0.12/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.dNUC7TLal1 true 0.14/0.33 % Computer : n027.cluster.edu 0.14/0.33 % Model : x86_64 x86_64 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.33 % Memory : 8042.1875MB 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.33 % CPULimit : 1440 0.14/0.33 % WCLimit : 180 0.14/0.33 % DateTime : Mon Jul 3 04:28:16 EDT 2023 0.14/0.33 % CPUTime : 0.14/0.33 % Running portfolio for 1440 s 0.14/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.33 % Number of cores: 8 0.14/0.34 % Python version: Python 3.6.8 0.14/0.34 % Running in HO mode 0.20/0.60 % Total configuration time : 828 0.20/0.60 % Estimated wc time : 1656 0.20/0.60 % Estimated cpu time (8 cpus) : 207.0 1.28/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 1.28/0.71 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 1.28/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 1.39/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 1.39/0.73 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 1.39/0.73 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 1.39/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 1.39/0.73 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 75.01/10.18 % Solved by lams/20_acsne_simpl.sh. 75.01/10.18 % done 762 iterations in 9.297s 75.01/10.18 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 75.01/10.18 % SZS output start Refutation 75.01/10.18 thf(iS_type, type, iS: $tType). 75.01/10.18 thf('#sk1544_type', type, '#sk1544': (iS > iS > iS > $o) > iS). 75.01/10.18 thf('#sk8_type', type, '#sk8': iS). 75.01/10.18 thf('#sk857_type', type, '#sk857': (iS > iS > iS > $o) > iS). 75.01/10.18 thf('#sk1_type', type, '#sk1': iS). 75.01/10.18 thf('#sk974_type', type, '#sk974': (iS > iS > iS > $o) > iS). 75.01/10.18 thf('#sk14_type', type, '#sk14': iS). 75.01/10.18 thf('#sk160_type', type, '#sk160': (iS > iS > iS > $o) > iS). 75.01/10.18 thf('#sk82_type', type, '#sk82': (iS > iS > iS > $o) > iS). 75.01/10.18 thf('#sk1190_type', type, '#sk1190': (iS > iS > iS > $o) > iS). 75.01/10.18 thf(c0_type, type, c0: iS). 75.01/10.18 thf('#sk1357_type', type, '#sk1357': (iS > iS > iS > $o) > iS). 75.01/10.18 thf('#sk603_type', type, '#sk603': (iS > iS > iS > $o) > iS). 75.01/10.18 thf('#sk916_type', type, '#sk916': (iS > iS > iS > $o) > iS). 75.01/10.18 thf('#sk481_type', type, '#sk481': (iS > iS > iS > $o) > iS). 75.01/10.18 thf('#sk128_type', type, '#sk128': (iS > iS > iS > $o) > iS). 75.01/10.18 thf('#sk1268_type', type, '#sk1268': (iS > iS > iS > $o) > iS). 75.01/10.18 thf('#form2426_type', type, '#form2426': $o). 75.01/10.18 thf('#sk1111_type', type, '#sk1111': (iS > iS > iS > $o) > iS). 75.01/10.18 thf('#form658_type', type, '#form658': (iS > iS > iS > $o) > $o). 75.01/10.18 thf('#sk1445_type', type, '#sk1445': (iS > iS > iS > $o) > iS). 75.01/10.18 thf('#sk2_type', type, '#sk2': iS). 75.01/10.18 thf(cP_type, type, cP: iS > iS > iS). 75.01/10.18 thf('#form542_type', type, '#form542': (iS > iS > iS > $o) > $o). 75.01/10.18 thf('#sk72_type', type, '#sk72': (iS > iS > iS > $o) > iS). 75.01/10.18 thf('#sk107_type', type, '#sk107': (iS > iS > iS > $o) > iS). 75.01/10.18 thf('#sk192_type', type, '#sk192': (iS > iS > iS > $o) > iS). 75.01/10.18 thf('#sk27_type', type, '#sk27': iS > iS > iS > $o). 75.01/10.18 thf('#form2610_type', type, '#form2610': $o). 75.01/10.18 thf('#sk1043_type', type, '#sk1043': (iS > iS > iS > $o) > iS). 75.01/10.18 thf(cS_LEM2_pme, conjecture, 75.01/10.18 (( ( ![Xx:iS,Xy:iS,Xu:iS,Xv:iS]: 75.01/10.18 ( ( ( cP @ Xx @ Xu ) = ( cP @ Xy @ Xv ) ) => 75.01/10.18 ( ( ( Xu ) = ( Xv ) ) & ( ( Xx ) = ( Xy ) ) ) ) ) & 75.01/10.18 ( ![X:( iS > $o )]: 75.01/10.18 ( ( ( X @ c0 ) & 75.01/10.18 ( ![Xx:iS,Xy:iS]: 75.01/10.18 ( ( ( X @ Xx ) & ( X @ Xy ) ) => ( X @ ( cP @ Xx @ Xy ) ) ) ) ) => 75.01/10.18 ( ![Xx:iS]: ( X @ Xx ) ) ) ) & 75.01/10.18 ( ![Xx:iS,Xy:iS]: ( ( cP @ Xx @ Xy ) != ( c0 ) ) ) ) => 75.01/10.18 ( ![Xx:iS,Xy:iS,Xu:iS,Xv:iS]: 75.01/10.18 ( ( ( ![R:( iS > iS > iS > $o )]: 75.01/10.18 ( ( ![Xa:iS,Xb:iS,Xc:iS]: 75.01/10.18 ( ( ( ( ( Xa ) = ( c0 ) ) & ( ( Xb ) = ( Xc ) ) ) | 75.01/10.18 ( ( ( Xb ) = ( c0 ) ) & ( ( Xa ) = ( Xc ) ) ) | 75.01/10.18 ( ?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]: 75.01/10.18 ( ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) & 75.01/10.18 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) & 75.01/10.18 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 75.01/10.18 ( R @ Xx1 @ Xy1 @ Xz1 ) & ( R @ Xx2 @ Xy2 @ Xz2 ) ) ) ) => 75.01/10.18 ( R @ Xa @ Xb @ Xc ) ) ) => 75.01/10.18 ( R @ Xx @ Xy @ Xy ) ) ) & 75.01/10.18 ( ![R:( iS > iS > iS > $o )]: 75.01/10.18 ( ( ![Xa:iS,Xb:iS,Xc:iS]: 75.01/10.18 ( ( ( ( ( Xb ) = ( Xc ) ) & ( ( Xa ) = ( c0 ) ) ) | 75.01/10.18 ( ( ( Xb ) = ( c0 ) ) & ( ( Xa ) = ( Xc ) ) ) | 75.01/10.18 ( ?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]: 75.01/10.18 ( ( R @ Xx2 @ Xy2 @ Xz2 ) & ( R @ Xx1 @ Xy1 @ Xz1 ) & 75.01/10.18 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 75.01/10.18 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) & 75.01/10.18 ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) ) ) ) => 75.01/10.18 ( R @ Xa @ Xb @ Xc ) ) ) => 75.01/10.18 ( R @ Xu @ Xv @ Xv ) ) ) ) => 75.01/10.18 ( ![R:( iS > iS > iS > $o )]: 75.01/10.18 ( ( ![Xa:iS,Xb:iS,Xc:iS]: 75.01/10.18 ( ( ( ( ( Xa ) = ( c0 ) ) & ( ( Xb ) = ( Xc ) ) ) | 75.01/10.18 ( ?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]: 75.01/10.18 ( ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) & 75.01/10.18 ( R @ Xx1 @ Xy1 @ Xz1 ) & ( R @ Xx2 @ Xy2 @ Xz2 ) & 75.01/10.18 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 75.01/10.18 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) ) ) | 75.01/10.18 ( ( ( Xa ) = ( Xc ) ) & ( ( Xb ) = ( c0 ) ) ) ) => 75.01/10.18 ( R @ Xa @ Xb @ Xc ) ) ) => 75.01/10.18 ( R @ ( cP @ Xx @ Xu ) @ ( cP @ Xy @ Xv ) @ ( cP @ Xy @ Xv ) ) ) ) ) ))). 75.01/10.18 thf(zf_stmt_0, negated_conjecture, 75.01/10.18 (~( ( ( ![Xx:iS,Xy:iS,Xu:iS,Xv:iS]: 75.01/10.18 ( ( ( cP @ Xx @ Xu ) = ( cP @ Xy @ Xv ) ) => 75.01/10.18 ( ( ( Xu ) = ( Xv ) ) & ( ( Xx ) = ( Xy ) ) ) ) ) & 75.01/10.18 ( ![X:( iS > $o )]: 75.01/10.18 ( ( ( X @ c0 ) & 75.01/10.18 ( ![Xx:iS,Xy:iS]: 75.01/10.18 ( ( ( X @ Xx ) & ( X @ Xy ) ) => ( X @ ( cP @ Xx @ Xy ) ) ) ) ) => 75.01/10.18 ( ![Xx:iS]: ( X @ Xx ) ) ) ) & 75.01/10.18 ( ![Xx:iS,Xy:iS]: ( ( cP @ Xx @ Xy ) != ( c0 ) ) ) ) => 75.01/10.18 ( ![Xx:iS,Xy:iS,Xu:iS,Xv:iS]: 75.01/10.18 ( ( ( ![R:( iS > iS > iS > $o )]: 75.01/10.18 ( ( ![Xa:iS,Xb:iS,Xc:iS]: 75.01/10.18 ( ( ( ( ( Xa ) = ( c0 ) ) & ( ( Xb ) = ( Xc ) ) ) | 75.01/10.18 ( ( ( Xb ) = ( c0 ) ) & ( ( Xa ) = ( Xc ) ) ) | 75.01/10.18 ( ?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]: 75.01/10.18 ( ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) & 75.01/10.18 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) & 75.01/10.18 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 75.01/10.18 ( R @ Xx1 @ Xy1 @ Xz1 ) & ( R @ Xx2 @ Xy2 @ Xz2 ) ) ) ) => 75.01/10.18 ( R @ Xa @ Xb @ Xc ) ) ) => 75.01/10.18 ( R @ Xx @ Xy @ Xy ) ) ) & 75.01/10.18 ( ![R:( iS > iS > iS > $o )]: 75.01/10.18 ( ( ![Xa:iS,Xb:iS,Xc:iS]: 75.01/10.18 ( ( ( ( ( Xb ) = ( Xc ) ) & ( ( Xa ) = ( c0 ) ) ) | 75.01/10.18 ( ( ( Xb ) = ( c0 ) ) & ( ( Xa ) = ( Xc ) ) ) | 75.01/10.18 ( ?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]: 75.01/10.18 ( ( R @ Xx2 @ Xy2 @ Xz2 ) & 75.01/10.18 ( R @ Xx1 @ Xy1 @ Xz1 ) & 75.01/10.18 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 75.01/10.18 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) & 75.01/10.18 ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) ) ) ) => 75.01/10.18 ( R @ Xa @ Xb @ Xc ) ) ) => 75.01/10.18 ( R @ Xu @ Xv @ Xv ) ) ) ) => 75.01/10.18 ( ![R:( iS > iS > iS > $o )]: 75.01/10.18 ( ( ![Xa:iS,Xb:iS,Xc:iS]: 75.01/10.18 ( ( ( ( ( Xa ) = ( c0 ) ) & ( ( Xb ) = ( Xc ) ) ) | 75.01/10.18 ( ?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]: 75.01/10.18 ( ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) & 75.01/10.18 ( R @ Xx1 @ Xy1 @ Xz1 ) & ( R @ Xx2 @ Xy2 @ Xz2 ) & 75.01/10.18 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 75.01/10.18 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) ) ) | 75.01/10.18 ( ( ( Xa ) = ( Xc ) ) & ( ( Xb ) = ( c0 ) ) ) ) => 75.01/10.18 ( R @ Xa @ Xb @ Xc ) ) ) => 75.01/10.18 ( R @ ( cP @ Xx @ Xu ) @ ( cP @ Xy @ Xv ) @ ( cP @ Xy @ Xv ) ) ) ) ) ) )), 75.01/10.18 inference('cnf.neg', [status(esa)], [cS_LEM2_pme])). 75.01/10.18 thf(zip_derived_cl0, plain, 75.01/10.18 (~ (((((((!!) @ (^[Y0 : iS]: 75.01/10.18 (((!!) @ (^[Y1 : iS]: 75.01/10.18 (((!!) @ (^[Y2 : iS]: 75.01/10.18 (((!!) @ (^[Y3 : iS]: 75.01/10.18 (((((cP @ Y0 @ 75.01/10.18 Y2) = (cP @ 75.01/10.18 Y1 @ Y3))) => 75.01/10.18 (((((Y2) = (Y3))) & 75.01/10.18 (((Y0) = (Y1))))))))))))))))))) & 75.01/10.18 (((!!) @ (^[Y0 : iS > $o]: 75.01/10.18 (((((Y0 @ c0) & 75.01/10.18 (((!!) @ (^[Y1 : iS]: 75.01/10.18 (((!!) @ (^[Y2 : iS]: 75.01/10.18 (((((Y0 @ Y1) & (Y0 @ Y2))) => 75.01/10.18 (Y0 @ (cP @ Y1 @ Y2)))))))))))) => 75.01/10.18 (((!!) @ (^[Y1 : iS]: (Y0 @ Y1))))))))) & 75.01/10.18 (((!!) @ (^[Y0 : iS]: 75.01/10.18 (((!!) @ (^[Y1 : iS]: (((cP @ Y0 @ Y1) != (c0))))))))))) => 75.01/10.18 (((!!) @ (^[Y0 : iS]: 75.01/10.18 (((!!) @ (^[Y1 : iS]: 75.01/10.18 (((!!) @ (^[Y2 : iS]: 75.01/10.18 (((!!) @ (^[Y3 : iS]: 75.01/10.18 (((((((!!) @ ( 75.01/10.18 ^[Y4 : 75.01/10.18 iS > iS > iS > $o]: 75.01/10.18 (((( 75.01/10.18 (!!) @ ( 75.01/10.18 ^[Y5 : iS]: 75.01/10.18 (( 75.01/10.18 (!!) @ ( 75.01/10.18 ^[Y6 : iS]: 75.01/10.18 (( 75.01/10.18 (!!) @ ( 75.01/10.18 ^[Y7 : iS]: 75.01/10.18 (( 75.01/10.18 (( 75.01/10.18 ( 75.01/10.18 ( 75.01/10.18 (( 75.01/10.18 (Y5) = 75.01/10.18 (c0))) & 75.01/10.18 (( 75.01/10.18 (Y6) = 75.01/10.18 (Y7))))) | 75.01/10.18 ( 75.01/10.18 ( 75.01/10.18 (( 75.01/10.18 (Y6) = 75.01/10.18 (c0))) & 75.01/10.18 (( 75.01/10.18 (Y5) = 75.01/10.19 (Y7))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y10 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y11 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y12 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y13 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y5) = 75.01/10.19 (cP @ 75.01/10.19 Y8 @ Y9))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y6) = 75.01/10.19 (cP @ 75.01/10.19 Y10 @ 75.01/10.19 Y11))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y7) = 75.01/10.19 (cP @ 75.01/10.19 Y12 @ 75.01/10.19 Y13))) & 75.01/10.19 ( 75.01/10.19 Y4 @ 75.01/10.19 Y8 @ 75.01/10.19 Y10 @ Y12) & 75.01/10.19 ( 75.01/10.19 Y4 @ 75.01/10.19 Y9 @ 75.01/10.19 Y11 @ Y13))))))))))))))))))))))) => 75.01/10.19 (Y4 @ 75.01/10.19 Y5 @ 75.01/10.19 Y6 @ Y7)))))))))))) => 75.01/10.19 (Y4 @ 75.01/10.19 Y0 @ Y1 @ 75.01/10.19 Y1)))))) & 75.01/10.19 (((!!) @ ( 75.01/10.19 ^[Y4 : 75.01/10.19 iS > iS > iS > $o]: 75.01/10.19 (((( 75.01/10.19 (!!) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (!!) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (!!) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y6) = 75.01/10.19 (Y7))) & 75.01/10.19 (( 75.01/10.19 (Y5) = 75.01/10.19 (c0))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y6) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y5) = 75.01/10.19 (Y7))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y10 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y11 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y12 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y13 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 Y4 @ 75.01/10.19 Y9 @ 75.01/10.19 Y11 @ Y13) & 75.01/10.19 ( 75.01/10.19 Y4 @ 75.01/10.19 Y8 @ 75.01/10.19 Y10 @ Y12) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y7) = 75.01/10.19 (cP @ 75.01/10.19 Y12 @ 75.01/10.19 Y13))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y6) = 75.01/10.19 (cP @ 75.01/10.19 Y10 @ 75.01/10.19 Y11))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y5) = 75.01/10.19 (cP @ 75.01/10.19 Y8 @ Y9))))))))))))))))))))))))) => 75.01/10.19 (Y4 @ 75.01/10.19 Y5 @ 75.01/10.19 Y6 @ Y7)))))))))))) => 75.01/10.19 (Y4 @ 75.01/10.19 Y2 @ Y3 @ 75.01/10.19 Y3)))))))) => 75.01/10.19 (((!!) @ ( 75.01/10.19 ^[Y4 : iS > 75.01/10.19 iS > iS > $o]: 75.01/10.19 (((((!!) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (!!) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (!!) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y5) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y6) = 75.01/10.19 (Y7))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y10 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y11 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y12 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y13 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y5) = 75.01/10.19 (cP @ 75.01/10.19 Y8 @ Y9))) & 75.01/10.19 ( 75.01/10.19 Y4 @ 75.01/10.19 Y8 @ 75.01/10.19 Y10 @ Y12) & 75.01/10.19 ( 75.01/10.19 Y4 @ 75.01/10.19 Y9 @ 75.01/10.19 Y11 @ Y13) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y7) = 75.01/10.19 (cP @ 75.01/10.19 Y12 @ 75.01/10.19 Y13))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y6) = 75.01/10.19 (cP @ 75.01/10.19 Y10 @ 75.01/10.19 Y11))))))))))))))))))))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y5) = 75.01/10.19 (Y7))) & 75.01/10.19 (( 75.01/10.19 (Y6) = 75.01/10.19 (c0))))))) => 75.01/10.19 (Y4 @ 75.01/10.19 Y5 @ 75.01/10.19 Y6 @ Y7)))))))))))) => 75.01/10.19 (Y4 @ 75.01/10.19 (cP @ Y0 @ 75.01/10.19 Y2) @ 75.01/10.19 (cP @ Y1 @ 75.01/10.19 Y3) @ 75.01/10.19 (cP @ Y1 @ 75.01/10.19 Y3)))))))))))))))))))))))), 75.01/10.19 inference('cnf', [status(esa)], [zf_stmt_0])). 75.01/10.19 thf(zip_derived_cl2, plain, 75.01/10.19 (~ (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((!!) @ (^[Y3 : iS]: 75.01/10.19 (((((((!!) @ ( 75.01/10.19 ^[Y4 : iS > 75.01/10.19 iS > iS > $o]: 75.01/10.19 (((((!!) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (!!) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (!!) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y5) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y6) = 75.01/10.19 (Y7))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y6) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y5) = 75.01/10.19 (Y7))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y10 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y11 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y12 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y13 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y5) = 75.01/10.19 (cP @ 75.01/10.19 Y8 @ Y9))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y6) = 75.01/10.19 (cP @ 75.01/10.19 Y10 @ 75.01/10.19 Y11))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y7) = 75.01/10.19 (cP @ 75.01/10.19 Y12 @ 75.01/10.19 Y13))) & 75.01/10.19 ( 75.01/10.19 Y4 @ 75.01/10.19 Y8 @ 75.01/10.19 Y10 @ Y12) & 75.01/10.19 ( 75.01/10.19 Y4 @ 75.01/10.19 Y9 @ 75.01/10.19 Y11 @ Y13))))))))))))))))))))))) => 75.01/10.19 (Y4 @ 75.01/10.19 Y5 @ 75.01/10.19 Y6 @ Y7)))))))))))) => 75.01/10.19 (Y4 @ Y0 @ 75.01/10.19 Y1 @ Y1)))))) & 75.01/10.19 (((!!) @ ( 75.01/10.19 ^[Y4 : iS > 75.01/10.19 iS > iS > $o]: 75.01/10.19 (((((!!) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (!!) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (!!) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y6) = 75.01/10.19 (Y7))) & 75.01/10.19 (( 75.01/10.19 (Y5) = 75.01/10.19 (c0))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y6) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y5) = 75.01/10.19 (Y7))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y10 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y11 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y12 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y13 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 Y4 @ 75.01/10.19 Y9 @ 75.01/10.19 Y11 @ Y13) & 75.01/10.19 ( 75.01/10.19 Y4 @ 75.01/10.19 Y8 @ 75.01/10.19 Y10 @ Y12) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y7) = 75.01/10.19 (cP @ 75.01/10.19 Y12 @ 75.01/10.19 Y13))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y6) = 75.01/10.19 (cP @ 75.01/10.19 Y10 @ 75.01/10.19 Y11))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y5) = 75.01/10.19 (cP @ 75.01/10.19 Y8 @ Y9))))))))))))))))))))))))) => 75.01/10.19 (Y4 @ 75.01/10.19 Y5 @ 75.01/10.19 Y6 @ Y7)))))))))))) => 75.01/10.19 (Y4 @ Y2 @ 75.01/10.19 Y3 @ Y3)))))))) => 75.01/10.19 (((!!) @ (^[Y4 : 75.01/10.19 iS > 75.01/10.19 iS > iS > $o]: 75.01/10.19 (( 75.01/10.19 (( 75.01/10.19 (!!) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (!!) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (!!) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y5) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y6) = 75.01/10.19 (Y7))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y10 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y11 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y12 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y13 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y5) = 75.01/10.19 (cP @ 75.01/10.19 Y8 @ Y9))) & 75.01/10.19 ( 75.01/10.19 Y4 @ 75.01/10.19 Y8 @ 75.01/10.19 Y10 @ Y12) & 75.01/10.19 ( 75.01/10.19 Y4 @ 75.01/10.19 Y9 @ 75.01/10.19 Y11 @ Y13) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y7) = 75.01/10.19 (cP @ 75.01/10.19 Y12 @ 75.01/10.19 Y13))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y6) = 75.01/10.19 (cP @ 75.01/10.19 Y10 @ 75.01/10.19 Y11))))))))))))))))))))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y5) = 75.01/10.19 (Y7))) & 75.01/10.19 (( 75.01/10.19 (Y6) = 75.01/10.19 (c0))))))) => 75.01/10.19 (Y4 @ 75.01/10.19 Y5 @ 75.01/10.19 Y6 @ Y7)))))))))))) => 75.01/10.19 (Y4 @ 75.01/10.19 ( 75.01/10.19 cP @ 75.01/10.19 Y0 @ Y2) @ 75.01/10.19 ( 75.01/10.19 cP @ 75.01/10.19 Y1 @ Y3) @ 75.01/10.19 ( 75.01/10.19 cP @ 75.01/10.19 Y1 @ Y3)))))))))))))))))))))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 75.01/10.19 thf(zip_derived_cl6, plain, 75.01/10.19 (~ (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((((((!!) @ (^[Y3 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((!!) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (!!) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y4) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y5) = 75.01/10.19 (Y6))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y5) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y4) = 75.01/10.19 (Y6))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y10 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y11 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y12 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y4) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y5) = 75.01/10.19 (cP @ 75.01/10.19 Y9 @ Y10))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y6) = 75.01/10.19 (cP @ 75.01/10.19 Y11 @ 75.01/10.19 Y12))) & 75.01/10.19 ( 75.01/10.19 Y3 @ 75.01/10.19 Y7 @ 75.01/10.19 Y9 @ Y11) & 75.01/10.19 ( 75.01/10.19 Y3 @ 75.01/10.19 Y8 @ 75.01/10.19 Y10 @ Y12))))))))))))))))))))))) => 75.01/10.19 (Y3 @ 75.01/10.19 Y4 @ 75.01/10.19 Y5 @ Y6)))))))))))) => 75.01/10.19 (Y3 @ '#sk1' @ 75.01/10.19 Y0 @ Y0)))))) & 75.01/10.19 (((!!) @ (^[Y3 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((!!) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (!!) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y5) = 75.01/10.19 (Y6))) & 75.01/10.19 (( 75.01/10.19 (Y4) = 75.01/10.19 (c0))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y5) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y4) = 75.01/10.19 (Y6))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y10 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y11 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y12 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 Y3 @ 75.01/10.19 Y8 @ 75.01/10.19 Y10 @ Y12) & 75.01/10.19 ( 75.01/10.19 Y3 @ 75.01/10.19 Y7 @ 75.01/10.19 Y9 @ Y11) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y6) = 75.01/10.19 (cP @ 75.01/10.19 Y11 @ 75.01/10.19 Y12))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y5) = 75.01/10.19 (cP @ 75.01/10.19 Y9 @ Y10))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y4) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))))))))))))))))))))))))) => 75.01/10.19 (Y3 @ 75.01/10.19 Y4 @ 75.01/10.19 Y5 @ Y6)))))))))))) => 75.01/10.19 (Y3 @ Y1 @ Y2 @ 75.01/10.19 Y2)))))))) => 75.01/10.19 (((!!) @ (^[Y3 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((!!) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (!!) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y4) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y5) = 75.01/10.19 (Y6))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y10 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y11 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y12 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y4) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))) & 75.01/10.19 ( 75.01/10.19 Y3 @ 75.01/10.19 Y7 @ 75.01/10.19 Y9 @ Y11) & 75.01/10.19 ( 75.01/10.19 Y3 @ 75.01/10.19 Y8 @ 75.01/10.19 Y10 @ Y12) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y6) = 75.01/10.19 (cP @ 75.01/10.19 Y11 @ 75.01/10.19 Y12))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y5) = 75.01/10.19 (cP @ 75.01/10.19 Y9 @ Y10))))))))))))))))))))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y4) = 75.01/10.19 (Y6))) & 75.01/10.19 (( 75.01/10.19 (Y5) = 75.01/10.19 (c0))))))) => 75.01/10.19 (Y3 @ 75.01/10.19 Y4 @ 75.01/10.19 Y5 @ Y6)))))))))))) => 75.01/10.19 (Y3 @ 75.01/10.19 (cP @ '#sk1' @ Y1) @ 75.01/10.19 (cP @ Y0 @ Y2) @ 75.01/10.19 (cP @ Y0 @ Y2))))))))))))))))))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 75.01/10.19 thf(zip_derived_cl10, plain, 75.01/10.19 (~ (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((((((!!) @ (^[Y2 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y3 : iS]: 75.01/10.19 (((!!) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((!!) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y3) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y4) = 75.01/10.19 (Y5))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y4) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y3) = 75.01/10.19 (Y5))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y10 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y11 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y3) = 75.01/10.19 (cP @ 75.01/10.19 Y6 @ Y7))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y4) = 75.01/10.19 (cP @ 75.01/10.19 Y8 @ Y9))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y5) = 75.01/10.19 (cP @ 75.01/10.19 Y10 @ 75.01/10.19 Y11))) & 75.01/10.19 ( 75.01/10.19 Y2 @ 75.01/10.19 Y6 @ 75.01/10.19 Y8 @ Y10) & 75.01/10.19 ( 75.01/10.19 Y2 @ 75.01/10.19 Y7 @ 75.01/10.19 Y9 @ Y11))))))))))))))))))))))) => 75.01/10.19 (Y2 @ 75.01/10.19 Y3 @ 75.01/10.19 Y4 @ Y5)))))))))))) => 75.01/10.19 (Y2 @ '#sk1' @ '#sk2' @ 75.01/10.19 '#sk2')))))) & 75.01/10.19 (((!!) @ (^[Y2 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y3 : iS]: 75.01/10.19 (((!!) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((!!) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y4) = 75.01/10.19 (Y5))) & 75.01/10.19 (( 75.01/10.19 (Y3) = 75.01/10.19 (c0))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y4) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y3) = 75.01/10.19 (Y5))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y10 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y11 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 Y2 @ 75.01/10.19 Y7 @ 75.01/10.19 Y9 @ Y11) & 75.01/10.19 ( 75.01/10.19 Y2 @ 75.01/10.19 Y6 @ 75.01/10.19 Y8 @ Y10) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y5) = 75.01/10.19 (cP @ 75.01/10.19 Y10 @ 75.01/10.19 Y11))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y4) = 75.01/10.19 (cP @ 75.01/10.19 Y8 @ Y9))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y3) = 75.01/10.19 (cP @ 75.01/10.19 Y6 @ Y7))))))))))))))))))))))))) => 75.01/10.19 (Y2 @ 75.01/10.19 Y3 @ 75.01/10.19 Y4 @ Y5)))))))))))) => 75.01/10.19 (Y2 @ Y0 @ Y1 @ Y1)))))))) => 75.01/10.19 (((!!) @ (^[Y2 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y3 : iS]: 75.01/10.19 (((!!) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((!!) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y3) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y4) = 75.01/10.19 (Y5))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y10 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y11 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y3) = 75.01/10.19 (cP @ 75.01/10.19 Y6 @ Y7))) & 75.01/10.19 ( 75.01/10.19 Y2 @ 75.01/10.19 Y6 @ 75.01/10.19 Y8 @ Y10) & 75.01/10.19 ( 75.01/10.19 Y2 @ 75.01/10.19 Y7 @ 75.01/10.19 Y9 @ Y11) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y5) = 75.01/10.19 (cP @ 75.01/10.19 Y10 @ 75.01/10.19 Y11))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y4) = 75.01/10.19 (cP @ 75.01/10.19 Y8 @ Y9))))))))))))))))))))))) | 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (( 75.01/10.19 (Y3) = 75.01/10.19 (Y5))) & 75.01/10.19 (( 75.01/10.19 (Y4) = 75.01/10.19 (c0))))))) => 75.01/10.19 (Y2 @ 75.01/10.19 Y3 @ 75.01/10.19 Y4 @ Y5)))))))))))) => 75.01/10.19 (Y2 @ (cP @ '#sk1' @ Y0) @ 75.01/10.19 (cP @ '#sk2' @ Y1) @ 75.01/10.19 (cP @ '#sk2' @ Y1)))))))))))))))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 75.01/10.19 thf(zip_derived_cl14, plain, 75.01/10.19 (~ (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((((((!!) @ (^[Y1 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y2 : iS]: 75.01/10.19 (((!!) @ (^[Y3 : iS]: 75.01/10.19 (((!!) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((( 75.01/10.19 (( 75.01/10.19 (( 75.01/10.19 (Y2) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y3) = 75.01/10.19 (Y4))))) | 75.01/10.19 (( 75.01/10.19 (( 75.01/10.19 (Y3) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y2) = 75.01/10.19 (Y4))))) | 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y10 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y3) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y4) = 75.01/10.19 (cP @ 75.01/10.19 Y9 @ Y10))) & 75.01/10.19 ( 75.01/10.19 Y1 @ 75.01/10.19 Y5 @ 75.01/10.19 Y7 @ Y9) & 75.01/10.19 ( 75.01/10.19 Y1 @ 75.01/10.19 Y6 @ 75.01/10.19 Y8 @ Y10))))))))))))))))))))))) => 75.01/10.19 (Y1 @ 75.01/10.19 Y2 @ Y3 @ 75.01/10.19 Y4)))))))))))) => 75.01/10.19 (Y1 @ '#sk1' @ '#sk2' @ '#sk2')))))) & 75.01/10.19 (((!!) @ (^[Y1 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y2 : iS]: 75.01/10.19 (((!!) @ (^[Y3 : iS]: 75.01/10.19 (((!!) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((( 75.01/10.19 (( 75.01/10.19 (( 75.01/10.19 (Y3) = 75.01/10.19 (Y4))) & 75.01/10.19 (( 75.01/10.19 (Y2) = 75.01/10.19 (c0))))) | 75.01/10.19 (( 75.01/10.19 (( 75.01/10.19 (Y3) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y2) = 75.01/10.19 (Y4))))) | 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y10 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 Y1 @ 75.01/10.19 Y6 @ 75.01/10.19 Y8 @ Y10) & 75.01/10.19 ( 75.01/10.19 Y1 @ 75.01/10.19 Y5 @ 75.01/10.19 Y7 @ Y9) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y4) = 75.01/10.19 (cP @ 75.01/10.19 Y9 @ Y10))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y3) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))))))))))))))))))))))))) => 75.01/10.19 (Y1 @ 75.01/10.19 Y2 @ Y3 @ 75.01/10.19 Y4)))))))))))) => 75.01/10.19 (Y1 @ '#sk8' @ Y0 @ Y0)))))))) => 75.01/10.19 (((!!) @ (^[Y1 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y2 : iS]: 75.01/10.19 (((!!) @ (^[Y3 : iS]: 75.01/10.19 (((!!) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((((( 75.01/10.19 (( 75.01/10.19 (Y2) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y3) = 75.01/10.19 (Y4))))) | 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y10 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))) & 75.01/10.19 ( 75.01/10.19 Y1 @ 75.01/10.19 Y5 @ 75.01/10.19 Y7 @ Y9) & 75.01/10.19 ( 75.01/10.19 Y1 @ 75.01/10.19 Y6 @ 75.01/10.19 Y8 @ Y10) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y4) = 75.01/10.19 (cP @ 75.01/10.19 Y9 @ Y10))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y3) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))))))))))))))))))))))) | 75.01/10.19 (( 75.01/10.19 (( 75.01/10.19 (Y2) = 75.01/10.19 (Y4))) & 75.01/10.19 (( 75.01/10.19 (Y3) = 75.01/10.19 (c0))))))) => 75.01/10.19 (Y1 @ Y2 @ 75.01/10.19 Y3 @ Y4)))))))))))) => 75.01/10.19 (Y1 @ (cP @ '#sk1' @ '#sk8') @ 75.01/10.19 (cP @ '#sk2' @ Y0) @ (cP @ '#sk2' @ Y0))))))))))))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl10])). 75.01/10.19 thf(zip_derived_cl18, plain, 75.01/10.19 (~ (((((((!!) @ (^[Y0 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((!!) @ (^[Y3 : iS]: 75.01/10.19 (((((((( 75.01/10.19 (Y1) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y2) = 75.01/10.19 (Y3))))) | 75.01/10.19 (((( 75.01/10.19 (Y2) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y1) = 75.01/10.19 (Y3))))) | 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y6 @ Y7))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y3) = 75.01/10.19 (cP @ 75.01/10.19 Y8 @ Y9))) & 75.01/10.19 ( 75.01/10.19 Y0 @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8) & 75.01/10.19 ( 75.01/10.19 Y0 @ 75.01/10.19 Y5 @ 75.01/10.19 Y7 @ Y9))))))))))))))))))))))) => 75.01/10.19 (Y0 @ Y1 @ 75.01/10.19 Y2 @ Y3)))))))))))) => 75.01/10.19 (Y0 @ '#sk1' @ '#sk2' @ '#sk2')))))) & 75.01/10.19 (((!!) @ (^[Y0 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((!!) @ (^[Y3 : iS]: 75.01/10.19 (((((((( 75.01/10.19 (Y2) = 75.01/10.19 (Y3))) & 75.01/10.19 (( 75.01/10.19 (Y1) = 75.01/10.19 (c0))))) | 75.01/10.19 (((( 75.01/10.19 (Y2) = 75.01/10.19 (c0))) & 75.01/10.19 (( 75.01/10.19 (Y1) = 75.01/10.19 (Y3))))) | 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 Y0 @ 75.01/10.19 Y5 @ 75.01/10.19 Y7 @ Y9) & 75.01/10.19 ( 75.01/10.19 Y0 @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y3) = 75.01/10.19 (cP @ 75.01/10.19 Y8 @ Y9))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y6 @ Y7))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))))))))))))))))))))))))) => 75.01/10.19 (Y0 @ Y1 @ 75.01/10.19 Y2 @ Y3)))))))))))) => 75.01/10.19 (Y0 @ '#sk8' @ '#sk14' @ '#sk14')))))))) => 75.01/10.19 (((!!) @ (^[Y0 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((!!) @ (^[Y3 : iS]: 75.01/10.19 (((((((((Y1) = 75.01/10.19 (c0))) & 75.01/10.19 (((Y2) = 75.01/10.19 (Y3))))) | 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 Y0 @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8) & 75.01/10.19 ( 75.01/10.19 Y0 @ 75.01/10.19 Y5 @ 75.01/10.19 Y7 @ Y9) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y3) = 75.01/10.19 (cP @ 75.01/10.19 Y8 @ Y9))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y6 @ Y7))))))))))))))))))))))) | 75.01/10.19 (((((Y1) = 75.01/10.19 (Y3))) & 75.01/10.19 (((Y2) = 75.01/10.19 (c0))))))) => 75.01/10.19 (Y0 @ Y1 @ Y2 @ 75.01/10.19 Y3)))))))))))) => 75.01/10.19 (Y0 @ (cP @ '#sk1' @ '#sk8') @ 75.01/10.19 (cP @ '#sk2' @ '#sk14') @ (cP @ '#sk2' @ '#sk14')))))))))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl14])). 75.01/10.19 thf(zip_derived_cl21, plain, 75.01/10.19 ( (((((!!) @ (^[Y0 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((!!) @ (^[Y3 : iS]: 75.01/10.19 (((((((((Y1) = (c0))) & 75.01/10.19 (((Y2) = (Y3))))) | 75.01/10.19 (((((Y2) = (c0))) & 75.01/10.19 (((Y1) = (Y3))))) | 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y6 @ Y7))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y3) = 75.01/10.19 (cP @ 75.01/10.19 Y8 @ Y9))) & 75.01/10.19 ( 75.01/10.19 Y0 @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8) & 75.01/10.19 ( 75.01/10.19 Y0 @ 75.01/10.19 Y5 @ 75.01/10.19 Y7 @ Y9))))))))))))))))))))))) => 75.01/10.19 (Y0 @ Y1 @ Y2 @ 75.01/10.19 Y3)))))))))))) => 75.01/10.19 (Y0 @ '#sk1' @ '#sk2' @ '#sk2')))))) & 75.01/10.19 (((!!) @ (^[Y0 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((!!) @ (^[Y3 : iS]: 75.01/10.19 (((((((((Y2) = (Y3))) & 75.01/10.19 (((Y1) = (c0))))) | 75.01/10.19 (((((Y2) = (c0))) & 75.01/10.19 (((Y1) = (Y3))))) | 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 Y0 @ 75.01/10.19 Y5 @ 75.01/10.19 Y7 @ Y9) & 75.01/10.19 ( 75.01/10.19 Y0 @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y3) = 75.01/10.19 (cP @ 75.01/10.19 Y8 @ Y9))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y6 @ Y7))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))))))))))))))))))))))))) => 75.01/10.19 (Y0 @ Y1 @ Y2 @ 75.01/10.19 Y3)))))))))))) => 75.01/10.19 (Y0 @ '#sk8' @ '#sk14' @ '#sk14'))))))))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 75.01/10.19 thf(zip_derived_cl26, plain, 75.01/10.19 ( (((!!) @ (^[Y0 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((!!) @ (^[Y3 : iS]: 75.01/10.19 (((((((((Y2) = (Y3))) & 75.01/10.19 (((Y1) = (c0))))) | 75.01/10.19 (((((Y2) = (c0))) & 75.01/10.19 (((Y1) = (Y3))))) | 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 Y0 @ 75.01/10.19 Y5 @ 75.01/10.19 Y7 @ Y9) & 75.01/10.19 ( 75.01/10.19 Y0 @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y3) = 75.01/10.19 (cP @ 75.01/10.19 Y8 @ Y9))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y6 @ Y7))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))))))))))))))))))))))))) => 75.01/10.19 (Y0 @ Y1 @ Y2 @ Y3)))))))))))) => 75.01/10.19 (Y0 @ '#sk8' @ '#sk14' @ '#sk14'))))))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 75.01/10.19 thf(zip_derived_cl35, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((((((((Y1) = (Y2))) & 75.01/10.19 (((Y0) = (c0))))) | 75.01/10.19 (((((Y1) = (c0))) & 75.01/10.19 (((Y0) = (Y2))))) | 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y3 @ 75.01/10.19 Y5 @ Y7) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))))))))))))))))))))))))) => 75.01/10.19 (X2 @ Y0 @ Y1 @ Y2)))))))))))) => 75.01/10.19 (X2 @ '#sk8' @ '#sk14' @ '#sk14')))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl26])). 75.01/10.19 thf(zip_derived_cl36, plain, 75.01/10.19 ( (((((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((((((((Y1) = (Y2))) & 75.01/10.19 (((Y0) = (c0))))) | 75.01/10.19 (((((Y1) = (c0))) & 75.01/10.19 (((Y0) = (Y2))))) | 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y3 @ 75.01/10.19 Y5 @ Y7) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))))))))))))))))))))))))) => 75.01/10.19 ('#sk27' @ Y0 @ Y1 @ Y2)))))))))))) => 75.01/10.19 ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14')))), 75.01/10.19 inference('triggered_bool_instantiation', [status(thm)], 75.01/10.19 [zip_derived_cl35])). 75.01/10.19 thf(zip_derived_cl194, plain, 75.01/10.19 ((~ (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((((((((Y1) = (Y2))) & 75.01/10.19 (((Y0) = (c0))))) | 75.01/10.19 (((((Y1) = (c0))) & 75.01/10.19 (((Y0) = (Y2))))) | 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y3 @ 75.01/10.19 Y5 @ Y7) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))))))))))))))))))))))))) => 75.01/10.19 ('#sk27' @ Y0 @ Y1 @ Y2)))))))))))) 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14'))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 75.01/10.19 thf(zip_derived_cl195, plain, 75.01/10.19 ((~ (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((((((((Y0) = (Y1))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))) | 75.01/10.19 (((((Y0) = (c0))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (Y1))))) | 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y3 @ 75.01/10.19 Y5 @ Y7) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y2 @ 75.01/10.19 Y4 @ Y6) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y6 @ Y7))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk82' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))))))))))))))))))))))))) => 75.01/10.19 ('#sk27' @ ('#sk82' @ '#sk27') @ Y0 @ Y1))))))))) 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl194])). 75.01/10.19 thf(zip_derived_cl196, plain, 75.01/10.19 ((~ (((!!) @ (^[Y0 : iS]: 75.01/10.19 ((((((((('#sk128' @ '#sk27') = (Y0))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))) | 75.01/10.19 ((((('#sk128' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (Y0))))) | 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y2 @ 75.01/10.19 Y4 @ Y6) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk128' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk82' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y1 @ Y2))))))))))))))))))))))))) => 75.01/10.19 ('#sk27' @ ('#sk82' @ '#sk27') @ 75.01/10.19 ('#sk128' @ '#sk27') @ Y0)))))) 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl195])). 75.01/10.19 thf(zip_derived_cl197, plain, 75.01/10.19 ((~ ((((((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))) | 75.01/10.19 ((((('#sk128' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk82' @ '#sk27') = ('#sk192' @ '#sk27'))))) | 75.01/10.19 (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk192' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk128' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk82' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))))))))))))))))))))))))) => 75.01/10.19 ('#sk27' @ ('#sk82' @ '#sk27') @ ('#sk128' @ '#sk27') @ 75.01/10.19 ('#sk192' @ '#sk27')))) 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl196])). 75.01/10.19 thf(zip_derived_cl198, plain, 75.01/10.19 (( ((((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))) | 75.01/10.19 ((((('#sk128' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk82' @ '#sk27') = ('#sk192' @ '#sk27'))))) | 75.01/10.19 (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ (^[Y4 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk192' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk128' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk82' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))))))))))))))))))))))))) 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14'))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl197])). 75.01/10.19 thf(zip_derived_cl200, plain, 75.01/10.19 (( ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))) 75.01/10.19 | ((((('#sk128' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk82' @ '#sk27') = ('#sk192' @ '#sk27'))))) 75.01/10.19 | (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ (^[Y4 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk192' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk128' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk82' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))))))))))))))))))))))) 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14'))), 75.01/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl198])). 75.01/10.19 thf(zip_derived_cl35, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((((((((Y1) = (Y2))) & 75.01/10.19 (((Y0) = (c0))))) | 75.01/10.19 (((((Y1) = (c0))) & 75.01/10.19 (((Y0) = (Y2))))) | 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y3 @ 75.01/10.19 Y5 @ Y7) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))))))))))))))))))))))))) => 75.01/10.19 (X2 @ Y0 @ Y1 @ Y2)))))))))))) => 75.01/10.19 (X2 @ '#sk8' @ '#sk14' @ '#sk14')))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl26])). 75.01/10.19 thf(zip_derived_cl45, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (~ (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((((((((Y1) = (Y2))) & 75.01/10.19 (((Y0) = (c0))))) | 75.01/10.19 (((((Y1) = (c0))) & 75.01/10.19 (((Y0) = (Y2))))) | 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y3 @ 75.01/10.19 Y5 @ Y7) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))))))))))))))))))))))))) => 75.01/10.19 (X2 @ Y0 @ Y1 @ Y2)))))))))))) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 75.01/10.19 thf(zip_derived_cl50, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (~ (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((((((((Y0) = (Y1))) & 75.01/10.19 ((('#sk82' @ X2) = (c0))))) | 75.01/10.19 (((((Y0) = (c0))) & 75.01/10.19 ((('#sk82' @ X2) = (Y1))))) | 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y3 @ 75.01/10.19 Y5 @ Y7) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y2 @ 75.01/10.19 Y4 @ Y6) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y6 @ Y7))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk82' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))))))))))))))))))))))))) => 75.01/10.19 (X2 @ ('#sk82' @ X2) @ Y0 @ Y1))))))))) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl45])). 75.01/10.19 thf(zip_derived_cl55, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (~ (((!!) @ (^[Y0 : iS]: 75.01/10.19 ((((((((('#sk128' @ X2) = (Y0))) & 75.01/10.19 ((('#sk82' @ X2) = (c0))))) | 75.01/10.19 ((((('#sk128' @ X2) = (c0))) & 75.01/10.19 ((('#sk82' @ X2) = (Y0))))) | 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y2 @ 75.01/10.19 Y4 @ Y6) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk128' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk82' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y1 @ Y2))))))))))))))))))))))))) => 75.01/10.19 (X2 @ ('#sk82' @ X2) @ ('#sk128' @ X2) @ Y0)))))) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl50])). 75.01/10.19 thf(zip_derived_cl58, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (~ ((((((((('#sk128' @ X2) = ('#sk192' @ X2))) & 75.01/10.19 ((('#sk82' @ X2) = (c0))))) | 75.01/10.19 ((((('#sk128' @ X2) = (c0))) & 75.01/10.19 ((('#sk82' @ X2) = ('#sk192' @ X2))))) | 75.01/10.19 (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk192' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk128' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk82' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))))))))))))))))))))))))) => 75.01/10.19 (X2 @ ('#sk82' @ X2) @ ('#sk128' @ X2) @ ('#sk192' @ X2)))) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl55])). 75.01/10.19 thf(zip_derived_cl62, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ((((((('#sk128' @ X2) = ('#sk192' @ X2))) & 75.01/10.19 ((('#sk82' @ X2) = (c0))))) | 75.01/10.19 ((((('#sk128' @ X2) = (c0))) & 75.01/10.19 ((('#sk82' @ X2) = ('#sk192' @ X2))))) | 75.01/10.19 (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk192' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk128' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk82' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))))))))))))))))))))))))) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 75.01/10.19 thf(zip_derived_cl68, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ((((('#sk128' @ X2) = ('#sk192' @ X2))) & ((('#sk82' @ X2) = (c0))))) 75.01/10.19 | ((((('#sk128' @ X2) = (c0))) & 75.01/10.19 ((('#sk82' @ X2) = ('#sk192' @ X2))))) 75.01/10.19 | (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk192' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk128' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk82' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))))))))))))))))))))))) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 75.01/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl62])). 75.01/10.19 thf(zip_derived_cl75, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ((('#sk82' @ X2) = (c0))) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk192' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk128' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk82' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))))))))))))))))))))))) 75.01/10.19 | ((((('#sk128' @ X2) = (c0))) & 75.01/10.19 ((('#sk82' @ X2) = ('#sk192' @ X2))))))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl68])). 75.01/10.19 thf(zip_derived_cl90, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ((('#sk82' @ X2) = (c0)) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk192' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk128' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk82' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))))))))))))))))))))))) 75.01/10.19 | ((((('#sk128' @ X2) = (c0))) & 75.01/10.19 ((('#sk82' @ X2) = ('#sk192' @ X2))))))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], [zip_derived_cl75])). 75.01/10.19 thf(zip_derived_cl91, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (~ ('#form658' @ X2) 75.01/10.19 | ((((('#sk128' @ X2) = (c0))) & 75.01/10.19 ((('#sk82' @ X2) = ('#sk192' @ X2))))))), 75.01/10.19 define([status(thm)])). 75.01/10.19 thf(zip_derived_cl201, plain, 75.01/10.19 (( ('#form658' @ '#sk27') 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ (^[Y4 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk192' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk128' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk82' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))))))))))))))))))))))) 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))))), 75.01/10.19 inference('renaming', [status(thm)], 75.01/10.19 [zip_derived_cl200, zip_derived_cl91])). 75.01/10.19 thf(zip_derived_cl202, plain, 75.01/10.19 (( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ (^[Y4 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 ( 75.01/10.19 '#sk603' @ 75.01/10.19 '#sk27') @ 75.01/10.19 Y1 @ Y3) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk192' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk128' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y1 @ Y2))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk82' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 ( 75.01/10.19 '#sk603' @ 75.01/10.19 '#sk27') @ 75.01/10.19 Y0)))))))))))))))))))) 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))) 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ('#form658' @ '#sk27'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl201])). 75.01/10.19 thf(zip_derived_cl203, plain, 75.01/10.19 (( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 ((('#sk27' @ 75.01/10.19 ('#sk916' @ '#sk27') @ 75.01/10.19 Y1 @ Y3) & 75.01/10.19 ('#sk27' @ 75.01/10.19 ('#sk603' @ '#sk27') @ 75.01/10.19 Y0 @ Y2) & 75.01/10.19 ((('#sk192' @ 75.01/10.19 '#sk27') = (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ((('#sk128' @ 75.01/10.19 '#sk27') = (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ((('#sk82' @ 75.01/10.19 '#sk27') = (cP @ 75.01/10.19 ('#sk603' @ 75.01/10.19 '#sk27') @ 75.01/10.19 ('#sk916' @ 75.01/10.19 '#sk27')))))))))))))))))) 75.01/10.19 | ('#form658' @ '#sk27') 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl202])). 75.01/10.19 thf(zip_derived_cl204, plain, 75.01/10.19 (( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 ((('#sk27' @ 75.01/10.19 ('#sk916' @ '#sk27') @ Y0 @ Y2) & 75.01/10.19 ('#sk27' @ 75.01/10.19 ('#sk603' @ '#sk27') @ 75.01/10.19 ('#sk1043' @ '#sk27') @ Y1) & 75.01/10.19 ((('#sk192' @ '#sk27') = (cP @ 75.01/10.19 Y1 @ Y2))) & 75.01/10.19 ((('#sk128' @ '#sk27') = (cP @ 75.01/10.19 ('#sk1043' @ '#sk27') @ Y0))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (cP @ 75.01/10.19 ('#sk603' @ '#sk27') @ 75.01/10.19 ('#sk916' @ '#sk27'))))))))))))))) 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))) 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ('#form658' @ '#sk27'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl203])). 75.01/10.19 thf(zip_derived_cl205, plain, 75.01/10.19 (( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 ((('#sk27' @ ('#sk916' @ '#sk27') @ 75.01/10.19 ('#sk1190' @ '#sk27') @ Y1) & 75.01/10.19 ('#sk27' @ ('#sk603' @ '#sk27') @ 75.01/10.19 ('#sk1043' @ '#sk27') @ Y0) & 75.01/10.19 ((('#sk192' @ '#sk27') = (cP @ Y0 @ Y1))) & 75.01/10.19 ((('#sk128' @ '#sk27') = (cP @ 75.01/10.19 ('#sk1043' @ '#sk27') @ 75.01/10.19 ('#sk1190' @ '#sk27')))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (cP @ 75.01/10.19 ('#sk603' @ '#sk27') @ 75.01/10.19 ('#sk916' @ '#sk27')))))))))))) 75.01/10.19 | ('#form658' @ '#sk27') 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl204])). 75.01/10.19 thf(zip_derived_cl206, plain, 75.01/10.19 (( (((??) @ (^[Y0 : iS]: 75.01/10.19 ((('#sk27' @ ('#sk916' @ '#sk27') @ 75.01/10.19 ('#sk1190' @ '#sk27') @ Y0) & 75.01/10.19 ('#sk27' @ ('#sk603' @ '#sk27') @ 75.01/10.19 ('#sk1043' @ '#sk27') @ ('#sk1357' @ '#sk27')) & 75.01/10.19 ((('#sk192' @ '#sk27') = (cP @ ('#sk1357' @ '#sk27') @ 75.01/10.19 Y0))) & 75.01/10.19 ((('#sk128' @ '#sk27') = (cP @ ('#sk1043' @ '#sk27') @ 75.01/10.19 ('#sk1190' @ '#sk27')))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (cP @ ('#sk603' @ '#sk27') @ 75.01/10.19 ('#sk916' @ '#sk27'))))))))) 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))) 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ('#form658' @ '#sk27'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl205])). 75.01/10.19 thf(zip_derived_cl207, plain, 75.01/10.19 (( ((('#sk27' @ ('#sk916' @ '#sk27') @ ('#sk1190' @ '#sk27') @ 75.01/10.19 ('#sk1544' @ '#sk27')) & 75.01/10.19 ('#sk27' @ ('#sk603' @ '#sk27') @ ('#sk1043' @ '#sk27') @ 75.01/10.19 ('#sk1357' @ '#sk27')) & 75.01/10.19 ((('#sk192' @ '#sk27') = (cP @ ('#sk1357' @ '#sk27') @ 75.01/10.19 ('#sk1544' @ '#sk27')))) & 75.01/10.19 ((('#sk128' @ '#sk27') = (cP @ ('#sk1043' @ '#sk27') @ 75.01/10.19 ('#sk1190' @ '#sk27')))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (cP @ ('#sk603' @ '#sk27') @ 75.01/10.19 ('#sk916' @ '#sk27')))))) 75.01/10.19 | ('#form658' @ '#sk27') 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl206])). 75.01/10.19 thf(zip_derived_cl211, plain, 75.01/10.19 (( ((('#sk128' @ '#sk27') = (cP @ ('#sk1043' @ '#sk27') @ 75.01/10.19 ('#sk1190' @ '#sk27')))) 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))) 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ('#form658' @ '#sk27'))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl207])). 75.01/10.19 thf(zip_derived_cl220, plain, 75.01/10.19 (((('#sk128' @ '#sk27') 75.01/10.19 = (cP @ ('#sk1043' @ '#sk27') @ ('#sk1190' @ '#sk27'))) 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))) 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ('#form658' @ '#sk27'))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], 75.01/10.19 [zip_derived_cl211])). 75.01/10.19 thf(zip_derived_cl208, plain, 75.01/10.19 (( ('#sk27' @ ('#sk916' @ '#sk27') @ ('#sk1190' @ '#sk27') @ 75.01/10.19 ('#sk1544' @ '#sk27')) 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))) 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ('#form658' @ '#sk27'))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl207])). 75.01/10.19 thf(zip_derived_cl213, plain, 75.01/10.19 ((~ ('#form2610') 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))))), 75.01/10.19 define([status(thm)])). 75.01/10.19 thf(zip_derived_cl221, plain, 75.01/10.19 (( ('#form2610') 75.01/10.19 | ('#form658' @ '#sk27') 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | (('#sk128' @ '#sk27') 75.01/10.19 = (cP @ ('#sk1043' @ '#sk27') @ ('#sk1190' @ '#sk27'))))), 75.01/10.19 inference('renaming', [status(thm)], 75.01/10.19 [zip_derived_cl220, zip_derived_cl213])). 75.01/10.19 thf(zip_derived_cl209, plain, 75.01/10.19 (( ('#sk27' @ ('#sk603' @ '#sk27') @ ('#sk1043' @ '#sk27') @ 75.01/10.19 ('#sk1357' @ '#sk27')) 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))) 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ('#form658' @ '#sk27'))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl207])). 75.01/10.19 thf(zip_derived_cl213, plain, 75.01/10.19 ((~ ('#form2610') 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))))), 75.01/10.19 define([status(thm)])). 75.01/10.19 thf(zip_derived_cl217, plain, 75.01/10.19 (( ('#form2610') 75.01/10.19 | ('#form658' @ '#sk27') 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ('#sk27' @ ('#sk603' @ '#sk27') @ ('#sk1043' @ '#sk27') @ 75.01/10.19 ('#sk1357' @ '#sk27')))), 75.01/10.19 inference('renaming', [status(thm)], 75.01/10.19 [zip_derived_cl209, zip_derived_cl213])). 75.01/10.19 thf(zip_derived_cl90, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ((('#sk82' @ X2) = (c0)) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk192' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk128' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk82' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))))))))))))))))))))))) 75.01/10.19 | ((((('#sk128' @ X2) = (c0))) & 75.01/10.19 ((('#sk82' @ X2) = ('#sk192' @ X2))))))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], [zip_derived_cl75])). 75.01/10.19 thf(zip_derived_cl91, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (~ ('#form658' @ X2) 75.01/10.19 | ((((('#sk128' @ X2) = (c0))) & 75.01/10.19 ((('#sk82' @ X2) = ('#sk192' @ X2))))))), 75.01/10.19 define([status(thm)])). 75.01/10.19 thf(zip_derived_cl94, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ('#form658' @ X2) 75.01/10.19 | (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk192' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk128' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk82' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))))))))))))))))))))))) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | (('#sk82' @ X2) = (c0)))), 75.01/10.19 inference('renaming', [status(thm)], [zip_derived_cl90, zip_derived_cl91])). 75.01/10.19 thf(zip_derived_cl101, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ (^[Y4 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 ( 75.01/10.19 '#sk603' @ 75.01/10.19 X2) @ 75.01/10.19 Y1 @ Y3) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk192' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk128' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y1 @ Y2))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk82' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 ( 75.01/10.19 '#sk603' @ 75.01/10.19 X2) @ Y0)))))))))))))))))))) 75.01/10.19 | (('#sk82' @ X2) = (c0)) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ('#form658' @ X2))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl94])). 75.01/10.19 thf(zip_derived_cl108, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((X2 @ 75.01/10.19 ('#sk916' @ X2) @ 75.01/10.19 Y1 @ Y3) & 75.01/10.19 (X2 @ 75.01/10.19 ('#sk603' @ X2) @ 75.01/10.19 Y0 @ Y2) & 75.01/10.19 ((('#sk192' @ 75.01/10.19 X2) = (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ((('#sk128' @ 75.01/10.19 X2) = (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ((('#sk82' @ X2) = 75.01/10.19 (cP @ 75.01/10.19 ('#sk603' @ X2) @ 75.01/10.19 ('#sk916' @ X2)))))))))))))))))) 75.01/10.19 | ('#form658' @ X2) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | (('#sk82' @ X2) = (c0)))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl101])). 75.01/10.19 thf(zip_derived_cl113, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((X2 @ ('#sk916' @ X2) @ Y0 @ 75.01/10.19 Y2) & 75.01/10.19 (X2 @ ('#sk603' @ X2) @ 75.01/10.19 ('#sk1043' @ X2) @ Y1) & 75.01/10.19 ((('#sk192' @ X2) = (cP @ 75.01/10.19 Y1 @ Y2))) & 75.01/10.19 ((('#sk128' @ X2) = (cP @ 75.01/10.19 ('#sk1043' @ X2) @ Y0))) & 75.01/10.19 ((('#sk82' @ X2) = (cP @ 75.01/10.19 ('#sk603' @ X2) @ 75.01/10.19 ('#sk916' @ X2))))))))))))))) 75.01/10.19 | (('#sk82' @ X2) = (c0)) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ('#form658' @ X2))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl108])). 75.01/10.19 thf(zip_derived_cl118, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((X2 @ ('#sk916' @ X2) @ 75.01/10.19 ('#sk1190' @ X2) @ Y1) & 75.01/10.19 (X2 @ ('#sk603' @ X2) @ 75.01/10.19 ('#sk1043' @ X2) @ Y0) & 75.01/10.19 ((('#sk192' @ X2) = (cP @ Y0 @ Y1))) & 75.01/10.19 ((('#sk128' @ X2) = (cP @ 75.01/10.19 ('#sk1043' @ X2) @ ('#sk1190' @ X2)))) & 75.01/10.19 ((('#sk82' @ X2) = (cP @ 75.01/10.19 ('#sk603' @ X2) @ ('#sk916' @ X2)))))))))))) 75.01/10.19 | ('#form658' @ X2) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | (('#sk82' @ X2) = (c0)))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl113])). 75.01/10.19 thf(zip_derived_cl123, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((X2 @ ('#sk916' @ X2) @ ('#sk1190' @ X2) @ Y0) & 75.01/10.19 (X2 @ ('#sk603' @ X2) @ ('#sk1043' @ X2) @ 75.01/10.19 ('#sk1357' @ X2)) & 75.01/10.19 ((('#sk192' @ X2) = (cP @ ('#sk1357' @ X2) @ Y0))) & 75.01/10.19 ((('#sk128' @ X2) = (cP @ ('#sk1043' @ X2) @ 75.01/10.19 ('#sk1190' @ X2)))) & 75.01/10.19 ((('#sk82' @ X2) = (cP @ ('#sk603' @ X2) @ 75.01/10.19 ('#sk916' @ X2))))))))) 75.01/10.19 | (('#sk82' @ X2) = (c0)) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ('#form658' @ X2))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl118])). 75.01/10.19 thf(zip_derived_cl129, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (((X2 @ ('#sk916' @ X2) @ ('#sk1190' @ X2) @ ('#sk1544' @ X2)) & 75.01/10.19 (X2 @ ('#sk603' @ X2) @ ('#sk1043' @ X2) @ ('#sk1357' @ X2)) & 75.01/10.19 ((('#sk192' @ X2) = (cP @ ('#sk1357' @ X2) @ ('#sk1544' @ X2)))) & 75.01/10.19 ((('#sk128' @ X2) = (cP @ ('#sk1043' @ X2) @ ('#sk1190' @ X2)))) & 75.01/10.19 ((('#sk82' @ X2) = (cP @ ('#sk603' @ X2) @ ('#sk916' @ X2)))))) 75.01/10.19 | ('#form658' @ X2) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | (('#sk82' @ X2) = (c0)))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl123])). 75.01/10.19 thf(zip_derived_cl145, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (X2 @ ('#sk916' @ X2) @ ('#sk1190' @ X2) @ ('#sk1544' @ X2)) 75.01/10.19 | (('#sk82' @ X2) = (c0)) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ('#form658' @ X2))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl129])). 75.01/10.19 thf(zip_derived_cl210, plain, 75.01/10.19 (( ((('#sk192' @ '#sk27') = (cP @ ('#sk1357' @ '#sk27') @ 75.01/10.19 ('#sk1544' @ '#sk27')))) 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))) 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ('#form658' @ '#sk27'))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl207])). 75.01/10.19 thf(zip_derived_cl218, plain, 75.01/10.19 (((('#sk192' @ '#sk27') 75.01/10.19 = (cP @ ('#sk1357' @ '#sk27') @ ('#sk1544' @ '#sk27'))) 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))) 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ('#form658' @ '#sk27'))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], 75.01/10.19 [zip_derived_cl210])). 75.01/10.19 thf(zip_derived_cl213, plain, 75.01/10.19 ((~ ('#form2610') 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))))), 75.01/10.19 define([status(thm)])). 75.01/10.19 thf(zip_derived_cl219, plain, 75.01/10.19 (( ('#form2610') 75.01/10.19 | ('#form658' @ '#sk27') 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | (('#sk192' @ '#sk27') 75.01/10.19 = (cP @ ('#sk1357' @ '#sk27') @ ('#sk1544' @ '#sk27'))))), 75.01/10.19 inference('renaming', [status(thm)], 75.01/10.19 [zip_derived_cl218, zip_derived_cl213])). 75.01/10.19 thf(zip_derived_cl212, plain, 75.01/10.19 (( ((('#sk82' @ '#sk27') = (cP @ ('#sk603' @ '#sk27') @ 75.01/10.19 ('#sk916' @ '#sk27')))) 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))) 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ('#form658' @ '#sk27'))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl207])). 75.01/10.19 thf(zip_derived_cl222, plain, 75.01/10.19 (((('#sk82' @ '#sk27') 75.01/10.19 = (cP @ ('#sk603' @ '#sk27') @ ('#sk916' @ '#sk27'))) 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))) 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | ('#form658' @ '#sk27'))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], 75.01/10.19 [zip_derived_cl212])). 75.01/10.19 thf(zip_derived_cl213, plain, 75.01/10.19 ((~ ('#form2610') 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))))), 75.01/10.19 define([status(thm)])). 75.01/10.19 thf(zip_derived_cl223, plain, 75.01/10.19 (( ('#form2610') 75.01/10.19 | ('#form658' @ '#sk27') 75.01/10.19 | ('#sk27' @ '#sk8' @ '#sk14' @ '#sk14') 75.01/10.19 | (('#sk82' @ '#sk27') 75.01/10.19 = (cP @ ('#sk603' @ '#sk27') @ ('#sk916' @ '#sk27'))))), 75.01/10.19 inference('renaming', [status(thm)], 75.01/10.19 [zip_derived_cl222, zip_derived_cl213])). 75.01/10.19 thf(zip_derived_cl213, plain, 75.01/10.19 ((~ ('#form2610') 75.01/10.19 | ((((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) & 75.01/10.19 ((('#sk82' @ '#sk27') = (c0))))))), 75.01/10.19 define([status(thm)])). 75.01/10.19 thf(zip_derived_cl214, plain, 75.01/10.19 (( ((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27'))) | ~ ('#form2610'))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl213])). 75.01/10.19 thf(zip_derived_cl224, plain, 75.01/10.19 (((('#sk128' @ '#sk27') = ('#sk192' @ '#sk27')) | ~ ('#form2610'))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], 75.01/10.19 [zip_derived_cl214])). 75.01/10.19 thf(zip_derived_cl22, plain, 75.01/10.19 (~ (((!!) @ (^[Y0 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((!!) @ (^[Y3 : iS]: 75.01/10.19 (((((((((Y1) = (c0))) & 75.01/10.19 (((Y2) = (Y3))))) | 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 Y0 @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8) & 75.01/10.19 ( 75.01/10.19 Y0 @ 75.01/10.19 Y5 @ 75.01/10.19 Y7 @ Y9) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y3) = 75.01/10.19 (cP @ 75.01/10.19 Y8 @ Y9))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y6 @ Y7))))))))))))))))))))))) | 75.01/10.19 (((((Y1) = (Y3))) & 75.01/10.19 (((Y2) = (c0))))))) => 75.01/10.19 (Y0 @ Y1 @ Y2 @ 75.01/10.19 Y3)))))))))))) => 75.01/10.19 (Y0 @ (cP @ '#sk1' @ '#sk8') @ 75.01/10.19 (cP @ '#sk2' @ '#sk14') @ (cP @ '#sk2' @ '#sk14')))))))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 75.01/10.19 thf(zip_derived_cl27, plain, 75.01/10.19 (~ (((((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((((((((Y0) = (c0))) & 75.01/10.19 (((Y1) = (Y2))))) | 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y3 @ 75.01/10.19 Y5 @ Y7) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))))))))))))))))))))))) | 75.01/10.19 (((((Y0) = (Y2))) & 75.01/10.19 (((Y1) = (c0))))))) => 75.01/10.19 ('#sk27' @ Y0 @ Y1 @ Y2)))))))))))) => 75.01/10.19 ('#sk27' @ (cP @ '#sk1' @ '#sk8') @ (cP @ '#sk2' @ '#sk14') @ 75.01/10.19 (cP @ '#sk2' @ '#sk14'))))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl22])). 75.01/10.19 thf(zip_derived_cl38, plain, 75.01/10.19 (~ ('#sk27' @ (cP @ '#sk1' @ '#sk8') @ (cP @ '#sk2' @ '#sk14') @ 75.01/10.19 (cP @ '#sk2' @ '#sk14'))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])). 75.01/10.19 thf(zip_derived_cl25, plain, 75.01/10.19 ( (((!!) @ (^[Y0 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((!!) @ (^[Y3 : iS]: 75.01/10.19 (((((((((Y1) = (c0))) & 75.01/10.19 (((Y2) = (Y3))))) | 75.01/10.19 (((((Y2) = (c0))) & 75.01/10.19 (((Y1) = (Y3))))) | 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y9 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y6 @ Y7))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y3) = 75.01/10.19 (cP @ 75.01/10.19 Y8 @ Y9))) & 75.01/10.19 ( 75.01/10.19 Y0 @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8) & 75.01/10.19 ( 75.01/10.19 Y0 @ 75.01/10.19 Y5 @ 75.01/10.19 Y7 @ Y9))))))))))))))))))))))) => 75.01/10.19 (Y0 @ Y1 @ Y2 @ Y3)))))))))))) => 75.01/10.19 (Y0 @ '#sk1' @ '#sk2' @ '#sk2'))))))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 75.01/10.19 thf(zip_derived_cl33, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((((((((Y0) = (c0))) & 75.01/10.19 (((Y1) = (Y2))))) | 75.01/10.19 (((((Y1) = (c0))) & 75.01/10.19 (((Y0) = (Y2))))) | 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y3 @ 75.01/10.19 Y5 @ Y7) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8))))))))))))))))))))))) => 75.01/10.19 (X2 @ Y0 @ Y1 @ Y2)))))))))))) => 75.01/10.19 (X2 @ '#sk1' @ '#sk2' @ '#sk2')))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl25])). 75.01/10.19 thf(zip_derived_cl34, plain, 75.01/10.19 ( (((((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((((((((Y0) = (c0))) & 75.01/10.19 (((Y1) = (Y2))))) | 75.01/10.19 (((((Y1) = (c0))) & 75.01/10.19 (((Y0) = (Y2))))) | 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y3 @ 75.01/10.19 Y5 @ Y7) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8))))))))))))))))))))))) => 75.01/10.19 ('#sk27' @ Y0 @ Y1 @ Y2)))))))))))) => 75.01/10.19 ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2')))), 75.01/10.19 inference('triggered_bool_instantiation', [status(thm)], 75.01/10.19 [zip_derived_cl33])). 75.01/10.19 thf(zip_derived_cl162, plain, 75.01/10.19 ((~ (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((((((((Y0) = (c0))) & 75.01/10.19 (((Y1) = (Y2))))) | 75.01/10.19 (((((Y1) = (c0))) & 75.01/10.19 (((Y0) = (Y2))))) | 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y3 @ 75.01/10.19 Y5 @ Y7) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8))))))))))))))))))))))) => 75.01/10.19 ('#sk27' @ Y0 @ Y1 @ Y2)))))))))))) 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 75.01/10.19 thf(zip_derived_cl163, plain, 75.01/10.19 ((~ (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 ((((((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 (((Y0) = (Y1))))) | 75.01/10.19 (((((Y0) = (c0))) & 75.01/10.19 ((('#sk72' @ '#sk27') = (Y1))))) | 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y6 @ Y7))) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y2 @ 75.01/10.19 Y4 @ Y6) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y3 @ 75.01/10.19 Y5 @ Y7))))))))))))))))))))))) => 75.01/10.19 ('#sk27' @ ('#sk72' @ '#sk27') @ Y0 @ Y1))))))))) 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl162])). 75.01/10.19 thf(zip_derived_cl164, plain, 75.01/10.19 ((~ (((!!) @ (^[Y0 : iS]: 75.01/10.19 ((((((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = (Y0))))) | 75.01/10.19 ((((('#sk107' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk72' @ '#sk27') = (Y0))))) | 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y1 @ Y2))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y2 @ 75.01/10.19 Y4 @ Y6))))))))))))))))))))))) => 75.01/10.19 ('#sk27' @ ('#sk72' @ '#sk27') @ 75.01/10.19 ('#sk107' @ '#sk27') @ Y0)))))) 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl163])). 75.01/10.19 thf(zip_derived_cl165, plain, 75.01/10.19 ((~ ((((((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) | 75.01/10.19 ((((('#sk107' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk72' @ '#sk27') = ('#sk160' @ '#sk27'))))) | 75.01/10.19 (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk160' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5))))))))))))))))))))))) => 75.01/10.19 ('#sk27' @ ('#sk72' @ '#sk27') @ ('#sk107' @ '#sk27') @ 75.01/10.19 ('#sk160' @ '#sk27')))) 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl164])). 75.01/10.19 thf(zip_derived_cl166, plain, 75.01/10.19 (( ((((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) | 75.01/10.19 ((((('#sk107' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk72' @ '#sk27') = ('#sk160' @ '#sk27'))))) | 75.01/10.19 (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ (^[Y4 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk160' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5))))))))))))))))))))))) 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl165])). 75.01/10.19 thf(zip_derived_cl168, plain, 75.01/10.19 (( ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 75.01/10.19 | ((((('#sk107' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk72' @ '#sk27') = ('#sk160' @ '#sk27'))))) 75.01/10.19 | (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ (^[Y4 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk160' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5))))))))))))))))))))) 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl166])). 75.01/10.19 thf(zip_derived_cl33, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (((((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((((((((Y0) = (c0))) & 75.01/10.19 (((Y1) = (Y2))))) | 75.01/10.19 (((((Y1) = (c0))) & 75.01/10.19 (((Y0) = (Y2))))) | 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y3 @ 75.01/10.19 Y5 @ Y7) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8))))))))))))))))))))))) => 75.01/10.19 (X2 @ Y0 @ Y1 @ Y2)))))))))))) => 75.01/10.19 (X2 @ '#sk1' @ '#sk2' @ '#sk2')))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl25])). 75.01/10.19 thf(zip_derived_cl44, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (~ (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((((((((Y0) = (c0))) & 75.01/10.19 (((Y1) = (Y2))))) | 75.01/10.19 (((((Y1) = (c0))) & 75.01/10.19 (((Y0) = (Y2))))) | 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y3 @ 75.01/10.19 Y5 @ Y7) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8))))))))))))))))))))))) => 75.01/10.19 (X2 @ Y0 @ Y1 @ Y2)))))))))))) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])). 75.01/10.19 thf(zip_derived_cl49, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (~ (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 ((((((((('#sk72' @ X2) = (c0))) & 75.01/10.19 (((Y0) = (Y1))))) | 75.01/10.19 (((((Y0) = (c0))) & 75.01/10.19 ((('#sk72' @ X2) = (Y1))))) | 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y6 @ Y7))) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y2 @ 75.01/10.19 Y4 @ Y6) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y3 @ 75.01/10.19 Y5 @ Y7))))))))))))))))))))))) => 75.01/10.19 (X2 @ ('#sk72' @ X2) @ Y0 @ Y1))))))))) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl44])). 75.01/10.19 thf(zip_derived_cl54, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (~ (((!!) @ (^[Y0 : iS]: 75.01/10.19 ((((((((('#sk72' @ X2) = (c0))) & 75.01/10.19 ((('#sk107' @ X2) = (Y0))))) | 75.01/10.19 ((((('#sk107' @ X2) = (c0))) & 75.01/10.19 ((('#sk72' @ X2) = (Y0))))) | 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y1 @ Y2))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y2 @ 75.01/10.19 Y4 @ Y6))))))))))))))))))))))) => 75.01/10.19 (X2 @ ('#sk72' @ X2) @ ('#sk107' @ X2) @ Y0)))))) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl49])). 75.01/10.19 thf(zip_derived_cl57, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (~ ((((((((('#sk72' @ X2) = (c0))) & 75.01/10.19 ((('#sk107' @ X2) = ('#sk160' @ X2))))) | 75.01/10.19 ((((('#sk107' @ X2) = (c0))) & 75.01/10.19 ((('#sk72' @ X2) = ('#sk160' @ X2))))) | 75.01/10.19 (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk160' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5))))))))))))))))))))))) => 75.01/10.19 (X2 @ ('#sk72' @ X2) @ ('#sk107' @ X2) @ ('#sk160' @ X2)))) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl54])). 75.01/10.19 thf(zip_derived_cl60, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ((((((('#sk72' @ X2) = (c0))) & 75.01/10.19 ((('#sk107' @ X2) = ('#sk160' @ X2))))) | 75.01/10.19 ((((('#sk107' @ X2) = (c0))) & 75.01/10.19 ((('#sk72' @ X2) = ('#sk160' @ X2))))) | 75.01/10.19 (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk160' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5))))))))))))))))))))))) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 75.01/10.19 thf(zip_derived_cl67, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ((((('#sk72' @ X2) = (c0))) & ((('#sk107' @ X2) = ('#sk160' @ X2))))) 75.01/10.19 | ((((('#sk107' @ X2) = (c0))) & 75.01/10.19 ((('#sk72' @ X2) = ('#sk160' @ X2))))) 75.01/10.19 | (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk160' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5))))))))))))))))))))) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl60])). 75.01/10.19 thf(zip_derived_cl73, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ((('#sk107' @ X2) = ('#sk160' @ X2))) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk160' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5))))))))))))))))))))) 75.01/10.19 | ((((('#sk107' @ X2) = (c0))) & 75.01/10.19 ((('#sk72' @ X2) = ('#sk160' @ X2))))))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl67])). 75.01/10.19 thf(zip_derived_cl83, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ((('#sk107' @ X2) = ('#sk160' @ X2)) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk160' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5))))))))))))))))))))) 75.01/10.19 | ((((('#sk107' @ X2) = (c0))) & 75.01/10.19 ((('#sk72' @ X2) = ('#sk160' @ X2))))))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], [zip_derived_cl73])). 75.01/10.19 thf(zip_derived_cl84, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (~ ('#form542' @ X2) 75.01/10.19 | ((((('#sk107' @ X2) = (c0))) & 75.01/10.19 ((('#sk72' @ X2) = ('#sk160' @ X2))))))), 75.01/10.19 define([status(thm)])). 75.01/10.19 thf(zip_derived_cl169, plain, 75.01/10.19 (( ('#form542' @ '#sk27') 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ (^[Y4 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk160' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5))))))))))))))))))))) 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))))), 75.01/10.19 inference('renaming', [status(thm)], 75.01/10.19 [zip_derived_cl168, zip_derived_cl84])). 75.01/10.19 thf(zip_derived_cl170, plain, 75.01/10.19 (( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ (^[Y4 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 ( 75.01/10.19 '#sk481' @ 75.01/10.19 '#sk27') @ 75.01/10.19 Y0))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y1 @ Y2))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk160' @ 75.01/10.19 '#sk27') = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 ( 75.01/10.19 '#sk481' @ 75.01/10.19 '#sk27') @ 75.01/10.19 Y1 @ Y3) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4)))))))))))))))))) 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ('#form542' @ '#sk27'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl169])). 75.01/10.19 thf(zip_derived_cl171, plain, 75.01/10.19 (( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 ((((('#sk72' @ 75.01/10.19 '#sk27') = (cP @ 75.01/10.19 ('#sk481' @ 75.01/10.19 '#sk27') @ 75.01/10.19 ('#sk857' @ 75.01/10.19 '#sk27')))) & 75.01/10.19 ((('#sk107' @ 75.01/10.19 '#sk27') = (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ((('#sk160' @ 75.01/10.19 '#sk27') = (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ('#sk27' @ 75.01/10.19 ('#sk481' @ '#sk27') @ 75.01/10.19 Y0 @ Y2) & 75.01/10.19 ('#sk27' @ 75.01/10.19 ('#sk857' @ '#sk27') @ 75.01/10.19 Y1 @ Y3))))))))))))))) 75.01/10.19 | ('#form542' @ '#sk27') 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl170])). 75.01/10.19 thf(zip_derived_cl172, plain, 75.01/10.19 (( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 ((((('#sk72' @ '#sk27') = (cP @ 75.01/10.19 ('#sk481' @ '#sk27') @ 75.01/10.19 ('#sk857' @ '#sk27')))) & 75.01/10.19 ((('#sk107' @ '#sk27') = (cP @ 75.01/10.19 ('#sk974' @ '#sk27') @ Y0))) & 75.01/10.19 ((('#sk160' @ '#sk27') = (cP @ 75.01/10.19 Y1 @ Y2))) & 75.01/10.19 ('#sk27' @ 75.01/10.19 ('#sk481' @ '#sk27') @ 75.01/10.19 ('#sk974' @ '#sk27') @ Y1) & 75.01/10.19 ('#sk27' @ 75.01/10.19 ('#sk857' @ '#sk27') @ Y0 @ Y2)))))))))))) 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ('#form542' @ '#sk27'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl171])). 75.01/10.19 thf(zip_derived_cl173, plain, 75.01/10.19 (( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 ((((('#sk72' @ '#sk27') = (cP @ 75.01/10.19 ('#sk481' @ '#sk27') @ 75.01/10.19 ('#sk857' @ '#sk27')))) & 75.01/10.19 ((('#sk107' @ '#sk27') = (cP @ 75.01/10.19 ('#sk974' @ '#sk27') @ 75.01/10.19 ('#sk1111' @ '#sk27')))) & 75.01/10.19 ((('#sk160' @ '#sk27') = (cP @ Y0 @ Y1))) & 75.01/10.19 ('#sk27' @ ('#sk481' @ '#sk27') @ 75.01/10.19 ('#sk974' @ '#sk27') @ Y0) & 75.01/10.19 ('#sk27' @ ('#sk857' @ '#sk27') @ 75.01/10.19 ('#sk1111' @ '#sk27') @ Y1))))))))) 75.01/10.19 | ('#form542' @ '#sk27') 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl172])). 75.01/10.19 thf(zip_derived_cl174, plain, 75.01/10.19 (( (((??) @ (^[Y0 : iS]: 75.01/10.19 ((((('#sk72' @ '#sk27') = (cP @ ('#sk481' @ '#sk27') @ 75.01/10.19 ('#sk857' @ '#sk27')))) & 75.01/10.19 ((('#sk107' @ '#sk27') = (cP @ ('#sk974' @ '#sk27') @ 75.01/10.19 ('#sk1111' @ '#sk27')))) & 75.01/10.19 ((('#sk160' @ '#sk27') = (cP @ ('#sk1268' @ '#sk27') @ 75.01/10.19 Y0))) & 75.01/10.19 ('#sk27' @ ('#sk481' @ '#sk27') @ 75.01/10.19 ('#sk974' @ '#sk27') @ ('#sk1268' @ '#sk27')) & 75.01/10.19 ('#sk27' @ ('#sk857' @ '#sk27') @ 75.01/10.19 ('#sk1111' @ '#sk27') @ Y0)))))) 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ('#form542' @ '#sk27'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl173])). 75.01/10.19 thf(zip_derived_cl175, plain, 75.01/10.19 (( ((((('#sk72' @ '#sk27') = (cP @ ('#sk481' @ '#sk27') @ 75.01/10.19 ('#sk857' @ '#sk27')))) & 75.01/10.19 ((('#sk107' @ '#sk27') = (cP @ ('#sk974' @ '#sk27') @ 75.01/10.19 ('#sk1111' @ '#sk27')))) & 75.01/10.19 ((('#sk160' @ '#sk27') = (cP @ ('#sk1268' @ '#sk27') @ 75.01/10.19 ('#sk1445' @ '#sk27')))) & 75.01/10.19 ('#sk27' @ ('#sk481' @ '#sk27') @ ('#sk974' @ '#sk27') @ 75.01/10.19 ('#sk1268' @ '#sk27')) & 75.01/10.19 ('#sk27' @ ('#sk857' @ '#sk27') @ ('#sk1111' @ '#sk27') @ 75.01/10.19 ('#sk1445' @ '#sk27')))) 75.01/10.19 | ('#form542' @ '#sk27') 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl174])). 75.01/10.19 thf(zip_derived_cl179, plain, 75.01/10.19 (( ('#sk27' @ ('#sk481' @ '#sk27') @ ('#sk974' @ '#sk27') @ 75.01/10.19 ('#sk1268' @ '#sk27')) 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ('#form542' @ '#sk27'))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl175])). 75.01/10.19 thf(zip_derived_cl176, plain, 75.01/10.19 (( ((('#sk72' @ '#sk27') = (cP @ ('#sk481' @ '#sk27') @ 75.01/10.19 ('#sk857' @ '#sk27')))) 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ('#form542' @ '#sk27'))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl175])). 75.01/10.19 thf(zip_derived_cl181, plain, 75.01/10.19 (((('#sk72' @ '#sk27') 75.01/10.19 = (cP @ ('#sk481' @ '#sk27') @ ('#sk857' @ '#sk27'))) 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ('#form542' @ '#sk27'))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], 75.01/10.19 [zip_derived_cl176])). 75.01/10.19 thf(zip_derived_cl182, plain, 75.01/10.19 ((~ ('#form2426') 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))))), 75.01/10.19 define([status(thm)])). 75.01/10.19 thf(zip_derived_cl190, plain, 75.01/10.19 (( ('#form2426') 75.01/10.19 | ('#form542' @ '#sk27') 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ('#sk27' @ ('#sk481' @ '#sk27') @ ('#sk974' @ '#sk27') @ 75.01/10.19 ('#sk1268' @ '#sk27')))), 75.01/10.19 inference('renaming', [status(thm)], 75.01/10.19 [zip_derived_cl179, zip_derived_cl182])). 75.01/10.19 thf(zip_derived_cl215, plain, 75.01/10.19 (( ((('#sk82' @ '#sk27') = (c0))) | ~ ('#form2610'))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl213])). 75.01/10.19 thf(zip_derived_cl225, plain, 75.01/10.19 (((('#sk82' @ '#sk27') = (c0)) | ~ ('#form2610'))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], 75.01/10.19 [zip_derived_cl215])). 75.01/10.19 thf(zip_derived_cl91, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (~ ('#form658' @ X2) 75.01/10.19 | ((((('#sk128' @ X2) = (c0))) & 75.01/10.19 ((('#sk82' @ X2) = ('#sk192' @ X2))))))), 75.01/10.19 define([status(thm)])). 75.01/10.19 thf(zip_derived_cl93, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ((('#sk82' @ X2) = ('#sk192' @ X2))) | ~ ('#form658' @ X2))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl91])). 75.01/10.19 thf(zip_derived_cl103, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ((('#sk82' @ X2) = ('#sk192' @ X2)) | ~ ('#form658' @ X2))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], [zip_derived_cl93])). 75.01/10.19 thf(zip_derived_cl92, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ((('#sk128' @ X2) = (c0))) | ~ ('#form658' @ X2))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl91])). 75.01/10.19 thf(zip_derived_cl102, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ((('#sk128' @ X2) = (c0)) | ~ ('#form658' @ X2))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], [zip_derived_cl92])). 75.01/10.19 thf(zip_derived_cl63, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (~ (X2 @ ('#sk82' @ X2) @ ('#sk128' @ X2) @ ('#sk192' @ X2)) 75.01/10.19 | (X2 @ '#sk8' @ '#sk14' @ '#sk14'))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 75.01/10.19 thf(zip_derived_cl83, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ((('#sk107' @ X2) = ('#sk160' @ X2)) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk160' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5))))))))))))))))))))) 75.01/10.19 | ((((('#sk107' @ X2) = (c0))) & 75.01/10.19 ((('#sk72' @ X2) = ('#sk160' @ X2))))))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], [zip_derived_cl73])). 75.01/10.19 thf(zip_derived_cl84, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (~ ('#form542' @ X2) 75.01/10.19 | ((((('#sk107' @ X2) = (c0))) & 75.01/10.19 ((('#sk72' @ X2) = ('#sk160' @ X2))))))), 75.01/10.19 define([status(thm)])). 75.01/10.19 thf(zip_derived_cl87, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ('#form542' @ X2) 75.01/10.19 | (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk160' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5))))))))))))))))))))) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (('#sk107' @ X2) = ('#sk160' @ X2)))), 75.01/10.19 inference('renaming', [status(thm)], [zip_derived_cl83, zip_derived_cl84])). 75.01/10.19 thf(zip_derived_cl97, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ (^[Y4 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 ( 75.01/10.19 '#sk481' @ 75.01/10.19 X2) @ Y0))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y1 @ Y2))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk160' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 ( 75.01/10.19 '#sk481' @ 75.01/10.19 X2) @ 75.01/10.19 Y1 @ Y3) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4)))))))))))))))))) 75.01/10.19 | (('#sk107' @ X2) = ('#sk160' @ X2)) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ('#form542' @ X2))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl87])). 75.01/10.19 thf(zip_derived_cl106, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 ((((('#sk72' @ X2) = 75.01/10.19 (cP @ 75.01/10.19 ('#sk481' @ X2) @ 75.01/10.19 ('#sk857' @ X2)))) & 75.01/10.19 ((('#sk107' @ 75.01/10.19 X2) = (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ((('#sk160' @ 75.01/10.19 X2) = (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 (X2 @ 75.01/10.19 ('#sk481' @ X2) @ 75.01/10.19 Y0 @ Y2) & 75.01/10.19 (X2 @ 75.01/10.19 ('#sk857' @ X2) @ 75.01/10.19 Y1 @ Y3))))))))))))))) 75.01/10.19 | ('#form542' @ X2) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (('#sk107' @ X2) = ('#sk160' @ X2)))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl97])). 75.01/10.19 thf(zip_derived_cl111, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 ((((('#sk72' @ X2) = (cP @ 75.01/10.19 ('#sk481' @ X2) @ 75.01/10.19 ('#sk857' @ X2)))) & 75.01/10.19 ((('#sk107' @ X2) = (cP @ 75.01/10.19 ('#sk974' @ X2) @ Y0))) & 75.01/10.19 ((('#sk160' @ X2) = (cP @ 75.01/10.19 Y1 @ Y2))) & 75.01/10.19 (X2 @ ('#sk481' @ X2) @ 75.01/10.19 ('#sk974' @ X2) @ Y1) & 75.01/10.19 (X2 @ ('#sk857' @ X2) @ Y0 @ 75.01/10.19 Y2)))))))))))) 75.01/10.19 | (('#sk107' @ X2) = ('#sk160' @ X2)) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ('#form542' @ X2))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl106])). 75.01/10.19 thf(zip_derived_cl116, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 ((((('#sk72' @ X2) = (cP @ 75.01/10.19 ('#sk481' @ X2) @ ('#sk857' @ X2)))) & 75.01/10.19 ((('#sk107' @ X2) = (cP @ 75.01/10.19 ('#sk974' @ X2) @ ('#sk1111' @ X2)))) & 75.01/10.19 ((('#sk160' @ X2) = (cP @ Y0 @ Y1))) & 75.01/10.19 (X2 @ ('#sk481' @ X2) @ ('#sk974' @ X2) @ 75.01/10.19 Y0) & 75.01/10.19 (X2 @ ('#sk857' @ X2) @ 75.01/10.19 ('#sk1111' @ X2) @ Y1))))))))) 75.01/10.19 | ('#form542' @ X2) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (('#sk107' @ X2) = ('#sk160' @ X2)))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl111])). 75.01/10.19 thf(zip_derived_cl121, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (((??) @ (^[Y0 : iS]: 75.01/10.19 ((((('#sk72' @ X2) = (cP @ ('#sk481' @ X2) @ 75.01/10.19 ('#sk857' @ X2)))) & 75.01/10.19 ((('#sk107' @ X2) = (cP @ ('#sk974' @ X2) @ 75.01/10.19 ('#sk1111' @ X2)))) & 75.01/10.19 ((('#sk160' @ X2) = (cP @ ('#sk1268' @ X2) @ Y0))) & 75.01/10.19 (X2 @ ('#sk481' @ X2) @ ('#sk974' @ X2) @ 75.01/10.19 ('#sk1268' @ X2)) & 75.01/10.19 (X2 @ ('#sk857' @ X2) @ ('#sk1111' @ X2) @ Y0)))))) 75.01/10.19 | (('#sk107' @ X2) = ('#sk160' @ X2)) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ('#form542' @ X2))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl116])). 75.01/10.19 thf(zip_derived_cl127, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ((((('#sk72' @ X2) = (cP @ ('#sk481' @ X2) @ ('#sk857' @ X2)))) & 75.01/10.19 ((('#sk107' @ X2) = (cP @ ('#sk974' @ X2) @ ('#sk1111' @ X2)))) & 75.01/10.19 ((('#sk160' @ X2) = (cP @ ('#sk1268' @ X2) @ ('#sk1445' @ X2)))) & 75.01/10.19 (X2 @ ('#sk481' @ X2) @ ('#sk974' @ X2) @ ('#sk1268' @ X2)) & 75.01/10.19 (X2 @ ('#sk857' @ X2) @ ('#sk1111' @ X2) @ ('#sk1445' @ X2)))) 75.01/10.19 | ('#form542' @ X2) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (('#sk107' @ X2) = ('#sk160' @ X2)))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl121])). 75.01/10.19 thf(zip_derived_cl136, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ((('#sk107' @ X2) = (cP @ ('#sk974' @ X2) @ ('#sk1111' @ X2)))) 75.01/10.19 | (('#sk107' @ X2) = ('#sk160' @ X2)) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ('#form542' @ X2))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl127])). 75.01/10.19 thf(zip_derived_cl154, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ((('#sk107' @ X2) = (cP @ ('#sk974' @ X2) @ ('#sk1111' @ X2))) 75.01/10.19 | (('#sk107' @ X2) = ('#sk160' @ X2)) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ('#form542' @ X2))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], 75.01/10.19 [zip_derived_cl136])). 75.01/10.19 thf(zip_derived_cl72, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ((('#sk72' @ X2) = (c0))) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk160' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5))))))))))))))))))))) 75.01/10.19 | ((((('#sk107' @ X2) = (c0))) & 75.01/10.19 ((('#sk72' @ X2) = ('#sk160' @ X2))))))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl67])). 75.01/10.19 thf(zip_derived_cl81, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ((('#sk72' @ X2) = (c0)) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk160' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5))))))))))))))))))))) 75.01/10.19 | ((((('#sk107' @ X2) = (c0))) & 75.01/10.19 ((('#sk72' @ X2) = ('#sk160' @ X2))))))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], [zip_derived_cl72])). 75.01/10.19 thf(zip_derived_cl82, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ (^[Y4 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk72' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 ( 75.01/10.19 '#sk481' @ 75.01/10.19 X2) @ Y0))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk107' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y1 @ Y2))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ('#sk160' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 ( 75.01/10.19 '#sk481' @ 75.01/10.19 X2) @ 75.01/10.19 Y1 @ Y3) & 75.01/10.19 ( 75.01/10.19 X2 @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4)))))))))))))))))) 75.01/10.19 | ((((('#sk107' @ X2) = (c0))) & 75.01/10.19 ((('#sk72' @ X2) = ('#sk160' @ X2))))) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (('#sk72' @ X2) = (c0)))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl81])). 75.01/10.19 thf(zip_derived_cl84, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (~ ('#form542' @ X2) 75.01/10.19 | ((((('#sk107' @ X2) = (c0))) & 75.01/10.19 ((('#sk72' @ X2) = ('#sk160' @ X2))))))), 75.01/10.19 define([status(thm)])). 75.01/10.19 thf(zip_derived_cl96, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ('#form542' @ X2) 75.01/10.19 | (('#sk72' @ X2) = (c0)) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 ((((('#sk72' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 ('#sk481' @ 75.01/10.19 X2) @ 75.01/10.19 Y0))) & 75.01/10.19 ((('#sk107' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y1 @ Y2))) & 75.01/10.19 ((('#sk160' @ 75.01/10.19 X2) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 (X2 @ 75.01/10.19 ('#sk481' @ 75.01/10.19 X2) @ 75.01/10.19 Y1 @ Y3) & 75.01/10.19 (X2 @ Y0 @ 75.01/10.19 Y2 @ Y4)))))))))))))))))))), 75.01/10.19 inference('renaming', [status(thm)], [zip_derived_cl82, zip_derived_cl84])). 75.01/10.19 thf(zip_derived_cl105, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 ((((('#sk72' @ X2) = 75.01/10.19 (cP @ 75.01/10.19 ('#sk481' @ X2) @ 75.01/10.19 ('#sk857' @ X2)))) & 75.01/10.19 ((('#sk107' @ 75.01/10.19 X2) = (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ((('#sk160' @ 75.01/10.19 X2) = (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 (X2 @ 75.01/10.19 ('#sk481' @ X2) @ 75.01/10.19 Y0 @ Y2) & 75.01/10.19 (X2 @ 75.01/10.19 ('#sk857' @ X2) @ 75.01/10.19 Y1 @ Y3))))))))))))))) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (('#sk72' @ X2) = (c0)) 75.01/10.19 | ('#form542' @ X2))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 75.01/10.19 thf(zip_derived_cl110, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 ((((('#sk72' @ X2) = (cP @ 75.01/10.19 ('#sk481' @ X2) @ 75.01/10.19 ('#sk857' @ X2)))) & 75.01/10.19 ((('#sk107' @ X2) = (cP @ 75.01/10.19 ('#sk974' @ X2) @ Y0))) & 75.01/10.19 ((('#sk160' @ X2) = (cP @ 75.01/10.19 Y1 @ Y2))) & 75.01/10.19 (X2 @ ('#sk481' @ X2) @ 75.01/10.19 ('#sk974' @ X2) @ Y1) & 75.01/10.19 (X2 @ ('#sk857' @ X2) @ Y0 @ 75.01/10.19 Y2)))))))))))) 75.01/10.19 | ('#form542' @ X2) 75.01/10.19 | (('#sk72' @ X2) = (c0)) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl105])). 75.01/10.19 thf(zip_derived_cl115, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 ((((('#sk72' @ X2) = (cP @ 75.01/10.19 ('#sk481' @ X2) @ ('#sk857' @ X2)))) & 75.01/10.19 ((('#sk107' @ X2) = (cP @ 75.01/10.19 ('#sk974' @ X2) @ ('#sk1111' @ X2)))) & 75.01/10.19 ((('#sk160' @ X2) = (cP @ Y0 @ Y1))) & 75.01/10.19 (X2 @ ('#sk481' @ X2) @ ('#sk974' @ X2) @ 75.01/10.19 Y0) & 75.01/10.19 (X2 @ ('#sk857' @ X2) @ 75.01/10.19 ('#sk1111' @ X2) @ Y1))))))))) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (('#sk72' @ X2) = (c0)) 75.01/10.19 | ('#form542' @ X2))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl110])). 75.01/10.19 thf(zip_derived_cl120, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (((??) @ (^[Y0 : iS]: 75.01/10.19 ((((('#sk72' @ X2) = (cP @ ('#sk481' @ X2) @ 75.01/10.19 ('#sk857' @ X2)))) & 75.01/10.19 ((('#sk107' @ X2) = (cP @ ('#sk974' @ X2) @ 75.01/10.19 ('#sk1111' @ X2)))) & 75.01/10.19 ((('#sk160' @ X2) = (cP @ ('#sk1268' @ X2) @ Y0))) & 75.01/10.19 (X2 @ ('#sk481' @ X2) @ ('#sk974' @ X2) @ 75.01/10.19 ('#sk1268' @ X2)) & 75.01/10.19 (X2 @ ('#sk857' @ X2) @ ('#sk1111' @ X2) @ Y0)))))) 75.01/10.19 | ('#form542' @ X2) 75.01/10.19 | (('#sk72' @ X2) = (c0)) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl115])). 75.01/10.19 thf(zip_derived_cl126, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ((((('#sk72' @ X2) = (cP @ ('#sk481' @ X2) @ ('#sk857' @ X2)))) & 75.01/10.19 ((('#sk107' @ X2) = (cP @ ('#sk974' @ X2) @ ('#sk1111' @ X2)))) & 75.01/10.19 ((('#sk160' @ X2) = (cP @ ('#sk1268' @ X2) @ ('#sk1445' @ X2)))) & 75.01/10.19 (X2 @ ('#sk481' @ X2) @ ('#sk974' @ X2) @ ('#sk1268' @ X2)) & 75.01/10.19 (X2 @ ('#sk857' @ X2) @ ('#sk1111' @ X2) @ ('#sk1445' @ X2)))) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (('#sk72' @ X2) = (c0)) 75.01/10.19 | ('#form542' @ X2))), 75.01/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl120])). 75.01/10.19 thf(zip_derived_cl134, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( (X2 @ ('#sk857' @ X2) @ ('#sk1111' @ X2) @ ('#sk1445' @ X2)) 75.01/10.19 | ('#form542' @ X2) 75.01/10.19 | (('#sk72' @ X2) = (c0)) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl126])). 75.01/10.19 thf(zip_derived_cl132, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ((('#sk160' @ X2) = (cP @ ('#sk1268' @ X2) @ ('#sk1445' @ X2)))) 75.01/10.19 | ('#form542' @ X2) 75.01/10.19 | (('#sk72' @ X2) = (c0)) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl126])). 75.01/10.19 thf(zip_derived_cl152, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ((('#sk160' @ X2) = (cP @ ('#sk1268' @ X2) @ ('#sk1445' @ X2))) 75.01/10.19 | ('#form542' @ X2) 75.01/10.19 | (('#sk72' @ X2) = (c0)) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], 75.01/10.19 [zip_derived_cl132])). 75.01/10.19 thf(zip_derived_cl1, plain, 75.01/10.19 ( (((((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((!!) @ (^[Y3 : iS]: 75.01/10.19 (((((cP @ Y0 @ Y2) = 75.01/10.19 (cP @ Y1 @ Y3))) => 75.01/10.19 (((((Y2) = (Y3))) & 75.01/10.19 (((Y0) = (Y1))))))))))))))))))) & 75.01/10.19 (((!!) @ (^[Y0 : iS > $o]: 75.01/10.19 (((((Y0 @ c0) & 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((((Y0 @ Y1) & (Y0 @ Y2))) => 75.01/10.19 (Y0 @ (cP @ Y1 @ Y2)))))))))))) => 75.01/10.19 (((!!) @ (^[Y1 : iS]: (Y0 @ Y1))))))))) & 75.01/10.19 (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: (((cP @ Y0 @ Y1) != (c0)))))))))))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 75.01/10.19 thf(zip_derived_cl3, plain, 75.01/10.19 ( (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((!!) @ (^[Y3 : iS]: 75.01/10.19 (((((cP @ Y0 @ Y2) = 75.01/10.19 (cP @ Y1 @ Y3))) => 75.01/10.19 (((((Y2) = (Y3))) & 75.01/10.19 (((Y0) = (Y1)))))))))))))))))))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1])). 75.01/10.19 thf(zip_derived_cl7, plain, 75.01/10.19 (![X2 : iS]: 75.01/10.19 (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((((cP @ X2 @ Y1) = (cP @ Y0 @ 75.01/10.19 Y2))) => 75.01/10.19 (((((Y1) = (Y2))) & 75.01/10.19 (((X2) = (Y0))))))))))))))))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 75.01/10.19 thf(zip_derived_cl11, plain, 75.01/10.19 (![X2 : iS, X4 : iS]: 75.01/10.19 (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((((cP @ X2 @ Y0) = (cP @ X4 @ Y1))) => 75.01/10.19 (((((Y0) = (Y1))) & (((X2) = (X4)))))))))))))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 75.01/10.19 thf(zip_derived_cl15, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS]: 75.01/10.19 (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((((cP @ X2 @ X6) = (cP @ X4 @ Y0))) => 75.01/10.19 (((((X6) = (Y0))) & (((X2) = (X4))))))))))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl11])). 75.01/10.19 thf(zip_derived_cl19, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS]: 75.01/10.19 (((((cP @ X2 @ X6) = (cP @ X4 @ X8))) => 75.01/10.19 (((((X6) = (X8))) & (((X2) = (X4)))))))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 75.01/10.19 thf(zip_derived_cl23, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS]: 75.01/10.19 (~ (((cP @ X2 @ X6) = (cP @ X4 @ X8))) 75.01/10.19 | (((((X6) = (X8))) & (((X2) = (X4))))))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 75.01/10.19 thf(zip_derived_cl28, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS]: 75.01/10.19 (((cP @ X2 @ X6) != (cP @ X4 @ X8)) 75.01/10.19 | (((((X6) = (X8))) & (((X2) = (X4))))))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], [zip_derived_cl23])). 75.01/10.19 thf(zip_derived_cl30, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS]: 75.01/10.19 ( (((X2) = (X4))) | ((cP @ X2 @ X6) != (cP @ X4 @ X8)))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl28])). 75.01/10.19 thf(zip_derived_cl40, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS]: 75.01/10.19 (((X2) = (X4)) | ((cP @ X2 @ X6) != (cP @ X4 @ X8)))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], [zip_derived_cl30])). 75.01/10.19 thf(zip_derived_cl37, plain, 75.01/10.19 ( (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((!!) @ (^[Y2 : iS]: 75.01/10.19 (((((((((Y0) = (c0))) & 75.01/10.19 (((Y1) = (Y2))))) | 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ (^[Y4 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y8 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y3 @ 75.01/10.19 Y5 @ Y7) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y4 @ 75.01/10.19 Y6 @ Y8) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y2) = 75.01/10.19 (cP @ 75.01/10.19 Y7 @ Y8))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))))))))))))))))))))))) | 75.01/10.19 (((((Y0) = (Y2))) & 75.01/10.19 (((Y1) = (c0))))))) => 75.01/10.19 ('#sk27' @ Y0 @ Y1 @ Y2))))))))))))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])). 75.01/10.19 thf(zip_derived_cl46, plain, 75.01/10.19 (![X2 : iS]: 75.01/10.19 (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: 75.01/10.19 (((((((((X2) = (c0))) & (((Y0) = (Y1))))) | 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y7 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (X2) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y2 @ 75.01/10.19 Y4 @ Y6) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y3 @ 75.01/10.19 Y5 @ Y7) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y1) = 75.01/10.19 (cP @ 75.01/10.19 Y6 @ Y7))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))))))))))))))))))))))) | 75.01/10.19 (((((X2) = (Y1))) & (((Y0) = (c0))))))) => 75.01/10.19 ('#sk27' @ X2 @ Y0 @ Y1)))))))))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 75.01/10.19 thf(zip_derived_cl51, plain, 75.01/10.19 (![X2 : iS, X4 : iS]: 75.01/10.19 (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((((((((X2) = (c0))) & (((X4) = (Y0))))) | 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y6 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (X2) = 75.01/10.19 (cP @ 75.01/10.19 Y1 @ Y2))) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y2 @ 75.01/10.19 Y4 @ Y6) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (Y0) = 75.01/10.19 (cP @ 75.01/10.19 Y5 @ Y6))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (X4) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))))))))))))))))))))))) | 75.01/10.19 (((((X2) = (Y0))) & (((X4) = (c0))))))) => 75.01/10.19 ('#sk27' @ X2 @ X4 @ Y0))))))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl46])). 75.01/10.19 thf(zip_derived_cl56, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS]: 75.01/10.19 (((((((((X2) = (c0))) & (((X4) = (X6))))) | 75.01/10.19 (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (X6) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (X4) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))))))))))))))))))))))) | 75.01/10.19 (((((X2) = (X6))) & (((X4) = (c0))))))) => 75.01/10.19 ('#sk27' @ X2 @ X4 @ X6)))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl51])). 75.01/10.19 thf(zip_derived_cl59, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS]: 75.01/10.19 (~ (((((((X2) = (c0))) & (((X4) = (X6))))) | 75.01/10.19 (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y4 : iS]: 75.01/10.19 (((??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (X6) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (X4) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))))))))))))))))))))))) | 75.01/10.19 (((((X2) = (X6))) & (((X4) = (c0))))))) 75.01/10.19 | ('#sk27' @ X2 @ X4 @ X6))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl56])). 75.01/10.19 thf(zip_derived_cl66, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS]: 75.01/10.19 (~ (((((X2) = (X6))) & (((X4) = (c0))))) | ('#sk27' @ X2 @ X4 @ X6))), 75.01/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl59])). 75.01/10.19 thf(zip_derived_cl71, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS]: 75.01/10.19 (~ (((X2) = (X6))) | ~ (((X4) = (c0))) | ('#sk27' @ X2 @ X4 @ X6))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl66])). 75.01/10.19 thf(zip_derived_cl79, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS]: 75.01/10.19 (((X2) != (X6)) | ((X4) != (c0)) | ('#sk27' @ X2 @ X4 @ X6))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], [zip_derived_cl71])). 75.01/10.19 thf(zip_derived_cl80, plain, (![X6 : iS]: ('#sk27' @ X6 @ c0 @ X6)), 75.01/10.19 inference('simplify', [status(thm)], [zip_derived_cl79])). 75.01/10.19 thf(zip_derived_cl178, plain, 75.01/10.19 (( ((('#sk160' @ '#sk27') = (cP @ ('#sk1268' @ '#sk27') @ 75.01/10.19 ('#sk1445' @ '#sk27')))) 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ('#form542' @ '#sk27'))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl175])). 75.01/10.19 thf(zip_derived_cl188, plain, 75.01/10.19 (((('#sk160' @ '#sk27') 75.01/10.19 = (cP @ ('#sk1268' @ '#sk27') @ ('#sk1445' @ '#sk27'))) 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ('#form542' @ '#sk27'))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], 75.01/10.19 [zip_derived_cl178])). 75.01/10.19 thf(zip_derived_cl182, plain, 75.01/10.19 ((~ ('#form2426') 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))))), 75.01/10.19 define([status(thm)])). 75.01/10.19 thf(zip_derived_cl189, plain, 75.01/10.19 (( ('#form2426') 75.01/10.19 | ('#form542' @ '#sk27') 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (('#sk160' @ '#sk27') 75.01/10.19 = (cP @ ('#sk1268' @ '#sk27') @ ('#sk1445' @ '#sk27'))))), 75.01/10.19 inference('renaming', [status(thm)], 75.01/10.19 [zip_derived_cl188, zip_derived_cl182])). 75.01/10.19 thf(zip_derived_cl177, plain, 75.01/10.19 (( ((('#sk107' @ '#sk27') = (cP @ ('#sk974' @ '#sk27') @ 75.01/10.19 ('#sk1111' @ '#sk27')))) 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ('#form542' @ '#sk27'))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl175])). 75.01/10.19 thf(zip_derived_cl186, plain, 75.01/10.19 (((('#sk107' @ '#sk27') 75.01/10.19 = (cP @ ('#sk974' @ '#sk27') @ ('#sk1111' @ '#sk27'))) 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ('#form542' @ '#sk27'))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], 75.01/10.19 [zip_derived_cl177])). 75.01/10.19 thf(zip_derived_cl182, plain, 75.01/10.19 ((~ ('#form2426') 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))))), 75.01/10.19 define([status(thm)])). 75.01/10.19 thf(zip_derived_cl187, plain, 75.01/10.19 (( ('#form2426') 75.01/10.19 | ('#form542' @ '#sk27') 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (('#sk107' @ '#sk27') 75.01/10.19 = (cP @ ('#sk974' @ '#sk27') @ ('#sk1111' @ '#sk27'))))), 75.01/10.19 inference('renaming', [status(thm)], 75.01/10.19 [zip_derived_cl186, zip_derived_cl182])). 75.01/10.19 thf(zip_derived_cl29, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS]: 75.01/10.19 ( (((X6) = (X8))) | ((cP @ X2 @ X6) != (cP @ X4 @ X8)))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl28])). 75.01/10.19 thf(zip_derived_cl39, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS]: 75.01/10.19 (((X6) = (X8)) | ((cP @ X2 @ X6) != (cP @ X4 @ X8)))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], [zip_derived_cl29])). 75.01/10.19 thf(zip_derived_cl65, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS]: 75.01/10.19 (~ (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ (^[Y4 : iS]: 75.01/10.19 (( 75.01/10.19 (??) @ ( 75.01/10.19 ^[Y5 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (X2) = 75.01/10.19 (cP @ 75.01/10.19 Y0 @ Y1))) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y1 @ 75.01/10.19 Y3 @ Y5) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (X6) = 75.01/10.19 (cP @ 75.01/10.19 Y4 @ Y5))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (X4) = 75.01/10.19 (cP @ 75.01/10.19 Y2 @ Y3))))))))))))))))))))))) 75.01/10.19 | ('#sk27' @ X2 @ X4 @ X6))), 75.01/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl59])). 75.01/10.19 thf(zip_derived_cl70, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS]: 75.01/10.19 (~ (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((??) @ (^[Y4 : iS]: 75.01/10.19 (( 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (X2) = 75.01/10.19 (cP @ 75.01/10.19 X8 @ Y0))) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 X8 @ 75.01/10.19 Y1 @ Y3) & 75.01/10.19 ( 75.01/10.19 '#sk27' @ 75.01/10.19 Y0 @ 75.01/10.19 Y2 @ Y4) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (X6) = 75.01/10.19 (cP @ 75.01/10.19 Y3 @ Y4))) & 75.01/10.19 ( 75.01/10.19 ( 75.01/10.19 (X4) = 75.01/10.19 (cP @ 75.01/10.19 Y1 @ Y2)))))))))))))))))))) 75.01/10.19 | ('#sk27' @ X2 @ X4 @ X6))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl65])). 75.01/10.19 thf(zip_derived_cl78, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS, X10 : iS]: 75.01/10.19 (~ (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((??) @ (^[Y3 : iS]: 75.01/10.19 (((((X2) = (cP @ 75.01/10.19 X8 @ X10))) & 75.01/10.19 ('#sk27' @ X8 @ 75.01/10.19 Y0 @ Y2) & 75.01/10.19 ('#sk27' @ X10 @ 75.01/10.19 Y1 @ Y3) & 75.01/10.19 (((X6) = (cP @ 75.01/10.19 Y2 @ Y3))) & 75.01/10.19 (((X4) = (cP @ 75.01/10.19 Y0 @ Y1))))))))))))))))) 75.01/10.19 | ('#sk27' @ X2 @ X4 @ X6))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl70])). 75.01/10.19 thf(zip_derived_cl95, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS, X10 : iS, X12 : iS]: 75.01/10.19 (~ (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((??) @ (^[Y2 : iS]: 75.01/10.19 (((((X2) = (cP @ X8 @ X10))) & 75.01/10.19 ('#sk27' @ X8 @ X12 @ Y1) & 75.01/10.19 ('#sk27' @ X10 @ Y0 @ Y2) & 75.01/10.19 (((X6) = (cP @ Y1 @ Y2))) & 75.01/10.19 (((X4) = (cP @ X12 @ Y0)))))))))))))) 75.01/10.19 | ('#sk27' @ X2 @ X4 @ X6))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl78])). 75.01/10.19 thf(zip_derived_cl104, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS, X10 : iS, X12 : iS, X14 : iS]: 75.01/10.19 (~ (((??) @ (^[Y0 : iS]: 75.01/10.19 (((??) @ (^[Y1 : iS]: 75.01/10.19 (((((X2) = (cP @ X8 @ X10))) & 75.01/10.19 ('#sk27' @ X8 @ X12 @ Y0) & 75.01/10.19 ('#sk27' @ X10 @ X14 @ Y1) & 75.01/10.19 (((X6) = (cP @ Y0 @ Y1))) & 75.01/10.19 (((X4) = (cP @ X12 @ X14))))))))))) 75.01/10.19 | ('#sk27' @ X2 @ X4 @ X6))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl95])). 75.01/10.19 thf(zip_derived_cl109, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS, X10 : iS, X12 : iS, X14 : iS, 75.01/10.19 X16 : iS]: 75.01/10.19 (~ (((??) @ (^[Y0 : iS]: 75.01/10.19 (((((X2) = (cP @ X8 @ X10))) & 75.01/10.19 ('#sk27' @ X8 @ X12 @ X16) & 75.01/10.19 ('#sk27' @ X10 @ X14 @ Y0) & 75.01/10.19 (((X6) = (cP @ X16 @ Y0))) & 75.01/10.19 (((X4) = (cP @ X12 @ X14)))))))) 75.01/10.19 | ('#sk27' @ X2 @ X4 @ X6))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl104])). 75.01/10.19 thf(zip_derived_cl114, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS, X10 : iS, X12 : iS, X14 : iS, 75.01/10.19 X16 : iS, X18 : iS]: 75.01/10.19 (~ (((((X2) = (cP @ X8 @ X10))) & ('#sk27' @ X8 @ X12 @ X16) & 75.01/10.19 ('#sk27' @ X10 @ X14 @ X18) & (((X6) = (cP @ X16 @ X18))) & 75.01/10.19 (((X4) = (cP @ X12 @ X14))))) 75.01/10.19 | ('#sk27' @ X2 @ X4 @ X6))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl109])). 75.01/10.19 thf(zip_derived_cl119, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS, X10 : iS, X12 : iS, X14 : iS, 75.01/10.19 X16 : iS, X18 : iS]: 75.01/10.19 (~ (((X2) = (cP @ X8 @ X10))) 75.01/10.19 | ~ ('#sk27' @ X8 @ X12 @ X16) 75.01/10.19 | ~ ('#sk27' @ X10 @ X14 @ X18) 75.01/10.19 | ~ (((X6) = (cP @ X16 @ X18))) 75.01/10.19 | ~ (((X4) = (cP @ X12 @ X14))) 75.01/10.19 | ('#sk27' @ X2 @ X4 @ X6))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl114])). 75.01/10.19 thf(zip_derived_cl124, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS, X8 : iS, X10 : iS, X12 : iS, X14 : iS, 75.01/10.19 X16 : iS, X18 : iS]: 75.01/10.19 (((X2) != (cP @ X8 @ X10)) 75.01/10.19 | ~ ('#sk27' @ X8 @ X12 @ X16) 75.01/10.19 | ~ ('#sk27' @ X10 @ X14 @ X18) 75.01/10.19 | ((X6) != (cP @ X16 @ X18)) 75.01/10.19 | ((X4) != (cP @ X12 @ X14)) 75.01/10.19 | ('#sk27' @ X2 @ X4 @ X6))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], 75.01/10.19 [zip_derived_cl119])). 75.01/10.19 thf(zip_derived_cl125, plain, 75.01/10.19 (![X8 : iS, X10 : iS, X12 : iS, X14 : iS, X16 : iS, X18 : iS]: 75.01/10.19 ( ('#sk27' @ (cP @ X8 @ X10) @ (cP @ X12 @ X14) @ (cP @ X16 @ X18)) 75.01/10.19 | ~ ('#sk27' @ X10 @ X14 @ X18) 75.01/10.19 | ~ ('#sk27' @ X8 @ X12 @ X16))), 75.01/10.19 inference('simplify', [status(thm)], [zip_derived_cl124])). 75.01/10.19 thf(zip_derived_cl84, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (~ ('#form542' @ X2) 75.01/10.19 | ((((('#sk107' @ X2) = (c0))) & 75.01/10.19 ((('#sk72' @ X2) = ('#sk160' @ X2))))))), 75.01/10.19 define([status(thm)])). 75.01/10.19 thf(zip_derived_cl86, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ((('#sk72' @ X2) = ('#sk160' @ X2))) | ~ ('#form542' @ X2))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl84])). 75.01/10.19 thf(zip_derived_cl99, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ((('#sk72' @ X2) = ('#sk160' @ X2)) | ~ ('#form542' @ X2))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], [zip_derived_cl86])). 75.01/10.19 thf(zip_derived_cl181, plain, 75.01/10.19 (((('#sk72' @ '#sk27') 75.01/10.19 = (cP @ ('#sk481' @ '#sk27') @ ('#sk857' @ '#sk27'))) 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))) 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | ('#form542' @ '#sk27'))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], 75.01/10.19 [zip_derived_cl176])). 75.01/10.19 thf(zip_derived_cl182, plain, 75.01/10.19 ((~ ('#form2426') 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))))), 75.01/10.19 define([status(thm)])). 75.01/10.19 thf(zip_derived_cl185, plain, 75.01/10.19 (( ('#form2426') 75.01/10.19 | ('#form542' @ '#sk27') 75.01/10.19 | ('#sk27' @ '#sk1' @ '#sk2' @ '#sk2') 75.01/10.19 | (('#sk72' @ '#sk27') 75.01/10.19 = (cP @ ('#sk481' @ '#sk27') @ ('#sk857' @ '#sk27'))))), 75.01/10.19 inference('renaming', [status(thm)], 75.01/10.19 [zip_derived_cl181, zip_derived_cl182])). 75.01/10.19 thf(zip_derived_cl64, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS]: 75.01/10.19 (~ (((((X2) = (c0))) & (((X4) = (X6))))) | ('#sk27' @ X2 @ X4 @ X6))), 75.01/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl59])). 75.01/10.19 thf(zip_derived_cl69, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS]: 75.01/10.19 (~ (((X2) = (c0))) | ~ (((X4) = (X6))) | ('#sk27' @ X2 @ X4 @ X6))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl64])). 75.01/10.19 thf(zip_derived_cl76, plain, 75.01/10.19 (![X2 : iS, X4 : iS, X6 : iS]: 75.01/10.19 (((X2) != (c0)) | ((X4) != (X6)) | ('#sk27' @ X2 @ X4 @ X6))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], [zip_derived_cl69])). 75.01/10.19 thf(zip_derived_cl77, plain, (![X6 : iS]: ('#sk27' @ c0 @ X6 @ X6)), 75.01/10.19 inference('simplify', [status(thm)], [zip_derived_cl76])). 75.01/10.19 thf(zip_derived_cl182, plain, 75.01/10.19 ((~ ('#form2426') 75.01/10.19 | ((((('#sk72' @ '#sk27') = (c0))) & 75.01/10.19 ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))))))), 75.01/10.19 define([status(thm)])). 75.01/10.19 thf(zip_derived_cl184, plain, 75.01/10.19 (( ((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27'))) | ~ ('#form2426'))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl182])). 75.01/10.19 thf(zip_derived_cl193, plain, 75.01/10.19 (((('#sk107' @ '#sk27') = ('#sk160' @ '#sk27')) | ~ ('#form2426'))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], 75.01/10.19 [zip_derived_cl184])). 75.01/10.19 thf(zip_derived_cl5, plain, 75.01/10.19 ( (((!!) @ (^[Y0 : iS]: 75.01/10.19 (((!!) @ (^[Y1 : iS]: (((cP @ Y0 @ Y1) != (c0)))))))))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1])). 75.01/10.19 thf(zip_derived_cl9, plain, 75.01/10.19 (![X2 : iS]: (((!!) @ (^[Y0 : iS]: (((cP @ X2 @ Y0) != (c0))))))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 75.01/10.19 thf(zip_derived_cl13, plain, 75.01/10.19 (![X2 : iS, X4 : iS]: (((cP @ X2 @ X4) != (c0)))), 75.01/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])). 75.01/10.19 thf(zip_derived_cl17, plain, (![X2 : iS, X4 : iS]: ((cP @ X2 @ X4) != (c0))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], [zip_derived_cl13])). 75.01/10.19 thf(zip_derived_cl85, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ( ((('#sk107' @ X2) = (c0))) | ~ ('#form542' @ X2))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl84])). 75.01/10.19 thf(zip_derived_cl98, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 ((('#sk107' @ X2) = (c0)) | ~ ('#form542' @ X2))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], [zip_derived_cl85])). 75.01/10.19 thf(zip_derived_cl183, plain, 75.01/10.19 (( ((('#sk72' @ '#sk27') = (c0))) | ~ ('#form2426'))), 75.01/10.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl182])). 75.01/10.19 thf(zip_derived_cl192, plain, 75.01/10.19 (((('#sk72' @ '#sk27') = (c0)) | ~ ('#form2426'))), 75.01/10.19 inference('simplify nested equalities', [status(thm)], 75.01/10.19 [zip_derived_cl183])). 75.01/10.19 thf(zip_derived_cl61, plain, 75.01/10.19 (![X2 : iS > iS > iS > $o]: 75.01/10.19 (~ (X2 @ ('#sk72' @ X2) @ ('#sk107' @ X2) @ ('#sk160' @ X2)) 75.01/10.19 | (X2 @ '#sk1' @ '#sk2' @ '#sk2'))), 75.01/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 75.01/10.19 thf(zip_derived_cl7153, plain, ($false), 75.01/10.19 inference('eprover', [status(thm)], 75.01/10.19 [zip_derived_cl221, zip_derived_cl217, zip_derived_cl145, 75.01/10.19 zip_derived_cl219, zip_derived_cl223, zip_derived_cl224, 75.01/10.20 zip_derived_cl38, zip_derived_cl190, zip_derived_cl225, 75.01/10.20 zip_derived_cl103, zip_derived_cl102, zip_derived_cl63, 75.01/10.20 zip_derived_cl154, zip_derived_cl134, zip_derived_cl152, 75.01/10.20 zip_derived_cl40, zip_derived_cl80, zip_derived_cl189, 75.01/10.20 zip_derived_cl187, zip_derived_cl39, zip_derived_cl125, 75.01/10.20 zip_derived_cl99, zip_derived_cl185, zip_derived_cl77, 75.01/10.20 zip_derived_cl193, zip_derived_cl17, zip_derived_cl98, 75.01/10.20 zip_derived_cl192, zip_derived_cl61])). 75.01/10.20 75.01/10.20 % SZS output end Refutation 75.01/10.20 75.01/10.20 75.01/10.20 % Terminating... 75.01/10.27 % Runner terminated. 75.01/10.28 % Zipperpin 1.5 exiting 75.01/10.28 EOF