0.10/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.10MlgAx2N8 true 0.13/0.36 % Computer : n006.cluster.edu 0.13/0.36 % Model : x86_64 x86_64 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.36 % Memory : 8042.1875MB 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.36 % CPULimit : 1200 0.13/0.36 % WCLimit : 120 0.13/0.36 % DateTime : Tue Jul 13 10:53:41 EDT 2021 0.13/0.36 % CPUTime : 0.13/0.36 % Running portfolio for 120 s 0.13/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.36 % Number of cores: 8 0.13/0.37 % Python version: Python 3.6.8 0.13/0.37 % Running in HO mode 0.52/0.64 % Total configuration time : 828 0.52/0.64 % Estimated wc time : 983 0.52/0.64 % Estimated cpu time (8 cpus) : 122.875 0.52/0.68 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 47s 0.52/0.70 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 47s 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 47s 0.52/0.73 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 18s 0.52/0.73 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 53s 0.52/0.73 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 41s 0.52/0.74 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.52/0.75 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 35s 31.57/4.59 % Solved by lams/20_acsne_simpl.sh. 31.57/4.59 % running E: timeout 13 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.10MlgAx2N8/e_inputf2288e --cpu-limit=11 --auto -s -p 31.57/4.59 % done 476 iterations in 3.704s 31.57/4.59 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 31.57/4.59 % SZS output start Refutation 31.57/4.59 thf(a_type, type, a: $tType). 31.57/4.59 thf('#sk186_type', type, '#sk186': (a > a > $o) > a). 31.57/4.59 thf('#sk3_type', type, '#sk3': a). 31.57/4.59 thf('#form29_type', type, '#form29': $o). 31.57/4.59 thf('#sk139_type', type, '#sk139': (a > a > $o) > a). 31.57/4.59 thf('#sk2_type', type, '#sk2': a > a > $o). 31.57/4.59 thf('#sk199_type', type, '#sk199': (a > a > $o) > a). 31.57/4.59 thf('#sk258_type', type, '#sk258': (a > a > $o) > a). 31.57/4.59 thf('#sk20_type', type, '#sk20': a). 31.57/4.59 thf('#sk386_type', type, '#sk386': (a > a > $o) > a). 31.57/4.59 thf('#sk128_type', type, '#sk128': (a > a > $o) > a). 31.57/4.59 thf('#form633_type', type, '#form633': (a > a > $o) > $o). 31.57/4.59 thf('#sk313_type', type, '#sk313': (a > a > $o) > a). 31.57/4.59 thf('#sk5_type', type, '#sk5': a > a > $o). 31.57/4.59 thf('#form19_type', type, '#form19': $o). 31.57/4.59 thf('#sk1_type', type, '#sk1': a > a > $o). 31.57/4.59 thf('#sk7_type', type, '#sk7': a). 31.57/4.59 thf('#sk87_type', type, '#sk87': (a > a > $o) > a). 31.57/4.59 thf('#form9_type', type, '#form9': $o). 31.57/4.59 thf('#sk362_type', type, '#sk362': (a > a > $o) > a). 31.57/4.59 thf('#sk6_type', type, '#sk6': a). 31.57/4.59 thf('#sk247_type', type, '#sk247': (a > a > $o) > a). 31.57/4.59 thf('#sk119_type', type, '#sk119': (a > a > $o) > a). 31.57/4.59 thf('#form185_type', type, '#form185': (a > a > $o) > $o). 31.57/4.59 thf('#sk38_type', type, '#sk38': a). 31.57/4.59 thf('#sk8_type', type, '#sk8': a > a > $o). 31.57/4.59 thf('#form1067_type', type, '#form1067': $o). 31.57/4.59 thf('#form361_type', type, '#form361': (a > a > $o) > $o). 31.57/4.59 thf('#sk10_type', type, '#sk10': a). 31.57/4.59 thf('#sk4_type', type, '#sk4': a). 31.57/4.59 thf('#sk105_type', type, '#sk105': (a > a > $o) > a). 31.57/4.59 thf('#sk88_type', type, '#sk88': a > a > $o). 31.57/4.59 thf('#sk448_type', type, '#sk448': (a > a > $o) > a). 31.57/4.59 thf('#sk344_type', type, '#sk344': (a > a > $o) > a). 31.57/4.59 thf(cTHM250D_pme, conjecture, 31.57/4.59 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 31.57/4.59 ( ( ( ( ![Xx0:a,Xy0:a]: 31.57/4.59 ( ( ( ![Xp1:( a > a > $o )]: 31.57/4.59 ( ( ( ![Xx1:a,Xy1:a]: 31.57/4.59 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) & 31.57/4.59 ( ![Xx1:a,Xy1:a,Xz:a]: 31.57/4.59 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 31.57/4.59 ( ![Xp1:( a > a > $o )]: 31.57/4.59 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 31.57/4.59 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xz ) ) ) & 31.57/4.59 ( ![Xx1:a,Xy1:a]: 31.57/4.59 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 31.57/4.59 ( ![Xp1:( a > a > $o )]: 31.57/4.59 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 31.57/4.59 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xz ) ) ) & 31.57/4.59 ( ![Xx1:a,Xy1:a]: 31.57/4.59 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) & 31.57/4.59 ( ![Xx0:a,Xy0:a,Xz:a]: 31.57/4.59 ( ( ( ![Xp1:( a > a > $o )]: 31.57/4.59 ( ( ( ![Xx1:a,Xy1:a]: 31.57/4.59 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 31.57/4.59 ( ![Xx1:a,Xy1:a,Xz0:a]: 31.57/4.59 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 31.57/4.59 ( Xp1 @ Xy0 @ Xz ) ) ) & 31.57/4.59 ( ![Xp1:( a > a > $o )]: 31.57/4.59 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 31.57/4.59 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 31.57/4.59 ( ![Xx1:a,Xy1:a]: 31.57/4.59 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 31.57/4.59 ( ![Xp1:( a > a > $o )]: 31.57/4.59 ( ( ( ![Xx1:a,Xy1:a]: 31.57/4.59 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 31.57/4.59 ( ![Xx1:a,Xy1:a,Xz0:a]: 31.57/4.59 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) ) => 31.57/4.59 ( ![Xp1:( a > a > $o )]: 31.57/4.59 ( ( ( ![Xx0:a,Xy0:a]: 31.57/4.59 ( ( ( R @ Xx0 @ Xy0 ) | ( S @ Xx0 @ Xy0 ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 31.57/4.59 ( ![Xx0:a,Xy0:a,Xz:a]: 31.57/4.59 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 31.57/4.59 ( Xp1 @ Xx @ Xy ) ) ) ) => 31.57/4.59 ( ![Xp1:( a > a > $o )]: 31.57/4.59 ( ( ( ![Xx0:a,Xy0:a]: 31.57/4.59 ( ( ( R @ Xx0 @ Xy0 ) | ( S @ Xx0 @ Xy0 ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 31.57/4.59 ( ![Xx0:a,Xy0:a,Xz:a]: 31.57/4.59 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 31.57/4.59 ( Xp1 @ Xx @ Xy ) ) ) ))). 31.57/4.59 thf(zf_stmt_0, negated_conjecture, 31.57/4.59 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 31.57/4.59 ( ( ( ( ![Xx0:a,Xy0:a]: 31.57/4.59 ( ( ( ![Xp1:( a > a > $o )]: 31.57/4.59 ( ( ( ![Xx1:a,Xy1:a]: 31.57/4.59 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) & 31.57/4.59 ( ![Xx1:a,Xy1:a,Xz:a]: 31.57/4.59 ( ( ( Xp1 @ Xy1 @ Xz ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 31.57/4.59 ( ![Xp1:( a > a > $o )]: 31.57/4.59 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 31.57/4.59 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xz ) ) ) & 31.57/4.59 ( ![Xx1:a,Xy1:a]: 31.57/4.59 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 31.57/4.59 ( ![Xp1:( a > a > $o )]: 31.57/4.59 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 31.57/4.59 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xz ) ) ) & 31.57/4.59 ( ![Xx1:a,Xy1:a]: 31.57/4.59 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) & 31.57/4.59 ( ![Xx0:a,Xy0:a,Xz:a]: 31.57/4.59 ( ( ( ![Xp1:( a > a > $o )]: 31.57/4.59 ( ( ( ![Xx1:a,Xy1:a]: 31.57/4.59 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 31.57/4.59 ( ![Xx1:a,Xy1:a,Xz0:a]: 31.57/4.59 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 31.57/4.59 ( Xp1 @ Xy0 @ Xz ) ) ) & 31.57/4.59 ( ![Xp1:( a > a > $o )]: 31.57/4.59 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 31.57/4.59 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 31.57/4.59 ( ![Xx1:a,Xy1:a]: 31.57/4.59 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 31.57/4.59 ( ![Xp1:( a > a > $o )]: 31.57/4.59 ( ( ( ![Xx1:a,Xy1:a]: 31.57/4.59 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 31.57/4.59 ( ![Xx1:a,Xy1:a,Xz0:a]: 31.57/4.59 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 31.57/4.59 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) ) => 31.57/4.59 ( ![Xp1:( a > a > $o )]: 31.57/4.59 ( ( ( ![Xx0:a,Xy0:a]: 31.57/4.59 ( ( ( R @ Xx0 @ Xy0 ) | ( S @ Xx0 @ Xy0 ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 31.57/4.59 ( ![Xx0:a,Xy0:a,Xz:a]: 31.57/4.59 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 31.57/4.59 ( Xp1 @ Xx @ Xy ) ) ) ) => 31.57/4.59 ( ![Xp1:( a > a > $o )]: 31.57/4.59 ( ( ( ![Xx0:a,Xy0:a]: 31.57/4.59 ( ( ( R @ Xx0 @ Xy0 ) | ( S @ Xx0 @ Xy0 ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xy0 ) ) ) & 31.57/4.59 ( ![Xx0:a,Xy0:a,Xz:a]: 31.57/4.59 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 31.57/4.59 ( Xp1 @ Xx0 @ Xz ) ) ) ) => 31.57/4.59 ( Xp1 @ Xx @ Xy ) ) ) ) )), 31.57/4.59 inference('cnf.neg', [status(esa)], [cTHM250D_pme])). 31.57/4.59 thf(zip_derived_cl0, plain, 31.57/4.59 (~ (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.59 (((!!) @ (^[Y1 : a > a > $o]: 31.57/4.59 (((!!) @ (^[Y2 : a]: 31.57/4.59 (((!!) @ (^[Y3 : a]: 31.57/4.59 (((((((((!!) @ ( 31.57/4.59 ^[Y4 : a]: 31.57/4.59 (((!!) @ ( 31.57/4.59 ^[Y5 : a]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y6 : 31.57/4.59 a > a > $o]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y7 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y8 : a]: 31.57/4.59 (( 31.57/4.59 (Y0 @ 31.57/4.59 Y7 @ 31.57/4.59 Y8) => 31.57/4.59 (Y6 @ 31.57/4.59 Y7 @ Y8))))))))) & 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y7 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y8 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y9 : a]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (Y6 @ 31.57/4.59 Y8 @ 31.57/4.59 Y9) & 31.57/4.59 (Y6 @ 31.57/4.59 Y7 @ Y8))) => 31.57/4.59 (Y6 @ 31.57/4.59 Y7 @ Y9)))))))))))))) => 31.57/4.59 (Y6 @ 31.57/4.59 Y4 @ Y5)))))) | 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y6 : 31.57/4.59 a > a > $o]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y7 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y8 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y9 : a]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (Y6 @ 31.57/4.59 Y7 @ 31.57/4.59 Y8) & 31.57/4.59 (Y6 @ 31.57/4.59 Y8 @ Y9))) => 31.57/4.59 (Y6 @ 31.57/4.59 Y7 @ Y9)))))))))))) & 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y7 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y8 : a]: 31.57/4.59 (( 31.57/4.59 (Y1 @ 31.57/4.59 Y7 @ 31.57/4.59 Y8) => 31.57/4.59 (Y6 @ 31.57/4.59 Y7 @ Y8))))))))))) => 31.57/4.59 (Y6 @ 31.57/4.59 Y4 @ Y5)))))))) => 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y6 : 31.57/4.59 a > a > $o]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y7 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y8 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y9 : a]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (Y6 @ 31.57/4.59 Y7 @ 31.57/4.59 Y8) & 31.57/4.59 (Y6 @ 31.57/4.59 Y8 @ Y9))) => 31.57/4.59 (Y6 @ 31.57/4.59 Y7 @ Y9)))))))))))) & 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y7 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y8 : a]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (Y1 @ 31.57/4.59 Y7 @ 31.57/4.59 Y8) | 31.57/4.59 (Y0 @ 31.57/4.59 Y7 @ Y8))) => 31.57/4.59 (Y6 @ 31.57/4.59 Y7 @ Y8))))))))))) => 31.57/4.59 (Y6 @ 31.57/4.59 Y4 @ Y5)))))))))))))) & 31.57/4.59 (((!!) @ ( 31.57/4.59 ^[Y4 : a]: 31.57/4.59 (((!!) @ ( 31.57/4.59 ^[Y5 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y6 : a]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y7 : 31.57/4.59 a > a > $o]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y8 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y9 : a]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (Y1 @ 31.57/4.59 Y8 @ 31.57/4.59 Y9) | 31.57/4.59 (Y0 @ 31.57/4.59 Y8 @ Y9))) => 31.57/4.59 (Y7 @ 31.57/4.59 Y8 @ Y9))))))))) & 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y8 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y9 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y10 : a]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (Y7 @ 31.57/4.59 Y8 @ 31.57/4.59 Y9) & 31.57/4.59 (Y7 @ 31.57/4.59 Y9 @ Y10))) => 31.57/4.59 (Y7 @ 31.57/4.59 Y8 @ Y10)))))))))))))) => 31.57/4.59 (Y7 @ 31.57/4.59 Y5 @ Y6)))))) & 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y7 : 31.57/4.59 a > a > $o]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y8 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y9 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y10 : a]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (Y7 @ 31.57/4.59 Y8 @ 31.57/4.59 Y9) & 31.57/4.59 (Y7 @ 31.57/4.59 Y9 @ Y10))) => 31.57/4.59 (Y7 @ 31.57/4.59 Y8 @ Y10)))))))))))) & 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y8 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y9 : a]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (Y1 @ 31.57/4.59 Y8 @ 31.57/4.59 Y9) | 31.57/4.59 (Y0 @ 31.57/4.59 Y8 @ Y9))) => 31.57/4.59 (Y7 @ 31.57/4.59 Y8 @ Y9))))))))))) => 31.57/4.59 (Y7 @ 31.57/4.59 Y4 @ Y5)))))))) => 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y7 : 31.57/4.59 a > a > $o]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y8 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y9 : a]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (Y0 @ 31.57/4.59 Y8 @ 31.57/4.59 Y9) | 31.57/4.59 (Y1 @ 31.57/4.59 Y8 @ Y9))) => 31.57/4.59 (Y7 @ 31.57/4.59 Y8 @ Y9))))))))) & 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y8 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y9 : a]: 31.57/4.59 (( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y10 : a]: 31.57/4.59 (( 31.57/4.59 (( 31.57/4.59 (Y7 @ 31.57/4.59 Y8 @ 31.57/4.59 Y9) & 31.57/4.59 (Y7 @ 31.57/4.59 Y9 @ Y10))) => 31.57/4.59 (Y7 @ 31.57/4.59 Y8 @ Y10)))))))))))))) => 31.57/4.59 (Y7 @ 31.57/4.59 Y4 @ Y6))))))))))))))))))) => 31.57/4.59 (((!!) @ ( 31.57/4.59 ^[Y4 : a > a > $o]: 31.57/4.59 (((((( 31.57/4.59 (!!) @ ( 31.57/4.59 ^[Y5 : a]: 31.57/4.59 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y0 @ 31.57/4.60 Y5 @ 31.57/4.60 Y6) | 31.57/4.60 (Y1 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y6))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y4 @ 31.57/4.60 Y6 @ 31.57/4.60 Y7) & 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y7)))))))))))))) => 31.57/4.60 (Y4 @ Y2 @ 31.57/4.60 Y3)))))))) => 31.57/4.60 (((!!) @ (^[Y4 : 31.57/4.60 a > a > $o]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y0 @ 31.57/4.60 Y5 @ 31.57/4.60 Y6) | 31.57/4.60 (Y1 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y6))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ 31.57/4.60 Y6) & 31.57/4.60 (Y4 @ 31.57/4.60 Y6 @ Y7))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y7)))))))))))))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y2 @ Y3))))))))))))))))))))), 31.57/4.60 inference('cnf', [status(esa)], [zf_stmt_0])). 31.57/4.60 thf(zip_derived_cl1, plain, 31.57/4.60 (~ (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((((((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (((( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : 31.57/4.60 a > a > $o]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y6 @ 31.57/4.60 Y7) => 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ Y7))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y8 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y5 @ 31.57/4.60 Y7 @ 31.57/4.60 Y8) & 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ Y7))) => 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ Y8)))))))))))))) => 31.57/4.60 (Y5 @ 31.57/4.60 Y3 @ Y4)))))) | 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : 31.57/4.60 a > a > $o]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y8 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ 31.57/4.60 Y7) & 31.57/4.60 (Y5 @ 31.57/4.60 Y7 @ Y8))) => 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ Y8)))))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (Y0 @ 31.57/4.60 Y6 @ 31.57/4.60 Y7) => 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ Y7))))))))))) => 31.57/4.60 (Y5 @ 31.57/4.60 Y3 @ Y4)))))))) => 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : 31.57/4.60 a > a > $o]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y8 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ 31.57/4.60 Y7) & 31.57/4.60 (Y5 @ 31.57/4.60 Y7 @ Y8))) => 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ Y8)))))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y0 @ 31.57/4.60 Y6 @ 31.57/4.60 Y7) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y6 @ Y7))) => 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ Y7))))))))))) => 31.57/4.60 (Y5 @ 31.57/4.60 Y3 @ Y4)))))))))))))) & 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : 31.57/4.60 a > a > $o]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y8 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y0 @ 31.57/4.60 Y7 @ 31.57/4.60 Y8) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y7 @ Y8))) => 31.57/4.60 (Y6 @ 31.57/4.60 Y7 @ Y8))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y8 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y9 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y6 @ 31.57/4.60 Y7 @ 31.57/4.60 Y8) & 31.57/4.60 (Y6 @ 31.57/4.60 Y8 @ Y9))) => 31.57/4.60 (Y6 @ 31.57/4.60 Y7 @ Y9)))))))))))))) => 31.57/4.60 (Y6 @ 31.57/4.60 Y4 @ Y5)))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : 31.57/4.60 a > a > $o]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y8 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y9 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y6 @ 31.57/4.60 Y7 @ 31.57/4.60 Y8) & 31.57/4.60 (Y6 @ 31.57/4.60 Y8 @ Y9))) => 31.57/4.60 (Y6 @ 31.57/4.60 Y7 @ Y9)))))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y8 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y0 @ 31.57/4.60 Y7 @ 31.57/4.60 Y8) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y7 @ Y8))) => 31.57/4.60 (Y6 @ 31.57/4.60 Y7 @ Y8))))))))))) => 31.57/4.60 (Y6 @ 31.57/4.60 Y3 @ Y4)))))))) => 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : 31.57/4.60 a > a > $o]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y8 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y7 @ 31.57/4.60 Y8) | 31.57/4.60 (Y0 @ 31.57/4.60 Y7 @ Y8))) => 31.57/4.60 (Y6 @ 31.57/4.60 Y7 @ Y8))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y8 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y9 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y6 @ 31.57/4.60 Y7 @ 31.57/4.60 Y8) & 31.57/4.60 (Y6 @ 31.57/4.60 Y8 @ Y9))) => 31.57/4.60 (Y6 @ 31.57/4.60 Y7 @ Y9)))))))))))))) => 31.57/4.60 (Y6 @ 31.57/4.60 Y3 @ Y5))))))))))))))))))) => 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 (Y0 @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ 31.57/4.60 Y6) & 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y1 @ Y2)))))))) => 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 (Y0 @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y1 @ Y2)))))))))))))))))), 31.57/4.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 31.57/4.60 thf(zip_derived_cl2, plain, 31.57/4.60 (~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((((((((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : 31.57/4.60 a > a > $o]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y5 @ 31.57/4.60 Y6) => 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y6))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y4 @ 31.57/4.60 Y6 @ 31.57/4.60 Y7) & 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y7)))))))))))))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y2 @ Y3)))))) | 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : 31.57/4.60 a > a > $o]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ 31.57/4.60 Y6) & 31.57/4.60 (Y4 @ 31.57/4.60 Y6 @ Y7))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y7)))))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y5 @ 31.57/4.60 Y6) => 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y6))))))))))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y2 @ Y3)))))))) => 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : 31.57/4.60 a > a > $o]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ 31.57/4.60 Y6) & 31.57/4.60 (Y4 @ 31.57/4.60 Y6 @ Y7))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y7)))))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y5 @ 31.57/4.60 Y6) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y6))))))))))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y2 @ Y3)))))))))))))) & 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (((( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : 31.57/4.60 a > a > $o]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y6 @ 31.57/4.60 Y7) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y6 @ Y7))) => 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ Y7))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y8 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ 31.57/4.60 Y7) & 31.57/4.60 (Y5 @ 31.57/4.60 Y7 @ Y8))) => 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ Y8)))))))))))))) => 31.57/4.60 (Y5 @ 31.57/4.60 Y3 @ Y4)))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : 31.57/4.60 a > a > $o]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y8 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ 31.57/4.60 Y7) & 31.57/4.60 (Y5 @ 31.57/4.60 Y7 @ Y8))) => 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ Y8)))))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y6 @ 31.57/4.60 Y7) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y6 @ Y7))) => 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ Y7))))))))))) => 31.57/4.60 (Y5 @ 31.57/4.60 Y2 @ Y3)))))))) => 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : 31.57/4.60 a > a > $o]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y6 @ 31.57/4.60 Y7) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y6 @ Y7))) => 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ Y7))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y8 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ 31.57/4.60 Y7) & 31.57/4.60 (Y5 @ 31.57/4.60 Y7 @ Y8))) => 31.57/4.60 (Y5 @ 31.57/4.60 Y6 @ Y8)))))))))))))) => 31.57/4.60 (Y5 @ 31.57/4.60 Y2 @ Y4))))))))))))))))))) => 31.57/4.60 (((!!) @ (^[Y2 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y3 @ Y4))) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y4))))))))) & 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y2 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y4))) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y5)))))))))))))) => 31.57/4.60 (Y2 @ Y0 @ Y1)))))))) => 31.57/4.60 (((!!) @ (^[Y2 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (((( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y3 @ Y4) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y3 @ Y4))) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y4))))))))) & 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) & 31.57/4.60 (Y2 @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y5)))))))))))))) => 31.57/4.60 (Y2 @ Y0 @ Y1))))))))))))))), 31.57/4.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 31.57/4.60 thf(zip_derived_cl3, plain, 31.57/4.60 (~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((((!!) @ (^[Y3 : 31.57/4.60 a > a > $o]: 31.57/4.60 (((( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ 31.57/4.60 Y6) & 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y1 @ Y2)))))) | 31.57/4.60 (((!!) @ (^[Y3 : 31.57/4.60 a > a > $o]: 31.57/4.60 (((( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y1 @ Y2)))))))) => 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))))) => 31.57/4.60 (Y3 @ Y1 @ 31.57/4.60 Y2)))))))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : 31.57/4.60 a > a > $o]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y5 @ 31.57/4.60 Y6) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y6))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ 31.57/4.60 Y6) & 31.57/4.60 (Y4 @ 31.57/4.60 Y6 @ Y7))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y7)))))))))))))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y2 @ Y3)))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : 31.57/4.60 a > a > $o]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ 31.57/4.60 Y6) & 31.57/4.60 (Y4 @ 31.57/4.60 Y6 @ Y7))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y7)))))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y5 @ 31.57/4.60 Y6) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y6))))))))))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y1 @ Y2)))))))) => 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : 31.57/4.60 a > a > $o]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y5 @ 31.57/4.60 Y6) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y6))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y7 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ 31.57/4.60 Y6) & 31.57/4.60 (Y4 @ 31.57/4.60 Y6 @ Y7))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y5 @ Y7)))))))))))))) => 31.57/4.60 (Y4 @ 31.57/4.60 Y1 @ Y3))))))))))))))))))) => 31.57/4.60 (((!!) @ (^[Y1 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 ((((('#sk1' @ 31.57/4.60 Y2 @ Y3) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y2 @ Y3))) => 31.57/4.60 (Y1 @ Y2 @ 31.57/4.60 Y3))))))))) & 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y1 @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) & 31.57/4.60 (Y1 @ 31.57/4.60 Y2 @ Y3))) => 31.57/4.60 (Y1 @ 31.57/4.60 Y2 @ Y4)))))))))))))) => 31.57/4.60 (Y1 @ '#sk3' @ Y0)))))))) => 31.57/4.60 (((!!) @ (^[Y1 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 ((((('#sk1' @ 31.57/4.60 Y2 @ Y3) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y2 @ Y3))) => 31.57/4.60 (Y1 @ Y2 @ Y3))))))))) & 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (((( 31.57/4.60 (Y1 @ 31.57/4.60 Y2 @ Y3) & 31.57/4.60 (Y1 @ 31.57/4.60 Y3 @ Y4))) => 31.57/4.60 (Y1 @ 31.57/4.60 Y2 @ Y4)))))))))))))) => 31.57/4.60 (Y1 @ '#sk3' @ Y0)))))))))))), 31.57/4.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 31.57/4.60 thf(zip_derived_cl4, plain, 31.57/4.60 (~ (((((((((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((((((!!) @ (^[Y2 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y3 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y4))))))))) & 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y2 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y4))) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y5)))))))))))))) => 31.57/4.60 (Y2 @ Y0 @ Y1)))))) | 31.57/4.60 (((!!) @ (^[Y2 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y3 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) & 31.57/4.60 (Y2 @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y5)))))))))))) & 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y4))))))))))) => 31.57/4.60 (Y2 @ Y0 @ Y1)))))))) => 31.57/4.60 (((!!) @ (^[Y2 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y3 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) & 31.57/4.60 (Y2 @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y5)))))))))))) & 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y3 @ Y4))) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y4))))))))))) => 31.57/4.60 (Y2 @ Y0 @ Y1)))))))))))))) & 31.57/4.60 (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((((!!) @ (^[Y3 : 31.57/4.60 a > a > $o]: 31.57/4.60 (((( 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 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31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y0 @ Y1)))))))) => 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y0 @ 31.57/4.60 Y2))))))))))))))))))) => 31.57/4.60 (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.60 ('#sk2' @ Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ 31.57/4.60 Y2 @ Y3) & 31.57/4.60 (Y0 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ 31.57/4.60 Y3)))))))))))))) => 31.57/4.60 (Y0 @ '#sk3' @ '#sk4')))))))) => 31.57/4.60 (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.60 ('#sk2' @ Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ Y1 @ 31.57/4.60 Y2) & (Y0 @ 31.57/4.60 Y2 @ Y3))) => 31.57/4.60 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.60 (Y0 @ '#sk3' @ '#sk4'))))))))), 31.57/4.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 31.57/4.60 thf(zip_derived_cl5, plain, 31.57/4.60 ( (((((((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((((((!!) @ (^[Y2 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y4))))))))) & 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y2 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y4))) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y5)))))))))))))) => 31.57/4.60 (Y2 @ Y0 @ Y1)))))) | 31.57/4.60 (((!!) @ (^[Y2 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) & 31.57/4.60 (Y2 @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y5)))))))))))) & 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y4))))))))))) => 31.57/4.60 (Y2 @ Y0 @ Y1)))))))) => 31.57/4.60 (((!!) @ (^[Y2 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) & 31.57/4.60 (Y2 @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y5)))))))))))) & 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y3 @ Y4))) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y4))))))))))) => 31.57/4.60 (Y2 @ Y0 @ Y1)))))))))))))) & 31.57/4.60 (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y1 @ 31.57/4.60 Y2)))))) & 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 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(Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y1 @ 31.57/4.60 Y2)))))) & 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))))) => 31.57/4.60 (Y3 @ Y0 @ 31.57/4.60 Y1)))))))) => 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y0 @ Y2))))))))))))))))))) 31.57/4.60 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.60 ('#sk2' @ Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ Y2 @ 31.57/4.60 Y3) & (Y0 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.60 (Y0 @ '#sk3' @ '#sk4')))))))), 31.57/4.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 31.57/4.60 thf(zip_derived_cl9, plain, 31.57/4.60 ((~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((((((!!) @ (^[Y2 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y4))))))))) & 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y2 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y4))) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y5)))))))))))))) => 31.57/4.60 (Y2 @ Y0 @ Y1)))))) | 31.57/4.60 (((!!) @ (^[Y2 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) & 31.57/4.60 (Y2 @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y5)))))))))))) & 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y4))))))))))) => 31.57/4.60 (Y2 @ Y0 @ Y1)))))))) => 31.57/4.60 (((!!) @ (^[Y2 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) & 31.57/4.60 (Y2 @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y5)))))))))))) & 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (((( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y3 @ Y4))) => 31.57/4.60 (Y2 @ 31.57/4.60 Y3 @ Y4))))))))))) => 31.57/4.60 (Y2 @ Y0 @ Y1)))))))))))))) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y1 @ 31.57/4.60 Y2)))))) & 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))))) => 31.57/4.60 (Y3 @ Y0 @ 31.57/4.60 Y1)))))))) => 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y0 @ Y2))))))))))))))))) 31.57/4.60 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.60 ('#sk2' @ Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ Y2 @ 31.57/4.60 Y3) & (Y0 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.60 (Y0 @ '#sk3' @ '#sk4')))))))), 31.57/4.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl7])). 31.57/4.60 thf(zip_derived_cl12, plain, 31.57/4.60 ((~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((((((!!) @ (^[Y1 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 ((('#sk1' @ 31.57/4.60 Y2 @ Y3) => 31.57/4.60 (Y1 @ Y2 @ 31.57/4.60 Y3))))))))) & 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (( 31.57/4.60 (Y1 @ 31.57/4.60 Y3 @ 31.57/4.60 Y4) & 31.57/4.60 (Y1 @ 31.57/4.60 Y2 @ Y3))) => 31.57/4.60 (Y1 @ 31.57/4.60 Y2 @ Y4)))))))))))))) => 31.57/4.60 (Y1 @ '#sk6' @ Y0)))))) | 31.57/4.60 (((!!) @ (^[Y1 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (( 31.57/4.60 (Y1 @ 31.57/4.60 Y2 @ 31.57/4.60 Y3) & 31.57/4.60 (Y1 @ 31.57/4.60 Y3 @ Y4))) => 31.57/4.60 (Y1 @ 31.57/4.60 Y2 @ Y4)))))))))))) & 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 ((('#sk2' @ 31.57/4.60 Y2 @ Y3) => 31.57/4.60 (Y1 @ Y2 @ 31.57/4.60 Y3))))))))))) => 31.57/4.60 (Y1 @ '#sk6' @ Y0)))))))) => 31.57/4.60 (((!!) @ (^[Y1 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (((( 31.57/4.60 (Y1 @ 31.57/4.60 Y2 @ 31.57/4.60 Y3) & 31.57/4.60 (Y1 @ 31.57/4.60 Y3 @ Y4))) => 31.57/4.60 (Y1 @ 31.57/4.60 Y2 @ Y4)))))))))))) & 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 ((((('#sk2' @ 31.57/4.60 Y2 @ Y3) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y2 @ Y3))) => 31.57/4.60 (Y1 @ Y2 @ 31.57/4.60 Y3))))))))))) => 31.57/4.60 (Y1 @ '#sk6' @ Y0))))))))))) 31.57/4.60 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.60 ('#sk2' @ Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ Y2 @ 31.57/4.60 Y3) & (Y0 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.60 (Y0 @ '#sk3' @ '#sk4')))))) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y1 @ 31.57/4.60 Y2)))))) & 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))))) => 31.57/4.60 (Y3 @ Y0 @ 31.57/4.60 Y1)))))))) => 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y0 @ Y2))))))))))))))))))), 31.57/4.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl9])). 31.57/4.60 thf(zip_derived_cl15, plain, 31.57/4.60 ((~ (((((((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((('#sk1' @ Y1 @ Y2) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ 31.57/4.60 Y2 @ 31.57/4.60 Y3) & 31.57/4.60 (Y0 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ 31.57/4.60 Y3)))))))))))))) => 31.57/4.60 (Y0 @ '#sk6' @ '#sk7')))))) | 31.57/4.60 (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ 31.57/4.60 Y1 @ 31.57/4.60 Y2) & 31.57/4.60 (Y0 @ 31.57/4.60 Y2 @ Y3))) => 31.57/4.60 (Y0 @ Y1 @ 31.57/4.60 Y3)))))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((('#sk2' @ Y1 @ Y2) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.60 (Y0 @ '#sk6' @ '#sk7')))))))) => 31.57/4.60 (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ Y1 @ 31.57/4.60 Y2) & 31.57/4.60 (Y0 @ Y2 @ 31.57/4.60 Y3))) => 31.57/4.60 (Y0 @ Y1 @ 31.57/4.60 Y3)))))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((((('#sk2' @ Y1 @ Y2) | 31.57/4.60 ('#sk1' @ Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.60 (Y0 @ '#sk6' @ '#sk7')))))))) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y1 @ 31.57/4.60 Y2)))))) & 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))))) => 31.57/4.60 (Y3 @ Y0 @ 31.57/4.60 Y1)))))))) => 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y0 @ Y2))))))))))))))))) 31.57/4.60 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.60 ('#sk2' @ Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ Y2 @ 31.57/4.60 Y3) & (Y0 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.60 (Y0 @ '#sk3' @ '#sk4')))))))), 31.57/4.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 31.57/4.60 thf(zip_derived_cl18, plain, 31.57/4.60 (( (((((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((('#sk1' @ Y1 @ Y2) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ Y2 @ 31.57/4.60 Y3) & (Y0 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.60 (Y0 @ '#sk6' @ '#sk7')))))) | 31.57/4.60 (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ Y1 @ 31.57/4.60 Y2) & (Y0 @ 31.57/4.60 Y2 @ Y3))) => 31.57/4.60 (Y0 @ Y1 @ Y3)))))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((('#sk2' @ Y1 @ Y2) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.60 (Y0 @ '#sk6' @ '#sk7')))))))) 31.57/4.60 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.60 ('#sk2' @ Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ Y2 @ 31.57/4.60 Y3) & (Y0 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.60 (Y0 @ '#sk3' @ '#sk4')))))) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y1 @ 31.57/4.60 Y2)))))) & 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))))) => 31.57/4.60 (Y3 @ Y0 @ 31.57/4.60 Y1)))))))) => 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y0 @ Y2))))))))))))))))))), 31.57/4.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 31.57/4.60 thf(zip_derived_cl22, plain, 31.57/4.60 (( (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 31.57/4.60 Y1 @ Y2))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ Y2 @ 31.57/4.60 Y3) & (Y0 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.60 (Y0 @ '#sk6' @ '#sk7')))))) 31.57/4.60 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ Y1 @ 31.57/4.60 Y2) & (Y0 @ 31.57/4.60 Y2 @ Y3))) => 31.57/4.60 (Y0 @ Y1 @ Y3)))))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((('#sk2' @ Y1 @ Y2) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.60 (Y0 @ '#sk6' @ '#sk7')))))) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y1 @ 31.57/4.60 Y2)))))) & 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))))) => 31.57/4.60 (Y3 @ Y0 @ 31.57/4.60 Y1)))))))) => 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y0 @ Y2))))))))))))))))) 31.57/4.60 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.60 ('#sk2' @ Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ Y2 @ 31.57/4.60 Y3) & (Y0 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.60 (Y0 @ '#sk3' @ '#sk4')))))))), 31.57/4.60 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl18])). 31.57/4.60 thf(zip_derived_cl26, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 ( (((((((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 31.57/4.60 (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((X2 @ Y1 @ Y2) & (X2 @ 31.57/4.60 Y0 @ Y1))) => 31.57/4.60 (X2 @ Y0 @ Y2)))))))))))))) => 31.57/4.60 (X2 @ '#sk6' @ '#sk7'))) 31.57/4.60 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.60 ('#sk2' @ Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ 31.57/4.60 Y2 @ Y3) & 31.57/4.60 (Y0 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ 31.57/4.60 Y3)))))))))))))) => 31.57/4.60 (Y0 @ '#sk3' @ '#sk4')))))) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((((!!) @ (^[Y3 : 31.57/4.60 a > a > $o]: 31.57/4.60 (((((( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y1 @ 31.57/4.60 Y2)))))) & 31.57/4.60 (((!!) @ (^[Y3 : 31.57/4.60 a > a > $o]: 31.57/4.60 (((((( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))))) => 31.57/4.60 (Y3 @ Y0 @ 31.57/4.60 Y1)))))))) => 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y0 @ 31.57/4.60 Y2))))))))))))))))) 31.57/4.60 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ 31.57/4.60 Y1 @ Y2) & 31.57/4.60 (Y0 @ 31.57/4.60 Y2 @ Y3))) => 31.57/4.60 (Y0 @ Y1 @ 31.57/4.60 Y3)))))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((('#sk2' @ Y1 @ Y2) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.60 (Y0 @ '#sk6' @ '#sk7')))))))), 31.57/4.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 31.57/4.60 thf(zip_derived_cl26, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 ( (((((((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 31.57/4.60 (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((X2 @ Y1 @ Y2) & (X2 @ 31.57/4.60 Y0 @ Y1))) => 31.57/4.60 (X2 @ Y0 @ Y2)))))))))))))) => 31.57/4.60 (X2 @ '#sk6' @ '#sk7'))) 31.57/4.60 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.60 ('#sk2' @ Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ 31.57/4.60 Y2 @ Y3) & 31.57/4.60 (Y0 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ 31.57/4.60 Y3)))))))))))))) => 31.57/4.60 (Y0 @ '#sk3' @ '#sk4')))))) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((((!!) @ (^[Y3 : 31.57/4.60 a > a > $o]: 31.57/4.60 (((((( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y1 @ 31.57/4.60 Y2)))))) & 31.57/4.60 (((!!) @ (^[Y3 : 31.57/4.60 a > a > $o]: 31.57/4.60 (((((( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))))) => 31.57/4.60 (Y3 @ Y0 @ 31.57/4.60 Y1)))))))) => 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y0 @ 31.57/4.60 Y2))))))))))))))))) 31.57/4.60 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ 31.57/4.60 Y1 @ Y2) & 31.57/4.60 (Y0 @ 31.57/4.60 Y2 @ Y3))) => 31.57/4.60 (Y0 @ Y1 @ 31.57/4.60 Y3)))))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((('#sk2' @ Y1 @ Y2) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.60 (Y0 @ '#sk6' @ '#sk7')))))))), 31.57/4.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 31.57/4.60 thf(zip_derived_cl37, plain, 31.57/4.60 ((~ ('#form19') 31.57/4.60 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.60 ('#sk2' @ Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ Y2 @ 31.57/4.60 Y3) & (Y0 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.60 (Y0 @ '#sk3' @ '#sk4')))))))), 31.57/4.60 define([status(thm)])). 31.57/4.60 thf(zip_derived_cl43, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 ( ('#form19') 31.57/4.60 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ 31.57/4.60 Y1 @ Y2) & 31.57/4.60 (Y0 @ 31.57/4.60 Y2 @ Y3))) => 31.57/4.60 (Y0 @ Y1 @ 31.57/4.60 Y3)))))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((('#sk2' @ Y1 @ Y2) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.60 (Y0 @ '#sk6' @ '#sk7')))))) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((((!!) @ (^[Y3 : 31.57/4.60 a > a > $o]: 31.57/4.60 (((((( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y1 @ 31.57/4.60 Y2)))))) & 31.57/4.60 (((!!) @ (^[Y3 : 31.57/4.60 a > a > $o]: 31.57/4.60 (((((( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))) & 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))))) => 31.57/4.60 (Y3 @ Y0 @ 31.57/4.60 Y1)))))))) => 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y0 @ 31.57/4.60 Y2))))))))))))))))) 31.57/4.60 | (((((((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 31.57/4.60 (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((X2 @ Y1 @ Y2) & 31.57/4.60 (X2 @ Y0 @ Y1))) => 31.57/4.60 (X2 @ Y0 @ Y2)))))))))))))) => 31.57/4.60 (X2 @ '#sk6' @ '#sk7'))))), 31.57/4.60 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl37])). 31.57/4.60 thf(zip_derived_cl47, plain, 31.57/4.60 ((~ ('#form29') 31.57/4.60 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ Y1 @ 31.57/4.60 Y2) & (Y0 @ 31.57/4.60 Y2 @ Y3))) => 31.57/4.60 (Y0 @ Y1 @ Y3)))))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((('#sk2' @ Y1 @ Y2) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.60 (Y0 @ '#sk6' @ '#sk7')))))))), 31.57/4.60 define([status(thm)])). 31.57/4.60 thf(zip_derived_cl48, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 ( (((((((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((X2 @ Y0 @ Y1) & (X2 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (X2 @ Y0 @ Y2)))))))))))) & 31.57/4.60 (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 31.57/4.60 (X2 @ '#sk6' @ '#sk7'))) 31.57/4.60 | ~ ('#form29'))), 31.57/4.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl47])). 31.57/4.60 thf(zip_derived_cl59, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 (~ (((((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((X2 @ Y0 @ Y1) & (X2 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (X2 @ Y0 @ Y2)))))))))))) & 31.57/4.60 (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) 31.57/4.60 | (X2 @ '#sk6' @ '#sk7') 31.57/4.60 | ~ ('#form29'))), 31.57/4.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 31.57/4.60 thf(zip_derived_cl66, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 (~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((X2 @ Y0 @ Y1) & (X2 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (X2 @ Y0 @ Y2)))))))))))) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 31.57/4.60 | ~ ('#form29') 31.57/4.60 | (X2 @ '#sk6' @ '#sk7'))), 31.57/4.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl59])). 31.57/4.60 thf(zip_derived_cl77, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 (~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((((X2 @ ('#sk105' @ X2) @ Y0) & (X2 @ 31.57/4.60 Y0 @ Y1))) => 31.57/4.60 (X2 @ ('#sk105' @ X2) @ Y1))))))))) 31.57/4.60 | (X2 @ '#sk6' @ '#sk7') 31.57/4.60 | ~ ('#form29') 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 31.57/4.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl66])). 31.57/4.60 thf(zip_derived_cl96, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 (~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((((X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) & (X2 @ 31.57/4.60 ('#sk139' @ X2) @ Y0))) => 31.57/4.60 (X2 @ ('#sk105' @ X2) @ Y0)))))) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 31.57/4.60 | ~ ('#form29') 31.57/4.60 | (X2 @ '#sk6' @ '#sk7'))), 31.57/4.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl77])). 31.57/4.60 thf(zip_derived_cl108, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 (~ (((((X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) & (X2 @ 31.57/4.60 ('#sk139' @ X2) @ ('#sk199' @ X2)))) => 31.57/4.60 (X2 @ ('#sk105' @ X2) @ ('#sk199' @ X2)))) 31.57/4.60 | (X2 @ '#sk6' @ '#sk7') 31.57/4.60 | ~ ('#form29') 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 31.57/4.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 31.57/4.60 thf(zip_derived_cl121, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 (~ (X2 @ ('#sk105' @ X2) @ ('#sk199' @ X2)) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 31.57/4.60 | ~ ('#form29') 31.57/4.60 | (X2 @ '#sk6' @ '#sk7'))), 31.57/4.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 31.57/4.60 thf(zip_derived_cl121, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 (~ (X2 @ ('#sk105' @ X2) @ ('#sk199' @ X2)) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 31.57/4.60 | ~ ('#form29') 31.57/4.60 | (X2 @ '#sk6' @ '#sk7'))), 31.57/4.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 31.57/4.60 thf(zip_derived_cl135, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 ( ('#form361' @ X2) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 31.57/4.60 define([status(thm)])). 31.57/4.60 thf(zip_derived_cl137, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 (~ ('#form361' @ X2) 31.57/4.60 | (X2 @ '#sk6' @ '#sk7') 31.57/4.60 | ~ ('#form29') 31.57/4.60 | ~ (X2 @ ('#sk105' @ X2) @ ('#sk199' @ X2)))), 31.57/4.60 inference('renaming', [status(thm)], 31.57/4.60 [zip_derived_cl121, zip_derived_cl135])). 31.57/4.60 thf(zip_derived_cl120, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 ( (((X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) & (X2 @ 31.57/4.60 ('#sk139' @ X2) @ ('#sk199' @ X2)))) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 31.57/4.60 | ~ ('#form29') 31.57/4.60 | (X2 @ '#sk6' @ '#sk7'))), 31.57/4.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 31.57/4.60 thf(zip_derived_cl133, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 ( (X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) 31.57/4.60 | (X2 @ '#sk6' @ '#sk7') 31.57/4.60 | ~ ('#form29') 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 31.57/4.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl120])). 31.57/4.60 thf(zip_derived_cl135, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 ( ('#form361' @ X2) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 31.57/4.60 define([status(thm)])). 31.57/4.60 thf(zip_derived_cl144, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 (~ ('#form361' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 31.57/4.60 | ~ ('#form29') 31.57/4.60 | (X2 @ '#sk6' @ '#sk7') 31.57/4.60 | (X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)))), 31.57/4.60 inference('renaming', [status(thm)], 31.57/4.60 [zip_derived_cl133, zip_derived_cl135])). 31.57/4.60 thf(zip_derived_cl155, plain, 31.57/4.60 (![X2 : a > a > $o]: 31.57/4.60 (~ ('#form361' @ X2) 31.57/4.60 | ~ ('#form29') 31.57/4.60 | (X2 @ '#sk6' @ '#sk7') 31.57/4.60 | (X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)))), 31.57/4.60 inference('ho_norm', [status(thm)], [zip_derived_cl144])). 31.57/4.60 thf(zip_derived_cl19, plain, 31.57/4.60 ((~ (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ Y1 @ 31.57/4.60 Y2) & (Y0 @ 31.57/4.60 Y2 @ Y3))) => 31.57/4.60 (Y0 @ Y1 @ Y3)))))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((((('#sk2' @ Y1 @ Y2) | 31.57/4.60 ('#sk1' @ Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.60 (Y0 @ '#sk6' @ '#sk7')))))) 31.57/4.60 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.60 ('#sk2' @ Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ Y2 @ 31.57/4.60 Y3) & (Y0 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.60 (Y0 @ '#sk3' @ '#sk4')))))) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y1 @ 31.57/4.60 Y2)))))) & 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))))) => 31.57/4.60 (Y3 @ Y0 @ 31.57/4.60 Y1)))))))) => 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y0 @ Y2))))))))))))))))))), 31.57/4.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 31.57/4.60 thf(zip_derived_cl23, plain, 31.57/4.60 ((~ (((((((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((((('#sk8' @ Y0 @ Y1) & 31.57/4.60 ('#sk8' @ Y1 @ Y2))) => 31.57/4.60 ('#sk8' @ Y0 @ Y2)))))))))))) & 31.57/4.60 (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.57/4.60 Y1))) => 31.57/4.60 ('#sk8' @ Y0 @ Y1))))))))))) => 31.57/4.60 ('#sk8' @ '#sk6' @ '#sk7'))) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y1 @ 31.57/4.60 Y2)))))) & 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))))) => 31.57/4.60 (Y3 @ Y0 @ 31.57/4.60 Y1)))))))) => 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y0 @ Y2))))))))))))))))) 31.57/4.60 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.60 (((((((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.60 ('#sk2' @ Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((!!) @ (^[Y3 : a]: 31.57/4.60 (((((Y0 @ Y2 @ 31.57/4.60 Y3) & (Y0 @ 31.57/4.60 Y1 @ Y2))) => 31.57/4.60 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.60 (Y0 @ '#sk3' @ '#sk4')))))))), 31.57/4.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 31.57/4.60 thf(zip_derived_cl23, plain, 31.57/4.60 ((~ (((((((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 ((((('#sk8' @ Y0 @ Y1) & 31.57/4.60 ('#sk8' @ Y1 @ Y2))) => 31.57/4.60 ('#sk8' @ Y0 @ Y2)))))))))))) & 31.57/4.60 (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.57/4.60 Y1))) => 31.57/4.60 ('#sk8' @ Y0 @ Y1))))))))))) => 31.57/4.60 ('#sk8' @ '#sk6' @ '#sk7'))) 31.57/4.60 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.60 (((!!) @ (^[Y1 : a]: 31.57/4.60 (((!!) @ (^[Y2 : a]: 31.57/4.60 (((((((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))))) => 31.57/4.60 (Y3 @ Y1 @ 31.57/4.60 Y2)))))) & 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y6 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) & 31.57/4.60 (Y3 @ 31.57/4.60 Y5 @ Y6))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y6)))))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 (( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))))) => 31.57/4.60 (Y3 @ Y0 @ 31.57/4.60 Y1)))))))) => 31.57/4.60 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.60 (((((((!!) @ ( 31.57/4.60 ^[Y4 : a]: 31.57/4.60 ( 31.57/4.60 ( 31.57/4.60 (!!) @ ( 31.57/4.60 ^[Y5 : a]: 31.57/4.60 (( 31.57/4.60 (( 31.57/4.60 ('#sk1' @ 31.57/4.60 Y4 @ 31.57/4.60 Y5) | 31.57/4.60 ('#sk2' @ 31.57/4.60 Y4 @ Y5))) => 31.57/4.60 (Y3 @ 31.57/4.60 Y4 @ Y5))))))))) & 31.57/4.60 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y0 @ Y2))))))))))))))))) 31.57/4.61 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.61 ('#sk2' @ Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ Y2 @ 31.57/4.61 Y3) & (Y0 @ 31.57/4.61 Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.61 (Y0 @ '#sk3' @ '#sk4')))))))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 31.57/4.61 thf(zip_derived_cl31, plain, 31.57/4.61 (( ('#form9') 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y1 @ 31.57/4.61 Y2)))))) & 31.57/4.61 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))))) => 31.57/4.61 (Y3 @ Y0 @ 31.57/4.61 Y1)))))))) => 31.57/4.61 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y0 @ Y2))))))))))))))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl33, plain, 31.57/4.61 ((~ ('#form9') 31.57/4.61 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.61 ('#sk2' @ Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ Y2 @ 31.57/4.61 Y3) & (Y0 @ 31.57/4.61 Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.61 (Y0 @ '#sk3' @ '#sk4')))))) 31.57/4.61 | ~ (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk8' @ Y0 @ Y1) & 31.57/4.61 ('#sk8' @ Y1 @ Y2))) => 31.57/4.61 ('#sk8' @ Y0 @ Y2)))))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 31.57/4.61 Y0 @ Y1))) => 31.57/4.61 ('#sk8' @ Y0 @ Y1))))))))))) => 31.57/4.61 ('#sk8' @ '#sk6' @ '#sk7'))))), 31.57/4.61 inference('renaming', [status(thm)], [zip_derived_cl23, zip_derived_cl31])). 31.57/4.61 thf(zip_derived_cl37, plain, 31.57/4.61 ((~ ('#form19') 31.57/4.61 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.61 ('#sk2' @ Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ Y2 @ 31.57/4.61 Y3) & (Y0 @ 31.57/4.61 Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.61 (Y0 @ '#sk3' @ '#sk4')))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl44, plain, 31.57/4.61 (( ('#form19') 31.57/4.61 | ~ (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk8' @ Y0 @ Y1) & 31.57/4.61 ('#sk8' @ Y1 @ Y2))) => 31.57/4.61 ('#sk8' @ Y0 @ Y2)))))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 31.57/4.61 Y0 @ Y1))) => 31.57/4.61 ('#sk8' @ Y0 @ Y1))))))))))) => 31.57/4.61 ('#sk8' @ '#sk6' @ '#sk7'))) 31.57/4.61 | ~ ('#form9'))), 31.57/4.61 inference('renaming', [status(thm)], [zip_derived_cl33, zip_derived_cl37])). 31.57/4.61 thf(zip_derived_cl56, plain, 31.57/4.61 ((~ ('#sk8' @ '#sk6' @ '#sk7') | ~ ('#form9') | ('#form19'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 31.57/4.61 thf(zip_derived_cl135, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( ('#form361' @ X2) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl136, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ (((!!) @ (^[Y0 : a]: 31.57/4.61 ((('#sk2' @ ('#sk362' @ X2) @ Y0) => (X2 @ 31.57/4.61 ('#sk362' @ X2) @ Y0)))))) 31.57/4.61 | ('#form361' @ X2))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl135])). 31.57/4.61 thf(zip_derived_cl146, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ ((('#sk2' @ ('#sk362' @ X2) @ ('#sk448' @ X2)) => (X2 @ 31.57/4.61 ('#sk362' @ X2) @ ('#sk448' @ X2)))) 31.57/4.61 | ('#form361' @ X2))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl136])). 31.57/4.61 thf(zip_derived_cl157, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( ('#sk2' @ ('#sk362' @ X2) @ ('#sk448' @ X2)) | ('#form361' @ X2))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl146])). 31.57/4.61 thf(zip_derived_cl158, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ (X2 @ ('#sk362' @ X2) @ ('#sk448' @ X2)) | ('#form361' @ X2))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl146])). 31.57/4.61 thf(zip_derived_cl134, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( (X2 @ ('#sk139' @ X2) @ ('#sk199' @ X2)) 31.57/4.61 | (X2 @ '#sk6' @ '#sk7') 31.57/4.61 | ~ ('#form29') 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl120])). 31.57/4.61 thf(zip_derived_cl135, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( ('#form361' @ X2) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl145, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ ('#form361' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 31.57/4.61 | ~ ('#form29') 31.57/4.61 | (X2 @ '#sk6' @ '#sk7') 31.57/4.61 | (X2 @ ('#sk139' @ X2) @ ('#sk199' @ X2)))), 31.57/4.61 inference('renaming', [status(thm)], 31.57/4.61 [zip_derived_cl134, zip_derived_cl135])). 31.57/4.61 thf(zip_derived_cl156, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ ('#form361' @ X2) 31.57/4.61 | ~ ('#form29') 31.57/4.61 | (X2 @ '#sk6' @ '#sk7') 31.57/4.61 | (X2 @ ('#sk139' @ X2) @ ('#sk199' @ X2)))), 31.57/4.61 inference('ho_norm', [status(thm)], [zip_derived_cl145])). 31.57/4.61 thf(zip_derived_cl55, plain, 31.57/4.61 (( (((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk8' @ Y0 @ Y1) & 31.57/4.61 ('#sk8' @ Y1 @ Y2))) => 31.57/4.61 ('#sk8' @ Y0 @ Y2)))))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 31.57/4.61 ('#sk8' @ Y0 @ Y1))))))))))) 31.57/4.61 | ~ ('#form9') 31.57/4.61 | ('#form19'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 31.57/4.61 thf(zip_derived_cl62, plain, 31.57/4.61 (( (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 31.57/4.61 ('#sk8' @ Y0 @ Y1))))))))) 31.57/4.61 | ('#form19') 31.57/4.61 | ~ ('#form9'))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 31.57/4.61 thf(zip_derived_cl69, plain, 31.57/4.61 (![X2 : a]: 31.57/4.61 ( (((!!) @ (^[Y0 : a]: 31.57/4.61 ((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) => 31.57/4.61 ('#sk8' @ X2 @ Y0)))))) 31.57/4.61 | ~ ('#form9') 31.57/4.61 | ('#form19'))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl62])). 31.57/4.61 thf(zip_derived_cl80, plain, 31.57/4.61 (![X2 : a, X4 : a]: 31.57/4.61 ( ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) => ('#sk8' @ X2 @ X4))) 31.57/4.61 | ('#form19') 31.57/4.61 | ~ ('#form9'))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl69])). 31.57/4.61 thf(zip_derived_cl100, plain, 31.57/4.61 (![X2 : a, X4 : a]: 31.57/4.61 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 31.57/4.61 | ('#sk8' @ X2 @ X4) 31.57/4.61 | ~ ('#form9') 31.57/4.61 | ('#form19'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])). 31.57/4.61 thf(zip_derived_cl112, plain, 31.57/4.61 (![X2 : a, X4 : a]: 31.57/4.61 (~ ('#sk2' @ X2 @ X4) 31.57/4.61 | ('#form19') 31.57/4.61 | ~ ('#form9') 31.57/4.61 | ('#sk8' @ X2 @ X4))), 31.57/4.61 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl100])). 31.57/4.61 thf(zip_derived_cl26, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((X2 @ Y1 @ Y2) & (X2 @ 31.57/4.61 Y0 @ Y1))) => 31.57/4.61 (X2 @ Y0 @ Y2)))))))))))))) => 31.57/4.61 (X2 @ '#sk6' @ '#sk7'))) 31.57/4.61 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.61 ('#sk2' @ Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ 31.57/4.61 Y2 @ Y3) & 31.57/4.61 (Y0 @ 31.57/4.61 Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ 31.57/4.61 Y3)))))))))))))) => 31.57/4.61 (Y0 @ '#sk3' @ '#sk4')))))) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((((!!) @ (^[Y3 : 31.57/4.61 a > a > $o]: 31.57/4.61 (((((( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y1 @ 31.57/4.61 Y2)))))) & 31.57/4.61 (((!!) @ (^[Y3 : 31.57/4.61 a > a > $o]: 31.57/4.61 (((((( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))) & 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))))) => 31.57/4.61 (Y3 @ Y0 @ 31.57/4.61 Y1)))))))) => 31.57/4.61 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y0 @ 31.57/4.61 Y2))))))))))))))))) 31.57/4.61 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ 31.57/4.61 Y1 @ Y2) & 31.57/4.61 (Y0 @ 31.57/4.61 Y2 @ Y3))) => 31.57/4.61 (Y0 @ Y1 @ 31.57/4.61 Y3)))))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((('#sk2' @ Y1 @ Y2) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.61 (Y0 @ '#sk6' @ '#sk7')))))))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 31.57/4.61 thf(zip_derived_cl27, plain, 31.57/4.61 (( (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((('#sk1' @ Y0 @ Y1) => ('#sk8' @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk8' @ Y1 @ Y2) & 31.57/4.61 ('#sk8' @ Y0 @ Y1))) => 31.57/4.61 ('#sk8' @ Y0 @ Y2)))))))))))))) => 31.57/4.61 ('#sk8' @ '#sk6' @ '#sk7'))) 31.57/4.61 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.61 ('#sk2' @ Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ Y2 @ 31.57/4.61 Y3) & (Y0 @ 31.57/4.61 Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.61 (Y0 @ '#sk3' @ '#sk4')))))) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y1 @ 31.57/4.61 Y2)))))) & 31.57/4.61 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))))) => 31.57/4.61 (Y3 @ Y0 @ 31.57/4.61 Y1)))))))) => 31.57/4.61 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y0 @ Y2))))))))))))))))) 31.57/4.61 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ Y1 @ 31.57/4.61 Y2) & (Y0 @ 31.57/4.61 Y2 @ Y3))) => 31.57/4.61 (Y0 @ Y1 @ Y3)))))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((('#sk2' @ Y1 @ Y2) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.61 (Y0 @ '#sk6' @ '#sk7')))))))), 31.57/4.61 inference('triggered_bool_instantiation', [status(thm)], 31.57/4.61 [zip_derived_cl26])). 31.57/4.61 thf(zip_derived_cl37, plain, 31.57/4.61 ((~ ('#form19') 31.57/4.61 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.61 ('#sk2' @ Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ Y2 @ 31.57/4.61 Y3) & (Y0 @ 31.57/4.61 Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.61 (Y0 @ '#sk3' @ '#sk4')))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl210, plain, 31.57/4.61 (( ('#form19') 31.57/4.61 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ Y1 @ 31.57/4.61 Y2) & (Y0 @ 31.57/4.61 Y2 @ Y3))) => 31.57/4.61 (Y0 @ Y1 @ Y3)))))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((('#sk2' @ Y1 @ Y2) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.61 (Y0 @ '#sk6' @ '#sk7')))))) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y1 @ 31.57/4.61 Y2)))))) & 31.57/4.61 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))))) => 31.57/4.61 (Y3 @ Y0 @ 31.57/4.61 Y1)))))))) => 31.57/4.61 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y0 @ Y2))))))))))))))))) 31.57/4.61 | (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((('#sk1' @ Y0 @ Y1) => ('#sk8' @ Y0 @ 31.57/4.61 Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk8' @ Y1 @ Y2) & 31.57/4.61 ('#sk8' @ Y0 @ Y1))) => 31.57/4.61 ('#sk8' @ Y0 @ Y2)))))))))))))) => 31.57/4.61 ('#sk8' @ '#sk6' @ '#sk7'))))), 31.57/4.61 inference('renaming', [status(thm)], [zip_derived_cl27, zip_derived_cl37])). 31.57/4.61 thf(zip_derived_cl47, plain, 31.57/4.61 ((~ ('#form29') 31.57/4.61 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ Y1 @ 31.57/4.61 Y2) & (Y0 @ 31.57/4.61 Y2 @ Y3))) => 31.57/4.61 (Y0 @ Y1 @ Y3)))))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((('#sk2' @ Y1 @ Y2) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.61 (Y0 @ '#sk6' @ '#sk7')))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl211, plain, 31.57/4.61 (( ('#form29') 31.57/4.61 | (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((('#sk1' @ Y0 @ Y1) => ('#sk8' @ Y0 @ 31.57/4.61 Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk8' @ Y1 @ Y2) & 31.57/4.61 ('#sk8' @ Y0 @ Y1))) => 31.57/4.61 ('#sk8' @ Y0 @ Y2)))))))))))))) => 31.57/4.61 ('#sk8' @ '#sk6' @ '#sk7'))) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y1 @ 31.57/4.61 Y2)))))) & 31.57/4.61 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))))) => 31.57/4.61 (Y3 @ Y0 @ 31.57/4.61 Y1)))))))) => 31.57/4.61 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y0 @ Y2))))))))))))))))) 31.57/4.61 | ('#form19'))), 31.57/4.61 inference('renaming', [status(thm)], 31.57/4.61 [zip_derived_cl210, zip_derived_cl47])). 31.57/4.61 thf(zip_derived_cl31, plain, 31.57/4.61 (( ('#form9') 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y1 @ 31.57/4.61 Y2)))))) & 31.57/4.61 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))))) => 31.57/4.61 (Y3 @ Y0 @ 31.57/4.61 Y1)))))))) => 31.57/4.61 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y0 @ Y2))))))))))))))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl212, plain, 31.57/4.61 ((~ ('#form9') 31.57/4.61 | ('#form19') 31.57/4.61 | (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((('#sk1' @ Y0 @ Y1) => ('#sk8' @ Y0 @ 31.57/4.61 Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk8' @ Y1 @ Y2) & 31.57/4.61 ('#sk8' @ Y0 @ Y1))) => 31.57/4.61 ('#sk8' @ Y0 @ Y2)))))))))))))) => 31.57/4.61 ('#sk8' @ '#sk6' @ '#sk7'))) 31.57/4.61 | ('#form29'))), 31.57/4.61 inference('renaming', [status(thm)], 31.57/4.61 [zip_derived_cl211, zip_derived_cl31])). 31.57/4.61 thf(zip_derived_cl213, plain, 31.57/4.61 ((~ (((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((('#sk1' @ Y0 @ Y1) => ('#sk8' @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk8' @ Y1 @ Y2) & 31.57/4.61 ('#sk8' @ Y0 @ Y1))) => 31.57/4.61 ('#sk8' @ Y0 @ Y2)))))))))))))) 31.57/4.61 | ('#sk8' @ '#sk6' @ '#sk7') 31.57/4.61 | ('#form29') 31.57/4.61 | ('#form19') 31.57/4.61 | ~ ('#form9'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl212])). 31.57/4.61 thf(zip_derived_cl56, plain, 31.57/4.61 ((~ ('#sk8' @ '#sk6' @ '#sk7') | ~ ('#form9') | ('#form19'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 31.57/4.61 thf(zip_derived_cl214, plain, 31.57/4.61 ((~ ('#form9') 31.57/4.61 | ('#form19') 31.57/4.61 | ('#form29') 31.57/4.61 | ~ (((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((('#sk1' @ Y0 @ Y1) => ('#sk8' @ Y0 @ 31.57/4.61 Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk8' @ Y1 @ Y2) & 31.57/4.61 ('#sk8' @ Y0 @ Y1))) => 31.57/4.61 ('#sk8' @ Y0 @ Y2)))))))))))))))), 31.57/4.61 inference('clc', [status(thm)], [zip_derived_cl213, zip_derived_cl56])). 31.57/4.61 thf(zip_derived_cl215, plain, 31.57/4.61 ((~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((('#sk1' @ Y0 @ Y1) => ('#sk8' @ Y0 @ Y1))))))))) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk8' @ Y1 @ Y2) & 31.57/4.61 ('#sk8' @ Y0 @ Y1))) => 31.57/4.61 ('#sk8' @ Y0 @ Y2)))))))))))) 31.57/4.61 | ('#form29') 31.57/4.61 | ('#form19') 31.57/4.61 | ~ ('#form9'))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl214])). 31.57/4.61 thf(zip_derived_cl43, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( ('#form19') 31.57/4.61 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ 31.57/4.61 Y1 @ Y2) & 31.57/4.61 (Y0 @ 31.57/4.61 Y2 @ Y3))) => 31.57/4.61 (Y0 @ Y1 @ 31.57/4.61 Y3)))))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((('#sk2' @ Y1 @ Y2) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.61 (Y0 @ '#sk6' @ '#sk7')))))) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((((!!) @ (^[Y3 : 31.57/4.61 a > a > $o]: 31.57/4.61 (((((( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y1 @ 31.57/4.61 Y2)))))) & 31.57/4.61 (((!!) @ (^[Y3 : 31.57/4.61 a > a > $o]: 31.57/4.61 (((((( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))) & 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))))) => 31.57/4.61 (Y3 @ Y0 @ 31.57/4.61 Y1)))))))) => 31.57/4.61 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y0 @ 31.57/4.61 Y2))))))))))))))))) 31.57/4.61 | (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((X2 @ Y1 @ Y2) & 31.57/4.61 (X2 @ Y0 @ Y1))) => 31.57/4.61 (X2 @ Y0 @ Y2)))))))))))))) => 31.57/4.61 (X2 @ '#sk6' @ '#sk7'))))), 31.57/4.61 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl37])). 31.57/4.61 thf(zip_derived_cl47, plain, 31.57/4.61 ((~ ('#form29') 31.57/4.61 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ Y1 @ 31.57/4.61 Y2) & (Y0 @ 31.57/4.61 Y2 @ Y3))) => 31.57/4.61 (Y0 @ Y1 @ Y3)))))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((('#sk2' @ Y1 @ Y2) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.61 (Y0 @ '#sk6' @ '#sk7')))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl53, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( ('#form29') 31.57/4.61 | (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((X2 @ Y1 @ Y2) & 31.57/4.61 (X2 @ Y0 @ Y1))) => 31.57/4.61 (X2 @ Y0 @ Y2)))))))))))))) => 31.57/4.61 (X2 @ '#sk6' @ '#sk7'))) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((((!!) @ (^[Y3 : 31.57/4.61 a > a > $o]: 31.57/4.61 (((((( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y1 @ 31.57/4.61 Y2)))))) & 31.57/4.61 (((!!) @ (^[Y3 : 31.57/4.61 a > a > $o]: 31.57/4.61 (((((( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))) & 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))))) => 31.57/4.61 (Y3 @ Y0 @ 31.57/4.61 Y1)))))))) => 31.57/4.61 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y0 @ 31.57/4.61 Y2))))))))))))))))) 31.57/4.61 | ('#form19'))), 31.57/4.61 inference('renaming', [status(thm)], [zip_derived_cl43, zip_derived_cl47])). 31.57/4.61 thf(zip_derived_cl31, plain, 31.57/4.61 (( ('#form9') 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y1 @ 31.57/4.61 Y2)))))) & 31.57/4.61 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))))) => 31.57/4.61 (Y3 @ Y0 @ 31.57/4.61 Y1)))))))) => 31.57/4.61 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y0 @ Y2))))))))))))))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl58, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ ('#form9') 31.57/4.61 | ('#form19') 31.57/4.61 | (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((X2 @ Y1 @ Y2) & 31.57/4.61 (X2 @ Y0 @ Y1))) => 31.57/4.61 (X2 @ Y0 @ Y2)))))))))))))) => 31.57/4.61 (X2 @ '#sk6' @ '#sk7'))) 31.57/4.61 | ('#form29'))), 31.57/4.61 inference('renaming', [status(thm)], [zip_derived_cl53, zip_derived_cl31])). 31.57/4.61 thf(zip_derived_cl65, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ (((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((X2 @ Y1 @ Y2) & (X2 @ 31.57/4.61 Y0 @ Y1))) => 31.57/4.61 (X2 @ Y0 @ Y2)))))))))))))) 31.57/4.61 | (X2 @ '#sk6' @ '#sk7') 31.57/4.61 | ('#form29') 31.57/4.61 | ('#form19') 31.57/4.61 | ~ ('#form9'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 31.57/4.61 thf(zip_derived_cl76, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((X2 @ Y1 @ Y2) & (X2 @ 31.57/4.61 Y0 @ Y1))) => 31.57/4.61 (X2 @ Y0 @ Y2)))))))))))) 31.57/4.61 | ~ ('#form9') 31.57/4.61 | ('#form19') 31.57/4.61 | ('#form29') 31.57/4.61 | (X2 @ '#sk6' @ '#sk7'))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl65])). 31.57/4.61 thf(zip_derived_cl95, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ (((!!) @ (^[Y0 : a]: 31.57/4.61 ((('#sk1' @ ('#sk128' @ X2) @ Y0) => (X2 @ 31.57/4.61 ('#sk128' @ X2) @ Y0)))))) 31.57/4.61 | (X2 @ '#sk6' @ '#sk7') 31.57/4.61 | ('#form29') 31.57/4.61 | ('#form19') 31.57/4.61 | ~ ('#form9') 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((X2 @ Y1 @ Y2) & (X2 @ 31.57/4.61 Y0 @ Y1))) => 31.57/4.61 (X2 @ Y0 @ Y2)))))))))))))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl76])). 31.57/4.61 thf(zip_derived_cl105, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( ('#form185' @ X2) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((X2 @ Y1 @ Y2) & (X2 @ 31.57/4.61 Y0 @ Y1))) => 31.57/4.61 (X2 @ Y0 @ Y2)))))))))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl216, plain, 31.57/4.61 ((~ ('#form185' @ '#sk8') 31.57/4.61 | ~ ('#form9') 31.57/4.61 | ('#form19') 31.57/4.61 | ('#form29') 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((('#sk1' @ Y0 @ Y1) => ('#sk8' @ Y0 @ Y1))))))))))), 31.57/4.61 inference('renaming', [status(thm)], 31.57/4.61 [zip_derived_cl215, zip_derived_cl105])). 31.57/4.61 thf(zip_derived_cl217, plain, 31.57/4.61 ((~ (((!!) @ (^[Y0 : a]: 31.57/4.61 ((('#sk1' @ ('#sk128' @ '#sk8') @ Y0) => ('#sk8' @ 31.57/4.61 ('#sk128' @ '#sk8') @ Y0)))))) 31.57/4.61 | ('#form29') 31.57/4.61 | ('#form19') 31.57/4.61 | ~ ('#form9') 31.57/4.61 | ~ ('#form185' @ '#sk8'))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl216])). 31.57/4.61 thf(zip_derived_cl218, plain, 31.57/4.61 ((~ ((('#sk1' @ ('#sk128' @ '#sk8') @ ('#sk247' @ '#sk8')) => ('#sk8' @ 31.57/4.61 ('#sk128' @ '#sk8') @ ('#sk247' @ '#sk8')))) 31.57/4.61 | ~ ('#form185' @ '#sk8') 31.57/4.61 | ~ ('#form9') 31.57/4.61 | ('#form19') 31.57/4.61 | ('#form29'))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl217])). 31.57/4.61 thf(zip_derived_cl219, plain, 31.57/4.61 (( ('#sk1' @ ('#sk128' @ '#sk8') @ ('#sk247' @ '#sk8')) 31.57/4.61 | ('#form29') 31.57/4.61 | ('#form19') 31.57/4.61 | ~ ('#form9') 31.57/4.61 | ~ ('#form185' @ '#sk8'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl218])). 31.57/4.61 thf(zip_derived_cl220, plain, 31.57/4.61 ((~ ('#sk8' @ ('#sk128' @ '#sk8') @ ('#sk247' @ '#sk8')) 31.57/4.61 | ('#form29') 31.57/4.61 | ('#form19') 31.57/4.61 | ~ ('#form9') 31.57/4.61 | ~ ('#form185' @ '#sk8'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl218])). 31.57/4.61 thf(zip_derived_cl113, plain, 31.57/4.61 (![X2 : a, X4 : a]: 31.57/4.61 (~ ('#sk1' @ X2 @ X4) 31.57/4.61 | ('#form19') 31.57/4.61 | ~ ('#form9') 31.57/4.61 | ('#sk8' @ X2 @ X4))), 31.57/4.61 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl100])). 31.57/4.61 thf(zip_derived_cl31, plain, 31.57/4.61 (( ('#form9') 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y1 @ 31.57/4.61 Y2)))))) & 31.57/4.61 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))))) => 31.57/4.61 (Y3 @ Y0 @ 31.57/4.61 Y1)))))))) => 31.57/4.61 (((!!) @ (^[Y3 : a > a > $o]: 31.57/4.61 (((((((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 ('#sk1' @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) | 31.57/4.61 ('#sk2' @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y5))))))))) & 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y6 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ 31.57/4.61 Y5) & 31.57/4.61 (Y3 @ 31.57/4.61 Y5 @ Y6))) => 31.57/4.61 (Y3 @ 31.57/4.61 Y4 @ Y6)))))))))))))) => 31.57/4.61 (Y3 @ Y0 @ Y2))))))))))))))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl32, plain, 31.57/4.61 ((~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((((((!!) @ (^[Y2 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y3 : a]: 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y3 @ 31.57/4.61 Y4) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y3 @ Y4))) => 31.57/4.61 (Y2 @ 31.57/4.61 Y3 @ Y4))))))))) & 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y2 @ 31.57/4.61 Y3 @ 31.57/4.61 Y4) & 31.57/4.61 (Y2 @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y2 @ 31.57/4.61 Y3 @ Y5)))))))))))))) => 31.57/4.61 (Y2 @ Y0 @ Y1)))))) & 31.57/4.61 (((!!) @ (^[Y2 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y3 : a]: 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y2 @ 31.57/4.61 Y3 @ 31.57/4.61 Y4) & 31.57/4.61 (Y2 @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y2 @ 31.57/4.61 Y3 @ Y5)))))))))))) & 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (( 31.57/4.61 ('#sk2' @ 31.57/4.61 Y3 @ 31.57/4.61 Y4) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y3 @ Y4))) => 31.57/4.61 (Y2 @ 31.57/4.61 Y3 @ Y4))))))))))) => 31.57/4.61 (Y2 @ '#sk10' @ Y0)))))))) => 31.57/4.61 (((!!) @ (^[Y2 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y3 : a]: 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (((( 31.57/4.61 ('#sk1' @ 31.57/4.61 Y3 @ 31.57/4.61 Y4) | 31.57/4.61 ('#sk2' @ 31.57/4.61 Y3 @ Y4))) => 31.57/4.61 (Y2 @ 31.57/4.61 Y3 @ Y4))))))))) & 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y5 : a]: 31.57/4.61 (( 31.57/4.61 (( 31.57/4.61 (Y2 @ 31.57/4.61 Y3 @ 31.57/4.61 Y4) & 31.57/4.61 (Y2 @ 31.57/4.61 Y4 @ Y5))) => 31.57/4.61 (Y2 @ 31.57/4.61 Y3 @ Y5)))))))))))))) => 31.57/4.61 (Y2 @ '#sk10' @ Y1)))))))))))))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl31])). 31.57/4.61 thf(zip_derived_cl45, plain, 31.57/4.61 ((~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((((((!!) @ (^[Y1 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 ((((('#sk2' @ 31.57/4.61 Y2 @ 31.57/4.61 Y3) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y2 @ Y3))) => 31.57/4.61 (Y1 @ Y2 @ 31.57/4.61 Y3))))))))) & 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (( 31.57/4.61 (Y1 @ 31.57/4.61 Y2 @ 31.57/4.61 Y3) & 31.57/4.61 (Y1 @ 31.57/4.61 Y3 @ Y4))) => 31.57/4.61 (Y1 @ 31.57/4.61 Y2 @ Y4)))))))))))))) => 31.57/4.61 (Y1 @ '#sk20' @ Y0)))))) & 31.57/4.61 (((!!) @ (^[Y1 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 ( 31.57/4.61 ( 31.57/4.61 (( 31.57/4.61 (Y1 @ 31.57/4.61 Y2 @ 31.57/4.61 Y3) & 31.57/4.61 (Y1 @ 31.57/4.61 Y3 @ Y4))) => 31.57/4.61 (Y1 @ 31.57/4.61 Y2 @ Y4)))))))))))) & 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 ((((('#sk2' @ 31.57/4.61 Y2 @ 31.57/4.61 Y3) | 31.57/4.61 ('#sk1' @ 31.57/4.61 Y2 @ Y3))) => 31.57/4.61 (Y1 @ Y2 @ 31.57/4.61 Y3))))))))))) => 31.57/4.61 (Y1 @ '#sk10' @ '#sk20')))))))) => 31.57/4.61 (((!!) @ (^[Y1 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 ((((('#sk1' @ 31.57/4.61 Y2 @ Y3) | 31.57/4.61 ('#sk2' @ 31.57/4.61 Y2 @ Y3))) => 31.57/4.61 (Y1 @ Y2 @ 31.57/4.61 Y3))))))))) & 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((!!) @ ( 31.57/4.61 ^[Y4 : a]: 31.57/4.61 (((( 31.57/4.61 (Y1 @ 31.57/4.61 Y2 @ 31.57/4.61 Y3) & 31.57/4.61 (Y1 @ 31.57/4.61 Y3 @ Y4))) => 31.57/4.61 (Y1 @ 31.57/4.61 Y2 @ Y4)))))))))))))) => 31.57/4.61 (Y1 @ '#sk10' @ Y0))))))))))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl32])). 31.57/4.61 thf(zip_derived_cl57, plain, 31.57/4.61 ((~ (((((((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk2' @ Y1 @ Y2) | 31.57/4.61 ('#sk1' @ Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ 31.57/4.61 Y1 @ 31.57/4.61 Y2) & 31.57/4.61 (Y0 @ 31.57/4.61 Y2 @ Y3))) => 31.57/4.61 (Y0 @ Y1 @ 31.57/4.61 Y3)))))))))))))) => 31.57/4.61 (Y0 @ '#sk20' @ '#sk38')))))) & 31.57/4.61 (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ 31.57/4.61 Y1 @ 31.57/4.61 Y2) & 31.57/4.61 (Y0 @ 31.57/4.61 Y2 @ Y3))) => 31.57/4.61 (Y0 @ Y1 @ 31.57/4.61 Y3)))))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk2' @ Y1 @ Y2) | 31.57/4.61 ('#sk1' @ Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.61 (Y0 @ '#sk10' @ '#sk20')))))))) => 31.57/4.61 (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.61 ('#sk2' @ Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ Y1 @ 31.57/4.61 Y2) & 31.57/4.61 (Y0 @ Y2 @ 31.57/4.61 Y3))) => 31.57/4.61 (Y0 @ Y1 @ 31.57/4.61 Y3)))))))))))))) => 31.57/4.61 (Y0 @ '#sk10' @ '#sk38')))))))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl45])). 31.57/4.61 thf(zip_derived_cl64, plain, 31.57/4.61 ((~ (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.61 ('#sk2' @ Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ Y1 @ 31.57/4.61 Y2) & (Y0 @ 31.57/4.61 Y2 @ Y3))) => 31.57/4.61 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.61 (Y0 @ '#sk10' @ '#sk38')))))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 31.57/4.61 thf(zip_derived_cl75, plain, 31.57/4.61 ((~ (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 ('#sk88' @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk88' @ Y0 @ Y1) & 31.57/4.61 ('#sk88' @ Y1 @ Y2))) => 31.57/4.61 ('#sk88' @ Y0 @ Y2)))))))))))))) => 31.57/4.61 ('#sk88' @ '#sk10' @ '#sk38'))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl64])). 31.57/4.61 thf(zip_derived_cl94, plain, 31.57/4.61 ((~ ('#sk88' @ '#sk10' @ '#sk38') | ('#form9'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 31.57/4.61 thf(zip_derived_cl61, plain, 31.57/4.61 (( (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk8' @ Y0 @ Y1) & 31.57/4.61 ('#sk8' @ Y1 @ Y2))) => 31.57/4.61 ('#sk8' @ Y0 @ Y2)))))))))))) 31.57/4.61 | ('#form19') 31.57/4.61 | ~ ('#form9'))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 31.57/4.61 thf(zip_derived_cl68, plain, 31.57/4.61 (![X2 : a]: 31.57/4.61 ( (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk8' @ X2 @ Y0) & ('#sk8' @ Y0 @ Y1))) => 31.57/4.61 ('#sk8' @ X2 @ Y1))))))))) 31.57/4.61 | ~ ('#form9') 31.57/4.61 | ('#form19'))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl61])). 31.57/4.61 thf(zip_derived_cl79, plain, 31.57/4.61 (![X2 : a, X4 : a]: 31.57/4.61 ( (((!!) @ (^[Y0 : a]: 31.57/4.61 ((((('#sk8' @ X2 @ X4) & ('#sk8' @ X4 @ Y0))) => 31.57/4.61 ('#sk8' @ X2 @ Y0)))))) 31.57/4.61 | ('#form19') 31.57/4.61 | ~ ('#form9'))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl68])). 31.57/4.61 thf(zip_derived_cl99, plain, 31.57/4.61 (![X2 : a, X4 : a, X6 : a]: 31.57/4.61 ( ((((('#sk8' @ X2 @ X4) & ('#sk8' @ X4 @ X6))) => ('#sk8' @ X2 @ X6))) 31.57/4.61 | ~ ('#form9') 31.57/4.61 | ('#form19'))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl79])). 31.57/4.61 thf(zip_derived_cl111, plain, 31.57/4.61 (![X2 : a, X4 : a, X6 : a]: 31.57/4.61 (~ ((('#sk8' @ X2 @ X4) & ('#sk8' @ X4 @ X6))) 31.57/4.61 | ('#sk8' @ X2 @ X6) 31.57/4.61 | ('#form19') 31.57/4.61 | ~ ('#form9'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl99])). 31.57/4.61 thf(zip_derived_cl125, plain, 31.57/4.61 (![X2 : a, X4 : a, X6 : a]: 31.57/4.61 (~ ('#sk8' @ X2 @ X4) 31.57/4.61 | ~ ('#sk8' @ X4 @ X6) 31.57/4.61 | ~ ('#form9') 31.57/4.61 | ('#form19') 31.57/4.61 | ('#sk8' @ X2 @ X6))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl111])). 31.57/4.61 thf(zip_derived_cl63, plain, 31.57/4.61 (( (((((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk2' @ Y1 @ Y2) | 31.57/4.61 ('#sk1' @ Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ Y1 @ 31.57/4.61 Y2) & (Y0 @ 31.57/4.61 Y2 @ Y3))) => 31.57/4.61 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.61 (Y0 @ '#sk20' @ '#sk38')))))) & 31.57/4.61 (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ Y1 @ 31.57/4.61 Y2) & (Y0 @ 31.57/4.61 Y2 @ Y3))) => 31.57/4.61 (Y0 @ Y1 @ Y3)))))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk2' @ Y1 @ Y2) | 31.57/4.61 ('#sk1' @ Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.61 (Y0 @ '#sk10' @ '#sk20')))))))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 31.57/4.61 thf(zip_derived_cl71, plain, 31.57/4.61 (( (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ Y1 @ 31.57/4.61 Y2) & (Y0 @ 31.57/4.61 Y2 @ Y3))) => 31.57/4.61 (Y0 @ Y1 @ Y3)))))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk2' @ Y1 @ Y2) | 31.57/4.61 ('#sk1' @ Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))))) => 31.57/4.61 (Y0 @ '#sk10' @ '#sk20')))))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl63])). 31.57/4.61 thf(zip_derived_cl87, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((X2 @ Y0 @ Y1) & (X2 @ 31.57/4.61 Y1 @ Y2))) => 31.57/4.61 (X2 @ Y0 @ Y2)))))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 (X2 @ Y0 @ Y1))))))))))) => 31.57/4.61 (X2 @ '#sk10' @ '#sk20'))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl71])). 31.57/4.61 thf(zip_derived_cl88, plain, 31.57/4.61 (( (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk88' @ Y0 @ Y1) & 31.57/4.61 ('#sk88' @ Y1 @ Y2))) => 31.57/4.61 ('#sk88' @ Y0 @ Y2)))))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 ('#sk88' @ Y0 @ Y1))))))))))) => 31.57/4.61 ('#sk88' @ '#sk10' @ '#sk20'))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('triggered_bool_instantiation', [status(thm)], 31.57/4.61 [zip_derived_cl87])). 31.57/4.61 thf(zip_derived_cl380, plain, 31.57/4.61 ((~ (((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk88' @ Y0 @ Y1) & 31.57/4.61 ('#sk88' @ Y1 @ Y2))) => 31.57/4.61 ('#sk88' @ Y0 @ Y2)))))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 31.57/4.61 ('#sk88' @ Y0 @ Y1))))))))))) 31.57/4.61 | ('#sk88' @ '#sk10' @ '#sk20') 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl88])). 31.57/4.61 thf(zip_derived_cl381, plain, 31.57/4.61 ((~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk88' @ Y0 @ Y1) & 31.57/4.61 ('#sk88' @ Y1 @ Y2))) => 31.57/4.61 ('#sk88' @ Y0 @ Y2)))))))))))) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 31.57/4.61 ('#sk88' @ Y0 @ Y1))))))))) 31.57/4.61 | ('#form9') 31.57/4.61 | ('#sk88' @ '#sk10' @ '#sk20'))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl380])). 31.57/4.61 thf(zip_derived_cl382, plain, 31.57/4.61 (( ('#form1067') 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk88' @ Y0 @ Y1) & 31.57/4.61 ('#sk88' @ Y1 @ Y2))) => 31.57/4.61 ('#sk88' @ Y0 @ Y2)))))))))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl383, plain, 31.57/4.61 ((~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk88' @ ('#sk105' @ '#sk88') @ Y0) & 31.57/4.61 ('#sk88' @ Y0 @ Y1))) => 31.57/4.61 ('#sk88' @ ('#sk105' @ '#sk88') @ Y1))))))))) 31.57/4.61 | ('#form1067'))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl382])). 31.57/4.61 thf(zip_derived_cl386, plain, 31.57/4.61 ((~ (((!!) @ (^[Y0 : a]: 31.57/4.61 ((((('#sk88' @ ('#sk105' @ '#sk88') @ 31.57/4.61 ('#sk139' @ '#sk88')) & ('#sk88' @ 31.57/4.61 ('#sk139' @ '#sk88') @ Y0))) => 31.57/4.61 ('#sk88' @ ('#sk105' @ '#sk88') @ Y0)))))) 31.57/4.61 | ('#form1067'))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl383])). 31.57/4.61 thf(zip_derived_cl387, plain, 31.57/4.61 ((~ ((((('#sk88' @ ('#sk105' @ '#sk88') @ ('#sk139' @ '#sk88')) & 31.57/4.61 ('#sk88' @ ('#sk139' @ '#sk88') @ ('#sk199' @ '#sk88')))) => 31.57/4.61 ('#sk88' @ ('#sk105' @ '#sk88') @ ('#sk199' @ '#sk88')))) 31.57/4.61 | ('#form1067'))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl386])). 31.57/4.61 thf(zip_derived_cl388, plain, 31.57/4.61 (( ((('#sk88' @ ('#sk105' @ '#sk88') @ ('#sk139' @ '#sk88')) & 31.57/4.61 ('#sk88' @ ('#sk139' @ '#sk88') @ ('#sk199' @ '#sk88')))) 31.57/4.61 | ('#form1067'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl387])). 31.57/4.61 thf(zip_derived_cl390, plain, 31.57/4.61 (( ('#sk88' @ ('#sk105' @ '#sk88') @ ('#sk139' @ '#sk88')) 31.57/4.61 | ('#form1067'))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl388])). 31.57/4.61 thf(zip_derived_cl381, plain, 31.57/4.61 ((~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk88' @ Y0 @ Y1) & 31.57/4.61 ('#sk88' @ Y1 @ Y2))) => 31.57/4.61 ('#sk88' @ Y0 @ Y2)))))))))))) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 31.57/4.61 ('#sk88' @ Y0 @ Y1))))))))) 31.57/4.61 | ('#form9') 31.57/4.61 | ('#sk88' @ '#sk10' @ '#sk20'))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl380])). 31.57/4.61 thf(zip_derived_cl382, plain, 31.57/4.61 (( ('#form1067') 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk88' @ Y0 @ Y1) & 31.57/4.61 ('#sk88' @ Y1 @ Y2))) => 31.57/4.61 ('#sk88' @ Y0 @ Y2)))))))))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl384, plain, 31.57/4.61 ((~ ('#form1067') 31.57/4.61 | ('#sk88' @ '#sk10' @ '#sk20') 31.57/4.61 | ('#form9') 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 31.57/4.61 ('#sk88' @ Y0 @ Y1))))))))))), 31.57/4.61 inference('renaming', [status(thm)], 31.57/4.61 [zip_derived_cl381, zip_derived_cl382])). 31.57/4.61 thf(zip_derived_cl87, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((X2 @ Y0 @ Y1) & (X2 @ 31.57/4.61 Y1 @ Y2))) => 31.57/4.61 (X2 @ Y0 @ Y2)))))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 (X2 @ Y0 @ Y1))))))))))) => 31.57/4.61 (X2 @ '#sk10' @ '#sk20'))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl71])). 31.57/4.61 thf(zip_derived_cl102, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ (((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((X2 @ Y0 @ Y1) & (X2 @ 31.57/4.61 Y1 @ Y2))) => 31.57/4.61 (X2 @ Y0 @ Y2)))))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 (X2 @ Y0 @ Y1))))))))))) 31.57/4.61 | (X2 @ '#sk10' @ '#sk20') 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl87])). 31.57/4.61 thf(zip_derived_cl115, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((X2 @ Y0 @ Y1) & (X2 @ 31.57/4.61 Y1 @ Y2))) => 31.57/4.61 (X2 @ Y0 @ Y2)))))))))))) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 (X2 @ Y0 @ Y1))))))))) 31.57/4.61 | ('#form9') 31.57/4.61 | (X2 @ '#sk10' @ '#sk20'))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl102])). 31.57/4.61 thf(zip_derived_cl127, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((((X2 @ ('#sk105' @ X2) @ Y0) & (X2 @ 31.57/4.61 Y0 @ Y1))) => 31.57/4.61 (X2 @ ('#sk105' @ X2) @ Y1))))))))) 31.57/4.61 | (X2 @ '#sk10' @ '#sk20') 31.57/4.61 | ('#form9') 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 (X2 @ Y0 @ Y1))))))))))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl115])). 31.57/4.61 thf(zip_derived_cl139, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((((X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) & (X2 @ 31.57/4.61 ('#sk139' @ X2) @ Y0))) => 31.57/4.61 (X2 @ ('#sk105' @ X2) @ Y0)))))) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 (X2 @ Y0 @ Y1))))))))) 31.57/4.61 | ('#form9') 31.57/4.61 | (X2 @ '#sk10' @ '#sk20'))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl127])). 31.57/4.61 thf(zip_derived_cl149, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ (((((X2 @ ('#sk105' @ X2) @ ('#sk139' @ X2)) & (X2 @ 31.57/4.61 ('#sk139' @ X2) @ ('#sk199' @ X2)))) => 31.57/4.61 (X2 @ ('#sk105' @ X2) @ ('#sk199' @ X2)))) 31.57/4.61 | (X2 @ '#sk10' @ '#sk20') 31.57/4.61 | ('#form9') 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 (X2 @ Y0 @ Y1))))))))))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl139])). 31.57/4.61 thf(zip_derived_cl162, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ (X2 @ ('#sk105' @ X2) @ ('#sk199' @ X2)) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 (X2 @ Y0 @ Y1))))))))) 31.57/4.61 | ('#form9') 31.57/4.61 | (X2 @ '#sk10' @ '#sk20'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl149])). 31.57/4.61 thf(zip_derived_cl168, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( ('#form633' @ X2) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 (X2 @ Y0 @ Y1))))))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl385, plain, 31.57/4.61 ((~ ('#form633' @ '#sk88') 31.57/4.61 | ('#form9') 31.57/4.61 | ('#sk88' @ '#sk10' @ '#sk20') 31.57/4.61 | ~ ('#form1067'))), 31.57/4.61 inference('renaming', [status(thm)], 31.57/4.61 [zip_derived_cl384, zip_derived_cl168])). 31.57/4.61 thf(zip_derived_cl105, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( ('#form185' @ X2) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((X2 @ Y1 @ Y2) & (X2 @ 31.57/4.61 Y0 @ Y1))) => 31.57/4.61 (X2 @ Y0 @ Y2)))))))))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl106, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((((X2 @ Y0 @ Y1) & (X2 @ 31.57/4.61 ('#sk186' @ X2) @ Y0))) => 31.57/4.61 (X2 @ ('#sk186' @ X2) @ Y1))))))))) 31.57/4.61 | ('#form185' @ X2))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl105])). 31.57/4.61 thf(zip_derived_cl119, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((((X2 @ ('#sk258' @ X2) @ Y0) & (X2 @ 31.57/4.61 ('#sk186' @ X2) @ ('#sk258' @ X2)))) => 31.57/4.61 (X2 @ ('#sk186' @ X2) @ Y0)))))) 31.57/4.61 | ('#form185' @ X2))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl106])). 31.57/4.61 thf(zip_derived_cl132, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ (((((X2 @ ('#sk258' @ X2) @ ('#sk344' @ X2)) & (X2 @ 31.57/4.61 ('#sk186' @ X2) @ ('#sk258' @ X2)))) => 31.57/4.61 (X2 @ ('#sk186' @ X2) @ ('#sk344' @ X2)))) 31.57/4.61 | ('#form185' @ X2))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl119])). 31.57/4.61 thf(zip_derived_cl142, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( (((X2 @ ('#sk258' @ X2) @ ('#sk344' @ X2)) & (X2 @ 31.57/4.61 ('#sk186' @ X2) @ ('#sk258' @ X2)))) 31.57/4.61 | ('#form185' @ X2))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl132])). 31.57/4.61 thf(zip_derived_cl154, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( (X2 @ ('#sk186' @ X2) @ ('#sk258' @ X2)) | ('#form185' @ X2))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl142])). 31.57/4.61 thf(zip_derived_cl37, plain, 31.57/4.61 ((~ ('#form19') 31.57/4.61 | (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.61 ('#sk2' @ Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ Y2 @ 31.57/4.61 Y3) & (Y0 @ 31.57/4.61 Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.61 (Y0 @ '#sk3' @ '#sk4')))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl38, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 (X2 @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((X2 @ Y1 @ Y2) & (X2 @ 31.57/4.61 Y0 @ Y1))) => 31.57/4.61 (X2 @ Y0 @ Y2)))))))))))))) => 31.57/4.61 (X2 @ '#sk3' @ '#sk4'))) 31.57/4.61 | ~ ('#form19'))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 31.57/4.61 thf(zip_derived_cl40, plain, 31.57/4.61 (( (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 ('#sk5' @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk5' @ Y1 @ Y2) & 31.57/4.61 ('#sk5' @ Y0 @ Y1))) => 31.57/4.61 ('#sk5' @ Y0 @ Y2)))))))))))))) => 31.57/4.61 ('#sk5' @ '#sk3' @ '#sk4'))) 31.57/4.61 | ~ ('#form19'))), 31.57/4.61 inference('triggered_bool_instantiation', [status(thm)], 31.57/4.61 [zip_derived_cl38])). 31.57/4.61 thf(zip_derived_cl6, plain, 31.57/4.61 (~ (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk1' @ Y1 @ Y2) | 31.57/4.61 ('#sk2' @ Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ Y1 @ 31.57/4.61 Y2) & (Y0 @ 31.57/4.61 Y2 @ Y3))) => 31.57/4.61 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.61 (Y0 @ '#sk3' @ '#sk4'))))))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 31.57/4.61 thf(zip_derived_cl8, plain, 31.57/4.61 (~ (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 ('#sk5' @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk5' @ Y0 @ Y1) & 31.57/4.61 ('#sk5' @ Y1 @ Y2))) => 31.57/4.61 ('#sk5' @ Y0 @ Y2)))))))))))))) => 31.57/4.61 ('#sk5' @ '#sk3' @ '#sk4')))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 31.57/4.61 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk3' @ '#sk4')), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 31.57/4.61 thf(zip_derived_cl268, plain, 31.57/4.61 (( (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 ('#sk5' @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk5' @ Y1 @ Y2) & 31.57/4.61 ('#sk5' @ Y0 @ Y1))) => 31.57/4.61 ('#sk5' @ Y0 @ Y2)))))))))))))) => 31.57/4.61 ($false))) 31.57/4.61 | ~ ('#form19'))), 31.57/4.61 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl11])). 31.57/4.61 thf(zip_derived_cl269, plain, 31.57/4.61 (( (((~) @ (((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.57/4.61 Y0 @ Y1))) => 31.57/4.61 ('#sk5' @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk5' @ Y1 @ Y2) & 31.57/4.61 ('#sk5' @ Y0 @ Y1))) => 31.57/4.61 ('#sk5' @ Y0 @ Y2)))))))))))))))) 31.57/4.61 | ~ ('#form19'))), 31.57/4.61 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl268])). 31.57/4.61 thf(zip_derived_cl270, plain, 31.57/4.61 ((~ (((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 31.57/4.61 ('#sk5' @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk5' @ Y1 @ Y2) & 31.57/4.61 ('#sk5' @ Y0 @ Y1))) => 31.57/4.61 ('#sk5' @ Y0 @ Y2)))))))))))))) 31.57/4.61 | ~ ('#form19'))), 31.57/4.61 inference('simplify nested equalities', [status(thm)], 31.57/4.61 [zip_derived_cl269])). 31.57/4.61 thf(zip_derived_cl271, plain, 31.57/4.61 ((~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 31.57/4.61 ('#sk5' @ Y0 @ Y1))))))))) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk5' @ Y1 @ Y2) & 31.57/4.61 ('#sk5' @ Y0 @ Y1))) => 31.57/4.61 ('#sk5' @ Y0 @ Y2)))))))))))) 31.57/4.61 | ~ ('#form19'))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl270])). 31.57/4.61 thf(zip_derived_cl105, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( ('#form185' @ X2) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((X2 @ Y1 @ Y2) & (X2 @ 31.57/4.61 Y0 @ Y1))) => 31.57/4.61 (X2 @ Y0 @ Y2)))))))))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl272, plain, 31.57/4.61 ((~ ('#form185' @ '#sk5') 31.57/4.61 | ~ ('#form19') 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 31.57/4.61 ('#sk5' @ Y0 @ Y1))))))))))), 31.57/4.61 inference('renaming', [status(thm)], 31.57/4.61 [zip_derived_cl271, zip_derived_cl105])). 31.57/4.61 thf(zip_derived_cl273, plain, 31.57/4.61 ((~ (((!!) @ (^[Y0 : a]: 31.57/4.61 ((((('#sk1' @ ('#sk87' @ '#sk5') @ Y0) | ('#sk2' @ 31.57/4.61 ('#sk87' @ '#sk5') @ Y0))) => 31.57/4.61 ('#sk5' @ ('#sk87' @ '#sk5') @ Y0)))))) 31.57/4.61 | ~ ('#form19') 31.57/4.61 | ~ ('#form185' @ '#sk5'))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl272])). 31.57/4.61 thf(zip_derived_cl274, plain, 31.57/4.61 ((~ ((((('#sk1' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')) | ('#sk2' @ 31.57/4.61 ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')))) => 31.57/4.61 ('#sk5' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')))) 31.57/4.61 | ~ ('#form185' @ '#sk5') 31.57/4.61 | ~ ('#form19'))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl273])). 31.57/4.61 thf(zip_derived_cl275, plain, 31.57/4.61 (( ((('#sk1' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')) | ('#sk2' @ 31.57/4.61 ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')))) 31.57/4.61 | ~ ('#form19') 31.57/4.61 | ~ ('#form185' @ '#sk5'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl274])). 31.57/4.61 thf(zip_derived_cl277, plain, 31.57/4.61 (( ('#sk1' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')) 31.57/4.61 | ('#sk2' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')) 31.57/4.61 | ~ ('#form185' @ '#sk5') 31.57/4.61 | ~ ('#form19'))), 31.57/4.61 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl275])). 31.57/4.61 thf(zip_derived_cl389, plain, 31.57/4.61 ((~ ('#sk88' @ ('#sk105' @ '#sk88') @ ('#sk199' @ '#sk88')) 31.57/4.61 | ('#form1067'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl387])). 31.57/4.61 thf(zip_derived_cl391, plain, 31.57/4.61 (( ('#sk88' @ ('#sk139' @ '#sk88') @ ('#sk199' @ '#sk88')) 31.57/4.61 | ('#form1067'))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl388])). 31.57/4.61 thf(zip_derived_cl70, plain, 31.57/4.61 (( (((!!) @ (^[Y0 : a > a > $o]: 31.57/4.61 (((((((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk2' @ Y1 @ Y2) | 31.57/4.61 ('#sk1' @ Y1 @ Y2))) => 31.57/4.61 (Y0 @ Y1 @ Y2))))))))) & 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((!!) @ (^[Y3 : a]: 31.57/4.61 (((((Y0 @ Y1 @ 31.57/4.61 Y2) & (Y0 @ 31.57/4.61 Y2 @ Y3))) => 31.57/4.61 (Y0 @ Y1 @ Y3)))))))))))))) => 31.57/4.61 (Y0 @ '#sk20' @ '#sk38')))))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl63])). 31.57/4.61 thf(zip_derived_cl81, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 (X2 @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 (((((X2 @ Y0 @ Y1) & (X2 @ 31.57/4.61 Y1 @ Y2))) => 31.57/4.61 (X2 @ Y0 @ Y2)))))))))))))) => 31.57/4.61 (X2 @ '#sk20' @ '#sk38'))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl70])). 31.57/4.61 thf(zip_derived_cl82, plain, 31.57/4.61 (( (((((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 ('#sk88' @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk88' @ Y0 @ Y1) & 31.57/4.61 ('#sk88' @ Y1 @ Y2))) => 31.57/4.61 ('#sk88' @ Y0 @ Y2)))))))))))))) => 31.57/4.61 ('#sk88' @ '#sk20' @ '#sk38'))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('triggered_bool_instantiation', [status(thm)], 31.57/4.61 [zip_derived_cl81])). 31.57/4.61 thf(zip_derived_cl330, plain, 31.57/4.61 ((~ (((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 31.57/4.61 ('#sk88' @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk88' @ Y0 @ Y1) & 31.57/4.61 ('#sk88' @ Y1 @ Y2))) => 31.57/4.61 ('#sk88' @ Y0 @ Y2)))))))))))))) 31.57/4.61 | ('#sk88' @ '#sk20' @ '#sk38') 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 31.57/4.61 thf(zip_derived_cl331, plain, 31.57/4.61 ((~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 31.57/4.61 ('#sk88' @ Y0 @ Y1))))))))) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk88' @ Y0 @ Y1) & 31.57/4.61 ('#sk88' @ Y1 @ Y2))) => 31.57/4.61 ('#sk88' @ Y0 @ Y2)))))))))))) 31.57/4.61 | ('#form9') 31.57/4.61 | ('#sk88' @ '#sk20' @ '#sk38'))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl330])). 31.57/4.61 thf(zip_derived_cl168, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( ('#form633' @ X2) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 (X2 @ Y0 @ Y1))))))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl332, plain, 31.57/4.61 ((~ ('#form633' @ '#sk88') 31.57/4.61 | ('#sk88' @ '#sk20' @ '#sk38') 31.57/4.61 | ('#form9') 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk88' @ Y0 @ Y1) & 31.57/4.61 ('#sk88' @ Y1 @ Y2))) => 31.57/4.61 ('#sk88' @ Y0 @ Y2)))))))))))))), 31.57/4.61 inference('renaming', [status(thm)], 31.57/4.61 [zip_derived_cl331, zip_derived_cl168])). 31.57/4.61 thf(zip_derived_cl333, plain, 31.57/4.61 ((~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk88' @ ('#sk105' @ '#sk88') @ Y0) & 31.57/4.61 ('#sk88' @ Y0 @ Y1))) => 31.57/4.61 ('#sk88' @ ('#sk105' @ '#sk88') @ Y1))))))))) 31.57/4.61 | ('#form9') 31.57/4.61 | ('#sk88' @ '#sk20' @ '#sk38') 31.57/4.61 | ~ ('#form633' @ '#sk88'))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl332])). 31.57/4.61 thf(zip_derived_cl334, plain, 31.57/4.61 ((~ (((!!) @ (^[Y0 : a]: 31.57/4.61 ((((('#sk88' @ ('#sk105' @ '#sk88') @ 31.57/4.61 ('#sk139' @ '#sk88')) & ('#sk88' @ 31.57/4.61 ('#sk139' @ '#sk88') @ Y0))) => 31.57/4.61 ('#sk88' @ ('#sk105' @ '#sk88') @ Y0)))))) 31.57/4.61 | ~ ('#form633' @ '#sk88') 31.57/4.61 | ('#sk88' @ '#sk20' @ '#sk38') 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl333])). 31.57/4.61 thf(zip_derived_cl335, plain, 31.57/4.61 ((~ ((((('#sk88' @ ('#sk105' @ '#sk88') @ ('#sk139' @ '#sk88')) & 31.57/4.61 ('#sk88' @ ('#sk139' @ '#sk88') @ ('#sk199' @ '#sk88')))) => 31.57/4.61 ('#sk88' @ ('#sk105' @ '#sk88') @ ('#sk199' @ '#sk88')))) 31.57/4.61 | ('#form9') 31.57/4.61 | ('#sk88' @ '#sk20' @ '#sk38') 31.57/4.61 | ~ ('#form633' @ '#sk88'))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl334])). 31.57/4.61 thf(zip_derived_cl337, plain, 31.57/4.61 ((~ ('#sk88' @ ('#sk105' @ '#sk88') @ ('#sk199' @ '#sk88')) 31.57/4.61 | ~ ('#form633' @ '#sk88') 31.57/4.61 | ('#sk88' @ '#sk20' @ '#sk38') 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl335])). 31.57/4.61 thf(zip_derived_cl336, plain, 31.57/4.61 (( ((('#sk88' @ ('#sk105' @ '#sk88') @ ('#sk139' @ '#sk88')) & 31.57/4.61 ('#sk88' @ ('#sk139' @ '#sk88') @ ('#sk199' @ '#sk88')))) 31.57/4.61 | ~ ('#form633' @ '#sk88') 31.57/4.61 | ('#sk88' @ '#sk20' @ '#sk38') 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl335])). 31.57/4.61 thf(zip_derived_cl338, plain, 31.57/4.61 (( ('#sk88' @ ('#sk105' @ '#sk88') @ ('#sk139' @ '#sk88')) 31.57/4.61 | ('#form9') 31.57/4.61 | ('#sk88' @ '#sk20' @ '#sk38') 31.57/4.61 | ~ ('#form633' @ '#sk88'))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl336])). 31.57/4.61 thf(zip_derived_cl143, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ (X2 @ ('#sk186' @ X2) @ ('#sk344' @ X2)) | ('#form185' @ X2))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl132])). 31.57/4.61 thf(zip_derived_cl153, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( (X2 @ ('#sk258' @ X2) @ ('#sk344' @ X2)) | ('#form185' @ X2))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl142])). 31.57/4.61 thf(zip_derived_cl276, plain, 31.57/4.61 ((~ ('#sk5' @ ('#sk87' @ '#sk5') @ ('#sk119' @ '#sk5')) 31.57/4.61 | ~ ('#form19') 31.57/4.61 | ~ ('#form185' @ '#sk5'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl274])). 31.57/4.61 thf(zip_derived_cl339, plain, 31.57/4.61 (( ('#sk88' @ ('#sk139' @ '#sk88') @ ('#sk199' @ '#sk88')) 31.57/4.61 | ('#form9') 31.57/4.61 | ('#sk88' @ '#sk20' @ '#sk38') 31.57/4.61 | ~ ('#form633' @ '#sk88'))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl336])). 31.57/4.61 thf(zip_derived_cl10, plain, 31.57/4.61 ( (((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 31.57/4.61 ('#sk5' @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk5' @ Y0 @ Y1) & 31.57/4.61 ('#sk5' @ Y1 @ Y2))) => 31.57/4.61 ('#sk5' @ Y0 @ Y2))))))))))))))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 31.57/4.61 thf(zip_derived_cl14, plain, 31.57/4.61 ( (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk5' @ Y0 @ Y1) & ('#sk5' @ 31.57/4.61 Y1 @ Y2))) => 31.57/4.61 ('#sk5' @ Y0 @ Y2))))))))))))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 31.57/4.61 thf(zip_derived_cl17, plain, 31.57/4.61 (![X2 : a]: 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk5' @ X2 @ Y0) & ('#sk5' @ Y0 @ Y1))) => 31.57/4.61 ('#sk5' @ X2 @ Y1)))))))))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 31.57/4.61 thf(zip_derived_cl21, plain, 31.57/4.61 (![X2 : a, X4 : a]: 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 ((((('#sk5' @ X2 @ X4) & ('#sk5' @ X4 @ Y0))) => 31.57/4.61 ('#sk5' @ X2 @ Y0))))))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 31.57/4.61 thf(zip_derived_cl25, plain, 31.57/4.61 (![X2 : a, X4 : a, X6 : a]: 31.57/4.61 ((((('#sk5' @ X2 @ X4) & ('#sk5' @ X4 @ X6))) => ('#sk5' @ X2 @ X6)))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl21])). 31.57/4.61 thf(zip_derived_cl36, plain, 31.57/4.61 (![X2 : a, X4 : a, X6 : a]: 31.57/4.61 (~ ((('#sk5' @ X2 @ X4) & ('#sk5' @ X4 @ X6))) | ('#sk5' @ X2 @ X6))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 31.57/4.61 thf(zip_derived_cl46, plain, 31.57/4.61 (![X2 : a, X4 : a, X6 : a]: 31.57/4.61 (~ ('#sk5' @ X2 @ X4) | ~ ('#sk5' @ X4 @ X6) | ('#sk5' @ X2 @ X6))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl36])). 31.57/4.61 thf(zip_derived_cl13, plain, 31.57/4.61 ( (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 31.57/4.61 ('#sk5' @ Y0 @ Y1)))))))))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 31.57/4.61 thf(zip_derived_cl16, plain, 31.57/4.61 (![X2 : a]: 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 ((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) => 31.57/4.61 ('#sk5' @ X2 @ Y0))))))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 31.57/4.61 thf(zip_derived_cl20, plain, 31.57/4.61 (![X2 : a, X4 : a]: 31.57/4.61 ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) => ('#sk5' @ X2 @ X4)))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 31.57/4.61 thf(zip_derived_cl24, plain, 31.57/4.61 (![X2 : a, X4 : a]: 31.57/4.61 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) | ('#sk5' @ X2 @ X4))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 31.57/4.61 thf(zip_derived_cl35, plain, 31.57/4.61 (![X2 : a, X4 : a]: (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 31.57/4.61 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl24])). 31.57/4.61 thf(zip_derived_cl34, plain, 31.57/4.61 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 31.57/4.61 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl24])). 31.57/4.61 thf(zip_derived_cl93, plain, 31.57/4.61 (( (((((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 31.57/4.61 ('#sk88' @ Y0 @ Y1))))))))) & 31.57/4.61 (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk88' @ Y0 @ Y1) & 31.57/4.61 ('#sk88' @ Y1 @ Y2))) => 31.57/4.61 ('#sk88' @ Y0 @ Y2)))))))))))))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 31.57/4.61 thf(zip_derived_cl104, plain, 31.57/4.61 (( (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 (((!!) @ (^[Y2 : a]: 31.57/4.61 ((((('#sk88' @ Y0 @ Y1) & 31.57/4.61 ('#sk88' @ Y1 @ Y2))) => 31.57/4.61 ('#sk88' @ Y0 @ Y2)))))))))))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl93])). 31.57/4.61 thf(zip_derived_cl117, plain, 31.57/4.61 (![X2 : a]: 31.57/4.61 ( (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk88' @ X2 @ Y0) & ('#sk88' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 ('#sk88' @ X2 @ Y1))))))))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl104])). 31.57/4.61 thf(zip_derived_cl129, plain, 31.57/4.61 (![X2 : a, X4 : a]: 31.57/4.61 ( (((!!) @ (^[Y0 : a]: 31.57/4.61 ((((('#sk88' @ X2 @ X4) & ('#sk88' @ X4 @ Y0))) => 31.57/4.61 ('#sk88' @ X2 @ Y0)))))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl117])). 31.57/4.61 thf(zip_derived_cl141, plain, 31.57/4.61 (![X2 : a, X4 : a, X6 : a]: 31.57/4.61 ( ((((('#sk88' @ X2 @ X4) & ('#sk88' @ X4 @ X6))) => ('#sk88' @ X2 @ 31.57/4.61 X6))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl129])). 31.57/4.61 thf(zip_derived_cl152, plain, 31.57/4.61 (![X2 : a, X4 : a, X6 : a]: 31.57/4.61 (~ ((('#sk88' @ X2 @ X4) & ('#sk88' @ X4 @ X6))) 31.57/4.61 | ('#sk88' @ X2 @ X6) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl141])). 31.57/4.61 thf(zip_derived_cl163, plain, 31.57/4.61 (![X2 : a, X4 : a, X6 : a]: 31.57/4.61 (~ ('#sk88' @ X2 @ X4) 31.57/4.61 | ~ ('#sk88' @ X4 @ X6) 31.57/4.61 | ('#form9') 31.57/4.61 | ('#sk88' @ X2 @ X6))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl152])). 31.57/4.61 thf(zip_derived_cl168, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( ('#form633' @ X2) 31.57/4.61 | ~ (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.57/4.61 Y1))) => 31.57/4.61 (X2 @ Y0 @ Y1))))))))))), 31.57/4.61 define([status(thm)])). 31.57/4.61 thf(zip_derived_cl169, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ (((!!) @ (^[Y0 : a]: 31.57/4.61 ((((('#sk2' @ ('#sk313' @ X2) @ Y0) | ('#sk1' @ 31.57/4.61 ('#sk313' @ X2) @ Y0))) => 31.57/4.61 (X2 @ ('#sk313' @ X2) @ Y0)))))) 31.57/4.61 | ('#form633' @ X2))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl168])). 31.57/4.61 thf(zip_derived_cl175, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ ((((('#sk2' @ ('#sk313' @ X2) @ ('#sk386' @ X2)) | ('#sk1' @ 31.57/4.61 ('#sk313' @ X2) @ ('#sk386' @ X2)))) => 31.57/4.61 (X2 @ ('#sk313' @ X2) @ ('#sk386' @ X2)))) 31.57/4.61 | ('#form633' @ X2))), 31.57/4.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl169])). 31.57/4.61 thf(zip_derived_cl181, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( ((('#sk2' @ ('#sk313' @ X2) @ ('#sk386' @ X2)) | ('#sk1' @ 31.57/4.61 ('#sk313' @ X2) @ ('#sk386' @ X2)))) 31.57/4.61 | ('#form633' @ X2))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl175])). 31.57/4.61 thf(zip_derived_cl187, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 ( ('#sk2' @ ('#sk313' @ X2) @ ('#sk386' @ X2)) 31.57/4.61 | ('#sk1' @ ('#sk313' @ X2) @ ('#sk386' @ X2)) 31.57/4.61 | ('#form633' @ X2))), 31.57/4.61 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl181])). 31.57/4.61 thf(zip_derived_cl182, plain, 31.57/4.61 (![X2 : a > a > $o]: 31.57/4.61 (~ (X2 @ ('#sk313' @ X2) @ ('#sk386' @ X2)) | ('#form633' @ X2))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl175])). 31.57/4.61 thf(zip_derived_cl103, plain, 31.57/4.61 (( (((!!) @ (^[Y0 : a]: 31.57/4.61 (((!!) @ (^[Y1 : a]: 31.57/4.61 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 31.57/4.61 ('#sk88' @ Y0 @ Y1))))))))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl93])). 31.57/4.61 thf(zip_derived_cl116, plain, 31.57/4.61 (![X2 : a]: 31.57/4.61 ( (((!!) @ (^[Y0 : a]: 31.57/4.61 ((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) => 31.57/4.61 ('#sk88' @ X2 @ Y0)))))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl103])). 31.57/4.61 thf(zip_derived_cl128, plain, 31.57/4.61 (![X2 : a, X4 : a]: 31.57/4.61 ( ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) => ('#sk88' @ X2 @ X4))) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl116])). 31.57/4.61 thf(zip_derived_cl140, plain, 31.57/4.61 (![X2 : a, X4 : a]: 31.57/4.61 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 31.57/4.61 | ('#sk88' @ X2 @ X4) 31.57/4.61 | ('#form9'))), 31.57/4.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl128])). 31.57/4.61 thf(zip_derived_cl150, plain, 31.57/4.61 (![X2 : a, X4 : a]: 31.57/4.61 (~ ('#sk1' @ X2 @ X4) | ('#form9') | ('#sk88' @ X2 @ X4))), 31.57/4.61 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl140])). 31.57/4.61 thf(zip_derived_cl151, plain, 31.57/4.61 (![X2 : a, X4 : a]: 31.57/4.61 (~ ('#sk2' @ X2 @ X4) | ('#form9') | ('#sk88' @ X2 @ X4))), 31.57/4.61 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl140])). 31.57/4.61 thf(zip_derived_cl4319, plain, ($false), 31.57/4.61 inference('eprover', [status(thm)], 31.57/4.61 [zip_derived_cl137, zip_derived_cl155, zip_derived_cl56, 31.57/4.61 zip_derived_cl157, zip_derived_cl158, zip_derived_cl156, 31.57/4.61 zip_derived_cl112, zip_derived_cl219, zip_derived_cl220, 31.57/4.61 zip_derived_cl113, zip_derived_cl94, zip_derived_cl125, 31.57/4.61 zip_derived_cl390, zip_derived_cl385, zip_derived_cl154, 31.57/4.61 zip_derived_cl277, zip_derived_cl389, zip_derived_cl391, 31.57/4.61 zip_derived_cl337, zip_derived_cl338, zip_derived_cl143, 31.57/4.61 zip_derived_cl153, zip_derived_cl276, zip_derived_cl339, 31.57/4.61 zip_derived_cl46, zip_derived_cl35, zip_derived_cl34, 31.57/4.61 zip_derived_cl163, zip_derived_cl187, zip_derived_cl182, 31.57/4.61 zip_derived_cl150, zip_derived_cl151])). 31.57/4.61 31.57/4.61 % SZS output end Refutation 31.57/4.61 31.57/4.61 31.57/4.61 % Terminating... 31.94/4.74 % Runner terminated. 31.94/4.74 % Zipperpin 1.5 exiting 31.94/4.75 EOF