0.08/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.83LshbXyvI true 0.13/0.34 % Computer : n023.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1440 0.13/0.34 % WCLimit : 180 0.13/0.34 % DateTime : Mon Jul 3 05:11:06 EDT 2023 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 1440 s 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.55/0.66 % Total configuration time : 828 0.55/0.66 % Estimated wc time : 1656 0.55/0.66 % Estimated cpu time (8 cpus) : 207.0 0.55/0.69 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.56/0.72 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.56/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 52.66/7.23 % Solved by lams/20_acsne_simpl.sh. 52.66/7.23 % done 475 iterations in 6.342s 52.66/7.23 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 52.66/7.23 % SZS output start Refutation 52.66/7.23 thf(a_type, type, a: $tType). 52.66/7.23 thf('#sk250_type', type, '#sk250': (a > a > $o) > a). 52.66/7.23 thf('#sk4_type', type, '#sk4': a). 52.66/7.23 thf('#sk197_type', type, '#sk197': (a > a > $o) > a). 52.66/7.23 thf('#form1275_type', type, '#form1275': $o). 52.66/7.23 thf('#sk835_type', type, '#sk835': (a > a > $o) > a). 52.66/7.23 thf('#form744_type', type, '#form744': (a > a > $o) > $o). 52.66/7.23 thf('#sk3_type', type, '#sk3': a). 52.66/7.23 thf('#form408_type', type, '#form408': (a > a > $o) > $o). 52.66/7.23 thf('#sk409_type', type, '#sk409': (a > a > $o) > a). 52.66/7.23 thf('#sk139_type', type, '#sk139': (a > a > $o) > a). 52.66/7.23 thf('#sk338_type', type, '#sk338': (a > a > $o) > a). 52.66/7.23 thf('#sk435_type', type, '#sk435': (a > a > $o) > a). 52.66/7.23 thf('#sk6_type', type, '#sk6': a). 52.66/7.23 thf('#sk20_type', type, '#sk20': a). 52.66/7.23 thf('#sk2_type', type, '#sk2': a > a > $o). 52.66/7.23 thf('#sk8_type', type, '#sk8': a > a > $o). 52.66/7.23 thf('#sk88_type', type, '#sk88': a > a > $o). 52.66/7.23 thf('#sk10_type', type, '#sk10': a). 52.66/7.23 thf('#sk87_type', type, '#sk87': (a > a > $o) > a). 52.66/7.23 thf('#sk7_type', type, '#sk7': a). 52.66/7.23 thf('#form19_type', type, '#form19': $o). 52.66/7.23 thf('#sk38_type', type, '#sk38': a). 52.66/7.23 thf('#form29_type', type, '#form29': $o). 52.66/7.23 thf('#form9_type', type, '#form9': $o). 52.66/7.23 thf('#sk105_type', type, '#sk105': (a > a > $o) > a). 52.66/7.23 thf('#sk128_type', type, '#sk128': (a > a > $o) > a). 52.66/7.23 thf('#sk5_type', type, '#sk5': a > a > $o). 52.66/7.23 thf('#form337_type', type, '#form337': (a > a > $o) > $o). 52.66/7.23 thf('#sk745_type', type, '#sk745': (a > a > $o) > a). 52.66/7.23 thf('#sk1_type', type, '#sk1': a > a > $o). 52.66/7.23 thf('#form1290_type', type, '#form1290': $o). 52.66/7.23 thf('#sk119_type', type, '#sk119': (a > a > $o) > a). 52.66/7.23 thf('#sk525_type', type, '#sk525': (a > a > $o) > a). 52.66/7.23 thf('#sk184_type', type, '#sk184': (a > a > $o) > a). 52.66/7.23 thf(cTHM250D_pme, conjecture, 52.66/7.23 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 52.66/7.23 ( ( ( ( ![Xx0:a,Xy0:a]: 52.66/7.23 ( ( ( ![Xp1:( a > a > $o )]: 52.66/7.23 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 52.66/7.23 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xz ) ) ) & 52.66/7.23 ( ![Xx1:a,Xy1:a]: 52.66/7.23 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 52.66/7.23 ( ![Xp1:( a > a > $o )]: 52.66/7.23 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 52.66/7.23 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xz ) ) ) & 52.66/7.23 ( ![Xx1:a,Xy1:a]: 52.66/7.23 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 52.66/7.23 ( ![Xp1:( a > a > $o )]: 52.66/7.23 ( ( ( ![Xx1:a,Xy1:a]: 52.66/7.23 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 52.66/7.23 ( ![Xx1:a,Xy1:a,Xz:a]: 52.66/7.23 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) & 52.66/7.23 ( ![Xx0:a,Xy0:a,Xz:a]: 52.66/7.23 ( ( ( ![Xp1:( a > a > $o )]: 52.66/7.23 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 52.66/7.23 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 52.66/7.23 ( ![Xx1:a,Xy1:a]: 52.66/7.23 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 52.66/7.23 ( Xp1 @ Xy0 @ Xz ) ) ) & 52.66/7.23 ( ![Xp1:( a > a > $o )]: 52.66/7.23 ( ( ( ![Xx1:a,Xy1:a]: 52.66/7.23 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 52.66/7.23 ( ![Xx1:a,Xy1:a,Xz0:a]: 52.66/7.23 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 52.66/7.23 ( ![Xp1:( a > a > $o )]: 52.66/7.23 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 52.66/7.23 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 52.66/7.23 ( ![Xx1:a,Xy1:a]: 52.66/7.23 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) ) => 52.66/7.23 ( ![Xp1:( a > a > $o )]: 52.66/7.23 ( ( ( ![Xx0:a,Xy0:a]: 52.66/7.23 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 52.66/7.23 ( ![Xx0:a,Xy0:a,Xz:a]: 52.66/7.23 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 52.66/7.23 ( Xp1 @ Xx @ Xy ) ) ) ) => 52.66/7.23 ( ![Xp1:( a > a > $o )]: 52.66/7.23 ( ( ( ![Xx0:a,Xy0:a]: 52.66/7.23 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 52.66/7.23 ( ![Xx0:a,Xy0:a,Xz:a]: 52.66/7.23 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 52.66/7.23 ( Xp1 @ Xx @ Xy ) ) ) ))). 52.66/7.23 thf(zf_stmt_0, negated_conjecture, 52.66/7.23 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 52.66/7.23 ( ( ( ( ![Xx0:a,Xy0:a]: 52.66/7.23 ( ( ( ![Xp1:( a > a > $o )]: 52.66/7.23 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 52.66/7.23 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xz ) ) ) & 52.66/7.23 ( ![Xx1:a,Xy1:a]: 52.66/7.23 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 52.66/7.23 ( ![Xp1:( a > a > $o )]: 52.66/7.23 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 52.66/7.23 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xz ) ) ) & 52.66/7.23 ( ![Xx1:a,Xy1:a]: 52.66/7.23 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 52.66/7.23 ( ![Xp1:( a > a > $o )]: 52.66/7.23 ( ( ( ![Xx1:a,Xy1:a]: 52.66/7.23 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 52.66/7.23 ( ![Xx1:a,Xy1:a,Xz:a]: 52.66/7.23 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) & 52.66/7.23 ( ![Xx0:a,Xy0:a,Xz:a]: 52.66/7.23 ( ( ( ![Xp1:( a > a > $o )]: 52.66/7.23 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 52.66/7.23 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 52.66/7.23 ( ![Xx1:a,Xy1:a]: 52.66/7.23 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 52.66/7.23 ( Xp1 @ Xy0 @ Xz ) ) ) & 52.66/7.23 ( ![Xp1:( a > a > $o )]: 52.66/7.23 ( ( ( ![Xx1:a,Xy1:a]: 52.66/7.23 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 52.66/7.23 ( ![Xx1:a,Xy1:a,Xz0:a]: 52.66/7.23 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 52.66/7.23 ( ![Xp1:( a > a > $o )]: 52.66/7.23 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 52.66/7.23 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 52.66/7.23 ( ![Xx1:a,Xy1:a]: 52.66/7.23 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 52.66/7.23 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) ) => 52.66/7.23 ( ![Xp1:( a > a > $o )]: 52.66/7.23 ( ( ( ![Xx0:a,Xy0:a]: 52.66/7.23 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 52.66/7.23 ( ![Xx0:a,Xy0:a,Xz:a]: 52.66/7.23 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 52.66/7.23 ( Xp1 @ Xx @ Xy ) ) ) ) => 52.66/7.23 ( ![Xp1:( a > a > $o )]: 52.66/7.23 ( ( ( ![Xx0:a,Xy0:a]: 52.66/7.23 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 52.66/7.23 ( ![Xx0:a,Xy0:a,Xz:a]: 52.66/7.23 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 52.66/7.23 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 52.66/7.23 ( Xp1 @ Xx @ Xy ) ) ) ) )), 52.66/7.23 inference('cnf.neg', [status(esa)], [cTHM250D_pme])). 52.66/7.23 thf(zip_derived_cl0, plain, 52.66/7.23 (~ (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.23 (((!!) @ (^[Y1 : a > a > $o]: 52.66/7.23 (((!!) @ (^[Y2 : a]: 52.66/7.23 (((!!) @ (^[Y3 : a]: 52.66/7.23 (((((((((!!) @ ( 52.66/7.23 ^[Y4 : a]: 52.66/7.23 (((!!) @ ( 52.66/7.23 ^[Y5 : a]: 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y6 : 52.66/7.23 a > a > $o]: 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y7 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y8 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y9 : a]: 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (Y6 @ 52.66/7.23 Y8 @ 52.66/7.23 Y9) & 52.66/7.23 (Y6 @ 52.66/7.23 Y7 @ Y8))) => 52.66/7.23 (Y6 @ 52.66/7.23 Y7 @ Y9)))))))))))) & 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y7 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y8 : a]: 52.66/7.23 (( 52.66/7.23 (Y0 @ 52.66/7.23 Y7 @ 52.66/7.23 Y8) => 52.66/7.23 (Y6 @ 52.66/7.23 Y7 @ Y8))))))))))) => 52.66/7.23 (Y6 @ 52.66/7.23 Y4 @ Y5)))))) | 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y6 : 52.66/7.23 a > a > $o]: 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y7 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y8 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y9 : a]: 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (Y6 @ 52.66/7.23 Y7 @ 52.66/7.23 Y8) & 52.66/7.23 (Y6 @ 52.66/7.23 Y8 @ Y9))) => 52.66/7.23 (Y6 @ 52.66/7.23 Y7 @ Y9)))))))))))) & 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y7 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y8 : a]: 52.66/7.23 (( 52.66/7.23 (Y1 @ 52.66/7.23 Y7 @ 52.66/7.23 Y8) => 52.66/7.23 (Y6 @ 52.66/7.23 Y7 @ Y8))))))))))) => 52.66/7.23 (Y6 @ 52.66/7.23 Y4 @ Y5)))))))) => 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y6 : 52.66/7.23 a > a > $o]: 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y7 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y8 : a]: 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (Y0 @ 52.66/7.23 Y7 @ 52.66/7.23 Y8) | 52.66/7.23 (Y1 @ 52.66/7.23 Y7 @ Y8))) => 52.66/7.23 (Y6 @ 52.66/7.23 Y7 @ Y8))))))))) & 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y7 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y8 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y9 : a]: 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (Y6 @ 52.66/7.23 Y8 @ 52.66/7.23 Y9) & 52.66/7.23 (Y6 @ 52.66/7.23 Y7 @ Y8))) => 52.66/7.23 (Y6 @ 52.66/7.23 Y7 @ Y9)))))))))))))) => 52.66/7.23 (Y6 @ 52.66/7.23 Y4 @ Y5)))))))))))))) & 52.66/7.23 (((!!) @ ( 52.66/7.23 ^[Y4 : a]: 52.66/7.23 (((!!) @ ( 52.66/7.23 ^[Y5 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y6 : a]: 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y7 : 52.66/7.23 a > a > $o]: 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y8 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y9 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y10 : a]: 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (Y7 @ 52.66/7.23 Y8 @ 52.66/7.23 Y9) & 52.66/7.23 (Y7 @ 52.66/7.23 Y9 @ Y10))) => 52.66/7.23 (Y7 @ 52.66/7.23 Y8 @ Y10)))))))))))) & 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y8 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y9 : a]: 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (Y0 @ 52.66/7.23 Y8 @ 52.66/7.23 Y9) | 52.66/7.23 (Y1 @ 52.66/7.23 Y8 @ Y9))) => 52.66/7.23 (Y7 @ 52.66/7.23 Y8 @ Y9))))))))))) => 52.66/7.23 (Y7 @ 52.66/7.23 Y5 @ Y6)))))) & 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y7 : 52.66/7.23 a > a > $o]: 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y8 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y9 : a]: 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (Y1 @ 52.66/7.23 Y8 @ 52.66/7.23 Y9) | 52.66/7.23 (Y0 @ 52.66/7.23 Y8 @ Y9))) => 52.66/7.23 (Y7 @ 52.66/7.23 Y8 @ Y9))))))))) & 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y8 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y9 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y10 : a]: 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (Y7 @ 52.66/7.23 Y9 @ 52.66/7.23 Y10) & 52.66/7.23 (Y7 @ 52.66/7.23 Y8 @ Y9))) => 52.66/7.23 (Y7 @ 52.66/7.23 Y8 @ Y10)))))))))))))) => 52.66/7.23 (Y7 @ 52.66/7.23 Y4 @ Y5)))))))) => 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y7 : 52.66/7.23 a > a > $o]: 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y8 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y9 : a]: 52.66/7.23 (( 52.66/7.23 (!!) @ ( 52.66/7.23 ^[Y10 : a]: 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Y5))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ 52.66/7.24 Y6) & 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))))) => 52.66/7.24 (Y3 @ Y1 @ Y2)))))))))))))))))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 52.66/7.24 thf(zip_derived_cl2, plain, 52.66/7.24 (~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((((((((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : 52.66/7.24 a > a > $o]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y7 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y4 @ 52.66/7.24 Y6 @ 52.66/7.24 Y7) & 52.66/7.24 (Y4 @ 52.66/7.24 Y5 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52.66/7.24 (Y4 @ 52.66/7.24 Y2 @ Y3)))))))) => 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : 52.66/7.24 a > a > $o]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y5 @ 52.66/7.24 Y6) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y5 @ Y6))) => 52.66/7.24 (Y4 @ 52.66/7.24 Y5 @ Y6))))))))) & 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y7 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y4 @ 52.66/7.24 Y6 @ 52.66/7.24 Y7) & 52.66/7.24 (Y4 @ 52.66/7.24 Y5 @ Y6))) => 52.66/7.24 (Y4 @ 52.66/7.24 Y5 @ Y7)))))))))))))) => 52.66/7.24 (Y4 @ 52.66/7.24 Y2 @ Y3)))))))))))))) & 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (((( 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : 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52.66/7.24 Y5) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))))) => 52.66/7.24 (Y3 @ Y0 @ 52.66/7.24 Y2))))))))))))))))) 52.66/7.24 | (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ 52.66/7.24 Y1 @ Y2) & 52.66/7.24 (Y0 @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y0 @ Y1 @ 52.66/7.24 Y3)))))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((('#sk2' @ Y1 @ Y2) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))))) => 52.66/7.24 (Y0 @ '#sk6' @ '#sk7')))))))), 52.66/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 52.66/7.24 thf(zip_derived_cl26, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 ( (((((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((((X2 @ Y1 @ Y2) & (X2 @ 52.66/7.24 Y0 @ Y1))) => 52.66/7.24 (X2 @ Y0 @ Y2)))))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 52.66/7.24 (X2 @ '#sk6' @ '#sk7'))) 52.66/7.24 | (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk2' @ Y1 @ Y2) | 52.66/7.24 ('#sk1' @ Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ 52.66/7.24 Y1 @ Y2) & 52.66/7.24 (Y0 @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y0 @ Y1 @ 52.66/7.24 Y3)))))))))))))) => 52.66/7.24 (Y0 @ '#sk3' @ '#sk4')))))) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((((((!!) @ (^[Y3 : 52.66/7.24 a > a > $o]: 52.66/7.24 (((((( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) & 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ Y6))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))) & 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))))) => 52.66/7.24 (Y3 @ Y1 @ 52.66/7.24 Y2)))))) & 52.66/7.24 (((!!) @ (^[Y3 : 52.66/7.24 a > a > $o]: 52.66/7.24 (((((( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))) & 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ 52.66/7.24 Y6) & 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))))) => 52.66/7.24 (Y3 @ Y0 @ 52.66/7.24 Y1)))))))) => 52.66/7.24 (((!!) @ (^[Y3 : a > a > $o]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) & 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ Y6))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))))) => 52.66/7.24 (Y3 @ Y0 @ 52.66/7.24 Y2))))))))))))))))) 52.66/7.24 | (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ 52.66/7.24 Y1 @ Y2) & 52.66/7.24 (Y0 @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y0 @ Y1 @ 52.66/7.24 Y3)))))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((('#sk2' @ Y1 @ Y2) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))))) => 52.66/7.24 (Y0 @ '#sk6' @ '#sk7')))))))), 52.66/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 52.66/7.24 thf(zip_derived_cl37, plain, 52.66/7.24 ((~ ('#form19') 52.66/7.24 | (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk2' @ Y1 @ Y2) | 52.66/7.24 ('#sk1' @ Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ Y1 @ 52.66/7.24 Y2) & (Y0 @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y0 @ Y1 @ Y3)))))))))))))) => 52.66/7.24 (Y0 @ '#sk3' @ '#sk4')))))))), 52.66/7.24 define([status(thm)])). 52.66/7.24 thf(zip_derived_cl43, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 ( ('#form19') 52.66/7.24 | (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ 52.66/7.24 Y1 @ Y2) & 52.66/7.24 (Y0 @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y0 @ Y1 @ 52.66/7.24 Y3)))))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((('#sk2' @ Y1 @ Y2) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))))) => 52.66/7.24 (Y0 @ '#sk6' @ '#sk7')))))) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((((((!!) @ (^[Y3 : 52.66/7.24 a > a > $o]: 52.66/7.24 (((((( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) & 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ Y6))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))) & 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))))) => 52.66/7.24 (Y3 @ Y1 @ 52.66/7.24 Y2)))))) & 52.66/7.24 (((!!) @ (^[Y3 : 52.66/7.24 a > a > $o]: 52.66/7.24 (((((( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))) & 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ 52.66/7.24 Y6) & 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))))) => 52.66/7.24 (Y3 @ Y0 @ 52.66/7.24 Y1)))))))) => 52.66/7.24 (((!!) @ (^[Y3 : a > a > $o]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) & 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ Y6))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))))) => 52.66/7.24 (Y3 @ Y0 @ 52.66/7.24 Y2))))))))))))))))) 52.66/7.24 | (((((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((((X2 @ Y1 @ Y2) & 52.66/7.24 (X2 @ Y0 @ Y1))) => 52.66/7.24 (X2 @ Y0 @ Y2)))))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 52.66/7.24 (X2 @ '#sk6' @ '#sk7'))))), 52.66/7.24 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl37])). 52.66/7.24 thf(zip_derived_cl47, plain, 52.66/7.24 ((~ ('#form29') 52.66/7.24 | (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ Y1 @ 52.66/7.24 Y2) & (Y0 @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y0 @ Y1 @ Y3)))))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((('#sk2' @ Y1 @ Y2) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))))) => 52.66/7.24 (Y0 @ '#sk6' @ '#sk7')))))))), 52.66/7.24 define([status(thm)])). 52.66/7.24 thf(zip_derived_cl48, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 ( (((((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((((X2 @ Y0 @ Y1) & (X2 @ 52.66/7.24 Y1 @ Y2))) => 52.66/7.24 (X2 @ Y0 @ Y2)))))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 52.66/7.24 (X2 @ '#sk6' @ '#sk7'))) 52.66/7.24 | ~ ('#form29'))), 52.66/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl47])). 52.66/7.24 thf(zip_derived_cl59, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 (~ (((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((((X2 @ Y0 @ Y1) & (X2 @ 52.66/7.24 Y1 @ Y2))) => 52.66/7.24 (X2 @ Y0 @ Y2)))))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) 52.66/7.24 | (X2 @ '#sk6' @ '#sk7') 52.66/7.24 | ~ ('#form29'))), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 52.66/7.24 thf(zip_derived_cl66, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 (~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((((X2 @ Y0 @ Y1) & (X2 @ 52.66/7.24 Y1 @ Y2))) => 52.66/7.24 (X2 @ Y0 @ Y2)))))))))))) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 52.66/7.24 | ~ ('#form29') 52.66/7.24 | (X2 @ '#sk6' @ '#sk7'))), 52.66/7.24 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl59])). 52.66/7.24 thf(zip_derived_cl77, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 (~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((((X2 @ ('#sk105' @ X2) @ Y0) & (X2 @ 52.66/7.24 Y0 @ Y1))) => 52.66/7.24 (X2 @ ('#sk105' @ X2) @ Y1))))))))) 52.66/7.24 | (X2 @ '#sk6' @ '#sk7') 52.66/7.24 | ~ ('#form29') 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl66])). 52.66/7.24 thf(zip_derived_cl96, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 (~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((((X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) & (X2 @ 52.66/7.24 ('#sk139' @ X2) @ Y0))) => 52.66/7.24 (X2 @ ('#sk105' @ X2) @ Y0)))))) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 52.66/7.24 | ~ ('#form29') 52.66/7.24 | (X2 @ '#sk6' @ '#sk7'))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl77])). 52.66/7.24 thf(zip_derived_cl106, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 (~ (((((X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) & (X2 @ 52.66/7.24 ('#sk139' @ X2) @ ('#sk197' @ X2)))) => 52.66/7.24 (X2 @ ('#sk105' @ X2) @ ('#sk197' @ X2)))) 52.66/7.24 | (X2 @ '#sk6' @ '#sk7') 52.66/7.24 | ~ ('#form29') 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 52.66/7.24 thf(zip_derived_cl117, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 ( (((X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) & (X2 @ 52.66/7.24 ('#sk139' @ X2) @ ('#sk197' @ X2)))) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 52.66/7.24 | ~ ('#form29') 52.66/7.24 | (X2 @ '#sk6' @ '#sk7'))), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl106])). 52.66/7.24 thf(zip_derived_cl129, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 ( (X2 @ ('#sk139' @ X2) @ ('#sk197' @ X2)) 52.66/7.24 | (X2 @ '#sk6' @ '#sk7') 52.66/7.24 | ~ ('#form29') 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 52.66/7.24 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl117])). 52.66/7.24 thf(zip_derived_cl118, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 (~ (X2 @ ('#sk105' @ X2) @ ('#sk197' @ X2)) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 52.66/7.24 | ~ ('#form29') 52.66/7.24 | (X2 @ '#sk6' @ '#sk7'))), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl106])). 52.66/7.24 thf(zip_derived_cl130, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 ( ('#form337' @ X2) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 52.66/7.24 define([status(thm)])). 52.66/7.24 thf(zip_derived_cl145, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 (~ ('#form337' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 52.66/7.24 | ~ ('#form29') 52.66/7.24 | (X2 @ '#sk6' @ '#sk7') 52.66/7.24 | (X2 @ ('#sk139' @ X2) @ ('#sk197' @ X2)))), 52.66/7.24 inference('renaming', [status(thm)], 52.66/7.24 [zip_derived_cl129, zip_derived_cl130])). 52.66/7.24 thf(zip_derived_cl160, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 (~ ('#form337' @ X2) 52.66/7.24 | ~ ('#form29') 52.66/7.24 | (X2 @ '#sk6' @ '#sk7') 52.66/7.24 | (X2 @ ('#sk139' @ X2) @ ('#sk197' @ X2)))), 52.66/7.24 inference('ho_norm', [status(thm)], [zip_derived_cl145])). 52.66/7.24 thf(zip_derived_cl19, plain, 52.66/7.24 ((~ (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk1' @ Y1 @ Y2) | 52.66/7.24 ('#sk2' @ Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ Y2 @ 52.66/7.24 Y3) & (Y0 @ 52.66/7.24 Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y3)))))))))))))) => 52.66/7.24 (Y0 @ '#sk6' @ '#sk7')))))) 52.66/7.24 | (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk2' @ Y1 @ Y2) | 52.66/7.24 ('#sk1' @ Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ Y1 @ 52.66/7.24 Y2) & (Y0 @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y0 @ Y1 @ Y3)))))))))))))) => 52.66/7.24 (Y0 @ '#sk3' @ '#sk4')))))) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((((((!!) @ (^[Y3 : a > a > $o]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) & 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ Y6))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))))) => 52.66/7.24 (Y3 @ Y1 @ 52.66/7.24 Y2)))))) & 52.66/7.24 (((!!) @ (^[Y3 : a > a > $o]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ 52.66/7.24 Y6) & 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))))) => 52.66/7.24 (Y3 @ Y0 @ 52.66/7.24 Y1)))))))) => 52.66/7.24 (((!!) @ (^[Y3 : a > a > $o]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 ( 52.66/7.24 ( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) & 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ Y6))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 ( 52.66/7.24 ( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))))) => 52.66/7.24 (Y3 @ Y0 @ Y2))))))))))))))))))), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 52.66/7.24 thf(zip_derived_cl23, plain, 52.66/7.24 ((~ (((((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.24 Y1))) => 52.66/7.24 ('#sk8' @ Y0 @ Y1))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk8' @ Y1 @ Y2) & 52.66/7.24 ('#sk8' @ Y0 @ Y1))) => 52.66/7.24 ('#sk8' @ Y0 @ Y2)))))))))))))) => 52.66/7.24 ('#sk8' @ '#sk6' @ '#sk7'))) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((((((!!) @ (^[Y3 : a > a > $o]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) & 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ Y6))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))))) => 52.66/7.24 (Y3 @ Y1 @ 52.66/7.24 Y2)))))) & 52.66/7.24 (((!!) @ (^[Y3 : a > a > $o]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ 52.66/7.24 Y6) & 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))))) => 52.66/7.24 (Y3 @ Y0 @ 52.66/7.24 Y1)))))))) => 52.66/7.24 (((!!) @ (^[Y3 : a > a > $o]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 ( 52.66/7.24 ( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) & 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ Y6))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 ( 52.66/7.24 ( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))))) => 52.66/7.24 (Y3 @ Y0 @ Y2))))))))))))))))) 52.66/7.24 | (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk2' @ Y1 @ Y2) | 52.66/7.24 ('#sk1' @ Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ Y1 @ 52.66/7.24 Y2) & (Y0 @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y0 @ Y1 @ Y3)))))))))))))) => 52.66/7.24 (Y0 @ '#sk3' @ '#sk4')))))))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 52.66/7.24 thf(zip_derived_cl23, plain, 52.66/7.24 ((~ (((((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.24 Y1))) => 52.66/7.24 ('#sk8' @ Y0 @ Y1))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk8' @ Y1 @ Y2) & 52.66/7.24 ('#sk8' @ Y0 @ Y1))) => 52.66/7.24 ('#sk8' @ Y0 @ Y2)))))))))))))) => 52.66/7.24 ('#sk8' @ '#sk6' @ '#sk7'))) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((((((!!) @ (^[Y3 : a > a > $o]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) & 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ Y6))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))))) => 52.66/7.24 (Y3 @ Y1 @ 52.66/7.24 Y2)))))) & 52.66/7.24 (((!!) @ (^[Y3 : a > a > $o]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ 52.66/7.24 Y6) & 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))))) => 52.66/7.24 (Y3 @ Y0 @ 52.66/7.24 Y1)))))))) => 52.66/7.24 (((!!) @ (^[Y3 : a > a > $o]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 ( 52.66/7.24 ( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) & 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ Y6))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 ( 52.66/7.24 ( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))))) => 52.66/7.24 (Y3 @ Y0 @ Y2))))))))))))))))) 52.66/7.24 | (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk2' @ Y1 @ Y2) | 52.66/7.24 ('#sk1' @ Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ Y1 @ 52.66/7.24 Y2) & (Y0 @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y0 @ Y1 @ Y3)))))))))))))) => 52.66/7.24 (Y0 @ '#sk3' @ '#sk4')))))))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 52.66/7.24 thf(zip_derived_cl31, plain, 52.66/7.24 (( ('#form9') 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((((((!!) @ (^[Y3 : a > a > $o]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) & 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ Y6))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))))) => 52.66/7.24 (Y3 @ Y1 @ 52.66/7.24 Y2)))))) & 52.66/7.24 (((!!) @ (^[Y3 : a > a > $o]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ 52.66/7.24 Y6) & 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))))) => 52.66/7.24 (Y3 @ Y0 @ 52.66/7.24 Y1)))))))) => 52.66/7.24 (((!!) @ (^[Y3 : a > a > $o]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 ( 52.66/7.24 ( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) & 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ Y6))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 ( 52.66/7.24 ( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))))) => 52.66/7.24 (Y3 @ Y0 @ Y2))))))))))))))))))), 52.66/7.24 define([status(thm)])). 52.66/7.24 thf(zip_derived_cl33, plain, 52.66/7.24 ((~ ('#form9') 52.66/7.24 | (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk2' @ Y1 @ Y2) | 52.66/7.24 ('#sk1' @ Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ Y1 @ 52.66/7.24 Y2) & (Y0 @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y0 @ Y1 @ Y3)))))))))))))) => 52.66/7.24 (Y0 @ '#sk3' @ '#sk4')))))) 52.66/7.24 | ~ (((((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 52.66/7.24 Y0 @ Y1))) => 52.66/7.24 ('#sk8' @ Y0 @ Y1))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk8' @ Y1 @ Y2) & 52.66/7.24 ('#sk8' @ Y0 @ Y1))) => 52.66/7.24 ('#sk8' @ Y0 @ Y2)))))))))))))) => 52.66/7.24 ('#sk8' @ '#sk6' @ '#sk7'))))), 52.66/7.24 inference('renaming', [status(thm)], [zip_derived_cl23, zip_derived_cl31])). 52.66/7.24 thf(zip_derived_cl37, plain, 52.66/7.24 ((~ ('#form19') 52.66/7.24 | (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk2' @ Y1 @ Y2) | 52.66/7.24 ('#sk1' @ Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ Y1 @ 52.66/7.24 Y2) & (Y0 @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y0 @ Y1 @ Y3)))))))))))))) => 52.66/7.24 (Y0 @ '#sk3' @ '#sk4')))))))), 52.66/7.24 define([status(thm)])). 52.66/7.24 thf(zip_derived_cl44, plain, 52.66/7.24 (( ('#form19') 52.66/7.24 | ~ (((((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 52.66/7.24 Y0 @ Y1))) => 52.66/7.24 ('#sk8' @ Y0 @ Y1))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk8' @ Y1 @ Y2) & 52.66/7.24 ('#sk8' @ Y0 @ Y1))) => 52.66/7.24 ('#sk8' @ Y0 @ Y2)))))))))))))) => 52.66/7.24 ('#sk8' @ '#sk6' @ '#sk7'))) 52.66/7.24 | ~ ('#form9'))), 52.66/7.24 inference('renaming', [status(thm)], [zip_derived_cl33, zip_derived_cl37])). 52.66/7.24 thf(zip_derived_cl56, plain, 52.66/7.24 ((~ ('#sk8' @ '#sk6' @ '#sk7') | ~ ('#form9') | ('#form19'))), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 52.66/7.24 thf(zip_derived_cl118, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 (~ (X2 @ ('#sk105' @ X2) @ ('#sk197' @ X2)) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 52.66/7.24 | ~ ('#form29') 52.66/7.24 | (X2 @ '#sk6' @ '#sk7'))), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl106])). 52.66/7.24 thf(zip_derived_cl130, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 ( ('#form337' @ X2) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 52.66/7.24 define([status(thm)])). 52.66/7.24 thf(zip_derived_cl132, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 (~ ('#form337' @ X2) 52.66/7.24 | (X2 @ '#sk6' @ '#sk7') 52.66/7.24 | ~ ('#form29') 52.66/7.24 | ~ (X2 @ ('#sk105' @ X2) @ ('#sk197' @ X2)))), 52.66/7.24 inference('renaming', [status(thm)], 52.66/7.24 [zip_derived_cl118, zip_derived_cl130])). 52.66/7.24 thf(zip_derived_cl130, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 ( ('#form337' @ X2) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 52.66/7.24 define([status(thm)])). 52.66/7.24 thf(zip_derived_cl131, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 (~ (((!!) @ (^[Y0 : a]: 52.66/7.24 ((('#sk2' @ ('#sk338' @ X2) @ Y0) => (X2 @ 52.66/7.24 ('#sk338' @ X2) @ Y0)))))) 52.66/7.24 | ('#form337' @ X2))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl130])). 52.66/7.24 thf(zip_derived_cl146, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 (~ ((('#sk2' @ ('#sk338' @ X2) @ ('#sk435' @ X2)) => (X2 @ 52.66/7.24 ('#sk338' @ X2) @ ('#sk435' @ X2)))) 52.66/7.24 | ('#form337' @ X2))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl131])). 52.66/7.24 thf(zip_derived_cl161, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 ( ('#sk2' @ ('#sk338' @ X2) @ ('#sk435' @ X2)) | ('#form337' @ X2))), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl146])). 52.66/7.24 thf(zip_derived_cl128, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 ( (X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) 52.66/7.24 | (X2 @ '#sk6' @ '#sk7') 52.66/7.24 | ~ ('#form29') 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 52.66/7.24 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl117])). 52.66/7.24 thf(zip_derived_cl130, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 ( ('#form337' @ X2) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 52.66/7.24 define([status(thm)])). 52.66/7.24 thf(zip_derived_cl144, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 (~ ('#form337' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 52.66/7.24 | ~ ('#form29') 52.66/7.24 | (X2 @ '#sk6' @ '#sk7') 52.66/7.24 | (X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)))), 52.66/7.24 inference('renaming', [status(thm)], 52.66/7.24 [zip_derived_cl128, zip_derived_cl130])). 52.66/7.24 thf(zip_derived_cl159, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 (~ ('#form337' @ X2) 52.66/7.24 | ~ ('#form29') 52.66/7.24 | (X2 @ '#sk6' @ '#sk7') 52.66/7.24 | (X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)))), 52.66/7.24 inference('ho_norm', [status(thm)], [zip_derived_cl144])). 52.66/7.24 thf(zip_derived_cl55, plain, 52.66/7.24 (( (((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 52.66/7.24 ('#sk8' @ Y0 @ Y1))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk8' @ Y1 @ Y2) & 52.66/7.24 ('#sk8' @ Y0 @ Y1))) => 52.66/7.24 ('#sk8' @ Y0 @ Y2)))))))))))))) 52.66/7.24 | ~ ('#form9') 52.66/7.24 | ('#form19'))), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 52.66/7.24 thf(zip_derived_cl61, plain, 52.66/7.24 (( (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 52.66/7.24 ('#sk8' @ Y0 @ Y1))))))))) 52.66/7.24 | ('#form19') 52.66/7.24 | ~ ('#form9'))), 52.66/7.24 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 52.66/7.24 thf(zip_derived_cl68, plain, 52.66/7.24 (![X2 : a]: 52.66/7.24 ( (((!!) @ (^[Y0 : a]: 52.66/7.24 ((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) => 52.66/7.24 ('#sk8' @ X2 @ Y0)))))) 52.66/7.24 | ~ ('#form9') 52.66/7.24 | ('#form19'))), 52.66/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl61])). 52.66/7.24 thf(zip_derived_cl79, plain, 52.66/7.24 (![X2 : a, X4 : a]: 52.66/7.24 ( ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) => ('#sk8' @ X2 @ X4))) 52.66/7.24 | ('#form19') 52.66/7.24 | ~ ('#form9'))), 52.66/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl68])). 52.66/7.24 thf(zip_derived_cl99, plain, 52.66/7.24 (![X2 : a, X4 : a]: 52.66/7.24 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 52.66/7.24 | ('#sk8' @ X2 @ X4) 52.66/7.24 | ~ ('#form9') 52.66/7.24 | ('#form19'))), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])). 52.66/7.24 thf(zip_derived_cl110, plain, 52.66/7.24 (![X2 : a, X4 : a]: 52.66/7.24 (~ ('#sk2' @ X2 @ X4) 52.66/7.24 | ('#form19') 52.66/7.24 | ~ ('#form9') 52.66/7.24 | ('#sk8' @ X2 @ X4))), 52.66/7.24 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl99])). 52.66/7.24 thf(zip_derived_cl162, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 (~ (X2 @ ('#sk338' @ X2) @ ('#sk435' @ X2)) | ('#form337' @ X2))), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl146])). 52.66/7.24 thf(zip_derived_cl37, plain, 52.66/7.24 ((~ ('#form19') 52.66/7.24 | (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk2' @ Y1 @ Y2) | 52.66/7.24 ('#sk1' @ Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ Y1 @ 52.66/7.24 Y2) & (Y0 @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y0 @ Y1 @ Y3)))))))))))))) => 52.66/7.24 (Y0 @ '#sk3' @ '#sk4')))))))), 52.66/7.24 define([status(thm)])). 52.66/7.24 thf(zip_derived_cl38, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 ( (((((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.66/7.24 Y1))) => 52.66/7.24 (X2 @ Y0 @ Y1))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((((X2 @ Y0 @ Y1) & (X2 @ 52.66/7.24 Y1 @ Y2))) => 52.66/7.24 (X2 @ Y0 @ Y2)))))))))))))) => 52.66/7.24 (X2 @ '#sk3' @ '#sk4'))) 52.66/7.24 | ~ ('#form19'))), 52.66/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 52.66/7.24 thf(zip_derived_cl40, plain, 52.66/7.24 (( (((((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.66/7.24 Y1))) => 52.66/7.24 ('#sk5' @ Y0 @ Y1))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk5' @ Y0 @ Y1) & 52.66/7.24 ('#sk5' @ Y1 @ Y2))) => 52.66/7.24 ('#sk5' @ Y0 @ Y2)))))))))))))) => 52.66/7.24 ('#sk5' @ '#sk3' @ '#sk4'))) 52.66/7.24 | ~ ('#form19'))), 52.66/7.24 inference('triggered_bool_instantiation', [status(thm)], 52.66/7.24 [zip_derived_cl38])). 52.66/7.24 thf(zip_derived_cl6, plain, 52.66/7.24 (~ (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk2' @ Y1 @ Y2) | 52.66/7.24 ('#sk1' @ Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ Y2 @ 52.66/7.24 Y3) & (Y0 @ 52.66/7.24 Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y3)))))))))))))) => 52.66/7.24 (Y0 @ '#sk3' @ '#sk4'))))))), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 52.66/7.24 thf(zip_derived_cl8, plain, 52.66/7.24 (~ (((((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.66/7.24 Y1))) => 52.66/7.24 ('#sk5' @ Y0 @ Y1))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk5' @ Y1 @ Y2) & 52.66/7.24 ('#sk5' @ Y0 @ Y1))) => 52.66/7.24 ('#sk5' @ Y0 @ Y2)))))))))))))) => 52.66/7.24 ('#sk5' @ '#sk3' @ '#sk4')))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 52.66/7.24 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk3' @ '#sk4')), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 52.66/7.24 thf(zip_derived_cl310, plain, 52.66/7.24 (( (((((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.66/7.24 Y1))) => 52.66/7.24 ('#sk5' @ Y0 @ Y1))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk5' @ Y0 @ Y1) & 52.66/7.24 ('#sk5' @ Y1 @ Y2))) => 52.66/7.24 ('#sk5' @ Y0 @ Y2)))))))))))))) => 52.66/7.24 ($false))) 52.66/7.24 | ~ ('#form19'))), 52.66/7.24 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl11])). 52.66/7.24 thf(zip_derived_cl311, plain, 52.66/7.24 (( (((~) @ (((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.66/7.24 Y0 @ Y1))) => 52.66/7.24 ('#sk5' @ Y0 @ Y1))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk5' @ Y0 @ Y1) & 52.66/7.24 ('#sk5' @ Y1 @ Y2))) => 52.66/7.24 ('#sk5' @ Y0 @ Y2)))))))))))))))) 52.66/7.24 | ~ ('#form19'))), 52.66/7.24 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl310])). 52.66/7.24 thf(zip_derived_cl312, plain, 52.66/7.24 ((~ (((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 52.66/7.24 ('#sk5' @ Y0 @ Y1))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk5' @ Y0 @ Y1) & 52.66/7.24 ('#sk5' @ Y1 @ Y2))) => 52.66/7.24 ('#sk5' @ Y0 @ Y2)))))))))))))) 52.66/7.24 | ~ ('#form19'))), 52.66/7.24 inference('simplify nested equalities', [status(thm)], 52.66/7.24 [zip_derived_cl311])). 52.66/7.24 thf(zip_derived_cl313, plain, 52.66/7.24 ((~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 52.66/7.24 ('#sk5' @ Y0 @ Y1))))))))) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk5' @ Y0 @ Y1) & 52.66/7.24 ('#sk5' @ Y1 @ Y2))) => 52.66/7.24 ('#sk5' @ Y0 @ Y2)))))))))))) 52.66/7.24 | ~ ('#form19'))), 52.66/7.24 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl312])). 52.66/7.24 thf(zip_derived_cl314, plain, 52.66/7.24 ((~ (((!!) @ (^[Y0 : a]: 52.66/7.24 ((((('#sk2' @ ('#sk87' @ '#sk5') @ Y0) | ('#sk1' @ 52.66/7.24 ('#sk87' @ '#sk5') @ Y0))) => 52.66/7.24 ('#sk5' @ ('#sk87' @ '#sk5') @ Y0)))))) 52.66/7.24 | ~ ('#form19') 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk5' @ Y0 @ Y1) & 52.66/7.24 ('#sk5' @ Y1 @ Y2))) => 52.66/7.24 ('#sk5' @ Y0 @ Y2)))))))))))))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl313])). 52.66/7.24 thf(zip_derived_cl315, plain, 52.66/7.24 ((~ ((((('#sk2' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')) | ('#sk1' @ 52.66/7.24 ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')))) => 52.66/7.24 ('#sk5' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')))) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk5' @ Y0 @ Y1) & 52.66/7.24 ('#sk5' @ Y1 @ Y2))) => 52.66/7.24 ('#sk5' @ Y0 @ Y2)))))))))))) 52.66/7.24 | ~ ('#form19'))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl314])). 52.66/7.24 thf(zip_derived_cl316, plain, 52.66/7.24 (( ((('#sk2' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')) | ('#sk1' @ 52.66/7.24 ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')))) 52.66/7.24 | ~ ('#form19') 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk5' @ Y0 @ Y1) & 52.66/7.24 ('#sk5' @ Y1 @ Y2))) => 52.66/7.24 ('#sk5' @ Y0 @ Y2)))))))))))))), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl315])). 52.66/7.24 thf(zip_derived_cl318, plain, 52.66/7.24 (( ('#form1275') 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk5' @ Y0 @ Y1) & 52.66/7.24 ('#sk5' @ Y1 @ Y2))) => 52.66/7.24 ('#sk5' @ Y0 @ Y2)))))))))))))), 52.66/7.24 define([status(thm)])). 52.66/7.24 thf(zip_derived_cl319, plain, 52.66/7.24 ((~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk5' @ ('#sk105' @ '#sk5') @ Y0) & 52.66/7.24 ('#sk5' @ Y0 @ Y1))) => 52.66/7.24 ('#sk5' @ ('#sk105' @ '#sk5') @ Y1))))))))) 52.66/7.24 | ('#form1275'))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl318])). 52.66/7.24 thf(zip_derived_cl323, plain, 52.66/7.24 ((~ (((!!) @ (^[Y0 : a]: 52.66/7.24 ((((('#sk5' @ ('#sk105' @ '#sk5') @ 52.66/7.24 ('#sk139' @ '#sk5')) & ('#sk5' @ 52.66/7.24 ('#sk139' @ '#sk5') @ Y0))) => 52.66/7.24 ('#sk5' @ ('#sk105' @ '#sk5') @ Y0)))))) 52.66/7.24 | ('#form1275'))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl319])). 52.66/7.24 thf(zip_derived_cl324, plain, 52.66/7.24 ((~ ((((('#sk5' @ ('#sk105' @ '#sk5') @ ('#sk139' @ '#sk5')) & ('#sk5' @ 52.66/7.24 ('#sk139' @ '#sk5') @ ('#sk197' @ '#sk5')))) => 52.66/7.24 ('#sk5' @ ('#sk105' @ '#sk5') @ ('#sk197' @ '#sk5')))) 52.66/7.24 | ('#form1275'))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl323])). 52.66/7.24 thf(zip_derived_cl325, plain, 52.66/7.24 (( ((('#sk5' @ ('#sk105' @ '#sk5') @ ('#sk139' @ '#sk5')) & ('#sk5' @ 52.66/7.24 ('#sk139' @ '#sk5') @ ('#sk197' @ '#sk5')))) 52.66/7.24 | ('#form1275'))), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl324])). 52.66/7.24 thf(zip_derived_cl328, plain, 52.66/7.24 (( ('#sk5' @ ('#sk139' @ '#sk5') @ ('#sk197' @ '#sk5')) | ('#form1275'))), 52.66/7.24 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl325])). 52.66/7.24 thf(zip_derived_cl31, plain, 52.66/7.24 (( ('#form9') 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((((((!!) @ (^[Y3 : a > a > $o]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) & 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ Y6))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))))) => 52.66/7.24 (Y3 @ Y1 @ 52.66/7.24 Y2)))))) & 52.66/7.24 (((!!) @ (^[Y3 : a > a > $o]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ 52.66/7.24 Y6) & 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))))) => 52.66/7.24 (Y3 @ Y0 @ 52.66/7.24 Y1)))))))) => 52.66/7.24 (((!!) @ (^[Y3 : a > a > $o]: 52.66/7.24 (((((((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 ( 52.66/7.24 ( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) & 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ Y6))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))) & 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 ( 52.66/7.24 ( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))))) => 52.66/7.24 (Y3 @ Y0 @ Y2))))))))))))))))))), 52.66/7.24 define([status(thm)])). 52.66/7.24 thf(zip_derived_cl32, plain, 52.66/7.24 ((~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((((((!!) @ (^[Y2 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y3 : a]: 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 ( 52.66/7.24 ( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y2 @ 52.66/7.24 Y3 @ 52.66/7.24 Y4) & 52.66/7.24 (Y2 @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y2 @ 52.66/7.24 Y3 @ Y5)))))))))))) & 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 ( 52.66/7.24 ( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y3 @ 52.66/7.24 Y4) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y3 @ Y4))) => 52.66/7.24 (Y2 @ 52.66/7.24 Y3 @ Y4))))))))))) => 52.66/7.24 (Y2 @ Y0 @ Y1)))))) & 52.66/7.24 (((!!) @ (^[Y2 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y3 : a]: 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 ( 52.66/7.24 ( 52.66/7.24 (( 52.66/7.24 ('#sk2' @ 52.66/7.24 Y3 @ 52.66/7.24 Y4) | 52.66/7.24 ('#sk1' @ 52.66/7.24 Y3 @ Y4))) => 52.66/7.24 (Y2 @ 52.66/7.24 Y3 @ Y4))))))))) & 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 ( 52.66/7.24 ( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y2 @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) & 52.66/7.24 (Y2 @ 52.66/7.24 Y3 @ Y4))) => 52.66/7.24 (Y2 @ 52.66/7.24 Y3 @ Y5)))))))))))))) => 52.66/7.24 (Y2 @ '#sk10' @ Y0)))))))) => 52.66/7.24 (((!!) @ (^[Y2 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y3 : a]: 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y2 @ 52.66/7.24 Y3 @ 52.66/7.24 Y4) & 52.66/7.24 (Y2 @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y2 @ 52.66/7.24 Y3 @ Y5)))))))))))) & 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (((( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y3 @ 52.66/7.24 Y4) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y3 @ Y4))) => 52.66/7.24 (Y2 @ 52.66/7.24 Y3 @ Y4))))))))))) => 52.66/7.24 (Y2 @ '#sk10' @ Y1)))))))))))))) 52.66/7.24 | ('#form9'))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl31])). 52.66/7.24 thf(zip_derived_cl45, plain, 52.66/7.24 ((~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((((((!!) @ (^[Y1 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 ( 52.66/7.24 ( 52.66/7.24 (( 52.66/7.24 (Y1 @ 52.66/7.24 Y2 @ 52.66/7.24 Y3) & 52.66/7.24 (Y1 @ 52.66/7.24 Y3 @ Y4))) => 52.66/7.24 (Y1 @ 52.66/7.24 Y2 @ Y4)))))))))))) & 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 ((((('#sk1' @ 52.66/7.24 Y2 @ 52.66/7.24 Y3) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y1 @ Y2 @ 52.66/7.24 Y3))))))))))) => 52.66/7.24 (Y1 @ '#sk20' @ Y0)))))) & 52.66/7.24 (((!!) @ (^[Y1 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 ((((('#sk2' @ 52.66/7.24 Y2 @ 52.66/7.24 Y3) | 52.66/7.24 ('#sk1' @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y1 @ Y2 @ 52.66/7.24 Y3))))))))) & 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 ( 52.66/7.24 ( 52.66/7.24 (( 52.66/7.24 (Y1 @ 52.66/7.24 Y3 @ 52.66/7.24 Y4) & 52.66/7.24 (Y1 @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y1 @ 52.66/7.24 Y2 @ Y4)))))))))))))) => 52.66/7.24 (Y1 @ '#sk10' @ '#sk20')))))))) => 52.66/7.24 (((!!) @ (^[Y1 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (((( 52.66/7.24 (Y1 @ 52.66/7.24 Y2 @ 52.66/7.24 Y3) & 52.66/7.24 (Y1 @ 52.66/7.24 Y3 @ Y4))) => 52.66/7.24 (Y1 @ 52.66/7.24 Y2 @ Y4)))))))))))) & 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 ((((('#sk1' @ 52.66/7.24 Y2 @ Y3) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y1 @ Y2 @ 52.66/7.24 Y3))))))))))) => 52.66/7.24 (Y1 @ '#sk10' @ Y0))))))))))) 52.66/7.24 | ('#form9'))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl32])). 52.66/7.24 thf(zip_derived_cl57, plain, 52.66/7.24 ((~ (((((((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ 52.66/7.24 Y1 @ 52.66/7.24 Y2) & 52.66/7.24 (Y0 @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y0 @ Y1 @ 52.66/7.24 Y3)))))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk1' @ Y1 @ Y2) | 52.66/7.24 ('#sk2' @ Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))))) => 52.66/7.24 (Y0 @ '#sk20' @ '#sk38')))))) & 52.66/7.24 (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk2' @ Y1 @ Y2) | 52.66/7.24 ('#sk1' @ Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ 52.66/7.24 Y2 @ 52.66/7.24 Y3) & 52.66/7.24 (Y0 @ 52.66/7.24 Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ 52.66/7.24 Y3)))))))))))))) => 52.66/7.24 (Y0 @ '#sk10' @ '#sk20')))))))) => 52.66/7.24 (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ Y1 @ 52.66/7.24 Y2) & 52.66/7.24 (Y0 @ Y2 @ 52.66/7.24 Y3))) => 52.66/7.24 (Y0 @ Y1 @ 52.66/7.24 Y3)))))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk1' @ Y1 @ Y2) | 52.66/7.24 ('#sk2' @ Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))))) => 52.66/7.24 (Y0 @ '#sk10' @ '#sk38')))))))) 52.66/7.24 | ('#form9'))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl45])). 52.66/7.24 thf(zip_derived_cl63, plain, 52.66/7.24 (( (((((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ Y1 @ 52.66/7.24 Y2) & (Y0 @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y0 @ Y1 @ Y3)))))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk1' @ Y1 @ Y2) | 52.66/7.24 ('#sk2' @ Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))))) => 52.66/7.24 (Y0 @ '#sk20' @ '#sk38')))))) & 52.66/7.24 (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk2' @ Y1 @ Y2) | 52.66/7.24 ('#sk1' @ Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ Y2 @ 52.66/7.24 Y3) & (Y0 @ 52.66/7.24 Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y3)))))))))))))) => 52.66/7.24 (Y0 @ '#sk10' @ '#sk20')))))))) 52.66/7.24 | ('#form9'))), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 52.66/7.24 thf(zip_derived_cl71, plain, 52.66/7.24 (( (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk2' @ Y1 @ Y2) | 52.66/7.24 ('#sk1' @ Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ Y2 @ 52.66/7.24 Y3) & (Y0 @ 52.66/7.24 Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y3)))))))))))))) => 52.66/7.24 (Y0 @ '#sk10' @ '#sk20')))))) 52.66/7.24 | ('#form9'))), 52.66/7.24 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl63])). 52.66/7.24 thf(zip_derived_cl87, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 ( (((((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.66/7.24 Y1))) => 52.66/7.24 (X2 @ Y0 @ Y1))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((((X2 @ Y1 @ Y2) & (X2 @ 52.66/7.24 Y0 @ Y1))) => 52.66/7.24 (X2 @ Y0 @ Y2)))))))))))))) => 52.66/7.24 (X2 @ '#sk10' @ '#sk20'))) 52.66/7.24 | ('#form9'))), 52.66/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl71])). 52.66/7.24 thf(zip_derived_cl88, plain, 52.66/7.24 (( (((((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.66/7.24 Y1))) => 52.66/7.24 ('#sk88' @ Y0 @ Y1))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk88' @ Y1 @ Y2) & 52.66/7.24 ('#sk88' @ Y0 @ Y1))) => 52.66/7.24 ('#sk88' @ Y0 @ Y2)))))))))))))) => 52.66/7.24 ('#sk88' @ '#sk10' @ '#sk20'))) 52.66/7.24 | ('#form9'))), 52.66/7.24 inference('triggered_bool_instantiation', [status(thm)], 52.66/7.24 [zip_derived_cl87])). 52.66/7.24 thf(zip_derived_cl444, plain, 52.66/7.24 ((~ (((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 52.66/7.24 ('#sk88' @ Y0 @ Y1))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk88' @ Y1 @ Y2) & 52.66/7.24 ('#sk88' @ Y0 @ Y1))) => 52.66/7.24 ('#sk88' @ Y0 @ Y2)))))))))))))) 52.66/7.24 | ('#sk88' @ '#sk10' @ '#sk20') 52.66/7.24 | ('#form9'))), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl88])). 52.66/7.24 thf(zip_derived_cl445, plain, 52.66/7.24 ((~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 52.66/7.24 ('#sk88' @ Y0 @ Y1))))))))) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk88' @ Y1 @ Y2) & 52.66/7.24 ('#sk88' @ Y0 @ Y1))) => 52.66/7.24 ('#sk88' @ Y0 @ Y2)))))))))))) 52.66/7.24 | ('#form9') 52.66/7.24 | ('#sk88' @ '#sk10' @ '#sk20'))), 52.66/7.24 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl444])). 52.66/7.24 thf(zip_derived_cl446, plain, 52.66/7.24 ((~ (((!!) @ (^[Y0 : a]: 52.66/7.24 ((((('#sk2' @ ('#sk87' @ '#sk88') @ Y0) | ('#sk1' @ 52.66/7.24 ('#sk87' @ '#sk88') @ Y0))) => 52.66/7.24 ('#sk88' @ ('#sk87' @ '#sk88') @ Y0)))))) 52.66/7.24 | ('#sk88' @ '#sk10' @ '#sk20') 52.66/7.24 | ('#form9') 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk88' @ Y1 @ Y2) & 52.66/7.24 ('#sk88' @ Y0 @ Y1))) => 52.66/7.24 ('#sk88' @ Y0 @ Y2)))))))))))))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl445])). 52.66/7.24 thf(zip_derived_cl447, plain, 52.66/7.24 ((~ ((((('#sk2' @ ('#sk87' @ '#sk88') @ ('#sk119' @ '#sk88')) | 52.66/7.24 ('#sk1' @ ('#sk87' @ '#sk88') @ ('#sk119' @ '#sk88')))) => 52.66/7.24 ('#sk88' @ ('#sk87' @ '#sk88') @ ('#sk119' @ '#sk88')))) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk88' @ Y1 @ Y2) & 52.66/7.24 ('#sk88' @ Y0 @ Y1))) => 52.66/7.24 ('#sk88' @ Y0 @ Y2)))))))))))) 52.66/7.24 | ('#form9') 52.66/7.24 | ('#sk88' @ '#sk10' @ '#sk20'))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl446])). 52.66/7.24 thf(zip_derived_cl448, plain, 52.66/7.24 (( ((('#sk2' @ ('#sk87' @ '#sk88') @ ('#sk119' @ '#sk88')) | ('#sk1' @ 52.66/7.24 ('#sk87' @ '#sk88') @ ('#sk119' @ '#sk88')))) 52.66/7.24 | ('#sk88' @ '#sk10' @ '#sk20') 52.66/7.24 | ('#form9') 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk88' @ Y1 @ Y2) & 52.66/7.24 ('#sk88' @ Y0 @ Y1))) => 52.66/7.24 ('#sk88' @ Y0 @ Y2)))))))))))))), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl447])). 52.66/7.24 thf(zip_derived_cl450, plain, 52.66/7.24 (( ('#form1290') 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk88' @ Y1 @ Y2) & 52.66/7.24 ('#sk88' @ Y0 @ Y1))) => 52.66/7.24 ('#sk88' @ Y0 @ Y2)))))))))))))), 52.66/7.24 define([status(thm)])). 52.66/7.24 thf(zip_derived_cl451, plain, 52.66/7.24 ((~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((((('#sk88' @ Y0 @ Y1) & ('#sk88' @ 52.66/7.24 ('#sk128' @ '#sk88') @ Y0))) => 52.66/7.24 ('#sk88' @ ('#sk128' @ '#sk88') @ Y1))))))))) 52.66/7.24 | ('#form1290'))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl450])). 52.66/7.24 thf(zip_derived_cl455, plain, 52.66/7.24 ((~ (((!!) @ (^[Y0 : a]: 52.66/7.24 ((((('#sk88' @ ('#sk184' @ '#sk88') @ Y0) & ('#sk88' @ 52.66/7.24 ('#sk128' @ '#sk88') @ ('#sk184' @ '#sk88')))) => 52.66/7.24 ('#sk88' @ ('#sk128' @ '#sk88') @ Y0)))))) 52.66/7.24 | ('#form1290'))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl451])). 52.66/7.24 thf(zip_derived_cl456, plain, 52.66/7.24 ((~ ((((('#sk88' @ ('#sk184' @ '#sk88') @ ('#sk250' @ '#sk88')) & 52.66/7.24 ('#sk88' @ ('#sk128' @ '#sk88') @ ('#sk184' @ '#sk88')))) => 52.66/7.24 ('#sk88' @ ('#sk128' @ '#sk88') @ ('#sk250' @ '#sk88')))) 52.66/7.24 | ('#form1290'))), 52.66/7.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl455])). 52.66/7.24 thf(zip_derived_cl457, plain, 52.66/7.24 (( ((('#sk88' @ ('#sk184' @ '#sk88') @ ('#sk250' @ '#sk88')) & 52.66/7.24 ('#sk88' @ ('#sk128' @ '#sk88') @ ('#sk184' @ '#sk88')))) 52.66/7.24 | ('#form1290'))), 52.66/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl456])). 52.66/7.24 thf(zip_derived_cl460, plain, 52.66/7.24 (( ('#sk88' @ ('#sk128' @ '#sk88') @ ('#sk184' @ '#sk88')) 52.66/7.24 | ('#form1290'))), 52.66/7.24 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl457])). 52.66/7.24 thf(zip_derived_cl26, plain, 52.66/7.24 (![X2 : a > a > $o]: 52.66/7.24 ( (((((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((((X2 @ Y1 @ Y2) & (X2 @ 52.66/7.24 Y0 @ Y1))) => 52.66/7.24 (X2 @ Y0 @ Y2)))))))))))) & 52.66/7.24 (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 52.66/7.24 (X2 @ '#sk6' @ '#sk7'))) 52.66/7.24 | (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((((('#sk2' @ Y1 @ Y2) | 52.66/7.24 ('#sk1' @ Y1 @ Y2))) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ 52.66/7.24 Y1 @ Y2) & 52.66/7.24 (Y0 @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y0 @ Y1 @ 52.66/7.24 Y3)))))))))))))) => 52.66/7.24 (Y0 @ '#sk3' @ '#sk4')))))) 52.66/7.24 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((((((!!) @ (^[Y3 : 52.66/7.24 a > a > $o]: 52.66/7.24 (((((( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y6 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) & 52.66/7.24 (Y3 @ 52.66/7.24 Y5 @ Y6))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y6)))))))))))) & 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))))) => 52.66/7.24 (Y3 @ Y1 @ 52.66/7.24 Y2)))))) & 52.66/7.24 (((!!) @ (^[Y3 : 52.66/7.24 a > a > $o]: 52.66/7.24 (((((( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y4 : 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52.66/7.24 (((!!) @ ( 52.66/7.24 ^[Y4 : a]: 52.66/7.24 (( 52.66/7.24 (!!) @ ( 52.66/7.24 ^[Y5 : a]: 52.66/7.24 (( 52.66/7.24 (( 52.66/7.24 ('#sk1' @ 52.66/7.24 Y4 @ 52.66/7.24 Y5) | 52.66/7.24 ('#sk2' @ 52.66/7.24 Y4 @ Y5))) => 52.66/7.24 (Y3 @ 52.66/7.24 Y4 @ Y5))))))))))) => 52.66/7.24 (Y3 @ Y0 @ 52.66/7.24 Y2))))))))))))))))) 52.66/7.24 | (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.24 (((((((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 (((!!) @ (^[Y3 : a]: 52.66/7.24 (((((Y0 @ 52.66/7.24 Y1 @ Y2) & 52.66/7.24 (Y0 @ 52.66/7.24 Y2 @ Y3))) => 52.66/7.24 (Y0 @ Y1 @ 52.66/7.24 Y3)))))))))))) & 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ (^[Y2 : a]: 52.66/7.24 ((('#sk2' @ Y1 @ Y2) => 52.66/7.24 (Y0 @ Y1 @ Y2))))))))))) => 52.66/7.24 (Y0 @ '#sk6' @ '#sk7')))))))), 52.66/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 52.66/7.24 thf(zip_derived_cl27, plain, 52.66/7.24 (( (((((((!!) @ (^[Y0 : a]: 52.66/7.24 (((!!) @ (^[Y1 : a]: 52.66/7.24 (((!!) @ 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52.66/7.25 | ('#form19'))), 52.66/7.25 inference('renaming', [status(thm)], [zip_derived_cl43, zip_derived_cl47])). 52.66/7.25 thf(zip_derived_cl31, plain, 52.66/7.25 (( ('#form9') 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 (((((((!!) @ (^[Y3 : a > a > $o]: 52.66/7.25 (((((((!!) @ ( 52.66/7.25 ^[Y4 : a]: 52.66/7.25 (( 52.66/7.25 (!!) @ ( 52.66/7.25 ^[Y5 : a]: 52.66/7.25 (( 52.66/7.25 (!!) @ ( 52.66/7.25 ^[Y6 : a]: 52.66/7.25 (( 52.66/7.25 (( 52.66/7.25 (Y3 @ 52.66/7.25 Y4 @ 52.66/7.25 Y5) & 52.66/7.25 (Y3 @ 52.66/7.25 Y5 @ Y6))) => 52.66/7.25 (Y3 @ 52.66/7.25 Y4 @ Y6)))))))))))) & 52.66/7.25 (((!!) @ ( 52.66/7.25 ^[Y4 : a]: 52.66/7.25 (( 52.66/7.25 (!!) @ ( 52.66/7.25 ^[Y5 : a]: 52.66/7.25 (( 52.66/7.25 (( 52.66/7.25 ('#sk1' @ 52.66/7.25 Y4 @ 52.66/7.25 Y5) | 52.66/7.25 ('#sk2' @ 52.66/7.25 Y4 @ Y5))) => 52.66/7.25 (Y3 @ 52.66/7.25 Y4 @ Y5))))))))))) => 52.66/7.25 (Y3 @ Y1 @ 52.66/7.25 Y2)))))) & 52.66/7.25 (((!!) @ (^[Y3 : a > a > $o]: 52.66/7.25 (((((((!!) @ ( 52.66/7.25 ^[Y4 : a]: 52.66/7.25 (( 52.66/7.25 (!!) @ ( 52.66/7.25 ^[Y5 : a]: 52.66/7.25 (( 52.66/7.25 (( 52.66/7.25 ('#sk2' @ 52.66/7.25 Y4 @ 52.66/7.25 Y5) | 52.66/7.25 ('#sk1' @ 52.66/7.25 Y4 @ Y5))) => 52.66/7.25 (Y3 @ 52.66/7.25 Y4 @ Y5))))))))) & 52.66/7.25 (((!!) @ ( 52.66/7.25 ^[Y4 : a]: 52.66/7.25 (( 52.66/7.25 (!!) @ ( 52.66/7.25 ^[Y5 : a]: 52.66/7.25 (( 52.66/7.25 (!!) @ ( 52.66/7.25 ^[Y6 : a]: 52.66/7.25 (( 52.66/7.25 (( 52.66/7.25 (Y3 @ 52.66/7.25 Y5 @ 52.66/7.25 Y6) & 52.66/7.25 (Y3 @ 52.66/7.25 Y4 @ Y5))) => 52.66/7.25 (Y3 @ 52.66/7.25 Y4 @ Y6)))))))))))))) => 52.66/7.25 (Y3 @ Y0 @ 52.66/7.25 Y1)))))))) => 52.66/7.25 (((!!) @ (^[Y3 : a > a > $o]: 52.66/7.25 (((((((!!) @ ( 52.66/7.25 ^[Y4 : a]: 52.66/7.25 ( 52.66/7.25 ( 52.66/7.25 (!!) @ ( 52.66/7.25 ^[Y5 : a]: 52.66/7.25 (( 52.66/7.25 (!!) @ ( 52.66/7.25 ^[Y6 : a]: 52.66/7.25 (( 52.66/7.25 (( 52.66/7.25 (Y3 @ 52.66/7.25 Y4 @ 52.66/7.25 Y5) & 52.66/7.25 (Y3 @ 52.66/7.25 Y5 @ Y6))) => 52.66/7.25 (Y3 @ 52.66/7.25 Y4 @ Y6)))))))))))) & 52.66/7.25 (((!!) @ ( 52.66/7.25 ^[Y4 : a]: 52.66/7.25 ( 52.66/7.25 ( 52.66/7.25 (!!) @ ( 52.66/7.25 ^[Y5 : a]: 52.66/7.25 (( 52.66/7.25 (( 52.66/7.25 ('#sk1' @ 52.66/7.25 Y4 @ 52.66/7.25 Y5) | 52.66/7.25 ('#sk2' @ 52.66/7.25 Y4 @ Y5))) => 52.66/7.25 (Y3 @ 52.66/7.25 Y4 @ Y5))))))))))) => 52.66/7.25 (Y3 @ Y0 @ Y2))))))))))))))))))), 52.66/7.25 define([status(thm)])). 52.66/7.25 thf(zip_derived_cl58, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ ('#form9') 52.66/7.25 | ('#form19') 52.66/7.25 | (((((((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 (((((X2 @ Y1 @ Y2) & 52.66/7.25 (X2 @ Y0 @ Y1))) => 52.66/7.25 (X2 @ Y0 @ Y2)))))))))))) & 52.66/7.25 (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 52.66/7.25 (X2 @ '#sk6' @ '#sk7'))) 52.66/7.25 | ('#form29'))), 52.66/7.25 inference('renaming', [status(thm)], [zip_derived_cl53, zip_derived_cl31])). 52.66/7.25 thf(zip_derived_cl65, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ (((((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 (((((X2 @ Y1 @ Y2) & (X2 @ 52.66/7.25 Y0 @ Y1))) => 52.66/7.25 (X2 @ Y0 @ Y2)))))))))))) & 52.66/7.25 (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) 52.66/7.25 | (X2 @ '#sk6' @ '#sk7') 52.66/7.25 | ('#form29') 52.66/7.25 | ('#form19') 52.66/7.25 | ~ ('#form9'))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 52.66/7.25 thf(zip_derived_cl76, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 (((((X2 @ Y1 @ Y2) & (X2 @ 52.66/7.25 Y0 @ Y1))) => 52.66/7.25 (X2 @ Y0 @ Y2)))))))))))) 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 52.66/7.25 | ~ ('#form9') 52.66/7.25 | ('#form19') 52.66/7.25 | ('#form29') 52.66/7.25 | (X2 @ '#sk6' @ '#sk7'))), 52.66/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl65])). 52.66/7.25 thf(zip_derived_cl95, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((((X2 @ Y0 @ Y1) & (X2 @ 52.66/7.25 ('#sk128' @ X2) @ Y0))) => 52.66/7.25 (X2 @ ('#sk128' @ X2) @ Y1))))))))) 52.66/7.25 | (X2 @ '#sk6' @ '#sk7') 52.66/7.25 | ('#form29') 52.66/7.25 | ('#form19') 52.66/7.25 | ~ ('#form9') 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 52.66/7.25 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl76])). 52.66/7.25 thf(zip_derived_cl105, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((((X2 @ ('#sk184' @ X2) @ Y0) & (X2 @ 52.66/7.25 ('#sk128' @ X2) @ ('#sk184' @ X2)))) => 52.66/7.25 (X2 @ ('#sk128' @ X2) @ Y0)))))) 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 52.66/7.25 | ~ ('#form9') 52.66/7.25 | ('#form19') 52.66/7.25 | ('#form29') 52.66/7.25 | (X2 @ '#sk6' @ '#sk7'))), 52.66/7.25 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl95])). 52.66/7.25 thf(zip_derived_cl116, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ (((((X2 @ ('#sk184' @ X2) @ ('#sk250' @ X2)) & (X2 @ 52.66/7.25 ('#sk128' @ X2) @ ('#sk184' @ X2)))) => 52.66/7.25 (X2 @ ('#sk128' @ X2) @ ('#sk250' @ X2)))) 52.66/7.25 | (X2 @ '#sk6' @ '#sk7') 52.66/7.25 | ('#form29') 52.66/7.25 | ('#form19') 52.66/7.25 | ~ ('#form9') 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 52.66/7.25 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl105])). 52.66/7.25 thf(zip_derived_cl127, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ (X2 @ ('#sk128' @ X2) @ ('#sk250' @ X2)) 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 52.66/7.25 | ~ ('#form9') 52.66/7.25 | ('#form19') 52.66/7.25 | ('#form29') 52.66/7.25 | (X2 @ '#sk6' @ '#sk7'))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl116])). 52.66/7.25 thf(zip_derived_cl141, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 ( ('#form408' @ X2) 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 52.66/7.25 define([status(thm)])). 52.66/7.25 thf(zip_derived_cl230, plain, 52.66/7.25 ((~ ('#form408' @ '#sk8') 52.66/7.25 | ~ ('#form9') 52.66/7.25 | ('#form19') 52.66/7.25 | ('#form29') 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 ((((('#sk8' @ Y1 @ Y2) & 52.66/7.25 ('#sk8' @ Y0 @ Y1))) => 52.66/7.25 ('#sk8' @ Y0 @ Y2)))))))))))))), 52.66/7.25 inference('renaming', [status(thm)], 52.66/7.25 [zip_derived_cl229, zip_derived_cl141])). 52.66/7.25 thf(zip_derived_cl231, plain, 52.66/7.25 ((~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk8' @ Y0 @ Y1) & ('#sk8' @ 52.66/7.25 ('#sk128' @ '#sk8') @ Y0))) => 52.66/7.25 ('#sk8' @ ('#sk128' @ '#sk8') @ Y1))))))))) 52.66/7.25 | ('#form29') 52.66/7.25 | ('#form19') 52.66/7.25 | ~ ('#form9') 52.66/7.25 | ~ ('#form408' @ '#sk8'))), 52.66/7.25 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl230])). 52.66/7.25 thf(zip_derived_cl232, plain, 52.66/7.25 ((~ (((!!) @ (^[Y0 : a]: 52.66/7.25 ((((('#sk8' @ ('#sk184' @ '#sk8') @ Y0) & ('#sk8' @ 52.66/7.25 ('#sk128' @ '#sk8') @ ('#sk184' @ '#sk8')))) => 52.66/7.25 ('#sk8' @ ('#sk128' @ '#sk8') @ Y0)))))) 52.66/7.25 | ~ ('#form408' @ '#sk8') 52.66/7.25 | ~ ('#form9') 52.66/7.25 | ('#form19') 52.66/7.25 | ('#form29'))), 52.66/7.25 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl231])). 52.66/7.25 thf(zip_derived_cl233, plain, 52.66/7.25 ((~ ((((('#sk8' @ ('#sk184' @ '#sk8') @ ('#sk250' @ '#sk8')) & ('#sk8' @ 52.66/7.25 ('#sk128' @ '#sk8') @ ('#sk184' @ '#sk8')))) => 52.66/7.25 ('#sk8' @ ('#sk128' @ '#sk8') @ ('#sk250' @ '#sk8')))) 52.66/7.25 | ('#form29') 52.66/7.25 | ('#form19') 52.66/7.25 | ~ ('#form9') 52.66/7.25 | ~ ('#form408' @ '#sk8'))), 52.66/7.25 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl232])). 52.66/7.25 thf(zip_derived_cl235, plain, 52.66/7.25 ((~ ('#sk8' @ ('#sk128' @ '#sk8') @ ('#sk250' @ '#sk8')) 52.66/7.25 | ~ ('#form408' @ '#sk8') 52.66/7.25 | ~ ('#form9') 52.66/7.25 | ('#form19') 52.66/7.25 | ('#form29'))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl233])). 52.66/7.25 thf(zip_derived_cl327, plain, 52.66/7.25 (( ('#sk5' @ ('#sk105' @ '#sk5') @ ('#sk139' @ '#sk5')) | ('#form1275'))), 52.66/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl325])). 52.66/7.25 thf(zip_derived_cl326, plain, 52.66/7.25 ((~ ('#sk5' @ ('#sk105' @ '#sk5') @ ('#sk197' @ '#sk5')) | ('#form1275'))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl324])). 52.66/7.25 thf(zip_derived_cl316, plain, 52.66/7.25 (( ((('#sk2' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')) | ('#sk1' @ 52.66/7.25 ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')))) 52.66/7.25 | ~ ('#form19') 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 ((((('#sk5' @ Y0 @ Y1) & 52.66/7.25 ('#sk5' @ Y1 @ Y2))) => 52.66/7.25 ('#sk5' @ Y0 @ Y2)))))))))))))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl315])). 52.66/7.25 thf(zip_derived_cl318, plain, 52.66/7.25 (( ('#form1275') 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 ((((('#sk5' @ Y0 @ Y1) & 52.66/7.25 ('#sk5' @ Y1 @ Y2))) => 52.66/7.25 ('#sk5' @ Y0 @ Y2)))))))))))))), 52.66/7.25 define([status(thm)])). 52.66/7.25 thf(zip_derived_cl320, plain, 52.66/7.25 ((~ ('#form1275') 52.66/7.25 | ~ ('#form19') 52.66/7.25 | ((('#sk2' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')) | ('#sk1' @ 52.66/7.25 ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')))))), 52.66/7.25 inference('renaming', [status(thm)], 52.66/7.25 [zip_derived_cl316, zip_derived_cl318])). 52.66/7.25 thf(zip_derived_cl322, plain, 52.66/7.25 (( ('#sk2' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')) 52.66/7.25 | ('#sk1' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')) 52.66/7.25 | ~ ('#form19') 52.66/7.25 | ~ ('#form1275'))), 52.66/7.25 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl320])). 52.66/7.25 thf(zip_derived_cl458, plain, 52.66/7.25 ((~ ('#sk88' @ ('#sk128' @ '#sk88') @ ('#sk250' @ '#sk88')) 52.66/7.25 | ('#form1290'))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl456])). 52.66/7.25 thf(zip_derived_cl459, plain, 52.66/7.25 (( ('#sk88' @ ('#sk184' @ '#sk88') @ ('#sk250' @ '#sk88')) 52.66/7.25 | ('#form1290'))), 52.66/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl457])). 52.66/7.25 thf(zip_derived_cl448, plain, 52.66/7.25 (( ((('#sk2' @ ('#sk87' @ '#sk88') @ ('#sk119' @ '#sk88')) | ('#sk1' @ 52.66/7.25 ('#sk87' @ '#sk88') @ ('#sk119' @ '#sk88')))) 52.66/7.25 | ('#sk88' @ '#sk10' @ '#sk20') 52.66/7.25 | ('#form9') 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 ((((('#sk88' @ Y1 @ Y2) & 52.66/7.25 ('#sk88' @ Y0 @ Y1))) => 52.66/7.25 ('#sk88' @ Y0 @ Y2)))))))))))))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl447])). 52.66/7.25 thf(zip_derived_cl450, plain, 52.66/7.25 (( ('#form1290') 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 ((((('#sk88' @ Y1 @ Y2) & 52.66/7.25 ('#sk88' @ Y0 @ Y1))) => 52.66/7.25 ('#sk88' @ Y0 @ Y2)))))))))))))), 52.66/7.25 define([status(thm)])). 52.66/7.25 thf(zip_derived_cl452, plain, 52.66/7.25 ((~ ('#form1290') 52.66/7.25 | ('#form9') 52.66/7.25 | ('#sk88' @ '#sk10' @ '#sk20') 52.66/7.25 | ((('#sk2' @ ('#sk87' @ '#sk88') @ ('#sk119' @ '#sk88')) | ('#sk1' @ 52.66/7.25 ('#sk87' @ '#sk88') @ ('#sk119' @ '#sk88')))))), 52.66/7.25 inference('renaming', [status(thm)], 52.66/7.25 [zip_derived_cl448, zip_derived_cl450])). 52.66/7.25 thf(zip_derived_cl454, plain, 52.66/7.25 (( ('#sk2' @ ('#sk87' @ '#sk88') @ ('#sk119' @ '#sk88')) 52.66/7.25 | ('#sk1' @ ('#sk87' @ '#sk88') @ ('#sk119' @ '#sk88')) 52.66/7.25 | ('#sk88' @ '#sk10' @ '#sk20') 52.66/7.25 | ('#form9') 52.66/7.25 | ~ ('#form1290'))), 52.66/7.25 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl452])). 52.66/7.25 thf(zip_derived_cl64, plain, 52.66/7.25 ((~ (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.25 (((((((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 (((!!) @ (^[Y3 : a]: 52.66/7.25 (((((Y0 @ Y1 @ 52.66/7.25 Y2) & (Y0 @ 52.66/7.25 Y2 @ Y3))) => 52.66/7.25 (Y0 @ Y1 @ Y3)))))))))))) & 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 ((((('#sk1' @ Y1 @ Y2) | 52.66/7.25 ('#sk2' @ Y1 @ Y2))) => 52.66/7.25 (Y0 @ Y1 @ Y2))))))))))) => 52.66/7.25 (Y0 @ '#sk10' @ '#sk38')))))) 52.66/7.25 | ('#form9'))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 52.66/7.25 thf(zip_derived_cl75, plain, 52.66/7.25 ((~ (((((((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 ((((('#sk88' @ Y0 @ Y1) & 52.66/7.25 ('#sk88' @ Y1 @ Y2))) => 52.66/7.25 ('#sk88' @ Y0 @ Y2)))))))))))) & 52.66/7.25 (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.25 Y1))) => 52.66/7.25 ('#sk88' @ Y0 @ Y1))))))))))) => 52.66/7.25 ('#sk88' @ '#sk10' @ '#sk38'))) 52.66/7.25 | ('#form9'))), 52.66/7.25 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl64])). 52.66/7.25 thf(zip_derived_cl94, plain, 52.66/7.25 ((~ ('#sk88' @ '#sk10' @ '#sk38') | ('#form9'))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 52.66/7.25 thf(zip_derived_cl234, plain, 52.66/7.25 (( ((('#sk8' @ ('#sk184' @ '#sk8') @ ('#sk250' @ '#sk8')) & ('#sk8' @ 52.66/7.25 ('#sk128' @ '#sk8') @ ('#sk184' @ '#sk8')))) 52.66/7.25 | ~ ('#form408' @ '#sk8') 52.66/7.25 | ~ ('#form9') 52.66/7.25 | ('#form19') 52.66/7.25 | ('#form29'))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl233])). 52.66/7.25 thf(zip_derived_cl236, plain, 52.66/7.25 (( ('#sk8' @ ('#sk184' @ '#sk8') @ ('#sk250' @ '#sk8')) 52.66/7.25 | ('#form29') 52.66/7.25 | ('#form19') 52.66/7.25 | ~ ('#form9') 52.66/7.25 | ~ ('#form408' @ '#sk8'))), 52.66/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl234])). 52.66/7.25 thf(zip_derived_cl317, plain, 52.66/7.25 ((~ ('#sk5' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')) 52.66/7.25 | ~ ('#form19') 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 ((((('#sk5' @ Y0 @ Y1) & 52.66/7.25 ('#sk5' @ Y1 @ Y2))) => 52.66/7.25 ('#sk5' @ Y0 @ Y2)))))))))))))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl315])). 52.66/7.25 thf(zip_derived_cl318, plain, 52.66/7.25 (( ('#form1275') 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 ((((('#sk5' @ Y0 @ Y1) & 52.66/7.25 ('#sk5' @ Y1 @ Y2))) => 52.66/7.25 ('#sk5' @ Y0 @ Y2)))))))))))))), 52.66/7.25 define([status(thm)])). 52.66/7.25 thf(zip_derived_cl321, plain, 52.66/7.25 ((~ ('#form1275') 52.66/7.25 | ~ ('#form19') 52.66/7.25 | ~ ('#sk5' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')))), 52.66/7.25 inference('renaming', [status(thm)], 52.66/7.25 [zip_derived_cl317, zip_derived_cl318])). 52.66/7.25 thf(zip_derived_cl449, plain, 52.66/7.25 ((~ ('#sk88' @ ('#sk87' @ '#sk88') @ ('#sk119' @ '#sk88')) 52.66/7.25 | ('#sk88' @ '#sk10' @ '#sk20') 52.66/7.25 | ('#form9') 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 ((((('#sk88' @ Y1 @ Y2) & 52.66/7.25 ('#sk88' @ Y0 @ Y1))) => 52.66/7.25 ('#sk88' @ Y0 @ Y2)))))))))))))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl447])). 52.66/7.25 thf(zip_derived_cl450, plain, 52.66/7.25 (( ('#form1290') 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 ((((('#sk88' @ Y1 @ Y2) & 52.66/7.25 ('#sk88' @ Y0 @ Y1))) => 52.66/7.25 ('#sk88' @ Y0 @ Y2)))))))))))))), 52.66/7.25 define([status(thm)])). 52.66/7.25 thf(zip_derived_cl453, plain, 52.66/7.25 ((~ ('#form1290') 52.66/7.25 | ('#form9') 52.66/7.25 | ('#sk88' @ '#sk10' @ '#sk20') 52.66/7.25 | ~ ('#sk88' @ ('#sk87' @ '#sk88') @ ('#sk119' @ '#sk88')))), 52.66/7.25 inference('renaming', [status(thm)], 52.66/7.25 [zip_derived_cl449, zip_derived_cl450])). 52.66/7.25 thf(zip_derived_cl237, plain, 52.66/7.25 (( ('#sk8' @ ('#sk128' @ '#sk8') @ ('#sk184' @ '#sk8')) 52.66/7.25 | ('#form29') 52.66/7.25 | ('#form19') 52.66/7.25 | ~ ('#form9') 52.66/7.25 | ~ ('#form408' @ '#sk8'))), 52.66/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl234])). 52.66/7.25 thf(zip_derived_cl10, plain, 52.66/7.25 ( (((((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 52.66/7.25 ('#sk5' @ Y0 @ Y1))))))))) & 52.66/7.25 (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 ((((('#sk5' @ Y1 @ Y2) & 52.66/7.25 ('#sk5' @ Y0 @ Y1))) => 52.66/7.25 ('#sk5' @ Y0 @ Y2))))))))))))))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 52.66/7.25 thf(zip_derived_cl14, plain, 52.66/7.25 ( (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 ((((('#sk5' @ Y1 @ Y2) & ('#sk5' @ 52.66/7.25 Y0 @ Y1))) => 52.66/7.25 ('#sk5' @ Y0 @ Y2))))))))))))), 52.66/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 52.66/7.25 thf(zip_derived_cl17, plain, 52.66/7.25 (![X2 : a]: 52.66/7.25 (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk5' @ Y0 @ Y1) & ('#sk5' @ X2 @ Y0))) => 52.66/7.25 ('#sk5' @ X2 @ Y1)))))))))), 52.66/7.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 52.66/7.25 thf(zip_derived_cl21, plain, 52.66/7.25 (![X2 : a, X4 : a]: 52.66/7.25 (((!!) @ (^[Y0 : a]: 52.66/7.25 ((((('#sk5' @ X4 @ Y0) & ('#sk5' @ X2 @ X4))) => 52.66/7.25 ('#sk5' @ X2 @ Y0))))))), 52.66/7.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 52.66/7.25 thf(zip_derived_cl25, plain, 52.66/7.25 (![X2 : a, X4 : a, X6 : a]: 52.66/7.25 ((((('#sk5' @ X4 @ X6) & ('#sk5' @ X2 @ X4))) => ('#sk5' @ X2 @ X6)))), 52.66/7.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl21])). 52.66/7.25 thf(zip_derived_cl36, plain, 52.66/7.25 (![X2 : a, X4 : a, X6 : a]: 52.66/7.25 (~ ((('#sk5' @ X4 @ X6) & ('#sk5' @ X2 @ X4))) | ('#sk5' @ X2 @ X6))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 52.66/7.25 thf(zip_derived_cl46, plain, 52.66/7.25 (![X2 : a, X4 : a, X6 : a]: 52.66/7.25 (~ ('#sk5' @ X4 @ X6) | ~ ('#sk5' @ X2 @ X4) | ('#sk5' @ X2 @ X6))), 52.66/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl36])). 52.66/7.25 thf(zip_derived_cl13, plain, 52.66/7.25 ( (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 52.66/7.25 ('#sk5' @ Y0 @ Y1)))))))))), 52.66/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 52.66/7.25 thf(zip_derived_cl16, plain, 52.66/7.25 (![X2 : a]: 52.66/7.25 (((!!) @ (^[Y0 : a]: 52.66/7.25 ((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) => 52.66/7.25 ('#sk5' @ X2 @ Y0))))))), 52.66/7.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 52.66/7.25 thf(zip_derived_cl20, plain, 52.66/7.25 (![X2 : a, X4 : a]: 52.66/7.25 ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) => ('#sk5' @ X2 @ X4)))), 52.66/7.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 52.66/7.25 thf(zip_derived_cl24, plain, 52.66/7.25 (![X2 : a, X4 : a]: 52.66/7.25 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) | ('#sk5' @ X2 @ X4))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 52.66/7.25 thf(zip_derived_cl35, plain, 52.66/7.25 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 52.66/7.25 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl24])). 52.66/7.25 thf(zip_derived_cl34, plain, 52.66/7.25 (![X2 : a, X4 : a]: (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 52.66/7.25 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl24])). 52.66/7.25 thf(zip_derived_cl141, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 ( ('#form408' @ X2) 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 52.66/7.25 define([status(thm)])). 52.66/7.25 thf(zip_derived_cl142, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ (((!!) @ (^[Y0 : a]: 52.66/7.25 ((('#sk1' @ ('#sk409' @ X2) @ Y0) => (X2 @ 52.66/7.25 ('#sk409' @ X2) @ Y0)))))) 52.66/7.25 | ('#form408' @ X2))), 52.66/7.25 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl141])). 52.66/7.25 thf(zip_derived_cl158, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ ((('#sk1' @ ('#sk409' @ X2) @ ('#sk525' @ X2)) => (X2 @ 52.66/7.25 ('#sk409' @ X2) @ ('#sk525' @ X2)))) 52.66/7.25 | ('#form408' @ X2))), 52.66/7.25 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl142])). 52.66/7.25 thf(zip_derived_cl174, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 ( ('#sk1' @ ('#sk409' @ X2) @ ('#sk525' @ X2)) | ('#form408' @ X2))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])). 52.66/7.25 thf(zip_derived_cl62, plain, 52.66/7.25 (( (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 ((((('#sk8' @ Y1 @ Y2) & 52.66/7.25 ('#sk8' @ Y0 @ Y1))) => 52.66/7.25 ('#sk8' @ Y0 @ Y2)))))))))))) 52.66/7.25 | ('#form19') 52.66/7.25 | ~ ('#form9'))), 52.66/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 52.66/7.25 thf(zip_derived_cl69, plain, 52.66/7.25 (![X2 : a]: 52.66/7.25 ( (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk8' @ Y0 @ Y1) & ('#sk8' @ X2 @ Y0))) => 52.66/7.25 ('#sk8' @ X2 @ Y1))))))))) 52.66/7.25 | ~ ('#form9') 52.66/7.25 | ('#form19'))), 52.66/7.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl62])). 52.66/7.25 thf(zip_derived_cl80, plain, 52.66/7.25 (![X2 : a, X4 : a]: 52.66/7.25 ( (((!!) @ (^[Y0 : a]: 52.66/7.25 ((((('#sk8' @ X4 @ Y0) & ('#sk8' @ X2 @ X4))) => 52.66/7.25 ('#sk8' @ X2 @ Y0)))))) 52.66/7.25 | ('#form19') 52.66/7.25 | ~ ('#form9'))), 52.66/7.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl69])). 52.66/7.25 thf(zip_derived_cl100, plain, 52.66/7.25 (![X2 : a, X4 : a, X6 : a]: 52.66/7.25 ( ((((('#sk8' @ X4 @ X6) & ('#sk8' @ X2 @ X4))) => ('#sk8' @ X2 @ X6))) 52.66/7.25 | ~ ('#form9') 52.66/7.25 | ('#form19'))), 52.66/7.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl80])). 52.66/7.25 thf(zip_derived_cl111, plain, 52.66/7.25 (![X2 : a, X4 : a, X6 : a]: 52.66/7.25 (~ ((('#sk8' @ X4 @ X6) & ('#sk8' @ X2 @ X4))) 52.66/7.25 | ('#sk8' @ X2 @ X6) 52.66/7.25 | ('#form19') 52.66/7.25 | ~ ('#form9'))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 52.66/7.25 thf(zip_derived_cl121, plain, 52.66/7.25 (![X2 : a, X4 : a, X6 : a]: 52.66/7.25 (~ ('#sk8' @ X4 @ X6) 52.66/7.25 | ~ ('#sk8' @ X2 @ X4) 52.66/7.25 | ~ ('#form9') 52.66/7.25 | ('#form19') 52.66/7.25 | ('#sk8' @ X2 @ X6))), 52.66/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl111])). 52.66/7.25 thf(zip_derived_cl70, plain, 52.66/7.25 (( (((!!) @ (^[Y0 : a > a > $o]: 52.66/7.25 (((((((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 (((!!) @ (^[Y3 : a]: 52.66/7.25 (((((Y0 @ Y1 @ 52.66/7.25 Y2) & (Y0 @ 52.66/7.25 Y2 @ Y3))) => 52.66/7.25 (Y0 @ Y1 @ Y3)))))))))))) & 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 ((((('#sk1' @ Y1 @ Y2) | 52.66/7.25 ('#sk2' @ Y1 @ Y2))) => 52.66/7.25 (Y0 @ Y1 @ Y2))))))))))) => 52.66/7.25 (Y0 @ '#sk20' @ '#sk38')))))) 52.66/7.25 | ('#form9'))), 52.66/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl63])). 52.66/7.25 thf(zip_derived_cl81, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 ( (((((((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 (((((X2 @ Y0 @ Y1) & (X2 @ 52.66/7.25 Y1 @ Y2))) => 52.66/7.25 (X2 @ Y0 @ Y2)))))))))))) & 52.66/7.25 (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.25 Y1))) => 52.66/7.25 (X2 @ Y0 @ Y1))))))))))) => 52.66/7.25 (X2 @ '#sk20' @ '#sk38'))) 52.66/7.25 | ('#form9'))), 52.66/7.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl70])). 52.66/7.25 thf(zip_derived_cl101, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ (((((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 (((((X2 @ Y0 @ Y1) & (X2 @ 52.66/7.25 Y1 @ Y2))) => 52.66/7.25 (X2 @ Y0 @ Y2)))))))))))) & 52.66/7.25 (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.25 Y1))) => 52.66/7.25 (X2 @ Y0 @ Y1))))))))))) 52.66/7.25 | (X2 @ '#sk20' @ '#sk38') 52.66/7.25 | ('#form9'))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 52.66/7.25 thf(zip_derived_cl112, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 (((((X2 @ Y0 @ Y1) & (X2 @ 52.66/7.25 Y1 @ Y2))) => 52.66/7.25 (X2 @ Y0 @ Y2)))))))))))) 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.25 Y1))) => 52.66/7.25 (X2 @ Y0 @ Y1))))))))) 52.66/7.25 | ('#form9') 52.66/7.25 | (X2 @ '#sk20' @ '#sk38'))), 52.66/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl101])). 52.66/7.25 thf(zip_derived_cl122, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((((X2 @ ('#sk105' @ X2) @ Y0) & (X2 @ 52.66/7.25 Y0 @ Y1))) => 52.66/7.25 (X2 @ ('#sk105' @ X2) @ Y1))))))))) 52.66/7.25 | (X2 @ '#sk20' @ '#sk38') 52.66/7.25 | ('#form9') 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.25 Y1))) => 52.66/7.25 (X2 @ Y0 @ Y1))))))))))), 52.66/7.25 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl112])). 52.66/7.25 thf(zip_derived_cl135, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((((X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) & (X2 @ 52.66/7.25 ('#sk139' @ X2) @ Y0))) => 52.66/7.25 (X2 @ ('#sk105' @ X2) @ Y0)))))) 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.25 Y1))) => 52.66/7.25 (X2 @ Y0 @ Y1))))))))) 52.66/7.25 | ('#form9') 52.66/7.25 | (X2 @ '#sk20' @ '#sk38'))), 52.66/7.25 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl122])). 52.66/7.25 thf(zip_derived_cl150, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ (((((X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) & (X2 @ 52.66/7.25 ('#sk139' @ X2) @ ('#sk197' @ X2)))) => 52.66/7.25 (X2 @ ('#sk105' @ X2) @ ('#sk197' @ X2)))) 52.66/7.25 | (X2 @ '#sk20' @ '#sk38') 52.66/7.25 | ('#form9') 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.25 Y1))) => 52.66/7.25 (X2 @ Y0 @ Y1))))))))))), 52.66/7.25 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl135])). 52.66/7.25 thf(zip_derived_cl167, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 ( (((X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) & (X2 @ 52.66/7.25 ('#sk139' @ X2) @ ('#sk197' @ X2)))) 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.25 Y1))) => 52.66/7.25 (X2 @ Y0 @ Y1))))))))) 52.66/7.25 | ('#form9') 52.66/7.25 | (X2 @ '#sk20' @ '#sk38'))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl150])). 52.66/7.25 thf(zip_derived_cl178, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 ( (X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) 52.66/7.25 | (X2 @ '#sk20' @ '#sk38') 52.66/7.25 | ('#form9') 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.25 Y1))) => 52.66/7.25 (X2 @ Y0 @ Y1))))))))))), 52.66/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl167])). 52.66/7.25 thf(zip_derived_cl168, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ (X2 @ ('#sk105' @ X2) @ ('#sk197' @ X2)) 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.25 Y1))) => 52.66/7.25 (X2 @ Y0 @ Y1))))))))) 52.66/7.25 | ('#form9') 52.66/7.25 | (X2 @ '#sk20' @ '#sk38'))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl150])). 52.66/7.25 thf(zip_derived_cl180, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 ( ('#form744' @ X2) 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.25 Y1))) => 52.66/7.25 (X2 @ Y0 @ Y1))))))))))), 52.66/7.25 define([status(thm)])). 52.66/7.25 thf(zip_derived_cl185, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ ('#form744' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 52.66/7.25 | ('#form9') 52.66/7.25 | (X2 @ '#sk20' @ '#sk38') 52.66/7.25 | (X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)))), 52.66/7.25 inference('renaming', [status(thm)], 52.66/7.25 [zip_derived_cl178, zip_derived_cl180])). 52.66/7.25 thf(zip_derived_cl190, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ ('#form744' @ X2) 52.66/7.25 | ('#form9') 52.66/7.25 | (X2 @ '#sk20' @ '#sk38') 52.66/7.25 | (X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)))), 52.66/7.25 inference('ho_norm', [status(thm)], [zip_derived_cl185])). 52.66/7.25 thf(zip_derived_cl109, plain, 52.66/7.25 (![X2 : a, X4 : a]: 52.66/7.25 (~ ('#sk1' @ X2 @ X4) 52.66/7.25 | ('#form19') 52.66/7.25 | ~ ('#form9') 52.66/7.25 | ('#sk8' @ X2 @ X4))), 52.66/7.25 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl99])). 52.66/7.25 thf(zip_derived_cl175, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ (X2 @ ('#sk409' @ X2) @ ('#sk525' @ X2)) | ('#form408' @ X2))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])). 52.66/7.25 thf(zip_derived_cl168, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ (X2 @ ('#sk105' @ X2) @ ('#sk197' @ X2)) 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.25 Y1))) => 52.66/7.25 (X2 @ Y0 @ Y1))))))))) 52.66/7.25 | ('#form9') 52.66/7.25 | (X2 @ '#sk20' @ '#sk38'))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl150])). 52.66/7.25 thf(zip_derived_cl180, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 ( ('#form744' @ X2) 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.25 Y1))) => 52.66/7.25 (X2 @ Y0 @ Y1))))))))))), 52.66/7.25 define([status(thm)])). 52.66/7.25 thf(zip_derived_cl182, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ ('#form744' @ X2) 52.66/7.25 | (X2 @ '#sk20' @ '#sk38') 52.66/7.25 | ('#form9') 52.66/7.25 | ~ (X2 @ ('#sk105' @ X2) @ ('#sk197' @ X2)))), 52.66/7.25 inference('renaming', [status(thm)], 52.66/7.25 [zip_derived_cl168, zip_derived_cl180])). 52.66/7.25 thf(zip_derived_cl180, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 ( ('#form744' @ X2) 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.25 Y1))) => 52.66/7.25 (X2 @ Y0 @ Y1))))))))))), 52.66/7.25 define([status(thm)])). 52.66/7.25 thf(zip_derived_cl181, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ (((!!) @ (^[Y0 : a]: 52.66/7.25 ((((('#sk1' @ ('#sk745' @ X2) @ Y0) | ('#sk2' @ 52.66/7.25 ('#sk745' @ X2) @ Y0))) => 52.66/7.25 (X2 @ ('#sk745' @ X2) @ Y0)))))) 52.66/7.25 | ('#form744' @ X2))), 52.66/7.25 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl180])). 52.66/7.25 thf(zip_derived_cl187, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ ((((('#sk1' @ ('#sk745' @ X2) @ ('#sk835' @ X2)) | ('#sk2' @ 52.66/7.25 ('#sk745' @ X2) @ ('#sk835' @ X2)))) => 52.66/7.25 (X2 @ ('#sk745' @ X2) @ ('#sk835' @ X2)))) 52.66/7.25 | ('#form744' @ X2))), 52.66/7.25 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl181])). 52.66/7.25 thf(zip_derived_cl192, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 ( ((('#sk1' @ ('#sk745' @ X2) @ ('#sk835' @ X2)) | ('#sk2' @ 52.66/7.25 ('#sk745' @ X2) @ ('#sk835' @ X2)))) 52.66/7.25 | ('#form744' @ X2))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl187])). 52.66/7.25 thf(zip_derived_cl197, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 ( ('#sk1' @ ('#sk745' @ X2) @ ('#sk835' @ X2)) 52.66/7.25 | ('#sk2' @ ('#sk745' @ X2) @ ('#sk835' @ X2)) 52.66/7.25 | ('#form744' @ X2))), 52.66/7.25 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl192])). 52.66/7.25 thf(zip_derived_cl179, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 ( (X2 @ ('#sk139' @ X2) @ ('#sk197' @ X2)) 52.66/7.25 | (X2 @ '#sk20' @ '#sk38') 52.66/7.25 | ('#form9') 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.25 Y1))) => 52.66/7.25 (X2 @ Y0 @ Y1))))))))))), 52.66/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl167])). 52.66/7.25 thf(zip_derived_cl180, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 ( ('#form744' @ X2) 52.66/7.25 | ~ (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.66/7.25 Y1))) => 52.66/7.25 (X2 @ Y0 @ Y1))))))))))), 52.66/7.25 define([status(thm)])). 52.66/7.25 thf(zip_derived_cl186, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ ('#form744' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 52.66/7.25 | ('#form9') 52.66/7.25 | (X2 @ '#sk20' @ '#sk38') 52.66/7.25 | (X2 @ ('#sk139' @ X2) @ ('#sk197' @ X2)))), 52.66/7.25 inference('renaming', [status(thm)], 52.66/7.25 [zip_derived_cl179, zip_derived_cl180])). 52.66/7.25 thf(zip_derived_cl191, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ ('#form744' @ X2) 52.66/7.25 | ('#form9') 52.66/7.25 | (X2 @ '#sk20' @ '#sk38') 52.66/7.25 | (X2 @ ('#sk139' @ X2) @ ('#sk197' @ X2)))), 52.66/7.25 inference('ho_norm', [status(thm)], [zip_derived_cl186])). 52.66/7.25 thf(zip_derived_cl93, plain, 52.66/7.25 (( (((((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 ((((('#sk88' @ Y0 @ Y1) & 52.66/7.25 ('#sk88' @ Y1 @ Y2))) => 52.66/7.25 ('#sk88' @ Y0 @ Y2)))))))))))) & 52.66/7.25 (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 52.66/7.25 ('#sk88' @ Y0 @ Y1))))))))))) 52.66/7.25 | ('#form9'))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 52.66/7.25 thf(zip_derived_cl103, plain, 52.66/7.25 (( (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 (((!!) @ (^[Y2 : a]: 52.66/7.25 ((((('#sk88' @ Y0 @ Y1) & 52.66/7.25 ('#sk88' @ Y1 @ Y2))) => 52.66/7.25 ('#sk88' @ Y0 @ Y2)))))))))))) 52.66/7.25 | ('#form9'))), 52.66/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl93])). 52.66/7.25 thf(zip_derived_cl114, plain, 52.66/7.25 (![X2 : a]: 52.66/7.25 ( (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk88' @ X2 @ Y0) & ('#sk88' @ Y0 @ 52.66/7.25 Y1))) => 52.66/7.25 ('#sk88' @ X2 @ Y1))))))))) 52.66/7.25 | ('#form9'))), 52.66/7.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl103])). 52.66/7.25 thf(zip_derived_cl124, plain, 52.66/7.25 (![X2 : a, X4 : a]: 52.66/7.25 ( (((!!) @ (^[Y0 : a]: 52.66/7.25 ((((('#sk88' @ X2 @ X4) & ('#sk88' @ X4 @ Y0))) => 52.66/7.25 ('#sk88' @ X2 @ Y0)))))) 52.66/7.25 | ('#form9'))), 52.66/7.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl114])). 52.66/7.25 thf(zip_derived_cl137, plain, 52.66/7.25 (![X2 : a, X4 : a, X6 : a]: 52.66/7.25 ( ((((('#sk88' @ X2 @ X4) & ('#sk88' @ X4 @ X6))) => ('#sk88' @ X2 @ 52.66/7.25 X6))) 52.66/7.25 | ('#form9'))), 52.66/7.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl124])). 52.66/7.25 thf(zip_derived_cl153, plain, 52.66/7.25 (![X2 : a, X4 : a, X6 : a]: 52.66/7.25 (~ ((('#sk88' @ X2 @ X4) & ('#sk88' @ X4 @ X6))) 52.66/7.25 | ('#sk88' @ X2 @ X6) 52.66/7.25 | ('#form9'))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])). 52.66/7.25 thf(zip_derived_cl171, plain, 52.66/7.25 (![X2 : a, X4 : a, X6 : a]: 52.66/7.25 (~ ('#sk88' @ X2 @ X4) 52.66/7.25 | ~ ('#sk88' @ X4 @ X6) 52.66/7.25 | ('#form9') 52.66/7.25 | ('#sk88' @ X2 @ X6))), 52.66/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl153])). 52.66/7.25 thf(zip_derived_cl104, plain, 52.66/7.25 (( (((!!) @ (^[Y0 : a]: 52.66/7.25 (((!!) @ (^[Y1 : a]: 52.66/7.25 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 52.66/7.25 ('#sk88' @ Y0 @ Y1))))))))) 52.66/7.25 | ('#form9'))), 52.66/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl93])). 52.66/7.25 thf(zip_derived_cl115, plain, 52.66/7.25 (![X2 : a]: 52.66/7.25 ( (((!!) @ (^[Y0 : a]: 52.66/7.25 ((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) => 52.66/7.25 ('#sk88' @ X2 @ Y0)))))) 52.66/7.25 | ('#form9'))), 52.66/7.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl104])). 52.66/7.25 thf(zip_derived_cl125, plain, 52.66/7.25 (![X2 : a, X4 : a]: 52.66/7.25 ( ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) => ('#sk88' @ X2 @ X4))) 52.66/7.25 | ('#form9'))), 52.66/7.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl115])). 52.66/7.25 thf(zip_derived_cl138, plain, 52.66/7.25 (![X2 : a, X4 : a]: 52.66/7.25 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 52.66/7.25 | ('#sk88' @ X2 @ X4) 52.66/7.25 | ('#form9'))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])). 52.66/7.25 thf(zip_derived_cl154, plain, 52.66/7.25 (![X2 : a, X4 : a]: 52.66/7.25 (~ ('#sk1' @ X2 @ X4) | ('#form9') | ('#sk88' @ X2 @ X4))), 52.66/7.25 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl138])). 52.66/7.25 thf(zip_derived_cl155, plain, 52.66/7.25 (![X2 : a, X4 : a]: 52.66/7.25 (~ ('#sk2' @ X2 @ X4) | ('#form9') | ('#sk88' @ X2 @ X4))), 52.66/7.25 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl138])). 52.66/7.25 thf(zip_derived_cl193, plain, 52.66/7.25 (![X2 : a > a > $o]: 52.66/7.25 (~ (X2 @ ('#sk745' @ X2) @ ('#sk835' @ X2)) | ('#form744' @ X2))), 52.66/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl187])). 52.66/7.25 thf(zip_derived_cl8467, plain, ($false), 52.66/7.25 inference('eprover', [status(thm)], 52.66/7.25 [zip_derived_cl160, zip_derived_cl56, zip_derived_cl132, 52.66/7.25 zip_derived_cl161, zip_derived_cl159, zip_derived_cl110, 52.66/7.25 zip_derived_cl162, zip_derived_cl328, zip_derived_cl460, 52.66/7.25 zip_derived_cl235, zip_derived_cl327, zip_derived_cl326, 52.66/7.25 zip_derived_cl322, zip_derived_cl458, zip_derived_cl459, 52.66/7.25 zip_derived_cl454, zip_derived_cl94, zip_derived_cl236, 52.66/7.25 zip_derived_cl321, zip_derived_cl453, zip_derived_cl237, 52.66/7.25 zip_derived_cl46, zip_derived_cl35, zip_derived_cl34, 52.66/7.25 zip_derived_cl174, zip_derived_cl121, zip_derived_cl190, 52.66/7.25 zip_derived_cl109, zip_derived_cl175, zip_derived_cl182, 52.66/7.25 zip_derived_cl197, zip_derived_cl191, zip_derived_cl171, 52.66/7.25 zip_derived_cl154, zip_derived_cl155, zip_derived_cl193])). 52.66/7.25 52.66/7.25 % SZS output end Refutation 52.66/7.25 52.66/7.25 52.66/7.25 % Terminating... 52.66/7.29 % Runner terminated. 52.66/7.31 % Zipperpin 1.5 exiting 52.66/7.31 EOF