0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Yq6bOKh9Cy true 0.13/0.34 % Computer : n013.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1440 0.13/0.34 % WCLimit : 180 0.13/0.34 % DateTime : Mon Jul 3 04:01:02 EDT 2023 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 1440 s 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.34 % Python version: Python 3.6.8 0.13/0.34 % Running in HO mode 0.53/0.65 % Total configuration time : 828 0.53/0.65 % Estimated wc time : 1656 0.53/0.65 % Estimated cpu time (8 cpus) : 207.0 0.53/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.53/0.70 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.55/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.55/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.55/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.55/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.55/0.74 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 55.43/7.60 % Solved by lams/20_acsne_simpl.sh. 55.43/7.60 % done 885 iterations in 6.741s 55.43/7.60 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 55.43/7.60 % SZS output start Refutation 55.43/7.60 thf(iS_type, type, iS: $tType). 55.43/7.60 thf('#sk1544_type', type, '#sk1544': (iS > iS > iS > $o) > iS). 55.43/7.60 thf('#sk8_type', type, '#sk8': iS). 55.43/7.60 thf('#sk857_type', type, '#sk857': (iS > iS > iS > $o) > iS). 55.43/7.60 thf('#sk1_type', type, '#sk1': iS). 55.43/7.60 thf('#sk974_type', type, '#sk974': (iS > iS > iS > $o) > iS). 55.43/7.60 thf('#sk14_type', type, '#sk14': iS). 55.43/7.60 thf('#sk160_type', type, '#sk160': (iS > iS > iS > $o) > iS). 55.43/7.60 thf('#sk82_type', type, '#sk82': (iS > iS > iS > $o) > iS). 55.43/7.60 thf('#sk1190_type', type, '#sk1190': (iS > iS > iS > $o) > iS). 55.43/7.60 thf(c0_type, type, c0: iS). 55.43/7.60 thf('#sk1357_type', type, '#sk1357': (iS > iS > iS > $o) > iS). 55.43/7.60 thf('#sk603_type', type, '#sk603': (iS > iS > iS > $o) > iS). 55.43/7.60 thf('#sk916_type', type, '#sk916': (iS > iS > iS > $o) > iS). 55.43/7.60 thf('#sk481_type', type, '#sk481': (iS > iS > iS > $o) > iS). 55.43/7.60 thf('#sk128_type', type, '#sk128': (iS > iS > iS > $o) > iS). 55.43/7.60 thf('#sk1268_type', type, '#sk1268': (iS > iS > iS > $o) > iS). 55.43/7.60 thf('#form2426_type', type, '#form2426': $o). 55.43/7.60 thf('#sk1111_type', type, '#sk1111': (iS > iS > iS > $o) > iS). 55.43/7.60 thf('#form658_type', type, '#form658': (iS > iS > iS > $o) > $o). 55.43/7.60 thf('#sk1445_type', type, '#sk1445': (iS > iS > iS > $o) > iS). 55.43/7.60 thf('#sk2_type', type, '#sk2': iS). 55.43/7.60 thf(cP_type, type, cP: iS > iS > iS). 55.43/7.60 thf('#form542_type', type, '#form542': (iS > iS > iS > $o) > $o). 55.43/7.60 thf('#sk72_type', type, '#sk72': (iS > iS > iS > $o) > iS). 55.43/7.60 thf('#sk107_type', type, '#sk107': (iS > iS > iS > $o) > iS). 55.43/7.60 thf('#sk192_type', type, '#sk192': (iS > iS > iS > $o) > iS). 55.43/7.60 thf('#sk27_type', type, '#sk27': iS > iS > iS > $o). 55.43/7.60 thf('#sk1043_type', type, '#sk1043': (iS > iS > iS > $o) > iS). 55.43/7.60 thf(cS_LEM2_pme, conjecture, 55.43/7.60 (( ( ![Xx:iS,Xy:iS,Xu:iS,Xv:iS]: 55.43/7.60 ( ( ( cP @ Xx @ Xu ) = ( cP @ Xy @ Xv ) ) => 55.43/7.60 ( ( ( Xu ) = ( Xv ) ) & ( ( Xx ) = ( Xy ) ) ) ) ) & 55.43/7.60 ( ![X:( iS > $o )]: 55.43/7.60 ( ( ( X @ c0 ) & 55.43/7.60 ( ![Xx:iS,Xy:iS]: 55.43/7.60 ( ( ( X @ Xx ) & ( X @ Xy ) ) => ( X @ ( cP @ Xx @ Xy ) ) ) ) ) => 55.43/7.60 ( ![Xx:iS]: ( X @ Xx ) ) ) ) & 55.43/7.60 ( ![Xx:iS,Xy:iS]: ( ( cP @ Xx @ Xy ) != ( c0 ) ) ) ) => 55.43/7.60 ( ![Xx:iS,Xy:iS,Xu:iS,Xv:iS]: 55.43/7.60 ( ( ( ![R:( iS > iS > iS > $o )]: 55.43/7.60 ( ( ![Xa:iS,Xb:iS,Xc:iS]: 55.43/7.60 ( ( ( ( ( Xa ) = ( c0 ) ) & ( ( Xb ) = ( Xc ) ) ) | 55.43/7.60 ( ( ( Xb ) = ( c0 ) ) & ( ( Xa ) = ( Xc ) ) ) | 55.43/7.60 ( ?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]: 55.43/7.60 ( ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) & 55.43/7.60 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) & 55.43/7.60 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 55.43/7.60 ( R @ Xx1 @ Xy1 @ Xz1 ) & ( R @ Xx2 @ Xy2 @ Xz2 ) ) ) ) => 55.43/7.60 ( R @ Xa @ Xb @ Xc ) ) ) => 55.43/7.60 ( R @ Xx @ Xy @ Xy ) ) ) & 55.43/7.60 ( ![R:( iS > iS > iS > $o )]: 55.43/7.60 ( ( ![Xa:iS,Xb:iS,Xc:iS]: 55.43/7.60 ( ( ( ( ( Xb ) = ( Xc ) ) & ( ( Xa ) = ( c0 ) ) ) | 55.43/7.60 ( ( ( Xb ) = ( c0 ) ) & ( ( Xa ) = ( Xc ) ) ) | 55.43/7.60 ( ?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]: 55.43/7.60 ( ( R @ Xx2 @ Xy2 @ Xz2 ) & ( R @ Xx1 @ Xy1 @ Xz1 ) & 55.43/7.60 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 55.43/7.60 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) & 55.43/7.60 ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) ) ) ) => 55.43/7.60 ( R @ Xa @ Xb @ Xc ) ) ) => 55.43/7.60 ( R @ Xu @ Xv @ Xv ) ) ) ) => 55.43/7.60 ( ![R:( iS > iS > iS > $o )]: 55.43/7.60 ( ( ![Xa:iS,Xb:iS,Xc:iS]: 55.43/7.60 ( ( ( ( ( Xa ) = ( c0 ) ) & ( ( Xb ) = ( Xc ) ) ) | 55.43/7.60 ( ?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]: 55.43/7.60 ( ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) & 55.43/7.60 ( R @ Xx1 @ Xy1 @ Xz1 ) & ( R @ Xx2 @ Xy2 @ Xz2 ) & 55.43/7.60 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 55.43/7.60 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) ) ) | 55.43/7.60 ( ( ( Xa ) = ( Xc ) ) & ( ( Xb ) = ( c0 ) ) ) ) => 55.43/7.60 ( R @ Xa @ Xb @ Xc ) ) ) => 55.43/7.60 ( R @ ( cP @ Xx @ Xu ) @ ( cP @ Xy @ Xv ) @ ( cP @ Xy @ Xv ) ) ) ) ) ))). 55.43/7.60 thf(zf_stmt_0, negated_conjecture, 55.43/7.60 (~( ( ( ![Xx:iS,Xy:iS,Xu:iS,Xv:iS]: 55.43/7.60 ( ( ( cP @ Xx @ Xu ) = ( cP @ Xy @ Xv ) ) => 55.43/7.60 ( ( ( Xu ) = ( Xv ) ) & ( ( Xx ) = ( Xy ) ) ) ) ) & 55.43/7.60 ( ![X:( iS > $o )]: 55.43/7.60 ( ( ( X @ c0 ) & 55.43/7.60 ( ![Xx:iS,Xy:iS]: 55.43/7.60 ( ( ( X @ Xx ) & ( X @ Xy ) ) => ( X @ ( cP @ Xx @ Xy ) ) ) ) ) => 55.43/7.60 ( ![Xx:iS]: ( X @ Xx ) ) ) ) & 55.43/7.60 ( ![Xx:iS,Xy:iS]: ( ( cP @ Xx @ Xy ) != ( c0 ) ) ) ) => 55.43/7.60 ( ![Xx:iS,Xy:iS,Xu:iS,Xv:iS]: 55.43/7.60 ( ( ( ![R:( iS > iS > iS > $o )]: 55.43/7.60 ( ( ![Xa:iS,Xb:iS,Xc:iS]: 55.43/7.60 ( ( ( ( ( Xa ) = ( c0 ) ) & ( ( Xb ) = ( Xc ) ) ) | 55.43/7.60 ( ( ( Xb ) = ( c0 ) ) & ( ( Xa ) = ( Xc ) ) ) | 55.43/7.60 ( ?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]: 55.43/7.60 ( ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) & 55.43/7.60 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) & 55.43/7.60 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 55.43/7.60 ( R @ Xx1 @ Xy1 @ Xz1 ) & ( R @ Xx2 @ Xy2 @ Xz2 ) ) ) ) => 55.43/7.60 ( R @ Xa @ Xb @ Xc ) ) ) => 55.43/7.60 ( R @ Xx @ Xy @ Xy ) ) ) & 55.43/7.60 ( ![R:( iS > iS > iS > $o )]: 55.43/7.60 ( ( ![Xa:iS,Xb:iS,Xc:iS]: 55.43/7.60 ( ( ( ( ( Xb ) = ( Xc ) ) & ( ( Xa ) = ( c0 ) ) ) | 55.43/7.60 ( ( ( Xb ) = ( c0 ) ) & ( ( Xa ) = ( Xc ) ) ) | 55.43/7.60 ( ?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]: 55.43/7.60 ( ( R @ Xx2 @ Xy2 @ Xz2 ) & 55.43/7.60 ( R @ Xx1 @ Xy1 @ Xz1 ) & 55.43/7.60 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 55.43/7.60 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) & 55.43/7.60 ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) ) ) ) => 55.43/7.60 ( R @ Xa @ Xb @ Xc ) ) ) => 55.43/7.60 ( R @ Xu @ Xv @ Xv ) ) ) ) => 55.43/7.60 ( ![R:( iS > iS > iS > $o )]: 55.43/7.60 ( ( ![Xa:iS,Xb:iS,Xc:iS]: 55.43/7.60 ( ( ( ( ( Xa ) = ( c0 ) ) & ( ( Xb ) = ( Xc ) ) ) | 55.43/7.60 ( ?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]: 55.43/7.60 ( ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) & 55.43/7.60 ( R @ Xx1 @ Xy1 @ Xz1 ) & ( R @ Xx2 @ Xy2 @ Xz2 ) & 55.43/7.60 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 55.43/7.60 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) ) ) | 55.43/7.60 ( ( ( Xa ) = ( Xc ) ) & ( ( Xb ) = ( c0 ) ) ) ) => 55.43/7.60 ( R @ Xa @ Xb @ Xc ) ) ) => 55.43/7.60 ( R @ ( cP @ Xx @ Xu ) @ ( cP @ Xy @ Xv ) @ ( cP @ Xy @ Xv ) ) ) ) ) ) )), 55.43/7.60 inference('cnf.neg', [status(esa)], [cS_LEM2_pme])). 55.43/7.60 thf(zip_derived_cl0, plain, 55.43/7.60 (~ (((((((!!) @ (^[Y0 : iS]: 55.43/7.60 (((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((!!) @ (^[Y3 : iS]: 55.43/7.60 (((((cP @ Y0 @ 55.43/7.60 Y2) = (cP @ 55.43/7.60 Y1 @ Y3))) => 55.43/7.60 (((((Y2) = (Y3))) & 55.43/7.60 (((Y0) = (Y1))))))))))))))))))) & 55.43/7.60 (((!!) @ (^[Y0 : iS > $o]: 55.43/7.60 (((((Y0 @ c0) & 55.43/7.60 (((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((((Y0 @ Y1) & (Y0 @ Y2))) => 55.43/7.60 (Y0 @ (cP @ Y1 @ Y2)))))))))))) => 55.43/7.60 (((!!) @ (^[Y1 : iS]: (Y0 @ Y1))))))))) & 55.43/7.60 (((!!) @ (^[Y0 : iS]: 55.43/7.60 (((!!) @ (^[Y1 : iS]: (((cP @ Y0 @ Y1) != (c0))))))))))) => 55.43/7.60 (((!!) @ (^[Y0 : iS]: 55.43/7.60 (((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((!!) @ (^[Y3 : iS]: 55.43/7.60 (((((((!!) @ ( 55.43/7.60 ^[Y4 : 55.43/7.60 iS > iS > iS > $o]: 55.43/7.60 (((( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y6) = 55.43/7.60 (Y7))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y6) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (Y7))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y10 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y11 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y12 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y13 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y5) = 55.43/7.60 (cP @ 55.43/7.60 Y8 @ Y9))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y6) = 55.43/7.60 (cP @ 55.43/7.60 Y10 @ 55.43/7.60 Y11))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y7) = 55.43/7.60 (cP @ 55.43/7.60 Y12 @ 55.43/7.60 Y13))) & 55.43/7.60 ( 55.43/7.60 Y4 @ 55.43/7.60 Y8 @ 55.43/7.60 Y10 @ Y12) & 55.43/7.60 ( 55.43/7.60 Y4 @ 55.43/7.60 Y9 @ 55.43/7.60 Y11 @ Y13))))))))))))))))))))))) => 55.43/7.60 (Y4 @ 55.43/7.60 Y5 @ 55.43/7.60 Y6 @ Y7)))))))))))) => 55.43/7.60 (Y4 @ 55.43/7.60 Y0 @ Y1 @ 55.43/7.60 Y1)))))) & 55.43/7.60 (((!!) @ ( 55.43/7.60 ^[Y4 : 55.43/7.60 iS > iS > iS > $o]: 55.43/7.60 (((( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y6) = 55.43/7.60 (Y7))) & 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (c0))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y6) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (Y7))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y10 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y11 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y12 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y13 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 Y4 @ 55.43/7.60 Y9 @ 55.43/7.60 Y11 @ Y13) & 55.43/7.60 ( 55.43/7.60 Y4 @ 55.43/7.60 Y8 @ 55.43/7.60 Y10 @ Y12) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y7) = 55.43/7.60 (cP @ 55.43/7.60 Y12 @ 55.43/7.60 Y13))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y6) = 55.43/7.60 (cP @ 55.43/7.60 Y10 @ 55.43/7.60 Y11))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y5) = 55.43/7.60 (cP @ 55.43/7.60 Y8 @ Y9))))))))))))))))))))))))) => 55.43/7.60 (Y4 @ 55.43/7.60 Y5 @ 55.43/7.60 Y6 @ Y7)))))))))))) => 55.43/7.60 (Y4 @ 55.43/7.60 Y2 @ Y3 @ 55.43/7.60 Y3)))))))) => 55.43/7.60 (((!!) @ ( 55.43/7.60 ^[Y4 : iS > 55.43/7.60 iS > iS > $o]: 55.43/7.60 (((((!!) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y6) = 55.43/7.60 (Y7))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y10 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y11 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y12 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y13 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y5) = 55.43/7.60 (cP @ 55.43/7.60 Y8 @ Y9))) & 55.43/7.60 ( 55.43/7.60 Y4 @ 55.43/7.60 Y8 @ 55.43/7.60 Y10 @ Y12) & 55.43/7.60 ( 55.43/7.60 Y4 @ 55.43/7.60 Y9 @ 55.43/7.60 Y11 @ Y13) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y7) = 55.43/7.60 (cP @ 55.43/7.60 Y12 @ 55.43/7.60 Y13))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y6) = 55.43/7.60 (cP @ 55.43/7.60 Y10 @ 55.43/7.60 Y11))))))))))))))))))))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (Y7))) & 55.43/7.60 (( 55.43/7.60 (Y6) = 55.43/7.60 (c0))))))) => 55.43/7.60 (Y4 @ 55.43/7.60 Y5 @ 55.43/7.60 Y6 @ Y7)))))))))))) => 55.43/7.60 (Y4 @ 55.43/7.60 (cP @ Y0 @ 55.43/7.60 Y2) @ 55.43/7.60 (cP @ Y1 @ 55.43/7.60 Y3) @ 55.43/7.60 (cP @ Y1 @ 55.43/7.60 Y3)))))))))))))))))))))))), 55.43/7.60 inference('cnf', [status(esa)], [zf_stmt_0])). 55.43/7.60 thf(zip_derived_cl2, plain, 55.43/7.60 (~ (((!!) @ (^[Y0 : iS]: 55.43/7.60 (((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((!!) @ (^[Y3 : iS]: 55.43/7.60 (((((((!!) @ ( 55.43/7.60 ^[Y4 : iS > 55.43/7.60 iS > iS > $o]: 55.43/7.60 (((((!!) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y6) = 55.43/7.60 (Y7))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y6) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (Y7))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y10 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y11 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y12 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y13 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y5) = 55.43/7.60 (cP @ 55.43/7.60 Y8 @ Y9))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y6) = 55.43/7.60 (cP @ 55.43/7.60 Y10 @ 55.43/7.60 Y11))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y7) = 55.43/7.60 (cP @ 55.43/7.60 Y12 @ 55.43/7.60 Y13))) & 55.43/7.60 ( 55.43/7.60 Y4 @ 55.43/7.60 Y8 @ 55.43/7.60 Y10 @ Y12) & 55.43/7.60 ( 55.43/7.60 Y4 @ 55.43/7.60 Y9 @ 55.43/7.60 Y11 @ Y13))))))))))))))))))))))) => 55.43/7.60 (Y4 @ 55.43/7.60 Y5 @ 55.43/7.60 Y6 @ Y7)))))))))))) => 55.43/7.60 (Y4 @ Y0 @ 55.43/7.60 Y1 @ Y1)))))) & 55.43/7.60 (((!!) @ ( 55.43/7.60 ^[Y4 : iS > 55.43/7.60 iS > iS > $o]: 55.43/7.60 (((((!!) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y6) = 55.43/7.60 (Y7))) & 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (c0))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y6) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (Y7))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y10 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y11 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y12 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y13 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 Y4 @ 55.43/7.60 Y9 @ 55.43/7.60 Y11 @ Y13) & 55.43/7.60 ( 55.43/7.60 Y4 @ 55.43/7.60 Y8 @ 55.43/7.60 Y10 @ Y12) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y7) = 55.43/7.60 (cP @ 55.43/7.60 Y12 @ 55.43/7.60 Y13))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y6) = 55.43/7.60 (cP @ 55.43/7.60 Y10 @ 55.43/7.60 Y11))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y5) = 55.43/7.60 (cP @ 55.43/7.60 Y8 @ Y9))))))))))))))))))))))))) => 55.43/7.60 (Y4 @ 55.43/7.60 Y5 @ 55.43/7.60 Y6 @ Y7)))))))))))) => 55.43/7.60 (Y4 @ Y2 @ 55.43/7.60 Y3 @ Y3)))))))) => 55.43/7.60 (((!!) @ (^[Y4 : 55.43/7.60 iS > 55.43/7.60 iS > iS > $o]: 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y6) = 55.43/7.60 (Y7))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y10 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y11 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y12 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y13 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y5) = 55.43/7.60 (cP @ 55.43/7.60 Y8 @ Y9))) & 55.43/7.60 ( 55.43/7.60 Y4 @ 55.43/7.60 Y8 @ 55.43/7.60 Y10 @ Y12) & 55.43/7.60 ( 55.43/7.60 Y4 @ 55.43/7.60 Y9 @ 55.43/7.60 Y11 @ Y13) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y7) = 55.43/7.60 (cP @ 55.43/7.60 Y12 @ 55.43/7.60 Y13))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y6) = 55.43/7.60 (cP @ 55.43/7.60 Y10 @ 55.43/7.60 Y11))))))))))))))))))))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (Y7))) & 55.43/7.60 (( 55.43/7.60 (Y6) = 55.43/7.60 (c0))))))) => 55.43/7.60 (Y4 @ 55.43/7.60 Y5 @ 55.43/7.60 Y6 @ Y7)))))))))))) => 55.43/7.60 (Y4 @ 55.43/7.60 ( 55.43/7.60 cP @ 55.43/7.60 Y0 @ Y2) @ 55.43/7.60 ( 55.43/7.60 cP @ 55.43/7.60 Y1 @ Y3) @ 55.43/7.60 ( 55.43/7.60 cP @ 55.43/7.60 Y1 @ Y3)))))))))))))))))))))), 55.43/7.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 55.43/7.60 thf(zip_derived_cl6, plain, 55.43/7.60 (~ (((!!) @ (^[Y0 : iS]: 55.43/7.60 (((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((((((!!) @ (^[Y3 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((!!) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y4) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (Y6))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y4) = 55.43/7.60 (Y6))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y10 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y11 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y12 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y4) = 55.43/7.60 (cP @ 55.43/7.60 Y7 @ Y8))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y5) = 55.43/7.60 (cP @ 55.43/7.60 Y9 @ Y10))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y6) = 55.43/7.60 (cP @ 55.43/7.60 Y11 @ 55.43/7.60 Y12))) & 55.43/7.60 ( 55.43/7.60 Y3 @ 55.43/7.60 Y7 @ 55.43/7.60 Y9 @ Y11) & 55.43/7.60 ( 55.43/7.60 Y3 @ 55.43/7.60 Y8 @ 55.43/7.60 Y10 @ Y12))))))))))))))))))))))) => 55.43/7.60 (Y3 @ 55.43/7.60 Y4 @ 55.43/7.60 Y5 @ Y6)))))))))))) => 55.43/7.60 (Y3 @ '#sk1' @ 55.43/7.60 Y0 @ Y0)))))) & 55.43/7.60 (((!!) @ (^[Y3 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((!!) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (Y6))) & 55.43/7.60 (( 55.43/7.60 (Y4) = 55.43/7.60 (c0))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y4) = 55.43/7.60 (Y6))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y10 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y11 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y12 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 Y3 @ 55.43/7.60 Y8 @ 55.43/7.60 Y10 @ Y12) & 55.43/7.60 ( 55.43/7.60 Y3 @ 55.43/7.60 Y7 @ 55.43/7.60 Y9 @ Y11) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y6) = 55.43/7.60 (cP @ 55.43/7.60 Y11 @ 55.43/7.60 Y12))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y5) = 55.43/7.60 (cP @ 55.43/7.60 Y9 @ Y10))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y4) = 55.43/7.60 (cP @ 55.43/7.60 Y7 @ Y8))))))))))))))))))))))))) => 55.43/7.60 (Y3 @ 55.43/7.60 Y4 @ 55.43/7.60 Y5 @ Y6)))))))))))) => 55.43/7.60 (Y3 @ Y1 @ Y2 @ 55.43/7.60 Y2)))))))) => 55.43/7.60 (((!!) @ (^[Y3 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((!!) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (!!) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y4) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (Y6))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y10 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y11 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y12 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y4) = 55.43/7.60 (cP @ 55.43/7.60 Y7 @ Y8))) & 55.43/7.60 ( 55.43/7.60 Y3 @ 55.43/7.60 Y7 @ 55.43/7.60 Y9 @ Y11) & 55.43/7.60 ( 55.43/7.60 Y3 @ 55.43/7.60 Y8 @ 55.43/7.60 Y10 @ Y12) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y6) = 55.43/7.60 (cP @ 55.43/7.60 Y11 @ 55.43/7.60 Y12))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y5) = 55.43/7.60 (cP @ 55.43/7.60 Y9 @ Y10))))))))))))))))))))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y4) = 55.43/7.60 (Y6))) & 55.43/7.60 (( 55.43/7.60 (Y5) = 55.43/7.60 (c0))))))) => 55.43/7.60 (Y3 @ 55.43/7.60 Y4 @ 55.43/7.60 Y5 @ Y6)))))))))))) => 55.43/7.60 (Y3 @ 55.43/7.60 (cP @ '#sk1' @ Y1) @ 55.43/7.60 (cP @ Y0 @ Y2) @ 55.43/7.60 (cP @ Y0 @ Y2))))))))))))))))))), 55.43/7.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 55.43/7.60 thf(zip_derived_cl10, plain, 55.43/7.60 (~ (((!!) @ (^[Y0 : iS]: 55.43/7.60 (((!!) @ (^[Y1 : iS]: 55.43/7.60 (((((((!!) @ (^[Y2 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ (^[Y3 : iS]: 55.43/7.60 (((!!) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((!!) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y3) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y4) = 55.43/7.60 (Y5))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y4) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y3) = 55.43/7.60 (Y5))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y10 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y11 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y3) = 55.43/7.60 (cP @ 55.43/7.60 Y6 @ Y7))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y4) = 55.43/7.60 (cP @ 55.43/7.60 Y8 @ Y9))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y5) = 55.43/7.60 (cP @ 55.43/7.60 Y10 @ 55.43/7.60 Y11))) & 55.43/7.60 ( 55.43/7.60 Y2 @ 55.43/7.60 Y6 @ 55.43/7.60 Y8 @ Y10) & 55.43/7.60 ( 55.43/7.60 Y2 @ 55.43/7.60 Y7 @ 55.43/7.60 Y9 @ Y11))))))))))))))))))))))) => 55.43/7.60 (Y2 @ 55.43/7.60 Y3 @ 55.43/7.60 Y4 @ Y5)))))))))))) => 55.43/7.60 (Y2 @ '#sk1' @ '#sk2' @ 55.43/7.60 '#sk2')))))) & 55.43/7.60 (((!!) @ (^[Y2 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ (^[Y3 : iS]: 55.43/7.60 (((!!) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((!!) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y4) = 55.43/7.60 (Y5))) & 55.43/7.60 (( 55.43/7.60 (Y3) = 55.43/7.60 (c0))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y4) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y3) = 55.43/7.60 (Y5))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y10 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y11 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 Y2 @ 55.43/7.60 Y7 @ 55.43/7.60 Y9 @ Y11) & 55.43/7.60 ( 55.43/7.60 Y2 @ 55.43/7.60 Y6 @ 55.43/7.60 Y8 @ Y10) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y5) = 55.43/7.60 (cP @ 55.43/7.60 Y10 @ 55.43/7.60 Y11))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y4) = 55.43/7.60 (cP @ 55.43/7.60 Y8 @ Y9))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y3) = 55.43/7.60 (cP @ 55.43/7.60 Y6 @ Y7))))))))))))))))))))))))) => 55.43/7.60 (Y2 @ 55.43/7.60 Y3 @ 55.43/7.60 Y4 @ Y5)))))))))))) => 55.43/7.60 (Y2 @ Y0 @ Y1 @ Y1)))))))) => 55.43/7.60 (((!!) @ (^[Y2 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ (^[Y3 : iS]: 55.43/7.60 (((!!) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((!!) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y3) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y4) = 55.43/7.60 (Y5))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y10 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y11 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y3) = 55.43/7.60 (cP @ 55.43/7.60 Y6 @ Y7))) & 55.43/7.60 ( 55.43/7.60 Y2 @ 55.43/7.60 Y6 @ 55.43/7.60 Y8 @ Y10) & 55.43/7.60 ( 55.43/7.60 Y2 @ 55.43/7.60 Y7 @ 55.43/7.60 Y9 @ Y11) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y5) = 55.43/7.60 (cP @ 55.43/7.60 Y10 @ 55.43/7.60 Y11))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y4) = 55.43/7.60 (cP @ 55.43/7.60 Y8 @ Y9))))))))))))))))))))))) | 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (( 55.43/7.60 (Y3) = 55.43/7.60 (Y5))) & 55.43/7.60 (( 55.43/7.60 (Y4) = 55.43/7.60 (c0))))))) => 55.43/7.60 (Y2 @ 55.43/7.60 Y3 @ 55.43/7.60 Y4 @ Y5)))))))))))) => 55.43/7.60 (Y2 @ (cP @ '#sk1' @ Y0) @ 55.43/7.60 (cP @ '#sk2' @ Y1) @ 55.43/7.60 (cP @ '#sk2' @ Y1)))))))))))))))), 55.43/7.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 55.43/7.60 thf(zip_derived_cl14, plain, 55.43/7.60 (~ (((!!) @ (^[Y0 : iS]: 55.43/7.60 (((((((!!) @ (^[Y1 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ (^[Y2 : iS]: 55.43/7.60 (((!!) @ (^[Y3 : iS]: 55.43/7.60 (((!!) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((( 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 (Y2) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y3) = 55.43/7.60 (Y4))))) | 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 (Y3) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y2) = 55.43/7.60 (Y4))))) | 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y10 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y5 @ Y6))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y3) = 55.43/7.60 (cP @ 55.43/7.60 Y7 @ Y8))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y4) = 55.43/7.60 (cP @ 55.43/7.60 Y9 @ Y10))) & 55.43/7.60 ( 55.43/7.60 Y1 @ 55.43/7.60 Y5 @ 55.43/7.60 Y7 @ Y9) & 55.43/7.60 ( 55.43/7.60 Y1 @ 55.43/7.60 Y6 @ 55.43/7.60 Y8 @ Y10))))))))))))))))))))))) => 55.43/7.60 (Y1 @ 55.43/7.60 Y2 @ Y3 @ 55.43/7.60 Y4)))))))))))) => 55.43/7.60 (Y1 @ '#sk1' @ '#sk2' @ '#sk2')))))) & 55.43/7.60 (((!!) @ (^[Y1 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ (^[Y2 : iS]: 55.43/7.60 (((!!) @ (^[Y3 : iS]: 55.43/7.60 (((!!) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((( 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 (Y3) = 55.43/7.60 (Y4))) & 55.43/7.60 (( 55.43/7.60 (Y2) = 55.43/7.60 (c0))))) | 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 (Y3) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y2) = 55.43/7.60 (Y4))))) | 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y10 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 Y1 @ 55.43/7.60 Y6 @ 55.43/7.60 Y8 @ Y10) & 55.43/7.60 ( 55.43/7.60 Y1 @ 55.43/7.60 Y5 @ 55.43/7.60 Y7 @ Y9) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y4) = 55.43/7.60 (cP @ 55.43/7.60 Y9 @ Y10))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y3) = 55.43/7.60 (cP @ 55.43/7.60 Y7 @ Y8))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y5 @ Y6))))))))))))))))))))))))) => 55.43/7.60 (Y1 @ 55.43/7.60 Y2 @ Y3 @ 55.43/7.60 Y4)))))))))))) => 55.43/7.60 (Y1 @ '#sk8' @ Y0 @ Y0)))))))) => 55.43/7.60 (((!!) @ (^[Y1 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ (^[Y2 : iS]: 55.43/7.60 (((!!) @ (^[Y3 : iS]: 55.43/7.60 (((!!) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((((( 55.43/7.60 (( 55.43/7.60 (Y2) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y3) = 55.43/7.60 (Y4))))) | 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y10 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y5 @ Y6))) & 55.43/7.60 ( 55.43/7.60 Y1 @ 55.43/7.60 Y5 @ 55.43/7.60 Y7 @ Y9) & 55.43/7.60 ( 55.43/7.60 Y1 @ 55.43/7.60 Y6 @ 55.43/7.60 Y8 @ Y10) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y4) = 55.43/7.60 (cP @ 55.43/7.60 Y9 @ Y10))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y3) = 55.43/7.60 (cP @ 55.43/7.60 Y7 @ Y8))))))))))))))))))))))) | 55.43/7.60 (( 55.43/7.60 (( 55.43/7.60 (Y2) = 55.43/7.60 (Y4))) & 55.43/7.60 (( 55.43/7.60 (Y3) = 55.43/7.60 (c0))))))) => 55.43/7.60 (Y1 @ Y2 @ 55.43/7.60 Y3 @ Y4)))))))))))) => 55.43/7.60 (Y1 @ (cP @ '#sk1' @ '#sk8') @ 55.43/7.60 (cP @ '#sk2' @ Y0) @ (cP @ '#sk2' @ Y0))))))))))))), 55.43/7.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl10])). 55.43/7.60 thf(zip_derived_cl18, plain, 55.43/7.60 (~ (((((((!!) @ (^[Y0 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((!!) @ (^[Y3 : iS]: 55.43/7.60 (((((((( 55.43/7.60 (Y1) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y2) = 55.43/7.60 (Y3))))) | 55.43/7.60 (((( 55.43/7.60 (Y2) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y1) = 55.43/7.60 (Y3))))) | 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y6 @ Y7))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y3) = 55.43/7.60 (cP @ 55.43/7.60 Y8 @ Y9))) & 55.43/7.60 ( 55.43/7.60 Y0 @ 55.43/7.60 Y4 @ 55.43/7.60 Y6 @ Y8) & 55.43/7.60 ( 55.43/7.60 Y0 @ 55.43/7.60 Y5 @ 55.43/7.60 Y7 @ Y9))))))))))))))))))))))) => 55.43/7.60 (Y0 @ Y1 @ 55.43/7.60 Y2 @ Y3)))))))))))) => 55.43/7.60 (Y0 @ '#sk1' @ '#sk2' @ '#sk2')))))) & 55.43/7.60 (((!!) @ (^[Y0 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((!!) @ (^[Y3 : iS]: 55.43/7.60 (((((((( 55.43/7.60 (Y2) = 55.43/7.60 (Y3))) & 55.43/7.60 (( 55.43/7.60 (Y1) = 55.43/7.60 (c0))))) | 55.43/7.60 (((( 55.43/7.60 (Y2) = 55.43/7.60 (c0))) & 55.43/7.60 (( 55.43/7.60 (Y1) = 55.43/7.60 (Y3))))) | 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 Y0 @ 55.43/7.60 Y5 @ 55.43/7.60 Y7 @ Y9) & 55.43/7.60 ( 55.43/7.60 Y0 @ 55.43/7.60 Y4 @ 55.43/7.60 Y6 @ Y8) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y3) = 55.43/7.60 (cP @ 55.43/7.60 Y8 @ Y9))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y6 @ Y7))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))))))))))))))))))))))))) => 55.43/7.60 (Y0 @ Y1 @ 55.43/7.60 Y2 @ Y3)))))))))))) => 55.43/7.60 (Y0 @ '#sk8' @ '#sk14' @ '#sk14')))))))) => 55.43/7.60 (((!!) @ (^[Y0 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((!!) @ (^[Y3 : iS]: 55.43/7.60 (((((((((Y1) = 55.43/7.60 (c0))) & 55.43/7.60 (((Y2) = 55.43/7.60 (Y3))))) | 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 Y0 @ 55.43/7.60 Y4 @ 55.43/7.60 Y6 @ Y8) & 55.43/7.60 ( 55.43/7.60 Y0 @ 55.43/7.60 Y5 @ 55.43/7.60 Y7 @ Y9) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y3) = 55.43/7.60 (cP @ 55.43/7.60 Y8 @ Y9))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y6 @ Y7))))))))))))))))))))))) | 55.43/7.60 (((((Y1) = 55.43/7.60 (Y3))) & 55.43/7.60 (((Y2) = 55.43/7.60 (c0))))))) => 55.43/7.60 (Y0 @ Y1 @ Y2 @ 55.43/7.60 Y3)))))))))))) => 55.43/7.60 (Y0 @ (cP @ '#sk1' @ '#sk8') @ 55.43/7.60 (cP @ '#sk2' @ '#sk14') @ (cP @ '#sk2' @ '#sk14')))))))))), 55.43/7.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl14])). 55.43/7.60 thf(zip_derived_cl21, plain, 55.43/7.60 ( (((((!!) @ (^[Y0 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((!!) @ (^[Y3 : iS]: 55.43/7.60 (((((((((Y1) = (c0))) & 55.43/7.60 (((Y2) = (Y3))))) | 55.43/7.60 (((((Y2) = (c0))) & 55.43/7.60 (((Y1) = (Y3))))) | 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y6 @ Y7))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y3) = 55.43/7.60 (cP @ 55.43/7.60 Y8 @ Y9))) & 55.43/7.60 ( 55.43/7.60 Y0 @ 55.43/7.60 Y4 @ 55.43/7.60 Y6 @ Y8) & 55.43/7.60 ( 55.43/7.60 Y0 @ 55.43/7.60 Y5 @ 55.43/7.60 Y7 @ Y9))))))))))))))))))))))) => 55.43/7.60 (Y0 @ Y1 @ Y2 @ 55.43/7.60 Y3)))))))))))) => 55.43/7.60 (Y0 @ '#sk1' @ '#sk2' @ '#sk2')))))) & 55.43/7.60 (((!!) @ (^[Y0 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((!!) @ (^[Y3 : iS]: 55.43/7.60 (((((((((Y2) = (Y3))) & 55.43/7.60 (((Y1) = (c0))))) | 55.43/7.60 (((((Y2) = (c0))) & 55.43/7.60 (((Y1) = (Y3))))) | 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 Y0 @ 55.43/7.60 Y5 @ 55.43/7.60 Y7 @ Y9) & 55.43/7.60 ( 55.43/7.60 Y0 @ 55.43/7.60 Y4 @ 55.43/7.60 Y6 @ Y8) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y3) = 55.43/7.60 (cP @ 55.43/7.60 Y8 @ Y9))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y6 @ Y7))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))))))))))))))))))))))))) => 55.43/7.60 (Y0 @ Y1 @ Y2 @ 55.43/7.60 Y3)))))))))))) => 55.43/7.60 (Y0 @ '#sk8' @ '#sk14' @ '#sk14'))))))))), 55.43/7.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 55.43/7.60 thf(zip_derived_cl25, plain, 55.43/7.60 ( (((!!) @ (^[Y0 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((!!) @ (^[Y3 : iS]: 55.43/7.60 (((((((((Y1) = (c0))) & 55.43/7.60 (((Y2) = (Y3))))) | 55.43/7.60 (((((Y2) = (c0))) & 55.43/7.60 (((Y1) = (Y3))))) | 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y6 @ Y7))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y3) = 55.43/7.60 (cP @ 55.43/7.60 Y8 @ Y9))) & 55.43/7.60 ( 55.43/7.60 Y0 @ 55.43/7.60 Y4 @ 55.43/7.60 Y6 @ Y8) & 55.43/7.60 ( 55.43/7.60 Y0 @ 55.43/7.60 Y5 @ 55.43/7.60 Y7 @ Y9))))))))))))))))))))))) => 55.43/7.60 (Y0 @ Y1 @ Y2 @ Y3)))))))))))) => 55.43/7.60 (Y0 @ '#sk1' @ '#sk2' @ '#sk2'))))))), 55.43/7.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 55.43/7.60 thf(zip_derived_cl33, plain, 55.43/7.60 (![X2 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ (^[Y0 : iS]: 55.43/7.60 (((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((((((((Y0) = (c0))) & 55.43/7.60 (((Y1) = (Y2))))) | 55.43/7.60 (((((Y1) = (c0))) & 55.43/7.60 (((Y0) = (Y2))))) | 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y0) = 55.43/7.60 (cP @ 55.43/7.60 Y3 @ Y4))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y5 @ Y6))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y7 @ Y8))) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y3 @ 55.43/7.60 Y5 @ Y7) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y4 @ 55.43/7.60 Y6 @ Y8))))))))))))))))))))))) => 55.43/7.60 (X2 @ Y0 @ Y1 @ Y2)))))))))))) => 55.43/7.60 (X2 @ '#sk1' @ '#sk2' @ '#sk2')))), 55.43/7.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl25])). 55.43/7.60 thf(zip_derived_cl34, plain, 55.43/7.60 ( (((((!!) @ (^[Y0 : iS]: 55.43/7.60 (((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((((((((Y0) = (c0))) & 55.43/7.60 (((Y1) = (Y2))))) | 55.43/7.60 (((((Y1) = (c0))) & 55.43/7.60 (((Y0) = (Y2))))) | 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y0) = 55.43/7.60 (cP @ 55.43/7.60 Y3 @ Y4))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y5 @ Y6))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y7 @ Y8))) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y3 @ 55.43/7.60 Y5 @ Y7) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y4 @ 55.43/7.60 Y6 @ Y8))))))))))))))))))))))) => 55.43/7.60 ('#sk27' @ Y0 @ Y1 @ Y2)))))))))))) => 55.43/7.60 ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2')))), 55.43/7.60 inference('triggered_bool_instantiation', [status(thm)], 55.43/7.60 [zip_derived_cl33])). 55.43/7.60 thf(zip_derived_cl162, plain, 55.43/7.60 ((~ (((!!) @ (^[Y0 : iS]: 55.43/7.60 (((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((((((((Y0) = (c0))) & 55.43/7.60 (((Y1) = (Y2))))) | 55.43/7.60 (((((Y1) = (c0))) & 55.43/7.60 (((Y0) = (Y2))))) | 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y0) = 55.43/7.60 (cP @ 55.43/7.60 Y3 @ Y4))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y5 @ Y6))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y7 @ Y8))) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y3 @ 55.43/7.60 Y5 @ Y7) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y4 @ 55.43/7.60 Y6 @ Y8))))))))))))))))))))))) => 55.43/7.60 ('#sk27' @ Y0 @ Y1 @ Y2)))))))))))) 55.43/7.60 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 55.43/7.60 thf(zip_derived_cl163, plain, 55.43/7.60 ((~ (((!!) @ (^[Y0 : iS]: 55.43/7.60 (((!!) @ (^[Y1 : iS]: 55.43/7.60 ((((((((('#sk72' @ '#sk27') = (c0))) & 55.43/7.60 (((Y0) = (Y1))))) | 55.43/7.60 (((((Y0) = (c0))) & 55.43/7.60 ((('#sk72' @ '#sk27') = (Y1))))) | 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk72' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 Y2 @ Y3))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y0) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y6 @ Y7))) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y2 @ 55.43/7.60 Y4 @ Y6) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y3 @ 55.43/7.60 Y5 @ Y7))))))))))))))))))))))) => 55.43/7.60 ('#sk27' @ ('#sk72' @ '#sk27') @ Y0 @ Y1))))))))) 55.43/7.60 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl162])). 55.43/7.60 thf(zip_derived_cl164, plain, 55.43/7.60 ((~ (((!!) @ (^[Y0 : iS]: 55.43/7.60 ((((((((('#sk72' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk107' @ '#sk27') = (Y0))))) | 55.43/7.60 ((((('#sk107' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk72' @ '#sk27') = (Y0))))) | 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk72' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 Y1 @ Y2))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk107' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 Y3 @ Y4))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y0) = 55.43/7.60 (cP @ 55.43/7.60 Y5 @ Y6))) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y1 @ 55.43/7.60 Y3 @ Y5) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y2 @ 55.43/7.60 Y4 @ Y6))))))))))))))))))))))) => 55.43/7.60 ('#sk27' @ ('#sk72' @ '#sk27') @ 55.43/7.60 ('#sk107' @ '#sk27') @ Y0)))))) 55.43/7.60 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl163])). 55.43/7.60 thf(zip_derived_cl165, plain, 55.43/7.60 ((~ ((((((((('#sk72' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) | 55.43/7.60 ((((('#sk107' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk72' @ '#sk27') = ('#sk160' @ '#sk27'))))) | 55.43/7.60 (((??) @ (^[Y0 : iS]: 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk72' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 Y0 @ Y1))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk107' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 Y2 @ Y3))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk160' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y0 @ 55.43/7.60 Y2 @ Y4) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y1 @ 55.43/7.60 Y3 @ Y5))))))))))))))))))))))) => 55.43/7.60 ('#sk27' @ ('#sk72' @ '#sk27') @ ('#sk107' @ '#sk27') @ 55.43/7.60 ('#sk160' @ '#sk27')))) 55.43/7.60 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl164])). 55.43/7.60 thf(zip_derived_cl166, plain, 55.43/7.60 (( ((((((('#sk72' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) | 55.43/7.60 ((((('#sk107' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk72' @ '#sk27') = ('#sk160' @ '#sk27'))))) | 55.43/7.60 (((??) @ (^[Y0 : iS]: 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ (^[Y4 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk72' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 Y0 @ Y1))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk107' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 Y2 @ Y3))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk160' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y0 @ 55.43/7.60 Y2 @ Y4) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y1 @ 55.43/7.60 Y3 @ Y5))))))))))))))))))))))) 55.43/7.60 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl165])). 55.43/7.60 thf(zip_derived_cl168, plain, 55.43/7.60 (( ((((('#sk72' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 55.43/7.60 | ((((('#sk107' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk72' @ '#sk27') = ('#sk160' @ '#sk27'))))) 55.43/7.60 | (((??) @ (^[Y0 : iS]: 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ (^[Y4 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk72' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 Y0 @ Y1))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk107' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 Y2 @ Y3))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk160' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y0 @ 55.43/7.60 Y2 @ Y4) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y1 @ 55.43/7.60 Y3 @ Y5))))))))))))))))))))) 55.43/7.60 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.60 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl166])). 55.43/7.60 thf(zip_derived_cl33, plain, 55.43/7.60 (![X2 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ (^[Y0 : iS]: 55.43/7.60 (((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((((((((Y0) = (c0))) & 55.43/7.60 (((Y1) = (Y2))))) | 55.43/7.60 (((((Y1) = (c0))) & 55.43/7.60 (((Y0) = (Y2))))) | 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y0) = 55.43/7.60 (cP @ 55.43/7.60 Y3 @ Y4))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y5 @ Y6))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y7 @ Y8))) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y3 @ 55.43/7.60 Y5 @ Y7) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y4 @ 55.43/7.60 Y6 @ Y8))))))))))))))))))))))) => 55.43/7.60 (X2 @ Y0 @ Y1 @ Y2)))))))))))) => 55.43/7.60 (X2 @ '#sk1' @ '#sk2' @ '#sk2')))), 55.43/7.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl25])). 55.43/7.60 thf(zip_derived_cl44, plain, 55.43/7.60 (![X2 : iS > iS > iS > $o]: 55.43/7.60 (~ (((!!) @ (^[Y0 : iS]: 55.43/7.60 (((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((((((((Y0) = (c0))) & 55.43/7.60 (((Y1) = (Y2))))) | 55.43/7.60 (((((Y1) = (c0))) & 55.43/7.60 (((Y0) = (Y2))))) | 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y0) = 55.43/7.60 (cP @ 55.43/7.60 Y3 @ Y4))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y5 @ Y6))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y7 @ Y8))) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y3 @ 55.43/7.60 Y5 @ Y7) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y4 @ 55.43/7.60 Y6 @ Y8))))))))))))))))))))))) => 55.43/7.60 (X2 @ Y0 @ Y1 @ Y2)))))))))))) 55.43/7.60 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])). 55.43/7.60 thf(zip_derived_cl49, plain, 55.43/7.60 (![X2 : iS > iS > iS > $o]: 55.43/7.60 (~ (((!!) @ (^[Y0 : iS]: 55.43/7.60 (((!!) @ (^[Y1 : iS]: 55.43/7.60 ((((((((('#sk72' @ X2) = (c0))) & 55.43/7.60 (((Y0) = (Y1))))) | 55.43/7.60 (((((Y0) = (c0))) & 55.43/7.60 ((('#sk72' @ X2) = (Y1))))) | 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk72' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y2 @ Y3))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y0) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y6 @ Y7))) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y2 @ 55.43/7.60 Y4 @ Y6) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y3 @ 55.43/7.60 Y5 @ Y7))))))))))))))))))))))) => 55.43/7.60 (X2 @ ('#sk72' @ X2) @ Y0 @ Y1))))))))) 55.43/7.60 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl44])). 55.43/7.60 thf(zip_derived_cl54, plain, 55.43/7.60 (![X2 : iS > iS > iS > $o]: 55.43/7.60 (~ (((!!) @ (^[Y0 : iS]: 55.43/7.60 ((((((((('#sk72' @ X2) = (c0))) & 55.43/7.60 ((('#sk107' @ X2) = (Y0))))) | 55.43/7.60 ((((('#sk107' @ X2) = (c0))) & 55.43/7.60 ((('#sk72' @ X2) = (Y0))))) | 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk72' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y1 @ Y2))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk107' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y3 @ Y4))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y0) = 55.43/7.60 (cP @ 55.43/7.60 Y5 @ Y6))) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y1 @ 55.43/7.60 Y3 @ Y5) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y2 @ 55.43/7.60 Y4 @ Y6))))))))))))))))))))))) => 55.43/7.60 (X2 @ ('#sk72' @ X2) @ ('#sk107' @ X2) @ Y0)))))) 55.43/7.60 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl49])). 55.43/7.60 thf(zip_derived_cl57, plain, 55.43/7.60 (![X2 : iS > iS > iS > $o]: 55.43/7.60 (~ ((((((((('#sk72' @ X2) = (c0))) & 55.43/7.60 ((('#sk107' @ X2) = ('#sk160' @ X2))))) | 55.43/7.60 ((((('#sk107' @ X2) = (c0))) & 55.43/7.60 ((('#sk72' @ X2) = ('#sk160' @ X2))))) | 55.43/7.60 (((??) @ (^[Y0 : iS]: 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk72' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y0 @ Y1))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk107' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y2 @ Y3))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk160' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y0 @ 55.43/7.60 Y2 @ Y4) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y1 @ 55.43/7.60 Y3 @ Y5))))))))))))))))))))))) => 55.43/7.60 (X2 @ ('#sk72' @ X2) @ ('#sk107' @ X2) @ ('#sk160' @ X2)))) 55.43/7.60 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl54])). 55.43/7.60 thf(zip_derived_cl60, plain, 55.43/7.60 (![X2 : iS > iS > iS > $o]: 55.43/7.60 ( ((((((('#sk72' @ X2) = (c0))) & 55.43/7.60 ((('#sk107' @ X2) = ('#sk160' @ X2))))) | 55.43/7.60 ((((('#sk107' @ X2) = (c0))) & 55.43/7.60 ((('#sk72' @ X2) = ('#sk160' @ X2))))) | 55.43/7.60 (((??) @ (^[Y0 : iS]: 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk72' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y0 @ Y1))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk107' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y2 @ Y3))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk160' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y0 @ 55.43/7.60 Y2 @ Y4) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y1 @ 55.43/7.60 Y3 @ Y5))))))))))))))))))))))) 55.43/7.60 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 55.43/7.60 thf(zip_derived_cl67, plain, 55.43/7.60 (![X2 : iS > iS > iS > $o]: 55.43/7.60 ( ((((('#sk72' @ X2) = (c0))) & ((('#sk107' @ X2) = ('#sk160' @ X2))))) 55.43/7.60 | ((((('#sk107' @ X2) = (c0))) & 55.43/7.60 ((('#sk72' @ X2) = ('#sk160' @ X2))))) 55.43/7.60 | (((??) @ (^[Y0 : iS]: 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk72' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y0 @ Y1))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk107' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y2 @ Y3))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk160' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y0 @ 55.43/7.60 Y2 @ Y4) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y1 @ 55.43/7.60 Y3 @ Y5))))))))))))))))))))) 55.43/7.60 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.60 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl60])). 55.43/7.60 thf(zip_derived_cl73, plain, 55.43/7.60 (![X2 : iS > iS > iS > $o]: 55.43/7.60 ( ((('#sk107' @ X2) = ('#sk160' @ X2))) 55.43/7.60 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.60 | (((??) @ (^[Y0 : iS]: 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk72' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y0 @ Y1))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk107' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y2 @ Y3))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk160' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y0 @ 55.43/7.60 Y2 @ Y4) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y1 @ 55.43/7.60 Y3 @ Y5))))))))))))))))))))) 55.43/7.60 | ((((('#sk107' @ X2) = (c0))) & 55.43/7.60 ((('#sk72' @ X2) = ('#sk160' @ X2))))))), 55.43/7.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl67])). 55.43/7.60 thf(zip_derived_cl83, plain, 55.43/7.60 (![X2 : iS > iS > iS > $o]: 55.43/7.60 ((('#sk107' @ X2) = ('#sk160' @ X2)) 55.43/7.60 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.60 | (((??) @ (^[Y0 : iS]: 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk72' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y0 @ Y1))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk107' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y2 @ Y3))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk160' @ 55.43/7.60 X2) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y0 @ 55.43/7.60 Y2 @ Y4) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y1 @ 55.43/7.60 Y3 @ Y5))))))))))))))))))))) 55.43/7.60 | ((((('#sk107' @ X2) = (c0))) & 55.43/7.60 ((('#sk72' @ X2) = ('#sk160' @ X2))))))), 55.43/7.60 inference('simplify nested equalities', [status(thm)], [zip_derived_cl73])). 55.43/7.60 thf(zip_derived_cl84, plain, 55.43/7.60 (![X2 : iS > iS > iS > $o]: 55.43/7.60 (~ ('#form542' @ X2) 55.43/7.60 | ((((('#sk107' @ X2) = (c0))) & 55.43/7.60 ((('#sk72' @ X2) = ('#sk160' @ X2))))))), 55.43/7.60 define([status(thm)])). 55.43/7.60 thf(zip_derived_cl169, plain, 55.43/7.60 (( ('#form542' @ '#sk27') 55.43/7.60 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.60 | (((??) @ (^[Y0 : iS]: 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ (^[Y4 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk72' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 Y0 @ Y1))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk107' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 Y2 @ Y3))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk160' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y0 @ 55.43/7.60 Y2 @ Y4) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y1 @ 55.43/7.60 Y3 @ Y5))))))))))))))))))))) 55.43/7.60 | ((((('#sk72' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))))), 55.43/7.60 inference('renaming', [status(thm)], 55.43/7.60 [zip_derived_cl168, zip_derived_cl84])). 55.43/7.60 thf(zip_derived_cl170, plain, 55.43/7.60 (( (((??) @ (^[Y0 : iS]: 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ (^[Y4 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk72' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 ( 55.43/7.60 '#sk481' @ 55.43/7.60 '#sk27') @ 55.43/7.60 Y0))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk107' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 Y1 @ Y2))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ('#sk160' @ 55.43/7.60 '#sk27') = 55.43/7.60 (cP @ 55.43/7.60 Y3 @ Y4))) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 ( 55.43/7.60 '#sk481' @ 55.43/7.60 '#sk27') @ 55.43/7.60 Y1 @ Y3) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y0 @ 55.43/7.60 Y2 @ Y4)))))))))))))))))) 55.43/7.60 | ((((('#sk72' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 55.43/7.60 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.60 | ('#form542' @ '#sk27'))), 55.43/7.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl169])). 55.43/7.60 thf(zip_derived_cl171, plain, 55.43/7.60 (( (((??) @ (^[Y0 : iS]: 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 ((((('#sk72' @ 55.43/7.60 '#sk27') = (cP @ 55.43/7.60 ('#sk481' @ 55.43/7.60 '#sk27') @ 55.43/7.60 ('#sk857' @ 55.43/7.60 '#sk27')))) & 55.43/7.60 ((('#sk107' @ 55.43/7.60 '#sk27') = (cP @ 55.43/7.60 Y0 @ Y1))) & 55.43/7.60 ((('#sk160' @ 55.43/7.60 '#sk27') = (cP @ 55.43/7.60 Y2 @ Y3))) & 55.43/7.60 ('#sk27' @ 55.43/7.60 ('#sk481' @ '#sk27') @ 55.43/7.60 Y0 @ Y2) & 55.43/7.60 ('#sk27' @ 55.43/7.60 ('#sk857' @ '#sk27') @ 55.43/7.60 Y1 @ Y3))))))))))))))) 55.43/7.60 | ('#form542' @ '#sk27') 55.43/7.60 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.60 | ((((('#sk72' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))))), 55.43/7.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl170])). 55.43/7.60 thf(zip_derived_cl172, plain, 55.43/7.60 (( (((??) @ (^[Y0 : iS]: 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 ((((('#sk72' @ '#sk27') = (cP @ 55.43/7.60 ('#sk481' @ '#sk27') @ 55.43/7.60 ('#sk857' @ '#sk27')))) & 55.43/7.60 ((('#sk107' @ '#sk27') = (cP @ 55.43/7.60 ('#sk974' @ '#sk27') @ Y0))) & 55.43/7.60 ((('#sk160' @ '#sk27') = (cP @ 55.43/7.60 Y1 @ Y2))) & 55.43/7.60 ('#sk27' @ 55.43/7.60 ('#sk481' @ '#sk27') @ 55.43/7.60 ('#sk974' @ '#sk27') @ Y1) & 55.43/7.60 ('#sk27' @ 55.43/7.60 ('#sk857' @ '#sk27') @ Y0 @ Y2)))))))))))) 55.43/7.60 | ((((('#sk72' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 55.43/7.60 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.60 | ('#form542' @ '#sk27'))), 55.43/7.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl171])). 55.43/7.60 thf(zip_derived_cl173, plain, 55.43/7.60 (( (((??) @ (^[Y0 : iS]: 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 ((((('#sk72' @ '#sk27') = (cP @ 55.43/7.60 ('#sk481' @ '#sk27') @ 55.43/7.60 ('#sk857' @ '#sk27')))) & 55.43/7.60 ((('#sk107' @ '#sk27') = (cP @ 55.43/7.60 ('#sk974' @ '#sk27') @ 55.43/7.60 ('#sk1111' @ '#sk27')))) & 55.43/7.60 ((('#sk160' @ '#sk27') = (cP @ Y0 @ Y1))) & 55.43/7.60 ('#sk27' @ ('#sk481' @ '#sk27') @ 55.43/7.60 ('#sk974' @ '#sk27') @ Y0) & 55.43/7.60 ('#sk27' @ ('#sk857' @ '#sk27') @ 55.43/7.60 ('#sk1111' @ '#sk27') @ Y1))))))))) 55.43/7.60 | ('#form542' @ '#sk27') 55.43/7.60 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.60 | ((((('#sk72' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))))), 55.43/7.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl172])). 55.43/7.60 thf(zip_derived_cl174, plain, 55.43/7.60 (( (((??) @ (^[Y0 : iS]: 55.43/7.60 ((((('#sk72' @ '#sk27') = (cP @ ('#sk481' @ '#sk27') @ 55.43/7.60 ('#sk857' @ '#sk27')))) & 55.43/7.60 ((('#sk107' @ '#sk27') = (cP @ ('#sk974' @ '#sk27') @ 55.43/7.60 ('#sk1111' @ '#sk27')))) & 55.43/7.60 ((('#sk160' @ '#sk27') = (cP @ ('#sk1268' @ '#sk27') @ 55.43/7.60 Y0))) & 55.43/7.60 ('#sk27' @ ('#sk481' @ '#sk27') @ 55.43/7.60 ('#sk974' @ '#sk27') @ ('#sk1268' @ '#sk27')) & 55.43/7.60 ('#sk27' @ ('#sk857' @ '#sk27') @ 55.43/7.60 ('#sk1111' @ '#sk27') @ Y0)))))) 55.43/7.60 | ((((('#sk72' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 55.43/7.60 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.60 | ('#form542' @ '#sk27'))), 55.43/7.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl173])). 55.43/7.60 thf(zip_derived_cl175, plain, 55.43/7.60 (( ((((('#sk72' @ '#sk27') = (cP @ ('#sk481' @ '#sk27') @ 55.43/7.60 ('#sk857' @ '#sk27')))) & 55.43/7.60 ((('#sk107' @ '#sk27') = (cP @ ('#sk974' @ '#sk27') @ 55.43/7.60 ('#sk1111' @ '#sk27')))) & 55.43/7.60 ((('#sk160' @ '#sk27') = (cP @ ('#sk1268' @ '#sk27') @ 55.43/7.60 ('#sk1445' @ '#sk27')))) & 55.43/7.60 ('#sk27' @ ('#sk481' @ '#sk27') @ ('#sk974' @ '#sk27') @ 55.43/7.60 ('#sk1268' @ '#sk27')) & 55.43/7.60 ('#sk27' @ ('#sk857' @ '#sk27') @ ('#sk1111' @ '#sk27') @ 55.43/7.60 ('#sk1445' @ '#sk27')))) 55.43/7.60 | ('#form542' @ '#sk27') 55.43/7.60 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.60 | ((((('#sk72' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))))), 55.43/7.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl174])). 55.43/7.60 thf(zip_derived_cl176, plain, 55.43/7.60 (( ((('#sk72' @ '#sk27') = (cP @ ('#sk481' @ '#sk27') @ 55.43/7.60 ('#sk857' @ '#sk27')))) 55.43/7.60 | ((((('#sk72' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 55.43/7.60 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.60 | ('#form542' @ '#sk27'))), 55.43/7.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl175])). 55.43/7.60 thf(zip_derived_cl181, plain, 55.43/7.60 (((('#sk72' @ '#sk27') 55.43/7.60 = (cP @ ('#sk481' @ '#sk27') @ ('#sk857' @ '#sk27'))) 55.43/7.60 | ((((('#sk72' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 55.43/7.60 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.60 | ('#form542' @ '#sk27'))), 55.43/7.60 inference('simplify nested equalities', [status(thm)], 55.43/7.60 [zip_derived_cl176])). 55.43/7.60 thf(zip_derived_cl182, plain, 55.43/7.60 ((~ ('#form2426') 55.43/7.60 | ((((('#sk72' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))))), 55.43/7.60 define([status(thm)])). 55.43/7.60 thf(zip_derived_cl184, plain, 55.43/7.60 (( ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))) | ~ ('#form2426'))), 55.43/7.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl182])). 55.43/7.60 thf(zip_derived_cl193, plain, 55.43/7.60 (((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27')) | ~ ('#form2426'))), 55.43/7.60 inference('simplify nested equalities', [status(thm)], 55.43/7.60 [zip_derived_cl184])). 55.43/7.60 thf(zip_derived_cl22, plain, 55.43/7.60 (~ (((!!) @ (^[Y0 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((!!) @ (^[Y3 : iS]: 55.43/7.60 (((((((((Y1) = (c0))) & 55.43/7.60 (((Y2) = (Y3))))) | 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 Y0 @ 55.43/7.60 Y4 @ 55.43/7.60 Y6 @ Y8) & 55.43/7.60 ( 55.43/7.60 Y0 @ 55.43/7.60 Y5 @ 55.43/7.60 Y7 @ Y9) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y3) = 55.43/7.60 (cP @ 55.43/7.60 Y8 @ Y9))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y6 @ Y7))))))))))))))))))))))) | 55.43/7.60 (((((Y1) = (Y3))) & 55.43/7.60 (((Y2) = (c0))))))) => 55.43/7.60 (Y0 @ Y1 @ Y2 @ 55.43/7.60 Y3)))))))))))) => 55.43/7.60 (Y0 @ (cP @ '#sk1' @ '#sk8') @ 55.43/7.60 (cP @ '#sk2' @ '#sk14') @ (cP @ '#sk2' @ '#sk14')))))))), 55.43/7.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 55.43/7.60 thf(zip_derived_cl27, plain, 55.43/7.60 (~ (((((!!) @ (^[Y0 : iS]: 55.43/7.60 (((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((((((((Y0) = (c0))) & 55.43/7.60 (((Y1) = (Y2))))) | 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y0) = 55.43/7.60 (cP @ 55.43/7.60 Y3 @ Y4))) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y3 @ 55.43/7.60 Y5 @ Y7) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y4 @ 55.43/7.60 Y6 @ Y8) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y7 @ Y8))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y5 @ Y6))))))))))))))))))))))) | 55.43/7.60 (((((Y0) = (Y2))) & 55.43/7.60 (((Y1) = (c0))))))) => 55.43/7.60 ('#sk27' @ Y0 @ Y1 @ Y2)))))))))))) => 55.43/7.60 ('#sk27' @ (cP @ '#sk1' @ '#sk8') @ (cP @ '#sk2' @ '#sk14') @ 55.43/7.60 (cP @ '#sk2' @ '#sk14'))))), 55.43/7.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl22])). 55.43/7.60 thf(zip_derived_cl38, plain, 55.43/7.60 (~ ('#sk27' @ (cP @ '#sk1' @ '#sk8') @ (cP @ '#sk2' @ '#sk14') @ 55.43/7.60 (cP @ '#sk2' @ '#sk14'))), 55.43/7.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])). 55.43/7.60 thf(zip_derived_cl181, plain, 55.43/7.60 (((('#sk72' @ '#sk27') 55.43/7.60 = (cP @ ('#sk481' @ '#sk27') @ ('#sk857' @ '#sk27'))) 55.43/7.60 | ((((('#sk72' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 55.43/7.60 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.60 | ('#form542' @ '#sk27'))), 55.43/7.60 inference('simplify nested equalities', [status(thm)], 55.43/7.60 [zip_derived_cl176])). 55.43/7.60 thf(zip_derived_cl182, plain, 55.43/7.60 ((~ ('#form2426') 55.43/7.60 | ((((('#sk72' @ '#sk27') = (c0))) & 55.43/7.60 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))))), 55.43/7.60 define([status(thm)])). 55.43/7.60 thf(zip_derived_cl185, plain, 55.43/7.60 (( ('#form2426') 55.43/7.60 | ('#form542' @ '#sk27') 55.43/7.60 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.60 | (('#sk72' @ '#sk27') 55.43/7.60 = (cP @ ('#sk481' @ '#sk27') @ ('#sk857' @ '#sk27'))))), 55.43/7.60 inference('renaming', [status(thm)], 55.43/7.60 [zip_derived_cl181, zip_derived_cl182])). 55.43/7.60 thf(zip_derived_cl37, plain, 55.43/7.60 ( (((!!) @ (^[Y0 : iS]: 55.43/7.60 (((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((((((((Y0) = (c0))) & 55.43/7.60 (((Y1) = (Y2))))) | 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ (^[Y4 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y0) = 55.43/7.60 (cP @ 55.43/7.60 Y3 @ Y4))) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y3 @ 55.43/7.60 Y5 @ Y7) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y4 @ 55.43/7.60 Y6 @ Y8) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y7 @ Y8))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y5 @ Y6))))))))))))))))))))))) | 55.43/7.60 (((((Y0) = (Y2))) & 55.43/7.60 (((Y1) = (c0))))))) => 55.43/7.60 ('#sk27' @ Y0 @ Y1 @ Y2))))))))))))), 55.43/7.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])). 55.43/7.60 thf(zip_derived_cl46, plain, 55.43/7.60 (![X2 : iS]: 55.43/7.60 (((!!) @ (^[Y0 : iS]: 55.43/7.60 (((!!) @ (^[Y1 : iS]: 55.43/7.60 (((((((((X2) = (c0))) & (((Y0) = (Y1))))) | 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (X2) = 55.43/7.60 (cP @ 55.43/7.60 Y2 @ Y3))) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y2 @ 55.43/7.60 Y4 @ Y6) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y3 @ 55.43/7.60 Y5 @ Y7) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y6 @ Y7))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y0) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))))))))))))))))))))))) | 55.43/7.60 (((((X2) = (Y1))) & (((Y0) = (c0))))))) => 55.43/7.60 ('#sk27' @ X2 @ Y0 @ Y1)))))))))), 55.43/7.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 55.43/7.60 thf(zip_derived_cl51, plain, 55.43/7.60 (![X2 : iS, X4 : iS]: 55.43/7.60 (((!!) @ (^[Y0 : iS]: 55.43/7.60 (((((((((X2) = (c0))) & (((X4) = (Y0))))) | 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (X2) = 55.43/7.60 (cP @ 55.43/7.60 Y1 @ Y2))) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y1 @ 55.43/7.60 Y3 @ Y5) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y2 @ 55.43/7.60 Y4 @ Y6) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y0) = 55.43/7.60 (cP @ 55.43/7.60 Y5 @ Y6))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (X4) = 55.43/7.60 (cP @ 55.43/7.60 Y3 @ Y4))))))))))))))))))))))) | 55.43/7.60 (((((X2) = (Y0))) & (((X4) = (c0))))))) => 55.43/7.60 ('#sk27' @ X2 @ X4 @ Y0))))))), 55.43/7.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl46])). 55.43/7.60 thf(zip_derived_cl56, plain, 55.43/7.60 (![X2 : iS, X4 : iS, X6 : iS]: 55.43/7.60 (((((((((X2) = (c0))) & (((X4) = (X6))))) | 55.43/7.60 (((??) @ (^[Y0 : iS]: 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (X2) = 55.43/7.60 (cP @ 55.43/7.60 Y0 @ Y1))) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y0 @ 55.43/7.60 Y2 @ Y4) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y1 @ 55.43/7.60 Y3 @ Y5) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (X6) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (X4) = 55.43/7.60 (cP @ 55.43/7.60 Y2 @ Y3))))))))))))))))))))))) | 55.43/7.60 (((((X2) = (X6))) & (((X4) = (c0))))))) => 55.43/7.60 ('#sk27' @ X2 @ X4 @ X6)))), 55.43/7.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl51])). 55.43/7.60 thf(zip_derived_cl59, plain, 55.43/7.60 (![X2 : iS, X4 : iS, X6 : iS]: 55.43/7.60 (~ (((((((X2) = (c0))) & (((X4) = (X6))))) | 55.43/7.60 (((??) @ (^[Y0 : iS]: 55.43/7.60 (((??) @ (^[Y1 : iS]: 55.43/7.60 (((??) @ (^[Y2 : iS]: 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (X2) = 55.43/7.60 (cP @ 55.43/7.60 Y0 @ Y1))) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y0 @ 55.43/7.60 Y2 @ Y4) & 55.43/7.60 ( 55.43/7.60 '#sk27' @ 55.43/7.60 Y1 @ 55.43/7.60 Y3 @ Y5) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (X6) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (X4) = 55.43/7.60 (cP @ 55.43/7.60 Y2 @ Y3))))))))))))))))))))))) | 55.43/7.60 (((((X2) = (X6))) & (((X4) = (c0))))))) 55.43/7.60 | ('#sk27' @ X2 @ X4 @ X6))), 55.43/7.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl56])). 55.43/7.60 thf(zip_derived_cl64, plain, 55.43/7.60 (![X2 : iS, X4 : iS, X6 : iS]: 55.43/7.60 (~ (((((X2) = (c0))) & (((X4) = (X6))))) | ('#sk27' @ X2 @ X4 @ X6))), 55.43/7.60 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl59])). 55.43/7.60 thf(zip_derived_cl69, plain, 55.43/7.60 (![X2 : iS, X4 : iS, X6 : iS]: 55.43/7.60 (~ (((X2) = (c0))) | ~ (((X4) = (X6))) | ('#sk27' @ X2 @ X4 @ X6))), 55.43/7.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl64])). 55.43/7.60 thf(zip_derived_cl76, plain, 55.43/7.60 (![X2 : iS, X4 : iS, X6 : iS]: 55.43/7.60 (((X2) != (c0)) | ((X4) != (X6)) | ('#sk27' @ X2 @ X4 @ X6))), 55.43/7.60 inference('simplify nested equalities', [status(thm)], [zip_derived_cl69])). 55.43/7.60 thf(zip_derived_cl77, plain, (![X6 : iS]: ('#sk27' @ c0 @ X6 @ X6)), 55.43/7.60 inference('simplify', [status(thm)], [zip_derived_cl76])). 55.43/7.60 thf(zip_derived_cl26, plain, 55.43/7.60 ( (((!!) @ (^[Y0 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((!!) @ (^[Y3 : iS]: 55.43/7.60 (((((((((Y2) = (Y3))) & 55.43/7.60 (((Y1) = (c0))))) | 55.43/7.60 (((((Y2) = (c0))) & 55.43/7.60 (((Y1) = (Y3))))) | 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y9 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 Y0 @ 55.43/7.60 Y5 @ 55.43/7.60 Y7 @ Y9) & 55.43/7.60 ( 55.43/7.60 Y0 @ 55.43/7.60 Y4 @ 55.43/7.60 Y6 @ Y8) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y3) = 55.43/7.60 (cP @ 55.43/7.60 Y8 @ Y9))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y6 @ Y7))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y4 @ Y5))))))))))))))))))))))))) => 55.43/7.60 (Y0 @ Y1 @ Y2 @ Y3)))))))))))) => 55.43/7.60 (Y0 @ '#sk8' @ '#sk14' @ '#sk14'))))))), 55.43/7.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 55.43/7.60 thf(zip_derived_cl35, plain, 55.43/7.60 (![X2 : iS > iS > iS > $o]: 55.43/7.60 (((((!!) @ (^[Y0 : iS]: 55.43/7.60 (((!!) @ (^[Y1 : iS]: 55.43/7.60 (((!!) @ (^[Y2 : iS]: 55.43/7.60 (((((((((Y1) = (Y2))) & 55.43/7.60 (((Y0) = (c0))))) | 55.43/7.60 (((((Y1) = (c0))) & 55.43/7.60 (((Y0) = (Y2))))) | 55.43/7.60 (((??) @ (^[Y3 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y4 : iS]: 55.43/7.60 (((??) @ ( 55.43/7.60 ^[Y5 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y6 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y7 : iS]: 55.43/7.60 (( 55.43/7.60 (??) @ ( 55.43/7.60 ^[Y8 : iS]: 55.43/7.60 (( 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y4 @ 55.43/7.60 Y6 @ Y8) & 55.43/7.60 ( 55.43/7.60 X2 @ 55.43/7.60 Y3 @ 55.43/7.60 Y5 @ Y7) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y2) = 55.43/7.60 (cP @ 55.43/7.60 Y7 @ Y8))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y1) = 55.43/7.60 (cP @ 55.43/7.60 Y5 @ Y6))) & 55.43/7.60 ( 55.43/7.60 ( 55.43/7.60 (Y0) = 55.43/7.61 (cP @ 55.43/7.61 Y3 @ Y4))))))))))))))))))))))))) => 55.43/7.61 (X2 @ Y0 @ Y1 @ Y2)))))))))))) => 55.43/7.61 (X2 @ '#sk8' @ '#sk14' @ '#sk14')))), 55.43/7.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl26])). 55.43/7.61 thf(zip_derived_cl45, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 (~ (((!!) @ (^[Y0 : iS]: 55.43/7.61 (((!!) @ (^[Y1 : iS]: 55.43/7.61 (((!!) @ (^[Y2 : iS]: 55.43/7.61 (((((((((Y1) = (Y2))) & 55.43/7.61 (((Y0) = (c0))))) | 55.43/7.61 (((((Y1) = (c0))) & 55.43/7.61 (((Y0) = (Y2))))) | 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y4 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y5 : iS]: 55.43/7.61 (( 55.43/7.61 (??) @ ( 55.43/7.61 ^[Y6 : iS]: 55.43/7.61 (( 55.43/7.61 (??) @ ( 55.43/7.61 ^[Y7 : iS]: 55.43/7.61 (( 55.43/7.61 (??) @ ( 55.43/7.61 ^[Y8 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y4 @ 55.43/7.61 Y6 @ Y8) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y3 @ 55.43/7.61 Y5 @ Y7) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 (Y2) = 55.43/7.61 (cP @ 55.43/7.61 Y7 @ Y8))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 (Y1) = 55.43/7.61 (cP @ 55.43/7.61 Y5 @ Y6))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 (Y0) = 55.43/7.61 (cP @ 55.43/7.61 Y3 @ Y4))))))))))))))))))))))))) => 55.43/7.61 (X2 @ Y0 @ Y1 @ Y2)))))))))))) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 55.43/7.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 55.43/7.61 thf(zip_derived_cl50, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 (~ (((!!) @ (^[Y0 : iS]: 55.43/7.61 (((!!) @ (^[Y1 : iS]: 55.43/7.61 (((((((((Y0) = (Y1))) & 55.43/7.61 ((('#sk82' @ X2) = (c0))))) | 55.43/7.61 (((((Y0) = (c0))) & 55.43/7.61 ((('#sk82' @ X2) = (Y1))))) | 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y4 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y5 : iS]: 55.43/7.61 (( 55.43/7.61 (??) @ ( 55.43/7.61 ^[Y6 : iS]: 55.43/7.61 (( 55.43/7.61 (??) @ ( 55.43/7.61 ^[Y7 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y3 @ 55.43/7.61 Y5 @ Y7) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y2 @ 55.43/7.61 Y4 @ Y6) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 (Y1) = 55.43/7.61 (cP @ 55.43/7.61 Y6 @ Y7))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 (Y0) = 55.43/7.61 (cP @ 55.43/7.61 Y4 @ Y5))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk82' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y2 @ Y3))))))))))))))))))))))))) => 55.43/7.61 (X2 @ ('#sk82' @ X2) @ Y0 @ Y1))))))))) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl45])). 55.43/7.61 thf(zip_derived_cl55, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 (~ (((!!) @ (^[Y0 : iS]: 55.43/7.61 ((((((((('#sk128' @ X2) = (Y0))) & 55.43/7.61 ((('#sk82' @ X2) = (c0))))) | 55.43/7.61 ((((('#sk128' @ X2) = (c0))) & 55.43/7.61 ((('#sk82' @ X2) = (Y0))))) | 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y4 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y5 : iS]: 55.43/7.61 (( 55.43/7.61 (??) @ ( 55.43/7.61 ^[Y6 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y2 @ 55.43/7.61 Y4 @ Y6) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y1 @ 55.43/7.61 Y3 @ Y5) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 (Y0) = 55.43/7.61 (cP @ 55.43/7.61 Y5 @ Y6))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk128' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y3 @ Y4))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk82' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y1 @ Y2))))))))))))))))))))))))) => 55.43/7.61 (X2 @ ('#sk82' @ X2) @ ('#sk128' @ X2) @ Y0)))))) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl50])). 55.43/7.61 thf(zip_derived_cl58, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 (~ ((((((((('#sk128' @ X2) = ('#sk192' @ X2))) & 55.43/7.61 ((('#sk82' @ X2) = (c0))))) | 55.43/7.61 ((((('#sk128' @ X2) = (c0))) & 55.43/7.61 ((('#sk82' @ X2) = ('#sk192' @ X2))))) | 55.43/7.61 (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y4 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y5 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y1 @ 55.43/7.61 Y3 @ Y5) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y0 @ 55.43/7.61 Y2 @ Y4) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk192' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y4 @ Y5))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk128' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y2 @ Y3))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk82' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y0 @ Y1))))))))))))))))))))))))) => 55.43/7.61 (X2 @ ('#sk82' @ X2) @ ('#sk128' @ X2) @ ('#sk192' @ X2)))) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl55])). 55.43/7.61 thf(zip_derived_cl62, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((((((('#sk128' @ X2) = ('#sk192' @ X2))) & 55.43/7.61 ((('#sk82' @ X2) = (c0))))) | 55.43/7.61 ((((('#sk128' @ X2) = (c0))) & 55.43/7.61 ((('#sk82' @ X2) = ('#sk192' @ X2))))) | 55.43/7.61 (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y4 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y5 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y1 @ 55.43/7.61 Y3 @ Y5) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y0 @ 55.43/7.61 Y2 @ Y4) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk192' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y4 @ Y5))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk128' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y2 @ Y3))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk82' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y0 @ Y1))))))))))))))))))))))))) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 55.43/7.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 55.43/7.61 thf(zip_derived_cl68, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((((('#sk128' @ X2) = ('#sk192' @ X2))) & ((('#sk82' @ X2) = (c0))))) 55.43/7.61 | ((((('#sk128' @ X2) = (c0))) & 55.43/7.61 ((('#sk82' @ X2) = ('#sk192' @ X2))))) 55.43/7.61 | (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y4 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y5 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y1 @ 55.43/7.61 Y3 @ Y5) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y0 @ 55.43/7.61 Y2 @ Y4) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk192' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y4 @ Y5))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk128' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y2 @ Y3))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk82' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y0 @ Y1))))))))))))))))))))))) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 55.43/7.61 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl62])). 55.43/7.61 thf(zip_derived_cl74, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((('#sk128' @ X2) = ('#sk192' @ X2))) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y4 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y5 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y1 @ 55.43/7.61 Y3 @ Y5) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y0 @ 55.43/7.61 Y2 @ Y4) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk192' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y4 @ Y5))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk128' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y2 @ Y3))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk82' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y0 @ Y1))))))))))))))))))))))) 55.43/7.61 | ((((('#sk128' @ X2) = (c0))) & 55.43/7.61 ((('#sk82' @ X2) = ('#sk192' @ X2))))))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl68])). 55.43/7.61 thf(zip_derived_cl88, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ((('#sk128' @ X2) = ('#sk192' @ X2)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y4 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y5 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y1 @ 55.43/7.61 Y3 @ Y5) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y0 @ 55.43/7.61 Y2 @ Y4) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk192' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y4 @ Y5))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk128' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y2 @ Y3))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk82' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y0 @ Y1))))))))))))))))))))))) 55.43/7.61 | ((((('#sk128' @ X2) = (c0))) & 55.43/7.61 ((('#sk82' @ X2) = ('#sk192' @ X2))))))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], [zip_derived_cl74])). 55.43/7.61 thf(zip_derived_cl89, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ (^[Y4 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y0 @ 55.43/7.61 Y2 @ Y4) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 ( 55.43/7.61 '#sk603' @ 55.43/7.61 X2) @ 55.43/7.61 Y1 @ Y3) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk192' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y3 @ Y4))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk128' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y1 @ Y2))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk82' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 ( 55.43/7.61 '#sk603' @ 55.43/7.61 X2) @ Y0)))))))))))))))))))) 55.43/7.61 | ((((('#sk128' @ X2) = (c0))) & 55.43/7.61 ((('#sk82' @ X2) = ('#sk192' @ X2))))) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | (('#sk128' @ X2) = ('#sk192' @ X2)))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl88])). 55.43/7.61 thf(zip_derived_cl75, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((('#sk82' @ X2) = (c0))) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y4 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y5 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y1 @ 55.43/7.61 Y3 @ Y5) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y0 @ 55.43/7.61 Y2 @ Y4) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk192' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y4 @ Y5))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk128' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y2 @ Y3))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk82' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y0 @ Y1))))))))))))))))))))))) 55.43/7.61 | ((((('#sk128' @ X2) = (c0))) & 55.43/7.61 ((('#sk82' @ X2) = ('#sk192' @ X2))))))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl68])). 55.43/7.61 thf(zip_derived_cl90, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ((('#sk82' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y4 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y5 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y1 @ 55.43/7.61 Y3 @ Y5) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y0 @ 55.43/7.61 Y2 @ Y4) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk192' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y4 @ Y5))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk128' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y2 @ Y3))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk82' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y0 @ Y1))))))))))))))))))))))) 55.43/7.61 | ((((('#sk128' @ X2) = (c0))) & 55.43/7.61 ((('#sk82' @ X2) = ('#sk192' @ X2))))))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], [zip_derived_cl75])). 55.43/7.61 thf(zip_derived_cl91, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 (~ ('#form658' @ X2) 55.43/7.61 | ((((('#sk128' @ X2) = (c0))) & 55.43/7.61 ((('#sk82' @ X2) = ('#sk192' @ X2))))))), 55.43/7.61 define([status(thm)])). 55.43/7.61 thf(zip_derived_cl100, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ('#form658' @ X2) 55.43/7.61 | (('#sk128' @ X2) = ('#sk192' @ X2)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y4 : iS]: 55.43/7.61 (((X2 @ Y0 @ 55.43/7.61 Y2 @ Y4) & 55.43/7.61 (X2 @ 55.43/7.61 ('#sk603' @ 55.43/7.61 X2) @ 55.43/7.61 Y1 @ Y3) & 55.43/7.61 ((('#sk192' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y3 @ Y4))) & 55.43/7.61 ((('#sk128' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y1 @ Y2))) & 55.43/7.61 ((('#sk82' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 ('#sk603' @ 55.43/7.61 X2) @ 55.43/7.61 Y0)))))))))))))))))))))), 55.43/7.61 inference('renaming', [status(thm)], [zip_derived_cl89, zip_derived_cl91])). 55.43/7.61 thf(zip_derived_cl107, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((X2 @ 55.43/7.61 ('#sk916' @ X2) @ 55.43/7.61 Y1 @ Y3) & 55.43/7.61 (X2 @ 55.43/7.61 ('#sk603' @ X2) @ 55.43/7.61 Y0 @ Y2) & 55.43/7.61 ((('#sk192' @ 55.43/7.61 X2) = (cP @ 55.43/7.61 Y2 @ Y3))) & 55.43/7.61 ((('#sk128' @ 55.43/7.61 X2) = (cP @ 55.43/7.61 Y0 @ Y1))) & 55.43/7.61 ((('#sk82' @ X2) = 55.43/7.61 (cP @ 55.43/7.61 ('#sk603' @ X2) @ 55.43/7.61 ('#sk916' @ X2)))))))))))))))))) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | (('#sk128' @ X2) = ('#sk192' @ X2)) 55.43/7.61 | ('#form658' @ X2))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl100])). 55.43/7.61 thf(zip_derived_cl112, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((X2 @ ('#sk916' @ X2) @ Y0 @ 55.43/7.61 Y2) & 55.43/7.61 (X2 @ ('#sk603' @ X2) @ 55.43/7.61 ('#sk1043' @ X2) @ Y1) & 55.43/7.61 ((('#sk192' @ X2) = (cP @ 55.43/7.61 Y1 @ Y2))) & 55.43/7.61 ((('#sk128' @ X2) = (cP @ 55.43/7.61 ('#sk1043' @ X2) @ Y0))) & 55.43/7.61 ((('#sk82' @ X2) = (cP @ 55.43/7.61 ('#sk603' @ X2) @ 55.43/7.61 ('#sk916' @ X2))))))))))))))) 55.43/7.61 | ('#form658' @ X2) 55.43/7.61 | (('#sk128' @ X2) = ('#sk192' @ X2)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl107])). 55.43/7.61 thf(zip_derived_cl117, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((X2 @ ('#sk916' @ X2) @ 55.43/7.61 ('#sk1190' @ X2) @ Y1) & 55.43/7.61 (X2 @ ('#sk603' @ X2) @ 55.43/7.61 ('#sk1043' @ X2) @ Y0) & 55.43/7.61 ((('#sk192' @ X2) = (cP @ Y0 @ Y1))) & 55.43/7.61 ((('#sk128' @ X2) = (cP @ 55.43/7.61 ('#sk1043' @ X2) @ ('#sk1190' @ X2)))) & 55.43/7.61 ((('#sk82' @ X2) = (cP @ 55.43/7.61 ('#sk603' @ X2) @ ('#sk916' @ X2)))))))))))) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | (('#sk128' @ X2) = ('#sk192' @ X2)) 55.43/7.61 | ('#form658' @ X2))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl112])). 55.43/7.61 thf(zip_derived_cl122, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (((??) @ (^[Y0 : iS]: 55.43/7.61 (((X2 @ ('#sk916' @ X2) @ ('#sk1190' @ X2) @ Y0) & 55.43/7.61 (X2 @ ('#sk603' @ X2) @ ('#sk1043' @ X2) @ 55.43/7.61 ('#sk1357' @ X2)) & 55.43/7.61 ((('#sk192' @ X2) = (cP @ ('#sk1357' @ X2) @ Y0))) & 55.43/7.61 ((('#sk128' @ X2) = (cP @ ('#sk1043' @ X2) @ 55.43/7.61 ('#sk1190' @ X2)))) & 55.43/7.61 ((('#sk82' @ X2) = (cP @ ('#sk603' @ X2) @ 55.43/7.61 ('#sk916' @ X2))))))))) 55.43/7.61 | ('#form658' @ X2) 55.43/7.61 | (('#sk128' @ X2) = ('#sk192' @ X2)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl117])). 55.43/7.61 thf(zip_derived_cl128, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (((X2 @ ('#sk916' @ X2) @ ('#sk1190' @ X2) @ ('#sk1544' @ X2)) & 55.43/7.61 (X2 @ ('#sk603' @ X2) @ ('#sk1043' @ X2) @ ('#sk1357' @ X2)) & 55.43/7.61 ((('#sk192' @ X2) = (cP @ ('#sk1357' @ X2) @ ('#sk1544' @ X2)))) & 55.43/7.61 ((('#sk128' @ X2) = (cP @ ('#sk1043' @ X2) @ ('#sk1190' @ X2)))) & 55.43/7.61 ((('#sk82' @ X2) = (cP @ ('#sk603' @ X2) @ ('#sk916' @ X2)))))) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | (('#sk128' @ X2) = ('#sk192' @ X2)) 55.43/7.61 | ('#form658' @ X2))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl122])). 55.43/7.61 thf(zip_derived_cl143, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((('#sk128' @ X2) = (cP @ ('#sk1043' @ X2) @ ('#sk1190' @ X2)))) 55.43/7.61 | ('#form658' @ X2) 55.43/7.61 | (('#sk128' @ X2) = ('#sk192' @ X2)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl128])). 55.43/7.61 thf(zip_derived_cl157, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ((('#sk128' @ X2) = (cP @ ('#sk1043' @ X2) @ ('#sk1190' @ X2))) 55.43/7.61 | ('#form658' @ X2) 55.43/7.61 | (('#sk128' @ X2) = ('#sk192' @ X2)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], 55.43/7.61 [zip_derived_cl143])). 55.43/7.61 thf(zip_derived_cl84, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 (~ ('#form542' @ X2) 55.43/7.61 | ((((('#sk107' @ X2) = (c0))) & 55.43/7.61 ((('#sk72' @ X2) = ('#sk160' @ X2))))))), 55.43/7.61 define([status(thm)])). 55.43/7.61 thf(zip_derived_cl86, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((('#sk72' @ X2) = ('#sk160' @ X2))) | ~ ('#form542' @ X2))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl84])). 55.43/7.61 thf(zip_derived_cl99, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ((('#sk72' @ X2) = ('#sk160' @ X2)) | ~ ('#form542' @ X2))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], [zip_derived_cl86])). 55.43/7.61 thf(zip_derived_cl72, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((('#sk72' @ X2) = (c0))) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.61 | (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y4 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y5 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk72' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y0 @ Y1))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk107' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y2 @ Y3))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk160' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y4 @ Y5))) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y0 @ 55.43/7.61 Y2 @ Y4) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y1 @ 55.43/7.61 Y3 @ Y5))))))))))))))))))))) 55.43/7.61 | ((((('#sk107' @ X2) = (c0))) & 55.43/7.61 ((('#sk72' @ X2) = ('#sk160' @ X2))))))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl67])). 55.43/7.61 thf(zip_derived_cl81, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ((('#sk72' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.61 | (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y4 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y5 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk72' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y0 @ Y1))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk107' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y2 @ Y3))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk160' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y4 @ Y5))) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y0 @ 55.43/7.61 Y2 @ Y4) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y1 @ 55.43/7.61 Y3 @ Y5))))))))))))))))))))) 55.43/7.61 | ((((('#sk107' @ X2) = (c0))) & 55.43/7.61 ((('#sk72' @ X2) = ('#sk160' @ X2))))))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], [zip_derived_cl72])). 55.43/7.61 thf(zip_derived_cl82, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ (^[Y4 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk72' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 ( 55.43/7.61 '#sk481' @ 55.43/7.61 X2) @ Y0))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk107' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y1 @ Y2))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk160' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y3 @ Y4))) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 ( 55.43/7.61 '#sk481' @ 55.43/7.61 X2) @ 55.43/7.61 Y1 @ Y3) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y0 @ 55.43/7.61 Y2 @ Y4)))))))))))))))))) 55.43/7.61 | ((((('#sk107' @ X2) = (c0))) & 55.43/7.61 ((('#sk72' @ X2) = ('#sk160' @ X2))))) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.61 | (('#sk72' @ X2) = (c0)))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl81])). 55.43/7.61 thf(zip_derived_cl84, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 (~ ('#form542' @ X2) 55.43/7.61 | ((((('#sk107' @ X2) = (c0))) & 55.43/7.61 ((('#sk72' @ X2) = ('#sk160' @ X2))))))), 55.43/7.61 define([status(thm)])). 55.43/7.61 thf(zip_derived_cl96, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ('#form542' @ X2) 55.43/7.61 | (('#sk72' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.61 | (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y4 : iS]: 55.43/7.61 ((((('#sk72' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 ('#sk481' @ 55.43/7.61 X2) @ 55.43/7.61 Y0))) & 55.43/7.61 ((('#sk107' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y1 @ Y2))) & 55.43/7.61 ((('#sk160' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y3 @ Y4))) & 55.43/7.61 (X2 @ 55.43/7.61 ('#sk481' @ 55.43/7.61 X2) @ 55.43/7.61 Y1 @ Y3) & 55.43/7.61 (X2 @ Y0 @ 55.43/7.61 Y2 @ Y4)))))))))))))))))))), 55.43/7.61 inference('renaming', [status(thm)], [zip_derived_cl82, zip_derived_cl84])). 55.43/7.61 thf(zip_derived_cl105, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 ((((('#sk72' @ X2) = 55.43/7.61 (cP @ 55.43/7.61 ('#sk481' @ X2) @ 55.43/7.61 ('#sk857' @ X2)))) & 55.43/7.61 ((('#sk107' @ 55.43/7.61 X2) = (cP @ 55.43/7.61 Y0 @ Y1))) & 55.43/7.61 ((('#sk160' @ 55.43/7.61 X2) = (cP @ 55.43/7.61 Y2 @ Y3))) & 55.43/7.61 (X2 @ 55.43/7.61 ('#sk481' @ X2) @ 55.43/7.61 Y0 @ Y2) & 55.43/7.61 (X2 @ 55.43/7.61 ('#sk857' @ X2) @ 55.43/7.61 Y1 @ Y3))))))))))))))) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.61 | (('#sk72' @ X2) = (c0)) 55.43/7.61 | ('#form542' @ X2))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 55.43/7.61 thf(zip_derived_cl110, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 ((((('#sk72' @ X2) = (cP @ 55.43/7.61 ('#sk481' @ X2) @ 55.43/7.61 ('#sk857' @ X2)))) & 55.43/7.61 ((('#sk107' @ X2) = (cP @ 55.43/7.61 ('#sk974' @ X2) @ Y0))) & 55.43/7.61 ((('#sk160' @ X2) = (cP @ 55.43/7.61 Y1 @ Y2))) & 55.43/7.61 (X2 @ ('#sk481' @ X2) @ 55.43/7.61 ('#sk974' @ X2) @ Y1) & 55.43/7.61 (X2 @ ('#sk857' @ X2) @ Y0 @ 55.43/7.61 Y2)))))))))))) 55.43/7.61 | ('#form542' @ X2) 55.43/7.61 | (('#sk72' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl105])). 55.43/7.61 thf(zip_derived_cl115, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 ((((('#sk72' @ X2) = (cP @ 55.43/7.61 ('#sk481' @ X2) @ ('#sk857' @ X2)))) & 55.43/7.61 ((('#sk107' @ X2) = (cP @ 55.43/7.61 ('#sk974' @ X2) @ ('#sk1111' @ X2)))) & 55.43/7.61 ((('#sk160' @ X2) = (cP @ Y0 @ Y1))) & 55.43/7.61 (X2 @ ('#sk481' @ X2) @ ('#sk974' @ X2) @ 55.43/7.61 Y0) & 55.43/7.61 (X2 @ ('#sk857' @ X2) @ 55.43/7.61 ('#sk1111' @ X2) @ Y1))))))))) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.61 | (('#sk72' @ X2) = (c0)) 55.43/7.61 | ('#form542' @ X2))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl110])). 55.43/7.61 thf(zip_derived_cl120, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (((??) @ (^[Y0 : iS]: 55.43/7.61 ((((('#sk72' @ X2) = (cP @ ('#sk481' @ X2) @ 55.43/7.61 ('#sk857' @ X2)))) & 55.43/7.61 ((('#sk107' @ X2) = (cP @ ('#sk974' @ X2) @ 55.43/7.61 ('#sk1111' @ X2)))) & 55.43/7.61 ((('#sk160' @ X2) = (cP @ ('#sk1268' @ X2) @ Y0))) & 55.43/7.61 (X2 @ ('#sk481' @ X2) @ ('#sk974' @ X2) @ 55.43/7.61 ('#sk1268' @ X2)) & 55.43/7.61 (X2 @ ('#sk857' @ X2) @ ('#sk1111' @ X2) @ Y0)))))) 55.43/7.61 | ('#form542' @ X2) 55.43/7.61 | (('#sk72' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl115])). 55.43/7.61 thf(zip_derived_cl126, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((((('#sk72' @ X2) = (cP @ ('#sk481' @ X2) @ ('#sk857' @ X2)))) & 55.43/7.61 ((('#sk107' @ X2) = (cP @ ('#sk974' @ X2) @ ('#sk1111' @ X2)))) & 55.43/7.61 ((('#sk160' @ X2) = (cP @ ('#sk1268' @ X2) @ ('#sk1445' @ X2)))) & 55.43/7.61 (X2 @ ('#sk481' @ X2) @ ('#sk974' @ X2) @ ('#sk1268' @ X2)) & 55.43/7.61 (X2 @ ('#sk857' @ X2) @ ('#sk1111' @ X2) @ ('#sk1445' @ X2)))) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 55.43/7.61 | (('#sk72' @ X2) = (c0)) 55.43/7.61 | ('#form542' @ X2))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl120])). 55.43/7.61 thf(zip_derived_cl130, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((('#sk72' @ X2) = (cP @ ('#sk481' @ X2) @ ('#sk857' @ X2)))) 55.43/7.61 | ('#form542' @ X2) 55.43/7.61 | (('#sk72' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl126])). 55.43/7.61 thf(zip_derived_cl150, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ((('#sk72' @ X2) = (cP @ ('#sk481' @ X2) @ ('#sk857' @ X2))) 55.43/7.61 | ('#form542' @ X2) 55.43/7.61 | (('#sk72' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], 55.43/7.61 [zip_derived_cl130])). 55.43/7.61 thf(zip_derived_cl85, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((('#sk107' @ X2) = (c0))) | ~ ('#form542' @ X2))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl84])). 55.43/7.61 thf(zip_derived_cl98, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ((('#sk107' @ X2) = (c0)) | ~ ('#form542' @ X2))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], [zip_derived_cl85])). 55.43/7.61 thf(zip_derived_cl61, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 (~ (X2 @ ('#sk72' @ X2) @ ('#sk107' @ X2) @ ('#sk160' @ X2)) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 55.43/7.61 thf(zip_derived_cl131, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((('#sk107' @ X2) = (cP @ ('#sk974' @ X2) @ ('#sk1111' @ X2)))) 55.43/7.61 | ('#form542' @ X2) 55.43/7.61 | (('#sk72' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl126])). 55.43/7.61 thf(zip_derived_cl151, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ((('#sk107' @ X2) = (cP @ ('#sk974' @ X2) @ ('#sk1111' @ X2))) 55.43/7.61 | ('#form542' @ X2) 55.43/7.61 | (('#sk72' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], 55.43/7.61 [zip_derived_cl131])). 55.43/7.61 thf(zip_derived_cl66, plain, 55.43/7.61 (![X2 : iS, X4 : iS, X6 : iS]: 55.43/7.61 (~ (((((X2) = (X6))) & (((X4) = (c0))))) | ('#sk27' @ X2 @ X4 @ X6))), 55.43/7.61 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl59])). 55.43/7.61 thf(zip_derived_cl71, plain, 55.43/7.61 (![X2 : iS, X4 : iS, X6 : iS]: 55.43/7.61 (~ (((X2) = (X6))) | ~ (((X4) = (c0))) | ('#sk27' @ X2 @ X4 @ X6))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl66])). 55.43/7.61 thf(zip_derived_cl79, plain, 55.43/7.61 (![X2 : iS, X4 : iS, X6 : iS]: 55.43/7.61 (((X2) != (X6)) | ((X4) != (c0)) | ('#sk27' @ X2 @ X4 @ X6))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], [zip_derived_cl71])). 55.43/7.61 thf(zip_derived_cl80, plain, (![X6 : iS]: ('#sk27' @ X6 @ c0 @ X6)), 55.43/7.61 inference('simplify', [status(thm)], [zip_derived_cl79])). 55.43/7.61 thf(zip_derived_cl144, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((('#sk82' @ X2) = (cP @ ('#sk603' @ X2) @ ('#sk916' @ X2)))) 55.43/7.61 | ('#form658' @ X2) 55.43/7.61 | (('#sk128' @ X2) = ('#sk192' @ X2)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl128])). 55.43/7.61 thf(zip_derived_cl158, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ((('#sk82' @ X2) = (cP @ ('#sk603' @ X2) @ ('#sk916' @ X2))) 55.43/7.61 | ('#form658' @ X2) 55.43/7.61 | (('#sk128' @ X2) = ('#sk192' @ X2)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], 55.43/7.61 [zip_derived_cl144])). 55.43/7.61 thf(zip_derived_cl1, plain, 55.43/7.61 ( (((((!!) @ (^[Y0 : iS]: 55.43/7.61 (((!!) @ (^[Y1 : iS]: 55.43/7.61 (((!!) @ (^[Y2 : iS]: 55.43/7.61 (((!!) @ (^[Y3 : iS]: 55.43/7.61 (((((cP @ Y0 @ Y2) = 55.43/7.61 (cP @ Y1 @ Y3))) => 55.43/7.61 (((((Y2) = (Y3))) & 55.43/7.61 (((Y0) = (Y1))))))))))))))))))) & 55.43/7.61 (((!!) @ (^[Y0 : iS > $o]: 55.43/7.61 (((((Y0 @ c0) & 55.43/7.61 (((!!) @ (^[Y1 : iS]: 55.43/7.61 (((!!) @ (^[Y2 : iS]: 55.43/7.61 (((((Y0 @ Y1) & (Y0 @ Y2))) => 55.43/7.61 (Y0 @ (cP @ Y1 @ Y2)))))))))))) => 55.43/7.61 (((!!) @ (^[Y1 : iS]: (Y0 @ Y1))))))))) & 55.43/7.61 (((!!) @ (^[Y0 : iS]: 55.43/7.61 (((!!) @ (^[Y1 : iS]: (((cP @ Y0 @ Y1) != (c0)))))))))))), 55.43/7.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 55.43/7.61 thf(zip_derived_cl5, plain, 55.43/7.61 ( (((!!) @ (^[Y0 : iS]: 55.43/7.61 (((!!) @ (^[Y1 : iS]: (((cP @ Y0 @ Y1) != (c0)))))))))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1])). 55.43/7.61 thf(zip_derived_cl9, plain, 55.43/7.61 (![X2 : iS]: (((!!) @ (^[Y0 : iS]: (((cP @ X2 @ Y0) != (c0))))))), 55.43/7.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 55.43/7.61 thf(zip_derived_cl13, plain, 55.43/7.61 (![X2 : iS, X4 : iS]: (((cP @ X2 @ X4) != (c0)))), 55.43/7.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])). 55.43/7.61 thf(zip_derived_cl17, plain, (![X2 : iS, X4 : iS]: ((cP @ X2 @ X4) != (c0))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], [zip_derived_cl13])). 55.43/7.61 thf(zip_derived_cl132, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((('#sk160' @ X2) = (cP @ ('#sk1268' @ X2) @ ('#sk1445' @ X2)))) 55.43/7.61 | ('#form542' @ X2) 55.43/7.61 | (('#sk72' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl126])). 55.43/7.61 thf(zip_derived_cl152, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ((('#sk160' @ X2) = (cP @ ('#sk1268' @ X2) @ ('#sk1445' @ X2))) 55.43/7.61 | ('#form542' @ X2) 55.43/7.61 | (('#sk72' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], 55.43/7.61 [zip_derived_cl132])). 55.43/7.61 thf(zip_derived_cl133, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (X2 @ ('#sk481' @ X2) @ ('#sk974' @ X2) @ ('#sk1268' @ X2)) 55.43/7.61 | ('#form542' @ X2) 55.43/7.61 | (('#sk72' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl126])). 55.43/7.61 thf(zip_derived_cl91, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 (~ ('#form658' @ X2) 55.43/7.61 | ((((('#sk128' @ X2) = (c0))) & 55.43/7.61 ((('#sk82' @ X2) = ('#sk192' @ X2))))))), 55.43/7.61 define([status(thm)])). 55.43/7.61 thf(zip_derived_cl93, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((('#sk82' @ X2) = ('#sk192' @ X2))) | ~ ('#form658' @ X2))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl91])). 55.43/7.61 thf(zip_derived_cl103, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ((('#sk82' @ X2) = ('#sk192' @ X2)) | ~ ('#form658' @ X2))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], [zip_derived_cl93])). 55.43/7.61 thf(zip_derived_cl134, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (X2 @ ('#sk857' @ X2) @ ('#sk1111' @ X2) @ ('#sk1445' @ X2)) 55.43/7.61 | ('#form542' @ X2) 55.43/7.61 | (('#sk72' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl126])). 55.43/7.61 thf(zip_derived_cl90, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ((('#sk82' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y4 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y5 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y1 @ 55.43/7.61 Y3 @ Y5) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y0 @ 55.43/7.61 Y2 @ Y4) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk192' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y4 @ Y5))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk128' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y2 @ Y3))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk82' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y0 @ Y1))))))))))))))))))))))) 55.43/7.61 | ((((('#sk128' @ X2) = (c0))) & 55.43/7.61 ((('#sk82' @ X2) = ('#sk192' @ X2))))))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], [zip_derived_cl75])). 55.43/7.61 thf(zip_derived_cl91, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 (~ ('#form658' @ X2) 55.43/7.61 | ((((('#sk128' @ X2) = (c0))) & 55.43/7.61 ((('#sk82' @ X2) = ('#sk192' @ X2))))))), 55.43/7.61 define([status(thm)])). 55.43/7.61 thf(zip_derived_cl94, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ('#form658' @ X2) 55.43/7.61 | (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y4 : iS]: 55.43/7.61 (((??) @ ( 55.43/7.61 ^[Y5 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y1 @ 55.43/7.61 Y3 @ Y5) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y0 @ 55.43/7.61 Y2 @ Y4) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk192' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y4 @ Y5))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk128' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y2 @ Y3))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk82' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y0 @ Y1))))))))))))))))))))))) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | (('#sk82' @ X2) = (c0)))), 55.43/7.61 inference('renaming', [status(thm)], [zip_derived_cl90, zip_derived_cl91])). 55.43/7.61 thf(zip_derived_cl101, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ (^[Y4 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 Y0 @ 55.43/7.61 Y2 @ Y4) & 55.43/7.61 ( 55.43/7.61 X2 @ 55.43/7.61 ( 55.43/7.61 '#sk603' @ 55.43/7.61 X2) @ 55.43/7.61 Y1 @ Y3) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk192' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y3 @ Y4))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk128' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 Y1 @ Y2))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 ('#sk82' @ 55.43/7.61 X2) = 55.43/7.61 (cP @ 55.43/7.61 ( 55.43/7.61 '#sk603' @ 55.43/7.61 X2) @ Y0)))))))))))))))))))) 55.43/7.61 | (('#sk82' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | ('#form658' @ X2))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl94])). 55.43/7.61 thf(zip_derived_cl108, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((X2 @ 55.43/7.61 ('#sk916' @ X2) @ 55.43/7.61 Y1 @ Y3) & 55.43/7.61 (X2 @ 55.43/7.61 ('#sk603' @ X2) @ 55.43/7.61 Y0 @ Y2) & 55.43/7.61 ((('#sk192' @ 55.43/7.61 X2) = (cP @ 55.43/7.61 Y2 @ Y3))) & 55.43/7.61 ((('#sk128' @ 55.43/7.61 X2) = (cP @ 55.43/7.61 Y0 @ Y1))) & 55.43/7.61 ((('#sk82' @ X2) = 55.43/7.61 (cP @ 55.43/7.61 ('#sk603' @ X2) @ 55.43/7.61 ('#sk916' @ X2)))))))))))))))))) 55.43/7.61 | ('#form658' @ X2) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | (('#sk82' @ X2) = (c0)))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl101])). 55.43/7.61 thf(zip_derived_cl113, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((X2 @ ('#sk916' @ X2) @ Y0 @ 55.43/7.61 Y2) & 55.43/7.61 (X2 @ ('#sk603' @ X2) @ 55.43/7.61 ('#sk1043' @ X2) @ Y1) & 55.43/7.61 ((('#sk192' @ X2) = (cP @ 55.43/7.61 Y1 @ Y2))) & 55.43/7.61 ((('#sk128' @ X2) = (cP @ 55.43/7.61 ('#sk1043' @ X2) @ Y0))) & 55.43/7.61 ((('#sk82' @ X2) = (cP @ 55.43/7.61 ('#sk603' @ X2) @ 55.43/7.61 ('#sk916' @ X2))))))))))))))) 55.43/7.61 | (('#sk82' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | ('#form658' @ X2))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl108])). 55.43/7.61 thf(zip_derived_cl118, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((X2 @ ('#sk916' @ X2) @ 55.43/7.61 ('#sk1190' @ X2) @ Y1) & 55.43/7.61 (X2 @ ('#sk603' @ X2) @ 55.43/7.61 ('#sk1043' @ X2) @ Y0) & 55.43/7.61 ((('#sk192' @ X2) = (cP @ Y0 @ Y1))) & 55.43/7.61 ((('#sk128' @ X2) = (cP @ 55.43/7.61 ('#sk1043' @ X2) @ ('#sk1190' @ X2)))) & 55.43/7.61 ((('#sk82' @ X2) = (cP @ 55.43/7.61 ('#sk603' @ X2) @ ('#sk916' @ X2)))))))))))) 55.43/7.61 | ('#form658' @ X2) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | (('#sk82' @ X2) = (c0)))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl113])). 55.43/7.61 thf(zip_derived_cl123, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (((??) @ (^[Y0 : iS]: 55.43/7.61 (((X2 @ ('#sk916' @ X2) @ ('#sk1190' @ X2) @ Y0) & 55.43/7.61 (X2 @ ('#sk603' @ X2) @ ('#sk1043' @ X2) @ 55.43/7.61 ('#sk1357' @ X2)) & 55.43/7.61 ((('#sk192' @ X2) = (cP @ ('#sk1357' @ X2) @ Y0))) & 55.43/7.61 ((('#sk128' @ X2) = (cP @ ('#sk1043' @ X2) @ 55.43/7.61 ('#sk1190' @ X2)))) & 55.43/7.61 ((('#sk82' @ X2) = (cP @ ('#sk603' @ X2) @ 55.43/7.61 ('#sk916' @ X2))))))))) 55.43/7.61 | (('#sk82' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | ('#form658' @ X2))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl118])). 55.43/7.61 thf(zip_derived_cl129, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (((X2 @ ('#sk916' @ X2) @ ('#sk1190' @ X2) @ ('#sk1544' @ X2)) & 55.43/7.61 (X2 @ ('#sk603' @ X2) @ ('#sk1043' @ X2) @ ('#sk1357' @ X2)) & 55.43/7.61 ((('#sk192' @ X2) = (cP @ ('#sk1357' @ X2) @ ('#sk1544' @ X2)))) & 55.43/7.61 ((('#sk128' @ X2) = (cP @ ('#sk1043' @ X2) @ ('#sk1190' @ X2)))) & 55.43/7.61 ((('#sk82' @ X2) = (cP @ ('#sk603' @ X2) @ ('#sk916' @ X2)))))) 55.43/7.61 | ('#form658' @ X2) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | (('#sk82' @ X2) = (c0)))), 55.43/7.61 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl123])). 55.43/7.61 thf(zip_derived_cl149, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((('#sk82' @ X2) = (cP @ ('#sk603' @ X2) @ ('#sk916' @ X2)))) 55.43/7.61 | (('#sk82' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | ('#form658' @ X2))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl129])). 55.43/7.61 thf(zip_derived_cl161, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ((('#sk82' @ X2) = (cP @ ('#sk603' @ X2) @ ('#sk916' @ X2))) 55.43/7.61 | (('#sk82' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | ('#form658' @ X2))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], 55.43/7.61 [zip_derived_cl149])). 55.43/7.61 thf(zip_derived_cl92, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((('#sk128' @ X2) = (c0))) | ~ ('#form658' @ X2))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl91])). 55.43/7.61 thf(zip_derived_cl102, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ((('#sk128' @ X2) = (c0)) | ~ ('#form658' @ X2))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], [zip_derived_cl92])). 55.43/7.61 thf(zip_derived_cl63, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 (~ (X2 @ ('#sk82' @ X2) @ ('#sk128' @ X2) @ ('#sk192' @ X2)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 55.43/7.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 55.43/7.61 thf(zip_derived_cl148, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((('#sk128' @ X2) = (cP @ ('#sk1043' @ X2) @ ('#sk1190' @ X2)))) 55.43/7.61 | (('#sk82' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | ('#form658' @ X2))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl129])). 55.43/7.61 thf(zip_derived_cl160, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ((('#sk128' @ X2) = (cP @ ('#sk1043' @ X2) @ ('#sk1190' @ X2))) 55.43/7.61 | (('#sk82' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | ('#form658' @ X2))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], 55.43/7.61 [zip_derived_cl148])). 55.43/7.61 thf(zip_derived_cl147, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( ((('#sk192' @ X2) = (cP @ ('#sk1357' @ X2) @ ('#sk1544' @ X2)))) 55.43/7.61 | (('#sk82' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | ('#form658' @ X2))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl129])). 55.43/7.61 thf(zip_derived_cl159, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ((('#sk192' @ X2) = (cP @ ('#sk1357' @ X2) @ ('#sk1544' @ X2))) 55.43/7.61 | (('#sk82' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | ('#form658' @ X2))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], 55.43/7.61 [zip_derived_cl147])). 55.43/7.61 thf(zip_derived_cl146, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (X2 @ ('#sk603' @ X2) @ ('#sk1043' @ X2) @ ('#sk1357' @ X2)) 55.43/7.61 | (('#sk82' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | ('#form658' @ X2))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl129])). 55.43/7.61 thf(zip_derived_cl145, plain, 55.43/7.61 (![X2 : iS > iS > iS > $o]: 55.43/7.61 ( (X2 @ ('#sk916' @ X2) @ ('#sk1190' @ X2) @ ('#sk1544' @ X2)) 55.43/7.61 | (('#sk82' @ X2) = (c0)) 55.43/7.61 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 55.43/7.61 | ('#form658' @ X2))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl129])). 55.43/7.61 thf(zip_derived_cl65, plain, 55.43/7.61 (![X2 : iS, X4 : iS, X6 : iS]: 55.43/7.61 (~ (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ (^[Y4 : iS]: 55.43/7.61 (( 55.43/7.61 (??) @ ( 55.43/7.61 ^[Y5 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 (X2) = 55.43/7.61 (cP @ 55.43/7.61 Y0 @ Y1))) & 55.43/7.61 ( 55.43/7.61 '#sk27' @ 55.43/7.61 Y0 @ 55.43/7.61 Y2 @ Y4) & 55.43/7.61 ( 55.43/7.61 '#sk27' @ 55.43/7.61 Y1 @ 55.43/7.61 Y3 @ Y5) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 (X6) = 55.43/7.61 (cP @ 55.43/7.61 Y4 @ Y5))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 (X4) = 55.43/7.61 (cP @ 55.43/7.61 Y2 @ Y3))))))))))))))))))))))) 55.43/7.61 | ('#sk27' @ X2 @ X4 @ X6))), 55.43/7.61 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl59])). 55.43/7.61 thf(zip_derived_cl70, plain, 55.43/7.61 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS]: 55.43/7.61 (~ (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((??) @ (^[Y4 : iS]: 55.43/7.61 (( 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 (X2) = 55.43/7.61 (cP @ 55.43/7.61 X8 @ Y0))) & 55.43/7.61 ( 55.43/7.61 '#sk27' @ 55.43/7.61 X8 @ 55.43/7.61 Y1 @ Y3) & 55.43/7.61 ( 55.43/7.61 '#sk27' @ 55.43/7.61 Y0 @ 55.43/7.61 Y2 @ Y4) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 (X6) = 55.43/7.61 (cP @ 55.43/7.61 Y3 @ Y4))) & 55.43/7.61 ( 55.43/7.61 ( 55.43/7.61 (X4) = 55.43/7.61 (cP @ 55.43/7.61 Y1 @ Y2)))))))))))))))))))) 55.43/7.61 | ('#sk27' @ X2 @ X4 @ X6))), 55.43/7.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl65])). 55.43/7.61 thf(zip_derived_cl78, plain, 55.43/7.61 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS, X10 : iS]: 55.43/7.61 (~ (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((??) @ (^[Y3 : iS]: 55.43/7.61 (((((X2) = (cP @ 55.43/7.61 X8 @ X10))) & 55.43/7.61 ('#sk27' @ X8 @ 55.43/7.61 Y0 @ Y2) & 55.43/7.61 ('#sk27' @ X10 @ 55.43/7.61 Y1 @ Y3) & 55.43/7.61 (((X6) = (cP @ 55.43/7.61 Y2 @ Y3))) & 55.43/7.61 (((X4) = (cP @ 55.43/7.61 Y0 @ Y1))))))))))))))))) 55.43/7.61 | ('#sk27' @ X2 @ X4 @ X6))), 55.43/7.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl70])). 55.43/7.61 thf(zip_derived_cl95, plain, 55.43/7.61 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS, X10 : iS, X12 : iS]: 55.43/7.61 (~ (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((??) @ (^[Y2 : iS]: 55.43/7.61 (((((X2) = (cP @ X8 @ X10))) & 55.43/7.61 ('#sk27' @ X8 @ X12 @ Y1) & 55.43/7.61 ('#sk27' @ X10 @ Y0 @ Y2) & 55.43/7.61 (((X6) = (cP @ Y1 @ Y2))) & 55.43/7.61 (((X4) = (cP @ X12 @ Y0)))))))))))))) 55.43/7.61 | ('#sk27' @ X2 @ X4 @ X6))), 55.43/7.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl78])). 55.43/7.61 thf(zip_derived_cl104, plain, 55.43/7.61 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS, X10 : iS, X12 : iS, X14 : iS]: 55.43/7.61 (~ (((??) @ (^[Y0 : iS]: 55.43/7.61 (((??) @ (^[Y1 : iS]: 55.43/7.61 (((((X2) = (cP @ X8 @ X10))) & 55.43/7.61 ('#sk27' @ X8 @ X12 @ Y0) & 55.43/7.61 ('#sk27' @ X10 @ X14 @ Y1) & 55.43/7.61 (((X6) = (cP @ Y0 @ Y1))) & 55.43/7.61 (((X4) = (cP @ X12 @ X14))))))))))) 55.43/7.61 | ('#sk27' @ X2 @ X4 @ X6))), 55.43/7.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl95])). 55.43/7.61 thf(zip_derived_cl109, plain, 55.43/7.61 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS, X10 : iS, X12 : iS, X14 : iS, 55.43/7.61 X16 : iS]: 55.43/7.61 (~ (((??) @ (^[Y0 : iS]: 55.43/7.61 (((((X2) = (cP @ X8 @ X10))) & 55.43/7.61 ('#sk27' @ X8 @ X12 @ X16) & 55.43/7.61 ('#sk27' @ X10 @ X14 @ Y0) & 55.43/7.61 (((X6) = (cP @ X16 @ Y0))) & 55.43/7.61 (((X4) = (cP @ X12 @ X14)))))))) 55.43/7.61 | ('#sk27' @ X2 @ X4 @ X6))), 55.43/7.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl104])). 55.43/7.61 thf(zip_derived_cl114, plain, 55.43/7.61 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS, X10 : iS, X12 : iS, X14 : iS, 55.43/7.61 X16 : iS, X18 : iS]: 55.43/7.61 (~ (((((X2) = (cP @ X8 @ X10))) & ('#sk27' @ X8 @ X12 @ X16) & 55.43/7.61 ('#sk27' @ X10 @ X14 @ X18) & (((X6) = (cP @ X16 @ X18))) & 55.43/7.61 (((X4) = (cP @ X12 @ X14))))) 55.43/7.61 | ('#sk27' @ X2 @ X4 @ X6))), 55.43/7.61 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl109])). 55.43/7.61 thf(zip_derived_cl119, plain, 55.43/7.61 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS, X10 : iS, X12 : iS, X14 : iS, 55.43/7.61 X16 : iS, X18 : iS]: 55.43/7.61 (~ (((X2) = (cP @ X8 @ X10))) 55.43/7.61 | ~ ('#sk27' @ X8 @ X12 @ X16) 55.43/7.61 | ~ ('#sk27' @ X10 @ X14 @ X18) 55.43/7.61 | ~ (((X6) = (cP @ X16 @ X18))) 55.43/7.61 | ~ (((X4) = (cP @ X12 @ X14))) 55.43/7.61 | ('#sk27' @ X2 @ X4 @ X6))), 55.43/7.61 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl114])). 55.43/7.61 thf(zip_derived_cl124, plain, 55.43/7.61 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS, X10 : iS, X12 : iS, X14 : iS, 55.43/7.61 X16 : iS, X18 : iS]: 55.43/7.61 (((X2) != (cP @ X8 @ X10)) 55.43/7.61 | ~ ('#sk27' @ X8 @ X12 @ X16) 55.43/7.61 | ~ ('#sk27' @ X10 @ X14 @ X18) 55.43/7.61 | ((X6) != (cP @ X16 @ X18)) 55.43/7.61 | ((X4) != (cP @ X12 @ X14)) 55.43/7.61 | ('#sk27' @ X2 @ X4 @ X6))), 55.43/7.61 inference('simplify nested equalities', [status(thm)], 55.43/7.61 [zip_derived_cl119])). 55.43/7.61 thf(zip_derived_cl125, plain, 55.43/7.61 (![X8 : iS, X10 : iS, X12 : iS, X14 : iS, X16 : iS, X18 : iS]: 55.43/7.61 ( ('#sk27' @ (cP @ X8 @ X10) @ (cP @ X12 @ X14) @ (cP @ X16 @ X18)) 55.43/7.61 | ~ ('#sk27' @ X10 @ X14 @ X18) 55.43/7.61 | ~ ('#sk27' @ X8 @ X12 @ X16))), 55.43/7.61 inference('simplify', [status(thm)], [zip_derived_cl124])). 55.43/7.61 thf(zip_derived_cl8157, plain, ($false), 55.43/7.61 inference('eprover', [status(thm)], 55.43/7.61 [zip_derived_cl193, zip_derived_cl38, zip_derived_cl185, 55.43/7.61 zip_derived_cl77, zip_derived_cl157, zip_derived_cl99, 55.43/7.61 zip_derived_cl150, zip_derived_cl98, zip_derived_cl61, 55.43/7.61 zip_derived_cl151, zip_derived_cl80, zip_derived_cl158, 55.43/7.61 zip_derived_cl17, zip_derived_cl152, zip_derived_cl133, 55.43/7.61 zip_derived_cl103, zip_derived_cl134, zip_derived_cl161, 55.43/7.61 zip_derived_cl102, zip_derived_cl63, zip_derived_cl160, 55.43/7.61 zip_derived_cl159, zip_derived_cl146, zip_derived_cl145, 55.43/7.61 zip_derived_cl125])). 55.43/7.61 55.43/7.61 % SZS output end Refutation 55.43/7.61 55.43/7.61 55.43/7.61 % Terminating... 55.43/7.67 % Runner terminated. 55.43/7.68 % Zipperpin 1.5 exiting 55.43/7.70 EOF