0.05/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.F2pljpgzxD true 0.10/0.34 % Computer : n013.cluster.edu 0.10/0.34 % Model : x86_64 x86_64 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.34 % Memory : 8042.1875MB 0.10/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.34 % CPULimit : 1440 0.10/0.34 % WCLimit : 180 0.10/0.34 % DateTime : Thu Jul 4 08:42:39 EDT 2024 0.10/0.34 % CPUTime : 0.10/0.35 % Running portfolio for 1440 s 0.10/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.10/0.35 % Number of cores: 8 0.10/0.35 % Python version: Python 3.6.8 0.10/0.35 % Running in HO mode 0.48/0.68 % Total configuration time : 828 0.48/0.68 % Estimated wc time : 1656 0.48/0.68 % Estimated cpu time (8 cpus) : 207.0 0.49/0.84 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.50/0.87 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.50/0.95 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.50/1.10 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.50/1.13 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 1.82/1.18 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 1.82/1.19 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 1.87/1.20 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 46.08/8.05 % Solved by lams/20_acsne_simpl.sh. 46.08/8.05 % done 395 iterations in 6.593s 46.08/8.05 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 46.08/8.05 % SZS output start Refutation 46.08/8.05 thf(a_type, type, a: $tType). 46.08/8.05 thf(w_type, type, w: a). 46.08/8.05 thf('#sk743_type', type, '#sk743': (a > a > a > $o) > a). 46.08/8.05 thf('#form611_type', type, '#form611': (a > a > a > $o) > $o). 46.08/8.05 thf('#sk963_type', type, '#sk963': (a > a > a > $o) > a). 46.08/8.05 thf('#sk1432_type', type, '#sk1432': (a > a > a > $o) > a). 46.08/8.05 thf(y_type, type, y: a). 46.08/8.05 thf('#sk145_type', type, '#sk145': (a > a > a > $o) > a). 46.08/8.05 thf(c0_type, type, c0: a). 46.08/8.05 thf('#sk1058_type', type, '#sk1058': (a > a > a > $o) > a). 46.08/8.05 thf('#sk1293_type', type, '#sk1293': (a > a > a > $o) > a). 46.08/8.05 thf('#sk933_type', type, '#sk933': (a > a > a > $o) > a). 46.08/8.05 thf('#form2251_type', type, '#form2251': $o). 46.08/8.05 thf('#sk29_type', type, '#sk29': (a > a > a > $o) > a). 46.08/8.05 thf('#sk556_type', type, '#sk556': (a > a > a > $o) > a). 46.08/8.05 thf('#sk113_type', type, '#sk113': (a > a > a > $o) > a). 46.08/8.05 thf('#sk1023_type', type, '#sk1023': (a > a > a > $o) > a). 46.08/8.05 thf('#sk60_type', type, '#sk60': (a > a > a > $o) > a). 46.08/8.05 thf(x_type, type, x: a). 46.08/8.05 thf(cP_type, type, cP: a > a > a). 46.08/8.05 thf('#form494_type', type, '#form494': (a > a > a > $o) > $o). 46.08/8.05 thf('#sk1128_type', type, '#sk1128': (a > a > a > $o) > a). 46.08/8.05 thf('#sk81_type', type, '#sk81': (a > a > a > $o) > a). 46.08/8.05 thf('#sk1248_type', type, '#sk1248': (a > a > a > $o) > a). 46.08/8.05 thf(z_type, type, z: a). 46.08/8.05 thf('#sk1_type', type, '#sk1': a > a > a > $o). 46.08/8.05 thf('#sk39_type', type, '#sk39': (a > a > a > $o) > a). 46.08/8.05 thf('#sk1168_type', type, '#sk1168': (a > a > a > $o) > a). 46.08/8.05 thf('#sk495_type', type, '#sk495': (a > a > a > $o) > a). 46.08/8.05 thf('#form2115_type', type, '#form2115': $o). 46.08/8.05 thf(cS_INCL_LEM1_pme, conjecture, 46.08/8.05 (( ( ![R:( a > a > a > $o )]: 46.08/8.05 ( ( ![Xa:a,Xb:a,Xc:a]: 46.08/8.05 ( ( ( ( ( Xb ) = ( c0 ) ) & ( ( Xa ) = ( Xc ) ) ) | 46.08/8.05 ( ?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]: 46.08/8.05 ( ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) & 46.08/8.05 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 46.08/8.05 ( R @ Xx2 @ Xy2 @ Xz2 ) & ( R @ Xx1 @ Xy1 @ Xz1 ) & 46.08/8.05 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) ) ) | 46.08/8.05 ( ( ( Xa ) = ( c0 ) ) & ( ( Xb ) = ( Xc ) ) ) ) => 46.08/8.05 ( R @ Xa @ Xb @ Xc ) ) ) => 46.08/8.05 ( R @ w @ z @ z ) ) ) & 46.08/8.05 ( ![R:( a > a > a > $o )]: 46.08/8.05 ( ( ![Xa:a,Xb:a,Xc:a]: 46.08/8.05 ( ( ( ( ( Xb ) = ( Xc ) ) & ( ( Xa ) = ( c0 ) ) ) | 46.08/8.05 ( ( ( Xa ) = ( Xc ) ) & ( ( Xb ) = ( c0 ) ) ) | 46.08/8.05 ( ?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]: 46.08/8.05 ( ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) & 46.08/8.05 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 46.08/8.05 ( R @ Xx1 @ Xy1 @ Xz1 ) & ( R @ Xx2 @ Xy2 @ Xz2 ) & 46.08/8.05 ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) ) ) ) => 46.08/8.05 ( R @ Xa @ Xb @ Xc ) ) ) => 46.08/8.05 ( R @ x @ y @ y ) ) ) ) => 46.08/8.05 ( ![R:( a > a > a > $o )]: 46.08/8.05 ( ( ![Xa:a,Xb:a,Xc:a]: 46.08/8.05 ( ( ( ( ( Xa ) = ( c0 ) ) & ( ( Xb ) = ( Xc ) ) ) | 46.08/8.05 ( ?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]: 46.08/8.05 ( ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) & ( R @ Xx1 @ Xy1 @ Xz1 ) & 46.08/8.05 ( R @ Xx2 @ Xy2 @ Xz2 ) & ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 46.08/8.05 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) ) ) | 46.08/8.05 ( ( ( Xa ) = ( Xc ) ) & ( ( Xb ) = ( c0 ) ) ) ) => 46.08/8.05 ( R @ Xa @ Xb @ Xc ) ) ) => 46.08/8.05 ( R @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ))). 46.08/8.05 thf(zf_stmt_0, negated_conjecture, 46.08/8.05 (~( ( ( ![R:( a > a > a > $o )]: 46.08/8.05 ( ( ![Xa:a,Xb:a,Xc:a]: 46.08/8.05 ( ( ( ( ( Xb ) = ( c0 ) ) & ( ( Xa ) = ( Xc ) ) ) | 46.08/8.05 ( ?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]: 46.08/8.05 ( ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) & 46.08/8.05 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 46.08/8.05 ( R @ Xx2 @ Xy2 @ Xz2 ) & ( R @ Xx1 @ Xy1 @ Xz1 ) & 46.08/8.05 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) ) ) | 46.08/8.05 ( ( ( Xa ) = ( c0 ) ) & ( ( Xb ) = ( Xc ) ) ) ) => 46.08/8.05 ( R @ Xa @ Xb @ Xc ) ) ) => 46.08/8.05 ( R @ w @ z @ z ) ) ) & 46.08/8.05 ( ![R:( a > a > a > $o )]: 46.08/8.05 ( ( ![Xa:a,Xb:a,Xc:a]: 46.08/8.05 ( ( ( ( ( Xb ) = ( Xc ) ) & ( ( Xa ) = ( c0 ) ) ) | 46.08/8.05 ( ( ( Xa ) = ( Xc ) ) & ( ( Xb ) = ( c0 ) ) ) | 46.08/8.05 ( ?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]: 46.08/8.05 ( ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) & 46.08/8.05 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 46.08/8.05 ( R @ Xx1 @ Xy1 @ Xz1 ) & ( R @ Xx2 @ Xy2 @ Xz2 ) & 46.08/8.05 ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) ) ) ) => 46.08/8.05 ( R @ Xa @ Xb @ Xc ) ) ) => 46.08/8.05 ( R @ x @ y @ y ) ) ) ) => 46.08/8.05 ( ![R:( a > a > a > $o )]: 46.08/8.05 ( ( ![Xa:a,Xb:a,Xc:a]: 46.08/8.05 ( ( ( ( ( Xa ) = ( c0 ) ) & ( ( Xb ) = ( Xc ) ) ) | 46.08/8.05 ( ?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]: 46.08/8.05 ( ( ( Xa ) = ( cP @ Xx1 @ Xx2 ) ) & 46.08/8.05 ( R @ Xx1 @ Xy1 @ Xz1 ) & ( R @ Xx2 @ Xy2 @ Xz2 ) & 46.08/8.05 ( ( Xc ) = ( cP @ Xz1 @ Xz2 ) ) & 46.08/8.05 ( ( Xb ) = ( cP @ Xy1 @ Xy2 ) ) ) ) | 46.08/8.05 ( ( ( Xa ) = ( Xc ) ) & ( ( Xb ) = ( c0 ) ) ) ) => 46.08/8.05 ( R @ Xa @ Xb @ Xc ) ) ) => 46.08/8.05 ( R @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ) )), 46.08/8.05 inference('cnf.neg', [status(esa)], [cS_INCL_LEM1_pme])). 46.08/8.05 thf(zip_derived_cl0, plain, 46.08/8.05 (~ (((((((!!) @ (^[Y0 : a > a > a > $o]: 46.08/8.05 (((((!!) @ (^[Y1 : a]: 46.08/8.05 (((!!) @ (^[Y2 : a]: 46.08/8.05 (((!!) @ (^[Y3 : a]: 46.08/8.05 (((((((( 46.08/8.05 (Y2) = 46.08/8.05 (c0))) & 46.08/8.05 (( 46.08/8.05 (Y1) = 46.08/8.05 (Y3))))) | 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y8 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y9 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y3) = 46.08/8.05 (cP @ 46.08/8.05 Y8 @ Y9))) & 46.08/8.05 ( 46.08/8.05 Y0 @ 46.08/8.05 Y5 @ 46.08/8.05 Y7 @ Y9) & 46.08/8.05 ( 46.08/8.05 Y0 @ 46.08/8.05 Y4 @ 46.08/8.05 Y6 @ Y8) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y2) = 46.08/8.05 (cP @ 46.08/8.05 Y6 @ Y7))))))))))))))))))))))) | 46.08/8.05 (((( 46.08/8.05 (Y1) = 46.08/8.05 (c0))) & 46.08/8.05 (( 46.08/8.05 (Y2) = 46.08/8.05 (Y3))))))) => 46.08/8.05 (Y0 @ Y1 @ 46.08/8.05 Y2 @ Y3)))))))))))) => 46.08/8.05 (Y0 @ w @ z @ z)))))) & 46.08/8.05 (((!!) @ (^[Y0 : a > a > a > $o]: 46.08/8.05 (((((!!) @ (^[Y1 : a]: 46.08/8.05 (((!!) @ (^[Y2 : a]: 46.08/8.05 (((!!) @ (^[Y3 : a]: 46.08/8.05 (((((((( 46.08/8.05 (Y2) = 46.08/8.05 (Y3))) & 46.08/8.05 (( 46.08/8.05 (Y1) = 46.08/8.05 (c0))))) | 46.08/8.05 (((( 46.08/8.05 (Y1) = 46.08/8.05 (Y3))) & 46.08/8.05 (( 46.08/8.05 (Y2) = 46.08/8.05 (c0))))) | 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y8 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y9 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y2) = 46.08/8.05 (cP @ 46.08/8.05 Y6 @ Y7))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y3) = 46.08/8.05 (cP @ 46.08/8.05 Y8 @ Y9))) & 46.08/8.05 ( 46.08/8.05 Y0 @ 46.08/8.05 Y4 @ 46.08/8.05 Y6 @ Y8) & 46.08/8.05 ( 46.08/8.05 Y0 @ 46.08/8.05 Y5 @ 46.08/8.05 Y7 @ Y9) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))))))))))))))))))))))))) => 46.08/8.05 (Y0 @ Y1 @ 46.08/8.05 Y2 @ Y3)))))))))))) => 46.08/8.05 (Y0 @ x @ y @ y)))))))) => 46.08/8.05 (((!!) @ (^[Y0 : a > a > a > $o]: 46.08/8.05 (((((!!) @ (^[Y1 : a]: 46.08/8.05 (((!!) @ (^[Y2 : a]: 46.08/8.05 (((!!) @ (^[Y3 : a]: 46.08/8.05 (((((((((Y1) = 46.08/8.05 (c0))) & 46.08/8.05 (((Y2) = 46.08/8.05 (Y3))))) | 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y8 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y9 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 Y0 @ 46.08/8.05 Y4 @ 46.08/8.05 Y6 @ Y8) & 46.08/8.05 ( 46.08/8.05 Y0 @ 46.08/8.05 Y5 @ 46.08/8.05 Y7 @ Y9) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y3) = 46.08/8.05 (cP @ 46.08/8.05 Y8 @ Y9))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y2) = 46.08/8.05 (cP @ 46.08/8.05 Y6 @ Y7))))))))))))))))))))))) | 46.08/8.05 (((((Y1) = 46.08/8.05 (Y3))) & 46.08/8.05 (((Y2) = 46.08/8.05 (c0))))))) => 46.08/8.05 (Y0 @ Y1 @ Y2 @ 46.08/8.05 Y3)))))))))))) => 46.08/8.05 (Y0 @ (cP @ x @ w) @ (cP @ y @ z) @ (cP @ y @ z)))))))))), 46.08/8.05 inference('cnf', [status(esa)], [zf_stmt_0])). 46.08/8.05 thf(zip_derived_cl1, plain, 46.08/8.05 ( (((((!!) @ (^[Y0 : a > a > a > $o]: 46.08/8.05 (((((!!) @ (^[Y1 : a]: 46.08/8.05 (((!!) @ (^[Y2 : a]: 46.08/8.05 (((!!) @ (^[Y3 : a]: 46.08/8.05 (((((((((Y2) = (c0))) & 46.08/8.05 (((Y1) = (Y3))))) | 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y8 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y9 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y3) = 46.08/8.05 (cP @ 46.08/8.05 Y8 @ Y9))) & 46.08/8.05 ( 46.08/8.05 Y0 @ 46.08/8.05 Y5 @ 46.08/8.05 Y7 @ Y9) & 46.08/8.05 ( 46.08/8.05 Y0 @ 46.08/8.05 Y4 @ 46.08/8.05 Y6 @ Y8) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y2) = 46.08/8.05 (cP @ 46.08/8.05 Y6 @ Y7))))))))))))))))))))))) | 46.08/8.05 (((((Y1) = (c0))) & 46.08/8.05 (((Y2) = (Y3))))))) => 46.08/8.05 (Y0 @ Y1 @ Y2 @ 46.08/8.05 Y3)))))))))))) => 46.08/8.05 (Y0 @ w @ z @ z)))))) & 46.08/8.05 (((!!) @ (^[Y0 : a > a > a > $o]: 46.08/8.05 (((((!!) @ (^[Y1 : a]: 46.08/8.05 (((!!) @ (^[Y2 : a]: 46.08/8.05 (((!!) @ (^[Y3 : a]: 46.08/8.05 (((((((((Y2) = (Y3))) & 46.08/8.05 (((Y1) = (c0))))) | 46.08/8.05 (((((Y1) = (Y3))) & 46.08/8.05 (((Y2) = (c0))))) | 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y8 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y9 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y2) = 46.08/8.05 (cP @ 46.08/8.05 Y6 @ Y7))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y3) = 46.08/8.05 (cP @ 46.08/8.05 Y8 @ Y9))) & 46.08/8.05 ( 46.08/8.05 Y0 @ 46.08/8.05 Y4 @ 46.08/8.05 Y6 @ Y8) & 46.08/8.05 ( 46.08/8.05 Y0 @ 46.08/8.05 Y5 @ 46.08/8.05 Y7 @ Y9) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))))))))))))))))))))))))) => 46.08/8.05 (Y0 @ Y1 @ Y2 @ 46.08/8.05 Y3)))))))))))) => 46.08/8.05 (Y0 @ x @ y @ y))))))))), 46.08/8.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 46.08/8.05 thf(zip_derived_cl4, plain, 46.08/8.05 ( (((!!) @ (^[Y0 : a > a > a > $o]: 46.08/8.05 (((((!!) @ (^[Y1 : a]: 46.08/8.05 (((!!) @ (^[Y2 : a]: 46.08/8.05 (((!!) @ (^[Y3 : a]: 46.08/8.05 (((((((((Y2) = (Y3))) & 46.08/8.05 (((Y1) = (c0))))) | 46.08/8.05 (((((Y1) = (Y3))) & 46.08/8.05 (((Y2) = (c0))))) | 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y8 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y9 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y2) = 46.08/8.05 (cP @ 46.08/8.05 Y6 @ Y7))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y3) = 46.08/8.05 (cP @ 46.08/8.05 Y8 @ Y9))) & 46.08/8.05 ( 46.08/8.05 Y0 @ 46.08/8.05 Y4 @ 46.08/8.05 Y6 @ Y8) & 46.08/8.05 ( 46.08/8.05 Y0 @ 46.08/8.05 Y5 @ 46.08/8.05 Y7 @ Y9) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))))))))))))))))))))))))) => 46.08/8.05 (Y0 @ Y1 @ Y2 @ Y3)))))))))))) => 46.08/8.05 (Y0 @ x @ y @ y))))))), 46.08/8.05 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1])). 46.08/8.05 thf(zip_derived_cl8, plain, 46.08/8.05 (![X2 : a > a > a > $o]: 46.08/8.05 (((((!!) @ (^[Y0 : a]: 46.08/8.05 (((!!) @ (^[Y1 : a]: 46.08/8.05 (((!!) @ (^[Y2 : a]: 46.08/8.05 (((((((((Y1) = (Y2))) & 46.08/8.05 (((Y0) = (c0))))) | 46.08/8.05 (((((Y0) = (Y2))) & 46.08/8.05 (((Y1) = (c0))))) | 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y8 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y5 @ Y6))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y2) = 46.08/8.05 (cP @ 46.08/8.05 Y7 @ Y8))) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y3 @ 46.08/8.05 Y5 @ Y7) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y4 @ 46.08/8.05 Y6 @ Y8) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y0) = 46.08/8.05 (cP @ 46.08/8.05 Y3 @ Y4))))))))))))))))))))))))) => 46.08/8.05 (X2 @ Y0 @ Y1 @ Y2)))))))))))) => 46.08/8.05 (X2 @ x @ y @ y)))), 46.08/8.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 46.08/8.05 thf(zip_derived_cl13, plain, 46.08/8.05 (![X2 : a > a > a > $o]: 46.08/8.05 (~ (((!!) @ (^[Y0 : a]: 46.08/8.05 (((!!) @ (^[Y1 : a]: 46.08/8.05 (((!!) @ (^[Y2 : a]: 46.08/8.05 (((((((((Y1) = (Y2))) & 46.08/8.05 (((Y0) = (c0))))) | 46.08/8.05 (((((Y0) = (Y2))) & 46.08/8.05 (((Y1) = (c0))))) | 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y8 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y5 @ Y6))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y2) = 46.08/8.05 (cP @ 46.08/8.05 Y7 @ Y8))) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y3 @ 46.08/8.05 Y5 @ Y7) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y4 @ 46.08/8.05 Y6 @ Y8) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y0) = 46.08/8.05 (cP @ 46.08/8.05 Y3 @ Y4))))))))))))))))))))))))) => 46.08/8.05 (X2 @ Y0 @ Y1 @ Y2)))))))))))) 46.08/8.05 | (X2 @ x @ y @ y))), 46.08/8.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 46.08/8.05 thf(zip_derived_cl16, plain, 46.08/8.05 (![X2 : a > a > a > $o]: 46.08/8.05 (~ (((!!) @ (^[Y0 : a]: 46.08/8.05 (((!!) @ (^[Y1 : a]: 46.08/8.05 (((((((((Y0) = (Y1))) & 46.08/8.05 ((('#sk39' @ X2) = (c0))))) | 46.08/8.05 ((((('#sk39' @ X2) = (Y1))) & 46.08/8.05 (((Y0) = (c0))))) | 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y0) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y6 @ Y7))) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y2 @ 46.08/8.05 Y4 @ Y6) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y3 @ 46.08/8.05 Y5 @ Y7) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk39' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y2 @ Y3))))))))))))))))))))))))) => 46.08/8.05 (X2 @ ('#sk39' @ X2) @ Y0 @ Y1))))))))) 46.08/8.05 | (X2 @ x @ y @ y))), 46.08/8.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl13])). 46.08/8.05 thf(zip_derived_cl19, plain, 46.08/8.05 (![X2 : a > a > a > $o]: 46.08/8.05 (~ (((!!) @ (^[Y0 : a]: 46.08/8.05 ((((((((('#sk81' @ X2) = (Y0))) & 46.08/8.05 ((('#sk39' @ X2) = (c0))))) | 46.08/8.05 ((((('#sk39' @ X2) = (Y0))) & 46.08/8.05 ((('#sk81' @ X2) = (c0))))) | 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk81' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y3 @ Y4))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y0) = 46.08/8.05 (cP @ 46.08/8.05 Y5 @ Y6))) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y1 @ 46.08/8.05 Y3 @ Y5) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y2 @ 46.08/8.05 Y4 @ Y6) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk39' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y1 @ Y2))))))))))))))))))))))))) => 46.08/8.05 (X2 @ ('#sk39' @ X2) @ ('#sk81' @ X2) @ Y0)))))) 46.08/8.05 | (X2 @ x @ y @ y))), 46.08/8.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl16])). 46.08/8.05 thf(zip_derived_cl22, plain, 46.08/8.05 (![X2 : a > a > a > $o]: 46.08/8.05 (~ ((((((((('#sk81' @ X2) = ('#sk145' @ X2))) & 46.08/8.05 ((('#sk39' @ X2) = (c0))))) | 46.08/8.05 ((((('#sk39' @ X2) = ('#sk145' @ X2))) & 46.08/8.05 ((('#sk81' @ X2) = (c0))))) | 46.08/8.05 (((??) @ (^[Y0 : a]: 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk81' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y2 @ Y3))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk145' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y0 @ 46.08/8.05 Y2 @ Y4) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y1 @ 46.08/8.05 Y3 @ Y5) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk39' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y0 @ Y1))))))))))))))))))))))))) => 46.08/8.05 (X2 @ ('#sk39' @ X2) @ ('#sk81' @ X2) @ ('#sk145' @ X2)))) 46.08/8.05 | (X2 @ x @ y @ y))), 46.08/8.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 46.08/8.05 thf(zip_derived_cl26, plain, 46.08/8.05 (![X2 : a > a > a > $o]: 46.08/8.05 ( ((((((('#sk81' @ X2) = ('#sk145' @ X2))) & ((('#sk39' @ X2) = (c0))))) | 46.08/8.05 ((((('#sk39' @ X2) = ('#sk145' @ X2))) & ((('#sk81' @ X2) = (c0))))) | 46.08/8.05 (((??) @ (^[Y0 : a]: 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk81' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y2 @ Y3))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk145' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y0 @ 46.08/8.05 Y2 @ Y4) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y1 @ 46.08/8.05 Y3 @ Y5) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk39' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y0 @ Y1))))))))))))))))))))))))) 46.08/8.05 | (X2 @ x @ y @ y))), 46.08/8.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 46.08/8.05 thf(zip_derived_cl32, plain, 46.08/8.05 (![X2 : a > a > a > $o]: 46.08/8.05 ( ((((('#sk81' @ X2) = ('#sk145' @ X2))) & ((('#sk39' @ X2) = (c0))))) 46.08/8.05 | ((((('#sk39' @ X2) = ('#sk145' @ X2))) & ((('#sk81' @ X2) = (c0))))) 46.08/8.05 | (((??) @ (^[Y0 : a]: 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk81' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y2 @ Y3))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk145' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y0 @ 46.08/8.05 Y2 @ Y4) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y1 @ 46.08/8.05 Y3 @ Y5) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk39' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y0 @ Y1))))))))))))))))))))))) 46.08/8.05 | (X2 @ x @ y @ y))), 46.08/8.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl26])). 46.08/8.05 thf(zip_derived_cl39, plain, 46.08/8.05 (![X2 : a > a > a > $o]: 46.08/8.05 ( ((('#sk39' @ X2) = (c0))) 46.08/8.05 | (X2 @ x @ y @ y) 46.08/8.05 | (((??) @ (^[Y0 : a]: 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk81' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y2 @ Y3))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk145' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y0 @ 46.08/8.05 Y2 @ Y4) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y1 @ 46.08/8.05 Y3 @ Y5) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk39' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y0 @ Y1))))))))))))))))))))))) 46.08/8.05 | ((((('#sk39' @ X2) = ('#sk145' @ X2))) & ((('#sk81' @ X2) = (c0))))))), 46.08/8.05 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl32])). 46.08/8.05 thf(zip_derived_cl54, plain, 46.08/8.05 (![X2 : a > a > a > $o]: 46.08/8.05 ((('#sk39' @ X2) = (c0)) 46.08/8.05 | (X2 @ x @ y @ y) 46.08/8.05 | (((??) @ (^[Y0 : a]: 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk81' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y2 @ Y3))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk145' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y0 @ 46.08/8.05 Y2 @ Y4) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y1 @ 46.08/8.05 Y3 @ Y5) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk39' @ 46.08/8.05 X2) = 46.08/8.05 (cP @ 46.08/8.05 Y0 @ Y1))))))))))))))))))))))) 46.08/8.05 | ((((('#sk39' @ X2) = ('#sk145' @ X2))) & ((('#sk81' @ X2) = (c0))))))), 46.08/8.05 inference('simplify nested equalities', [status(thm)], [zip_derived_cl39])). 46.08/8.05 thf(zip_derived_cl55, plain, 46.08/8.05 (![X2 : a > a > a > $o]: 46.08/8.05 (~ ('#form611' @ X2) 46.08/8.05 | ((((('#sk39' @ X2) = ('#sk145' @ X2))) & ((('#sk81' @ X2) = (c0))))))), 46.08/8.05 define([status(thm)])). 46.08/8.05 thf(zip_derived_cl57, plain, 46.08/8.05 (![X2 : a > a > a > $o]: 46.08/8.05 ( ((('#sk81' @ X2) = (c0))) | ~ ('#form611' @ X2))), 46.08/8.05 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 46.08/8.05 thf(zip_derived_cl70, plain, 46.08/8.05 (![X2 : a > a > a > $o]: ((('#sk81' @ X2) = (c0)) | ~ ('#form611' @ X2))), 46.08/8.05 inference('simplify nested equalities', [status(thm)], [zip_derived_cl57])). 46.08/8.05 thf(zip_derived_cl56, plain, 46.08/8.05 (![X2 : a > a > a > $o]: 46.08/8.05 ( ((('#sk39' @ X2) = ('#sk145' @ X2))) | ~ ('#form611' @ X2))), 46.08/8.05 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 46.08/8.05 thf(zip_derived_cl69, plain, 46.08/8.05 (![X2 : a > a > a > $o]: 46.08/8.05 ((('#sk39' @ X2) = ('#sk145' @ X2)) | ~ ('#form611' @ X2))), 46.08/8.05 inference('simplify nested equalities', [status(thm)], [zip_derived_cl56])). 46.08/8.05 thf(zip_derived_cl8, plain, 46.08/8.05 (![X2 : a > a > a > $o]: 46.08/8.05 (((((!!) @ (^[Y0 : a]: 46.08/8.05 (((!!) @ (^[Y1 : a]: 46.08/8.05 (((!!) @ (^[Y2 : a]: 46.08/8.05 (((((((((Y1) = (Y2))) & 46.08/8.05 (((Y0) = (c0))))) | 46.08/8.05 (((((Y0) = (Y2))) & 46.08/8.05 (((Y1) = (c0))))) | 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y8 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y5 @ Y6))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y2) = 46.08/8.05 (cP @ 46.08/8.05 Y7 @ Y8))) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y3 @ 46.08/8.05 Y5 @ Y7) & 46.08/8.05 ( 46.08/8.05 X2 @ 46.08/8.05 Y4 @ 46.08/8.05 Y6 @ Y8) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y0) = 46.08/8.05 (cP @ 46.08/8.05 Y3 @ Y4))))))))))))))))))))))))) => 46.08/8.05 (X2 @ Y0 @ Y1 @ Y2)))))))))))) => 46.08/8.05 (X2 @ x @ y @ y)))), 46.08/8.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 46.08/8.05 thf(zip_derived_cl9, plain, 46.08/8.05 ( (((((!!) @ (^[Y0 : a]: 46.08/8.05 (((!!) @ (^[Y1 : a]: 46.08/8.05 (((!!) @ (^[Y2 : a]: 46.08/8.05 (((((((((Y1) = (Y2))) & 46.08/8.05 (((Y0) = (c0))))) | 46.08/8.05 (((((Y0) = (Y2))) & 46.08/8.05 (((Y1) = (c0))))) | 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y8 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y5 @ Y6))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y2) = 46.08/8.05 (cP @ 46.08/8.05 Y7 @ Y8))) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y3 @ 46.08/8.05 Y5 @ Y7) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y4 @ 46.08/8.05 Y6 @ Y8) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y0) = 46.08/8.05 (cP @ 46.08/8.05 Y3 @ Y4))))))))))))))))))))))))) => 46.08/8.05 ('#sk1' @ Y0 @ Y1 @ Y2)))))))))))) => 46.08/8.05 ('#sk1' @ x @ y @ y)))), 46.08/8.05 inference('triggered_bool_instantiation', [status(thm)], 46.08/8.05 [zip_derived_cl8])). 46.08/8.05 thf(zip_derived_cl136, plain, 46.08/8.05 ((~ (((!!) @ (^[Y0 : a]: 46.08/8.05 (((!!) @ (^[Y1 : a]: 46.08/8.05 (((!!) @ (^[Y2 : a]: 46.08/8.05 (((((((((Y1) = (Y2))) & 46.08/8.05 (((Y0) = (c0))))) | 46.08/8.05 (((((Y0) = (Y2))) & 46.08/8.05 (((Y1) = (c0))))) | 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y8 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y5 @ Y6))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y2) = 46.08/8.05 (cP @ 46.08/8.05 Y7 @ Y8))) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y3 @ 46.08/8.05 Y5 @ Y7) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y4 @ 46.08/8.05 Y6 @ Y8) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y0) = 46.08/8.05 (cP @ 46.08/8.05 Y3 @ Y4))))))))))))))))))))))))) => 46.08/8.05 ('#sk1' @ Y0 @ Y1 @ Y2)))))))))))) 46.08/8.05 | ('#sk1' @ x @ y @ y))), 46.08/8.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl9])). 46.08/8.05 thf(zip_derived_cl137, plain, 46.08/8.05 ((~ (((!!) @ (^[Y0 : a]: 46.08/8.05 (((!!) @ (^[Y1 : a]: 46.08/8.05 (((((((((Y0) = (Y1))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))) | 46.08/8.05 ((((('#sk39' @ '#sk1') = (Y1))) & 46.08/8.05 (((Y0) = (c0))))) | 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y0) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y6 @ Y7))) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y2 @ 46.08/8.05 Y4 @ Y6) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y3 @ 46.08/8.05 Y5 @ Y7) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk39' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 Y2 @ Y3))))))))))))))))))))))))) => 46.08/8.05 ('#sk1' @ ('#sk39' @ '#sk1') @ Y0 @ Y1))))))))) 46.08/8.05 | ('#sk1' @ x @ y @ y))), 46.08/8.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl136])). 46.08/8.05 thf(zip_derived_cl138, plain, 46.08/8.05 ((~ (((!!) @ (^[Y0 : a]: 46.08/8.05 ((((((((('#sk81' @ '#sk1') = (Y0))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))) | 46.08/8.05 ((((('#sk39' @ '#sk1') = (Y0))) & 46.08/8.05 ((('#sk81' @ '#sk1') = (c0))))) | 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk81' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 Y3 @ Y4))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y0) = 46.08/8.05 (cP @ 46.08/8.05 Y5 @ Y6))) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y1 @ 46.08/8.05 Y3 @ Y5) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y2 @ 46.08/8.05 Y4 @ Y6) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk39' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 Y1 @ Y2))))))))))))))))))))))))) => 46.08/8.05 ('#sk1' @ ('#sk39' @ '#sk1') @ ('#sk81' @ '#sk1') @ Y0)))))) 46.08/8.05 | ('#sk1' @ x @ y @ y))), 46.08/8.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl137])). 46.08/8.05 thf(zip_derived_cl139, plain, 46.08/8.05 ((~ ((((((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))) | 46.08/8.05 ((((('#sk39' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk81' @ '#sk1') = (c0))))) | 46.08/8.05 (((??) @ (^[Y0 : a]: 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk81' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 Y2 @ Y3))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk145' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y0 @ 46.08/8.05 Y2 @ Y4) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y1 @ 46.08/8.05 Y3 @ Y5) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk39' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 Y0 @ Y1))))))))))))))))))))))))) => 46.08/8.05 ('#sk1' @ ('#sk39' @ '#sk1') @ ('#sk81' @ '#sk1') @ 46.08/8.05 ('#sk145' @ '#sk1')))) 46.08/8.05 | ('#sk1' @ x @ y @ y))), 46.08/8.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl138])). 46.08/8.05 thf(zip_derived_cl140, plain, 46.08/8.05 (( ((((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))) | 46.08/8.05 ((((('#sk39' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk81' @ '#sk1') = (c0))))) | 46.08/8.05 (((??) @ (^[Y0 : a]: 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ (^[Y4 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk81' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 Y2 @ Y3))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk145' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y0 @ 46.08/8.05 Y2 @ Y4) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y1 @ 46.08/8.05 Y3 @ Y5) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk39' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 Y0 @ Y1))))))))))))))))))))))))) 46.08/8.05 | ('#sk1' @ x @ y @ y))), 46.08/8.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl139])). 46.08/8.05 thf(zip_derived_cl142, plain, 46.08/8.05 (( ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))) 46.08/8.05 | ((((('#sk39' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk81' @ '#sk1') = (c0))))) 46.08/8.05 | (((??) @ (^[Y0 : a]: 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ (^[Y4 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk81' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 Y2 @ Y3))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk145' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y0 @ 46.08/8.05 Y2 @ Y4) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y1 @ 46.08/8.05 Y3 @ Y5) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk39' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 Y0 @ Y1))))))))))))))))))))))) 46.08/8.05 | ('#sk1' @ x @ y @ y))), 46.08/8.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl140])). 46.08/8.05 thf(zip_derived_cl55, plain, 46.08/8.05 (![X2 : a > a > a > $o]: 46.08/8.05 (~ ('#form611' @ X2) 46.08/8.05 | ((((('#sk39' @ X2) = ('#sk145' @ X2))) & ((('#sk81' @ X2) = (c0))))))), 46.08/8.05 define([status(thm)])). 46.08/8.05 thf(zip_derived_cl143, plain, 46.08/8.05 (( ('#form611' @ '#sk1') 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | (((??) @ (^[Y0 : a]: 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ (^[Y4 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk81' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 Y2 @ Y3))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk145' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y0 @ 46.08/8.05 Y2 @ Y4) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y1 @ 46.08/8.05 Y3 @ Y5) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk39' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 Y0 @ Y1))))))))))))))))))))))) 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))))), 46.08/8.05 inference('renaming', [status(thm)], 46.08/8.05 [zip_derived_cl142, zip_derived_cl55])). 46.08/8.05 thf(zip_derived_cl144, plain, 46.08/8.05 (( (((??) @ (^[Y0 : a]: 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ (^[Y4 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk81' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 Y1 @ Y2))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk145' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 Y3 @ Y4))) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 ( 46.08/8.05 '#sk556' @ 46.08/8.05 '#sk1') @ 46.08/8.05 Y1 @ Y3) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y0 @ 46.08/8.05 Y2 @ Y4) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ('#sk39' @ 46.08/8.05 '#sk1') = 46.08/8.05 (cP @ 46.08/8.05 ( 46.08/8.05 '#sk556' @ 46.08/8.05 '#sk1') @ 46.08/8.05 Y0)))))))))))))))))))) 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))) 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | ('#form611' @ '#sk1'))), 46.08/8.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl143])). 46.08/8.05 thf(zip_derived_cl145, plain, 46.08/8.05 (( (((??) @ (^[Y0 : a]: 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 ((((('#sk81' @ 46.08/8.05 '#sk1') = (cP @ 46.08/8.05 Y0 @ Y1))) & 46.08/8.05 ((('#sk145' @ 46.08/8.05 '#sk1') = (cP @ 46.08/8.05 Y2 @ Y3))) & 46.08/8.05 ('#sk1' @ 46.08/8.05 ('#sk556' @ '#sk1') @ 46.08/8.05 Y0 @ Y2) & 46.08/8.05 ('#sk1' @ 46.08/8.05 ('#sk963' @ '#sk1') @ 46.08/8.05 Y1 @ Y3) & 46.08/8.05 ((('#sk39' @ 46.08/8.05 '#sk1') = (cP @ 46.08/8.05 ('#sk556' @ '#sk1') @ 46.08/8.05 ('#sk963' @ '#sk1')))))))))))))))))) 46.08/8.05 | ('#form611' @ '#sk1') 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))))), 46.08/8.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl144])). 46.08/8.05 thf(zip_derived_cl146, plain, 46.08/8.05 (( (((??) @ (^[Y0 : a]: 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 ((((('#sk81' @ '#sk1') = (cP @ 46.08/8.05 ('#sk1058' @ '#sk1') @ Y0))) & 46.08/8.05 ((('#sk145' @ '#sk1') = (cP @ 46.08/8.05 Y1 @ Y2))) & 46.08/8.05 ('#sk1' @ ('#sk556' @ '#sk1') @ 46.08/8.05 ('#sk1058' @ '#sk1') @ Y1) & 46.08/8.05 ('#sk1' @ ('#sk963' @ '#sk1') @ 46.08/8.05 Y0 @ Y2) & 46.08/8.05 ((('#sk39' @ '#sk1') = (cP @ 46.08/8.05 ('#sk556' @ '#sk1') @ 46.08/8.05 ('#sk963' @ '#sk1'))))))))))))))) 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))) 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | ('#form611' @ '#sk1'))), 46.08/8.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl145])). 46.08/8.05 thf(zip_derived_cl147, plain, 46.08/8.05 (( (((??) @ (^[Y0 : a]: 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 ((((('#sk81' @ '#sk1') = (cP @ 46.08/8.05 ('#sk1058' @ '#sk1') @ 46.08/8.05 ('#sk1168' @ '#sk1')))) & 46.08/8.05 ((('#sk145' @ '#sk1') = (cP @ Y0 @ Y1))) & 46.08/8.05 ('#sk1' @ ('#sk556' @ '#sk1') @ 46.08/8.05 ('#sk1058' @ '#sk1') @ Y0) & 46.08/8.05 ('#sk1' @ ('#sk963' @ '#sk1') @ 46.08/8.05 ('#sk1168' @ '#sk1') @ Y1) & 46.08/8.05 ((('#sk39' @ '#sk1') = (cP @ 46.08/8.05 ('#sk556' @ '#sk1') @ ('#sk963' @ '#sk1')))))))))))) 46.08/8.05 | ('#form611' @ '#sk1') 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))))), 46.08/8.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl146])). 46.08/8.05 thf(zip_derived_cl148, plain, 46.08/8.05 (( (((??) @ (^[Y0 : a]: 46.08/8.05 ((((('#sk81' @ '#sk1') = (cP @ ('#sk1058' @ '#sk1') @ 46.08/8.05 ('#sk1168' @ '#sk1')))) & 46.08/8.05 ((('#sk145' @ '#sk1') = (cP @ ('#sk1293' @ '#sk1') @ Y0))) & 46.08/8.05 ('#sk1' @ ('#sk556' @ '#sk1') @ ('#sk1058' @ '#sk1') @ 46.08/8.05 ('#sk1293' @ '#sk1')) & 46.08/8.05 ('#sk1' @ ('#sk963' @ '#sk1') @ ('#sk1168' @ '#sk1') @ 46.08/8.05 Y0) & 46.08/8.05 ((('#sk39' @ '#sk1') = (cP @ ('#sk556' @ '#sk1') @ 46.08/8.05 ('#sk963' @ '#sk1'))))))))) 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))) 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | ('#form611' @ '#sk1'))), 46.08/8.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl147])). 46.08/8.05 thf(zip_derived_cl149, plain, 46.08/8.05 (( ((((('#sk81' @ '#sk1') = (cP @ ('#sk1058' @ '#sk1') @ 46.08/8.05 ('#sk1168' @ '#sk1')))) & 46.08/8.05 ((('#sk145' @ '#sk1') = (cP @ ('#sk1293' @ '#sk1') @ 46.08/8.05 ('#sk1432' @ '#sk1')))) & 46.08/8.05 ('#sk1' @ ('#sk556' @ '#sk1') @ ('#sk1058' @ '#sk1') @ 46.08/8.05 ('#sk1293' @ '#sk1')) & 46.08/8.05 ('#sk1' @ ('#sk963' @ '#sk1') @ ('#sk1168' @ '#sk1') @ 46.08/8.05 ('#sk1432' @ '#sk1')) & 46.08/8.05 ((('#sk39' @ '#sk1') = (cP @ ('#sk556' @ '#sk1') @ 46.08/8.05 ('#sk963' @ '#sk1')))))) 46.08/8.05 | ('#form611' @ '#sk1') 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))))), 46.08/8.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl148])). 46.08/8.05 thf(zip_derived_cl152, plain, 46.08/8.05 (( ('#sk1' @ ('#sk556' @ '#sk1') @ ('#sk1058' @ '#sk1') @ 46.08/8.05 ('#sk1293' @ '#sk1')) 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))) 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | ('#form611' @ '#sk1'))), 46.08/8.05 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl149])). 46.08/8.05 thf(zip_derived_cl150, plain, 46.08/8.05 (( ((('#sk81' @ '#sk1') = (cP @ ('#sk1058' @ '#sk1') @ 46.08/8.05 ('#sk1168' @ '#sk1')))) 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))) 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | ('#form611' @ '#sk1'))), 46.08/8.05 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl149])). 46.08/8.05 thf(zip_derived_cl155, plain, 46.08/8.05 (((('#sk81' @ '#sk1') 46.08/8.05 = (cP @ ('#sk1058' @ '#sk1') @ ('#sk1168' @ '#sk1'))) 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))) 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | ('#form611' @ '#sk1'))), 46.08/8.05 inference('simplify nested equalities', [status(thm)], 46.08/8.05 [zip_derived_cl150])). 46.08/8.05 thf(zip_derived_cl156, plain, 46.08/8.05 ((~ ('#form2251') 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))))), 46.08/8.05 define([status(thm)])). 46.08/8.05 thf(zip_derived_cl162, plain, 46.08/8.05 (( ('#form2251') 46.08/8.05 | ('#form611' @ '#sk1') 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | ('#sk1' @ ('#sk556' @ '#sk1') @ ('#sk1058' @ '#sk1') @ 46.08/8.05 ('#sk1293' @ '#sk1')))), 46.08/8.05 inference('renaming', [status(thm)], 46.08/8.05 [zip_derived_cl152, zip_derived_cl156])). 46.08/8.05 thf(zip_derived_cl154, plain, 46.08/8.05 (( ((('#sk39' @ '#sk1') = (cP @ ('#sk556' @ '#sk1') @ 46.08/8.05 ('#sk963' @ '#sk1')))) 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))) 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | ('#form611' @ '#sk1'))), 46.08/8.05 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl149])). 46.08/8.05 thf(zip_derived_cl164, plain, 46.08/8.05 (((('#sk39' @ '#sk1') = (cP @ ('#sk556' @ '#sk1') @ ('#sk963' @ '#sk1'))) 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))) 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | ('#form611' @ '#sk1'))), 46.08/8.05 inference('simplify nested equalities', [status(thm)], 46.08/8.05 [zip_derived_cl154])). 46.08/8.05 thf(zip_derived_cl156, plain, 46.08/8.05 ((~ ('#form2251') 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))))), 46.08/8.05 define([status(thm)])). 46.08/8.05 thf(zip_derived_cl165, plain, 46.08/8.05 (( ('#form2251') 46.08/8.05 | ('#form611' @ '#sk1') 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | (('#sk39' @ '#sk1') 46.08/8.05 = (cP @ ('#sk556' @ '#sk1') @ ('#sk963' @ '#sk1'))))), 46.08/8.05 inference('renaming', [status(thm)], 46.08/8.05 [zip_derived_cl164, zip_derived_cl156])). 46.08/8.05 thf(zip_derived_cl155, plain, 46.08/8.05 (((('#sk81' @ '#sk1') 46.08/8.05 = (cP @ ('#sk1058' @ '#sk1') @ ('#sk1168' @ '#sk1'))) 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))) 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | ('#form611' @ '#sk1'))), 46.08/8.05 inference('simplify nested equalities', [status(thm)], 46.08/8.05 [zip_derived_cl150])). 46.08/8.05 thf(zip_derived_cl156, plain, 46.08/8.05 ((~ ('#form2251') 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))))), 46.08/8.05 define([status(thm)])). 46.08/8.05 thf(zip_derived_cl159, plain, 46.08/8.05 (( ('#form2251') 46.08/8.05 | ('#form611' @ '#sk1') 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | (('#sk81' @ '#sk1') 46.08/8.05 = (cP @ ('#sk1058' @ '#sk1') @ ('#sk1168' @ '#sk1'))))), 46.08/8.05 inference('renaming', [status(thm)], 46.08/8.05 [zip_derived_cl155, zip_derived_cl156])). 46.08/8.05 thf(zip_derived_cl153, plain, 46.08/8.05 (( ('#sk1' @ ('#sk963' @ '#sk1') @ ('#sk1168' @ '#sk1') @ 46.08/8.05 ('#sk1432' @ '#sk1')) 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))) 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | ('#form611' @ '#sk1'))), 46.08/8.05 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl149])). 46.08/8.05 thf(zip_derived_cl156, plain, 46.08/8.05 ((~ ('#form2251') 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))))), 46.08/8.05 define([status(thm)])). 46.08/8.05 thf(zip_derived_cl163, plain, 46.08/8.05 (( ('#form2251') 46.08/8.05 | ('#form611' @ '#sk1') 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | ('#sk1' @ ('#sk963' @ '#sk1') @ ('#sk1168' @ '#sk1') @ 46.08/8.05 ('#sk1432' @ '#sk1')))), 46.08/8.05 inference('renaming', [status(thm)], 46.08/8.05 [zip_derived_cl153, zip_derived_cl156])). 46.08/8.05 thf(zip_derived_cl151, plain, 46.08/8.05 (( ((('#sk145' @ '#sk1') = (cP @ ('#sk1293' @ '#sk1') @ 46.08/8.05 ('#sk1432' @ '#sk1')))) 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))) 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | ('#form611' @ '#sk1'))), 46.08/8.05 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl149])). 46.08/8.05 thf(zip_derived_cl160, plain, 46.08/8.05 (((('#sk145' @ '#sk1') 46.08/8.05 = (cP @ ('#sk1293' @ '#sk1') @ ('#sk1432' @ '#sk1'))) 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))) 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | ('#form611' @ '#sk1'))), 46.08/8.05 inference('simplify nested equalities', [status(thm)], 46.08/8.05 [zip_derived_cl151])). 46.08/8.05 thf(zip_derived_cl156, plain, 46.08/8.05 ((~ ('#form2251') 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))))), 46.08/8.05 define([status(thm)])). 46.08/8.05 thf(zip_derived_cl161, plain, 46.08/8.05 (( ('#form2251') 46.08/8.05 | ('#form611' @ '#sk1') 46.08/8.05 | ('#sk1' @ x @ y @ y) 46.08/8.05 | (('#sk145' @ '#sk1') 46.08/8.05 = (cP @ ('#sk1293' @ '#sk1') @ ('#sk1432' @ '#sk1'))))), 46.08/8.05 inference('renaming', [status(thm)], 46.08/8.05 [zip_derived_cl160, zip_derived_cl156])). 46.08/8.05 thf(zip_derived_cl156, plain, 46.08/8.05 ((~ ('#form2251') 46.08/8.05 | ((((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) & 46.08/8.05 ((('#sk39' @ '#sk1') = (c0))))))), 46.08/8.05 define([status(thm)])). 46.08/8.05 thf(zip_derived_cl157, plain, 46.08/8.05 (( ((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1'))) | ~ ('#form2251'))), 46.08/8.05 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl156])). 46.08/8.05 thf(zip_derived_cl166, plain, 46.08/8.05 (((('#sk81' @ '#sk1') = ('#sk145' @ '#sk1')) | ~ ('#form2251'))), 46.08/8.05 inference('simplify nested equalities', [status(thm)], 46.08/8.05 [zip_derived_cl157])). 46.08/8.05 thf(zip_derived_cl2, plain, 46.08/8.05 (~ (((!!) @ (^[Y0 : a > a > a > $o]: 46.08/8.05 (((((!!) @ (^[Y1 : a]: 46.08/8.05 (((!!) @ (^[Y2 : a]: 46.08/8.05 (((!!) @ (^[Y3 : a]: 46.08/8.05 (((((((((Y1) = (c0))) & 46.08/8.05 (((Y2) = (Y3))))) | 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y8 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y9 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 Y0 @ 46.08/8.05 Y4 @ 46.08/8.05 Y6 @ Y8) & 46.08/8.05 ( 46.08/8.05 Y0 @ 46.08/8.05 Y5 @ 46.08/8.05 Y7 @ Y9) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y3) = 46.08/8.05 (cP @ 46.08/8.05 Y8 @ Y9))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y2) = 46.08/8.05 (cP @ 46.08/8.05 Y6 @ Y7))))))))))))))))))))))) | 46.08/8.05 (((((Y1) = (Y3))) & 46.08/8.05 (((Y2) = (c0))))))) => 46.08/8.05 (Y0 @ Y1 @ Y2 @ 46.08/8.05 Y3)))))))))))) => 46.08/8.05 (Y0 @ (cP @ x @ w) @ (cP @ y @ z) @ (cP @ y @ z)))))))), 46.08/8.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 46.08/8.05 thf(zip_derived_cl5, plain, 46.08/8.05 (~ (((((!!) @ (^[Y0 : a]: 46.08/8.05 (((!!) @ (^[Y1 : a]: 46.08/8.05 (((!!) @ (^[Y2 : a]: 46.08/8.05 (((((((((Y0) = (c0))) & 46.08/8.05 (((Y1) = (Y2))))) | 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y8 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y0) = 46.08/8.05 (cP @ 46.08/8.05 Y3 @ Y4))) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y3 @ 46.08/8.05 Y5 @ Y7) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y4 @ 46.08/8.05 Y6 @ Y8) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y2) = 46.08/8.05 (cP @ 46.08/8.05 Y7 @ Y8))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y5 @ Y6))))))))))))))))))))))) | 46.08/8.05 (((((Y0) = (Y2))) & 46.08/8.05 (((Y1) = (c0))))))) => 46.08/8.05 ('#sk1' @ Y0 @ Y1 @ Y2)))))))))))) => 46.08/8.05 ('#sk1' @ (cP @ x @ w) @ (cP @ y @ z) @ (cP @ y @ z))))), 46.08/8.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 46.08/8.05 thf(zip_derived_cl10, plain, 46.08/8.05 ( (((!!) @ (^[Y0 : a]: 46.08/8.05 (((!!) @ (^[Y1 : a]: 46.08/8.05 (((!!) @ (^[Y2 : a]: 46.08/8.05 (((((((((Y0) = (c0))) & 46.08/8.05 (((Y1) = (Y2))))) | 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ (^[Y4 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y8 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y0) = 46.08/8.05 (cP @ 46.08/8.05 Y3 @ Y4))) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y3 @ 46.08/8.05 Y5 @ Y7) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y4 @ 46.08/8.05 Y6 @ Y8) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y2) = 46.08/8.05 (cP @ 46.08/8.05 Y7 @ Y8))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y5 @ Y6))))))))))))))))))))))) | 46.08/8.05 (((((Y0) = (Y2))) & 46.08/8.05 (((Y1) = (c0))))))) => 46.08/8.05 ('#sk1' @ Y0 @ Y1 @ Y2))))))))))))), 46.08/8.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 46.08/8.05 thf(zip_derived_cl14, plain, 46.08/8.05 (![X2 : a]: 46.08/8.05 (((!!) @ (^[Y0 : a]: 46.08/8.05 (((!!) @ (^[Y1 : a]: 46.08/8.05 (((((((((X2) = (c0))) & (((Y0) = (Y1))))) | 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (X2) = 46.08/8.05 (cP @ 46.08/8.05 Y2 @ Y3))) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y2 @ 46.08/8.05 Y4 @ Y6) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y3 @ 46.08/8.05 Y5 @ Y7) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y6 @ Y7))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y0) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))))))))))))))))))))))) | 46.08/8.05 (((((X2) = (Y1))) & (((Y0) = (c0))))))) => 46.08/8.05 ('#sk1' @ X2 @ Y0 @ Y1)))))))))), 46.08/8.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 46.08/8.05 thf(zip_derived_cl17, plain, 46.08/8.05 (![X2 : a, X4 : a]: 46.08/8.05 (((!!) @ (^[Y0 : a]: 46.08/8.05 (((((((((X2) = (c0))) & (((X4) = (Y0))))) | 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (X2) = 46.08/8.05 (cP @ 46.08/8.05 Y1 @ Y2))) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y1 @ 46.08/8.05 Y3 @ Y5) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y2 @ 46.08/8.05 Y4 @ Y6) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y0) = 46.08/8.05 (cP @ 46.08/8.05 Y5 @ Y6))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (X4) = 46.08/8.05 (cP @ 46.08/8.05 Y3 @ Y4))))))))))))))))))))))) | 46.08/8.05 (((((X2) = (Y0))) & (((X4) = (c0))))))) => 46.08/8.05 ('#sk1' @ X2 @ X4 @ Y0))))))), 46.08/8.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 46.08/8.05 thf(zip_derived_cl20, plain, 46.08/8.05 (![X2 : a, X4 : a, X6 : a]: 46.08/8.05 (((((((((X2) = (c0))) & (((X4) = (X6))))) | 46.08/8.05 (((??) @ (^[Y0 : a]: 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (X2) = 46.08/8.05 (cP @ 46.08/8.05 Y0 @ Y1))) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y0 @ 46.08/8.05 Y2 @ Y4) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y1 @ 46.08/8.05 Y3 @ Y5) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (X6) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (X4) = 46.08/8.05 (cP @ 46.08/8.05 Y2 @ Y3))))))))))))))))))))))) | 46.08/8.05 (((((X2) = (X6))) & (((X4) = (c0))))))) => 46.08/8.05 ('#sk1' @ X2 @ X4 @ X6)))), 46.08/8.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 46.08/8.05 thf(zip_derived_cl23, plain, 46.08/8.05 (![X2 : a, X4 : a, X6 : a]: 46.08/8.05 (~ (((((((X2) = (c0))) & (((X4) = (X6))))) | 46.08/8.05 (((??) @ (^[Y0 : a]: 46.08/8.05 (((??) @ (^[Y1 : a]: 46.08/8.05 (((??) @ (^[Y2 : a]: 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (X2) = 46.08/8.05 (cP @ 46.08/8.05 Y0 @ Y1))) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y0 @ 46.08/8.05 Y2 @ Y4) & 46.08/8.05 ( 46.08/8.05 '#sk1' @ 46.08/8.05 Y1 @ 46.08/8.05 Y3 @ Y5) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (X6) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (X4) = 46.08/8.05 (cP @ 46.08/8.05 Y2 @ Y3))))))))))))))))))))))) | 46.08/8.05 (((((X2) = (X6))) & (((X4) = (c0))))))) 46.08/8.05 | ('#sk1' @ X2 @ X4 @ X6))), 46.08/8.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 46.08/8.05 thf(zip_derived_cl28, plain, 46.08/8.05 (![X2 : a, X4 : a, X6 : a]: 46.08/8.05 (~ (((((X2) = (c0))) & (((X4) = (X6))))) | ('#sk1' @ X2 @ X4 @ X6))), 46.08/8.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl23])). 46.08/8.05 thf(zip_derived_cl33, plain, 46.08/8.05 (![X2 : a, X4 : a, X6 : a]: 46.08/8.05 (~ (((X2) = (c0))) | ~ (((X4) = (X6))) | ('#sk1' @ X2 @ X4 @ X6))), 46.08/8.05 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl28])). 46.08/8.05 thf(zip_derived_cl40, plain, 46.08/8.05 (![X2 : a, X4 : a, X6 : a]: 46.08/8.05 (((X2) != (c0)) | ((X4) != (X6)) | ('#sk1' @ X2 @ X4 @ X6))), 46.08/8.05 inference('simplify nested equalities', [status(thm)], [zip_derived_cl33])). 46.08/8.05 thf(zip_derived_cl41, plain, (![X6 : a]: ('#sk1' @ c0 @ X6 @ X6)), 46.08/8.05 inference('simplify', [status(thm)], [zip_derived_cl40])). 46.08/8.05 thf(zip_derived_cl3, plain, 46.08/8.05 ( (((!!) @ (^[Y0 : a > a > a > $o]: 46.08/8.05 (((((!!) @ (^[Y1 : a]: 46.08/8.05 (((!!) @ (^[Y2 : a]: 46.08/8.05 (((!!) @ (^[Y3 : a]: 46.08/8.05 (((((((((Y2) = (c0))) & 46.08/8.05 (((Y1) = (Y3))))) | 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y6 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y7 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y8 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.05 ^[Y9 : a]: 46.08/8.05 (( 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y1) = 46.08/8.05 (cP @ 46.08/8.05 Y4 @ Y5))) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y3) = 46.08/8.05 (cP @ 46.08/8.05 Y8 @ Y9))) & 46.08/8.05 ( 46.08/8.05 Y0 @ 46.08/8.05 Y5 @ 46.08/8.05 Y7 @ Y9) & 46.08/8.05 ( 46.08/8.05 Y0 @ 46.08/8.05 Y4 @ 46.08/8.05 Y6 @ Y8) & 46.08/8.05 ( 46.08/8.05 ( 46.08/8.05 (Y2) = 46.08/8.05 (cP @ 46.08/8.05 Y6 @ Y7))))))))))))))))))))))) | 46.08/8.05 (((((Y1) = (c0))) & 46.08/8.05 (((Y2) = (Y3))))))) => 46.08/8.05 (Y0 @ Y1 @ Y2 @ Y3)))))))))))) => 46.08/8.05 (Y0 @ w @ z @ z))))))), 46.08/8.05 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1])). 46.08/8.05 thf(zip_derived_cl6, plain, 46.08/8.05 (![X2 : a > a > a > $o]: 46.08/8.05 (((((!!) @ (^[Y0 : a]: 46.08/8.05 (((!!) @ (^[Y1 : a]: 46.08/8.05 (((!!) @ (^[Y2 : a]: 46.08/8.05 (((((((((Y1) = (c0))) & 46.08/8.05 (((Y0) = (Y2))))) | 46.08/8.05 (((??) @ (^[Y3 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y4 : a]: 46.08/8.05 (((??) @ ( 46.08/8.05 ^[Y5 : a]: 46.08/8.05 (( 46.08/8.05 (??) @ ( 46.08/8.06 ^[Y6 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y7 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y8 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y0) = 46.08/8.06 (cP @ 46.08/8.06 Y3 @ Y4))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y2) = 46.08/8.06 (cP @ 46.08/8.06 Y7 @ Y8))) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y4 @ 46.08/8.06 Y6 @ Y8) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y3 @ 46.08/8.06 Y5 @ Y7) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y1) = 46.08/8.06 (cP @ 46.08/8.06 Y5 @ Y6))))))))))))))))))))))) | 46.08/8.06 (((((Y0) = (c0))) & 46.08/8.06 (((Y1) = (Y2))))))) => 46.08/8.06 (X2 @ Y0 @ Y1 @ Y2)))))))))))) => 46.08/8.06 (X2 @ w @ z @ z)))), 46.08/8.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 46.08/8.06 thf(zip_derived_cl7, plain, 46.08/8.06 ( (((((!!) @ (^[Y0 : a]: 46.08/8.06 (((!!) @ (^[Y1 : a]: 46.08/8.06 (((!!) @ (^[Y2 : a]: 46.08/8.06 (((((((((Y1) = (c0))) & 46.08/8.06 (((Y0) = (Y2))))) | 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y4 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y6 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y7 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y8 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y0) = 46.08/8.06 (cP @ 46.08/8.06 Y3 @ Y4))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y2) = 46.08/8.06 (cP @ 46.08/8.06 Y7 @ Y8))) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 Y4 @ 46.08/8.06 Y6 @ Y8) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 Y3 @ 46.08/8.06 Y5 @ Y7) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y1) = 46.08/8.06 (cP @ 46.08/8.06 Y5 @ Y6))))))))))))))))))))))) | 46.08/8.06 (((((Y0) = (c0))) & 46.08/8.06 (((Y1) = (Y2))))))) => 46.08/8.06 ('#sk1' @ Y0 @ Y1 @ Y2)))))))))))) => 46.08/8.06 ('#sk1' @ w @ z @ z)))), 46.08/8.06 inference('triggered_bool_instantiation', [status(thm)], 46.08/8.06 [zip_derived_cl6])). 46.08/8.06 thf(zip_derived_cl117, plain, 46.08/8.06 ((~ (((!!) @ (^[Y0 : a]: 46.08/8.06 (((!!) @ (^[Y1 : a]: 46.08/8.06 (((!!) @ (^[Y2 : a]: 46.08/8.06 (((((((((Y1) = (c0))) & 46.08/8.06 (((Y0) = (Y2))))) | 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y4 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y6 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y7 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y8 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y0) = 46.08/8.06 (cP @ 46.08/8.06 Y3 @ Y4))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y2) = 46.08/8.06 (cP @ 46.08/8.06 Y7 @ Y8))) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 Y4 @ 46.08/8.06 Y6 @ Y8) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 Y3 @ 46.08/8.06 Y5 @ Y7) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y1) = 46.08/8.06 (cP @ 46.08/8.06 Y5 @ Y6))))))))))))))))))))))) | 46.08/8.06 (((((Y0) = (c0))) & 46.08/8.06 (((Y1) = (Y2))))))) => 46.08/8.06 ('#sk1' @ Y0 @ Y1 @ Y2)))))))))))) 46.08/8.06 | ('#sk1' @ w @ z @ z))), 46.08/8.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 46.08/8.06 thf(zip_derived_cl118, plain, 46.08/8.06 ((~ (((!!) @ (^[Y0 : a]: 46.08/8.06 (((!!) @ (^[Y1 : a]: 46.08/8.06 (((((((((Y0) = (c0))) & 46.08/8.06 ((('#sk29' @ '#sk1') = (Y1))))) | 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y4 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y6 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y7 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk29' @ 46.08/8.06 '#sk1') = 46.08/8.06 (cP @ 46.08/8.06 Y2 @ Y3))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y1) = 46.08/8.06 (cP @ 46.08/8.06 Y6 @ Y7))) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 Y3 @ 46.08/8.06 Y5 @ Y7) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 Y2 @ 46.08/8.06 Y4 @ Y6) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y0) = 46.08/8.06 (cP @ 46.08/8.06 Y4 @ Y5))))))))))))))))))))))) | 46.08/8.06 ((((('#sk29' @ '#sk1') = (c0))) & 46.08/8.06 (((Y0) = (Y1))))))) => 46.08/8.06 ('#sk1' @ ('#sk29' @ '#sk1') @ Y0 @ Y1))))))))) 46.08/8.06 | ('#sk1' @ w @ z @ z))), 46.08/8.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl117])). 46.08/8.06 thf(zip_derived_cl119, plain, 46.08/8.06 ((~ (((!!) @ (^[Y0 : a]: 46.08/8.06 ((((((((('#sk60' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk29' @ '#sk1') = (Y0))))) | 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y4 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y6 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk29' @ 46.08/8.06 '#sk1') = 46.08/8.06 (cP @ 46.08/8.06 Y1 @ Y2))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y0) = 46.08/8.06 (cP @ 46.08/8.06 Y5 @ Y6))) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 Y2 @ 46.08/8.06 Y4 @ Y6) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 Y1 @ 46.08/8.06 Y3 @ Y5) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk60' @ 46.08/8.06 '#sk1') = 46.08/8.06 (cP @ 46.08/8.06 Y3 @ Y4))))))))))))))))))))))) | 46.08/8.06 ((((('#sk29' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk60' @ '#sk1') = (Y0))))))) => 46.08/8.06 ('#sk1' @ ('#sk29' @ '#sk1') @ ('#sk60' @ '#sk1') @ Y0)))))) 46.08/8.06 | ('#sk1' @ w @ z @ z))), 46.08/8.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl118])). 46.08/8.06 thf(zip_derived_cl120, plain, 46.08/8.06 ((~ ((((((((('#sk60' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk29' @ '#sk1') = ('#sk113' @ '#sk1'))))) | 46.08/8.06 (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y4 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk29' @ 46.08/8.06 '#sk1') = 46.08/8.06 (cP @ 46.08/8.06 Y0 @ Y1))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk113' @ 46.08/8.06 '#sk1') = 46.08/8.06 (cP @ 46.08/8.06 Y4 @ Y5))) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 Y1 @ 46.08/8.06 Y3 @ Y5) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 Y0 @ 46.08/8.06 Y2 @ Y4) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk60' @ 46.08/8.06 '#sk1') = 46.08/8.06 (cP @ 46.08/8.06 Y2 @ Y3))))))))))))))))))))))) | 46.08/8.06 ((((('#sk29' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk60' @ '#sk1') = ('#sk113' @ '#sk1'))))))) => 46.08/8.06 ('#sk1' @ ('#sk29' @ '#sk1') @ ('#sk60' @ '#sk1') @ 46.08/8.06 ('#sk113' @ '#sk1')))) 46.08/8.06 | ('#sk1' @ w @ z @ z))), 46.08/8.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl119])). 46.08/8.06 thf(zip_derived_cl121, plain, 46.08/8.06 (( ((((((('#sk60' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk29' @ '#sk1') = ('#sk113' @ '#sk1'))))) | 46.08/8.06 (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ (^[Y4 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk29' @ 46.08/8.06 '#sk1') = 46.08/8.06 (cP @ 46.08/8.06 Y0 @ Y1))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk113' @ 46.08/8.06 '#sk1') = 46.08/8.06 (cP @ 46.08/8.06 Y4 @ Y5))) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 Y1 @ 46.08/8.06 Y3 @ Y5) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 Y0 @ 46.08/8.06 Y2 @ Y4) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk60' @ 46.08/8.06 '#sk1') = 46.08/8.06 (cP @ 46.08/8.06 Y2 @ Y3))))))))))))))))))))))) | 46.08/8.06 ((((('#sk29' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk60' @ '#sk1') = ('#sk113' @ '#sk1'))))))) 46.08/8.06 | ('#sk1' @ w @ z @ z))), 46.08/8.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl120])). 46.08/8.06 thf(zip_derived_cl123, plain, 46.08/8.06 (( ((((('#sk60' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk29' @ '#sk1') = ('#sk113' @ '#sk1'))))) 46.08/8.06 | (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ (^[Y4 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk29' @ 46.08/8.06 '#sk1') = 46.08/8.06 (cP @ 46.08/8.06 Y0 @ Y1))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk113' @ 46.08/8.06 '#sk1') = 46.08/8.06 (cP @ 46.08/8.06 Y4 @ Y5))) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 Y1 @ 46.08/8.06 Y3 @ Y5) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 Y0 @ 46.08/8.06 Y2 @ Y4) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk60' @ 46.08/8.06 '#sk1') = 46.08/8.06 (cP @ 46.08/8.06 Y2 @ Y3))))))))))))))))))))))) 46.08/8.06 | ((((('#sk29' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk60' @ '#sk1') = ('#sk113' @ '#sk1'))))) 46.08/8.06 | ('#sk1' @ w @ z @ z))), 46.08/8.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl121])). 46.08/8.06 thf(zip_derived_cl6, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 (((((!!) @ (^[Y0 : a]: 46.08/8.06 (((!!) @ (^[Y1 : a]: 46.08/8.06 (((!!) @ (^[Y2 : a]: 46.08/8.06 (((((((((Y1) = (c0))) & 46.08/8.06 (((Y0) = (Y2))))) | 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y4 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y6 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y7 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y8 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y0) = 46.08/8.06 (cP @ 46.08/8.06 Y3 @ Y4))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y2) = 46.08/8.06 (cP @ 46.08/8.06 Y7 @ Y8))) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y4 @ 46.08/8.06 Y6 @ Y8) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y3 @ 46.08/8.06 Y5 @ Y7) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y1) = 46.08/8.06 (cP @ 46.08/8.06 Y5 @ Y6))))))))))))))))))))))) | 46.08/8.06 (((((Y0) = (c0))) & 46.08/8.06 (((Y1) = (Y2))))))) => 46.08/8.06 (X2 @ Y0 @ Y1 @ Y2)))))))))))) => 46.08/8.06 (X2 @ w @ z @ z)))), 46.08/8.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 46.08/8.06 thf(zip_derived_cl12, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 (~ (((!!) @ (^[Y0 : a]: 46.08/8.06 (((!!) @ (^[Y1 : a]: 46.08/8.06 (((!!) @ (^[Y2 : a]: 46.08/8.06 (((((((((Y1) = (c0))) & 46.08/8.06 (((Y0) = (Y2))))) | 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y4 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y6 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y7 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y8 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y0) = 46.08/8.06 (cP @ 46.08/8.06 Y3 @ Y4))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y2) = 46.08/8.06 (cP @ 46.08/8.06 Y7 @ Y8))) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y4 @ 46.08/8.06 Y6 @ Y8) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y3 @ 46.08/8.06 Y5 @ Y7) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y1) = 46.08/8.06 (cP @ 46.08/8.06 Y5 @ Y6))))))))))))))))))))))) | 46.08/8.06 (((((Y0) = (c0))) & 46.08/8.06 (((Y1) = (Y2))))))) => 46.08/8.06 (X2 @ Y0 @ Y1 @ Y2)))))))))))) 46.08/8.06 | (X2 @ w @ z @ z))), 46.08/8.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 46.08/8.06 thf(zip_derived_cl15, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 (~ (((!!) @ (^[Y0 : a]: 46.08/8.06 (((!!) @ (^[Y1 : a]: 46.08/8.06 (((((((((Y0) = (c0))) & 46.08/8.06 ((('#sk29' @ X2) = (Y1))))) | 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y4 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y6 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y7 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk29' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y2 @ Y3))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y1) = 46.08/8.06 (cP @ 46.08/8.06 Y6 @ Y7))) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y3 @ 46.08/8.06 Y5 @ Y7) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y2 @ 46.08/8.06 Y4 @ Y6) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y0) = 46.08/8.06 (cP @ 46.08/8.06 Y4 @ Y5))))))))))))))))))))))) | 46.08/8.06 ((((('#sk29' @ X2) = (c0))) & 46.08/8.06 (((Y0) = (Y1))))))) => 46.08/8.06 (X2 @ ('#sk29' @ X2) @ Y0 @ Y1))))))))) 46.08/8.06 | (X2 @ w @ z @ z))), 46.08/8.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 46.08/8.06 thf(zip_derived_cl18, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 (~ (((!!) @ (^[Y0 : a]: 46.08/8.06 ((((((((('#sk60' @ X2) = (c0))) & 46.08/8.06 ((('#sk29' @ X2) = (Y0))))) | 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y4 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y6 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk29' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y1 @ Y2))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (Y0) = 46.08/8.06 (cP @ 46.08/8.06 Y5 @ Y6))) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y2 @ 46.08/8.06 Y4 @ Y6) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y1 @ 46.08/8.06 Y3 @ Y5) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk60' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y3 @ Y4))))))))))))))))))))))) | 46.08/8.06 ((((('#sk29' @ X2) = (c0))) & 46.08/8.06 ((('#sk60' @ X2) = (Y0))))))) => 46.08/8.06 (X2 @ ('#sk29' @ X2) @ ('#sk60' @ X2) @ Y0)))))) 46.08/8.06 | (X2 @ w @ z @ z))), 46.08/8.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])). 46.08/8.06 thf(zip_derived_cl21, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 (~ ((((((((('#sk60' @ X2) = (c0))) & 46.08/8.06 ((('#sk29' @ X2) = ('#sk113' @ X2))))) | 46.08/8.06 (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y4 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk29' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y0 @ Y1))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk113' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y4 @ Y5))) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y1 @ 46.08/8.06 Y3 @ Y5) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y0 @ 46.08/8.06 Y2 @ Y4) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk60' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y2 @ Y3))))))))))))))))))))))) | 46.08/8.06 ((((('#sk29' @ X2) = (c0))) & 46.08/8.06 ((('#sk60' @ X2) = ('#sk113' @ X2))))))) => 46.08/8.06 (X2 @ ('#sk29' @ X2) @ ('#sk60' @ X2) @ ('#sk113' @ X2)))) 46.08/8.06 | (X2 @ w @ z @ z))), 46.08/8.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl18])). 46.08/8.06 thf(zip_derived_cl24, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ( ((((((('#sk60' @ X2) = (c0))) & ((('#sk29' @ X2) = ('#sk113' @ X2))))) | 46.08/8.06 (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y4 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk29' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y0 @ Y1))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk113' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y4 @ Y5))) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y1 @ 46.08/8.06 Y3 @ Y5) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y0 @ 46.08/8.06 Y2 @ Y4) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk60' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y2 @ Y3))))))))))))))))))))))) | 46.08/8.06 ((((('#sk29' @ X2) = (c0))) & ((('#sk60' @ X2) = ('#sk113' @ X2))))))) 46.08/8.06 | (X2 @ w @ z @ z))), 46.08/8.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 46.08/8.06 thf(zip_derived_cl31, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ( ((((('#sk60' @ X2) = (c0))) & ((('#sk29' @ X2) = ('#sk113' @ X2))))) 46.08/8.06 | (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y4 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk29' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y0 @ Y1))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk113' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y4 @ Y5))) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y1 @ 46.08/8.06 Y3 @ Y5) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y0 @ 46.08/8.06 Y2 @ Y4) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk60' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y2 @ Y3))))))))))))))))))))))) 46.08/8.06 | ((((('#sk29' @ X2) = (c0))) & ((('#sk60' @ X2) = ('#sk113' @ X2))))) 46.08/8.06 | (X2 @ w @ z @ z))), 46.08/8.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl24])). 46.08/8.06 thf(zip_derived_cl37, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ( ((('#sk29' @ X2) = ('#sk113' @ X2))) 46.08/8.06 | (X2 @ w @ z @ z) 46.08/8.06 | ((((('#sk29' @ X2) = (c0))) & ((('#sk60' @ X2) = ('#sk113' @ X2))))) 46.08/8.06 | (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y4 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk29' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y0 @ Y1))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk113' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y4 @ Y5))) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y1 @ 46.08/8.06 Y3 @ Y5) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y0 @ 46.08/8.06 Y2 @ Y4) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk60' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y2 @ Y3))))))))))))))))))))))))), 46.08/8.06 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl31])). 46.08/8.06 thf(zip_derived_cl48, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ((('#sk29' @ X2) = ('#sk113' @ X2)) 46.08/8.06 | (X2 @ w @ z @ z) 46.08/8.06 | ((((('#sk29' @ X2) = (c0))) & ((('#sk60' @ X2) = ('#sk113' @ X2))))) 46.08/8.06 | (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y4 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk29' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y0 @ Y1))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk113' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y4 @ Y5))) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y1 @ 46.08/8.06 Y3 @ Y5) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y0 @ 46.08/8.06 Y2 @ Y4) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk60' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y2 @ Y3))))))))))))))))))))))))), 46.08/8.06 inference('simplify nested equalities', [status(thm)], [zip_derived_cl37])). 46.08/8.06 thf(zip_derived_cl49, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 (~ ('#form494' @ X2) 46.08/8.06 | (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y4 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk29' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y0 @ Y1))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk113' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y4 @ Y5))) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y1 @ 46.08/8.06 Y3 @ Y5) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y0 @ 46.08/8.06 Y2 @ Y4) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk60' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y2 @ Y3))))))))))))))))))))))))), 46.08/8.06 define([status(thm)])). 46.08/8.06 thf(zip_derived_cl124, plain, 46.08/8.06 (( ('#form494' @ '#sk1') 46.08/8.06 | ('#sk1' @ w @ z @ z) 46.08/8.06 | ((((('#sk29' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk60' @ '#sk1') = ('#sk113' @ '#sk1'))))) 46.08/8.06 | ((((('#sk60' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk29' @ '#sk1') = ('#sk113' @ '#sk1'))))))), 46.08/8.06 inference('renaming', [status(thm)], 46.08/8.06 [zip_derived_cl123, zip_derived_cl49])). 46.08/8.06 thf(zip_derived_cl126, plain, 46.08/8.06 (( ((('#sk60' @ '#sk1') = ('#sk113' @ '#sk1'))) 46.08/8.06 | ((((('#sk60' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk29' @ '#sk1') = ('#sk113' @ '#sk1'))))) 46.08/8.06 | ('#sk1' @ w @ z @ z) 46.08/8.06 | ('#form494' @ '#sk1'))), 46.08/8.06 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl124])). 46.08/8.06 thf(zip_derived_cl132, plain, 46.08/8.06 (((('#sk60' @ '#sk1') = ('#sk113' @ '#sk1')) 46.08/8.06 | ((((('#sk60' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk29' @ '#sk1') = ('#sk113' @ '#sk1'))))) 46.08/8.06 | ('#sk1' @ w @ z @ z) 46.08/8.06 | ('#form494' @ '#sk1'))), 46.08/8.06 inference('simplify nested equalities', [status(thm)], 46.08/8.06 [zip_derived_cl126])). 46.08/8.06 thf(zip_derived_cl125, plain, 46.08/8.06 (( ((('#sk29' @ '#sk1') = (c0))) 46.08/8.06 | ((((('#sk60' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk29' @ '#sk1') = ('#sk113' @ '#sk1'))))) 46.08/8.06 | ('#sk1' @ w @ z @ z) 46.08/8.06 | ('#form494' @ '#sk1'))), 46.08/8.06 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl124])). 46.08/8.06 thf(zip_derived_cl127, plain, 46.08/8.06 (((('#sk29' @ '#sk1') = (c0)) 46.08/8.06 | ((((('#sk60' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk29' @ '#sk1') = ('#sk113' @ '#sk1'))))) 46.08/8.06 | ('#sk1' @ w @ z @ z) 46.08/8.06 | ('#form494' @ '#sk1'))), 46.08/8.06 inference('simplify nested equalities', [status(thm)], 46.08/8.06 [zip_derived_cl125])). 46.08/8.06 thf(zip_derived_cl128, plain, 46.08/8.06 ((~ ('#form2115') 46.08/8.06 | ((((('#sk60' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk29' @ '#sk1') = ('#sk113' @ '#sk1'))))))), 46.08/8.06 define([status(thm)])). 46.08/8.06 thf(zip_derived_cl133, plain, 46.08/8.06 (( ('#form2115') 46.08/8.06 | ('#form494' @ '#sk1') 46.08/8.06 | ('#sk1' @ w @ z @ z) 46.08/8.06 | (('#sk60' @ '#sk1') = ('#sk113' @ '#sk1')))), 46.08/8.06 inference('renaming', [status(thm)], 46.08/8.06 [zip_derived_cl132, zip_derived_cl128])). 46.08/8.06 thf(zip_derived_cl11, plain, 46.08/8.06 (~ ('#sk1' @ (cP @ x @ w) @ (cP @ y @ z) @ (cP @ y @ z))), 46.08/8.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 46.08/8.06 thf(zip_derived_cl158, plain, 46.08/8.06 (( ((('#sk39' @ '#sk1') = (c0))) | ~ ('#form2251'))), 46.08/8.06 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl156])). 46.08/8.06 thf(zip_derived_cl167, plain, 46.08/8.06 (((('#sk39' @ '#sk1') = (c0)) | ~ ('#form2251'))), 46.08/8.06 inference('simplify nested equalities', [status(thm)], 46.08/8.06 [zip_derived_cl158])). 46.08/8.06 thf(zip_derived_cl127, plain, 46.08/8.06 (((('#sk29' @ '#sk1') = (c0)) 46.08/8.06 | ((((('#sk60' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk29' @ '#sk1') = ('#sk113' @ '#sk1'))))) 46.08/8.06 | ('#sk1' @ w @ z @ z) 46.08/8.06 | ('#form494' @ '#sk1'))), 46.08/8.06 inference('simplify nested equalities', [status(thm)], 46.08/8.06 [zip_derived_cl125])). 46.08/8.06 thf(zip_derived_cl128, plain, 46.08/8.06 ((~ ('#form2115') 46.08/8.06 | ((((('#sk60' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk29' @ '#sk1') = ('#sk113' @ '#sk1'))))))), 46.08/8.06 define([status(thm)])). 46.08/8.06 thf(zip_derived_cl131, plain, 46.08/8.06 (( ('#form2115') 46.08/8.06 | ('#form494' @ '#sk1') 46.08/8.06 | ('#sk1' @ w @ z @ z) 46.08/8.06 | (('#sk29' @ '#sk1') = (c0)))), 46.08/8.06 inference('renaming', [status(thm)], 46.08/8.06 [zip_derived_cl127, zip_derived_cl128])). 46.08/8.06 thf(zip_derived_cl27, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 (~ (X2 @ ('#sk39' @ X2) @ ('#sk81' @ X2) @ ('#sk145' @ X2)) 46.08/8.06 | (X2 @ x @ y @ y))), 46.08/8.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 46.08/8.06 thf(zip_derived_cl30, plain, 46.08/8.06 (![X2 : a, X4 : a, X6 : a]: 46.08/8.06 (~ (((((X2) = (X6))) & (((X4) = (c0))))) | ('#sk1' @ X2 @ X4 @ X6))), 46.08/8.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl23])). 46.08/8.06 thf(zip_derived_cl35, plain, 46.08/8.06 (![X2 : a, X4 : a, X6 : a]: 46.08/8.06 (~ (((X2) = (X6))) | ~ (((X4) = (c0))) | ('#sk1' @ X2 @ X4 @ X6))), 46.08/8.06 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl30])). 46.08/8.06 thf(zip_derived_cl43, plain, 46.08/8.06 (![X2 : a, X4 : a, X6 : a]: 46.08/8.06 (((X2) != (X6)) | ((X4) != (c0)) | ('#sk1' @ X2 @ X4 @ X6))), 46.08/8.06 inference('simplify nested equalities', [status(thm)], [zip_derived_cl35])). 46.08/8.06 thf(zip_derived_cl44, plain, (![X6 : a]: ('#sk1' @ X6 @ c0 @ X6)), 46.08/8.06 inference('simplify', [status(thm)], [zip_derived_cl43])). 46.08/8.06 thf(zip_derived_cl128, plain, 46.08/8.06 ((~ ('#form2115') 46.08/8.06 | ((((('#sk60' @ '#sk1') = (c0))) & 46.08/8.06 ((('#sk29' @ '#sk1') = ('#sk113' @ '#sk1'))))))), 46.08/8.06 define([status(thm)])). 46.08/8.06 thf(zip_derived_cl130, plain, 46.08/8.06 (( ((('#sk29' @ '#sk1') = ('#sk113' @ '#sk1'))) | ~ ('#form2115'))), 46.08/8.06 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl128])). 46.08/8.06 thf(zip_derived_cl135, plain, 46.08/8.06 (((('#sk29' @ '#sk1') = ('#sk113' @ '#sk1')) | ~ ('#form2115'))), 46.08/8.06 inference('simplify nested equalities', [status(thm)], 46.08/8.06 [zip_derived_cl130])). 46.08/8.06 thf(zip_derived_cl129, plain, 46.08/8.06 (( ((('#sk60' @ '#sk1') = (c0))) | ~ ('#form2115'))), 46.08/8.06 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl128])). 46.08/8.06 thf(zip_derived_cl134, plain, 46.08/8.06 (((('#sk60' @ '#sk1') = (c0)) | ~ ('#form2115'))), 46.08/8.06 inference('simplify nested equalities', [status(thm)], 46.08/8.06 [zip_derived_cl129])). 46.08/8.06 thf(zip_derived_cl25, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 (~ (X2 @ ('#sk29' @ X2) @ ('#sk60' @ X2) @ ('#sk113' @ X2)) 46.08/8.06 | (X2 @ w @ z @ z))), 46.08/8.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 46.08/8.06 thf(zip_derived_cl49, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 (~ ('#form494' @ X2) 46.08/8.06 | (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y4 : a]: 46.08/8.06 (((??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk29' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y0 @ Y1))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk113' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y4 @ Y5))) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y1 @ 46.08/8.06 Y3 @ Y5) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y0 @ 46.08/8.06 Y2 @ Y4) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk60' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y2 @ Y3))))))))))))))))))))))))), 46.08/8.06 define([status(thm)])). 46.08/8.06 thf(zip_derived_cl50, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ( (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ (^[Y4 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk29' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 ( 46.08/8.06 '#sk495' @ 46.08/8.06 X2) @ Y0))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk113' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y3 @ Y4))) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 Y0 @ 46.08/8.06 Y2 @ Y4) & 46.08/8.06 ( 46.08/8.06 X2 @ 46.08/8.06 ( 46.08/8.06 '#sk495' @ 46.08/8.06 X2) @ 46.08/8.06 Y1 @ Y3) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 ('#sk60' @ 46.08/8.06 X2) = 46.08/8.06 (cP @ 46.08/8.06 Y1 @ Y2)))))))))))))))))))) 46.08/8.06 | ~ ('#form494' @ X2))), 46.08/8.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl49])). 46.08/8.06 thf(zip_derived_cl66, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ( (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 ((((('#sk29' @ X2) = 46.08/8.06 (cP @ 46.08/8.06 ('#sk495' @ X2) @ 46.08/8.06 ('#sk743' @ X2)))) & 46.08/8.06 ((('#sk113' @ 46.08/8.06 X2) = (cP @ 46.08/8.06 Y2 @ Y3))) & 46.08/8.06 (X2 @ 46.08/8.06 ('#sk743' @ X2) @ 46.08/8.06 Y1 @ Y3) & 46.08/8.06 (X2 @ 46.08/8.06 ('#sk495' @ X2) @ 46.08/8.06 Y0 @ Y2) & 46.08/8.06 ((('#sk60' @ X2) = 46.08/8.06 (cP @ Y0 @ Y1))))))))))))))))) 46.08/8.06 | ~ ('#form494' @ X2))), 46.08/8.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl50])). 46.08/8.06 thf(zip_derived_cl74, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ( (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 ((((('#sk29' @ X2) = (cP @ 46.08/8.06 ('#sk495' @ X2) @ 46.08/8.06 ('#sk743' @ X2)))) & 46.08/8.06 ((('#sk113' @ X2) = (cP @ 46.08/8.06 Y1 @ Y2))) & 46.08/8.06 (X2 @ ('#sk743' @ X2) @ Y0 @ 46.08/8.06 Y2) & 46.08/8.06 (X2 @ ('#sk495' @ X2) @ 46.08/8.06 ('#sk933' @ X2) @ Y1) & 46.08/8.06 ((('#sk60' @ X2) = (cP @ 46.08/8.06 ('#sk933' @ X2) @ Y0)))))))))))))) 46.08/8.06 | ~ ('#form494' @ X2))), 46.08/8.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl66])). 46.08/8.06 thf(zip_derived_cl78, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ( (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 ((((('#sk29' @ X2) = (cP @ 46.08/8.06 ('#sk495' @ X2) @ ('#sk743' @ X2)))) & 46.08/8.06 ((('#sk113' @ X2) = (cP @ Y0 @ Y1))) & 46.08/8.06 (X2 @ ('#sk743' @ X2) @ 46.08/8.06 ('#sk1023' @ X2) @ Y1) & 46.08/8.06 (X2 @ ('#sk495' @ X2) @ ('#sk933' @ X2) @ 46.08/8.06 Y0) & 46.08/8.06 ((('#sk60' @ X2) = (cP @ 46.08/8.06 ('#sk933' @ X2) @ ('#sk1023' @ X2)))))))))))) 46.08/8.06 | ~ ('#form494' @ X2))), 46.08/8.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl74])). 46.08/8.06 thf(zip_derived_cl82, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ( (((??) @ (^[Y0 : a]: 46.08/8.06 ((((('#sk29' @ X2) = (cP @ ('#sk495' @ X2) @ 46.08/8.06 ('#sk743' @ X2)))) & 46.08/8.06 ((('#sk113' @ X2) = (cP @ ('#sk1128' @ X2) @ Y0))) & 46.08/8.06 (X2 @ ('#sk743' @ X2) @ ('#sk1023' @ X2) @ Y0) & 46.08/8.06 (X2 @ ('#sk495' @ X2) @ ('#sk933' @ X2) @ 46.08/8.06 ('#sk1128' @ X2)) & 46.08/8.06 ((('#sk60' @ X2) = (cP @ ('#sk933' @ X2) @ 46.08/8.06 ('#sk1023' @ X2))))))))) 46.08/8.06 | ~ ('#form494' @ X2))), 46.08/8.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl78])). 46.08/8.06 thf(zip_derived_cl86, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ( ((((('#sk29' @ X2) = (cP @ ('#sk495' @ X2) @ ('#sk743' @ X2)))) & 46.08/8.06 ((('#sk113' @ X2) = (cP @ ('#sk1128' @ X2) @ ('#sk1248' @ X2)))) & 46.08/8.06 (X2 @ ('#sk743' @ X2) @ ('#sk1023' @ X2) @ ('#sk1248' @ X2)) & 46.08/8.06 (X2 @ ('#sk495' @ X2) @ ('#sk933' @ X2) @ ('#sk1128' @ X2)) & 46.08/8.06 ((('#sk60' @ X2) = (cP @ ('#sk933' @ X2) @ ('#sk1023' @ X2)))))) 46.08/8.06 | ~ ('#form494' @ X2))), 46.08/8.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl82])). 46.08/8.06 thf(zip_derived_cl94, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ( (X2 @ ('#sk495' @ X2) @ ('#sk933' @ X2) @ ('#sk1128' @ X2)) 46.08/8.06 | ~ ('#form494' @ X2))), 46.08/8.06 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl86])). 46.08/8.06 thf(zip_derived_cl91, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ( ((('#sk29' @ X2) = (cP @ ('#sk495' @ X2) @ ('#sk743' @ X2)))) 46.08/8.06 | ~ ('#form494' @ X2))), 46.08/8.06 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl86])). 46.08/8.06 thf(zip_derived_cl98, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ((('#sk29' @ X2) = (cP @ ('#sk495' @ X2) @ ('#sk743' @ X2))) 46.08/8.06 | ~ ('#form494' @ X2))), 46.08/8.06 inference('simplify nested equalities', [status(thm)], [zip_derived_cl91])). 46.08/8.06 thf(zip_derived_cl93, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ( (X2 @ ('#sk743' @ X2) @ ('#sk1023' @ X2) @ ('#sk1248' @ X2)) 46.08/8.06 | ~ ('#form494' @ X2))), 46.08/8.06 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl86])). 46.08/8.06 thf(zip_derived_cl95, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ( ((('#sk60' @ X2) = (cP @ ('#sk933' @ X2) @ ('#sk1023' @ X2)))) 46.08/8.06 | ~ ('#form494' @ X2))), 46.08/8.06 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl86])). 46.08/8.06 thf(zip_derived_cl100, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ((('#sk60' @ X2) = (cP @ ('#sk933' @ X2) @ ('#sk1023' @ X2))) 46.08/8.06 | ~ ('#form494' @ X2))), 46.08/8.06 inference('simplify nested equalities', [status(thm)], [zip_derived_cl95])). 46.08/8.06 thf(zip_derived_cl92, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ( ((('#sk113' @ X2) = (cP @ ('#sk1128' @ X2) @ ('#sk1248' @ X2)))) 46.08/8.06 | ~ ('#form494' @ X2))), 46.08/8.06 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl86])). 46.08/8.06 thf(zip_derived_cl99, plain, 46.08/8.06 (![X2 : a > a > a > $o]: 46.08/8.06 ((('#sk113' @ X2) = (cP @ ('#sk1128' @ X2) @ ('#sk1248' @ X2))) 46.08/8.06 | ~ ('#form494' @ X2))), 46.08/8.06 inference('simplify nested equalities', [status(thm)], [zip_derived_cl92])). 46.08/8.06 thf(zip_derived_cl29, plain, 46.08/8.06 (![X2 : a, X4 : a, X6 : a]: 46.08/8.06 (~ (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ (^[Y4 : a]: 46.08/8.06 (( 46.08/8.06 (??) @ ( 46.08/8.06 ^[Y5 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (X2) = 46.08/8.06 (cP @ 46.08/8.06 Y0 @ Y1))) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 Y0 @ 46.08/8.06 Y2 @ Y4) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 Y1 @ 46.08/8.06 Y3 @ Y5) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (X6) = 46.08/8.06 (cP @ 46.08/8.06 Y4 @ Y5))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (X4) = 46.08/8.06 (cP @ 46.08/8.06 Y2 @ Y3))))))))))))))))))))))) 46.08/8.06 | ('#sk1' @ X2 @ X4 @ X6))), 46.08/8.06 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl23])). 46.08/8.06 thf(zip_derived_cl34, plain, 46.08/8.06 (![X2 : a, X4 : a, X6 : a, X8 : a]: 46.08/8.06 (~ (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((??) @ (^[Y4 : a]: 46.08/8.06 (( 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (X2) = 46.08/8.06 (cP @ 46.08/8.06 X8 @ Y0))) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 X8 @ 46.08/8.06 Y1 @ Y3) & 46.08/8.06 ( 46.08/8.06 '#sk1' @ 46.08/8.06 Y0 @ 46.08/8.06 Y2 @ Y4) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (X6) = 46.08/8.06 (cP @ 46.08/8.06 Y3 @ Y4))) & 46.08/8.06 ( 46.08/8.06 ( 46.08/8.06 (X4) = 46.08/8.06 (cP @ 46.08/8.06 Y1 @ Y2)))))))))))))))))))) 46.08/8.06 | ('#sk1' @ X2 @ X4 @ X6))), 46.08/8.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl29])). 46.08/8.06 thf(zip_derived_cl42, plain, 46.08/8.06 (![X2 : a, X4 : a, X6 : a, X8 : a, X10 : a]: 46.08/8.06 (~ (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((??) @ (^[Y3 : a]: 46.08/8.06 (((((X2) = (cP @ 46.08/8.06 X8 @ X10))) & 46.08/8.06 ('#sk1' @ X8 @ 46.08/8.06 Y0 @ Y2) & 46.08/8.06 ('#sk1' @ X10 @ 46.08/8.06 Y1 @ Y3) & 46.08/8.06 (((X6) = (cP @ 46.08/8.06 Y2 @ Y3))) & 46.08/8.06 (((X4) = (cP @ 46.08/8.06 Y0 @ Y1))))))))))))))))) 46.08/8.06 | ('#sk1' @ X2 @ X4 @ X6))), 46.08/8.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 46.08/8.06 thf(zip_derived_cl59, plain, 46.08/8.06 (![X2 : a, X4 : a, X6 : a, X8 : a, X10 : a, X12 : a]: 46.08/8.06 (~ (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((??) @ (^[Y2 : a]: 46.08/8.06 (((((X2) = (cP @ X8 @ X10))) & 46.08/8.06 ('#sk1' @ X8 @ X12 @ Y1) & 46.08/8.06 ('#sk1' @ X10 @ Y0 @ Y2) & 46.08/8.06 (((X6) = (cP @ Y1 @ Y2))) & 46.08/8.06 (((X4) = (cP @ X12 @ Y0)))))))))))))) 46.08/8.06 | ('#sk1' @ X2 @ X4 @ X6))), 46.08/8.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl42])). 46.08/8.06 thf(zip_derived_cl71, plain, 46.08/8.06 (![X2 : a, X4 : a, X6 : a, X8 : a, X10 : a, X12 : a, X14 : a]: 46.08/8.06 (~ (((??) @ (^[Y0 : a]: 46.08/8.06 (((??) @ (^[Y1 : a]: 46.08/8.06 (((((X2) = (cP @ X8 @ X10))) & 46.08/8.06 ('#sk1' @ X8 @ X12 @ Y0) & 46.08/8.06 ('#sk1' @ X10 @ X14 @ Y1) & 46.08/8.06 (((X6) = (cP @ Y0 @ Y1))) & 46.08/8.06 (((X4) = (cP @ X12 @ X14))))))))))) 46.08/8.06 | ('#sk1' @ X2 @ X4 @ X6))), 46.08/8.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl59])). 46.08/8.06 thf(zip_derived_cl77, plain, 46.08/8.06 (![X2 : a, X4 : a, X6 : a, X8 : a, X10 : a, X12 : a, X14 : a, X16 : a]: 46.08/8.06 (~ (((??) @ (^[Y0 : a]: 46.08/8.06 (((((X2) = (cP @ X8 @ X10))) & 46.08/8.06 ('#sk1' @ X8 @ X12 @ X16) & 46.08/8.06 ('#sk1' @ X10 @ X14 @ Y0) & 46.08/8.06 (((X6) = (cP @ X16 @ Y0))) & 46.08/8.06 (((X4) = (cP @ X12 @ X14)))))))) 46.08/8.06 | ('#sk1' @ X2 @ X4 @ X6))), 46.08/8.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl71])). 46.08/8.06 thf(zip_derived_cl81, plain, 46.08/8.06 (![X2 : a, X4 : a, X6 : a, X8 : a, X10 : a, X12 : a, X14 : a, X16 : a, 46.08/8.06 X18 : a]: 46.08/8.06 (~ (((((X2) = (cP @ X8 @ X10))) & ('#sk1' @ X8 @ X12 @ X16) & 46.08/8.06 ('#sk1' @ X10 @ X14 @ X18) & (((X6) = (cP @ X16 @ X18))) & 46.08/8.06 (((X4) = (cP @ X12 @ X14))))) 46.08/8.06 | ('#sk1' @ X2 @ X4 @ X6))), 46.08/8.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl77])). 46.08/8.06 thf(zip_derived_cl85, plain, 46.08/8.06 (![X2 : a, X4 : a, X6 : a, X8 : a, X10 : a, X12 : a, X14 : a, X16 : a, 46.08/8.06 X18 : a]: 46.08/8.06 (~ (((X2) = (cP @ X8 @ X10))) 46.08/8.06 | ~ ('#sk1' @ X8 @ X12 @ X16) 46.08/8.06 | ~ ('#sk1' @ X10 @ X14 @ X18) 46.08/8.06 | ~ (((X6) = (cP @ X16 @ X18))) 46.08/8.06 | ~ (((X4) = (cP @ X12 @ X14))) 46.08/8.06 | ('#sk1' @ X2 @ X4 @ X6))), 46.08/8.06 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl81])). 46.08/8.06 thf(zip_derived_cl89, plain, 46.08/8.06 (![X2 : a, X4 : a, X6 : a, X8 : a, X10 : a, X12 : a, X14 : a, X16 : a, 46.08/8.06 X18 : a]: 46.08/8.06 (((X2) != (cP @ X8 @ X10)) 46.08/8.06 | ~ ('#sk1' @ X8 @ X12 @ X16) 46.08/8.06 | ~ ('#sk1' @ X10 @ X14 @ X18) 46.08/8.06 | ((X6) != (cP @ X16 @ X18)) 46.08/8.06 | ((X4) != (cP @ X12 @ X14)) 46.08/8.06 | ('#sk1' @ X2 @ X4 @ X6))), 46.08/8.06 inference('simplify nested equalities', [status(thm)], [zip_derived_cl85])). 46.08/8.06 thf(zip_derived_cl90, plain, 46.08/8.06 (![X8 : a, X10 : a, X12 : a, X14 : a, X16 : a, X18 : a]: 46.08/8.06 ( ('#sk1' @ (cP @ X8 @ X10) @ (cP @ X12 @ X14) @ (cP @ X16 @ X18)) 46.08/8.06 | ~ ('#sk1' @ X10 @ X14 @ X18) 46.08/8.06 | ~ ('#sk1' @ X8 @ X12 @ X16))), 46.08/8.06 inference('simplify', [status(thm)], [zip_derived_cl89])). 46.08/8.06 thf(zip_derived_cl3731, plain, ($false), 46.08/8.06 inference('eprover', [status(thm)], 46.08/8.06 [zip_derived_cl70, zip_derived_cl69, zip_derived_cl162, 46.08/8.06 zip_derived_cl165, zip_derived_cl159, zip_derived_cl163, 46.08/8.06 zip_derived_cl161, zip_derived_cl166, zip_derived_cl41, 46.08/8.06 zip_derived_cl133, zip_derived_cl11, zip_derived_cl167, 46.08/8.06 zip_derived_cl131, zip_derived_cl27, zip_derived_cl44, 46.08/8.06 zip_derived_cl135, zip_derived_cl134, zip_derived_cl25, 46.08/8.06 zip_derived_cl94, zip_derived_cl98, zip_derived_cl93, 46.08/8.06 zip_derived_cl100, zip_derived_cl99, zip_derived_cl90])). 46.08/8.06 46.08/8.06 % SZS output end Refutation 46.08/8.06 46.08/8.06 46.08/8.06 % Terminating... 46.77/8.25 % Runner terminated. 46.80/8.28 % Zipperpin 1.5 exiting 46.80/8.29 EOF