0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.aE6jNER26W true 0.13/0.34 % Computer : n010.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1920 0.13/0.34 % WCLimit : 240 0.13/0.34 % DateTime : Wed Jul 30 07:27:19 EDT 2025 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 1920 s 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.55/0.65 % Total configuration time : 828 0.55/0.65 % Estimated wc time : 1656 0.55/0.65 % Estimated cpu time (8 cpus) : 207.0 0.57/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.57/0.75 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.57/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.58/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.58/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.58/0.84 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 120.82/15.91 % Solved by lams/40_b.comb.sh. 120.82/15.91 % done 512 iterations in 14.803s 120.82/15.91 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 120.82/15.91 % SZS output start Refutation 120.82/15.91 thf(a_type, type, a: $tType). 120.82/15.91 thf('#sk7_type', type, '#sk7': (a > a > a > $o) > a). 120.82/15.91 thf('#sk15_type', type, '#sk15': (a > a > a > $o) > a). 120.82/15.91 thf(y_type, type, y: a). 120.82/15.91 thf('#sk8_type', type, '#sk8': (a > a > a > $o) > a). 120.82/15.91 thf('#sk11_type', type, '#sk11': (a > a > a > $o) > a). 120.82/15.91 thf('#sk1_type', type, '#sk1': a > a > a > $o). 120.82/15.91 thf('#sk14_type', type, '#sk14': (a > a > a > $o) > a). 120.82/15.91 thf('#sk9_type', type, '#sk9': (a > a > a > $o) > a). 120.82/15.91 thf(u_type, type, u: a). 120.82/15.91 thf(cZ_type, type, cZ: a). 120.82/15.91 thf('#sk10_type', type, '#sk10': (a > a > a > $o) > a). 120.82/15.91 thf('#sk17_type', type, '#sk17': (a > a > a > $o) > a). 120.82/15.91 thf('#sk4_type', type, '#sk4': (a > a > a > $o) > a). 120.82/15.91 thf('#sk13_type', type, '#sk13': (a > a > a > $o) > a). 120.82/15.91 thf('#sk19_type', type, '#sk19': (a > a > a > $o) > a). 120.82/15.91 thf('#sk21_type', type, '#sk21': (a > a > a > $o) > a). 120.82/15.91 thf('#sk18_type', type, '#sk18': (a > a > a > $o) > a). 120.82/15.91 thf(x_type, type, x: a). 120.82/15.91 thf('#sk20_type', type, '#sk20': (a > a > a > $o) > a). 120.82/15.91 thf(cP_type, type, cP: a > a > a). 120.82/15.91 thf('#sk2_type', type, '#sk2': (a > a > a > $o) > a). 120.82/15.91 thf('#sk16_type', type, '#sk16': (a > a > a > $o) > a). 120.82/15.91 thf(v_type, type, v: a). 120.82/15.91 thf('#sk12_type', type, '#sk12': (a > a > a > $o) > a). 120.82/15.91 thf('#sk5_type', type, '#sk5': (a > a > a > $o) > a). 120.82/15.91 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 120.82/15.91 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 120.82/15.91 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 120.82/15.91 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 120.82/15.91 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 120.82/15.91 thf(cS_LEM1E_pme, conjecture, 120.82/15.91 (( ( ![X:( a > $o )]: 120.82/15.91 ( ( ( X @ cZ ) & 120.82/15.91 ( ![Xx0:a,Xy0:a]: 120.82/15.91 ( ( ( X @ Xy0 ) & ( X @ Xx0 ) ) => ( X @ ( cP @ Xx0 @ Xy0 ) ) ) ) ) => 120.82/15.91 ( ![Xx0:a]: ( X @ Xx0 ) ) ) ) & 120.82/15.91 ( ![Xx0:a,Xy0:a,Xu0:a,Xv0:a]: 120.82/15.91 ( ( ( cP @ Xx0 @ Xu0 ) = ( cP @ Xy0 @ Xv0 ) ) => 120.82/15.91 ( ( ( Xu0 ) = ( Xv0 ) ) & ( ( Xx0 ) = ( Xy0 ) ) ) ) ) & 120.82/15.91 ( ![Xx0:a,Xy0:a]: ( ( cP @ Xx0 @ Xy0 ) != ( cZ ) ) ) ) => 120.82/15.91 ( ( ![R:( a > a > a > $o )]: 120.82/15.91 ( ( ![Xa:a,Xb:a,Xc:a]: 120.82/15.91 ( ( ( ( ( Xb ) = ( Xc ) ) & ( ( Xa ) = ( cZ ) ) ) | 120.82/15.91 ( ?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]: 120.82/15.91 ( ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 120.82/15.91 ( R @ Xx2 @ Xy2 @ Xz2 ) & ( R @ Xx1 @ Xy1 @ Xz1 ) & 120.82/15.91 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) & 120.82/15.91 ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) ) ) | 120.82/15.91 ( ( ( Xb ) = ( cZ ) ) & ( ( Xa ) = ( Xc ) ) ) ) => 120.82/15.91 ( R @ Xa @ Xb @ Xc ) ) ) => 120.82/15.91 ( R @ x @ u @ u ) ) ) => 120.82/15.91 ( ( ![R:( a > a > a > $o )]: 120.82/15.91 ( ( ![Xa:a,Xb:a,Xc:a]: 120.82/15.91 ( ( ( ( ( Xa ) = ( cZ ) ) & ( ( Xb ) = ( Xc ) ) ) | 120.82/15.91 ( ?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]: 120.82/15.91 ( ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) & 120.82/15.91 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) & 120.82/15.91 ( R @ Xx2 @ Xy2 @ Xz2 ) & ( R @ Xx1 @ Xy1 @ Xz1 ) & 120.82/15.91 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) ) ) | 120.82/15.91 ( ( ( Xa ) = ( Xc ) ) & ( ( Xb ) = ( cZ ) ) ) ) => 120.82/15.91 ( R @ Xa @ Xb @ Xc ) ) ) => 120.82/15.91 ( R @ y @ v @ v ) ) ) => 120.82/15.91 ( ![R:( a > a > a > $o )]: 120.82/15.91 ( ( ![Xa:a,Xb:a,Xc:a]: 120.82/15.91 ( ( ( ( ( Xa ) = ( cZ ) ) & ( ( Xb ) = ( Xc ) ) ) | 120.82/15.91 ( ( ( Xb ) = ( cZ ) ) & ( ( Xa ) = ( Xc ) ) ) | 120.82/15.91 ( ?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]: 120.82/15.91 ( ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) & 120.82/15.91 ( R @ Xx1 @ Xy1 @ Xz1 ) & ( R @ Xx2 @ Xy2 @ Xz2 ) & 120.82/15.91 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 120.82/15.91 ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) ) ) ) => 120.82/15.91 ( R @ Xa @ Xb @ Xc ) ) ) => 120.82/15.91 ( R @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ) ) ) ))). 120.82/15.91 thf(zf_stmt_0, negated_conjecture, 120.82/15.91 (~( ( ( ![X:( a > $o )]: 120.82/15.91 ( ( ( X @ cZ ) & 120.82/15.91 ( ![Xx0:a,Xy0:a]: 120.82/15.91 ( ( ( X @ Xy0 ) & ( X @ Xx0 ) ) => ( X @ ( cP @ Xx0 @ Xy0 ) ) ) ) ) => 120.82/15.91 ( ![Xx0:a]: ( X @ Xx0 ) ) ) ) & 120.82/15.91 ( ![Xx0:a,Xy0:a,Xu0:a,Xv0:a]: 120.82/15.91 ( ( ( cP @ Xx0 @ Xu0 ) = ( cP @ Xy0 @ Xv0 ) ) => 120.82/15.91 ( ( ( Xu0 ) = ( Xv0 ) ) & ( ( Xx0 ) = ( Xy0 ) ) ) ) ) & 120.82/15.91 ( ![Xx0:a,Xy0:a]: ( ( cP @ Xx0 @ Xy0 ) != ( cZ ) ) ) ) => 120.82/15.91 ( ( ![R:( a > a > a > $o )]: 120.82/15.91 ( ( ![Xa:a,Xb:a,Xc:a]: 120.82/15.91 ( ( ( ( ( Xb ) = ( Xc ) ) & ( ( Xa ) = ( cZ ) ) ) | 120.82/15.91 ( ?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]: 120.82/15.91 ( ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 120.82/15.91 ( R @ Xx2 @ Xy2 @ Xz2 ) & ( R @ Xx1 @ Xy1 @ Xz1 ) & 120.82/15.91 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) & 120.82/15.91 ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) ) ) | 120.82/15.91 ( ( ( Xb ) = ( cZ ) ) & ( ( Xa ) = ( Xc ) ) ) ) => 120.82/15.91 ( R @ Xa @ Xb @ Xc ) ) ) => 120.82/15.91 ( R @ x @ u @ u ) ) ) => 120.82/15.91 ( ( ![R:( a > a > a > $o )]: 120.82/15.91 ( ( ![Xa:a,Xb:a,Xc:a]: 120.82/15.91 ( ( ( ( ( Xa ) = ( cZ ) ) & ( ( Xb ) = ( Xc ) ) ) | 120.82/15.91 ( ?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]: 120.82/15.91 ( ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) & 120.82/15.91 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) & 120.82/15.91 ( R @ Xx2 @ Xy2 @ Xz2 ) & ( R @ Xx1 @ Xy1 @ Xz1 ) & 120.82/15.91 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) ) ) | 120.82/15.91 ( ( ( Xa ) = ( Xc ) ) & ( ( Xb ) = ( cZ ) ) ) ) => 120.82/15.91 ( R @ Xa @ Xb @ Xc ) ) ) => 120.82/15.91 ( R @ y @ v @ v ) ) ) => 120.82/15.91 ( ![R:( a > a > a > $o )]: 120.82/15.91 ( ( ![Xa:a,Xb:a,Xc:a]: 120.82/15.91 ( ( ( ( ( Xa ) = ( cZ ) ) & ( ( Xb ) = ( Xc ) ) ) | 120.82/15.91 ( ( ( Xb ) = ( cZ ) ) & ( ( Xa ) = ( Xc ) ) ) | 120.82/15.91 ( ?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]: 120.82/15.91 ( ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) & 120.82/15.91 ( R @ Xx1 @ Xy1 @ Xz1 ) & ( R @ Xx2 @ Xy2 @ Xz2 ) & 120.82/15.91 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 120.82/15.91 ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) ) ) ) => 120.82/15.91 ( R @ Xa @ Xb @ Xc ) ) ) => 120.82/15.91 ( R @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ) ) ) ) )), 120.82/15.91 inference('cnf.neg', [status(esa)], [cS_LEM1E_pme])). 120.82/15.91 thf(zip_derived_cl0, plain, 120.82/15.91 (~ (((((((!!) @ (^[Y0 : a > $o]: 120.82/15.91 (((((Y0 @ cZ) & 120.82/15.91 (((!!) @ (^[Y1 : a]: 120.82/15.91 (((!!) @ (^[Y2 : a]: 120.82/15.91 (((((Y0 @ Y2) & (Y0 @ Y1))) => 120.82/15.91 (Y0 @ (cP @ Y1 @ Y2)))))))))))) => 120.82/15.91 (((!!) @ (^[Y1 : a]: (Y0 @ Y1))))))))) & 120.82/15.91 (((!!) @ (^[Y0 : a]: 120.82/15.91 (((!!) @ (^[Y1 : a]: 120.82/15.91 (((!!) @ (^[Y2 : a]: 120.82/15.91 (((!!) @ (^[Y3 : a]: 120.82/15.91 (((((cP @ Y0 @ 120.82/15.91 Y2) = (cP @ 120.82/15.91 Y1 @ Y3))) => 120.82/15.91 (((((Y2) = (Y3))) & 120.82/15.91 (((Y0) = (Y1))))))))))))))))))) & 120.82/15.91 (((!!) @ (^[Y0 : a]: 120.82/15.91 (((!!) @ (^[Y1 : a]: (((cP @ Y0 @ Y1) != (cZ))))))))))) => 120.82/15.91 (((((!!) @ (^[Y0 : a > a > a > $o]: 120.82/15.91 (((((!!) @ (^[Y1 : a]: 120.82/15.91 (((!!) @ (^[Y2 : a]: 120.82/15.91 (((!!) @ (^[Y3 : a]: 120.82/15.91 (((((((( 120.82/15.91 (Y2) = 120.82/15.91 (Y3))) & 120.82/15.91 (( 120.82/15.91 (Y1) = 120.82/15.91 (cZ))))) | 120.82/15.91 (((??) @ ( 120.82/15.91 ^[Y4 : a]: 120.82/15.91 (( 120.82/15.91 (??) @ ( 120.82/15.91 ^[Y5 : a]: 120.82/15.91 (( 120.82/15.91 (??) @ ( 120.82/15.91 ^[Y6 : a]: 120.82/15.91 (( 120.82/15.91 (??) @ ( 120.82/15.91 ^[Y7 : a]: 120.82/15.91 (( 120.82/15.91 (??) @ ( 120.82/15.91 ^[Y8 : a]: 120.82/15.91 (( 120.82/15.91 (??) @ ( 120.82/15.91 ^[Y9 : a]: 120.82/15.91 (( 120.82/15.91 ( 120.82/15.91 ( 120.82/15.91 (Y3) = 120.82/15.91 (cP @ 120.82/15.91 Y8 @ Y9))) & 120.82/15.91 ( 120.82/15.91 Y0 @ 120.82/15.91 Y5 @ 120.82/15.91 Y7 @ Y9) & 120.82/15.91 ( 120.82/15.91 Y0 @ 120.82/15.91 Y4 @ 120.82/15.91 Y6 @ Y8) & 120.82/15.91 ( 120.82/15.91 ( 120.82/15.91 (Y2) = 120.82/15.91 (cP @ 120.82/15.91 Y6 @ Y7))) & 120.82/15.91 ( 120.82/15.91 ( 120.82/15.91 (Y1) = 120.82/15.91 (cP @ 120.82/15.91 Y4 @ Y5))))))))))))))))))))))) | 120.82/15.91 (((( 120.82/15.91 (Y2) = 120.82/15.91 (cZ))) & 120.82/15.91 (( 120.82/15.91 (Y1) = 120.82/15.91 (Y3))))))) => 120.82/15.91 (Y0 @ Y1 @ 120.82/15.91 Y2 @ Y3)))))))))))) => 120.82/15.91 (Y0 @ x @ u @ u)))))) => 120.82/15.91 (((((!!) @ (^[Y0 : a > a > a > $o]: 120.82/15.91 (((((!!) @ (^[Y1 : a]: 120.82/15.91 (((!!) @ (^[Y2 : a]: 120.82/15.91 (((!!) @ (^[Y3 : a]: 120.82/15.91 (((((( 120.82/15.91 (( 120.82/15.91 (Y1) = 120.82/15.91 (cZ))) & 120.82/15.91 (( 120.82/15.91 (Y2) = 120.82/15.91 (Y3))))) | 120.82/15.91 (( 120.82/15.91 (??) @ ( 120.82/15.91 ^[Y4 : a]: 120.82/15.91 (( 120.82/15.91 (??) @ ( 120.82/15.91 ^[Y5 : a]: 120.82/15.91 (( 120.82/15.91 (??) @ ( 120.82/15.91 ^[Y6 : a]: 120.82/15.91 (( 120.82/15.91 (??) @ ( 120.82/15.91 ^[Y7 : a]: 120.82/15.91 (( 120.82/15.91 (??) @ ( 120.82/15.91 ^[Y8 : a]: 120.82/15.91 (( 120.82/15.91 (??) @ ( 120.82/15.91 ^[Y9 : a]: 120.82/15.91 (( 120.82/15.91 ( 120.82/15.91 ( 120.82/15.91 (Y1) = 120.82/15.91 (cP @ 120.82/15.91 Y4 @ Y5))) & 120.82/15.91 ( 120.82/15.91 ( 120.82/15.91 (Y2) = 120.82/15.91 (cP @ 120.82/15.91 Y6 @ Y7))) & 120.82/15.91 ( 120.82/15.91 Y0 @ 120.82/15.91 Y5 @ 120.82/15.91 Y7 @ Y9) & 120.82/15.91 ( 120.82/15.91 Y0 @ 120.82/15.91 Y4 @ 120.82/15.91 Y6 @ Y8) & 120.82/15.91 ( 120.82/15.91 ( 120.82/15.91 (Y3) = 120.82/15.91 (cP @ 120.82/15.91 Y8 @ Y9))))))))))))))))))))))) | 120.82/15.91 (( 120.82/15.91 (( 120.82/15.91 (Y1) = 120.82/15.91 (Y3))) & 120.82/15.91 (( 120.82/15.91 (Y2) = 120.82/15.91 (cZ))))))) => 120.82/15.91 (Y0 @ Y1 @ 120.82/15.91 Y2 @ Y3)))))))))))) => 120.82/15.91 (Y0 @ y @ v @ v)))))) => 120.82/15.91 (((!!) @ (^[Y0 : a > a > a > $o]: 120.82/15.91 (((((!!) @ (^[Y1 : a]: 120.82/15.91 (((!!) @ (^[Y2 : a]: 120.82/15.91 (((!!) @ (^[Y3 : a]: 120.82/15.91 (((((( 120.82/15.91 (( 120.82/15.91 (Y1) = 120.82/15.91 (cZ))) & 120.82/15.91 (( 120.82/15.91 (Y2) = 120.82/15.91 (Y3))))) | 120.82/15.91 (( 120.82/15.91 (( 120.82/15.91 (Y2) = 120.82/15.91 (cZ))) & 120.82/15.91 (( 120.82/15.91 (Y1) = 120.82/15.91 (Y3))))) | 120.82/15.91 (( 120.82/15.91 (??) @ ( 120.82/15.91 ^[Y4 : a]: 120.82/15.91 (( 120.82/15.91 (??) @ ( 120.82/15.91 ^[Y5 : a]: 120.82/15.91 (( 120.82/15.91 (??) @ ( 120.82/15.91 ^[Y6 : a]: 120.82/15.91 (( 120.82/15.91 (??) @ ( 120.82/15.91 ^[Y7 : a]: 120.82/15.91 (( 120.82/15.91 (??) @ ( 120.82/15.91 ^[Y8 : a]: 120.82/15.91 (( 120.82/15.91 (??) @ ( 120.82/15.91 ^[Y9 : a]: 120.82/15.91 (( 120.82/15.91 ( 120.82/15.91 ( 120.82/15.91 (Y2) = 120.82/15.91 (cP @ 120.82/15.91 Y6 @ Y7))) & 120.82/15.91 ( 120.82/15.91 Y0 @ 120.82/15.91 Y4 @ 120.82/15.91 Y6 @ Y8) & 120.82/15.91 ( 120.82/15.91 Y0 @ 120.82/15.91 Y5 @ 120.82/15.91 Y7 @ Y9) & 120.82/15.91 ( 120.82/15.91 ( 120.82/15.91 (Y3) = 120.82/15.91 (cP @ 120.82/15.91 Y8 @ Y9))) & 120.82/15.91 ( 120.82/15.91 ( 120.82/15.91 (Y1) = 120.82/15.91 (cP @ 120.82/15.91 Y4 @ Y5))))))))))))))))))))))))) => 120.82/15.91 (Y0 @ Y1 @ 120.82/15.91 Y2 @ Y3)))))))))))) => 120.82/15.91 (Y0 @ (cP @ x @ y) @ (cP @ u @ v) @ (cP @ u @ v)))))))))))))), 120.82/15.91 inference('cnf', [status(esa)], [zf_stmt_0])). 120.82/15.91 thf(zip_derived_cl1, plain, 120.82/15.91 (~ (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @ 120.82/15.91 ((('#S') @ ((('#B') @ (&) @ 120.82/15.91 ((('#C') @ ('#I') @ cZ)))) @ 120.82/15.91 ((('#B') @ (!!) @ 120.82/15.91 ((('#B') @ ((('#B') @ (!!))) @ 120.82/15.91 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.91 ((('#B') @ ((('#B') @ ( 120.82/15.91 '#S'))) @ 120.82/15.91 ((('#B') @ ((('#B') @ ( 120.82/15.91 (('#B') @ ( 120.82/15.91 =>))))) @ 120.82/15.91 ((('#S') @ (( 120.82/15.91 ('#B') @ ( 120.82/15.91 '#B') @ 120.82/15.91 ( 120.82/15.91 ( 120.82/15.91 ('#B') @ ( 120.82/15.91 '#C') @ 120.82/15.91 ( 120.82/15.91 ( 120.82/15.91 ('#B') @ ( 120.82/15.91 &))))))) @ 120.82/15.91 ('#I'))))))))) @ 120.82/15.91 ((('#C') @ ((('#B') @ ('#B') @ 120.82/15.91 ('#B'))) @ 120.82/15.91 cP)))))))))))) @ 120.82/15.91 (!!))))) & 120.82/15.91 (((!!) @ ((('#B') @ (!!) @ 120.82/15.91 ((('#B') @ ((('#B') @ (!!))) @ 120.82/15.91 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 120.82/15.91 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.91 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.91 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.91 '#S'))))) @ 120.82/15.91 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.91 (('#B') @ ( 120.82/15.91 =>))))))) @ 120.82/15.91 ((('#C') @ ((('#B') @ ('#B') @ 120.82/15.91 ((('#B') @ ( 120.82/15.91 '#C') @ 120.82/15.91 ((('#B') @ ( 120.82/15.91 (('#B') @ ( 120.82/15.91 '#B'))) @ 120.82/15.91 ((('#B') @ ( 120.82/15.91 (('#B') @ (=))) @ 120.82/15.92 cP)))))))) @ 120.82/15.92 cP)))))))))) @ 120.82/15.92 ((('#B') @ ((('#B') @ ((('#C') @ ((('#B') @ ( 120.82/15.92 '#C') @ 120.82/15.92 ((('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 &))) @ 120.82/15.92 (=))))))))) @ 120.82/15.92 (=))))))))))))) & 120.82/15.92 (((!!) @ ((('#B') @ (!!) @ 120.82/15.92 ((('#C') @ ((('#B') @ ('#C') @ 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??))))))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B'))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))))) 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120.82/15.92 ('#S') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B'))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B'))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B'))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B'))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 &))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 =))))) @ 120.82/15.92 cP)))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 =))))) @ 120.82/15.92 cP)))))))))))))))))))))))))))))))))) @ 120.82/15.92 ( 120.82/15.92 '#I'))))))))))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 =))))) @ 120.82/15.92 cP)))))))))))))))))))))))) @ 120.82/15.92 ((('#C') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ((('#B') @ ( 120.82/15.92 '#C') @ 120.82/15.92 (( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 &))) @ 120.82/15.92 ( 120.82/15.92 =))))))) @ 120.82/15.92 ((('#C') @ ( 120.82/15.92 =) @ cZ)))))))))))))) @ 120.82/15.92 ('#I'))))))))))) @ 120.82/15.92 ((('#C') @ ((('#C') @ ((('#C') @ ('#I') @ y)) @ v)) @ 120.82/15.92 v)))))) => 120.82/15.92 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 120.82/15.92 ((('#B') @ (!!) @ 120.82/15.92 ((('#B') @ ((('#B') @ (!!))) @ 120.82/15.92 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 120.82/15.92 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.92 ((('#B') @ ((('#B') @ ( 120.82/15.92 '#S'))) @ 120.82/15.92 ((('#B') @ (( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))))) @ 120.82/15.92 ((('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ (=>))))))) @ 120.82/15.92 ((('#B') @ ( 120.82/15.92 (('#S') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 '#S') @ 120.82/15.92 ((('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 '#S'))) @ 120.82/15.92 ((('#S') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 |))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 &) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 =) @ cZ)))))))) @ 120.82/15.92 ( 120.82/15.92 =))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 &) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 =) @ cZ)))))))) @ 120.82/15.92 ( 120.82/15.92 =))))))))))) @ 120.82/15.92 ((('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 ??))))))) @ 120.82/15.92 ((('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ??))))))))) @ 120.82/15.92 ((('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ??))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ??))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ??))))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ??))))))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))))))) @ 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120.82/15.92 '#I'))))))))))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 =))))) @ 120.82/15.92 cP)))))))))))))))))))))))) @ 120.82/15.92 ((('#C') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ((('#B') @ ( 120.82/15.92 '#C') @ 120.82/15.92 ((('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 &))) @ 120.82/15.92 (=))))))) @ 120.82/15.92 ((('#C') @ ( 120.82/15.92 =) @ cZ)))))))))))))) @ 120.82/15.92 ('#I'))))))))))) @ 120.82/15.92 ((('#C') @ ((('#C') @ ((('#C') @ ('#I') @ y)) @ v)) @ v)))))) => 120.82/15.92 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 120.82/15.92 ((('#B') @ (!!) @ 120.82/15.92 ((('#B') @ ((('#B') @ (!!))) @ 120.82/15.92 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 120.82/15.92 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.92 ((('#B') @ ((('#B') @ ( 120.82/15.92 '#S'))) @ 120.82/15.92 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@ u @ v)))))))), 120.82/15.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 120.82/15.92 thf(zip_derived_cl20, plain, 120.82/15.92 (~ (((((!!) @ ((('#B') @ (!!) @ 120.82/15.92 ((('#B') @ ((('#B') @ (!!))) @ 120.82/15.92 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.92 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.92 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 120.82/15.92 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.92 ((('#B') @ ((('#B') @ ( 120.82/15.92 '#S'))) @ 120.82/15.92 ((('#S') @ ((('#B') @ ( 120.82/15.92 '#S') @ 120.82/15.92 (( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 |))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 &) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 =) @ cZ)))))))) @ 120.82/15.92 ( 120.82/15.92 =))))))))) @ 120.82/15.92 ((('#B') @ (( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 &) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 =) @ cZ)))))))) @ 120.82/15.92 (=))))))))) @ 120.82/15.92 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.92 ??))))) @ 120.82/15.92 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 ??))))))) @ 120.82/15.92 ((('#B') @ ((('#B') @ (( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ??))))))))) @ 120.82/15.92 ((('#B') @ ((('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ (??))))))))))) @ 120.82/15.92 ((('#B') @ ((('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 ??))))))))))))) @ 120.82/15.92 ((('#B') @ ((('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ??))))))))))))))) @ 120.82/15.92 ((('#B') @ ((('#C') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 '#C') @ 120.82/15.92 (( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B'))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B'))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 &))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 =))))) @ 120.82/15.92 cP)))))))))))) @ 120.82/15.92 '#sk1')))))))))))))) @ 120.82/15.92 '#sk1')))))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 =))))) @ 120.82/15.92 cP)))))))))))))))))))) @ 120.82/15.92 ((('#C') @ ((('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 =))))) @ 120.82/15.92 cP)))))))))))))))))))))))) @ 120.82/15.92 '#sk1')))))))) => 120.82/15.92 ('#sk1' @ (cP @ x @ y) @ (cP @ u @ v) @ (cP @ u @ v))))), 120.82/15.92 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl14])). 120.82/15.92 thf(zip_derived_cl27, plain, 120.82/15.92 (~ ('#sk1' @ (cP @ x @ y) @ (cP @ u @ v) @ (cP @ u @ v))), 120.82/15.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 120.82/15.92 thf(zip_derived_cl7, plain, 120.82/15.92 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 120.82/15.92 ((('#B') @ (!!) @ 120.82/15.92 ((('#B') @ ((('#B') @ (!!))) @ 120.82/15.92 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 120.82/15.92 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.92 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.92 ((('#B') @ ((('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 '#S'))))) @ 120.82/15.92 ((('#B') @ ((('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 =>))))))) @ 120.82/15.92 ((('#C') @ ((('#B') @ ( 120.82/15.92 '#S') @ 120.82/15.92 ((('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#S') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 |))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 &))) @ 120.82/15.92 ( 120.82/15.92 =))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 =) @ cZ)))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ??))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ??))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ??))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ??))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ??))))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ??))))))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#S'))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#S') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C'))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 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120.82/15.92 cP)))))))))))))))))))))))) @ 120.82/15.92 ((('#B') @ ((('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#B') @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 &) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 =) @ cZ)))))))) @ 120.82/15.92 (=))))))))))))) @ 120.82/15.92 ('#I'))))))))))) @ 120.82/15.92 ((('#C') @ ((('#C') @ ((('#C') @ ('#I') @ x)) @ u)) @ u))))))), 120.82/15.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])). 120.82/15.92 thf(zip_derived_cl12, plain, 120.82/15.92 (![X2 : a > a > a > $o]: 120.82/15.92 (((((!!) @ ((('#B') @ (!!) @ 120.82/15.92 ((('#B') @ ((('#B') @ (!!))) @ 120.82/15.92 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.92 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.92 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 120.82/15.92 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.92 ((('#B') @ ((('#B') @ ( 120.82/15.92 '#S'))) @ 120.82/15.92 ((('#S') @ ((('#B') @ ( 120.82/15.92 '#S') @ 120.82/15.92 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120.82/15.92 ((('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ??))))))))))) @ 120.82/15.92 ((('#B') @ ( 120.82/15.92 (('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ??))))))))))))) @ 120.82/15.92 (( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ??))))))))))))))) @ 120.82/15.92 ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 ( 120.82/15.92 ('#C') @ ( 120.82/15.92 ( 120.82/15.92 ('#B') @ ( 120.82/15.92 '#C') @ 120.82/15.92 ( 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cP)))))))))))) @ 120.82/15.93 X2)))))))))))))) @ 120.82/15.93 X2)))))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 =))))) @ 120.82/15.93 cP)))))))))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 =))))) @ 120.82/15.93 cP)))))))))))))))))))))) @ 120.82/15.93 ((('#B') @ ((('#C') @ ((('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 &) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 =) @ cZ)))))))) @ 120.82/15.93 (=))))))))))) @ 120.82/15.93 X2)))))))) => 120.82/15.93 (X2 @ x @ u @ u)))), 120.82/15.93 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 120.82/15.93 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cP)))))))))))) @ 120.82/15.93 X2)))))))))))))) @ 120.82/15.93 X2)))))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 =))))) @ 120.82/15.93 cP)))))))))))))))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk2' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ('#B') @ 120.82/15.93 ((('#B') @ (&) @ 120.82/15.93 ((('#C') @ (=) @ cZ)))))) @ 120.82/15.93 (((a) = ('#sk2' @ X2))))))))))) @ 120.82/15.93 (X2 @ ('#sk2' @ X2)))))))) 120.82/15.93 | (X2 @ x @ u @ u))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl18])). 120.82/15.93 thf(zip_derived_cl30, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 120.82/15.93 ((('#S') @ ((('#S') @ 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( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 =))))) @ 120.82/15.93 cP)))))))))))) @ 120.82/15.93 X2)))))))))))))) @ 120.82/15.93 X2)))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk4' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ((a) = 120.82/15.93 ('#sk2' @ X2))))) @ 120.82/15.93 cP)))))))))))))))))) @ 120.82/15.93 ((('#B') @ (((&) @ ((('#sk4' @ X2) = (cZ))))) @ 120.82/15.93 (((a) = ('#sk2' @ X2))))))))) @ 120.82/15.93 (X2 @ ('#sk2' @ X2) @ ('#sk4' @ X2)))))) 120.82/15.93 | (X2 @ x @ u @ u))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl24])). 120.82/15.93 thf(zip_derived_cl35, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 (~ ((((((((('#sk4' @ X2) = ('#sk7' @ X2))) & ((('#sk2' @ X2) = (cZ))))) | 120.82/15.93 (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ??))))))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ('#C'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 (( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 ((('#B') @ (( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk4' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (((a) = ('#sk2' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))))))) | 120.82/15.93 ((((('#sk4' @ X2) = (cZ))) & ((('#sk2' @ X2) = ('#sk7' @ X2))))))) => 120.82/15.93 (X2 @ ('#sk2' @ X2) @ ('#sk4' @ X2) @ ('#sk7' @ X2)))) 120.82/15.93 | (X2 @ x @ u @ u))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])). 120.82/15.93 thf(zip_derived_cl43, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( ((((((('#sk4' @ X2) = ('#sk7' @ X2))) & ((('#sk2' @ X2) = (cZ))))) | 120.82/15.93 (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ (??))))))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ('#C'))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 ((a) = 120.82/15.93 ('#sk4' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (((a) = ('#sk2' @ X2))))) @ 120.82/15.93 cP)))))))))))))))) | 120.82/15.93 ((((('#sk4' @ X2) = (cZ))) & ((('#sk2' @ X2) = ('#sk7' @ X2))))))) 120.82/15.93 | (X2 @ x @ u @ u))), 120.82/15.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 120.82/15.93 thf(zip_derived_cl52, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( ((((('#sk4' @ X2) = ('#sk7' @ X2))) & ((('#sk2' @ X2) = (cZ))))) 120.82/15.93 | (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ (??))))))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ('#C'))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 ((a) = 120.82/15.93 ('#sk4' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (((a) = ('#sk2' @ X2))))) @ 120.82/15.93 cP)))))))))))))))) 120.82/15.93 | ((((('#sk4' @ X2) = (cZ))) & ((('#sk2' @ X2) = ('#sk7' @ X2))))) 120.82/15.93 | (X2 @ x @ u @ u))), 120.82/15.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 120.82/15.93 thf(zip_derived_cl58, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( ((('#sk4' @ X2) = ('#sk7' @ X2))) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | ((((('#sk4' @ X2) = (cZ))) & ((('#sk2' @ X2) = ('#sk7' @ X2))))) 120.82/15.93 | (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ (??))))))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ('#C'))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 ((a) = 120.82/15.93 ('#sk4' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (((a) = ('#sk2' @ X2))))) @ 120.82/15.93 cP)))))))))))))))))), 120.82/15.93 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl52])). 120.82/15.93 thf(zip_derived_cl66, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ((('#sk4' @ X2) = ('#sk7' @ X2)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | ((((('#sk4' @ X2) = (cZ))) & ((('#sk2' @ X2) = ('#sk7' @ X2))))) 120.82/15.93 | (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ (??))))))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ('#C'))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 ((a) = 120.82/15.93 ('#sk4' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (((a) = ('#sk2' @ X2))))) @ 120.82/15.93 cP)))))))))))))))))), 120.82/15.93 inference('simplify nested equalities', [status(thm)], [zip_derived_cl58])). 120.82/15.93 thf(zip_derived_cl68, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( ((('#sk2' @ X2) = ('#sk7' @ X2))) 120.82/15.93 | (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ (??))))))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ('#C'))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 ((a) = 120.82/15.93 ('#sk4' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (((a) = ('#sk2' @ X2))))) @ 120.82/15.93 cP)))))))))))))))) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk4' @ X2) = ('#sk7' @ X2)))), 120.82/15.93 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl66])). 120.82/15.93 thf(zip_derived_cl79, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ((('#sk2' @ X2) = ('#sk7' @ X2)) 120.82/15.93 | (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ (??))))))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ('#C'))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 ((a) = 120.82/15.93 ('#sk4' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (((a) = ('#sk2' @ X2))))) @ 120.82/15.93 cP)))))))))))))))) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk4' @ X2) = ('#sk7' @ X2)))), 120.82/15.93 inference('simplify nested equalities', [status(thm)], [zip_derived_cl68])). 120.82/15.93 thf(zip_derived_cl80, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#C') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ('#S'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ((('#C') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 (( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 X2)))))))))) @ 120.82/15.93 (X2 @ 120.82/15.93 ('#sk10' @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 ((a) = ('#sk4' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))) @ 120.82/15.93 ((('#B') @ (((a) = ('#sk2' @ X2))) @ 120.82/15.93 (cP @ ('#sk10' @ X2)))))))))))))))) 120.82/15.93 | (('#sk4' @ X2) = ('#sk7' @ X2)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk2' @ X2) = ('#sk7' @ X2)))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl79])). 120.82/15.93 thf(zip_derived_cl95, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ((('#B') @ (( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#C') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#C') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))) @ 120.82/15.93 (X2 @ 120.82/15.93 ('#sk11' @ 120.82/15.93 X2)))))))))) @ 120.82/15.93 (X2 @ 120.82/15.93 ('#sk10' @ X2)))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (((a) = 120.82/15.93 ('#sk4' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ 120.82/15.93 ('#sk11' @ X2)))))))))))))) 120.82/15.93 | (('#sk2' @ X2) = ('#sk7' @ X2)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk4' @ X2) = ('#sk7' @ X2)))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl80])). 120.82/15.93 thf(zip_derived_cl108, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#C') @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 (( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))) @ 120.82/15.93 ( 120.82/15.93 X2 @ 120.82/15.93 ( 120.82/15.93 '#sk11' @ 120.82/15.93 X2)))))))) @ 120.82/15.93 (X2 @ ('#sk10' @ X2) @ 120.82/15.93 ('#sk13' @ X2)))))))) @ 120.82/15.93 ((('#B') @ (((a) = ('#sk4' @ X2))) @ 120.82/15.93 (cP @ ('#sk13' @ X2)))))))))) @ 120.82/15.93 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ 120.82/15.93 ('#sk11' @ X2)))))))))))) 120.82/15.93 | (('#sk4' @ X2) = ('#sk7' @ X2)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk2' @ X2) = ('#sk7' @ X2)))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl95])). 120.82/15.93 thf(zip_derived_cl117, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.93 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.93 ((('#S') @ ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ((('#C') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ (&))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ((a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))) @ 120.82/15.93 (X2 @ 120.82/15.93 ('#sk11' @ X2) @ 120.82/15.93 ('#sk15' @ X2)))))) @ 120.82/15.93 (X2 @ ('#sk10' @ X2) @ 120.82/15.93 ('#sk13' @ X2)))))) @ 120.82/15.93 ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ 120.82/15.93 ('#sk15' @ X2)))))))) @ 120.82/15.93 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ 120.82/15.93 ('#sk11' @ X2)))))))))) 120.82/15.93 | (('#sk2' @ X2) = ('#sk7' @ X2)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk4' @ X2) = ('#sk7' @ X2)))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl108])). 120.82/15.93 thf(zip_derived_cl126, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( (((??) @ ((('#C') @ ((('#C') @ ((('#C') @ ((('#S') @ ((('#B') @ ( 120.82/15.93 &) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 ((a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))) @ 120.82/15.93 (cP @ 120.82/15.93 ('#sk17' @ 120.82/15.93 X2)))))) @ 120.82/15.93 (X2 @ ('#sk11' @ X2) @ 120.82/15.93 ('#sk15' @ X2)))) @ 120.82/15.93 (X2 @ ('#sk10' @ X2) @ 120.82/15.93 ('#sk13' @ X2) @ ('#sk17' @ X2)))) @ 120.82/15.93 ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ 120.82/15.93 ('#sk15' @ X2)))))) @ 120.82/15.93 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ ('#sk11' @ X2)))))))) 120.82/15.93 | (('#sk4' @ X2) = ('#sk7' @ X2)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk2' @ X2) = ('#sk7' @ X2)))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl117])). 120.82/15.93 thf(zip_derived_cl135, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( ((((('#sk7' @ X2) = (cP @ ('#sk17' @ X2) @ ('#sk19' @ X2)))) & 120.82/15.93 (X2 @ ('#sk11' @ X2) @ ('#sk15' @ X2) @ ('#sk19' @ X2)) & 120.82/15.93 (X2 @ ('#sk10' @ X2) @ ('#sk13' @ X2) @ ('#sk17' @ X2)) & 120.82/15.93 ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ ('#sk15' @ X2)))) & 120.82/15.93 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ ('#sk11' @ X2)))))) 120.82/15.93 | (('#sk2' @ X2) = ('#sk7' @ X2)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk4' @ X2) = ('#sk7' @ X2)))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl126])). 120.82/15.93 thf(zip_derived_cl151, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ ('#sk15' @ X2)))) 120.82/15.93 | (('#sk4' @ X2) = ('#sk7' @ X2)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk2' @ X2) = ('#sk7' @ X2)))), 120.82/15.93 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl135])). 120.82/15.93 thf(zip_derived_cl172, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ ('#sk15' @ X2))) 120.82/15.93 | (('#sk4' @ X2) = ('#sk7' @ X2)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk2' @ X2) = ('#sk7' @ X2)))), 120.82/15.93 inference('simplify nested equalities', [status(thm)], 120.82/15.93 [zip_derived_cl151])). 120.82/15.93 thf(zip_derived_cl59, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( ((('#sk2' @ X2) = (cZ))) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | ((((('#sk4' @ X2) = (cZ))) & ((('#sk2' @ X2) = ('#sk7' @ X2))))) 120.82/15.93 | (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ (??))))))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ('#C'))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 ((a) = 120.82/15.93 ('#sk4' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (((a) = ('#sk2' @ X2))))) @ 120.82/15.93 cP)))))))))))))))))), 120.82/15.93 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl52])). 120.82/15.93 thf(zip_derived_cl69, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ((('#sk2' @ X2) = (cZ)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | ((((('#sk4' @ X2) = (cZ))) & ((('#sk2' @ X2) = ('#sk7' @ X2))))) 120.82/15.93 | (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ (??))))))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ('#C'))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 ((a) = 120.82/15.93 ('#sk4' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (((a) = ('#sk2' @ X2))))) @ 120.82/15.93 cP)))))))))))))))))), 120.82/15.93 inference('simplify nested equalities', [status(thm)], [zip_derived_cl59])). 120.82/15.93 thf(zip_derived_cl71, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( ((('#sk2' @ X2) = ('#sk7' @ X2))) 120.82/15.93 | (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ (??))))))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ('#C'))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 ((a) = 120.82/15.93 ('#sk4' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (((a) = ('#sk2' @ X2))))) @ 120.82/15.93 cP)))))))))))))))) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk2' @ X2) = (cZ)))), 120.82/15.93 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 120.82/15.93 thf(zip_derived_cl83, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ((('#sk2' @ X2) = ('#sk7' @ X2)) 120.82/15.93 | (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ (??))))))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ('#C'))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 ((a) = 120.82/15.93 ('#sk4' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (((a) = ('#sk2' @ X2))))) @ 120.82/15.93 cP)))))))))))))))) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk2' @ X2) = (cZ)))), 120.82/15.93 inference('simplify nested equalities', [status(thm)], [zip_derived_cl71])). 120.82/15.93 thf(zip_derived_cl84, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#C') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ('#S'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ((('#C') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 (( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 X2)))))))))) @ 120.82/15.93 (X2 @ 120.82/15.93 ('#sk10' @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 ((a) = ('#sk4' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))) @ 120.82/15.93 ((('#B') @ (((a) = ('#sk2' @ X2))) @ 120.82/15.93 (cP @ ('#sk10' @ X2)))))))))))))))) 120.82/15.93 | (('#sk2' @ X2) = (cZ)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk2' @ X2) = ('#sk7' @ X2)))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl83])). 120.82/15.93 thf(zip_derived_cl97, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ((('#B') @ (( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#C') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#C') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))) @ 120.82/15.93 (X2 @ 120.82/15.93 ('#sk11' @ 120.82/15.93 X2)))))))))) @ 120.82/15.93 (X2 @ 120.82/15.93 ('#sk10' @ X2)))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (((a) = 120.82/15.93 ('#sk4' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ 120.82/15.93 ('#sk11' @ X2)))))))))))))) 120.82/15.93 | (('#sk2' @ X2) = ('#sk7' @ X2)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk2' @ X2) = (cZ)))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl84])). 120.82/15.93 thf(zip_derived_cl110, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#C') @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 (( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))) @ 120.82/15.93 ( 120.82/15.93 X2 @ 120.82/15.93 ( 120.82/15.93 '#sk11' @ 120.82/15.93 X2)))))))) @ 120.82/15.93 (X2 @ ('#sk10' @ X2) @ 120.82/15.93 ('#sk13' @ X2)))))))) @ 120.82/15.93 ((('#B') @ (((a) = ('#sk4' @ X2))) @ 120.82/15.93 (cP @ ('#sk13' @ X2)))))))))) @ 120.82/15.93 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ 120.82/15.93 ('#sk11' @ X2)))))))))))) 120.82/15.93 | (('#sk2' @ X2) = (cZ)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk2' @ X2) = ('#sk7' @ X2)))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl97])). 120.82/15.93 thf(zip_derived_cl119, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.93 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.93 ((('#S') @ ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ((('#C') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ (&))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ((a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))) @ 120.82/15.93 (X2 @ 120.82/15.93 ('#sk11' @ X2) @ 120.82/15.93 ('#sk15' @ X2)))))) @ 120.82/15.93 (X2 @ ('#sk10' @ X2) @ 120.82/15.93 ('#sk13' @ X2)))))) @ 120.82/15.93 ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ 120.82/15.93 ('#sk15' @ X2)))))))) @ 120.82/15.93 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ 120.82/15.93 ('#sk11' @ X2)))))))))) 120.82/15.93 | (('#sk2' @ X2) = ('#sk7' @ X2)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk2' @ X2) = (cZ)))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl110])). 120.82/15.93 thf(zip_derived_cl128, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( (((??) @ ((('#C') @ ((('#C') @ ((('#C') @ ((('#S') @ ((('#B') @ ( 120.82/15.93 &) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 ((a) = 120.82/15.93 ('#sk7' @ 120.82/15.93 X2))) @ 120.82/15.93 (cP @ 120.82/15.93 ('#sk17' @ 120.82/15.93 X2)))))) @ 120.82/15.93 (X2 @ ('#sk11' @ X2) @ 120.82/15.93 ('#sk15' @ X2)))) @ 120.82/15.93 (X2 @ ('#sk10' @ X2) @ 120.82/15.93 ('#sk13' @ X2) @ ('#sk17' @ X2)))) @ 120.82/15.93 ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ 120.82/15.93 ('#sk15' @ X2)))))) @ 120.82/15.93 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ ('#sk11' @ X2)))))))) 120.82/15.93 | (('#sk2' @ X2) = (cZ)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk2' @ X2) = ('#sk7' @ X2)))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl119])). 120.82/15.93 thf(zip_derived_cl137, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( ((((('#sk7' @ X2) = (cP @ ('#sk17' @ X2) @ ('#sk19' @ X2)))) & 120.82/15.93 (X2 @ ('#sk11' @ X2) @ ('#sk15' @ X2) @ ('#sk19' @ X2)) & 120.82/15.93 (X2 @ ('#sk10' @ X2) @ ('#sk13' @ X2) @ ('#sk17' @ X2)) & 120.82/15.93 ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ ('#sk15' @ X2)))) & 120.82/15.93 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ ('#sk11' @ X2)))))) 120.82/15.93 | (('#sk2' @ X2) = ('#sk7' @ X2)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk2' @ X2) = (cZ)))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl128])). 120.82/15.93 thf(zip_derived_cl161, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ ('#sk15' @ X2)))) 120.82/15.93 | (('#sk2' @ X2) = (cZ)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk2' @ X2) = ('#sk7' @ X2)))), 120.82/15.93 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl137])). 120.82/15.93 thf(zip_derived_cl178, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ ('#sk15' @ X2))) 120.82/15.93 | (('#sk2' @ X2) = (cZ)) 120.82/15.93 | (X2 @ x @ u @ u) 120.82/15.93 | (('#sk2' @ X2) = ('#sk7' @ X2)))), 120.82/15.93 inference('simplify nested equalities', [status(thm)], 120.82/15.93 [zip_derived_cl161])). 120.82/15.93 thf(zip_derived_cl13, plain, 120.82/15.93 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 120.82/15.93 ((('#B') @ (!!) @ 120.82/15.93 ((('#B') @ ((('#B') @ (!!))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 =>))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#S') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 |))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 =) @ cZ)))))))) @ 120.82/15.93 ( 120.82/15.93 =))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ??))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ??))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ??))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ??))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ??))))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ??))))))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#S') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 =))))) @ 120.82/15.93 cP)))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 =))))) @ 120.82/15.93 cP)))))))))))))))))))))))))))))))))) @ 120.82/15.93 ( 120.82/15.93 '#I'))))))))))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 =))))) @ 120.82/15.93 cP)))))))))))))))))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 =))))))) @ 120.82/15.93 ((('#C') @ (=) @ cZ)))))))))))))) @ 120.82/15.93 ('#I'))))))))))) @ 120.82/15.93 ((('#C') @ ((('#C') @ ((('#C') @ ('#I') @ y)) @ v)) @ v))))))), 120.82/15.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 120.82/15.93 thf(zip_derived_cl19, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 (((((!!) @ ((('#B') @ (!!) @ 120.82/15.93 ((('#B') @ ((('#B') @ (!!))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 |))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 =) @ cZ)))))))) @ 120.82/15.93 ( 120.82/15.93 =))))))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ (??))))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ??))))))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ??))))))))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ??))))))))))))) @ 120.82/15.93 (( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ??))))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 =))))) @ 120.82/15.93 cP)))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 =))))) @ 120.82/15.93 cP)))))))))))))))) @ 120.82/15.93 X2)))))))))))))))) @ 120.82/15.93 X2)))))))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 =))))) @ 120.82/15.93 cP)))))))))))))))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ('#B') @ 120.82/15.93 ((('#B') @ ('#C') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ (&))) @ 120.82/15.93 (=))))))) @ 120.82/15.93 ((('#C') @ (=) @ cZ)))))))))))) @ 120.82/15.93 X2)))))))) => 120.82/15.93 (X2 @ y @ v @ v)))), 120.82/15.93 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 120.82/15.93 thf(zip_derived_cl25, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 (~ (((!!) @ ((('#B') @ (!!) @ 120.82/15.93 ((('#B') @ ((('#B') @ (!!))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 |))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 =) @ cZ)))))))) @ 120.82/15.93 ( 120.82/15.93 =))))))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ (??))))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ??))))))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ??))))))))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ??))))))))))))) @ 120.82/15.93 (( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ??))))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 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('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 =))))) @ 120.82/15.93 cP)))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 =))))) @ 120.82/15.93 cP)))))))))))))))) @ 120.82/15.93 X2)))))))))))))))) @ 120.82/15.93 X2)))))))))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 =))))) @ 120.82/15.93 cP)))))))))))))))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ('#B') @ 120.82/15.93 ((('#B') @ ('#C') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ (&))) @ 120.82/15.93 (=))))))) @ 120.82/15.93 ((('#C') @ (=) @ cZ)))))))))))) @ 120.82/15.93 X2)))))))) 120.82/15.93 | (X2 @ y @ v @ v))), 120.82/15.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 120.82/15.93 thf(zip_derived_cl31, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 (~ (((!!) @ ((('#B') @ (!!) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#B') @ ((('#B') @ (=>))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.93 ((('#S') @ ((('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ (|))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ((&) @ ( 120.82/15.93 ( 120.82/15.93 ('#sk5' @ 120.82/15.93 X2) = 120.82/15.93 (cZ))))))) @ 120.82/15.93 (=))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ??))))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ (??))))))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ??))))))))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ??))))))))))))) @ 120.82/15.93 ((('#C') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk5' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 =))))) @ 120.82/15.93 cP)))))))))))))) @ 120.82/15.93 X2)))))))))))))) @ 120.82/15.93 X2)))))))))))))))) @ 120.82/15.93 ((('#C') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ( 120.82/15.93 =))))) @ 120.82/15.93 cP)))))))))))))))))))) @ 120.82/15.93 ((('#B') @ ((('#C') @ ((('#B') @ ( 120.82/15.93 &) @ 120.82/15.93 (((a) = 120.82/15.93 ('#sk5' @ X2))))))) @ 120.82/15.93 ((('#C') @ (=) @ cZ)))))))))) @ 120.82/15.93 (X2 @ ('#sk5' @ X2)))))))) 120.82/15.93 | (X2 @ y @ v @ v))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl25])). 120.82/15.93 thf(zip_derived_cl36, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 120.82/15.93 ((('#S') @ ((('#S') @ ((('#B') @ (|) @ 120.82/15.93 ((('#B') @ (( 120.82/15.93 (&) @ ( 120.82/15.93 ( 120.82/15.93 ('#sk5' @ 120.82/15.93 X2) = 120.82/15.93 (cZ))))) @ 120.82/15.93 (((a) = ('#sk8' @ 120.82/15.93 X2))))))) @ 120.82/15.93 ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ??))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ??))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ??))))))))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#C') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))))) @ 120.82/15.93 (( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#S') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk5' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk8' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 X2)))))))))))))) @ 120.82/15.93 ((('#C') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#B') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 '#B') @ ( 120.82/15.93 =))))) @ 120.82/15.93 cP)))))))))))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ (&) @ 120.82/15.93 (((a) = ('#sk5' @ X2))))) @ 120.82/15.93 ((('#sk8' @ X2) = (cZ))))))))) @ 120.82/15.93 (X2 @ ('#sk5' @ X2) @ ('#sk8' @ X2)))))) 120.82/15.93 | (X2 @ y @ v @ v))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl31])). 120.82/15.93 thf(zip_derived_cl45, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 (~ ((((((((('#sk5' @ X2) = (cZ))) & ((('#sk8' @ X2) = ('#sk9' @ X2))))) | 120.82/15.93 (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 ??))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ('#C'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))))))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 (( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk5' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk8' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))))))) | 120.82/15.93 ((((('#sk5' @ X2) = ('#sk9' @ X2))) & ((('#sk8' @ X2) = (cZ))))))) => 120.82/15.93 (X2 @ ('#sk5' @ X2) @ ('#sk8' @ X2) @ ('#sk9' @ X2)))) 120.82/15.93 | (X2 @ y @ v @ v))), 120.82/15.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl36])). 120.82/15.93 thf(zip_derived_cl53, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( ((((((('#sk5' @ X2) = (cZ))) & ((('#sk8' @ X2) = ('#sk9' @ X2))))) | 120.82/15.93 (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ (??))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ('#S'))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))))))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk5' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk8' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.93 cP)))))))))))))))) | 120.82/15.93 ((((('#sk5' @ X2) = ('#sk9' @ X2))) & ((('#sk8' @ X2) = (cZ))))))) 120.82/15.93 | (X2 @ y @ v @ v))), 120.82/15.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 120.82/15.93 thf(zip_derived_cl60, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( ((((('#sk5' @ X2) = (cZ))) & ((('#sk8' @ X2) = ('#sk9' @ X2))))) 120.82/15.93 | (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ (??))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ('#S'))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))))))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 &))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk5' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 (a) = 120.82/15.93 ('#sk8' @ 120.82/15.93 X2))))) @ 120.82/15.93 cP)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 X2)))))))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.93 cP)))))))))))))))) 120.82/15.93 | ((((('#sk5' @ X2) = ('#sk9' @ X2))) & ((('#sk8' @ X2) = (cZ))))) 120.82/15.93 | (X2 @ y @ v @ v))), 120.82/15.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl53])). 120.82/15.93 thf(zip_derived_cl73, plain, 120.82/15.93 (![X2 : a > a > a > $o]: 120.82/15.93 ( ((('#sk8' @ X2) = ('#sk9' @ X2))) 120.82/15.93 | (X2 @ y @ v @ v) 120.82/15.93 | ((((('#sk5' @ X2) = ('#sk9' @ X2))) & ((('#sk8' @ X2) = (cZ))))) 120.82/15.93 | (((??) @ ((('#B') @ (??) @ 120.82/15.93 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ (??))))))))) @ 120.82/15.93 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.93 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.93 ((('#B') @ ((('#B') @ (( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ('#S'))))))) @ 120.82/15.93 ((('#B') @ ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))))))))) @ 120.82/15.93 ((('#S') @ ((('#B') @ ( 120.82/15.93 '#C') @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 (('#B') @ ( 120.82/15.93 '#S'))) @ 120.82/15.93 ((('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#C') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S') @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#C'))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#S'))))) @ 120.82/15.93 ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 ( 120.82/15.93 ('#B') @ ( 120.82/15.93 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk5' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))))))))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl60])). 120.82/15.94 thf(zip_derived_cl88, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk8' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | ((((('#sk5' @ X2) = ('#sk9' @ X2))) & ((('#sk8' @ X2) = (cZ))))) 120.82/15.94 | (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ('#S'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk5' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))))))))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], [zip_derived_cl73])). 120.82/15.94 thf(zip_derived_cl89, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((('#sk5' @ X2) = ('#sk9' @ X2))) 120.82/15.94 | (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ('#S'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk5' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))))))) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl88])). 120.82/15.94 thf(zip_derived_cl102, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk5' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ('#S'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk5' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))))))) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], [zip_derived_cl89])). 120.82/15.94 thf(zip_derived_cl103, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#B'))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#S') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk5' @ 120.82/15.94 X2))) @ 120.82/15.94 ( 120.82/15.94 cP @ 120.82/15.94 ( 120.82/15.94 '#sk12' @ 120.82/15.94 X2)))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 X2)))))))))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))))) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl102])). 120.82/15.94 thf(zip_derived_cl113, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ((('#C') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ((&) @ ( 120.82/15.94 (('#sk5' @ 120.82/15.94 X2) = 120.82/15.94 (cP @ 120.82/15.94 ( 120.82/15.94 '#sk12' @ 120.82/15.94 X2) @ 120.82/15.94 ( 120.82/15.94 '#sk14' @ 120.82/15.94 X2)))))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))) @ 120.82/15.94 (X2 @ 120.82/15.94 ('#sk14' @ X2)))))))))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2)))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))) 120.82/15.94 | (('#sk5' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl103])). 120.82/15.94 thf(zip_derived_cl122, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#B') @ 120.82/15.94 ((('#B') @ ('#C') @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ((&) @ ( 120.82/15.94 ( 120.82/15.94 ('#sk5' @ 120.82/15.94 X2) = 120.82/15.94 (cP @ 120.82/15.94 ( 120.82/15.94 '#sk12' @ 120.82/15.94 X2) @ 120.82/15.94 ( 120.82/15.94 '#sk14' @ 120.82/15.94 X2)))))) @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))) @ 120.82/15.94 ( 120.82/15.94 cP @ 120.82/15.94 ( 120.82/15.94 '#sk16' @ 120.82/15.94 X2)))))))) @ 120.82/15.94 (X2 @ ('#sk14' @ X2)))))))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2) @ ('#sk16' @ X2)))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ cP)))))))))) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl113])). 120.82/15.94 thf(zip_derived_cl131, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#C') @ ((('#B') @ (((( 120.82/15.94 ('#sk5' @ 120.82/15.94 X2) = 120.82/15.94 (cP @ 120.82/15.94 ( 120.82/15.94 '#sk12' @ 120.82/15.94 X2) @ 120.82/15.94 ( 120.82/15.94 '#sk14' @ 120.82/15.94 X2)))) & 120.82/15.94 (( 120.82/15.94 ('#sk8' @ 120.82/15.94 X2) = 120.82/15.94 (cP @ 120.82/15.94 ( 120.82/15.94 '#sk16' @ 120.82/15.94 X2) @ 120.82/15.94 ( 120.82/15.94 '#sk18' @ 120.82/15.94 X2)))))) @ 120.82/15.94 (X2 @ 120.82/15.94 ('#sk14' @ X2) @ 120.82/15.94 ('#sk18' @ X2)))))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2) @ ('#sk16' @ X2)))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ cP)))))))) 120.82/15.94 | (('#sk5' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl122])). 120.82/15.94 thf(zip_derived_cl140, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#S') @ ((('#C') @ ((('#B') @ ((((('#sk5' @ X2) = (cP @ 120.82/15.94 ('#sk12' @ X2) @ 120.82/15.94 ('#sk14' @ X2)))) & 120.82/15.94 ((('#sk8' @ X2) = (cP @ 120.82/15.94 ('#sk16' @ X2) @ 120.82/15.94 ('#sk18' @ X2)))))) @ 120.82/15.94 (X2 @ ('#sk14' @ X2) @ 120.82/15.94 ('#sk18' @ X2)))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2) @ ('#sk16' @ X2) @ 120.82/15.94 ('#sk20' @ X2)))) @ 120.82/15.94 ((('#B') @ (((a) = ('#sk9' @ X2))) @ 120.82/15.94 (cP @ ('#sk20' @ X2)))))))) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl131])). 120.82/15.94 thf(zip_derived_cl165, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((((('#sk5' @ X2) = (cP @ ('#sk12' @ X2) @ ('#sk14' @ X2)))) & 120.82/15.94 ((('#sk8' @ X2) = (cP @ ('#sk16' @ X2) @ ('#sk18' @ X2)))) & 120.82/15.94 (X2 @ ('#sk14' @ X2) @ ('#sk18' @ X2) @ ('#sk21' @ X2)) & 120.82/15.94 (X2 @ ('#sk12' @ X2) @ ('#sk16' @ X2) @ ('#sk20' @ X2)) & 120.82/15.94 ((('#sk9' @ X2) = (cP @ ('#sk20' @ X2) @ ('#sk21' @ X2)))))) 120.82/15.94 | (('#sk5' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl140])). 120.82/15.94 thf(zip_derived_cl191, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((('#sk8' @ X2) = (cP @ ('#sk16' @ X2) @ ('#sk18' @ X2)))) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl165])). 120.82/15.94 thf(zip_derived_cl207, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk8' @ X2) = (cP @ ('#sk16' @ X2) @ ('#sk18' @ X2))) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], 120.82/15.94 [zip_derived_cl191])). 120.82/15.94 thf(zip_derived_cl26, plain, 120.82/15.94 ( (((!!) @ ((('#B') @ (!!) @ 120.82/15.94 ((('#B') @ ((('#B') @ (!!))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 |))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 =) @ cZ)))))))) @ 120.82/15.94 ( 120.82/15.94 =))))))))) @ 120.82/15.94 ((('#B') @ ((('#C') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 &) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 =) @ cZ)))))))) @ 120.82/15.94 (=))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ??))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ??))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ??))))))))))))))) @ 120.82/15.94 ((('#B') @ ((('#C') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 =))))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 '#sk1')))))))))))))) @ 120.82/15.94 '#sk1')))))))))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 =))))) @ 120.82/15.94 cP)))))))))))))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 (=))))) @ 120.82/15.94 cP)))))))))))))))))))))))) @ 120.82/15.94 '#sk1'))))))))), 120.82/15.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 120.82/15.94 thf(zip_derived_cl32, plain, 120.82/15.94 (![X2 : a]: 120.82/15.94 (((!!) @ ((('#B') @ (!!) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ (=>))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ (|))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ((&) @ ( 120.82/15.94 ((X2) = 120.82/15.94 (cZ))))))) @ 120.82/15.94 (=))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 &) @ 120.82/15.94 ((('#C') @ ( 120.82/15.94 =) @ cZ)))))) @ 120.82/15.94 (((a) = (X2))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ??))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ??))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 =))))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 '#sk1')))))))))))))) @ 120.82/15.94 '#sk1')))))))))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 =))))) @ 120.82/15.94 cP)))))))))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 ((a) = (X2))))) @ 120.82/15.94 cP)))))))))))))))))))))) @ 120.82/15.94 ('#sk1' @ X2)))))))), 120.82/15.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl26])). 120.82/15.94 thf(zip_derived_cl37, plain, 120.82/15.94 (![X2 : a, X4 : a]: 120.82/15.94 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 120.82/15.94 ((('#S') @ ((('#S') @ ((('#B') @ (|) @ 120.82/15.94 ((('#B') @ (((&) @ ( 120.82/15.94 ((X2) = 120.82/15.94 (cZ))))) @ 120.82/15.94 (((a) = (X4))))))) @ 120.82/15.94 ((('#B') @ (((&) @ (((X4) = (cZ))))) @ 120.82/15.94 (((a) = (X2))))))) @ 120.82/15.94 ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ??))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ??))))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ('#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))))))) @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#S') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 (X4))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 '#sk1')))))))))))) @ 120.82/15.94 '#sk1')))))))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 =))))) @ 120.82/15.94 cP)))))))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 ((a) = (X2))))) @ 120.82/15.94 cP)))))))))))))))))))) @ 120.82/15.94 ('#sk1' @ X2 @ X4)))))), 120.82/15.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 120.82/15.94 thf(zip_derived_cl46, plain, 120.82/15.94 (![X2 : a, X4 : a, X6 : a]: 120.82/15.94 (((((((((X2) = (cZ))) & (((X4) = (X6))))) | 120.82/15.94 (((((X4) = (cZ))) & (((X2) = (X6))))) | 120.82/15.94 (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ??))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ('#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#S') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 (X4))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 '#sk1')))))))))))) @ 120.82/15.94 '#sk1')))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 ((a) = 120.82/15.94 (X6))))) @ 120.82/15.94 cP)))))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = (X2))))) @ cP)))))))))))))))))) => 120.82/15.94 ('#sk1' @ X2 @ X4 @ X6)))), 120.82/15.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 120.82/15.94 thf(zip_derived_cl55, plain, 120.82/15.94 (![X2 : a, X4 : a, X6 : a]: 120.82/15.94 (~ (((((((X2) = (cZ))) & (((X4) = (X6))))) | 120.82/15.94 (((((X4) = (cZ))) & (((X2) = (X6))))) | 120.82/15.94 (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ??))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ('#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#S') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 (X4))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 '#sk1')))))))))))) @ 120.82/15.94 '#sk1')))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 ((a) = 120.82/15.94 (X6))))) @ 120.82/15.94 cP)))))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = (X2))))) @ cP)))))))))))))))))) 120.82/15.94 | ('#sk1' @ X2 @ X4 @ X6))), 120.82/15.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])). 120.82/15.94 thf(zip_derived_cl62, plain, 120.82/15.94 (![X2 : a, X4 : a, X6 : a]: 120.82/15.94 (~ (((((X4) = (cZ))) & (((X2) = (X6))))) | ('#sk1' @ X2 @ X4 @ X6))), 120.82/15.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl55])). 120.82/15.94 thf(zip_derived_cl75, plain, 120.82/15.94 (![X2 : a, X4 : a, X6 : a]: 120.82/15.94 (~ (((X4) = (cZ))) | ~ (((X2) = (X6))) | ('#sk1' @ X2 @ X4 @ X6))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl62])). 120.82/15.94 thf(zip_derived_cl92, plain, 120.82/15.94 (![X2 : a, X4 : a, X6 : a]: 120.82/15.94 (((X4) != (cZ)) | ((X2) != (X6)) | ('#sk1' @ X2 @ X4 @ X6))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], [zip_derived_cl75])). 120.82/15.94 thf(zip_derived_cl72, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((('#sk5' @ X2) = (cZ))) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | ((((('#sk5' @ X2) = ('#sk9' @ X2))) & ((('#sk8' @ X2) = (cZ))))) 120.82/15.94 | (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ('#S'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk5' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))))))))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl60])). 120.82/15.94 thf(zip_derived_cl85, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk5' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | ((((('#sk5' @ X2) = ('#sk9' @ X2))) & ((('#sk8' @ X2) = (cZ))))) 120.82/15.94 | (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ('#S'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk5' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))))))))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], [zip_derived_cl72])). 120.82/15.94 thf(zip_derived_cl86, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((('#sk5' @ X2) = ('#sk9' @ X2))) 120.82/15.94 | (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ('#S'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk5' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))))))) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl85])). 120.82/15.94 thf(zip_derived_cl98, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk5' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ('#S'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk5' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))))))) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = (cZ)))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], [zip_derived_cl86])). 120.82/15.94 thf(zip_derived_cl99, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#B'))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#S') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk5' @ 120.82/15.94 X2))) @ 120.82/15.94 ( 120.82/15.94 cP @ 120.82/15.94 ( 120.82/15.94 '#sk12' @ 120.82/15.94 X2)))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 X2)))))))))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))))) 120.82/15.94 | (('#sk5' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl98])). 120.82/15.94 thf(zip_derived_cl111, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ((('#C') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ((&) @ ( 120.82/15.94 (('#sk5' @ 120.82/15.94 X2) = 120.82/15.94 (cP @ 120.82/15.94 ( 120.82/15.94 '#sk12' @ 120.82/15.94 X2) @ 120.82/15.94 ( 120.82/15.94 '#sk14' @ 120.82/15.94 X2)))))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))) @ 120.82/15.94 (X2 @ 120.82/15.94 ('#sk14' @ X2)))))))))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2)))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))) 120.82/15.94 | (('#sk5' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl99])). 120.82/15.94 thf(zip_derived_cl120, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#B') @ 120.82/15.94 ((('#B') @ ('#C') @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ((&) @ ( 120.82/15.94 ( 120.82/15.94 ('#sk5' @ 120.82/15.94 X2) = 120.82/15.94 (cP @ 120.82/15.94 ( 120.82/15.94 '#sk12' @ 120.82/15.94 X2) @ 120.82/15.94 ( 120.82/15.94 '#sk14' @ 120.82/15.94 X2)))))) @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))) @ 120.82/15.94 ( 120.82/15.94 cP @ 120.82/15.94 ( 120.82/15.94 '#sk16' @ 120.82/15.94 X2)))))))) @ 120.82/15.94 (X2 @ ('#sk14' @ X2)))))))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2) @ ('#sk16' @ X2)))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ cP)))))))))) 120.82/15.94 | (('#sk5' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl111])). 120.82/15.94 thf(zip_derived_cl129, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#C') @ ((('#B') @ (((( 120.82/15.94 ('#sk5' @ 120.82/15.94 X2) = 120.82/15.94 (cP @ 120.82/15.94 ( 120.82/15.94 '#sk12' @ 120.82/15.94 X2) @ 120.82/15.94 ( 120.82/15.94 '#sk14' @ 120.82/15.94 X2)))) & 120.82/15.94 (( 120.82/15.94 ('#sk8' @ 120.82/15.94 X2) = 120.82/15.94 (cP @ 120.82/15.94 ( 120.82/15.94 '#sk16' @ 120.82/15.94 X2) @ 120.82/15.94 ( 120.82/15.94 '#sk18' @ 120.82/15.94 X2)))))) @ 120.82/15.94 (X2 @ 120.82/15.94 ('#sk14' @ X2) @ 120.82/15.94 ('#sk18' @ X2)))))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2) @ ('#sk16' @ X2)))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ cP)))))))) 120.82/15.94 | (('#sk5' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl120])). 120.82/15.94 thf(zip_derived_cl138, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#S') @ ((('#C') @ ((('#B') @ ((((('#sk5' @ X2) = (cP @ 120.82/15.94 ('#sk12' @ X2) @ 120.82/15.94 ('#sk14' @ X2)))) & 120.82/15.94 ((('#sk8' @ X2) = (cP @ 120.82/15.94 ('#sk16' @ X2) @ 120.82/15.94 ('#sk18' @ X2)))))) @ 120.82/15.94 (X2 @ ('#sk14' @ X2) @ 120.82/15.94 ('#sk18' @ X2)))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2) @ ('#sk16' @ X2) @ 120.82/15.94 ('#sk20' @ X2)))) @ 120.82/15.94 ((('#B') @ (((a) = ('#sk9' @ X2))) @ 120.82/15.94 (cP @ ('#sk20' @ X2)))))))) 120.82/15.94 | (('#sk5' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl129])). 120.82/15.94 thf(zip_derived_cl163, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((((('#sk5' @ X2) = (cP @ ('#sk12' @ X2) @ ('#sk14' @ X2)))) & 120.82/15.94 ((('#sk8' @ X2) = (cP @ ('#sk16' @ X2) @ ('#sk18' @ X2)))) & 120.82/15.94 (X2 @ ('#sk14' @ X2) @ ('#sk18' @ X2) @ ('#sk21' @ X2)) & 120.82/15.94 (X2 @ ('#sk12' @ X2) @ ('#sk16' @ X2) @ ('#sk20' @ X2)) & 120.82/15.94 ((('#sk9' @ X2) = (cP @ ('#sk20' @ X2) @ ('#sk21' @ X2)))))) 120.82/15.94 | (('#sk5' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl138])). 120.82/15.94 thf(zip_derived_cl181, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((('#sk8' @ X2) = (cP @ ('#sk16' @ X2) @ ('#sk18' @ X2)))) 120.82/15.94 | (('#sk5' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl163])). 120.82/15.94 thf(zip_derived_cl201, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk8' @ X2) = (cP @ ('#sk16' @ X2) @ ('#sk18' @ X2))) 120.82/15.94 | (('#sk5' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], 120.82/15.94 [zip_derived_cl181])). 120.82/15.94 thf(zip_derived_cl67, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((('#sk4' @ X2) = (cZ))) 120.82/15.94 | (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ('#C'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk7' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 ((a) = 120.82/15.94 ('#sk4' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk2' @ X2))))) @ 120.82/15.94 cP)))))))))))))))) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = ('#sk7' @ X2)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl66])). 120.82/15.94 thf(zip_derived_cl77, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk4' @ X2) = (cZ)) 120.82/15.94 | (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ('#C'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk7' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 ((a) = 120.82/15.94 ('#sk4' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk2' @ X2))))) @ 120.82/15.94 cP)))))))))))))))) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = ('#sk7' @ X2)))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], [zip_derived_cl67])). 120.82/15.94 thf(zip_derived_cl78, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ('#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ((('#C') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk7' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 X2)))))))))) @ 120.82/15.94 (X2 @ 120.82/15.94 ('#sk10' @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 ((a) = ('#sk4' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 ((('#B') @ (((a) = ('#sk2' @ X2))) @ 120.82/15.94 (cP @ ('#sk10' @ X2)))))))))))))))) 120.82/15.94 | (('#sk4' @ X2) = ('#sk7' @ X2)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl77])). 120.82/15.94 thf(zip_derived_cl94, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#C') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#C') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk7' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))) @ 120.82/15.94 (X2 @ 120.82/15.94 ('#sk11' @ 120.82/15.94 X2)))))))))) @ 120.82/15.94 (X2 @ 120.82/15.94 ('#sk10' @ X2)))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = 120.82/15.94 ('#sk4' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ 120.82/15.94 ('#sk11' @ X2)))))))))))))) 120.82/15.94 | (('#sk4' @ X2) = (cZ)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = ('#sk7' @ X2)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl78])). 120.82/15.94 thf(zip_derived_cl107, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk7' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))) @ 120.82/15.94 ( 120.82/15.94 X2 @ 120.82/15.94 ( 120.82/15.94 '#sk11' @ 120.82/15.94 X2)))))))) @ 120.82/15.94 (X2 @ ('#sk10' @ X2) @ 120.82/15.94 ('#sk13' @ X2)))))))) @ 120.82/15.94 ((('#B') @ (((a) = ('#sk4' @ X2))) @ 120.82/15.94 (cP @ ('#sk13' @ X2)))))))))) @ 120.82/15.94 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ 120.82/15.94 ('#sk11' @ X2)))))))))))) 120.82/15.94 | (('#sk4' @ X2) = ('#sk7' @ X2)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl94])). 120.82/15.94 thf(zip_derived_cl116, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#C') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ (&))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ((a) = 120.82/15.94 ('#sk7' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))) @ 120.82/15.94 (X2 @ 120.82/15.94 ('#sk11' @ X2) @ 120.82/15.94 ('#sk15' @ X2)))))) @ 120.82/15.94 (X2 @ ('#sk10' @ X2) @ 120.82/15.94 ('#sk13' @ X2)))))) @ 120.82/15.94 ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ 120.82/15.94 ('#sk15' @ X2)))))))) @ 120.82/15.94 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ 120.82/15.94 ('#sk11' @ X2)))))))))) 120.82/15.94 | (('#sk4' @ X2) = (cZ)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = ('#sk7' @ X2)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl107])). 120.82/15.94 thf(zip_derived_cl125, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#C') @ ((('#C') @ ((('#C') @ ((('#S') @ ((('#B') @ ( 120.82/15.94 &) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ((a) = 120.82/15.94 ('#sk7' @ 120.82/15.94 X2))) @ 120.82/15.94 (cP @ 120.82/15.94 ('#sk17' @ 120.82/15.94 X2)))))) @ 120.82/15.94 (X2 @ ('#sk11' @ X2) @ 120.82/15.94 ('#sk15' @ X2)))) @ 120.82/15.94 (X2 @ ('#sk10' @ X2) @ 120.82/15.94 ('#sk13' @ X2) @ ('#sk17' @ X2)))) @ 120.82/15.94 ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ 120.82/15.94 ('#sk15' @ X2)))))) @ 120.82/15.94 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ ('#sk11' @ X2)))))))) 120.82/15.94 | (('#sk4' @ X2) = ('#sk7' @ X2)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl116])). 120.82/15.94 thf(zip_derived_cl134, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((((('#sk7' @ X2) = (cP @ ('#sk17' @ X2) @ ('#sk19' @ X2)))) & 120.82/15.94 (X2 @ ('#sk11' @ X2) @ ('#sk15' @ X2) @ ('#sk19' @ X2)) & 120.82/15.94 (X2 @ ('#sk10' @ X2) @ ('#sk13' @ X2) @ ('#sk17' @ X2)) & 120.82/15.94 ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ ('#sk15' @ X2)))) & 120.82/15.94 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ ('#sk11' @ X2)))))) 120.82/15.94 | (('#sk4' @ X2) = (cZ)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = ('#sk7' @ X2)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl125])). 120.82/15.94 thf(zip_derived_cl147, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ ('#sk11' @ X2)))) 120.82/15.94 | (('#sk4' @ X2) = ('#sk7' @ X2)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl134])). 120.82/15.94 thf(zip_derived_cl170, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ ('#sk11' @ X2))) 120.82/15.94 | (('#sk4' @ X2) = ('#sk7' @ X2)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = (cZ)))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], 120.82/15.94 [zip_derived_cl147])). 120.82/15.94 thf(zip_derived_cl70, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((('#sk4' @ X2) = (cZ))) 120.82/15.94 | (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ('#C'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk7' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 ((a) = 120.82/15.94 ('#sk4' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk2' @ X2))))) @ 120.82/15.94 cP)))))))))))))))) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk2' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 120.82/15.94 thf(zip_derived_cl81, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk4' @ X2) = (cZ)) 120.82/15.94 | (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ('#C'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk7' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 ((a) = 120.82/15.94 ('#sk4' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk2' @ X2))))) @ 120.82/15.94 cP)))))))))))))))) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk2' @ X2) = (cZ)))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], [zip_derived_cl70])). 120.82/15.94 thf(zip_derived_cl82, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ('#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ((('#C') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk7' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 X2)))))))))) @ 120.82/15.94 (X2 @ 120.82/15.94 ('#sk10' @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 ((a) = ('#sk4' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 ((('#B') @ (((a) = ('#sk2' @ X2))) @ 120.82/15.94 (cP @ ('#sk10' @ X2)))))))))))))))) 120.82/15.94 | (('#sk2' @ X2) = (cZ)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl81])). 120.82/15.94 thf(zip_derived_cl96, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#C') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#C') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk7' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))) @ 120.82/15.94 (X2 @ 120.82/15.94 ('#sk11' @ 120.82/15.94 X2)))))))))) @ 120.82/15.94 (X2 @ 120.82/15.94 ('#sk10' @ X2)))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = 120.82/15.94 ('#sk4' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ 120.82/15.94 ('#sk11' @ X2)))))))))))))) 120.82/15.94 | (('#sk4' @ X2) = (cZ)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk2' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl82])). 120.82/15.94 thf(zip_derived_cl109, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk7' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))) @ 120.82/15.94 ( 120.82/15.94 X2 @ 120.82/15.94 ( 120.82/15.94 '#sk11' @ 120.82/15.94 X2)))))))) @ 120.82/15.94 (X2 @ ('#sk10' @ X2) @ 120.82/15.94 ('#sk13' @ X2)))))))) @ 120.82/15.94 ((('#B') @ (((a) = ('#sk4' @ X2))) @ 120.82/15.94 (cP @ ('#sk13' @ X2)))))))))) @ 120.82/15.94 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ 120.82/15.94 ('#sk11' @ X2)))))))))))) 120.82/15.94 | (('#sk2' @ X2) = (cZ)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 120.82/15.94 thf(zip_derived_cl118, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#C') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ (&))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ((a) = 120.82/15.94 ('#sk7' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))) @ 120.82/15.94 (X2 @ 120.82/15.94 ('#sk11' @ X2) @ 120.82/15.94 ('#sk15' @ X2)))))) @ 120.82/15.94 (X2 @ ('#sk10' @ X2) @ 120.82/15.94 ('#sk13' @ X2)))))) @ 120.82/15.94 ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ 120.82/15.94 ('#sk15' @ X2)))))))) @ 120.82/15.94 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ 120.82/15.94 ('#sk11' @ X2)))))))))) 120.82/15.94 | (('#sk4' @ X2) = (cZ)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk2' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl109])). 120.82/15.94 thf(zip_derived_cl127, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#C') @ ((('#C') @ ((('#C') @ ((('#S') @ ((('#B') @ ( 120.82/15.94 &) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ((a) = 120.82/15.94 ('#sk7' @ 120.82/15.94 X2))) @ 120.82/15.94 (cP @ 120.82/15.94 ('#sk17' @ 120.82/15.94 X2)))))) @ 120.82/15.94 (X2 @ ('#sk11' @ X2) @ 120.82/15.94 ('#sk15' @ X2)))) @ 120.82/15.94 (X2 @ ('#sk10' @ X2) @ 120.82/15.94 ('#sk13' @ X2) @ ('#sk17' @ X2)))) @ 120.82/15.94 ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ 120.82/15.94 ('#sk15' @ X2)))))) @ 120.82/15.94 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ ('#sk11' @ X2)))))))) 120.82/15.94 | (('#sk2' @ X2) = (cZ)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl118])). 120.82/15.94 thf(zip_derived_cl136, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((((('#sk7' @ X2) = (cP @ ('#sk17' @ X2) @ ('#sk19' @ X2)))) & 120.82/15.94 (X2 @ ('#sk11' @ X2) @ ('#sk15' @ X2) @ ('#sk19' @ X2)) & 120.82/15.94 (X2 @ ('#sk10' @ X2) @ ('#sk13' @ X2) @ ('#sk17' @ X2)) & 120.82/15.94 ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ ('#sk15' @ X2)))) & 120.82/15.94 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ ('#sk11' @ X2)))))) 120.82/15.94 | (('#sk4' @ X2) = (cZ)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk2' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl127])). 120.82/15.94 thf(zip_derived_cl157, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ ('#sk11' @ X2)))) 120.82/15.94 | (('#sk2' @ X2) = (cZ)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl136])). 120.82/15.94 thf(zip_derived_cl176, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk2' @ X2) = (cP @ ('#sk10' @ X2) @ ('#sk11' @ X2))) 120.82/15.94 | (('#sk2' @ X2) = (cZ)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = (cZ)))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], 120.82/15.94 [zip_derived_cl157])). 120.82/15.94 thf(zip_derived_cl61, plain, 120.82/15.94 (![X2 : a, X4 : a, X6 : a]: 120.82/15.94 (~ (((((X2) = (cZ))) & (((X4) = (X6))))) | ('#sk1' @ X2 @ X4 @ X6))), 120.82/15.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl55])). 120.82/15.94 thf(zip_derived_cl74, plain, 120.82/15.94 (![X2 : a, X4 : a, X6 : a]: 120.82/15.94 (~ (((X2) = (cZ))) | ~ (((X4) = (X6))) | ('#sk1' @ X2 @ X4 @ X6))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl61])). 120.82/15.94 thf(zip_derived_cl91, plain, 120.82/15.94 (![X2 : a, X4 : a, X6 : a]: 120.82/15.94 (((X2) != (cZ)) | ((X4) != (X6)) | ('#sk1' @ X2 @ X4 @ X6))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], [zip_derived_cl74])). 120.82/15.94 thf(zip_derived_cl44, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 (~ (X2 @ ('#sk2' @ X2) @ ('#sk4' @ X2) @ ('#sk7' @ X2)) 120.82/15.94 | (X2 @ x @ u @ u))), 120.82/15.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 120.82/15.94 thf(zip_derived_cl156, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ ('#sk15' @ X2)))) 120.82/15.94 | (('#sk2' @ X2) = (cZ)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl136])). 120.82/15.94 thf(zip_derived_cl175, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk4' @ X2) = (cP @ ('#sk13' @ X2) @ ('#sk15' @ X2))) 120.82/15.94 | (('#sk2' @ X2) = (cZ)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = (cZ)))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], 120.82/15.94 [zip_derived_cl156])). 120.82/15.94 thf(zip_derived_cl153, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((('#sk7' @ X2) = (cP @ ('#sk17' @ X2) @ ('#sk19' @ X2)))) 120.82/15.94 | (('#sk2' @ X2) = (cZ)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl136])). 120.82/15.94 thf(zip_derived_cl174, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk7' @ X2) = (cP @ ('#sk17' @ X2) @ ('#sk19' @ X2))) 120.82/15.94 | (('#sk2' @ X2) = (cZ)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = (cZ)))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], 120.82/15.94 [zip_derived_cl153])). 120.82/15.94 thf(zip_derived_cl87, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((('#sk8' @ X2) = (cZ))) 120.82/15.94 | (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ('#S'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk5' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))))))) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl85])). 120.82/15.94 thf(zip_derived_cl100, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk8' @ X2) = (cZ)) 120.82/15.94 | (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ('#S'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk5' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))))))) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = (cZ)))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], [zip_derived_cl87])). 120.82/15.94 thf(zip_derived_cl101, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#B'))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#S') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk5' @ 120.82/15.94 X2))) @ 120.82/15.94 ( 120.82/15.94 cP @ 120.82/15.94 ( 120.82/15.94 '#sk12' @ 120.82/15.94 X2)))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 X2)))))))))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))))) 120.82/15.94 | (('#sk5' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl100])). 120.82/15.94 thf(zip_derived_cl112, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ((('#C') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ((&) @ ( 120.82/15.94 (('#sk5' @ 120.82/15.94 X2) = 120.82/15.94 (cP @ 120.82/15.94 ( 120.82/15.94 '#sk12' @ 120.82/15.94 X2) @ 120.82/15.94 ( 120.82/15.94 '#sk14' @ 120.82/15.94 X2)))))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))) @ 120.82/15.94 (X2 @ 120.82/15.94 ('#sk14' @ X2)))))))))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2)))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))) 120.82/15.94 | (('#sk8' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl101])). 120.82/15.94 thf(zip_derived_cl121, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#B') @ 120.82/15.94 ((('#B') @ ('#C') @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ((&) @ ( 120.82/15.94 ( 120.82/15.94 ('#sk5' @ 120.82/15.94 X2) = 120.82/15.94 (cP @ 120.82/15.94 ( 120.82/15.94 '#sk12' @ 120.82/15.94 X2) @ 120.82/15.94 ( 120.82/15.94 '#sk14' @ 120.82/15.94 X2)))))) @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))) @ 120.82/15.94 ( 120.82/15.94 cP @ 120.82/15.94 ( 120.82/15.94 '#sk16' @ 120.82/15.94 X2)))))))) @ 120.82/15.94 (X2 @ ('#sk14' @ X2)))))))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2) @ ('#sk16' @ X2)))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ cP)))))))))) 120.82/15.94 | (('#sk5' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl112])). 120.82/15.94 thf(zip_derived_cl130, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#C') @ ((('#B') @ (((( 120.82/15.94 ('#sk5' @ 120.82/15.94 X2) = 120.82/15.94 (cP @ 120.82/15.94 ( 120.82/15.94 '#sk12' @ 120.82/15.94 X2) @ 120.82/15.94 ( 120.82/15.94 '#sk14' @ 120.82/15.94 X2)))) & 120.82/15.94 (( 120.82/15.94 ('#sk8' @ 120.82/15.94 X2) = 120.82/15.94 (cP @ 120.82/15.94 ( 120.82/15.94 '#sk16' @ 120.82/15.94 X2) @ 120.82/15.94 ( 120.82/15.94 '#sk18' @ 120.82/15.94 X2)))))) @ 120.82/15.94 (X2 @ 120.82/15.94 ('#sk14' @ X2) @ 120.82/15.94 ('#sk18' @ X2)))))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2) @ ('#sk16' @ X2)))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ cP)))))))) 120.82/15.94 | (('#sk8' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl121])). 120.82/15.94 thf(zip_derived_cl139, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#S') @ ((('#C') @ ((('#B') @ ((((('#sk5' @ X2) = (cP @ 120.82/15.94 ('#sk12' @ X2) @ 120.82/15.94 ('#sk14' @ X2)))) & 120.82/15.94 ((('#sk8' @ X2) = (cP @ 120.82/15.94 ('#sk16' @ X2) @ 120.82/15.94 ('#sk18' @ X2)))))) @ 120.82/15.94 (X2 @ ('#sk14' @ X2) @ 120.82/15.94 ('#sk18' @ X2)))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2) @ ('#sk16' @ X2) @ 120.82/15.94 ('#sk20' @ X2)))) @ 120.82/15.94 ((('#B') @ (((a) = ('#sk9' @ X2))) @ 120.82/15.94 (cP @ ('#sk20' @ X2)))))))) 120.82/15.94 | (('#sk5' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl130])). 120.82/15.94 thf(zip_derived_cl164, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((((('#sk5' @ X2) = (cP @ ('#sk12' @ X2) @ ('#sk14' @ X2)))) & 120.82/15.94 ((('#sk8' @ X2) = (cP @ ('#sk16' @ X2) @ ('#sk18' @ X2)))) & 120.82/15.94 (X2 @ ('#sk14' @ X2) @ ('#sk18' @ X2) @ ('#sk21' @ X2)) & 120.82/15.94 (X2 @ ('#sk12' @ X2) @ ('#sk16' @ X2) @ ('#sk20' @ X2)) & 120.82/15.94 ((('#sk9' @ X2) = (cP @ ('#sk20' @ X2) @ ('#sk21' @ X2)))))) 120.82/15.94 | (('#sk8' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk5' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl139])). 120.82/15.94 thf(zip_derived_cl185, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((('#sk5' @ X2) = (cP @ ('#sk12' @ X2) @ ('#sk14' @ X2)))) 120.82/15.94 | (('#sk5' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl164])). 120.82/15.94 thf(zip_derived_cl203, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk5' @ X2) = (cP @ ('#sk12' @ X2) @ ('#sk14' @ X2))) 120.82/15.94 | (('#sk5' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = (cZ)))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], 120.82/15.94 [zip_derived_cl185])). 120.82/15.94 thf(zip_derived_cl90, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((('#sk8' @ X2) = (cZ))) 120.82/15.94 | (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ('#S'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk5' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))))))) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl88])). 120.82/15.94 thf(zip_derived_cl104, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk8' @ X2) = (cZ)) 120.82/15.94 | (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ('#S'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk5' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))))))) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], [zip_derived_cl90])). 120.82/15.94 thf(zip_derived_cl105, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#B'))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#S') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk5' @ 120.82/15.94 X2))) @ 120.82/15.94 ( 120.82/15.94 cP @ 120.82/15.94 ( 120.82/15.94 '#sk12' @ 120.82/15.94 X2)))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 X2)))))))))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2)))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))))) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl104])). 120.82/15.94 thf(zip_derived_cl114, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ((('#B') @ (( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ((('#C') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ((&) @ ( 120.82/15.94 (('#sk5' @ 120.82/15.94 X2) = 120.82/15.94 (cP @ 120.82/15.94 ( 120.82/15.94 '#sk12' @ 120.82/15.94 X2) @ 120.82/15.94 ( 120.82/15.94 '#sk14' @ 120.82/15.94 X2)))))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))))) @ 120.82/15.94 cP)))))))) @ 120.82/15.94 (X2 @ 120.82/15.94 ('#sk14' @ X2)))))))))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2)))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ 120.82/15.94 cP)))))))))))) 120.82/15.94 | (('#sk8' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl105])). 120.82/15.94 thf(zip_derived_cl123, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#B') @ 120.82/15.94 ((('#B') @ ('#C') @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ((&) @ ( 120.82/15.94 ( 120.82/15.94 ('#sk5' @ 120.82/15.94 X2) = 120.82/15.94 (cP @ 120.82/15.94 ( 120.82/15.94 '#sk12' @ 120.82/15.94 X2) @ 120.82/15.94 ( 120.82/15.94 '#sk14' @ 120.82/15.94 X2)))))) @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 ('#sk8' @ 120.82/15.94 X2))) @ 120.82/15.94 ( 120.82/15.94 cP @ 120.82/15.94 ( 120.82/15.94 '#sk16' @ 120.82/15.94 X2)))))))) @ 120.82/15.94 (X2 @ ('#sk14' @ X2)))))))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2) @ ('#sk16' @ X2)))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ cP)))))))))) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl114])). 120.82/15.94 thf(zip_derived_cl132, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#C') @ ((('#B') @ (((( 120.82/15.94 ('#sk5' @ 120.82/15.94 X2) = 120.82/15.94 (cP @ 120.82/15.94 ( 120.82/15.94 '#sk12' @ 120.82/15.94 X2) @ 120.82/15.94 ( 120.82/15.94 '#sk14' @ 120.82/15.94 X2)))) & 120.82/15.94 (( 120.82/15.94 ('#sk8' @ 120.82/15.94 X2) = 120.82/15.94 (cP @ 120.82/15.94 ( 120.82/15.94 '#sk16' @ 120.82/15.94 X2) @ 120.82/15.94 ( 120.82/15.94 '#sk18' @ 120.82/15.94 X2)))))) @ 120.82/15.94 (X2 @ 120.82/15.94 ('#sk14' @ X2) @ 120.82/15.94 ('#sk18' @ X2)))))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2) @ ('#sk16' @ X2)))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = ('#sk9' @ X2))))) @ cP)))))))) 120.82/15.94 | (('#sk8' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl123])). 120.82/15.94 thf(zip_derived_cl141, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (((??) @ ((('#S') @ ((('#C') @ ((('#B') @ ((((('#sk5' @ X2) = (cP @ 120.82/15.94 ('#sk12' @ X2) @ 120.82/15.94 ('#sk14' @ X2)))) & 120.82/15.94 ((('#sk8' @ X2) = (cP @ 120.82/15.94 ('#sk16' @ X2) @ 120.82/15.94 ('#sk18' @ X2)))))) @ 120.82/15.94 (X2 @ ('#sk14' @ X2) @ 120.82/15.94 ('#sk18' @ X2)))) @ 120.82/15.94 (X2 @ ('#sk12' @ X2) @ ('#sk16' @ X2) @ 120.82/15.94 ('#sk20' @ X2)))) @ 120.82/15.94 ((('#B') @ (((a) = ('#sk9' @ X2))) @ 120.82/15.94 (cP @ ('#sk20' @ X2)))))))) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl132])). 120.82/15.94 thf(zip_derived_cl166, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((((('#sk5' @ X2) = (cP @ ('#sk12' @ X2) @ ('#sk14' @ X2)))) & 120.82/15.94 ((('#sk8' @ X2) = (cP @ ('#sk16' @ X2) @ ('#sk18' @ X2)))) & 120.82/15.94 (X2 @ ('#sk14' @ X2) @ ('#sk18' @ X2) @ ('#sk21' @ X2)) & 120.82/15.94 (X2 @ ('#sk12' @ X2) @ ('#sk16' @ X2) @ ('#sk20' @ X2)) & 120.82/15.94 ((('#sk9' @ X2) = (cP @ ('#sk20' @ X2) @ ('#sk21' @ X2)))))) 120.82/15.94 | (('#sk8' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)))), 120.82/15.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl141])). 120.82/15.94 thf(zip_derived_cl195, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((('#sk5' @ X2) = (cP @ ('#sk12' @ X2) @ ('#sk14' @ X2)))) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl166])). 120.82/15.94 thf(zip_derived_cl209, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk5' @ X2) = (cP @ ('#sk12' @ X2) @ ('#sk14' @ X2))) 120.82/15.94 | (('#sk8' @ X2) = ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = (cZ)))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], 120.82/15.94 [zip_derived_cl195])). 120.82/15.94 thf(zip_derived_cl2, plain, 120.82/15.94 ( (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ 120.82/15.94 ((('#S') @ ((('#B') @ (&) @ 120.82/15.94 ((('#C') @ ('#I') @ cZ)))) @ 120.82/15.94 ((('#B') @ (!!) @ 120.82/15.94 ((('#B') @ ((('#B') @ (!!))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 =>))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))))))) @ 120.82/15.94 ('#I'))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#B') @ ('#B'))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 (!!))))) & 120.82/15.94 (((!!) @ ((('#B') @ (!!) @ 120.82/15.94 ((('#B') @ ((('#B') @ (!!))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#S'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ('#S'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 =>))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#B') @ 120.82/15.94 ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ('#B'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ (=))) @ 120.82/15.94 cP)))))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#C') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ (&))) @ 120.82/15.94 (=))))))))) @ 120.82/15.94 (=))))))))))))) & 120.82/15.94 (((!!) @ ((('#B') @ (!!) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ (!=))) @ cP)))) @ 120.82/15.94 cZ))))))))), 120.82/15.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 120.82/15.94 thf(zip_derived_cl6, plain, 120.82/15.94 ( (((!!) @ ((('#B') @ (!!) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ (!=))) @ cP)))) @ 120.82/15.94 cZ))))))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2])). 120.82/15.94 thf(zip_derived_cl11, plain, 120.82/15.94 (![X2 : a]: (((!!) @ ((('#C') @ ((('#B') @ (!=) @ (cP @ X2))) @ cZ))))), 120.82/15.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 120.82/15.94 thf(zip_derived_cl17, plain, 120.82/15.94 (![X2 : a, X4 : a]: (((cP @ X2 @ X4) != (cZ)))), 120.82/15.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl11])). 120.82/15.94 thf(zip_derived_cl23, plain, (![X2 : a, X4 : a]: ((cP @ X2 @ X4) != (cZ))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], [zip_derived_cl17])). 120.82/15.94 thf(zip_derived_cl155, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (X2 @ ('#sk10' @ X2) @ ('#sk13' @ X2) @ ('#sk17' @ X2)) 120.82/15.94 | (('#sk2' @ X2) = (cZ)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl136])). 120.82/15.94 thf(zip_derived_cl54, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 (~ (X2 @ ('#sk5' @ X2) @ ('#sk8' @ X2) @ ('#sk9' @ X2)) 120.82/15.94 | (X2 @ y @ v @ v))), 120.82/15.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 120.82/15.94 thf(zip_derived_cl186, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((('#sk8' @ X2) = (cP @ ('#sk16' @ X2) @ ('#sk18' @ X2)))) 120.82/15.94 | (('#sk5' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl164])). 120.82/15.94 thf(zip_derived_cl204, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk8' @ X2) = (cP @ ('#sk16' @ X2) @ ('#sk18' @ X2))) 120.82/15.94 | (('#sk5' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = (cZ)))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], 120.82/15.94 [zip_derived_cl186])). 120.82/15.94 thf(zip_derived_cl154, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (X2 @ ('#sk11' @ X2) @ ('#sk15' @ X2) @ ('#sk19' @ X2)) 120.82/15.94 | (('#sk2' @ X2) = (cZ)) 120.82/15.94 | (X2 @ x @ u @ u) 120.82/15.94 | (('#sk4' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl136])). 120.82/15.94 thf(zip_derived_cl189, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( ((('#sk9' @ X2) = (cP @ ('#sk20' @ X2) @ ('#sk21' @ X2)))) 120.82/15.94 | (('#sk5' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl164])). 120.82/15.94 thf(zip_derived_cl205, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ((('#sk9' @ X2) = (cP @ ('#sk20' @ X2) @ ('#sk21' @ X2))) 120.82/15.94 | (('#sk5' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = (cZ)))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], 120.82/15.94 [zip_derived_cl189])). 120.82/15.94 thf(zip_derived_cl188, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (X2 @ ('#sk12' @ X2) @ ('#sk16' @ X2) @ ('#sk20' @ X2)) 120.82/15.94 | (('#sk5' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl164])). 120.82/15.94 thf(zip_derived_cl187, plain, 120.82/15.94 (![X2 : a > a > a > $o]: 120.82/15.94 ( (X2 @ ('#sk14' @ X2) @ ('#sk18' @ X2) @ ('#sk21' @ X2)) 120.82/15.94 | (('#sk5' @ X2) = (cZ)) 120.82/15.94 | (X2 @ y @ v @ v) 120.82/15.94 | (('#sk8' @ X2) = (cZ)))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl164])). 120.82/15.94 thf(zip_derived_cl63, plain, 120.82/15.94 (![X2 : a, X4 : a, X6 : a]: 120.82/15.94 (~ (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ (??))))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ('#C'))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 (( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#S') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 (X4))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 '#sk1')))))))))))) @ 120.82/15.94 '#sk1')))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 ((a) = (X6))))) @ 120.82/15.94 cP)))))))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = (X2))))) @ cP)))))))))))))))) 120.82/15.94 | ('#sk1' @ X2 @ X4 @ X6))), 120.82/15.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl55])). 120.82/15.94 thf(zip_derived_cl76, plain, 120.82/15.94 (![X2 : a, X4 : a, X6 : a, X8 : a]: 120.82/15.94 (~ (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (??))))))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S'))))))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#S') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 (X4))))) @ 120.82/15.94 cP)))))))) @ 120.82/15.94 ( 120.82/15.94 '#sk1' @ 120.82/15.94 X8))))))))))) @ 120.82/15.94 '#sk1')))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 ((a) = (X6))))) @ 120.82/15.94 cP)))))))))))) @ 120.82/15.94 ((('#B') @ (((a) = (X2))) @ (cP @ X8))))))))))))))) 120.82/15.94 | ('#sk1' @ X2 @ X4 @ X6))), 120.82/15.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 120.82/15.94 thf(zip_derived_cl93, plain, 120.82/15.94 (![X2 : a, X4 : a, X6 : a, X8 : a, X10 : a]: 120.82/15.94 (~ (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ (??))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#B') @ ((('#B') @ ((('#B') @ ( 120.82/15.94 '#C'))))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ('#S'))))) @ 120.82/15.94 ((('#C') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#S') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#C'))) @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 (('#B') @ ( 120.82/15.94 '#B'))))) @ 120.82/15.94 ((('#S') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 (X4))))) @ 120.82/15.94 cP)))))))) @ 120.82/15.94 ( 120.82/15.94 '#sk1' @ 120.82/15.94 X8))))))))) @ 120.82/15.94 ('#sk1' @ X10))))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = 120.82/15.94 (X6))))) @ 120.82/15.94 cP)))))))))) @ 120.82/15.94 (((X2) = (cP @ X8 @ X10))))))))))))) 120.82/15.94 | ('#sk1' @ X2 @ X4 @ X6))), 120.82/15.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl76])). 120.82/15.94 thf(zip_derived_cl106, plain, 120.82/15.94 (![X2 : a, X4 : a, X6 : a, X8 : a, X10 : a, X12 : a]: 120.82/15.94 (~ (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#B') @ ((('#B') @ (??))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#B') @ ((('#B') @ ('#C'))) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#B') @ ((('#B') @ ( 120.82/15.94 '#S'))) @ 120.82/15.94 ((('#S') @ ((('#B') @ ( 120.82/15.94 '#C') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B'))) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#C') @ ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 &) @ 120.82/15.94 ( 120.82/15.94 ( 120.82/15.94 ('#B') @ ( 120.82/15.94 ( 120.82/15.94 (a) = 120.82/15.94 (X4))) @ 120.82/15.94 ( 120.82/15.94 cP @ X12))))))) @ 120.82/15.94 ( 120.82/15.94 '#sk1' @ 120.82/15.94 X8 @ X12))))))) @ 120.82/15.94 ('#sk1' @ X10))))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = (X6))))) @ 120.82/15.94 cP)))))))) @ 120.82/15.94 (((X2) = (cP @ X8 @ X10))))))))))) 120.82/15.94 | ('#sk1' @ X2 @ X4 @ X6))), 120.82/15.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl93])). 120.82/15.94 thf(zip_derived_cl115, plain, 120.82/15.94 (![X2 : a, X4 : a, X6 : a, X8 : a, X10 : a, X12 : a, X14 : a]: 120.82/15.94 (~ (((??) @ ((('#B') @ (??) @ 120.82/15.94 ((('#C') @ ((('#B') @ ('#C') @ 120.82/15.94 ((('#S') @ ((('#B') @ ('#S') @ 120.82/15.94 ((('#C') @ ((('#B') @ ( 120.82/15.94 '#B') @ 120.82/15.94 ((('#B') @ ( 120.82/15.94 ((&) @ ( 120.82/15.94 ((X4) = (cP @ 120.82/15.94 X12 @ X14))))) @ 120.82/15.94 ('#sk1' @ X8 @ 120.82/15.94 X12))))) @ 120.82/15.94 ('#sk1' @ X10 @ X14))))) @ 120.82/15.94 ((('#B') @ ((('#B') @ (((a) = (X6))))) @ 120.82/15.94 cP)))))) @ 120.82/15.94 (((X2) = (cP @ X8 @ X10))))))))) 120.82/15.94 | ('#sk1' @ X2 @ X4 @ X6))), 120.82/15.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl106])). 120.82/15.94 thf(zip_derived_cl124, plain, 120.82/15.94 (![X2 : a, X4 : a, X6 : a, X8 : a, X10 : a, X12 : a, X14 : a, X16 : a]: 120.82/15.94 (~ (((??) @ ((('#C') @ ((('#S') @ ((('#B') @ (((((X4) = (cP @ X12 @ 120.82/15.94 X14))) & 120.82/15.94 ('#sk1' @ X8 @ X12 @ 120.82/15.94 X16))) @ 120.82/15.94 ('#sk1' @ X10 @ X14))) @ 120.82/15.94 ((('#B') @ (((a) = (X6))) @ (cP @ X16))))) @ 120.82/15.94 (((X2) = (cP @ X8 @ X10))))))) 120.82/15.94 | ('#sk1' @ X2 @ X4 @ X6))), 120.82/15.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl115])). 120.82/15.94 thf(zip_derived_cl133, plain, 120.82/15.94 (![X2 : a, X4 : a, X6 : a, X8 : a, X10 : a, X12 : a, X14 : a, X16 : a, 120.82/15.94 X18 : a]: 120.82/15.94 (~ (((((X4) = (cP @ X12 @ X14))) & ('#sk1' @ X8 @ X12 @ X16) & 120.82/15.94 ('#sk1' @ X10 @ X14 @ X18) & (((X6) = (cP @ X16 @ X18))) & 120.82/15.94 (((X2) = (cP @ X8 @ X10))))) 120.82/15.94 | ('#sk1' @ X2 @ X4 @ X6))), 120.82/15.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl124])). 120.82/15.94 thf(zip_derived_cl142, plain, 120.82/15.94 (![X2 : a, X4 : a, X6 : a, X8 : a, X10 : a, X12 : a, X14 : a, X16 : a, 120.82/15.94 X18 : a]: 120.82/15.94 (~ (((X4) = (cP @ X12 @ X14))) 120.82/15.94 | ~ ('#sk1' @ X8 @ X12 @ X16) 120.82/15.94 | ~ ('#sk1' @ X10 @ X14 @ X18) 120.82/15.94 | ~ (((X6) = (cP @ X16 @ X18))) 120.82/15.94 | ~ (((X2) = (cP @ X8 @ X10))) 120.82/15.94 | ('#sk1' @ X2 @ X4 @ X6))), 120.82/15.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl133])). 120.82/15.94 thf(zip_derived_cl167, plain, 120.82/15.94 (![X2 : a, X4 : a, X6 : a, X8 : a, X10 : a, X12 : a, X14 : a, X16 : a, 120.82/15.94 X18 : a]: 120.82/15.94 (((X4) != (cP @ X12 @ X14)) 120.82/15.94 | ~ ('#sk1' @ X8 @ X12 @ X16) 120.82/15.94 | ~ ('#sk1' @ X10 @ X14 @ X18) 120.82/15.94 | ((X6) != (cP @ X16 @ X18)) 120.82/15.94 | ((X2) != (cP @ X8 @ X10)) 120.82/15.94 | ('#sk1' @ X2 @ X4 @ X6))), 120.82/15.94 inference('simplify nested equalities', [status(thm)], 120.82/15.94 [zip_derived_cl142])). 120.82/15.94 thf(zip_derived_cl19609, plain, ($false), 120.82/15.94 inference('eprover', [status(thm)], 120.82/15.94 [zip_derived_cl27, zip_derived_cl172, zip_derived_cl178, 120.82/15.94 zip_derived_cl207, zip_derived_cl92, zip_derived_cl201, 120.82/15.94 zip_derived_cl170, zip_derived_cl176, zip_derived_cl91, 120.82/15.94 zip_derived_cl44, zip_derived_cl175, zip_derived_cl174, 120.82/15.94 zip_derived_cl203, zip_derived_cl209, zip_derived_cl23, 120.82/15.94 zip_derived_cl155, zip_derived_cl54, zip_derived_cl204, 120.82/15.94 zip_derived_cl154, zip_derived_cl205, zip_derived_cl188, 120.82/15.94 zip_derived_cl187, zip_derived_cl167])). 120.82/15.94 120.82/15.94 % SZS output end Refutation 120.82/15.94 120.82/15.94 120.82/15.94 % Terminating... 120.82/15.94 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 121.00/15.99 % Runner terminated. 121.00/16.01 % Zipperpin 1.5 exiting 121.00/16.01 EOF