 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 343.88/44.57 ( ![Xu:a,Xv:a]: 343.88/44.57 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 343.88/44.57 ( Xq @ Xv ) ) ) ) => 343.88/44.57 ( Xq @ Xy ) ) ) ))). 343.88/44.57 thf(zf_stmt_0, negated_conjecture, 343.88/44.57 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 343.88/44.57 ( ( ~( ( ( ![Xx0:a,Xy0:a]: 343.88/44.57 ( ( ( ![Xq:( a > $o )]: 343.88/44.57 ( ( ( ![Xu:a,Xv:a]: 343.88/44.57 ( ( ( S @ Xu @ Xv ) & ( Xq @ Xu ) ) => 343.88/44.57 ( Xq @ Xv ) ) ) & 343.88/44.57 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 343.88/44.57 ( Xq @ Xy0 ) ) ) | 343.88/44.57 ( ![Xq:( a > $o )]: 343.88/44.57 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 343.88/44.57 ( ![Xu:a,Xv:a]: 343.88/44.57 ( ( ( R @ Xu @ Xv ) & ( Xq @ Xu ) ) => 343.88/44.57 ( Xq @ Xv ) ) ) ) => 343.88/44.57 ( Xq @ Xy0 ) ) ) ) => 343.88/44.57 ( ![Xq:( a > $o )]: 343.88/44.57 ( ( ( ![Xu:a,Xv:a]: 343.88/44.57 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & 343.88/44.57 ( Xq @ Xu ) ) => 343.88/44.57 ( Xq @ Xv ) ) ) & 343.88/44.57 ( ![Xw:a]: 343.88/44.57 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 343.88/44.57 ( Xq @ Xw ) ) ) ) => 343.88/44.57 ( Xq @ Xy0 ) ) ) ) ) & 343.88/44.57 ( ![Xx0:a,Xy0:a,Xz:a]: 343.88/44.57 ( ( ( ![Xq:( a > $o )]: 343.88/44.57 ( ( ( ![Xw:a]: 343.88/44.57 ( ( ( S @ Xy0 @ Xw ) | ( R @ Xy0 @ Xw ) ) => 343.88/44.57 ( Xq @ Xw ) ) ) & 343.88/44.57 ( ![Xu:a,Xv:a]: 343.88/44.57 ( ( ( Xq @ Xu ) & 343.88/44.57 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 343.88/44.57 ( Xq @ Xv ) ) ) ) => 343.88/44.57 ( Xq @ Xz ) ) ) & 343.88/44.57 ( ![Xq:( a > $o )]: 343.88/44.57 ( ( ( ![Xu:a,Xv:a]: 343.88/44.57 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & 343.88/44.57 ( Xq @ Xu ) ) => 343.88/44.57 ( Xq @ Xv ) ) ) & 343.88/44.57 ( ![Xw:a]: 343.88/44.57 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 343.88/44.57 ( Xq @ Xw ) ) ) ) => 343.88/44.57 ( Xq @ Xy0 ) ) ) ) => 343.88/44.57 ( ![Xq:( a > $o )]: 343.88/44.57 ( ( ( ![Xw:a]: 343.88/44.57 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 343.88/44.57 ( Xq @ Xw ) ) ) & 343.88/44.57 ( ![Xu:a,Xv:a]: 343.88/44.57 ( ( ( Xq @ Xu ) & 343.88/44.57 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 343.88/44.57 ( Xq @ Xv ) ) ) ) => 343.88/44.57 ( Xq @ Xz ) ) ) ) ) ) => 343.88/44.57 ( ![Xq:( a > $o )]: 343.88/44.57 ( ( ( ![Xu:a,Xv:a]: 343.88/44.57 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 343.88/44.57 ( Xq @ Xv ) ) ) & 343.88/44.57 ( ![Xw:a]: 343.88/44.57 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 343.88/44.57 ( Xq @ Xy ) ) ) ) ) | 343.88/44.57 ( ![Xq:( a > $o )]: 343.88/44.57 ( ( ( ![Xw:a]: 343.88/44.57 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 343.88/44.57 ( ![Xu:a,Xv:a]: 343.88/44.57 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 343.88/44.57 ( Xq @ Xv ) ) ) ) => 343.88/44.57 ( Xq @ Xy ) ) ) ) )), 343.88/44.57 inference('cnf.neg', [status(esa)], [cTHM251G_pme])). 343.88/44.57 thf(zip_derived_cl0, plain, 343.88/44.57 (~ (((!!) @ (^[Y0 : a > a > $o]: 343.88/44.57 (((!!) @ (^[Y1 : a > a > $o]: 343.88/44.57 (((!!) @ (^[Y2 : a]: 343.88/44.57 (((!!) @ (^[Y3 : a]: 343.88/44.57 (((((~) @ (((( 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y4 : a]: 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y5 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y6 : a > $o]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y7 : a]: 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y8 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (Y1 @ 343.88/44.57 Y7 @ 343.88/44.57 Y8) & 343.88/44.57 (Y6 @ Y7))) => 343.88/44.57 (Y6 @ Y8))))))))) & 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y7 : a]: 343.88/44.57 (( 343.88/44.57 (Y1 @ 343.88/44.57 Y4 @ 343.88/44.57 Y7) => 343.88/44.57 (Y6 @ Y7)))))))) => 343.88/44.57 (Y6 @ Y5)))))) | 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y6 : a > $o]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y7 : a]: 343.88/44.57 (( 343.88/44.57 (Y0 @ 343.88/44.57 Y4 @ 343.88/44.57 Y7) => 343.88/44.57 (Y6 @ Y7)))))) & 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y7 : a]: 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y8 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (Y0 @ 343.88/44.57 Y7 @ 343.88/44.57 Y8) & 343.88/44.57 (Y6 @ Y7))) => 343.88/44.57 (Y6 @ Y8))))))))))) => 343.88/44.57 (Y6 @ Y5)))))))) => 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y6 : a > $o]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y7 : a]: 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y8 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (Y0 @ 343.88/44.57 Y7 @ 343.88/44.57 Y8) | 343.88/44.57 (Y1 @ 343.88/44.57 Y7 @ Y8))) & 343.88/44.57 (Y6 @ Y7))) => 343.88/44.57 (Y6 @ Y8))))))))) & 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y7 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (Y0 @ 343.88/44.57 Y4 @ 343.88/44.57 Y7) | 343.88/44.57 (Y1 @ 343.88/44.57 Y4 @ Y7))) => 343.88/44.57 (Y6 @ Y7)))))))) => 343.88/44.57 (Y6 @ Y5)))))))))))))) & 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y4 : a]: 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y5 : a]: 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y6 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y7 : a > $o]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y8 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (Y1 @ 343.88/44.57 Y5 @ 343.88/44.57 Y8) | 343.88/44.57 (Y0 @ 343.88/44.57 Y5 @ Y8))) => 343.88/44.57 (Y7 @ Y8)))))) & 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y8 : a]: 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y9 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (Y7 @ 343.88/44.57 Y8) & 343.88/44.57 (( 343.88/44.57 (Y0 @ 343.88/44.57 Y8 @ 343.88/44.57 Y9) | 343.88/44.57 (Y1 @ 343.88/44.57 Y8 @ Y9))))) => 343.88/44.57 (Y7 @ Y9))))))))))) => 343.88/44.57 (Y7 @ Y6)))))) & 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y7 : a > $o]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y8 : a]: 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y9 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (Y1 @ 343.88/44.57 Y8 @ 343.88/44.57 Y9) | 343.88/44.57 (Y0 @ 343.88/44.57 Y8 @ Y9))) & 343.88/44.57 (Y7 @ Y8))) => 343.88/44.57 (Y7 @ Y9))))))))) & 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y8 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (Y1 @ 343.88/44.57 Y4 @ 343.88/44.57 Y8) | 343.88/44.57 (Y0 @ 343.88/44.57 Y4 @ Y8))) => 343.88/44.57 (Y7 @ Y8)))))))) => 343.88/44.57 (Y7 @ Y5)))))))) => 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y7 : a > $o]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y8 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (Y1 @ 343.88/44.57 Y4 @ 343.88/44.57 Y8) | 343.88/44.57 (Y0 @ 343.88/44.57 Y4 @ Y8))) => 343.88/44.57 (Y7 @ Y8)))))) & 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y8 : a]: 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y9 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (Y7 @ 343.88/44.57 Y8) & 343.88/44.57 (( 343.88/44.57 (Y0 @ 343.88/44.57 Y8 @ 343.88/44.57 Y9) | 343.88/44.57 (Y1 @ 343.88/44.57 Y8 @ Y9))))) => 343.88/44.57 (Y7 @ Y9))))))))))) => 343.88/44.57 (Y7 @ Y6))))))))))))))))))) => 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y4 : a > $o]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y5 : a]: 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y6 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (Y0 @ 343.88/44.57 Y5 @ 343.88/44.57 Y6) | 343.88/44.57 (Y1 @ 343.88/44.57 Y5 @ Y6))) & 343.88/44.57 (Y4 @ Y5))) => 343.88/44.57 (Y4 @ Y6))))))))) & 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y5 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (Y0 @ 343.88/44.57 Y2 @ 343.88/44.57 Y5) | 343.88/44.57 (Y1 @ 343.88/44.57 Y2 @ Y5))) => 343.88/44.57 (Y4 @ Y5)))))))) => 343.88/44.57 (Y4 @ Y3)))))))))) | 343.88/44.57 (((!!) @ (^[Y4 : a > $o]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y5 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (Y1 @ 343.88/44.57 Y2 @ 343.88/44.57 Y5) | 343.88/44.57 (Y0 @ 343.88/44.57 Y2 @ Y5))) => 343.88/44.57 (Y4 @ Y5)))))) & 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y5 : a]: 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(( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y7 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 ('#sk1' @ 343.88/44.57 Y6 @ 343.88/44.57 Y7) | 343.88/44.57 (Y0 @ 343.88/44.57 Y6 @ Y7))) & 343.88/44.57 (Y5 @ Y6))) => 343.88/44.57 (Y5 @ Y7))))))))) & 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y6 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 ('#sk1' @ 343.88/44.57 Y3 @ 343.88/44.57 Y6) | 343.88/44.57 (Y0 @ 343.88/44.57 Y3 @ Y6))) => 343.88/44.57 (Y5 @ Y6)))))))) => 343.88/44.57 (Y5 @ Y4)))))))))))))) & 343.88/44.57 (((!!) @ (^[Y3 : a]: 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y4 : a]: 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y5 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y6 : a > $o]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y7 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (Y0 @ 343.88/44.57 Y4 @ 343.88/44.57 Y7) | 343.88/44.57 ('#sk1' @ 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343.88/44.57 ^[Y4 : a]: 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y5 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 ('#sk1' @ 343.88/44.57 Y4 @ 343.88/44.57 Y5) | 343.88/44.57 (Y0 @ 343.88/44.57 Y4 @ Y5))) & 343.88/44.57 (Y3 @ Y4))) => 343.88/44.57 (Y3 @ Y5))))))))) & 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y4 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 ('#sk1' @ 343.88/44.57 Y1 @ 343.88/44.57 Y4) | 343.88/44.57 (Y0 @ 343.88/44.57 Y1 @ Y4))) => 343.88/44.57 (Y3 @ Y4)))))))) => 343.88/44.57 (Y3 @ Y2)))))))))) | 343.88/44.57 (((!!) @ (^[Y3 : a > $o]: 343.88/44.57 (((((((!!) @ ( 343.88/44.57 ^[Y4 : a]: 343.88/44.57 (((( 343.88/44.57 (Y0 @ 343.88/44.57 Y1 @ Y4) | 343.88/44.57 ('#sk1' @ 343.88/44.57 Y1 @ Y4))) => 343.88/44.57 (Y3 @ Y4)))))) & 343.88/44.57 (((!!) @ ( 343.88/44.57 ^[Y4 : a]: 343.88/44.57 (((!!) @ ( 343.88/44.57 ^[Y5 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 ('#sk1' @ 343.88/44.57 Y4 @ 343.88/44.57 Y5) | 343.88/44.57 (Y0 @ 343.88/44.57 Y4 @ Y5))) & 343.88/44.57 (Y3 @ Y4))) => 343.88/44.57 (Y3 @ Y5))))))))))) => 343.88/44.57 (Y3 @ Y2)))))))))))))))))), 343.88/44.57 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 343.88/44.57 thf(zip_derived_cl2, plain, 343.88/44.57 (~ (((!!) @ (^[Y0 : a]: 343.88/44.57 (((!!) @ (^[Y1 : a]: 343.88/44.57 (((((~) @ (((((((!!) @ (^[Y2 : a]: 343.88/44.57 (((!!) @ (^[Y3 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y4 : a > $o]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y5 : a]: 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y6 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 ('#sk2' @ 343.88/44.57 Y5 @ 343.88/44.57 Y6) & 343.88/44.57 (Y4 @ Y5))) => 343.88/44.57 (Y4 @ Y6))))))))) & 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y5 : a]: 343.88/44.57 (( 343.88/44.57 ('#sk2' @ 343.88/44.57 Y2 @ 343.88/44.57 Y5) => 343.88/44.57 (Y4 @ Y5)))))))) => 343.88/44.57 (Y4 @ Y3)))))) | 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y4 : a > $o]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y5 : a]: 343.88/44.57 (( 343.88/44.57 ('#sk1' @ 343.88/44.57 Y2 @ 343.88/44.57 Y5) => 343.88/44.57 (Y4 @ Y5)))))) & 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y5 : a]: 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y6 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 ('#sk1' @ 343.88/44.57 Y5 @ 343.88/44.57 Y6) & 343.88/44.57 (Y4 @ Y5))) => 343.88/44.57 (Y4 @ Y6))))))))))) => 343.88/44.57 (Y4 @ Y3)))))))) => 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y4 : a > $o]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y5 : a]: 343.88/44.57 (( 343.88/44.57 (!!) @ ( 343.88/44.57 ^[Y6 : a]: 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 (( 343.88/44.57 ('#sk1' @ 343.88/44.57 Y5 @ 343.88/44.57 Y6) | 343.88/44.57 ('#sk2' @ 343.88/44.57 Y5 @ Y6))) & 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(X2 @ ('#sk120' @ X2)))) => 343.88/44.58 (X2 @ Y0)))))) 343.88/44.58 | (X2 @ '#sk14') 343.88/44.58 | ('#form9') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl87])). 343.88/44.58 thf(zip_derived_cl110, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ((((((('#sk2' @ ('#sk120' @ X2) @ ('#sk150' @ X2)) | ('#sk1' @ 343.88/44.58 ('#sk120' @ X2) @ ('#sk150' @ X2)))) & 343.88/44.58 (X2 @ ('#sk120' @ X2)))) => 343.88/44.58 (X2 @ ('#sk150' @ X2)))) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))) 343.88/44.58 | ('#form9') 343.88/44.58 | (X2 @ '#sk14'))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl98])). 343.88/44.58 thf(zip_derived_cl124, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ((((('#sk2' @ ('#sk120' @ X2) @ ('#sk150' @ X2)) | ('#sk1' @ 343.88/44.58 ('#sk120' @ X2) @ ('#sk150' @ X2)))) & 343.88/44.58 (X2 @ ('#sk120' @ X2)))) 343.88/44.58 | (X2 @ '#sk14') 343.88/44.58 | ('#form9') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl110])). 343.88/44.58 thf(zip_derived_cl131, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form213' @ X2) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl132, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ((((('#sk2' @ '#sk10' @ ('#sk214' @ X2)) | ('#sk1' @ '#sk10' @ 343.88/44.58 ('#sk214' @ X2)))) => 343.88/44.58 (X2 @ ('#sk214' @ X2)))) 343.88/44.58 | ('#form213' @ X2))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl131])). 343.88/44.58 thf(zip_derived_cl143, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ((('#sk2' @ '#sk10' @ ('#sk214' @ X2)) | ('#sk1' @ '#sk10' @ 343.88/44.58 ('#sk214' @ X2)))) 343.88/44.58 | ('#form213' @ X2))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl132])). 343.88/44.58 thf(zip_derived_cl153, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#sk2' @ '#sk10' @ ('#sk214' @ X2)) 343.88/44.58 | ('#sk1' @ '#sk10' @ ('#sk214' @ X2)) 343.88/44.58 | ('#form213' @ X2))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl143])). 343.88/44.58 thf(zip_derived_cl48, plain, 343.88/44.58 ((~ (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk2' @ '#sk10' @ Y1) | ('#sk1' @ 343.88/44.58 '#sk10' @ Y1))) => 343.88/44.58 (Y0 @ Y1)))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 (((((Y0 @ Y1) & 343.88/44.58 ((('#sk1' @ Y1 @ Y2) | 343.88/44.58 ('#sk2' @ Y1 @ Y2))))) => 343.88/44.58 (Y0 @ Y2))))))))))) => 343.88/44.58 (Y0 @ '#sk19')))))) 343.88/44.58 | ('#form9'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])). 343.88/44.58 thf(zip_derived_cl55, plain, 343.88/44.58 ((~ (((((((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 343.88/44.58 ('#sk36' @ Y0)))))) & 343.88/44.58 (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk36' @ Y0) & 343.88/44.58 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 343.88/44.58 Y0 @ Y1))))) => 343.88/44.58 ('#sk36' @ Y1))))))))))) => 343.88/44.58 ('#sk36' @ '#sk19'))) 343.88/44.58 | ('#form9'))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl48])). 343.88/44.58 thf(zip_derived_cl64, plain, ((~ ('#sk36' @ '#sk19') | ('#form9'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 343.88/44.58 thf(zip_derived_cl53, plain, 343.88/44.58 (( (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk2' @ '#sk14' @ Y1) | ('#sk1' @ 343.88/44.58 '#sk14' @ Y1))) => 343.88/44.58 (Y0 @ Y1)))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 (((((Y0 @ Y1) & 343.88/44.58 ((('#sk1' @ Y1 @ Y2) | 343.88/44.58 ('#sk2' @ Y1 @ Y2))))) => 343.88/44.58 (Y0 @ Y2))))))))))) => 343.88/44.58 (Y0 @ '#sk19')))))) 343.88/44.58 | ('#form9'))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl47])). 343.88/44.58 thf(zip_derived_cl61, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( (((((((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ '#sk14' @ Y0) | ('#sk1' @ '#sk14' @ 343.88/44.58 Y0))) => 343.88/44.58 (X2 @ Y0)))))) & 343.88/44.58 (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((((X2 @ Y0) & 343.88/44.58 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 343.88/44.58 Y0 @ Y1))))) => 343.88/44.58 (X2 @ Y1))))))))))) => 343.88/44.58 (X2 @ '#sk19'))) 343.88/44.58 | ('#form9'))), 343.88/44.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl53])). 343.88/44.58 thf(zip_derived_cl72, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (((((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ '#sk14' @ Y0) | ('#sk1' @ '#sk14' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))) & 343.88/44.58 (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((((X2 @ Y0) & 343.88/44.58 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 343.88/44.58 Y0 @ Y1))))) => 343.88/44.58 (X2 @ Y1))))))))))) 343.88/44.58 | (X2 @ '#sk19') 343.88/44.58 | ('#form9'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 343.88/44.58 thf(zip_derived_cl86, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ '#sk14' @ Y0) | ('#sk1' @ '#sk14' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((((X2 @ Y0) & 343.88/44.58 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 343.88/44.58 Y0 @ Y1))))) => 343.88/44.58 (X2 @ Y1))))))))) 343.88/44.58 | ('#form9') 343.88/44.58 | (X2 @ '#sk19'))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl72])). 343.88/44.58 thf(zip_derived_cl97, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ((((('#sk2' @ '#sk14' @ ('#sk116' @ X2)) | ('#sk1' @ '#sk14' @ 343.88/44.58 ('#sk116' @ X2)))) => 343.88/44.58 (X2 @ ('#sk116' @ X2)))) 343.88/44.58 | (X2 @ '#sk19') 343.88/44.58 | ('#form9') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((((X2 @ Y0) & 343.88/44.58 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 343.88/44.58 Y0 @ Y1))))) => 343.88/44.58 (X2 @ Y1))))))))))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl86])). 343.88/44.58 thf(zip_derived_cl108, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ((('#sk2' @ '#sk14' @ ('#sk116' @ X2)) | ('#sk1' @ '#sk14' @ 343.88/44.58 ('#sk116' @ X2)))) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((((X2 @ Y0) & 343.88/44.58 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 343.88/44.58 Y0 @ Y1))))) => 343.88/44.58 (X2 @ Y1))))))))) 343.88/44.58 | ('#form9') 343.88/44.58 | (X2 @ '#sk19'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])). 343.88/44.58 thf(zip_derived_cl120, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form169' @ X2) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((((X2 @ Y0) & 343.88/44.58 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 343.88/44.58 Y0 @ Y1))))) => 343.88/44.58 (X2 @ Y1))))))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl121, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((((X2 @ ('#sk170' @ X2)) & 343.88/44.58 ((('#sk1' @ ('#sk170' @ X2) @ Y0) | ('#sk2' @ 343.88/44.58 ('#sk170' @ X2) @ Y0))))) => 343.88/44.58 (X2 @ Y0)))))) 343.88/44.58 | ('#form169' @ X2))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl120])). 343.88/44.58 thf(zip_derived_cl129, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (((((X2 @ ('#sk170' @ X2)) & 343.88/44.58 ((('#sk1' @ ('#sk170' @ X2) @ ('#sk202' @ X2)) | ('#sk2' @ 343.88/44.58 ('#sk170' @ X2) @ ('#sk202' @ X2)))))) => 343.88/44.58 (X2 @ ('#sk202' @ X2)))) 343.88/44.58 | ('#form169' @ X2))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl121])). 343.88/44.58 thf(zip_derived_cl139, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( (((X2 @ ('#sk170' @ X2)) & 343.88/44.58 ((('#sk1' @ ('#sk170' @ X2) @ ('#sk202' @ X2)) | ('#sk2' @ 343.88/44.58 ('#sk170' @ X2) @ ('#sk202' @ X2)))))) 343.88/44.58 | ('#form169' @ X2))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl129])). 343.88/44.58 thf(zip_derived_cl150, plain, 343.88/44.58 (![X2 : a > $o]: ( (X2 @ ('#sk170' @ X2)) | ('#form169' @ X2))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl139])). 343.88/44.58 thf(zip_derived_cl109, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (X2 @ ('#sk116' @ X2)) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((((X2 @ Y0) & 343.88/44.58 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 343.88/44.58 Y0 @ Y1))))) => 343.88/44.58 (X2 @ Y1))))))))) 343.88/44.58 | ('#form9') 343.88/44.58 | (X2 @ '#sk19'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])). 343.88/44.58 thf(zip_derived_cl120, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form169' @ X2) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((((X2 @ Y0) & 343.88/44.58 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 343.88/44.58 Y0 @ Y1))))) => 343.88/44.58 (X2 @ Y1))))))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl123, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ('#form169' @ (^[Y0 : a]: (X2 @ Y0))) 343.88/44.58 | (X2 @ '#sk19') 343.88/44.58 | ('#form9') 343.88/44.58 | ~ (X2 @ ('#sk116' @ X2)))), 343.88/44.58 inference('renaming', [status(thm)], 343.88/44.58 [zip_derived_cl109, zip_derived_cl120])). 343.88/44.58 thf(zip_derived_cl130, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ('#form169' @ X2) 343.88/44.58 | (X2 @ '#sk19') 343.88/44.58 | ('#form9') 343.88/44.58 | ~ (X2 @ ('#sk116' @ X2)))), 343.88/44.58 inference('ho_norm', [status(thm)], [zip_derived_cl123])). 343.88/44.58 thf(zip_derived_cl140, plain, 343.88/44.58 (![X2 : a > $o]: (~ (X2 @ ('#sk202' @ X2)) | ('#form169' @ X2))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl129])). 343.88/44.58 thf(zip_derived_cl151, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ((('#sk1' @ ('#sk170' @ X2) @ ('#sk202' @ X2)) | ('#sk2' @ 343.88/44.58 ('#sk170' @ X2) @ ('#sk202' @ X2)))) 343.88/44.58 | ('#form169' @ X2))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl139])). 343.88/44.58 thf(zip_derived_cl156, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#sk1' @ ('#sk170' @ X2) @ ('#sk202' @ X2)) 343.88/44.58 | ('#sk2' @ ('#sk170' @ X2) @ ('#sk202' @ X2)) 343.88/44.58 | ('#form169' @ X2))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl151])). 343.88/44.58 thf(zip_derived_cl108, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ((('#sk2' @ '#sk14' @ ('#sk116' @ X2)) | ('#sk1' @ '#sk14' @ 343.88/44.58 ('#sk116' @ X2)))) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((((X2 @ Y0) & 343.88/44.58 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 343.88/44.58 Y0 @ Y1))))) => 343.88/44.58 (X2 @ Y1))))))))) 343.88/44.58 | ('#form9') 343.88/44.58 | (X2 @ '#sk19'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])). 343.88/44.58 thf(zip_derived_cl120, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form169' @ X2) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((((X2 @ Y0) & 343.88/44.58 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 343.88/44.58 Y0 @ Y1))))) => 343.88/44.58 (X2 @ Y1))))))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl122, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ('#form169' @ X2) 343.88/44.58 | (X2 @ '#sk19') 343.88/44.58 | ('#form9') 343.88/44.58 | ((('#sk2' @ '#sk14' @ ('#sk116' @ X2)) | ('#sk1' @ '#sk14' @ 343.88/44.58 ('#sk116' @ X2)))))), 343.88/44.58 inference('renaming', [status(thm)], 343.88/44.58 [zip_derived_cl108, zip_derived_cl120])). 343.88/44.58 thf(zip_derived_cl128, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#sk2' @ '#sk14' @ ('#sk116' @ X2)) 343.88/44.58 | ('#sk1' @ '#sk14' @ ('#sk116' @ X2)) 343.88/44.58 | ('#form9') 343.88/44.58 | (X2 @ '#sk19') 343.88/44.58 | ~ ('#form169' @ X2))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl122])). 343.88/44.58 thf(zip_derived_cl63, plain, 343.88/44.58 (( (((((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 343.88/44.58 ('#sk36' @ Y0)))))) & 343.88/44.58 (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk36' @ Y0) & 343.88/44.58 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 343.88/44.58 Y1))))) => 343.88/44.58 ('#sk36' @ Y1))))))))))) 343.88/44.58 | ('#form9'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 343.88/44.58 thf(zip_derived_cl74, plain, 343.88/44.58 (( (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 343.88/44.58 ('#sk36' @ Y0)))))) 343.88/44.58 | ('#form9'))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl63])). 343.88/44.58 thf(zip_derived_cl88, plain, 343.88/44.58 (![X2 : a]: 343.88/44.58 ( ((((('#sk2' @ '#sk10' @ X2) | ('#sk1' @ '#sk10' @ X2))) => 343.88/44.58 ('#sk36' @ X2))) 343.88/44.58 | ('#form9'))), 343.88/44.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl74])). 343.88/44.58 thf(zip_derived_cl99, plain, 343.88/44.58 (![X2 : a]: 343.88/44.58 (~ ((('#sk2' @ '#sk10' @ X2) | ('#sk1' @ '#sk10' @ X2))) 343.88/44.58 | ('#sk36' @ X2) 343.88/44.58 | ('#form9'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl88])). 343.88/44.58 thf(zip_derived_cl112, plain, 343.88/44.58 (![X2 : a]: (~ ('#sk1' @ '#sk10' @ X2) | ('#form9') | ('#sk36' @ X2))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl99])). 343.88/44.58 thf(zip_derived_cl111, plain, 343.88/44.58 (![X2 : a]: (~ ('#sk2' @ '#sk10' @ X2) | ('#form9') | ('#sk36' @ X2))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl99])). 343.88/44.58 thf(zip_derived_cl144, plain, 343.88/44.58 (![X2 : a > $o]: (~ (X2 @ ('#sk214' @ X2)) | ('#form213' @ X2))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl132])). 343.88/44.58 thf(zip_derived_cl124, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ((((('#sk2' @ ('#sk120' @ X2) @ ('#sk150' @ X2)) | ('#sk1' @ 343.88/44.58 ('#sk120' @ X2) @ ('#sk150' @ X2)))) & 343.88/44.58 (X2 @ ('#sk120' @ X2)))) 343.88/44.58 | (X2 @ '#sk14') 343.88/44.58 | ('#form9') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl110])). 343.88/44.58 thf(zip_derived_cl131, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form213' @ X2) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl133, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ('#form213' @ X2) 343.88/44.58 | ('#form9') 343.88/44.58 | (X2 @ '#sk14') 343.88/44.58 | ((((('#sk2' @ ('#sk120' @ X2) @ ('#sk150' @ X2)) | ('#sk1' @ 343.88/44.58 ('#sk120' @ X2) @ ('#sk150' @ X2)))) & 343.88/44.58 (X2 @ ('#sk120' @ X2)))))), 343.88/44.58 inference('renaming', [status(thm)], 343.88/44.58 [zip_derived_cl124, zip_derived_cl131])). 343.88/44.58 thf(zip_derived_cl142, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( (X2 @ ('#sk120' @ X2)) 343.88/44.58 | (X2 @ '#sk14') 343.88/44.58 | ('#form9') 343.88/44.58 | ~ ('#form213' @ X2))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl133])). 343.88/44.58 thf(zip_derived_cl125, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (X2 @ ('#sk150' @ X2)) 343.88/44.58 | (X2 @ '#sk14') 343.88/44.58 | ('#form9') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl110])). 343.88/44.58 thf(zip_derived_cl131, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form213' @ X2) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl134, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ('#form213' @ (^[Y0 : a]: (X2 @ Y0))) 343.88/44.58 | ('#form9') 343.88/44.58 | (X2 @ '#sk14') 343.88/44.58 | ~ (X2 @ ('#sk150' @ X2)))), 343.88/44.58 inference('renaming', [status(thm)], 343.88/44.58 [zip_derived_cl125, zip_derived_cl131])). 343.88/44.58 thf(zip_derived_cl145, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ('#form213' @ X2) 343.88/44.58 | ('#form9') 343.88/44.58 | (X2 @ '#sk14') 343.88/44.58 | ~ (X2 @ ('#sk150' @ X2)))), 343.88/44.58 inference('ho_norm', [status(thm)], [zip_derived_cl134])). 343.88/44.58 thf(zip_derived_cl75, plain, 343.88/44.58 (( (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk36' @ Y0) & 343.88/44.58 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 343.88/44.58 ('#sk36' @ Y1))))))))) 343.88/44.58 | ('#form9'))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl63])). 343.88/44.58 thf(zip_derived_cl89, plain, 343.88/44.58 (![X2 : a]: 343.88/44.58 ( (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk36' @ X2) & 343.88/44.58 ((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))))) => 343.88/44.58 ('#sk36' @ Y0)))))) 343.88/44.58 | ('#form9'))), 343.88/44.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl75])). 343.88/44.58 thf(zip_derived_cl100, plain, 343.88/44.58 (![X2 : a, X4 : a]: 343.88/44.58 ( ((((('#sk36' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) => 343.88/44.58 ('#sk36' @ X4))) 343.88/44.58 | ('#form9'))), 343.88/44.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl89])). 343.88/44.58 thf(zip_derived_cl113, plain, 343.88/44.58 (![X2 : a, X4 : a]: 343.88/44.58 (~ ((('#sk36' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) 343.88/44.58 | ('#sk36' @ X4) 343.88/44.58 | ('#form9'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 343.88/44.58 thf(zip_derived_cl126, plain, 343.88/44.58 (![X2 : a, X4 : a]: 343.88/44.58 (~ ('#sk36' @ X2) 343.88/44.58 | ~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 343.88/44.58 | ('#form9') 343.88/44.58 | ('#sk36' @ X4))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl113])). 343.88/44.58 thf(zip_derived_cl136, plain, 343.88/44.58 (![X2 : a, X4 : a]: 343.88/44.58 (~ ('#sk2' @ X2 @ X4) 343.88/44.58 | ('#sk36' @ X4) 343.88/44.58 | ('#form9') 343.88/44.58 | ~ ('#sk36' @ X2))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl126])). 343.88/44.58 thf(zip_derived_cl141, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ((('#sk2' @ ('#sk120' @ X2) @ ('#sk150' @ X2)) | ('#sk1' @ 343.88/44.58 ('#sk120' @ X2) @ ('#sk150' @ X2)))) 343.88/44.58 | (X2 @ '#sk14') 343.88/44.58 | ('#form9') 343.88/44.58 | ~ ('#form213' @ X2))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl133])). 343.88/44.58 thf(zip_derived_cl152, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#sk2' @ ('#sk120' @ X2) @ ('#sk150' @ X2)) 343.88/44.58 | ('#sk1' @ ('#sk120' @ X2) @ ('#sk150' @ X2)) 343.88/44.58 | ~ ('#form213' @ X2) 343.88/44.58 | ('#form9') 343.88/44.58 | (X2 @ '#sk14'))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl141])). 343.88/44.58 thf(zip_derived_cl135, plain, 343.88/44.58 (![X2 : a, X4 : a]: 343.88/44.58 (~ ('#sk1' @ X2 @ X4) 343.88/44.58 | ('#sk36' @ X4) 343.88/44.58 | ('#form9') 343.88/44.58 | ~ ('#sk36' @ X2))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl126])). 343.88/44.58 thf(zip_derived_cl24, plain, 343.88/44.58 (( ('#form8') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 (((((((!!) @ (^[Y3 : a > $o]: 343.88/44.58 (((((((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y1 @ 343.88/44.58 Y4) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y1 @ Y4))) => 343.88/44.58 (Y3 @ Y4)))))) & 343.88/44.58 (((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (!!) @ ( 343.88/44.58 ^[Y5 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 (Y3 @ 343.88/44.58 Y4) & 343.88/44.58 (( 343.88/44.58 ('#sk1' @ 343.88/44.58 Y4 @ 343.88/44.58 Y5) | 343.88/44.58 ('#sk2' @ 343.88/44.58 Y4 @ Y5))))) => 343.88/44.58 (Y3 @ Y5))))))))))) => 343.88/44.58 (Y3 @ Y2)))))) & 343.88/44.58 (((!!) @ (^[Y3 : a > $o]: 343.88/44.58 (((((((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (!!) @ ( 343.88/44.58 ^[Y5 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y4 @ 343.88/44.58 Y5) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y4 @ Y5))) & 343.88/44.58 (Y3 @ Y4))) => 343.88/44.58 (Y3 @ Y5))))))))) & 343.88/44.58 (((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y0 @ 343.88/44.58 Y4) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y0 @ Y4))) => 343.88/44.58 (Y3 @ Y4)))))))) => 343.88/44.58 (Y3 @ Y1)))))))) => 343.88/44.58 (((!!) @ (^[Y3 : a > $o]: 343.88/44.58 (((((((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 ( 343.88/44.58 ( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y0 @ 343.88/44.58 Y4) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y0 @ Y4))) => 343.88/44.58 (Y3 @ Y4)))))) & 343.88/44.58 (((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 ( 343.88/44.58 ( 343.88/44.58 (!!) @ ( 343.88/44.58 ^[Y5 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 (Y3 @ 343.88/44.58 Y4) & 343.88/44.58 (( 343.88/44.58 ('#sk1' @ 343.88/44.58 Y4 @ 343.88/44.58 Y5) | 343.88/44.58 ('#sk2' @ 343.88/44.58 Y4 @ Y5))))) => 343.88/44.58 (Y3 @ Y5))))))))))) => 343.88/44.58 (Y3 @ Y2))))))))))))))))) 343.88/44.58 | (((((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((('#sk2' @ Y1 @ Y2) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 343.88/44.58 (Y0 @ '#sk7')))))) | 343.88/44.58 (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((('#sk1' @ Y1 @ Y2) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))))) => 343.88/44.58 (Y0 @ '#sk7')))))))))), 343.88/44.58 inference('renaming', [status(thm)], [zip_derived_cl18, zip_derived_cl22])). 343.88/44.58 thf(zip_derived_cl29, plain, 343.88/44.58 (( ('#form9') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 (((((((!!) @ (^[Y3 : a > $o]: 343.88/44.58 (((((((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y1 @ 343.88/44.58 Y4) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y1 @ Y4))) => 343.88/44.58 (Y3 @ Y4)))))) & 343.88/44.58 (((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (!!) @ ( 343.88/44.58 ^[Y5 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 (Y3 @ 343.88/44.58 Y4) & 343.88/44.58 (( 343.88/44.58 ('#sk1' @ 343.88/44.58 Y4 @ 343.88/44.58 Y5) | 343.88/44.58 ('#sk2' @ 343.88/44.58 Y4 @ Y5))))) => 343.88/44.58 (Y3 @ Y5))))))))))) => 343.88/44.58 (Y3 @ Y2)))))) & 343.88/44.58 (((!!) @ (^[Y3 : a > $o]: 343.88/44.58 (((((((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (!!) @ ( 343.88/44.58 ^[Y5 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y4 @ 343.88/44.58 Y5) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y4 @ Y5))) & 343.88/44.58 (Y3 @ Y4))) => 343.88/44.58 (Y3 @ Y5))))))))) & 343.88/44.58 (((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y0 @ 343.88/44.58 Y4) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y0 @ Y4))) => 343.88/44.58 (Y3 @ Y4)))))))) => 343.88/44.58 (Y3 @ Y1)))))))) => 343.88/44.58 (((!!) @ (^[Y3 : a > $o]: 343.88/44.58 (((((((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 ( 343.88/44.58 ( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y0 @ 343.88/44.58 Y4) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y0 @ Y4))) => 343.88/44.58 (Y3 @ Y4)))))) & 343.88/44.58 (((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 ( 343.88/44.58 ( 343.88/44.58 (!!) @ ( 343.88/44.58 ^[Y5 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 (Y3 @ 343.88/44.58 Y4) & 343.88/44.58 (( 343.88/44.58 ('#sk1' @ 343.88/44.58 Y4 @ 343.88/44.58 Y5) | 343.88/44.58 ('#sk2' @ 343.88/44.58 Y4 @ Y5))))) => 343.88/44.58 (Y3 @ Y5))))))))))) => 343.88/44.58 (Y3 @ Y2))))))))))))))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl31, plain, 343.88/44.58 ((~ ('#form9') 343.88/44.58 | (((((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((('#sk2' @ Y1 @ Y2) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 343.88/44.58 (Y0 @ '#sk7')))))) | 343.88/44.58 (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((('#sk1' @ Y1 @ Y2) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))))) => 343.88/44.58 (Y0 @ '#sk7')))))))) 343.88/44.58 | ('#form8'))), 343.88/44.58 inference('renaming', [status(thm)], [zip_derived_cl24, zip_derived_cl29])). 343.88/44.58 thf(zip_derived_cl35, plain, 343.88/44.58 (( (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((('#sk2' @ Y1 @ Y2) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 343.88/44.58 (Y0 @ '#sk7')))))) 343.88/44.58 | (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((('#sk1' @ Y1 @ Y2) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))))) => 343.88/44.58 (Y0 @ '#sk7')))))) 343.88/44.58 | ('#form8') 343.88/44.58 | ~ ('#form9'))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 343.88/44.58 thf(zip_derived_cl41, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( (((((((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 343.88/44.58 (X2 @ Y1))))))))) & 343.88/44.58 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) => 343.88/44.58 (X2 @ '#sk7'))) 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form8') 343.88/44.58 | (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((('#sk1' @ Y1 @ Y2) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))))) => 343.88/44.58 (Y0 @ '#sk7')))))))), 343.88/44.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl35])). 343.88/44.58 thf(zip_derived_cl46, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (((((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 343.88/44.58 (X2 @ Y1))))))))) & 343.88/44.58 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((('#sk1' @ Y1 @ Y2) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))))) => 343.88/44.58 (Y0 @ '#sk7')))))) 343.88/44.58 | ('#form8') 343.88/44.58 | ~ ('#form9'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])). 343.88/44.58 thf(zip_derived_cl52, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 343.88/44.58 (X2 @ Y1))))))))) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form8') 343.88/44.58 | (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((('#sk1' @ Y1 @ Y2) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))))) => 343.88/44.58 (Y0 @ '#sk7')))))) 343.88/44.58 | (X2 @ '#sk7'))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 343.88/44.58 thf(zip_derived_cl60, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ ('#sk47' @ X2) @ Y0) & (X2 @ 343.88/44.58 ('#sk47' @ X2)))) => 343.88/44.58 (X2 @ Y0)))))) 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((('#sk1' @ Y1 @ Y2) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))))) => 343.88/44.58 (Y0 @ '#sk7')))))) 343.88/44.58 | ('#form8') 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl52])). 343.88/44.58 thf(zip_derived_cl71, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ((((('#sk2' @ ('#sk47' @ X2) @ ('#sk62' @ X2)) & (X2 @ 343.88/44.58 ('#sk47' @ X2)))) => 343.88/44.58 (X2 @ ('#sk62' @ X2)))) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form8') 343.88/44.58 | (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((('#sk1' @ Y1 @ Y2) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))))) => 343.88/44.58 (Y0 @ '#sk7')))))) 343.88/44.58 | (X2 @ '#sk7'))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl60])). 343.88/44.58 thf(zip_derived_cl84, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ((('#sk2' @ ('#sk47' @ X2) @ ('#sk62' @ X2)) & (X2 @ ('#sk47' @ X2)))) 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((('#sk1' @ Y1 @ Y2) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))))) => 343.88/44.58 (Y0 @ '#sk7')))))) 343.88/44.58 | ('#form8') 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 343.88/44.58 thf(zip_derived_cl93, plain, 343.88/44.58 ((~ ('#form110') 343.88/44.58 | (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((('#sk1' @ Y1 @ Y2) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))))) => 343.88/44.58 (Y0 @ '#sk7')))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl94, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 343.88/44.58 (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 343.88/44.58 (X2 @ Y1))))))))))) => 343.88/44.58 (X2 @ '#sk7'))) 343.88/44.58 | ~ ('#form110'))), 343.88/44.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl93])). 343.88/44.58 thf(zip_derived_cl106, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 343.88/44.58 (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 343.88/44.58 (X2 @ Y1))))))))))) 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | ~ ('#form110'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl94])). 343.88/44.58 thf(zip_derived_cl118, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 343.88/44.58 (X2 @ Y1))))))))) 343.88/44.58 | ~ ('#form110') 343.88/44.58 | (X2 @ '#sk7'))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])). 343.88/44.58 thf(zip_derived_cl127, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ((('#sk1' @ '#sk6' @ ('#sk193' @ X2)) => (X2 @ ('#sk193' @ X2)))) 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | ~ ('#form110') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 343.88/44.58 (X2 @ Y1))))))))))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl118])). 343.88/44.58 thf(zip_derived_cl137, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#sk1' @ '#sk6' @ ('#sk193' @ X2)) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 343.88/44.58 (X2 @ Y1))))))))) 343.88/44.58 | ~ ('#form110') 343.88/44.58 | (X2 @ '#sk7'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 343.88/44.58 thf(zip_derived_cl146, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form248' @ X2) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 343.88/44.58 (X2 @ Y1))))))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl147, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk1' @ ('#sk249' @ X2) @ Y0) & (X2 @ 343.88/44.58 ('#sk249' @ X2)))) => 343.88/44.58 (X2 @ Y0)))))) 343.88/44.58 | ('#form248' @ X2))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl146])). 343.88/44.58 thf(zip_derived_cl154, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ((((('#sk1' @ ('#sk249' @ X2) @ ('#sk279' @ X2)) & (X2 @ 343.88/44.58 ('#sk249' @ X2)))) => 343.88/44.58 (X2 @ ('#sk279' @ X2)))) 343.88/44.58 | ('#form248' @ X2))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl147])). 343.88/44.58 thf(zip_derived_cl157, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ((('#sk1' @ ('#sk249' @ X2) @ ('#sk279' @ X2)) & (X2 @ 343.88/44.58 ('#sk249' @ X2)))) 343.88/44.58 | ('#form248' @ X2))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl154])). 343.88/44.58 thf(zip_derived_cl160, plain, 343.88/44.58 (![X2 : a > $o]: ( (X2 @ ('#sk249' @ X2)) | ('#form248' @ X2))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl157])). 343.88/44.58 thf(zip_derived_cl22, plain, 343.88/44.58 ((~ ('#form8') 343.88/44.58 | (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((((('#sk1' @ Y1 @ Y2) | 343.88/44.58 ('#sk2' @ Y1 @ Y2))) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 343.88/44.58 '#sk3' @ Y1))) => 343.88/44.58 (Y0 @ Y1)))))))) => 343.88/44.58 (Y0 @ '#sk4')))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl23, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( (((((((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 343.88/44.58 Y0 @ Y1))) & 343.88/44.58 (X2 @ Y0))) => 343.88/44.58 (X2 @ Y1))))))))) & 343.88/44.58 (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))))) => 343.88/44.58 (X2 @ '#sk4'))) 343.88/44.58 | ~ ('#form8'))), 343.88/44.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 343.88/44.58 thf(zip_derived_cl32, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (((((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 343.88/44.58 Y0 @ Y1))) & 343.88/44.58 (X2 @ Y0))) => 343.88/44.58 (X2 @ Y1))))))))) & 343.88/44.58 (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))))) 343.88/44.58 | (X2 @ '#sk4') 343.88/44.58 | ~ ('#form8'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl23])). 343.88/44.58 thf(zip_derived_cl37, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 343.88/44.58 Y1))) & 343.88/44.58 (X2 @ Y0))) => 343.88/44.58 (X2 @ Y1))))))))) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))) 343.88/44.58 | ~ ('#form8') 343.88/44.58 | (X2 @ '#sk4'))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl32])). 343.88/44.58 thf(zip_derived_cl43, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((((('#sk1' @ ('#sk23' @ X2) @ Y0) | ('#sk2' @ 343.88/44.58 ('#sk23' @ X2) @ Y0))) & 343.88/44.58 (X2 @ ('#sk23' @ X2)))) => 343.88/44.58 (X2 @ Y0)))))) 343.88/44.58 | (X2 @ '#sk4') 343.88/44.58 | ~ ('#form8') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl37])). 343.88/44.58 thf(zip_derived_cl49, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ((((((('#sk1' @ ('#sk23' @ X2) @ ('#sk32' @ X2)) | ('#sk2' @ 343.88/44.58 ('#sk23' @ X2) @ ('#sk32' @ X2)))) & 343.88/44.58 (X2 @ ('#sk23' @ X2)))) => 343.88/44.58 (X2 @ ('#sk32' @ X2)))) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))) 343.88/44.58 | ~ ('#form8') 343.88/44.58 | (X2 @ '#sk4'))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl43])). 343.88/44.58 thf(zip_derived_cl56, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ((((('#sk1' @ ('#sk23' @ X2) @ ('#sk32' @ X2)) | ('#sk2' @ 343.88/44.58 ('#sk23' @ X2) @ ('#sk32' @ X2)))) & 343.88/44.58 (X2 @ ('#sk23' @ X2)))) 343.88/44.58 | (X2 @ '#sk4') 343.88/44.58 | ~ ('#form8') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 343.88/44.58 thf(zip_derived_cl65, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form54' @ X2) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl66, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ((((('#sk1' @ '#sk3' @ ('#sk55' @ X2)) | ('#sk2' @ '#sk3' @ 343.88/44.58 ('#sk55' @ X2)))) => 343.88/44.58 (X2 @ ('#sk55' @ X2)))) 343.88/44.58 | ('#form54' @ X2))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl65])). 343.88/44.58 thf(zip_derived_cl79, plain, 343.88/44.58 (![X2 : a > $o]: (~ (X2 @ ('#sk55' @ X2)) | ('#form54' @ X2))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl66])). 343.88/44.58 thf(zip_derived_cl84, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ((('#sk2' @ ('#sk47' @ X2) @ ('#sk62' @ X2)) & (X2 @ ('#sk47' @ X2)))) 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((('#sk1' @ Y1 @ Y2) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))))) => 343.88/44.58 (Y0 @ '#sk7')))))) 343.88/44.58 | ('#form8') 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 343.88/44.58 thf(zip_derived_cl93, plain, 343.88/44.58 ((~ ('#form110') 343.88/44.58 | (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((('#sk1' @ Y1 @ Y2) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))))) => 343.88/44.58 (Y0 @ '#sk7')))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl95, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form110') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form8') 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | ((('#sk2' @ ('#sk47' @ X2) @ ('#sk62' @ X2)) & (X2 @ 343.88/44.58 ('#sk47' @ X2)))))), 343.88/44.58 inference('renaming', [status(thm)], [zip_derived_cl84, zip_derived_cl93])). 343.88/44.58 thf(zip_derived_cl95, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form110') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form8') 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | ((('#sk2' @ ('#sk47' @ X2) @ ('#sk62' @ X2)) & (X2 @ 343.88/44.58 ('#sk47' @ X2)))))), 343.88/44.58 inference('renaming', [status(thm)], [zip_derived_cl84, zip_derived_cl93])). 343.88/44.58 thf(zip_derived_cl103, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form133' @ X2) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl105, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ('#form133' @ X2) 343.88/44.58 | ((('#sk2' @ ('#sk47' @ X2) @ ('#sk62' @ X2)) & (X2 @ 343.88/44.58 ('#sk47' @ X2)))) 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | ('#form8') 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form110'))), 343.88/44.58 inference('renaming', [status(thm)], 343.88/44.58 [zip_derived_cl95, zip_derived_cl103])). 343.88/44.58 thf(zip_derived_cl115, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( (X2 @ ('#sk47' @ X2)) 343.88/44.58 | ('#form110') 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form8') 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | ~ ('#form133' @ X2))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl105])). 343.88/44.58 thf(zip_derived_cl19, plain, 343.88/44.58 ((~ (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((((('#sk1' @ Y1 @ Y2) | 343.88/44.58 ('#sk2' @ Y1 @ Y2))) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk1' @ '#sk6' @ Y1) | ('#sk2' @ 343.88/44.58 '#sk6' @ Y1))) => 343.88/44.58 (Y0 @ Y1)))))))) => 343.88/44.58 (Y0 @ '#sk7')))))) 343.88/44.58 | (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((((('#sk1' @ Y1 @ Y2) | 343.88/44.58 ('#sk2' @ Y1 @ Y2))) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 343.88/44.58 '#sk3' @ Y1))) => 343.88/44.58 (Y0 @ Y1)))))))) => 343.88/44.58 (Y0 @ '#sk4')))))) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 (((((((!!) @ (^[Y3 : a > $o]: 343.88/44.58 (((((((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y1 @ 343.88/44.58 Y4) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y1 @ Y4))) => 343.88/44.58 (Y3 @ Y4)))))) & 343.88/44.58 (((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (!!) @ ( 343.88/44.58 ^[Y5 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 (Y3 @ 343.88/44.58 Y4) & 343.88/44.58 (( 343.88/44.58 ('#sk1' @ 343.88/44.58 Y4 @ 343.88/44.58 Y5) | 343.88/44.58 ('#sk2' @ 343.88/44.58 Y4 @ Y5))))) => 343.88/44.58 (Y3 @ Y5))))))))))) => 343.88/44.58 (Y3 @ Y2)))))) & 343.88/44.58 (((!!) @ (^[Y3 : a > $o]: 343.88/44.58 (((((((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (!!) @ ( 343.88/44.58 ^[Y5 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y4 @ 343.88/44.58 Y5) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y4 @ Y5))) & 343.88/44.58 (Y3 @ Y4))) => 343.88/44.58 (Y3 @ Y5))))))))) & 343.88/44.58 (((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y0 @ 343.88/44.58 Y4) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y0 @ Y4))) => 343.88/44.58 (Y3 @ Y4)))))))) => 343.88/44.58 (Y3 @ Y1)))))))) => 343.88/44.58 (((!!) @ (^[Y3 : a > $o]: 343.88/44.58 (((((((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 ( 343.88/44.58 ( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y0 @ 343.88/44.58 Y4) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y0 @ Y4))) => 343.88/44.58 (Y3 @ Y4)))))) & 343.88/44.58 (((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 ( 343.88/44.58 ( 343.88/44.58 (!!) @ ( 343.88/44.58 ^[Y5 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 (Y3 @ 343.88/44.58 Y4) & 343.88/44.58 (( 343.88/44.58 ('#sk1' @ 343.88/44.58 Y4 @ 343.88/44.58 Y5) | 343.88/44.58 ('#sk2' @ 343.88/44.58 Y4 @ Y5))))) => 343.88/44.58 (Y3 @ Y5))))))))))) => 343.88/44.58 (Y3 @ Y2))))))))))))))))))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 343.88/44.58 thf(zip_derived_cl22, plain, 343.88/44.58 ((~ ('#form8') 343.88/44.58 | (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((((('#sk1' @ Y1 @ Y2) | 343.88/44.58 ('#sk2' @ Y1 @ Y2))) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 343.88/44.58 '#sk3' @ Y1))) => 343.88/44.58 (Y0 @ Y1)))))))) => 343.88/44.58 (Y0 @ '#sk4')))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl25, plain, 343.88/44.58 (( ('#form8') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 (((((((!!) @ (^[Y3 : a > $o]: 343.88/44.58 (((((((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y1 @ 343.88/44.58 Y4) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y1 @ Y4))) => 343.88/44.58 (Y3 @ Y4)))))) & 343.88/44.58 (((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (!!) @ ( 343.88/44.58 ^[Y5 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 (Y3 @ 343.88/44.58 Y4) & 343.88/44.58 (( 343.88/44.58 ('#sk1' @ 343.88/44.58 Y4 @ 343.88/44.58 Y5) | 343.88/44.58 ('#sk2' @ 343.88/44.58 Y4 @ Y5))))) => 343.88/44.58 (Y3 @ Y5))))))))))) => 343.88/44.58 (Y3 @ Y2)))))) & 343.88/44.58 (((!!) @ (^[Y3 : a > $o]: 343.88/44.58 (((((((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (!!) @ ( 343.88/44.58 ^[Y5 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y4 @ 343.88/44.58 Y5) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y4 @ Y5))) & 343.88/44.58 (Y3 @ Y4))) => 343.88/44.58 (Y3 @ Y5))))))))) & 343.88/44.58 (((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y0 @ 343.88/44.58 Y4) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y0 @ Y4))) => 343.88/44.58 (Y3 @ Y4)))))))) => 343.88/44.58 (Y3 @ Y1)))))))) => 343.88/44.58 (((!!) @ (^[Y3 : a > $o]: 343.88/44.58 (((((((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 ( 343.88/44.58 ( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y0 @ 343.88/44.58 Y4) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y0 @ Y4))) => 343.88/44.58 (Y3 @ Y4)))))) & 343.88/44.58 (((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 ( 343.88/44.58 ( 343.88/44.58 (!!) @ ( 343.88/44.58 ^[Y5 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 (Y3 @ 343.88/44.58 Y4) & 343.88/44.58 (( 343.88/44.58 ('#sk1' @ 343.88/44.58 Y4 @ 343.88/44.58 Y5) | 343.88/44.58 ('#sk2' @ 343.88/44.58 Y4 @ Y5))))) => 343.88/44.58 (Y3 @ Y5))))))))))) => 343.88/44.58 (Y3 @ Y2))))))))))))))))) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((((('#sk1' @ Y1 @ Y2) | 343.88/44.58 ('#sk2' @ Y1 @ Y2))) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk1' @ '#sk6' @ Y1) | ('#sk2' @ 343.88/44.58 '#sk6' @ Y1))) => 343.88/44.58 (Y0 @ Y1)))))))) => 343.88/44.58 (Y0 @ '#sk7')))))))), 343.88/44.58 inference('renaming', [status(thm)], [zip_derived_cl19, zip_derived_cl22])). 343.88/44.58 thf(zip_derived_cl29, plain, 343.88/44.58 (( ('#form9') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 (((((((!!) @ (^[Y3 : a > $o]: 343.88/44.58 (((((((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y1 @ 343.88/44.58 Y4) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y1 @ Y4))) => 343.88/44.58 (Y3 @ Y4)))))) & 343.88/44.58 (((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (!!) @ ( 343.88/44.58 ^[Y5 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 (Y3 @ 343.88/44.58 Y4) & 343.88/44.58 (( 343.88/44.58 ('#sk1' @ 343.88/44.58 Y4 @ 343.88/44.58 Y5) | 343.88/44.58 ('#sk2' @ 343.88/44.58 Y4 @ Y5))))) => 343.88/44.58 (Y3 @ Y5))))))))))) => 343.88/44.58 (Y3 @ Y2)))))) & 343.88/44.58 (((!!) @ (^[Y3 : a > $o]: 343.88/44.58 (((((((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (!!) @ ( 343.88/44.58 ^[Y5 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y4 @ 343.88/44.58 Y5) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y4 @ Y5))) & 343.88/44.58 (Y3 @ Y4))) => 343.88/44.58 (Y3 @ Y5))))))))) & 343.88/44.58 (((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y0 @ 343.88/44.58 Y4) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y0 @ Y4))) => 343.88/44.58 (Y3 @ Y4)))))))) => 343.88/44.58 (Y3 @ Y1)))))))) => 343.88/44.58 (((!!) @ (^[Y3 : a > $o]: 343.88/44.58 (((((((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 ( 343.88/44.58 ( 343.88/44.58 (( 343.88/44.58 ('#sk2' @ 343.88/44.58 Y0 @ 343.88/44.58 Y4) | 343.88/44.58 ('#sk1' @ 343.88/44.58 Y0 @ Y4))) => 343.88/44.58 (Y3 @ Y4)))))) & 343.88/44.58 (((!!) @ ( 343.88/44.58 ^[Y4 : a]: 343.88/44.58 ( 343.88/44.58 ( 343.88/44.58 (!!) @ ( 343.88/44.58 ^[Y5 : a]: 343.88/44.58 (( 343.88/44.58 (( 343.88/44.58 (Y3 @ 343.88/44.58 Y4) & 343.88/44.58 (( 343.88/44.58 ('#sk1' @ 343.88/44.58 Y4 @ 343.88/44.58 Y5) | 343.88/44.58 ('#sk2' @ 343.88/44.58 Y4 @ Y5))))) => 343.88/44.58 (Y3 @ Y5))))))))))) => 343.88/44.58 (Y3 @ Y2))))))))))))))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl33, plain, 343.88/44.58 ((~ ('#form9') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((((('#sk1' @ Y1 @ Y2) | 343.88/44.58 ('#sk2' @ Y1 @ Y2))) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk1' @ '#sk6' @ Y1) | ('#sk2' @ 343.88/44.58 '#sk6' @ Y1))) => 343.88/44.58 (Y0 @ Y1)))))))) => 343.88/44.58 (Y0 @ '#sk7')))))) 343.88/44.58 | ('#form8'))), 343.88/44.58 inference('renaming', [status(thm)], [zip_derived_cl25, zip_derived_cl29])). 343.88/44.58 thf(zip_derived_cl38, plain, 343.88/44.58 ((~ (((((((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 343.88/44.58 Y0 @ Y1))) & 343.88/44.58 ('#sk18' @ Y0))) => 343.88/44.58 ('#sk18' @ Y1))))))))) & 343.88/44.58 (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 343.88/44.58 ('#sk18' @ Y0)))))))) => 343.88/44.58 ('#sk18' @ '#sk7'))) 343.88/44.58 | ('#form8') 343.88/44.58 | ~ ('#form9'))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl33])). 343.88/44.58 thf(zip_derived_cl45, plain, 343.88/44.58 ((~ ('#sk18' @ '#sk7') | ~ ('#form9') | ('#form8'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 343.88/44.58 thf(zip_derived_cl158, plain, 343.88/44.58 (![X2 : a > $o]: (~ (X2 @ ('#sk279' @ X2)) | ('#form248' @ X2))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl154])). 343.88/44.58 thf(zip_derived_cl159, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#sk1' @ ('#sk249' @ X2) @ ('#sk279' @ X2)) | ('#form248' @ X2))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl157])). 343.88/44.58 thf(zip_derived_cl137, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#sk1' @ '#sk6' @ ('#sk193' @ X2)) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 343.88/44.58 (X2 @ Y1))))))))) 343.88/44.58 | ~ ('#form110') 343.88/44.58 | (X2 @ '#sk7'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 343.88/44.58 thf(zip_derived_cl146, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form248' @ X2) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 343.88/44.58 (X2 @ Y1))))))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl148, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ('#form248' @ X2) 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | ~ ('#form110') 343.88/44.58 | ('#sk1' @ '#sk6' @ ('#sk193' @ X2)))), 343.88/44.58 inference('renaming', [status(thm)], 343.88/44.58 [zip_derived_cl137, zip_derived_cl146])). 343.88/44.58 thf(zip_derived_cl44, plain, 343.88/44.58 (( (((((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 343.88/44.58 Y1))) & 343.88/44.58 ('#sk18' @ Y0))) => 343.88/44.58 ('#sk18' @ Y1))))))))) & 343.88/44.58 (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 343.88/44.58 ('#sk18' @ Y0)))))))) 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form8'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 343.88/44.58 thf(zip_derived_cl51, plain, 343.88/44.58 (( (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 343.88/44.58 ('#sk18' @ Y0)))))) 343.88/44.58 | ('#form8') 343.88/44.58 | ~ ('#form9'))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl44])). 343.88/44.58 thf(zip_derived_cl59, plain, 343.88/44.58 (![X2 : a]: 343.88/44.58 ( ((((('#sk1' @ '#sk6' @ X2) | ('#sk2' @ '#sk6' @ X2))) => ('#sk18' @ 343.88/44.58 X2))) 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form8'))), 343.88/44.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl51])). 343.88/44.58 thf(zip_derived_cl70, plain, 343.88/44.58 (![X2 : a]: 343.88/44.58 (~ ((('#sk1' @ '#sk6' @ X2) | ('#sk2' @ '#sk6' @ X2))) 343.88/44.58 | ('#sk18' @ X2) 343.88/44.58 | ('#form8') 343.88/44.58 | ~ ('#form9'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl59])). 343.88/44.58 thf(zip_derived_cl82, plain, 343.88/44.58 (![X2 : a]: 343.88/44.58 (~ ('#sk1' @ '#sk6' @ X2) 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form8') 343.88/44.58 | ('#sk18' @ X2))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl70])). 343.88/44.58 thf(zip_derived_cl138, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (X2 @ ('#sk193' @ X2)) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 343.88/44.58 (X2 @ Y1))))))))) 343.88/44.58 | ~ ('#form110') 343.88/44.58 | (X2 @ '#sk7'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 343.88/44.58 thf(zip_derived_cl146, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form248' @ X2) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 343.88/44.58 (X2 @ Y1))))))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl149, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ('#form248' @ (^[Y0 : a]: (X2 @ Y0))) 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | ~ ('#form110') 343.88/44.58 | ~ (X2 @ ('#sk193' @ X2)))), 343.88/44.58 inference('renaming', [status(thm)], 343.88/44.58 [zip_derived_cl138, zip_derived_cl146])). 343.88/44.58 thf(zip_derived_cl155, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ('#form248' @ X2) 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | ~ ('#form110') 343.88/44.58 | ~ (X2 @ ('#sk193' @ X2)))), 343.88/44.58 inference('ho_norm', [status(thm)], [zip_derived_cl149])). 343.88/44.58 thf(zip_derived_cl6, plain, 343.88/44.58 (~ (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 343.88/44.58 '#sk3' @ Y1))) => 343.88/44.58 (Y0 @ Y1)))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((((('#sk1' @ Y1 @ Y2) | 343.88/44.58 ('#sk2' @ Y1 @ Y2))) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))))) => 343.88/44.58 (Y0 @ '#sk4'))))))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 343.88/44.58 thf(zip_derived_cl8, plain, 343.88/44.58 (~ (((((((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 343.88/44.58 ('#sk5' @ Y0)))))) & 343.88/44.58 (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 343.88/44.58 Y1))) & 343.88/44.58 ('#sk5' @ Y0))) => 343.88/44.58 ('#sk5' @ Y1))))))))))) => 343.88/44.58 ('#sk5' @ '#sk4')))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 343.88/44.58 thf(zip_derived_cl10, plain, 343.88/44.58 ( (((((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 343.88/44.58 ('#sk5' @ Y0)))))) & 343.88/44.58 (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 343.88/44.58 ('#sk5' @ Y0))) => 343.88/44.58 ('#sk5' @ Y1)))))))))))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 343.88/44.58 thf(zip_derived_cl13, plain, 343.88/44.58 ( (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 343.88/44.58 ('#sk5' @ Y0))))))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 343.88/44.58 thf(zip_derived_cl16, plain, 343.88/44.58 (![X2 : a]: 343.88/44.58 ((((('#sk2' @ '#sk3' @ X2) | ('#sk1' @ '#sk3' @ X2))) => ('#sk5' @ 343.88/44.58 X2)))), 343.88/44.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 343.88/44.58 thf(zip_derived_cl20, plain, 343.88/44.58 (![X2 : a]: 343.88/44.58 (~ ((('#sk2' @ '#sk3' @ X2) | ('#sk1' @ '#sk3' @ X2))) 343.88/44.58 | ('#sk5' @ X2))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 343.88/44.58 thf(zip_derived_cl26, plain, 343.88/44.58 (![X2 : a]: (~ ('#sk2' @ '#sk3' @ X2) | ('#sk5' @ X2))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 343.88/44.58 thf(zip_derived_cl78, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ((('#sk1' @ '#sk3' @ ('#sk55' @ X2)) | ('#sk2' @ '#sk3' @ 343.88/44.58 ('#sk55' @ X2)))) 343.88/44.58 | ('#form54' @ X2))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl66])). 343.88/44.58 thf(zip_derived_cl91, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#sk1' @ '#sk3' @ ('#sk55' @ X2)) 343.88/44.58 | ('#sk2' @ '#sk3' @ ('#sk55' @ X2)) 343.88/44.58 | ('#form54' @ X2))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl78])). 343.88/44.58 thf(zip_derived_cl27, plain, 343.88/44.58 (![X2 : a]: (~ ('#sk1' @ '#sk3' @ X2) | ('#sk5' @ X2))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 343.88/44.58 thf(zip_derived_cl103, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form133' @ X2) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl104, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ((('#sk2' @ '#sk6' @ ('#sk134' @ X2)) => (X2 @ ('#sk134' @ X2)))) 343.88/44.58 | ('#form133' @ X2))), 343.88/44.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl103])). 343.88/44.58 thf(zip_derived_cl116, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#sk2' @ '#sk6' @ ('#sk134' @ X2)) | ('#form133' @ X2))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl104])). 343.88/44.58 thf(zip_derived_cl85, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (X2 @ ('#sk62' @ X2)) 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((('#sk1' @ Y1 @ Y2) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))))) => 343.88/44.58 (Y0 @ '#sk7')))))) 343.88/44.58 | ('#form8') 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 343.88/44.58 thf(zip_derived_cl93, plain, 343.88/44.58 ((~ ('#form110') 343.88/44.58 | (((!!) @ (^[Y0 : a > $o]: 343.88/44.58 (((((((!!) @ (^[Y1 : a]: 343.88/44.58 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 (((!!) @ (^[Y2 : a]: 343.88/44.58 ((((('#sk1' @ Y1 @ Y2) & 343.88/44.58 (Y0 @ Y1))) => 343.88/44.58 (Y0 @ Y2))))))))))) => 343.88/44.58 (Y0 @ '#sk7')))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl96, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form110') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form8') 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | ~ (X2 @ ('#sk62' @ X2)))), 343.88/44.58 inference('renaming', [status(thm)], [zip_derived_cl85, zip_derived_cl93])). 343.88/44.58 thf(zip_derived_cl103, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form133' @ X2) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl107, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ('#form133' @ (^[Y0 : a]: (X2 @ Y0))) 343.88/44.58 | ~ (X2 @ ('#sk62' @ X2)) 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | ('#form8') 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form110'))), 343.88/44.58 inference('renaming', [status(thm)], 343.88/44.58 [zip_derived_cl96, zip_derived_cl103])). 343.88/44.58 thf(zip_derived_cl119, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ('#form133' @ X2) 343.88/44.58 | ~ (X2 @ ('#sk62' @ X2)) 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | ('#form8') 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form110'))), 343.88/44.58 inference('ho_norm', [status(thm)], [zip_derived_cl107])). 343.88/44.58 thf(zip_derived_cl50, plain, 343.88/44.58 (( (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 343.88/44.58 ('#sk18' @ Y0))) => 343.88/44.58 ('#sk18' @ Y1))))))))) 343.88/44.58 | ('#form8') 343.88/44.58 | ~ ('#form9'))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl44])). 343.88/44.58 thf(zip_derived_cl58, plain, 343.88/44.58 (![X2 : a]: 343.88/44.58 ( (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) & 343.88/44.58 ('#sk18' @ X2))) => 343.88/44.58 ('#sk18' @ Y0)))))) 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form8'))), 343.88/44.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl50])). 343.88/44.58 thf(zip_derived_cl69, plain, 343.88/44.58 (![X2 : a, X4 : a]: 343.88/44.58 ( ((((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk18' @ X2))) => 343.88/44.58 ('#sk18' @ X4))) 343.88/44.58 | ('#form8') 343.88/44.58 | ~ ('#form9'))), 343.88/44.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl58])). 343.88/44.58 thf(zip_derived_cl81, plain, 343.88/44.58 (![X2 : a, X4 : a]: 343.88/44.58 (~ ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk18' @ X2))) 343.88/44.58 | ('#sk18' @ X4) 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form8'))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl69])). 343.88/44.58 thf(zip_derived_cl92, plain, 343.88/44.58 (![X2 : a, X4 : a]: 343.88/44.58 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 343.88/44.58 | ~ ('#sk18' @ X2) 343.88/44.58 | ('#form8') 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#sk18' @ X4))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl81])). 343.88/44.58 thf(zip_derived_cl101, plain, 343.88/44.58 (![X2 : a, X4 : a]: 343.88/44.58 (~ ('#sk1' @ X2 @ X4) 343.88/44.58 | ('#sk18' @ X4) 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form8') 343.88/44.58 | ~ ('#sk18' @ X2))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl92])). 343.88/44.58 thf(zip_derived_cl83, plain, 343.88/44.58 (![X2 : a]: 343.88/44.58 (~ ('#sk2' @ '#sk6' @ X2) 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form8') 343.88/44.58 | ('#sk18' @ X2))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl70])). 343.88/44.58 thf(zip_derived_cl117, plain, 343.88/44.58 (![X2 : a > $o]: (~ (X2 @ ('#sk134' @ X2)) | ('#form133' @ X2))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl104])). 343.88/44.58 thf(zip_derived_cl114, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#sk2' @ ('#sk47' @ X2) @ ('#sk62' @ X2)) 343.88/44.58 | ('#form110') 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form8') 343.88/44.58 | (X2 @ '#sk7') 343.88/44.58 | ~ ('#form133' @ X2))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl105])). 343.88/44.58 thf(zip_derived_cl102, plain, 343.88/44.58 (![X2 : a, X4 : a]: 343.88/44.58 (~ ('#sk2' @ X2 @ X4) 343.88/44.58 | ('#sk18' @ X4) 343.88/44.58 | ~ ('#form9') 343.88/44.58 | ('#form8') 343.88/44.58 | ~ ('#sk18' @ X2))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl92])). 343.88/44.58 thf(zip_derived_cl56, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ((((('#sk1' @ ('#sk23' @ X2) @ ('#sk32' @ X2)) | ('#sk2' @ 343.88/44.58 ('#sk23' @ X2) @ ('#sk32' @ X2)))) & 343.88/44.58 (X2 @ ('#sk23' @ X2)))) 343.88/44.58 | (X2 @ '#sk4') 343.88/44.58 | ~ ('#form8') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 343.88/44.58 thf(zip_derived_cl65, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form54' @ X2) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl67, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ('#form54' @ X2) 343.88/44.58 | ~ ('#form8') 343.88/44.58 | (X2 @ '#sk4') 343.88/44.58 | ((((('#sk1' @ ('#sk23' @ X2) @ ('#sk32' @ X2)) | ('#sk2' @ 343.88/44.58 ('#sk23' @ X2) @ ('#sk32' @ X2)))) & 343.88/44.58 (X2 @ ('#sk23' @ X2)))))), 343.88/44.58 inference('renaming', [status(thm)], [zip_derived_cl56, zip_derived_cl65])). 343.88/44.58 thf(zip_derived_cl77, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( (X2 @ ('#sk23' @ X2)) 343.88/44.58 | (X2 @ '#sk4') 343.88/44.58 | ~ ('#form8') 343.88/44.58 | ~ ('#form54' @ X2))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl67])). 343.88/44.58 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk4')), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 343.88/44.58 thf(zip_derived_cl57, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ (X2 @ ('#sk32' @ X2)) 343.88/44.58 | (X2 @ '#sk4') 343.88/44.58 | ~ ('#form8') 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 343.88/44.58 thf(zip_derived_cl65, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#form54' @ X2) 343.88/44.58 | ~ (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 343.88/44.58 (X2 @ Y0)))))))), 343.88/44.58 define([status(thm)])). 343.88/44.58 thf(zip_derived_cl68, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ('#form54' @ (^[Y0 : a]: (X2 @ Y0))) 343.88/44.58 | ~ ('#form8') 343.88/44.58 | (X2 @ '#sk4') 343.88/44.58 | ~ (X2 @ ('#sk32' @ X2)))), 343.88/44.58 inference('renaming', [status(thm)], [zip_derived_cl57, zip_derived_cl65])). 343.88/44.58 thf(zip_derived_cl80, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 (~ ('#form54' @ X2) 343.88/44.58 | ~ ('#form8') 343.88/44.58 | (X2 @ '#sk4') 343.88/44.58 | ~ (X2 @ ('#sk32' @ X2)))), 343.88/44.58 inference('ho_norm', [status(thm)], [zip_derived_cl68])). 343.88/44.58 thf(zip_derived_cl14, plain, 343.88/44.58 ( (((!!) @ (^[Y0 : a]: 343.88/44.58 (((!!) @ (^[Y1 : a]: 343.88/44.58 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 343.88/44.58 ('#sk5' @ Y0))) => 343.88/44.58 ('#sk5' @ Y1)))))))))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 343.88/44.58 thf(zip_derived_cl17, plain, 343.88/44.58 (![X2 : a]: 343.88/44.58 (((!!) @ (^[Y0 : a]: 343.88/44.58 ((((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) & 343.88/44.58 ('#sk5' @ X2))) => 343.88/44.58 ('#sk5' @ Y0))))))), 343.88/44.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 343.88/44.58 thf(zip_derived_cl21, plain, 343.88/44.58 (![X2 : a, X4 : a]: 343.88/44.58 ((((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk5' @ X2))) => 343.88/44.58 ('#sk5' @ X4)))), 343.88/44.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 343.88/44.58 thf(zip_derived_cl28, plain, 343.88/44.58 (![X2 : a, X4 : a]: 343.88/44.58 (~ ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk5' @ X2))) 343.88/44.58 | ('#sk5' @ X4))), 343.88/44.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 343.88/44.58 thf(zip_derived_cl34, plain, 343.88/44.58 (![X2 : a, X4 : a]: 343.88/44.58 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 343.88/44.58 | ~ ('#sk5' @ X2) 343.88/44.58 | ('#sk5' @ X4))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl28])). 343.88/44.58 thf(zip_derived_cl40, plain, 343.88/44.58 (![X2 : a, X4 : a]: 343.88/44.58 (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])). 343.88/44.58 thf(zip_derived_cl76, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ((('#sk1' @ ('#sk23' @ X2) @ ('#sk32' @ X2)) | ('#sk2' @ 343.88/44.58 ('#sk23' @ X2) @ ('#sk32' @ X2)))) 343.88/44.58 | (X2 @ '#sk4') 343.88/44.58 | ~ ('#form8') 343.88/44.58 | ~ ('#form54' @ X2))), 343.88/44.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl67])). 343.88/44.58 thf(zip_derived_cl90, plain, 343.88/44.58 (![X2 : a > $o]: 343.88/44.58 ( ('#sk1' @ ('#sk23' @ X2) @ ('#sk32' @ X2)) 343.88/44.58 | ('#sk2' @ ('#sk23' @ X2) @ ('#sk32' @ X2)) 343.88/44.58 | ~ ('#form54' @ X2) 343.88/44.58 | ~ ('#form8') 343.88/44.58 | (X2 @ '#sk4'))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl76])). 343.88/44.58 thf(zip_derived_cl39, plain, 343.88/44.58 (![X2 : a, X4 : a]: 343.88/44.58 (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 343.88/44.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])). 343.88/44.58 thf(zip_derived_cl12573, plain, ($false), 343.88/44.58 inference('eprover', [status(thm)], 343.88/44.58 [zip_derived_cl153, zip_derived_cl64, zip_derived_cl150, 343.88/44.58 zip_derived_cl130, zip_derived_cl140, zip_derived_cl156, 343.88/44.58 zip_derived_cl128, zip_derived_cl112, zip_derived_cl111, 343.88/44.58 zip_derived_cl144, zip_derived_cl142, zip_derived_cl145, 343.88/44.58 zip_derived_cl136, zip_derived_cl152, zip_derived_cl135, 343.88/44.58 zip_derived_cl160, zip_derived_cl79, zip_derived_cl115, 343.88/44.58 zip_derived_cl45, zip_derived_cl158, zip_derived_cl159, 343.88/44.58 zip_derived_cl148, zip_derived_cl82, zip_derived_cl155, 343.88/44.58 zip_derived_cl26, zip_derived_cl91, zip_derived_cl27, 343.88/44.58 zip_derived_cl116, zip_derived_cl119, zip_derived_cl101, 343.88/44.58 zip_derived_cl83, zip_derived_cl117, zip_derived_cl114, 343.88/44.58 zip_derived_cl102, zip_derived_cl77, zip_derived_cl11, 343.88/44.58 zip_derived_cl80, zip_derived_cl40, zip_derived_cl90, 343.88/44.58 zip_derived_cl39])). 343.88/44.58 343.88/44.58 % SZS output end Refutation 343.88/44.58 343.88/44.58 343.88/44.58 % Terminating... 344.34/44.66 % Runner terminated. 344.34/44.67 % Zipperpin 1.5 exiting 344.34/44.67 EOF