0.02/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.roTxnL4udB true 0.11/0.31 % Computer : n028.cluster.edu 0.11/0.31 % Model : x86_64 x86_64 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.31 % Memory : 8042.1875MB 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.31 % CPULimit : 1920 0.11/0.31 % WCLimit : 240 0.11/0.31 % DateTime : Wed Jul 30 09:47:49 EDT 2025 0.16/0.31 % CPUTime : 0.16/0.31 % Running portfolio for 1920 s 0.16/0.31 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.16/0.32 % Number of cores: 8 0.16/0.32 % Python version: Python 3.6.8 0.16/0.32 % Running in HO mode 0.48/0.60 % Total configuration time : 828 0.48/0.60 % Estimated wc time : 1656 0.48/0.60 % Estimated cpu time (8 cpus) : 207.0 0.50/0.67 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.50/0.70 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.50/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.50/0.70 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.50/0.70 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.50/0.70 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.50/0.70 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.51/0.71 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 236.99/30.53 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 326.01/42.02 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s 345.07/44.46 % Solved by lams/30_b.l.sh. 345.07/44.46 % done 337 iterations in 13.682s 345.07/44.46 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 345.07/44.46 % SZS output start Refutation 345.07/44.46 thf(a_type, type, a: $tType). 345.07/44.46 thf('#form28_type', type, '#form28': a > $o). 345.07/44.46 thf('#form24_type', type, '#form24': $o). 345.07/44.46 thf('#form92_type', type, '#form92': a > a > (a > $o) > $o). 345.07/44.46 thf('#sk27_type', type, '#sk27': a). 345.07/44.46 thf('#form110_type', type, '#form110': a > (a > $o) > $o). 345.07/44.46 thf('#sk7_type', type, '#sk7': a). 345.07/44.46 thf('#sk30_type', type, '#sk30': a). 345.07/44.46 thf('#sk2_type', type, '#sk2': a > a > a). 345.07/44.46 thf('#form26_type', type, '#form26': $o). 345.07/44.46 thf('#sk32_type', type, '#sk32': a > a > a). 345.07/44.46 thf('#sk111_type', type, '#sk111': a > (a > $o) > a). 345.07/44.46 thf('#sk31_type', type, '#sk31': a > a > a > $o). 345.07/44.46 thf('#sk57_type', type, '#sk57': a > (a > $o) > a). 345.07/44.46 thf('#sk6_type', type, '#sk6': a > $o). 345.07/44.46 thf('#sk29_type', type, '#sk29': a > a). 345.07/44.46 thf('#form56_type', type, '#form56': a > (a > $o) > $o). 345.07/44.46 thf('#sk39_type', type, '#sk39': a > a > $o). 345.07/44.46 thf('#form50_type', type, '#form50': a > $o). 345.07/44.46 thf('#sk25_type', type, '#sk25': a). 345.07/44.46 thf('#sk3_type', type, '#sk3': a > a). 345.07/44.46 thf('#sk4_type', type, '#sk4': a > a). 345.07/44.46 thf('#sk18_type', type, '#sk18': (a > $o) > a). 345.07/44.46 thf('#sk40_type', type, '#sk40': a > a > a > $o). 345.07/44.46 thf('#sk1_type', type, '#sk1': a). 345.07/44.46 thf('#sk5_type', type, '#sk5': a > $o). 345.07/44.46 thf('#sk93_type', type, '#sk93': a > a > (a > $o) > a). 345.07/44.46 thf(cPU_X238A_pme, conjecture, 345.07/44.46 (![Z:a,P:( a > a > a ),L:( a > a ),R:( a > a ),F:( a > $o )]: 345.07/44.46 ( ( ( ( L @ Z ) = ( Z ) ) & 345.07/44.46 ( ![X:( a > $o )]: 345.07/44.46 ( ( ?[Xt:a]: 345.07/44.46 ( ( ![Xu:a]: ( ( X @ Xu ) => ( X @ ( L @ Xu ) ) ) ) & ( X @ Xt ) ) ) => 345.07/44.46 ( X @ Z ) ) ) & 345.07/44.46 ( ![Xt:a]: 345.07/44.46 ( ( ( Xt ) = ( P @ ( L @ Xt ) @ ( R @ Xt ) ) ) <=> 345.07/44.46 ( ( Xt ) != ( Z ) ) ) ) & 345.07/44.46 ( ![Xx:a,Xy:a]: ( ( R @ ( P @ Xx @ Xy ) ) = ( Xy ) ) ) & 345.07/44.46 ( ![Xx:a,Xy:a]: ( ( L @ ( P @ Xx @ Xy ) ) = ( Xx ) ) ) & 345.07/44.46 ( ( R @ Z ) = ( Z ) ) ) => 345.07/44.46 ( ![X:( a > $o ),Xz:a]: 345.07/44.46 ( ( ?[Xx:a]: 345.07/44.46 ( ( ![Xx_6:a]: 345.07/44.46 ( ( ![X0:( a > $o )]: 345.07/44.46 ( ( ( X0 @ Xx ) & 345.07/44.46 ( ![Xz0:a]: ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) ) => 345.07/44.46 ( ?[Xv:a]: ( ( X0 @ Xv ) & ( ( R @ Xv ) = ( Xx_6 ) ) ) ) ) ) => 345.07/44.46 ( X @ Xx_6 ) ) ) & 345.07/44.46 ( ?[Xx_8:a]: 345.07/44.46 ( ( F @ ( P @ Xx_8 @ Xz ) ) & 345.07/44.46 ( ![Xx_7:a]: 345.07/44.46 ( ( ![X0:( a > $o )]: 345.07/44.46 ( ( ( ![Xz0:a]: 345.07/44.46 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) & 345.07/44.46 ( X0 @ Xx_8 ) ) => 345.07/44.46 ( ?[Xv:a]: 345.07/44.46 ( ( X0 @ Xv ) & ( ( R @ Xv ) = ( Xx_7 ) ) ) ) ) ) => 345.07/44.46 ( ![X0:( a > $o )]: 345.07/44.46 ( ( ( ![Xz0:a]: 345.07/44.46 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) & 345.07/44.46 ( X0 @ Xx ) ) => 345.07/44.46 ( ?[Xv:a]: 345.07/44.46 ( ( X0 @ Xv ) & ( ( R @ Xv ) = ( Xx_7 ) ) ) ) ) ) ) ) ) ) ) ) <=> 345.07/44.46 ( ?[Xx:a]: 345.07/44.46 ( ( ![Xx_5:a]: 345.07/44.46 ( ( ![X0:( a > $o )]: 345.07/44.46 ( ( ( X0 @ Xx ) & 345.07/44.46 ( ![Xz0:a]: ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) ) => 345.07/44.46 ( ?[Xv:a]: ( ( X0 @ Xv ) & ( ( R @ Xv ) = ( Xx_5 ) ) ) ) ) ) => 345.07/44.46 ( X @ Xx_5 ) ) ) & 345.07/44.46 ( F @ ( P @ Xx @ Xz ) ) ) ) ) ) ))). 345.07/44.46 thf(zf_stmt_0, negated_conjecture, 345.07/44.46 (~( ![Z:a,P:( a > a > a ),L:( a > a ),R:( a > a ),F:( a > $o )]: 345.07/44.46 ( ( ( ( L @ Z ) = ( Z ) ) & 345.07/44.46 ( ![X:( a > $o )]: 345.07/44.46 ( ( ?[Xt:a]: 345.07/44.46 ( ( ![Xu:a]: ( ( X @ Xu ) => ( X @ ( L @ Xu ) ) ) ) & 345.07/44.46 ( X @ Xt ) ) ) => 345.07/44.46 ( X @ Z ) ) ) & 345.07/44.46 ( ![Xt:a]: 345.07/44.46 ( ( ( Xt ) = ( P @ ( L @ Xt ) @ ( R @ Xt ) ) ) <=> 345.07/44.46 ( ( Xt ) != ( Z ) ) ) ) & 345.07/44.46 ( ![Xx:a,Xy:a]: ( ( R @ ( P @ Xx @ Xy ) ) = ( Xy ) ) ) & 345.07/44.46 ( ![Xx:a,Xy:a]: ( ( L @ ( P @ Xx @ Xy ) ) = ( Xx ) ) ) & 345.07/44.46 ( ( R @ Z ) = ( Z ) ) ) => 345.07/44.46 ( ![X:( a > $o ),Xz:a]: 345.07/44.46 ( ( ?[Xx:a]: 345.07/44.46 ( ( ![Xx_6:a]: 345.07/44.46 ( ( ![X0:( a > $o )]: 345.07/44.46 ( ( ( X0 @ Xx ) & 345.07/44.46 ( ![Xz0:a]: 345.07/44.46 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) ) => 345.07/44.46 ( ?[Xv:a]: 345.07/44.46 ( ( X0 @ Xv ) & ( ( R @ Xv ) = ( Xx_6 ) ) ) ) ) ) => 345.07/44.46 ( X @ Xx_6 ) ) ) & 345.07/44.46 ( ?[Xx_8:a]: 345.07/44.46 ( ( F @ ( P @ Xx_8 @ Xz ) ) & 345.07/44.46 ( ![Xx_7:a]: 345.07/44.46 ( ( ![X0:( a > $o )]: 345.07/44.46 ( ( ( ![Xz0:a]: 345.07/44.46 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) & 345.07/44.46 ( X0 @ Xx_8 ) ) => 345.07/44.46 ( ?[Xv:a]: 345.07/44.46 ( ( X0 @ Xv ) & ( ( R @ Xv ) = ( Xx_7 ) ) ) ) ) ) => 345.07/44.46 ( ![X0:( a > $o )]: 345.07/44.46 ( ( ( ![Xz0:a]: 345.07/44.46 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) & 345.07/44.46 ( X0 @ Xx ) ) => 345.07/44.46 ( ?[Xv:a]: 345.07/44.46 ( ( X0 @ Xv ) & ( ( R @ Xv ) = ( Xx_7 ) ) ) ) ) ) ) ) ) ) ) ) <=> 345.07/44.46 ( ?[Xx:a]: 345.07/44.46 ( ( ![Xx_5:a]: 345.07/44.46 ( ( ![X0:( a > $o )]: 345.07/44.46 ( ( ( X0 @ Xx ) & 345.07/44.46 ( ![Xz0:a]: 345.07/44.46 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) ) => 345.07/44.46 ( ?[Xv:a]: 345.07/44.46 ( ( X0 @ Xv ) & ( ( R @ Xv ) = ( Xx_5 ) ) ) ) ) ) => 345.07/44.46 ( X @ Xx_5 ) ) ) & 345.07/44.46 ( F @ ( P @ Xx @ Xz ) ) ) ) ) ) ) )), 345.07/44.46 inference('cnf.neg', [status(esa)], [cPU_X238A_pme])). 345.07/44.46 thf(zip_derived_cl0, plain, 345.07/44.46 (~ (((!!) @ (^[Y0 : a]: 345.07/44.46 (((!!) @ (^[Y1 : a > a > a]: 345.07/44.46 (((!!) @ (^[Y2 : a > a]: 345.07/44.46 (((!!) @ (^[Y3 : a > a]: 345.07/44.46 (((!!) @ (^[Y4 : a > $o]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 ( 345.07/44.46 ( 345.07/44.46 (Y2 @ 345.07/44.46 Y0) = 345.07/44.46 (Y0))) & 345.07/44.46 ( 345.07/44.46 ( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y5 : a > $o]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (??) @ ( 345.07/44.46 ^[Y6 : a]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y7 : a]: 345.07/44.46 (( 345.07/44.46 (Y5 @ 345.07/44.46 Y7) => 345.07/44.46 (Y5 @ 345.07/44.46 ( 345.07/44.46 Y2 @ Y7))))))) & 345.07/44.46 (Y5 @ Y6)))))) => 345.07/44.46 (Y5 @ Y0)))))) & 345.07/44.46 ( 345.07/44.46 ( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y5 : a]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (Y5) = 345.07/44.46 (Y1 @ 345.07/44.46 ( 345.07/44.46 Y2 @ Y5) @ 345.07/44.46 ( 345.07/44.46 Y3 @ Y5)))) <=> 345.07/44.46 (( 345.07/44.46 (Y5) != 345.07/44.46 (Y0)))))))) & 345.07/44.46 ( 345.07/44.46 ( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y5 : a]: 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y6 : a]: 345.07/44.46 (( 345.07/44.46 (Y3 @ 345.07/44.46 ( 345.07/44.46 Y1 @ 345.07/44.46 Y5 @ Y6)) = 345.07/44.46 (Y6))))))))) & 345.07/44.46 ( 345.07/44.46 ( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y5 : a]: 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y6 : a]: 345.07/44.46 (( 345.07/44.46 (Y2 @ 345.07/44.46 ( 345.07/44.46 Y1 @ 345.07/44.46 Y5 @ Y6)) = 345.07/44.46 (Y5))))))))) & 345.07/44.46 ( 345.07/44.46 ( 345.07/44.46 (Y3 @ 345.07/44.46 Y0) = 345.07/44.46 (Y0))))) => 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y5 : a > $o]: 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y6 : a]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (??) @ ( 345.07/44.46 ^[Y7 : a]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y8 : a]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y9 : a > $o]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (Y9 @ 345.07/44.46 Y7) & 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y10 : a]: 345.07/44.46 (( 345.07/44.46 (Y9 @ 345.07/44.46 Y10) => 345.07/44.46 (Y9 @ 345.07/44.46 ( 345.07/44.46 Y2 @ Y10))))))))) => 345.07/44.46 (( 345.07/44.46 (??) @ ( 345.07/44.46 ^[Y10 : a]: 345.07/44.46 (( 345.07/44.46 (Y9 @ 345.07/44.46 Y10) & 345.07/44.46 (( 345.07/44.46 (Y3 @ 345.07/44.46 Y10) = 345.07/44.46 (Y8))))))))))))) => 345.07/44.46 (Y5 @ Y8)))))) & 345.07/44.46 (( 345.07/44.46 (??) @ ( 345.07/44.46 ^[Y8 : a]: 345.07/44.46 (( 345.07/44.46 (Y4 @ 345.07/44.46 ( 345.07/44.46 Y1 @ 345.07/44.46 Y8 @ Y6)) & 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y9 : a]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y10 : a > $o]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y11 : a]: 345.07/44.46 (( 345.07/44.46 (Y10 @ 345.07/44.46 Y11) => 345.07/44.46 (Y10 @ 345.07/44.46 ( 345.07/44.46 Y2 @ Y11))))))) & 345.07/44.46 (Y10 @ 345.07/44.46 Y8))) => 345.07/44.46 (( 345.07/44.46 (??) @ ( 345.07/44.46 ^[Y11 : a]: 345.07/44.46 (( 345.07/44.46 (Y10 @ 345.07/44.46 Y11) & 345.07/44.46 (( 345.07/44.46 (Y3 @ 345.07/44.46 Y11) = 345.07/44.46 (Y9))))))))))))) => 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y10 : a > $o]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y11 : a]: 345.07/44.46 (( 345.07/44.46 (Y10 @ 345.07/44.46 Y11) => 345.07/44.46 (Y10 @ 345.07/44.46 ( 345.07/44.46 Y2 @ Y11))))))) & 345.07/44.46 (Y10 @ 345.07/44.46 Y7))) => 345.07/44.46 (( 345.07/44.46 (??) @ ( 345.07/44.46 ^[Y11 : a]: 345.07/44.46 (( 345.07/44.46 (Y10 @ 345.07/44.46 Y11) & 345.07/44.46 (( 345.07/44.46 (Y3 @ 345.07/44.46 Y11) = 345.07/44.46 (Y9)))))))))))))))))))))))))))) <=> 345.07/44.46 (( 345.07/44.46 (??) @ ( 345.07/44.46 ^[Y7 : a]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y8 : a]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y9 : a > $o]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (Y9 @ 345.07/44.46 Y7) & 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y10 : a]: 345.07/44.46 (( 345.07/44.46 (Y9 @ 345.07/44.46 Y10) => 345.07/44.46 (Y9 @ 345.07/44.46 ( 345.07/44.46 Y2 @ Y10))))))))) => 345.07/44.46 (( 345.07/44.46 (??) @ ( 345.07/44.46 ^[Y10 : a]: 345.07/44.46 (( 345.07/44.46 (Y9 @ 345.07/44.46 Y10) & 345.07/44.46 (( 345.07/44.46 (Y3 @ 345.07/44.46 Y10) = 345.07/44.46 (Y8))))))))))))) => 345.07/44.46 (Y5 @ Y8)))))) & 345.07/44.46 (Y4 @ 345.07/44.46 ( 345.07/44.46 Y1 @ 345.07/44.46 Y7 @ Y6))))))))))))))))))))))))))))))))), 345.07/44.46 inference('cnf', [status(esa)], [zf_stmt_0])). 345.07/44.46 thf(zip_derived_cl1, plain, 345.07/44.46 (~ (((!!) @ (^[Y0 : a > a > a]: 345.07/44.46 (((!!) @ (^[Y1 : a > a]: 345.07/44.46 (((!!) @ (^[Y2 : a > a]: 345.07/44.46 (((!!) @ (^[Y3 : a > $o]: 345.07/44.46 (((((((Y1 @ '#sk1') = 345.07/44.46 ('#sk1'))) & 345.07/44.46 (((!!) @ ( 345.07/44.46 ^[Y4 : a > $o]: 345.07/44.46 (((((??) @ ( 345.07/44.46 ^[Y5 : a]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y6 : a]: 345.07/44.46 (( 345.07/44.46 (Y4 @ 345.07/44.46 Y6) => 345.07/44.46 (Y4 @ 345.07/44.46 ( 345.07/44.46 Y1 @ Y6))))))) & 345.07/44.46 (Y4 @ Y5)))))) => 345.07/44.46 (Y4 @ 345.07/44.46 '#sk1')))))) & 345.07/44.46 (((!!) @ ( 345.07/44.46 ^[Y4 : a]: 345.07/44.46 (((((Y4) = 345.07/44.46 (Y0 @ 345.07/44.46 (Y1 @ Y4) @ 345.07/44.46 (Y2 @ Y4)))) <=> 345.07/44.46 (((Y4) != 345.07/44.46 ('#sk1')))))))) & 345.07/44.46 (((!!) @ ( 345.07/44.46 ^[Y4 : a]: 345.07/44.46 (((!!) @ ( 345.07/44.46 ^[Y5 : a]: 345.07/44.46 (( 345.07/44.46 (Y2 @ 345.07/44.46 ( 345.07/44.46 Y0 @ 345.07/44.46 Y4 @ Y5)) = 345.07/44.46 (Y5))))))))) & 345.07/44.46 (((!!) @ ( 345.07/44.46 ^[Y4 : a]: 345.07/44.46 (((!!) @ ( 345.07/44.46 ^[Y5 : a]: 345.07/44.46 (( 345.07/44.46 (Y1 @ 345.07/44.46 ( 345.07/44.46 Y0 @ 345.07/44.46 Y4 @ Y5)) = 345.07/44.46 (Y4))))))))) & 345.07/44.46 (((Y2 @ '#sk1') = 345.07/44.46 ('#sk1'))))) => 345.07/44.46 (((!!) @ (^[Y4 : a > $o]: 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y5 : a]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (??) @ ( 345.07/44.46 ^[Y6 : a]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y7 : a]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y8 : a > $o]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (Y8 @ 345.07/44.46 Y6) & 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y9 : a]: 345.07/44.46 (( 345.07/44.46 (Y8 @ 345.07/44.46 Y9) => 345.07/44.46 (Y8 @ 345.07/44.46 ( 345.07/44.46 Y1 @ Y9))))))))) => 345.07/44.46 (( 345.07/44.46 (??) @ ( 345.07/44.46 ^[Y9 : a]: 345.07/44.46 (( 345.07/44.46 (Y8 @ 345.07/44.46 Y9) & 345.07/44.46 (( 345.07/44.46 (Y2 @ 345.07/44.46 Y9) = 345.07/44.46 (Y7))))))))))))) => 345.07/44.46 (Y4 @ Y7)))))) & 345.07/44.46 (( 345.07/44.46 (??) @ ( 345.07/44.46 ^[Y7 : a]: 345.07/44.46 (( 345.07/44.46 (Y3 @ 345.07/44.46 ( 345.07/44.46 Y0 @ 345.07/44.46 Y7 @ Y5)) & 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y8 : a]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y9 : a > $o]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y10 : a]: 345.07/44.46 (( 345.07/44.46 (Y9 @ 345.07/44.46 Y10) => 345.07/44.46 (Y9 @ 345.07/44.46 ( 345.07/44.46 Y1 @ Y10))))))) & 345.07/44.46 (Y9 @ Y7))) => 345.07/44.46 (( 345.07/44.46 (??) @ ( 345.07/44.46 ^[Y10 : a]: 345.07/44.46 (( 345.07/44.46 (Y9 @ 345.07/44.46 Y10) & 345.07/44.46 (( 345.07/44.46 (Y2 @ 345.07/44.46 Y10) = 345.07/44.46 (Y8))))))))))))) => 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y9 : a > $o]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y10 : a]: 345.07/44.46 (( 345.07/44.46 (Y9 @ 345.07/44.46 Y10) => 345.07/44.46 (Y9 @ 345.07/44.46 ( 345.07/44.46 Y1 @ Y10))))))) & 345.07/44.46 (Y9 @ Y6))) => 345.07/44.46 (( 345.07/44.46 (??) @ ( 345.07/44.46 ^[Y10 : a]: 345.07/44.46 (( 345.07/44.46 (Y9 @ 345.07/44.46 Y10) & 345.07/44.46 (( 345.07/44.46 (Y2 @ 345.07/44.46 Y10) = 345.07/44.46 (Y8)))))))))))))))))))))))))))) <=> 345.07/44.46 (( 345.07/44.46 (??) @ ( 345.07/44.46 ^[Y6 : a]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y7 : a]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y8 : a > $o]: 345.07/44.46 (( 345.07/44.46 (( 345.07/44.46 (Y8 @ 345.07/44.46 Y6) & 345.07/44.46 (( 345.07/44.46 (!!) @ ( 345.07/44.46 ^[Y9 : a]: 345.07/44.46 (( 345.07/44.46 (Y8 @ 345.07/44.46 Y9) => 345.07/44.46 (Y8 @ 345.07/44.46 ( 345.07/44.46 Y1 @ Y9))))))))) => 345.07/44.46 (( 345.07/44.46 (??) @ ( 345.07/44.46 ^[Y9 : a]: 345.07/44.46 (( 345.07/44.46 (Y8 @ 345.07/44.46 Y9) & 345.07/44.46 (( 345.07/44.46 (Y2 @ 345.07/44.46 Y9) = 345.07/44.46 (Y7))))))))))))) => 345.07/44.46 (Y4 @ Y7)))))) & 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 Y0 @ 345.07/44.47 Y6 @ Y5)))))))))))))))))))))))))))))), 345.07/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 345.07/44.47 thf(zip_derived_cl2, plain, 345.07/44.47 (~ (((!!) @ (^[Y0 : a > a]: 345.07/44.47 (((!!) @ (^[Y1 : a > a]: 345.07/44.47 (((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((((Y0 @ '#sk1') = ('#sk1'))) & 345.07/44.47 (((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((((??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (((( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y5) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 Y0 @ Y5))))))) & 345.07/44.47 (Y3 @ Y4)))))) => 345.07/44.47 (Y3 @ '#sk1')))))) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((((Y3) = 345.07/44.47 ('#sk2' @ 345.07/44.47 (Y0 @ Y3) @ 345.07/44.47 (Y1 @ Y3)))) <=> 345.07/44.47 (((Y3) != 345.07/44.47 ('#sk1')))))))) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (((Y1 @ 345.07/44.47 ('#sk2' @ 345.07/44.47 Y3 @ Y4)) = 345.07/44.47 (Y4))))))))) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (((Y0 @ 345.07/44.47 ('#sk2' @ 345.07/44.47 Y3 @ Y4)) = 345.07/44.47 (Y3))))))))) & 345.07/44.47 (((Y1 @ '#sk1') = ('#sk1'))))) => 345.07/44.47 (((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((!!) @ (^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y6 : a]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y7 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (Y7 @ 345.07/44.47 Y5) & 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y8 : a]: 345.07/44.47 (( 345.07/44.47 (Y7 @ 345.07/44.47 Y8) => 345.07/44.47 (Y7 @ 345.07/44.47 ( 345.07/44.47 Y0 @ Y8))))))))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y8 : a]: 345.07/44.47 (( 345.07/44.47 (Y7 @ 345.07/44.47 Y8) & 345.07/44.47 (( 345.07/44.47 (Y1 @ 345.07/44.47 Y8) = 345.07/44.47 (Y6))))))))))))) => 345.07/44.47 (Y3 @ Y6)))))) & 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y6 : a]: 345.07/44.47 (( 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk2' @ 345.07/44.47 Y6 @ Y4)) & 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y7 : a]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y8 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y9 : a]: 345.07/44.47 (( 345.07/44.47 (Y8 @ 345.07/44.47 Y9) => 345.07/44.47 (Y8 @ 345.07/44.47 ( 345.07/44.47 Y0 @ Y9))))))) & 345.07/44.47 (Y8 @ Y6))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y9 : a]: 345.07/44.47 (( 345.07/44.47 (Y8 @ 345.07/44.47 Y9) & 345.07/44.47 (( 345.07/44.47 (Y1 @ 345.07/44.47 Y9) = 345.07/44.47 (Y7))))))))))))) => 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y8 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y9 : a]: 345.07/44.47 (( 345.07/44.47 (Y8 @ 345.07/44.47 Y9) => 345.07/44.47 (Y8 @ 345.07/44.47 ( 345.07/44.47 Y0 @ Y9))))))) & 345.07/44.47 (Y8 @ Y5))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y9 : a]: 345.07/44.47 (( 345.07/44.47 (Y8 @ 345.07/44.47 Y9) & 345.07/44.47 (( 345.07/44.47 (Y1 @ 345.07/44.47 Y9) = 345.07/44.47 (Y7)))))))))))))))))))))))))))) <=> 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y6 : a]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y7 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (Y7 @ 345.07/44.47 Y5) & 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y8 : a]: 345.07/44.47 (( 345.07/44.47 (Y7 @ 345.07/44.47 Y8) => 345.07/44.47 (Y7 @ 345.07/44.47 ( 345.07/44.47 Y0 @ Y8))))))))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y8 : a]: 345.07/44.47 (( 345.07/44.47 (Y7 @ 345.07/44.47 Y8) & 345.07/44.47 (( 345.07/44.47 (Y1 @ 345.07/44.47 Y8) = 345.07/44.47 (Y6))))))))))))) => 345.07/44.47 (Y3 @ Y6)))))) & 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk2' @ 345.07/44.47 Y5 @ Y4))))))))))))))))))))))))))), 345.07/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 345.07/44.47 thf(zip_derived_cl3, plain, 345.07/44.47 (~ (((!!) @ (^[Y0 : a > a]: 345.07/44.47 (((!!) @ (^[Y1 : a > $o]: 345.07/44.47 ((((((('#sk3' @ '#sk1') = ('#sk1'))) & 345.07/44.47 (((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((??) @ (^[Y3 : a]: 345.07/44.47 (((((!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y2 @ 345.07/44.47 Y4) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))) & 345.07/44.47 (Y2 @ Y3)))))) => 345.07/44.47 (Y2 @ '#sk1')))))) & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((((Y2) = ('#sk2' @ 345.07/44.47 ('#sk3' @ Y2) @ (Y0 @ Y2)))) <=> 345.07/44.47 (((Y2) != ('#sk1')))))))) & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y0 @ 345.07/44.47 ('#sk2' @ Y2 @ 345.07/44.47 Y3)) = 345.07/44.47 (Y3))))))))) & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 ((('#sk3' @ 345.07/44.47 ('#sk2' @ Y2 @ 345.07/44.47 Y3)) = 345.07/44.47 (Y2))))))))) & 345.07/44.47 (((Y0 @ '#sk1') = ('#sk1'))))) => 345.07/44.47 (((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((((??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (((((!!) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y6 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (Y6 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y7 : a]: 345.07/44.47 (( 345.07/44.47 (Y6 @ 345.07/44.47 Y7) => 345.07/44.47 (Y6 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y7))))))))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y7 : a]: 345.07/44.47 (( 345.07/44.47 (Y6 @ 345.07/44.47 Y7) & 345.07/44.47 (( 345.07/44.47 (Y0 @ 345.07/44.47 Y7) = 345.07/44.47 (Y5))))))))))))) => 345.07/44.47 (Y2 @ Y5)))))) & 345.07/44.47 (((??) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (Y1 @ 345.07/44.47 ( 345.07/44.47 '#sk2' @ 345.07/44.47 Y5 @ Y3)) & 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y6 : a]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y7 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y8 : a]: 345.07/44.47 (( 345.07/44.47 (Y7 @ 345.07/44.47 Y8) => 345.07/44.47 (Y7 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y8))))))) & 345.07/44.47 (Y7 @ Y5))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y8 : a]: 345.07/44.47 (( 345.07/44.47 (Y7 @ 345.07/44.47 Y8) & 345.07/44.47 (( 345.07/44.47 (Y0 @ 345.07/44.47 Y8) = 345.07/44.47 (Y6))))))))))))) => 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y7 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y8 : a]: 345.07/44.47 (( 345.07/44.47 (Y7 @ 345.07/44.47 Y8) => 345.07/44.47 (Y7 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y8))))))) & 345.07/44.47 (Y7 @ Y4))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y8 : a]: 345.07/44.47 (( 345.07/44.47 (Y7 @ 345.07/44.47 Y8) & 345.07/44.47 (( 345.07/44.47 (Y0 @ 345.07/44.47 Y8) = 345.07/44.47 (Y6)))))))))))))))))))))))))))) <=> 345.07/44.47 (((??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (((((!!) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y6 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (Y6 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y7 : a]: 345.07/44.47 (( 345.07/44.47 (Y6 @ 345.07/44.47 Y7) => 345.07/44.47 (Y6 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y7))))))))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y7 : a]: 345.07/44.47 (( 345.07/44.47 (Y6 @ 345.07/44.47 Y7) & 345.07/44.47 (( 345.07/44.47 (Y0 @ 345.07/44.47 Y7) = 345.07/44.47 (Y5))))))))))))) => 345.07/44.47 (Y2 @ Y5)))))) & 345.07/44.47 (Y1 @ 345.07/44.47 ('#sk2' @ 345.07/44.47 Y4 @ Y3)))))))))))))))))))))))), 345.07/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 345.07/44.47 thf(zip_derived_cl4, plain, 345.07/44.47 (~ (((!!) @ (^[Y0 : a > $o]: 345.07/44.47 ((((((('#sk3' @ '#sk1') = ('#sk1'))) & 345.07/44.47 (((!!) @ (^[Y1 : a > $o]: 345.07/44.47 (((((??) @ (^[Y2 : a]: 345.07/44.47 (((((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y1 @ Y3) => 345.07/44.47 (Y1 @ 345.07/44.47 ('#sk3' @ Y3))))))) & 345.07/44.47 (Y1 @ Y2)))))) => 345.07/44.47 (Y1 @ '#sk1')))))) & 345.07/44.47 (((!!) @ (^[Y1 : a]: 345.07/44.47 (((((Y1) = ('#sk2' @ ('#sk3' @ Y1) @ 345.07/44.47 ('#sk4' @ Y1)))) <=> 345.07/44.47 (((Y1) != ('#sk1')))))))) & 345.07/44.47 (((!!) @ (^[Y1 : a]: 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 ((('#sk4' @ 345.07/44.47 ('#sk2' @ Y1 @ Y2)) = (Y2))))))))) & 345.07/44.47 (((!!) @ (^[Y1 : a]: 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 ((('#sk3' @ 345.07/44.47 ('#sk2' @ Y1 @ Y2)) = (Y1))))))))) & 345.07/44.47 ((('#sk4' @ '#sk1') = ('#sk1'))))) => 345.07/44.47 (((!!) @ (^[Y1 : a > $o]: 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((((??) @ (^[Y3 : a]: 345.07/44.47 (((((!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (((( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y5 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (Y5 @ 345.07/44.47 Y3) & 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y6 : a]: 345.07/44.47 (( 345.07/44.47 (Y5 @ 345.07/44.47 Y6) => 345.07/44.47 (Y5 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y6))))))))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y6 : a]: 345.07/44.47 (( 345.07/44.47 (Y5 @ 345.07/44.47 Y6) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y6) = 345.07/44.47 (Y4))))))))))))) => 345.07/44.47 (Y1 @ Y4)))))) & 345.07/44.47 (((??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (((Y0 @ 345.07/44.47 ('#sk2' @ 345.07/44.47 Y4 @ Y2)) & 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y6 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y7 : a]: 345.07/44.47 (( 345.07/44.47 (Y6 @ 345.07/44.47 Y7) => 345.07/44.47 (Y6 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y7))))))) & 345.07/44.47 (Y6 @ Y4))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y7 : a]: 345.07/44.47 (( 345.07/44.47 (Y6 @ 345.07/44.47 Y7) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y7) = 345.07/44.47 (Y5))))))))))))) => 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y6 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y7 : a]: 345.07/44.47 (( 345.07/44.47 (Y6 @ 345.07/44.47 Y7) => 345.07/44.47 (Y6 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y7))))))) & 345.07/44.47 (Y6 @ Y3))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y7 : a]: 345.07/44.47 (( 345.07/44.47 (Y6 @ 345.07/44.47 Y7) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y7) = 345.07/44.47 (Y5)))))))))))))))))))))))))))) <=> 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((((!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (((( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y5 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (Y5 @ 345.07/44.47 Y3) & 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y6 : a]: 345.07/44.47 (( 345.07/44.47 (Y5 @ 345.07/44.47 Y6) => 345.07/44.47 (Y5 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y6))))))))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y6 : a]: 345.07/44.47 (( 345.07/44.47 (Y5 @ 345.07/44.47 Y6) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y6) = 345.07/44.47 (Y4))))))))))))) => 345.07/44.47 (Y1 @ Y4)))))) & 345.07/44.47 (Y0 @ 345.07/44.47 ('#sk2' @ Y3 @ 345.07/44.47 Y2))))))))))))))))))))), 345.07/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 345.07/44.47 thf(zip_derived_cl5, plain, 345.07/44.47 (~ ((((((('#sk3' @ '#sk1') = ('#sk1'))) & 345.07/44.47 (((!!) @ (^[Y0 : a > $o]: 345.07/44.47 (((((??) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a]: 345.07/44.47 (((Y0 @ Y2) => (Y0 @ 345.07/44.47 ('#sk3' @ Y2))))))) & 345.07/44.47 (Y0 @ Y1)))))) => 345.07/44.47 (Y0 @ '#sk1')))))) & 345.07/44.47 (((!!) @ (^[Y0 : a]: 345.07/44.47 (((((Y0) = ('#sk2' @ ('#sk3' @ Y0) @ ('#sk4' @ Y0)))) <=> 345.07/44.47 (((Y0) != ('#sk1')))))))) & 345.07/44.47 (((!!) @ (^[Y0 : a]: 345.07/44.47 (((!!) @ (^[Y1 : a]: 345.07/44.47 ((('#sk4' @ ('#sk2' @ Y0 @ Y1)) = (Y1))))))))) & 345.07/44.47 (((!!) @ (^[Y0 : a]: 345.07/44.47 (((!!) @ (^[Y1 : a]: 345.07/44.47 ((('#sk3' @ ('#sk2' @ Y0 @ Y1)) = (Y0))))))))) & 345.07/44.47 ((('#sk4' @ '#sk1') = ('#sk1'))))) => 345.07/44.47 (((!!) @ (^[Y0 : a > $o]: 345.07/44.47 (((!!) @ (^[Y1 : a]: 345.07/44.47 (((((??) @ (^[Y2 : a]: 345.07/44.47 (((((!!) @ (^[Y3 : a]: 345.07/44.47 (((((!!) @ ( 345.07/44.47 ^[Y4 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (Y4 @ 345.07/44.47 Y2) & 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (Y4 @ 345.07/44.47 Y5) => 345.07/44.47 (Y4 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y5))))))))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (Y4 @ 345.07/44.47 Y5) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y5) = 345.07/44.47 (Y3))))))))))))) => 345.07/44.47 (Y0 @ Y3)))))) & 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 ((('#sk5' @ 345.07/44.47 ('#sk2' @ 345.07/44.47 Y3 @ Y1)) & 345.07/44.47 (((!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y5 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y6 : a]: 345.07/44.47 (( 345.07/44.47 (Y5 @ 345.07/44.47 Y6) => 345.07/44.47 (Y5 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y6))))))) & 345.07/44.47 (Y5 @ Y3))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y6 : a]: 345.07/44.47 (( 345.07/44.47 (Y5 @ 345.07/44.47 Y6) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y6) = 345.07/44.47 (Y4))))))))))))) => 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y5 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y6 : a]: 345.07/44.47 (( 345.07/44.47 (Y5 @ 345.07/44.47 Y6) => 345.07/44.47 (Y5 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y6))))))) & 345.07/44.47 (Y5 @ Y2))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y6 : a]: 345.07/44.47 (( 345.07/44.47 (Y5 @ 345.07/44.47 Y6) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y6) = 345.07/44.47 (Y4)))))))))))))))))))))))))))) <=> 345.07/44.47 (((??) @ (^[Y2 : a]: 345.07/44.47 (((((!!) @ (^[Y3 : a]: 345.07/44.47 (((((!!) @ ( 345.07/44.47 ^[Y4 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (Y4 @ 345.07/44.47 Y2) & 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (Y4 @ 345.07/44.47 Y5) => 345.07/44.47 (Y4 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y5))))))))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (Y4 @ 345.07/44.47 Y5) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y5) = 345.07/44.47 (Y3))))))))))))) => 345.07/44.47 (Y0 @ Y3)))))) & 345.07/44.47 ('#sk5' @ 345.07/44.47 ('#sk2' @ Y2 @ Y1)))))))))))))))))), 345.07/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl4])). 345.07/44.47 thf(zip_derived_cl6, plain, 345.07/44.47 ( ((((('#sk3' @ '#sk1') = ('#sk1'))) & 345.07/44.47 (((!!) @ (^[Y0 : a > $o]: 345.07/44.47 (((((??) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a]: 345.07/44.47 (((Y0 @ Y2) => (Y0 @ 345.07/44.47 ('#sk3' @ Y2))))))) & 345.07/44.47 (Y0 @ Y1)))))) => 345.07/44.47 (Y0 @ '#sk1')))))) & 345.07/44.47 (((!!) @ (^[Y0 : a]: 345.07/44.47 (((((Y0) = ('#sk2' @ ('#sk3' @ Y0) @ ('#sk4' @ Y0)))) <=> 345.07/44.47 (((Y0) != ('#sk1')))))))) & 345.07/44.47 (((!!) @ (^[Y0 : a]: 345.07/44.47 (((!!) @ (^[Y1 : a]: 345.07/44.47 ((('#sk4' @ ('#sk2' @ Y0 @ Y1)) = (Y1))))))))) & 345.07/44.47 (((!!) @ (^[Y0 : a]: 345.07/44.47 (((!!) @ (^[Y1 : a]: 345.07/44.47 ((('#sk3' @ ('#sk2' @ Y0 @ Y1)) = (Y0))))))))) & 345.07/44.47 ((('#sk4' @ '#sk1') = ('#sk1')))))), 345.07/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 345.07/44.47 thf(zip_derived_cl8, plain, ( ((('#sk3' @ '#sk1') = ('#sk1')))), 345.07/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl6])). 345.07/44.47 thf(zip_derived_cl15, plain, ((('#sk3' @ '#sk1') = ('#sk1'))), 345.07/44.47 inference('simplify nested equalities', [status(thm)], [zip_derived_cl8])). 345.07/44.47 thf(zip_derived_cl10, plain, 345.07/44.47 ( (((!!) @ (^[Y0 : a]: 345.07/44.47 (((((Y0) = ('#sk2' @ ('#sk3' @ Y0) @ ('#sk4' @ Y0)))) <=> 345.07/44.47 (((Y0) != ('#sk1'))))))))), 345.07/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl6])). 345.07/44.47 thf(zip_derived_cl17, plain, 345.07/44.47 (![X2 : a]: 345.07/44.47 (((((X2) = ('#sk2' @ ('#sk3' @ X2) @ ('#sk4' @ X2)))) <=> 345.07/44.47 (((X2) != ('#sk1')))))), 345.07/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 345.07/44.47 thf(zip_derived_cl23, plain, 345.07/44.47 (![X2 : a]: 345.07/44.47 ((((X2) = ('#sk2' @ ('#sk3' @ X2) @ ('#sk4' @ X2)))) 345.07/44.47 = (((X2) != ('#sk1'))))), 345.07/44.47 inference('simplify nested equalities', [status(thm)], [zip_derived_cl17])). 345.07/44.47 thf(zip_derived_cl9, plain, 345.07/44.47 ( (((!!) @ (^[Y0 : a > $o]: 345.07/44.47 (((((??) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a]: 345.07/44.47 (((Y0 @ Y2) => (Y0 @ 345.07/44.47 ('#sk3' @ Y2))))))) & 345.07/44.47 (Y0 @ Y1)))))) => 345.07/44.47 (Y0 @ '#sk1'))))))), 345.07/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl6])). 345.07/44.47 thf(zip_derived_cl16, plain, 345.07/44.47 (![X2 : a > $o]: 345.07/44.47 (((((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((X2 @ Y1) => (X2 @ ('#sk3' @ Y1))))))) & 345.07/44.47 (X2 @ Y0)))))) => 345.07/44.47 (X2 @ '#sk1')))), 345.07/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])). 345.07/44.47 thf(zip_derived_cl22, plain, 345.07/44.47 (![X2 : a > $o]: 345.07/44.47 (~ (((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((X2 @ Y1) => (X2 @ ('#sk3' @ Y1))))))) & 345.07/44.47 (X2 @ Y0)))))) 345.07/44.47 | (X2 @ '#sk1'))), 345.07/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 345.07/44.47 thf(zip_derived_cl27, plain, 345.07/44.47 (![X2 : a > $o, X4 : a]: 345.07/44.47 (~ (((((!!) @ (^[Y0 : a]: (((X2 @ Y0) => (X2 @ ('#sk3' @ Y0))))))) & 345.07/44.47 (X2 @ X4))) 345.07/44.47 | (X2 @ '#sk1'))), 345.07/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 345.07/44.47 thf(zip_derived_cl30, plain, 345.07/44.47 (![X2 : a > $o, X4 : a]: 345.07/44.47 (~ (((!!) @ (^[Y0 : a]: (((X2 @ Y0) => (X2 @ ('#sk3' @ Y0))))))) 345.07/44.47 | ~ (X2 @ X4) 345.07/44.47 | (X2 @ '#sk1'))), 345.07/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl27])). 345.07/44.47 thf(zip_derived_cl31, plain, 345.07/44.47 (![X2 : a > $o, X4 : a]: 345.07/44.47 (~ (((X2 @ ('#sk18' @ X2)) => (X2 @ ('#sk3' @ ('#sk18' @ X2))))) 345.07/44.47 | (X2 @ '#sk1') 345.07/44.47 | ~ (X2 @ X4))), 345.07/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])). 345.07/44.47 thf(zip_derived_cl32, plain, 345.07/44.47 (![X2 : a > $o, X4 : a]: 345.07/44.47 ( (X2 @ ('#sk18' @ X2)) | ~ (X2 @ X4) | (X2 @ '#sk1'))), 345.07/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl31])). 345.07/44.47 thf(zip_derived_cl7, plain, 345.07/44.47 (~ (((!!) @ (^[Y0 : a > $o]: 345.07/44.47 (((!!) @ (^[Y1 : a]: 345.07/44.47 (((((??) @ (^[Y2 : a]: 345.07/44.47 (((((!!) @ (^[Y3 : a]: 345.07/44.47 (((((!!) @ ( 345.07/44.47 ^[Y4 : a > $o]: 345.07/44.47 (((( 345.07/44.47 (Y4 @ 345.07/44.47 Y2) & 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (Y4 @ 345.07/44.47 Y5) => 345.07/44.47 (Y4 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y5))))))))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (Y4 @ 345.07/44.47 Y5) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y5) = 345.07/44.47 (Y3))))))))))))) => 345.07/44.47 (Y0 @ Y3)))))) & 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 ((('#sk5' @ 345.07/44.47 ('#sk2' @ Y3 @ 345.07/44.47 Y1)) & 345.07/44.47 (((!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (((( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y5 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y6 : a]: 345.07/44.47 (( 345.07/44.47 (Y5 @ 345.07/44.47 Y6) => 345.07/44.47 (Y5 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y6))))))) & 345.07/44.47 (Y5 @ Y3))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y6 : a]: 345.07/44.47 (( 345.07/44.47 (Y5 @ 345.07/44.47 Y6) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y6) = 345.07/44.47 (Y4))))))))))))) => 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y5 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y6 : a]: 345.07/44.47 (( 345.07/44.47 (Y5 @ 345.07/44.47 Y6) => 345.07/44.47 (Y5 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y6))))))) & 345.07/44.47 (Y5 @ Y2))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y6 : a]: 345.07/44.47 (( 345.07/44.47 (Y5 @ 345.07/44.47 Y6) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y6) = 345.07/44.47 (Y4)))))))))))))))))))))))))))) <=> 345.07/44.47 (((??) @ (^[Y2 : a]: 345.07/44.47 (((((!!) @ (^[Y3 : a]: 345.07/44.47 (((((!!) @ ( 345.07/44.47 ^[Y4 : a > $o]: 345.07/44.47 (((( 345.07/44.47 (Y4 @ 345.07/44.47 Y2) & 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (Y4 @ 345.07/44.47 Y5) => 345.07/44.47 (Y4 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y5))))))))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (Y4 @ 345.07/44.47 Y5) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y5) = 345.07/44.47 (Y3))))))))))))) => 345.07/44.47 (Y0 @ Y3)))))) & 345.07/44.47 ('#sk5' @ ('#sk2' @ Y2 @ Y1)))))))))))))))), 345.07/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 345.07/44.47 thf(zip_derived_cl14, plain, 345.07/44.47 (~ (((!!) @ (^[Y0 : a]: 345.07/44.47 (((((??) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a]: 345.07/44.47 (((((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((((Y3 @ Y1) & 345.07/44.47 (((!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))))) => 345.07/44.47 (((??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2))))))))))))) => 345.07/44.47 ('#sk6' @ Y2)))))) & 345.07/44.47 (((??) @ (^[Y2 : a]: 345.07/44.47 ((('#sk5' @ 345.07/44.47 ('#sk2' @ Y2 @ Y0)) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((((!!) @ ( 345.07/44.47 ^[Y4 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (Y4 @ 345.07/44.47 Y5) => 345.07/44.47 (Y4 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y5))))))) & 345.07/44.47 (Y4 @ Y2))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (Y4 @ 345.07/44.47 Y5) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y5) = 345.07/44.47 (Y3))))))))))))) => 345.07/44.47 (((!!) @ ( 345.07/44.47 ^[Y4 : a > $o]: 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (Y4 @ 345.07/44.47 Y5) => 345.07/44.47 (Y4 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y5))))))) & 345.07/44.47 (Y4 @ Y1))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y5 : a]: 345.07/44.47 (( 345.07/44.47 (Y4 @ 345.07/44.47 Y5) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y5) = 345.07/44.47 (Y3)))))))))))))))))))))))))))) <=> 345.07/44.47 (((??) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a]: 345.07/44.47 (((((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((((Y3 @ Y1) & 345.07/44.47 (((!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))))) => 345.07/44.47 (((??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2))))))))))))) => 345.07/44.47 ('#sk6' @ Y2)))))) & 345.07/44.47 ('#sk5' @ ('#sk2' @ Y1 @ Y0))))))))))))), 345.07/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl7])). 345.07/44.47 thf(zip_derived_cl21, plain, 345.07/44.47 (~ (((((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ('#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 (((??) @ (^[Y1 : a]: 345.07/44.47 ((('#sk5' @ ('#sk2' @ Y1 @ '#sk7')) & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((((( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))) & 345.07/44.47 (Y3 @ Y1))) => 345.07/44.47 (((??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2))))))))))))) => 345.07/44.47 (((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((((( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))) & 345.07/44.47 (Y3 @ Y0))) => 345.07/44.47 (((??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2)))))))))))))))))))))))))))) <=> 345.07/44.47 (((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ('#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7')))))))))), 345.07/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl14])). 345.07/44.47 thf(zip_derived_cl26, plain, 345.07/44.47 (((((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ('#sk3' @ Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 (((??) @ (^[Y1 : a]: 345.07/44.47 ((('#sk5' @ ('#sk2' @ Y1 @ '#sk7')) & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((((((!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))) & 345.07/44.47 (Y3 @ Y1))) => 345.07/44.47 (((??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (((Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2))))))))))))) => 345.07/44.47 (((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((((((!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))) & 345.07/44.47 (Y3 @ Y0))) => 345.07/44.47 (((??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (((Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2)))))))))))))))))))))))))))) 345.07/44.47 != (((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = 345.07/44.47 (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 345.07/44.47 inference('simplify nested equalities', [status(thm)], [zip_derived_cl21])). 345.07/44.47 thf(zip_derived_cl35, plain, 345.07/44.47 (( ('#form24') 345.07/44.47 | ~ (((((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y3) = 345.07/44.47 (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 (((??) @ (^[Y1 : a]: 345.07/44.47 ((('#sk5' @ ('#sk2' @ Y1 @ '#sk7')) & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))) & 345.07/44.47 (Y3 @ Y1))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2))))))))))))) => 345.07/44.47 (((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))) & 345.07/44.47 (Y3 @ Y0))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2)))))))))))))))))))))))))))) <=> 345.07/44.47 (((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y3) = 345.07/44.47 (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))))), 345.07/44.47 define([status(thm)])). 345.07/44.47 thf(zip_derived_cl36, plain, 345.07/44.47 (( (((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ('#sk3' @ Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 (((??) @ (^[Y1 : a]: 345.07/44.47 ((('#sk5' @ ('#sk2' @ Y1 @ '#sk7')) & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((((((!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))) & 345.07/44.47 (Y3 @ Y1))) => 345.07/44.47 (((??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2))))))))))))) => 345.07/44.47 (((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((((((!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))) & 345.07/44.47 (Y3 @ Y0))) => 345.07/44.47 (((??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2)))))))))))))))))))))))))))) 345.07/44.47 | (((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ('#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))) 345.07/44.47 | ('#form24'))), 345.07/44.47 inference('lazy_cnf_xor', [status(thm)], [zip_derived_cl35])). 345.07/44.47 thf(zip_derived_cl40, plain, 345.07/44.47 (( (((((!!) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.07/44.47 (((((Y1 @ '#sk25') & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) => (Y1 @ 345.07/44.47 ('#sk3' @ Y2))))))))) => 345.07/44.47 (((??) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) & 345.07/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.07/44.47 ('#sk6' @ Y0)))))) & 345.07/44.47 (((??) @ (^[Y0 : a]: 345.07/44.47 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 345.07/44.47 (((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ('#sk3' @ 345.07/44.47 Y3))))))) & 345.07/44.47 (Y2 @ Y0))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))) => 345.07/44.47 (((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ('#sk3' @ 345.07/44.47 Y3))))))) & 345.07/44.47 (Y2 @ '#sk25'))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))))))))))))))) 345.07/44.47 | ('#form24') 345.07/44.47 | (((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ('#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 345.07/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl36])). 345.07/44.47 thf(zip_derived_cl40, plain, 345.07/44.47 (( (((((!!) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.07/44.47 (((((Y1 @ '#sk25') & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) => (Y1 @ 345.07/44.47 ('#sk3' @ Y2))))))))) => 345.07/44.47 (((??) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) & 345.07/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.07/44.47 ('#sk6' @ Y0)))))) & 345.07/44.47 (((??) @ (^[Y0 : a]: 345.07/44.47 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 345.07/44.47 (((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ('#sk3' @ 345.07/44.47 Y3))))))) & 345.07/44.47 (Y2 @ Y0))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))) => 345.07/44.47 (((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ('#sk3' @ 345.07/44.47 Y3))))))) & 345.07/44.47 (Y2 @ '#sk25'))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))))))))))))))) 345.07/44.47 | ('#form24') 345.07/44.47 | (((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ('#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 345.07/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl36])). 345.07/44.47 thf(zip_derived_cl44, plain, 345.07/44.47 ((~ ('#form26') 345.07/44.47 | (((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ('#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 345.07/44.47 define([status(thm)])). 345.07/44.47 thf(zip_derived_cl35, plain, 345.07/44.47 (( ('#form24') 345.07/44.47 | ~ (((((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y3) = 345.07/44.47 (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 (((??) @ (^[Y1 : a]: 345.07/44.47 ((('#sk5' @ ('#sk2' @ Y1 @ '#sk7')) & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))) & 345.07/44.47 (Y3 @ Y1))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2))))))))))))) => 345.07/44.47 (((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))) & 345.07/44.47 (Y3 @ Y0))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2)))))))))))))))))))))))))))) <=> 345.07/44.47 (((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y3) = 345.07/44.47 (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))))), 345.07/44.47 define([status(thm)])). 345.07/44.47 thf(zip_derived_cl37, plain, 345.07/44.47 ((~ (((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ('#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 (((??) @ (^[Y1 : a]: 345.07/44.47 ((('#sk5' @ ('#sk2' @ Y1 @ '#sk7')) & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((((((!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))) & 345.07/44.47 (Y3 @ Y1))) => 345.07/44.47 (((??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2))))))))))))) => 345.07/44.47 (((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((((((!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))) & 345.07/44.47 (Y3 @ Y0))) => 345.07/44.47 (((??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2)))))))))))))))))))))))))))) 345.07/44.47 | ~ (((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = 345.07/44.47 (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))) 345.07/44.47 | ('#form24'))), 345.07/44.47 inference('lazy_cnf_xor', [status(thm)], [zip_derived_cl35])). 345.07/44.47 thf(zip_derived_cl39, plain, 345.07/44.47 (![X2 : a]: 345.07/44.47 (~ (((((!!) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.07/44.47 (((((Y1 @ X2) & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) => (Y1 @ 345.07/44.47 ('#sk3' @ Y2))))))))) => 345.07/44.47 (((??) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) & 345.07/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.07/44.47 ('#sk6' @ Y0)))))) & 345.07/44.47 (((??) @ (^[Y0 : a]: 345.07/44.47 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 345.07/44.47 (((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((((!!) @ (^[Y3 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))) & 345.07/44.47 (Y2 @ Y0))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y3) = 345.07/44.47 (Y1))))))))))))) => 345.07/44.47 (((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((((!!) @ (^[Y3 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))) & 345.07/44.47 (Y2 @ X2))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y3) = 345.07/44.47 (Y1))))))))))))))))))))))))) 345.07/44.47 | ('#form24') 345.07/44.47 | ~ (((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y3) = 345.07/44.47 (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 345.07/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 345.07/44.47 thf(zip_derived_cl41, plain, 345.07/44.47 (( ('#form26') 345.07/44.47 | ~ (((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = 345.07/44.47 (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 345.07/44.47 define([status(thm)])). 345.07/44.47 thf(zip_derived_cl46, plain, 345.07/44.47 (( ('#form26') 345.07/44.47 | ('#form24') 345.07/44.47 | (((((!!) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.07/44.47 (((((Y1 @ '#sk25') & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) => (Y1 @ 345.07/44.47 ('#sk3' @ Y2))))))))) => 345.07/44.47 (((??) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) & 345.07/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.07/44.47 ('#sk6' @ Y0)))))) & 345.07/44.47 (((??) @ (^[Y0 : a]: 345.07/44.47 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 345.07/44.47 (((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((((!!) @ (^[Y3 : a]: 345.07/44.47 (( 345.07/44.47 (Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))) & 345.07/44.47 (Y2 @ Y0))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))) => 345.07/44.47 (((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((((!!) @ (^[Y3 : a]: 345.07/44.47 (( 345.07/44.47 (Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))) & 345.07/44.47 (Y2 @ '#sk25'))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))))))))))))))))), 345.07/44.47 inference('renaming', [status(thm)], 345.07/44.47 [zip_derived_cl40, zip_derived_cl44, zip_derived_cl41])). 345.07/44.47 thf(zip_derived_cl50, plain, 345.07/44.47 (( (((??) @ (^[Y0 : a]: 345.07/44.47 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 345.07/44.47 (((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ('#sk3' @ Y3))))))) & 345.07/44.47 (Y2 @ Y0))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))) => 345.07/44.47 (((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ('#sk3' @ Y3))))))) & 345.07/44.47 (Y2 @ '#sk25'))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))))))))))))) 345.07/44.47 | ('#form24') 345.07/44.47 | ('#form26'))), 345.07/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 345.07/44.47 thf(zip_derived_cl60, plain, 345.07/44.47 (( ((('#sk5' @ ('#sk2' @ '#sk30' @ '#sk7')) & 345.07/44.47 (((!!) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.07/44.47 (((((((!!) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) => (Y1 @ 345.07/44.47 ('#sk3' @ Y2))))))) & 345.07/44.47 (Y1 @ '#sk30'))) => 345.07/44.47 (((??) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) & 345.07/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.07/44.47 (((!!) @ (^[Y1 : a > $o]: 345.07/44.47 (((((((!!) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) => (Y1 @ 345.07/44.47 ('#sk3' @ Y2))))))) & 345.07/44.47 (Y1 @ '#sk25'))) => 345.07/44.47 (((??) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) & 345.07/44.47 ((('#sk4' @ Y2) = (Y0)))))))))))))))))))) 345.07/44.47 | ('#form26') 345.07/44.47 | ('#form24'))), 345.07/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl50])). 345.07/44.47 thf(zip_derived_cl66, plain, 345.07/44.47 (( ('#sk5' @ ('#sk2' @ '#sk30' @ '#sk7')) | ('#form24') | ('#form26'))), 345.07/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl60])). 345.07/44.47 thf(zip_derived_cl26, plain, 345.07/44.47 (((((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ('#sk3' @ Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 (((??) @ (^[Y1 : a]: 345.07/44.47 ((('#sk5' @ ('#sk2' @ Y1 @ '#sk7')) & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((((((!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))) & 345.07/44.47 (Y3 @ Y1))) => 345.07/44.47 (((??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (((Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2))))))))))))) => 345.07/44.47 (((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((((((!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))) & 345.07/44.47 (Y3 @ Y0))) => 345.07/44.47 (((??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (((Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2)))))))))))))))))))))))))))) 345.07/44.47 != (((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ Y3) & 345.07/44.47 ((('#sk4' @ 345.07/44.47 Y3) = 345.07/44.47 (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 345.07/44.47 inference('simplify nested equalities', [status(thm)], [zip_derived_cl21])). 345.07/44.47 thf(zip_derived_cl35, plain, 345.07/44.47 (( ('#form24') 345.07/44.47 | ~ (((((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y3) = 345.07/44.47 (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 (((??) @ (^[Y1 : a]: 345.07/44.47 ((('#sk5' @ ('#sk2' @ Y1 @ '#sk7')) & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))) & 345.07/44.47 (Y3 @ Y1))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2))))))))))))) => 345.07/44.47 (((!!) @ (^[Y3 : a > $o]: 345.07/44.47 (((( 345.07/44.47 (( 345.07/44.47 (!!) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) => 345.07/44.47 (Y3 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y4))))))) & 345.07/44.47 (Y3 @ Y0))) => 345.07/44.47 (( 345.07/44.47 (??) @ ( 345.07/44.47 ^[Y4 : a]: 345.07/44.47 (( 345.07/44.47 (Y3 @ 345.07/44.47 Y4) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y4) = 345.07/44.47 (Y2)))))))))))))))))))))))))))) <=> 345.07/44.47 (((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y3) = 345.07/44.47 (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))))), 345.07/44.47 define([status(thm)])). 345.07/44.47 thf(zip_derived_cl38, plain, (~ ('#form24')), 345.07/44.47 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 345.07/44.47 thf(zip_derived_cl164, plain, 345.07/44.47 (( ('#sk5' @ ('#sk2' @ '#sk30' @ '#sk7')) | ('#form26'))), 345.07/44.47 inference('demod', [status(thm)], [zip_derived_cl66, zip_derived_cl38])). 345.07/44.47 thf(zip_derived_cl49, plain, 345.07/44.47 (( (((!!) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.07/44.47 (((((Y1 @ '#sk25') & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) => (Y1 @ 345.07/44.47 ('#sk3' @ Y2))))))))) => 345.07/44.47 (((??) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) & 345.07/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.07/44.47 ('#sk6' @ Y0)))))) 345.07/44.47 | ('#form24') 345.07/44.47 | ('#form26'))), 345.07/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 345.07/44.47 thf(zip_derived_cl49, plain, 345.07/44.47 (( (((!!) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.07/44.47 (((((Y1 @ '#sk25') & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) => (Y1 @ 345.07/44.47 ('#sk3' @ Y2))))))))) => 345.07/44.47 (((??) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) & 345.07/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.07/44.47 ('#sk6' @ Y0)))))) 345.07/44.47 | ('#form24') 345.07/44.47 | ('#form26'))), 345.07/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 345.07/44.47 thf(zip_derived_cl57, plain, 345.07/44.47 (![X2 : a]: 345.07/44.47 (~ ('#form28' @ X2) 345.07/44.47 | (((!!) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.07/44.47 (((((Y1 @ X2) & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) => (Y1 @ 345.07/44.47 ('#sk3' @ Y2))))))))) => 345.07/44.47 (((??) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) & 345.07/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.07/44.47 ('#sk6' @ Y0)))))))), 345.07/44.47 define([status(thm)])). 345.07/44.47 thf(zip_derived_cl39, plain, 345.07/44.47 (![X2 : a]: 345.07/44.47 (~ (((((!!) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.07/44.47 (((((Y1 @ X2) & 345.07/44.47 (((!!) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) => (Y1 @ 345.07/44.47 ('#sk3' @ Y2))))))))) => 345.07/44.47 (((??) @ (^[Y2 : a]: 345.07/44.47 (((Y1 @ Y2) & 345.07/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.07/44.47 ('#sk6' @ Y0)))))) & 345.07/44.47 (((??) @ (^[Y0 : a]: 345.07/44.47 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 345.07/44.47 (((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((((!!) @ (^[Y3 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))) & 345.07/44.47 (Y2 @ Y0))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y3) = 345.07/44.47 (Y1))))))))))))) => 345.07/44.47 (((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((((!!) @ (^[Y3 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))) & 345.07/44.47 (Y2 @ X2))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y3) = 345.07/44.47 (Y1))))))))))))))))))))))))) 345.07/44.47 | ('#form24') 345.07/44.47 | ~ (((??) @ (^[Y0 : a]: 345.07/44.47 (((((!!) @ (^[Y1 : a]: 345.07/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.07/44.47 (((((Y2 @ Y0) & 345.07/44.47 (((!!) @ (^[Y3 : a]: 345.07/44.47 ( 345.07/44.47 ( 345.07/44.47 (Y2 @ 345.07/44.47 Y3) => 345.07/44.47 (Y2 @ 345.07/44.47 ( 345.07/44.47 '#sk3' @ 345.07/44.47 Y3))))))))) => 345.07/44.47 (((??) @ (^[Y3 : a]: 345.07/44.47 (((Y2 @ 345.07/44.47 Y3) & 345.07/44.47 (( 345.07/44.47 ('#sk4' @ 345.07/44.47 Y3) = 345.07/44.47 (Y1))))))))))))) => 345.07/44.47 ('#sk6' @ Y1)))))) & 345.07/44.47 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 345.35/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 345.35/44.47 thf(zip_derived_cl41, plain, 345.35/44.47 (( ('#form26') 345.35/44.47 | ~ (((??) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a]: 345.35/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.35/44.47 (((((Y2 @ Y0) & 345.35/44.47 (((!!) @ (^[Y3 : a]: 345.35/44.47 (((Y2 @ 345.35/44.47 Y3) => 345.35/44.47 (Y2 @ 345.35/44.47 ( 345.35/44.47 '#sk3' @ 345.35/44.47 Y3))))))))) => 345.35/44.47 (((??) @ (^[Y3 : a]: 345.35/44.47 (((Y2 @ Y3) & 345.35/44.47 ((('#sk4' @ 345.35/44.47 Y3) = 345.35/44.47 (Y1))))))))))))) => 345.35/44.47 ('#sk6' @ Y1)))))) & 345.35/44.47 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 345.35/44.47 define([status(thm)])). 345.35/44.47 thf(zip_derived_cl43, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ ('#form26') 345.35/44.47 | ('#form24') 345.35/44.47 | ~ (((((!!) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((Y1 @ X2) & 345.35/44.47 (((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = 345.35/44.47 (Y0))))))))))))) => 345.35/44.47 ('#sk6' @ Y0)))))) & 345.35/44.47 (((??) @ (^[Y0 : a]: 345.35/44.47 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 345.35/44.47 (((!!) @ (^[Y1 : a]: 345.35/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y3 : a]: 345.35/44.47 (( 345.35/44.47 (Y2 @ 345.35/44.47 Y3) => 345.35/44.47 (Y2 @ 345.35/44.47 ( 345.35/44.47 '#sk3' @ 345.35/44.47 Y3))))))) & 345.35/44.47 (Y2 @ Y0))) => 345.35/44.47 (((??) @ (^[Y3 : a]: 345.35/44.47 ( 345.35/44.47 ( 345.35/44.47 (Y2 @ 345.35/44.47 Y3) & 345.35/44.47 (( 345.35/44.47 ('#sk4' @ 345.35/44.47 Y3) = 345.35/44.47 (Y1))))))))))))) => 345.35/44.47 (((!!) @ (^[Y2 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y3 : a]: 345.35/44.47 (( 345.35/44.47 (Y2 @ 345.35/44.47 Y3) => 345.35/44.47 (Y2 @ 345.35/44.47 ( 345.35/44.47 '#sk3' @ 345.35/44.47 Y3))))))) & 345.35/44.47 (Y2 @ X2))) => 345.35/44.47 (((??) @ (^[Y3 : a]: 345.35/44.47 ( 345.35/44.47 ( 345.35/44.47 (Y2 @ 345.35/44.47 Y3) & 345.35/44.47 (( 345.35/44.47 ('#sk4' @ 345.35/44.47 Y3) = 345.35/44.47 (Y1))))))))))))))))))))))))))), 345.35/44.47 inference('renaming', [status(thm)], [zip_derived_cl39, zip_derived_cl41])). 345.35/44.47 thf(zip_derived_cl47, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ (((!!) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((Y1 @ X2) & 345.35/44.47 (((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.35/44.47 ('#sk6' @ Y0)))))) 345.35/44.47 | ~ (((??) @ (^[Y0 : a]: 345.35/44.47 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 345.35/44.47 (((!!) @ (^[Y1 : a]: 345.35/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y3 : a]: 345.35/44.47 ( 345.35/44.47 ( 345.35/44.47 (Y2 @ 345.35/44.47 Y3) => 345.35/44.47 (Y2 @ 345.35/44.47 ( 345.35/44.47 '#sk3' @ 345.35/44.47 Y3))))))) & 345.35/44.47 (Y2 @ Y0))) => 345.35/44.47 (((??) @ (^[Y3 : a]: 345.35/44.47 (((Y2 @ 345.35/44.47 Y3) & 345.35/44.47 (( 345.35/44.47 ('#sk4' @ 345.35/44.47 Y3) = 345.35/44.47 (Y1))))))))))))) => 345.35/44.47 (((!!) @ (^[Y2 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y3 : a]: 345.35/44.47 ( 345.35/44.47 ( 345.35/44.47 (Y2 @ 345.35/44.47 Y3) => 345.35/44.47 (Y2 @ 345.35/44.47 ( 345.35/44.47 '#sk3' @ 345.35/44.47 Y3))))))) & 345.35/44.47 (Y2 @ X2))) => 345.35/44.47 (((??) @ (^[Y3 : a]: 345.35/44.47 (((Y2 @ 345.35/44.47 Y3) & 345.35/44.47 (( 345.35/44.47 ('#sk4' @ 345.35/44.47 Y3) = 345.35/44.47 (Y1))))))))))))))))))))))) 345.35/44.47 | ('#form24') 345.35/44.47 | ~ ('#form26'))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl43])). 345.35/44.47 thf(zip_derived_cl53, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 ( ('#form28' @ X2) 345.35/44.47 | ~ (((!!) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((Y1 @ X2) & 345.35/44.47 (((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.35/44.47 ('#sk6' @ Y0)))))))), 345.35/44.47 define([status(thm)])). 345.35/44.47 thf(zip_derived_cl59, plain, 345.35/44.47 (( ('#form28' @ '#sk25') | ('#form26') | ('#form24'))), 345.35/44.47 inference('renaming', [status(thm)], 345.35/44.47 [zip_derived_cl49, zip_derived_cl57, zip_derived_cl53])). 345.35/44.47 thf(zip_derived_cl38, plain, (~ ('#form24')), 345.35/44.47 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 345.35/44.47 thf(zip_derived_cl163, plain, (( ('#form28' @ '#sk25') | ('#form26'))), 345.35/44.47 inference('demod', [status(thm)], [zip_derived_cl59, zip_derived_cl38])). 345.35/44.47 thf(zip_derived_cl67, plain, 345.35/44.47 (( (((!!) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))) & 345.35/44.47 (Y1 @ '#sk30'))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.35/44.47 (((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))) & 345.35/44.47 (Y1 @ '#sk25'))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = (Y0)))))))))))))))))) 345.35/44.47 | ('#form24') 345.35/44.47 | ('#form26'))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl60])). 345.35/44.47 thf(zip_derived_cl72, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 ( (((((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 345.35/44.47 (Y0 @ '#sk30'))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X2))))))))))))) => 345.35/44.47 (((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 345.35/44.47 (Y0 @ '#sk25'))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X2))))))))))))))) 345.35/44.47 | ('#form26') 345.35/44.47 | ('#form24'))), 345.35/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl67])). 345.35/44.47 thf(zip_derived_cl78, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ (((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 345.35/44.47 (Y0 @ '#sk30'))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X2))))))))))))) 345.35/44.47 | (((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 345.35/44.47 (Y0 @ '#sk25'))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X2))))))))))))) 345.35/44.47 | ('#form24') 345.35/44.47 | ('#form26'))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl72])). 345.35/44.47 thf(zip_derived_cl87, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ (((((((!!) @ (^[Y0 : a]: 345.35/44.47 ((('#sk39' @ X2 @ Y0) => ('#sk39' @ X2 @ 345.35/44.47 ('#sk3' @ Y0))))))) & 345.35/44.47 ('#sk39' @ X2 @ '#sk30'))) => 345.35/44.47 (((??) @ (^[Y0 : a]: 345.35/44.47 ((('#sk39' @ X2 @ Y0) & ((('#sk4' @ Y0) = (X2)))))))))) 345.35/44.47 | ('#form26') 345.35/44.47 | ('#form24') 345.35/44.47 | (((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 345.35/44.47 (Y0 @ '#sk25'))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X2))))))))))))))), 345.35/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl78])). 345.35/44.47 thf(zip_derived_cl96, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 ( (((((!!) @ (^[Y0 : a]: 345.35/44.47 ((('#sk39' @ X2 @ Y0) => ('#sk39' @ X2 @ 345.35/44.47 ('#sk3' @ Y0))))))) & 345.35/44.47 ('#sk39' @ X2 @ '#sk30'))) 345.35/44.47 | (((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 345.35/44.47 (Y0 @ '#sk25'))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X2))))))))))))) 345.35/44.47 | ('#form24') 345.35/44.47 | ('#form26'))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl87])). 345.35/44.47 thf(zip_derived_cl108, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ ('#form50' @ X2) 345.35/44.47 | (((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 345.35/44.47 (Y0 @ '#sk25'))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X2))))))))))))))), 345.35/44.47 define([status(thm)])). 345.35/44.47 thf(zip_derived_cl109, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( (((((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 345.35/44.47 (X4 @ '#sk25'))) => 345.35/44.47 (((??) @ (^[Y0 : a]: (((X4 @ Y0) & ((('#sk4' @ Y0) = (X2)))))))))) 345.35/44.47 | ~ ('#form50' @ X2))), 345.35/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl108])). 345.35/44.47 thf(zip_derived_cl125, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 (~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 345.35/44.47 (X4 @ '#sk25'))) 345.35/44.47 | (((??) @ (^[Y0 : a]: (((X4 @ Y0) & ((('#sk4' @ Y0) = (X2)))))))) 345.35/44.47 | ~ ('#form50' @ X2))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl109])). 345.35/44.47 thf(zip_derived_cl134, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 (~ (((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) 345.35/44.47 | ~ (X4 @ '#sk25') 345.35/44.47 | ~ ('#form50' @ X2) 345.35/44.47 | (((??) @ (^[Y0 : a]: (((X4 @ Y0) & ((('#sk4' @ Y0) = (X2)))))))))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl125])). 345.35/44.47 thf(zip_derived_cl142, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 (~ (((X4 @ ('#sk18' @ X4)) => (X4 @ ('#sk3' @ ('#sk18' @ X4))))) 345.35/44.47 | (((??) @ (^[Y0 : a]: (((X4 @ Y0) & ((('#sk4' @ Y0) = (X2)))))))) 345.35/44.47 | ~ ('#form50' @ X2) 345.35/44.47 | ~ (X4 @ '#sk25'))), 345.35/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl134])). 345.35/44.47 thf(zip_derived_cl150, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 (~ (X4 @ ('#sk3' @ ('#sk18' @ X4))) 345.35/44.47 | ~ (X4 @ '#sk25') 345.35/44.47 | ~ ('#form50' @ X2) 345.35/44.47 | (((??) @ (^[Y0 : a]: (((X4 @ Y0) & ((('#sk4' @ Y0) = (X2)))))))))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])). 345.35/44.47 thf(zip_derived_cl149, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( (X4 @ ('#sk18' @ X4)) 345.35/44.47 | ~ (X4 @ '#sk25') 345.35/44.47 | ~ ('#form50' @ X2) 345.35/44.47 | (((??) @ (^[Y0 : a]: (((X4 @ Y0) & ((('#sk4' @ Y0) = (X2)))))))))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])). 345.35/44.47 thf(zip_derived_cl154, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 (~ ('#form110' @ X2 @ X4) 345.35/44.47 | (((??) @ (^[Y0 : a]: (((X4 @ Y0) & ((('#sk4' @ Y0) = (X2)))))))))), 345.35/44.47 define([status(thm)])). 345.35/44.47 thf(zip_derived_cl157, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( ('#form110' @ X2 @ (^[Y0 : a]: (X4 @ Y0))) 345.35/44.47 | ~ ('#form50' @ X2) 345.35/44.47 | ~ (X4 @ '#sk25') 345.35/44.47 | ~ (X4 @ ('#sk3' @ ('#sk18' @ X4))))), 345.35/44.47 inference('renaming', [status(thm)], 345.35/44.47 [zip_derived_cl150, zip_derived_cl154])). 345.35/44.47 thf(zip_derived_cl161, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( ('#form110' @ X2 @ X4) 345.35/44.47 | ~ ('#form50' @ X2) 345.35/44.47 | ~ (X4 @ '#sk25') 345.35/44.47 | ~ (X4 @ ('#sk3' @ ('#sk18' @ X4))))), 345.35/44.47 inference('ho_norm', [status(thm)], [zip_derived_cl157])). 345.35/44.47 thf(zip_derived_cl33, plain, 345.35/44.47 (![X2 : a > $o, X4 : a]: 345.35/44.47 (~ (X2 @ ('#sk3' @ ('#sk18' @ X2))) | ~ (X2 @ X4) | (X2 @ '#sk1'))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl31])). 345.35/44.47 thf(zip_derived_cl34, plain, 345.35/44.47 (![X0 : a > $o]: (~ (X0 @ ('#sk3' @ ('#sk18' @ X0))) | (X0 @ '#sk1'))), 345.35/44.47 inference('condensation', [status(thm)], [zip_derived_cl33])). 345.35/44.47 thf(zip_derived_cl149, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( (X4 @ ('#sk18' @ X4)) 345.35/44.47 | ~ (X4 @ '#sk25') 345.35/44.47 | ~ ('#form50' @ X2) 345.35/44.47 | (((??) @ (^[Y0 : a]: (((X4 @ Y0) & ((('#sk4' @ Y0) = (X2)))))))))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])). 345.35/44.47 thf(zip_derived_cl154, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 (~ ('#form110' @ X2 @ X4) 345.35/44.47 | (((??) @ (^[Y0 : a]: (((X4 @ Y0) & ((('#sk4' @ Y0) = (X2)))))))))), 345.35/44.47 define([status(thm)])). 345.35/44.47 thf(zip_derived_cl156, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( ('#form110' @ X2 @ X4) 345.35/44.47 | ~ ('#form50' @ X2) 345.35/44.47 | ~ (X4 @ '#sk25') 345.35/44.47 | (X4 @ ('#sk18' @ X4)))), 345.35/44.47 inference('renaming', [status(thm)], 345.35/44.47 [zip_derived_cl149, zip_derived_cl154])). 345.35/44.47 thf(zip_derived_cl154, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 (~ ('#form110' @ X2 @ X4) 345.35/44.47 | (((??) @ (^[Y0 : a]: (((X4 @ Y0) & ((('#sk4' @ Y0) = (X2)))))))))), 345.35/44.47 define([status(thm)])). 345.35/44.47 thf(zip_derived_cl155, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( (((X4 @ ('#sk111' @ X2 @ X4)) & 345.35/44.47 ((('#sk4' @ ('#sk111' @ X2 @ X4)) = (X2))))) 345.35/44.47 | ~ ('#form110' @ X2 @ X4))), 345.35/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl154])). 345.35/44.47 thf(zip_derived_cl159, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( (X4 @ ('#sk111' @ X2 @ X4)) | ~ ('#form110' @ X2 @ X4))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl155])). 345.35/44.47 thf(zip_derived_cl12, plain, 345.35/44.47 ( (((!!) @ (^[Y0 : a]: 345.35/44.47 (((!!) @ (^[Y1 : a]: 345.35/44.47 ((('#sk3' @ ('#sk2' @ Y0 @ Y1)) = (Y0)))))))))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl6])). 345.35/44.47 thf(zip_derived_cl19, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (((!!) @ (^[Y0 : a]: ((('#sk3' @ ('#sk2' @ X2 @ Y0)) = (X2))))))), 345.35/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])). 345.35/44.47 thf(zip_derived_cl25, plain, 345.35/44.47 (![X2 : a, X4 : a]: ((('#sk3' @ ('#sk2' @ X2 @ X4)) = (X2)))), 345.35/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 345.35/44.47 thf(zip_derived_cl29, plain, 345.35/44.47 (![X2 : a, X4 : a]: (('#sk3' @ ('#sk2' @ X2 @ X4)) = (X2))), 345.35/44.47 inference('simplify nested equalities', [status(thm)], [zip_derived_cl25])). 345.35/44.47 thf(zip_derived_cl41, plain, 345.35/44.47 (( ('#form26') 345.35/44.47 | ~ (((??) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a]: 345.35/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.35/44.47 (((((Y2 @ Y0) & 345.35/44.47 (((!!) @ (^[Y3 : a]: 345.35/44.47 (((Y2 @ 345.35/44.47 Y3) => 345.35/44.47 (Y2 @ 345.35/44.47 ( 345.35/44.47 '#sk3' @ 345.35/44.47 Y3))))))))) => 345.35/44.47 (((??) @ (^[Y3 : a]: 345.35/44.47 (((Y2 @ Y3) & 345.35/44.47 ((('#sk4' @ 345.35/44.47 Y3) = 345.35/44.47 (Y1))))))))))))) => 345.35/44.47 ('#sk6' @ Y1)))))) & 345.35/44.47 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 345.35/44.47 define([status(thm)])). 345.35/44.47 thf(zip_derived_cl42, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ (((((!!) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((Y1 @ X2) & 345.35/44.47 (((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.35/44.47 ('#sk6' @ Y0)))))) & 345.35/44.47 ('#sk5' @ ('#sk2' @ X2 @ '#sk7')))) 345.35/44.47 | ('#form26'))), 345.35/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 345.35/44.47 thf(zip_derived_cl48, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ (((!!) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((Y1 @ X2) & 345.35/44.47 (((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.35/44.47 ('#sk6' @ Y0)))))) 345.35/44.47 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')) 345.35/44.47 | ('#form26'))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl42])). 345.35/44.47 thf(zip_derived_cl53, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 ( ('#form28' @ X2) 345.35/44.47 | ~ (((!!) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((Y1 @ X2) & 345.35/44.47 (((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.35/44.47 ('#sk6' @ Y0)))))))), 345.35/44.47 define([status(thm)])). 345.35/44.47 thf(zip_derived_cl56, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ ('#form28' @ X2) 345.35/44.47 | ('#form26') 345.35/44.47 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')))), 345.35/44.47 inference('renaming', [status(thm)], [zip_derived_cl48, zip_derived_cl53])). 345.35/44.47 thf(zip_derived_cl164, plain, 345.35/44.47 (( ('#sk5' @ ('#sk2' @ '#sk30' @ '#sk7')) | ('#form26'))), 345.35/44.47 inference('demod', [status(thm)], [zip_derived_cl66, zip_derived_cl38])). 345.35/44.47 thf(zip_derived_cl821, plain, 345.35/44.47 (( ('#form26') | ~ ('#form28' @ '#sk30') | ('#form26'))), 345.35/44.47 inference('sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl164])). 345.35/44.47 thf(zip_derived_cl886, plain, ((~ ('#form28' @ '#sk30') | ('#form26'))), 345.35/44.47 inference('simplify', [status(thm)], [zip_derived_cl821])). 345.35/44.47 thf(zip_derived_cl96, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 ( (((((!!) @ (^[Y0 : a]: 345.35/44.47 ((('#sk39' @ X2 @ Y0) => ('#sk39' @ X2 @ 345.35/44.47 ('#sk3' @ Y0))))))) & 345.35/44.47 ('#sk39' @ X2 @ '#sk30'))) 345.35/44.47 | (((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 345.35/44.47 (Y0 @ '#sk25'))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X2))))))))))))) 345.35/44.47 | ('#form24') 345.35/44.47 | ('#form26'))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl87])). 345.35/44.47 thf(zip_derived_cl108, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ ('#form50' @ X2) 345.35/44.47 | (((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 345.35/44.47 (Y0 @ '#sk25'))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X2))))))))))))))), 345.35/44.47 define([status(thm)])). 345.35/44.47 thf(zip_derived_cl110, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 ( ('#form50' @ X2) 345.35/44.47 | ('#form26') 345.35/44.47 | ('#form24') 345.35/44.47 | (((((!!) @ (^[Y0 : a]: 345.35/44.47 ((('#sk39' @ X2 @ Y0) => ('#sk39' @ X2 @ 345.35/44.47 ('#sk3' @ Y0))))))) & 345.35/44.47 ('#sk39' @ X2 @ '#sk30'))))), 345.35/44.47 inference('renaming', [status(thm)], 345.35/44.47 [zip_derived_cl96, zip_derived_cl108])). 345.35/44.47 thf(zip_derived_cl124, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 ( ('#sk39' @ X2 @ '#sk30') 345.35/44.47 | ('#form24') 345.35/44.47 | ('#form26') 345.35/44.47 | ('#form50' @ X2))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl110])). 345.35/44.47 thf(zip_derived_cl38, plain, (~ ('#form24')), 345.35/44.47 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 345.35/44.47 thf(zip_derived_cl165, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 ( ('#sk39' @ X2 @ '#sk30') | ('#form26') | ('#form50' @ X2))), 345.35/44.47 inference('demod', [status(thm)], [zip_derived_cl124, zip_derived_cl38])). 345.35/44.47 thf(zip_derived_cl160, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( ((('#sk4' @ ('#sk111' @ X2 @ X4)) = (X2))) 345.35/44.47 | ~ ('#form110' @ X2 @ X4))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl155])). 345.35/44.47 thf(zip_derived_cl162, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ((('#sk4' @ ('#sk111' @ X2 @ X4)) = (X2)) | ~ ('#form110' @ X2 @ X4))), 345.35/44.47 inference('simplify nested equalities', [status(thm)], 345.35/44.47 [zip_derived_cl160])). 345.35/44.47 thf(zip_derived_cl57, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ ('#form28' @ X2) 345.35/44.47 | (((!!) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((Y1 @ X2) & 345.35/44.47 (((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.35/44.47 ('#sk6' @ Y0)))))))), 345.35/44.47 define([status(thm)])). 345.35/44.47 thf(zip_derived_cl58, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 ( (((((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((Y0 @ X2) & 345.35/44.47 (((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X4))))))))))))) => 345.35/44.47 ('#sk6' @ X4))) 345.35/44.47 | ~ ('#form28' @ X2))), 345.35/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 345.35/44.47 thf(zip_derived_cl65, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 (~ (((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((Y0 @ X2) & 345.35/44.47 (((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X4))))))))))))) 345.35/44.47 | ('#sk6' @ X4) 345.35/44.47 | ~ ('#form28' @ X2))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 345.35/44.47 thf(zip_derived_cl71, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 (~ ((((('#sk31' @ X2 @ X4 @ X2) & 345.35/44.47 (((!!) @ (^[Y0 : a]: 345.35/44.47 ((('#sk31' @ X2 @ X4 @ Y0) => ('#sk31' @ X2 @ X4 @ 345.35/44.47 ('#sk3' @ Y0))))))))) => 345.35/44.47 (((??) @ (^[Y0 : a]: 345.35/44.47 ((('#sk31' @ X2 @ X4 @ Y0) & ((('#sk4' @ Y0) = (X4)))))))))) 345.35/44.47 | ~ ('#form28' @ X2) 345.35/44.47 | ('#sk6' @ X4))), 345.35/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl65])). 345.35/44.47 thf(zip_derived_cl76, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 ( ((('#sk31' @ X2 @ X4 @ X2) & 345.35/44.47 (((!!) @ (^[Y0 : a]: 345.35/44.47 ((('#sk31' @ X2 @ X4 @ Y0) => ('#sk31' @ X2 @ X4 @ 345.35/44.47 ('#sk3' @ Y0))))))))) 345.35/44.47 | ('#sk6' @ X4) 345.35/44.47 | ~ ('#form28' @ X2))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 345.35/44.47 thf(zip_derived_cl85, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 ( (((!!) @ (^[Y0 : a]: 345.35/44.47 ((('#sk31' @ X2 @ X4 @ Y0) => ('#sk31' @ X2 @ X4 @ 345.35/44.47 ('#sk3' @ Y0))))))) 345.35/44.47 | ~ ('#form28' @ X2) 345.35/44.47 | ('#sk6' @ X4))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl76])). 345.35/44.47 thf(zip_derived_cl94, plain, 345.35/44.47 (![X2 : a, X4 : a, X6 : a]: 345.35/44.47 ( ((('#sk31' @ X2 @ X4 @ X6) => ('#sk31' @ X2 @ X4 @ ('#sk3' @ X6)))) 345.35/44.47 | ('#sk6' @ X4) 345.35/44.47 | ~ ('#form28' @ X2))), 345.35/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 345.35/44.47 thf(zip_derived_cl105, plain, 345.35/44.47 (![X2 : a, X4 : a, X6 : a]: 345.35/44.47 (~ ('#sk31' @ X2 @ X4 @ X6) 345.35/44.47 | ('#sk31' @ X2 @ X4 @ ('#sk3' @ X6)) 345.35/44.47 | ~ ('#form28' @ X2) 345.35/44.47 | ('#sk6' @ X4))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl94])). 345.35/44.47 thf(zip_derived_cl84, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 ( ('#sk31' @ X2 @ X4 @ X2) | ~ ('#form28' @ X2) | ('#sk6' @ X4))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl76])). 345.35/44.47 thf(zip_derived_cl77, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 (~ (((??) @ (^[Y0 : a]: 345.35/44.47 ((('#sk31' @ X2 @ X4 @ Y0) & ((('#sk4' @ Y0) = (X4)))))))) 345.35/44.47 | ('#sk6' @ X4) 345.35/44.47 | ~ ('#form28' @ X2))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 345.35/44.47 thf(zip_derived_cl86, plain, 345.35/44.47 (![X2 : a, X4 : a, X6 : a]: 345.35/44.47 (~ ((('#sk31' @ X2 @ X4 @ X6) & ((('#sk4' @ X6) = (X4))))) 345.35/44.47 | ~ ('#form28' @ X2) 345.35/44.47 | ('#sk6' @ X4))), 345.35/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl77])). 345.35/44.47 thf(zip_derived_cl95, plain, 345.35/44.47 (![X2 : a, X4 : a, X6 : a]: 345.35/44.47 (~ ('#sk31' @ X2 @ X4 @ X6) 345.35/44.47 | ~ ((('#sk4' @ X6) = (X4))) 345.35/44.47 | ('#sk6' @ X4) 345.35/44.47 | ~ ('#form28' @ X2))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl86])). 345.35/44.47 thf(zip_derived_cl106, plain, 345.35/44.47 (![X2 : a, X4 : a, X6 : a]: 345.35/44.47 (~ ('#sk31' @ X2 @ X4 @ X6) 345.35/44.47 | (('#sk4' @ X6) != (X4)) 345.35/44.47 | ('#sk6' @ X4) 345.35/44.47 | ~ ('#form28' @ X2))), 345.35/44.47 inference('simplify nested equalities', [status(thm)], [zip_derived_cl95])). 345.35/44.47 thf(zip_derived_cl107, plain, 345.35/44.47 (![X2 : a, X6 : a]: 345.35/44.47 (~ ('#form28' @ X2) 345.35/44.47 | ('#sk6' @ ('#sk4' @ X6)) 345.35/44.47 | ~ ('#sk31' @ X2 @ ('#sk4' @ X6) @ X6))), 345.35/44.47 inference('simplify', [status(thm)], [zip_derived_cl106])). 345.35/44.47 thf(zip_derived_cl44, plain, 345.35/44.47 ((~ ('#form26') 345.35/44.47 | (((??) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a]: 345.35/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.35/44.47 (((((Y2 @ Y0) & 345.35/44.47 (((!!) @ (^[Y3 : a]: 345.35/44.47 (((Y2 @ 345.35/44.47 Y3) => 345.35/44.47 (Y2 @ 345.35/44.47 ('#sk3' @ 345.35/44.47 Y3))))))))) => 345.35/44.47 (((??) @ (^[Y3 : a]: 345.35/44.47 (((Y2 @ Y3) & 345.35/44.47 ((('#sk4' @ 345.35/44.47 Y3) = (Y1))))))))))))) => 345.35/44.47 ('#sk6' @ Y1)))))) & 345.35/44.47 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 345.35/44.47 define([status(thm)])). 345.35/44.47 thf(zip_derived_cl45, plain, 345.35/44.47 (( (((((!!) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((Y1 @ '#sk27') & 345.35/44.47 (((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.35/44.47 ('#sk6' @ Y0)))))) & 345.35/44.47 ('#sk5' @ ('#sk2' @ '#sk27' @ '#sk7')))) 345.35/44.47 | ~ ('#form26'))), 345.35/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl44])). 345.35/44.47 thf(zip_derived_cl52, plain, 345.35/44.47 (( ('#sk5' @ ('#sk2' @ '#sk27' @ '#sk7')) | ~ ('#form26'))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl45])). 345.35/44.47 thf(zip_derived_cl51, plain, 345.35/44.47 (( (((!!) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((Y1 @ '#sk27') & 345.35/44.47 (((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.35/44.47 ('#sk6' @ Y0)))))) 345.35/44.47 | ~ ('#form26'))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl45])). 345.35/44.47 thf(zip_derived_cl61, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 ( (((((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((Y0 @ '#sk27') & 345.35/44.47 (((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X2))))))))))))) => 345.35/44.47 ('#sk6' @ X2))) 345.35/44.47 | ~ ('#form26'))), 345.35/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl51])). 345.35/44.47 thf(zip_derived_cl68, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ (((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((Y0 @ '#sk27') & 345.35/44.47 (((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X2))))))))))))) 345.35/44.47 | ('#sk6' @ X2) 345.35/44.47 | ~ ('#form26'))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 345.35/44.47 thf(zip_derived_cl73, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ ((((('#sk31' @ '#sk27' @ X2 @ '#sk27') & 345.35/44.47 (((!!) @ (^[Y0 : a]: 345.35/44.47 ((('#sk31' @ '#sk27' @ X2 @ Y0) => ('#sk31' @ 345.35/44.47 '#sk27' @ X2 @ ('#sk3' @ Y0))))))))) => 345.35/44.47 (((??) @ (^[Y0 : a]: 345.35/44.47 ((('#sk31' @ '#sk27' @ X2 @ Y0) & 345.35/44.47 ((('#sk4' @ Y0) = (X2)))))))))) 345.35/44.47 | ~ ('#form26') 345.35/44.47 | ('#sk6' @ X2))), 345.35/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl68])). 345.35/44.47 thf(zip_derived_cl79, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 ( ((('#sk31' @ '#sk27' @ X2 @ '#sk27') & 345.35/44.47 (((!!) @ (^[Y0 : a]: 345.35/44.47 ((('#sk31' @ '#sk27' @ X2 @ Y0) => ('#sk31' @ 345.35/44.47 '#sk27' @ X2 @ ('#sk3' @ Y0))))))))) 345.35/44.47 | ('#sk6' @ X2) 345.35/44.47 | ~ ('#form26'))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 345.35/44.47 thf(zip_derived_cl88, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 ( ('#sk31' @ '#sk27' @ X2 @ '#sk27') | ~ ('#form26') | ('#sk6' @ X2))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl79])). 345.35/44.47 thf(zip_derived_cl53, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 ( ('#form28' @ X2) 345.35/44.47 | ~ (((!!) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((Y1 @ X2) & 345.35/44.47 (((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.35/44.47 ('#sk6' @ Y0)))))))), 345.35/44.47 define([status(thm)])). 345.35/44.47 thf(zip_derived_cl54, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ (((((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((Y0 @ X2) & 345.35/44.47 (((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & 345.35/44.47 ((('#sk4' @ Y1) = ('#sk29' @ X2))))))))))))) => 345.35/44.47 ('#sk6' @ ('#sk29' @ X2)))) 345.35/44.47 | ('#form28' @ X2))), 345.35/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl53])). 345.35/44.47 thf(zip_derived_cl64, plain, 345.35/44.47 (![X2 : a]: (~ ('#sk6' @ ('#sk29' @ X2)) | ('#form28' @ X2))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl54])). 345.35/44.47 thf(zip_derived_cl123, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 ( (((!!) @ (^[Y0 : a]: 345.35/44.47 ((('#sk39' @ X2 @ Y0) => ('#sk39' @ X2 @ ('#sk3' @ Y0))))))) 345.35/44.47 | ('#form24') 345.35/44.47 | ('#form26') 345.35/44.47 | ('#form50' @ X2))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl110])). 345.35/44.47 thf(zip_derived_cl133, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 ( ((('#sk39' @ X2 @ X4) => ('#sk39' @ X2 @ ('#sk3' @ X4)))) 345.35/44.47 | ('#form50' @ X2) 345.35/44.47 | ('#form26') 345.35/44.47 | ('#form24'))), 345.35/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl123])). 345.35/44.47 thf(zip_derived_cl141, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 (~ ('#sk39' @ X2 @ X4) 345.35/44.47 | ('#sk39' @ X2 @ ('#sk3' @ X4)) 345.35/44.47 | ('#form24') 345.35/44.47 | ('#form26') 345.35/44.47 | ('#form50' @ X2))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl133])). 345.35/44.47 thf(zip_derived_cl38, plain, (~ ('#form24')), 345.35/44.47 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 345.35/44.47 thf(zip_derived_cl169, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 (~ ('#sk39' @ X2 @ X4) 345.35/44.47 | ('#sk39' @ X2 @ ('#sk3' @ X4)) 345.35/44.47 | ('#form26') 345.35/44.47 | ('#form50' @ X2))), 345.35/44.47 inference('demod', [status(thm)], [zip_derived_cl141, zip_derived_cl38])). 345.35/44.47 thf(zip_derived_cl63, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 ( (((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((Y0 @ X2) & 345.35/44.47 (((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & 345.35/44.47 ((('#sk4' @ Y1) = ('#sk29' @ X2))))))))))))) 345.35/44.47 | ('#form28' @ X2))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl54])). 345.35/44.47 thf(zip_derived_cl70, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( (((((X4 @ X2) & 345.35/44.47 (((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))))) => 345.35/44.47 (((??) @ (^[Y0 : a]: 345.35/44.47 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk29' @ X2)))))))))) 345.35/44.47 | ('#form28' @ X2))), 345.35/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 345.35/44.47 thf(zip_derived_cl75, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 (~ (((X4 @ X2) & 345.35/44.47 (((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))))) 345.35/44.47 | (((??) @ (^[Y0 : a]: 345.35/44.47 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk29' @ X2)))))))) 345.35/44.47 | ('#form28' @ X2))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl70])). 345.35/44.47 thf(zip_derived_cl83, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 (~ (X4 @ X2) 345.35/44.47 | ~ (((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) 345.35/44.47 | ('#form28' @ X2) 345.35/44.47 | (((??) @ (^[Y0 : a]: 345.35/44.47 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk29' @ X2)))))))))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl75])). 345.35/44.47 thf(zip_derived_cl93, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 (~ (((X4 @ ('#sk18' @ X4)) => (X4 @ ('#sk3' @ ('#sk18' @ X4))))) 345.35/44.47 | (((??) @ (^[Y0 : a]: 345.35/44.47 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk29' @ X2)))))))) 345.35/44.47 | ('#form28' @ X2) 345.35/44.47 | ~ (X4 @ X2))), 345.35/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl83])). 345.35/44.47 thf(zip_derived_cl103, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( (X4 @ ('#sk18' @ X4)) 345.35/44.47 | ~ (X4 @ X2) 345.35/44.47 | ('#form28' @ X2) 345.35/44.47 | (((??) @ (^[Y0 : a]: 345.35/44.47 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk29' @ X2)))))))))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl93])). 345.35/44.47 thf(zip_derived_cl103, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( (X4 @ ('#sk18' @ X4)) 345.35/44.47 | ~ (X4 @ X2) 345.35/44.47 | ('#form28' @ X2) 345.35/44.47 | (((??) @ (^[Y0 : a]: 345.35/44.47 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk29' @ X2)))))))))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl93])). 345.35/44.47 thf(zip_derived_cl119, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 (~ ('#form56' @ X2 @ X4) 345.35/44.47 | (((??) @ (^[Y0 : a]: 345.35/44.47 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk29' @ X2)))))))))), 345.35/44.47 define([status(thm)])). 345.35/44.47 thf(zip_derived_cl121, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( ('#form56' @ X2 @ X4) 345.35/44.47 | ('#form28' @ X2) 345.35/44.47 | ~ (X4 @ X2) 345.35/44.47 | (X4 @ ('#sk18' @ X4)))), 345.35/44.47 inference('renaming', [status(thm)], 345.35/44.47 [zip_derived_cl103, zip_derived_cl119])). 345.35/44.47 thf(zip_derived_cl89, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 ( (((!!) @ (^[Y0 : a]: 345.35/44.47 ((('#sk31' @ '#sk27' @ X2 @ Y0) => ('#sk31' @ '#sk27' @ 345.35/44.47 X2 @ ('#sk3' @ Y0))))))) 345.35/44.47 | ~ ('#form26') 345.35/44.47 | ('#sk6' @ X2))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl79])). 345.35/44.47 thf(zip_derived_cl98, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 ( ((('#sk31' @ '#sk27' @ X2 @ X4) => ('#sk31' @ '#sk27' @ X2 @ 345.35/44.47 ('#sk3' @ X4)))) 345.35/44.47 | ('#sk6' @ X2) 345.35/44.47 | ~ ('#form26'))), 345.35/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl89])). 345.35/44.47 thf(zip_derived_cl112, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 (~ ('#sk31' @ '#sk27' @ X2 @ X4) 345.35/44.47 | ('#sk31' @ '#sk27' @ X2 @ ('#sk3' @ X4)) 345.35/44.47 | ~ ('#form26') 345.35/44.47 | ('#sk6' @ X2))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl98])). 345.35/44.47 thf(zip_derived_cl104, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 (~ (X4 @ ('#sk3' @ ('#sk18' @ X4))) 345.35/44.47 | ~ (X4 @ X2) 345.35/44.47 | ('#form28' @ X2) 345.35/44.47 | (((??) @ (^[Y0 : a]: 345.35/44.47 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk29' @ X2)))))))))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl93])). 345.35/44.47 thf(zip_derived_cl119, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 (~ ('#form56' @ X2 @ X4) 345.35/44.47 | (((??) @ (^[Y0 : a]: 345.35/44.47 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk29' @ X2)))))))))), 345.35/44.47 define([status(thm)])). 345.35/44.47 thf(zip_derived_cl122, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( ('#form56' @ X2 @ (^[Y0 : a]: (X4 @ Y0))) 345.35/44.47 | ('#form28' @ X2) 345.35/44.47 | ~ (X4 @ X2) 345.35/44.47 | ~ (X4 @ ('#sk3' @ ('#sk18' @ X4))))), 345.35/44.47 inference('renaming', [status(thm)], 345.35/44.47 [zip_derived_cl104, zip_derived_cl119])). 345.35/44.47 thf(zip_derived_cl132, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( ('#form56' @ X2 @ X4) 345.35/44.47 | ('#form28' @ X2) 345.35/44.47 | ~ (X4 @ X2) 345.35/44.47 | ~ (X4 @ ('#sk3' @ ('#sk18' @ X4))))), 345.35/44.47 inference('ho_norm', [status(thm)], [zip_derived_cl122])). 345.35/44.47 thf(zip_derived_cl119, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 (~ ('#form56' @ X2 @ X4) 345.35/44.47 | (((??) @ (^[Y0 : a]: 345.35/44.47 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk29' @ X2)))))))))), 345.35/44.47 define([status(thm)])). 345.35/44.47 thf(zip_derived_cl120, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( (((X4 @ ('#sk57' @ X2 @ X4)) & 345.35/44.47 ((('#sk4' @ ('#sk57' @ X2 @ X4)) = ('#sk29' @ X2))))) 345.35/44.47 | ~ ('#form56' @ X2 @ X4))), 345.35/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl119])). 345.35/44.47 thf(zip_derived_cl130, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( (X4 @ ('#sk57' @ X2 @ X4)) | ~ ('#form56' @ X2 @ X4))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl120])). 345.35/44.47 thf(zip_derived_cl97, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ (((??) @ (^[Y0 : a]: 345.35/44.47 ((('#sk39' @ X2 @ Y0) & ((('#sk4' @ Y0) = (X2)))))))) 345.35/44.47 | (((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 345.35/44.47 (Y0 @ '#sk25'))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X2))))))))))))) 345.35/44.47 | ('#form24') 345.35/44.47 | ('#form26'))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl87])). 345.35/44.47 thf(zip_derived_cl108, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ ('#form50' @ X2) 345.35/44.47 | (((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 345.35/44.47 (Y0 @ '#sk25'))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X2))))))))))))))), 345.35/44.47 define([status(thm)])). 345.35/44.47 thf(zip_derived_cl111, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 ( ('#form50' @ X2) 345.35/44.47 | ('#form26') 345.35/44.47 | ('#form24') 345.35/44.47 | ~ (((??) @ (^[Y0 : a]: 345.35/44.47 ((('#sk39' @ X2 @ Y0) & ((('#sk4' @ Y0) = (X2)))))))))), 345.35/44.47 inference('renaming', [status(thm)], 345.35/44.47 [zip_derived_cl97, zip_derived_cl108])). 345.35/44.47 thf(zip_derived_cl126, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 (~ ((('#sk39' @ X2 @ X4) & ((('#sk4' @ X4) = (X2))))) 345.35/44.47 | ('#form24') 345.35/44.47 | ('#form26') 345.35/44.47 | ('#form50' @ X2))), 345.35/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl111])). 345.35/44.47 thf(zip_derived_cl135, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 (~ ('#sk39' @ X2 @ X4) 345.35/44.47 | ~ ((('#sk4' @ X4) = (X2))) 345.35/44.47 | ('#form50' @ X2) 345.35/44.47 | ('#form26') 345.35/44.47 | ('#form24'))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl126])). 345.35/44.47 thf(zip_derived_cl143, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 (~ ('#sk39' @ X2 @ X4) 345.35/44.47 | (('#sk4' @ X4) != (X2)) 345.35/44.47 | ('#form50' @ X2) 345.35/44.47 | ('#form26') 345.35/44.47 | ('#form24'))), 345.35/44.47 inference('simplify nested equalities', [status(thm)], 345.35/44.47 [zip_derived_cl135])). 345.35/44.47 thf(zip_derived_cl144, plain, 345.35/44.47 (![X4 : a]: 345.35/44.47 ( ('#form24') 345.35/44.47 | ('#form26') 345.35/44.47 | ('#form50' @ ('#sk4' @ X4)) 345.35/44.47 | ~ ('#sk39' @ ('#sk4' @ X4) @ X4))), 345.35/44.47 inference('simplify', [status(thm)], [zip_derived_cl143])). 345.35/44.47 thf(zip_derived_cl38, plain, (~ ('#form24')), 345.35/44.47 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 345.35/44.47 thf(zip_derived_cl166, plain, 345.35/44.47 (![X4 : a]: 345.35/44.47 ( ('#form26') 345.35/44.47 | ('#form50' @ ('#sk4' @ X4)) 345.35/44.47 | ~ ('#sk39' @ ('#sk4' @ X4) @ X4))), 345.35/44.47 inference('demod', [status(thm)], [zip_derived_cl144, zip_derived_cl38])). 345.35/44.47 thf(zip_derived_cl56, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ ('#form28' @ X2) 345.35/44.47 | ('#form26') 345.35/44.47 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')))), 345.35/44.47 inference('renaming', [status(thm)], [zip_derived_cl48, zip_derived_cl53])). 345.35/44.47 thf(zip_derived_cl47, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ (((!!) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((Y1 @ X2) & 345.35/44.47 (((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.35/44.47 ('#sk6' @ Y0)))))) 345.35/44.47 | ~ (((??) @ (^[Y0 : a]: 345.35/44.47 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 345.35/44.47 (((!!) @ (^[Y1 : a]: 345.35/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y3 : a]: 345.35/44.47 ( 345.35/44.47 ( 345.35/44.47 (Y2 @ 345.35/44.47 Y3) => 345.35/44.47 (Y2 @ 345.35/44.47 ( 345.35/44.47 '#sk3' @ 345.35/44.47 Y3))))))) & 345.35/44.47 (Y2 @ Y0))) => 345.35/44.47 (((??) @ (^[Y3 : a]: 345.35/44.47 (((Y2 @ 345.35/44.47 Y3) & 345.35/44.47 (( 345.35/44.47 ('#sk4' @ 345.35/44.47 Y3) = 345.35/44.47 (Y1))))))))))))) => 345.35/44.47 (((!!) @ (^[Y2 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y3 : a]: 345.35/44.47 ( 345.35/44.47 ( 345.35/44.47 (Y2 @ 345.35/44.47 Y3) => 345.35/44.47 (Y2 @ 345.35/44.47 ( 345.35/44.47 '#sk3' @ 345.35/44.47 Y3))))))) & 345.35/44.47 (Y2 @ X2))) => 345.35/44.47 (((??) @ (^[Y3 : a]: 345.35/44.47 (((Y2 @ 345.35/44.47 Y3) & 345.35/44.47 (( 345.35/44.47 ('#sk4' @ 345.35/44.47 Y3) = 345.35/44.47 (Y1))))))))))))))))))))))) 345.35/44.47 | ('#form24') 345.35/44.47 | ~ ('#form26'))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl43])). 345.35/44.47 thf(zip_derived_cl53, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 ( ('#form28' @ X2) 345.35/44.47 | ~ (((!!) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((Y1 @ X2) & 345.35/44.47 (((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.35/44.47 ('#sk6' @ Y0)))))))), 345.35/44.47 define([status(thm)])). 345.35/44.47 thf(zip_derived_cl55, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ ('#form28' @ X2) 345.35/44.47 | ~ ('#form26') 345.35/44.47 | ('#form24') 345.35/44.47 | ~ (((??) @ (^[Y0 : a]: 345.35/44.47 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 345.35/44.47 (((!!) @ (^[Y1 : a]: 345.35/44.47 (((((!!) @ (^[Y2 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y3 : a]: 345.35/44.47 ( 345.35/44.47 ( 345.35/44.47 (Y2 @ 345.35/44.47 Y3) => 345.35/44.47 (Y2 @ 345.35/44.47 ( 345.35/44.47 '#sk3' @ 345.35/44.47 Y3))))))) & 345.35/44.47 (Y2 @ Y0))) => 345.35/44.47 (((??) @ (^[Y3 : a]: 345.35/44.47 (((Y2 @ 345.35/44.47 Y3) & 345.35/44.47 (( 345.35/44.47 ('#sk4' @ 345.35/44.47 Y3) = 345.35/44.47 (Y1))))))))))))) => 345.35/44.47 (((!!) @ (^[Y2 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y3 : a]: 345.35/44.47 ( 345.35/44.47 ( 345.35/44.47 (Y2 @ 345.35/44.47 Y3) => 345.35/44.47 (Y2 @ 345.35/44.47 ( 345.35/44.47 '#sk3' @ 345.35/44.47 Y3))))))) & 345.35/44.47 (Y2 @ X2))) => 345.35/44.47 (((??) @ (^[Y3 : a]: 345.35/44.47 (((Y2 @ 345.35/44.47 Y3) & 345.35/44.47 (( 345.35/44.47 ('#sk4' @ 345.35/44.47 Y3) = 345.35/44.47 (Y1))))))))))))))))))))))))), 345.35/44.47 inference('renaming', [status(thm)], [zip_derived_cl47, zip_derived_cl53])). 345.35/44.47 thf(zip_derived_cl62, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 (~ ((('#sk5' @ ('#sk2' @ X4 @ '#sk7')) & 345.35/44.47 (((!!) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))) & 345.35/44.47 (Y1 @ X4))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.35/44.47 (((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))) & 345.35/44.47 (Y1 @ X2))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = (Y0)))))))))))))))))))) 345.35/44.47 | ('#form24') 345.35/44.47 | ~ ('#form26') 345.35/44.47 | ~ ('#form28' @ X2))), 345.35/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl55])). 345.35/44.47 thf(zip_derived_cl69, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 (~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.47 | ~ (((!!) @ (^[Y0 : a]: 345.35/44.47 (((((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))) & 345.35/44.47 (Y1 @ X4))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = (Y0))))))))))))) => 345.35/44.47 (((!!) @ (^[Y1 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) => (Y1 @ 345.35/44.47 ('#sk3' @ Y2))))))) & 345.35/44.47 (Y1 @ X2))) => 345.35/44.47 (((??) @ (^[Y2 : a]: 345.35/44.47 (((Y1 @ Y2) & 345.35/44.47 ((('#sk4' @ Y2) = (Y0)))))))))))))))))) 345.35/44.47 | ~ ('#form28' @ X2) 345.35/44.47 | ~ ('#form26') 345.35/44.47 | ('#form24'))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl62])). 345.35/44.47 thf(zip_derived_cl74, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 (~ (((((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 345.35/44.47 (Y0 @ X4))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & 345.35/44.47 ((('#sk4' @ Y1) = ('#sk32' @ X2 @ X4))))))))))))) => 345.35/44.47 (((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 345.35/44.47 (Y0 @ X2))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & 345.35/44.47 ((('#sk4' @ Y1) = ('#sk32' @ X2 @ X4))))))))))))))) 345.35/44.47 | ('#form24') 345.35/44.47 | ~ ('#form26') 345.35/44.47 | ~ ('#form28' @ X2) 345.35/44.47 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 345.35/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl69])). 345.35/44.47 thf(zip_derived_cl82, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 (~ (((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 345.35/44.47 (Y0 @ X2))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & 345.35/44.47 ((('#sk4' @ Y1) = ('#sk32' @ X2 @ X4))))))))))))) 345.35/44.47 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.47 | ~ ('#form28' @ X2) 345.35/44.47 | ~ ('#form26') 345.35/44.47 | ('#form24'))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])). 345.35/44.47 thf(zip_derived_cl92, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 (~ (((((((!!) @ (^[Y0 : a]: 345.35/44.47 ((('#sk40' @ X2 @ X4 @ Y0) => ('#sk40' @ X2 @ X4 @ 345.35/44.47 ('#sk3' @ Y0))))))) & 345.35/44.47 ('#sk40' @ X2 @ X4 @ X2))) => 345.35/44.47 (((??) @ (^[Y0 : a]: 345.35/44.47 ((('#sk40' @ X2 @ X4 @ Y0) & 345.35/44.47 ((('#sk4' @ Y0) = ('#sk32' @ X2 @ X4)))))))))) 345.35/44.47 | ('#form24') 345.35/44.47 | ~ ('#form26') 345.35/44.47 | ~ ('#form28' @ X2) 345.35/44.47 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 345.35/44.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl82])). 345.35/44.47 thf(zip_derived_cl101, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 ( (((((!!) @ (^[Y0 : a]: 345.35/44.47 ((('#sk40' @ X2 @ X4 @ Y0) => ('#sk40' @ X2 @ X4 @ 345.35/44.47 ('#sk3' @ Y0))))))) & 345.35/44.47 ('#sk40' @ X2 @ X4 @ X2))) 345.35/44.47 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.47 | ~ ('#form28' @ X2) 345.35/44.47 | ~ ('#form26') 345.35/44.47 | ('#form24'))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])). 345.35/44.47 thf(zip_derived_cl117, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 ( ('#sk40' @ X2 @ X4 @ X2) 345.35/44.47 | ('#form24') 345.35/44.47 | ~ ('#form26') 345.35/44.47 | ~ ('#form28' @ X2) 345.35/44.47 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl101])). 345.35/44.47 thf(zip_derived_cl38, plain, (~ ('#form24')), 345.35/44.47 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 345.35/44.47 thf(zip_derived_cl168, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 ( ('#sk40' @ X2 @ X4 @ X2) 345.35/44.47 | ~ ('#form26') 345.35/44.47 | ~ ('#form28' @ X2) 345.35/44.47 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 345.35/44.47 inference('demod', [status(thm)], [zip_derived_cl117, zip_derived_cl38])). 345.35/44.47 thf(zip_derived_cl131, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ( ((('#sk4' @ ('#sk57' @ X2 @ X4)) = ('#sk29' @ X2))) 345.35/44.47 | ~ ('#form56' @ X2 @ X4))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl120])). 345.35/44.47 thf(zip_derived_cl140, plain, 345.35/44.47 (![X2 : a, X4 : a > $o]: 345.35/44.47 ((('#sk4' @ ('#sk57' @ X2 @ X4)) = ('#sk29' @ X2)) 345.35/44.47 | ~ ('#form56' @ X2 @ X4))), 345.35/44.47 inference('simplify nested equalities', [status(thm)], 345.35/44.47 [zip_derived_cl131])). 345.35/44.47 thf(zip_derived_cl80, plain, 345.35/44.47 (![X2 : a]: 345.35/44.47 (~ (((??) @ (^[Y0 : a]: 345.35/44.47 ((('#sk31' @ '#sk27' @ X2 @ Y0) & 345.35/44.47 ((('#sk4' @ Y0) = (X2)))))))) 345.35/44.47 | ('#sk6' @ X2) 345.35/44.47 | ~ ('#form26'))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 345.35/44.47 thf(zip_derived_cl90, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 (~ ((('#sk31' @ '#sk27' @ X2 @ X4) & ((('#sk4' @ X4) = (X2))))) 345.35/44.47 | ~ ('#form26') 345.35/44.47 | ('#sk6' @ X2))), 345.35/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl80])). 345.35/44.47 thf(zip_derived_cl99, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 (~ ('#sk31' @ '#sk27' @ X2 @ X4) 345.35/44.47 | ~ ((('#sk4' @ X4) = (X2))) 345.35/44.47 | ('#sk6' @ X2) 345.35/44.47 | ~ ('#form26'))), 345.35/44.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl90])). 345.35/44.47 thf(zip_derived_cl113, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 (~ ('#sk31' @ '#sk27' @ X2 @ X4) 345.35/44.47 | (('#sk4' @ X4) != (X2)) 345.35/44.47 | ('#sk6' @ X2) 345.35/44.47 | ~ ('#form26'))), 345.35/44.47 inference('simplify nested equalities', [status(thm)], [zip_derived_cl99])). 345.35/44.47 thf(zip_derived_cl114, plain, 345.35/44.47 (![X4 : a]: 345.35/44.47 (~ ('#form26') 345.35/44.47 | ('#sk6' @ ('#sk4' @ X4)) 345.35/44.47 | ~ ('#sk31' @ '#sk27' @ ('#sk4' @ X4) @ X4))), 345.35/44.47 inference('simplify', [status(thm)], [zip_derived_cl113])). 345.35/44.47 thf(zip_derived_cl81, plain, 345.35/44.47 (![X2 : a, X4 : a]: 345.35/44.47 ( (((!!) @ (^[Y0 : a > $o]: 345.35/44.47 (((((((!!) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 345.35/44.47 (Y0 @ X4))) => 345.35/44.47 (((??) @ (^[Y1 : a]: 345.35/44.47 (((Y0 @ Y1) & 345.35/44.47 ((('#sk4' @ Y1) = ('#sk32' @ X2 @ X4))))))))))))) 345.35/44.47 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.47 | ~ ('#form28' @ X2) 345.35/44.47 | ~ ('#form26') 345.35/44.47 | ('#form24'))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])). 345.35/44.47 thf(zip_derived_cl91, plain, 345.35/44.47 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.47 ( (((((((!!) @ (^[Y0 : a]: (((X6 @ Y0) => (X6 @ ('#sk3' @ Y0))))))) & 345.35/44.47 (X6 @ X4))) => 345.35/44.47 (((??) @ (^[Y0 : a]: 345.35/44.47 (((X6 @ Y0) & ((('#sk4' @ Y0) = ('#sk32' @ X2 @ X4)))))))))) 345.35/44.47 | ('#form24') 345.35/44.47 | ~ ('#form26') 345.35/44.47 | ~ ('#form28' @ X2) 345.35/44.47 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 345.35/44.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl81])). 345.35/44.47 thf(zip_derived_cl100, plain, 345.35/44.47 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.47 (~ (((((!!) @ (^[Y0 : a]: (((X6 @ Y0) => (X6 @ ('#sk3' @ Y0))))))) & 345.35/44.47 (X6 @ X4))) 345.35/44.47 | (((??) @ (^[Y0 : a]: 345.35/44.47 (((X6 @ Y0) & ((('#sk4' @ Y0) = ('#sk32' @ X2 @ X4)))))))) 345.35/44.47 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.47 | ~ ('#form28' @ X2) 345.35/44.47 | ~ ('#form26') 345.35/44.47 | ('#form24'))), 345.35/44.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl91])). 345.35/44.48 thf(zip_derived_cl115, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.48 (~ (((!!) @ (^[Y0 : a]: (((X6 @ Y0) => (X6 @ ('#sk3' @ Y0))))))) 345.35/44.48 | ~ (X6 @ X4) 345.35/44.48 | ('#form24') 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.48 | (((??) @ (^[Y0 : a]: 345.35/44.48 (((X6 @ Y0) & ((('#sk4' @ Y0) = ('#sk32' @ X2 @ X4)))))))))), 345.35/44.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl100])). 345.35/44.48 thf(zip_derived_cl127, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.48 (~ (((X6 @ ('#sk18' @ X6)) => (X6 @ ('#sk3' @ ('#sk18' @ X6))))) 345.35/44.48 | (((??) @ (^[Y0 : a]: 345.35/44.48 (((X6 @ Y0) & ((('#sk4' @ Y0) = ('#sk32' @ X2 @ X4)))))))) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ('#form24') 345.35/44.48 | ~ (X6 @ X4))), 345.35/44.48 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl115])). 345.35/44.48 thf(zip_derived_cl136, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.48 ( (X6 @ ('#sk18' @ X6)) 345.35/44.48 | ~ (X6 @ X4) 345.35/44.48 | ('#form24') 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.48 | (((??) @ (^[Y0 : a]: 345.35/44.48 (((X6 @ Y0) & ((('#sk4' @ Y0) = ('#sk32' @ X2 @ X4)))))))))), 345.35/44.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 345.35/44.48 thf(zip_derived_cl136, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.48 ( (X6 @ ('#sk18' @ X6)) 345.35/44.48 | ~ (X6 @ X4) 345.35/44.48 | ('#form24') 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.48 | (((??) @ (^[Y0 : a]: 345.35/44.48 (((X6 @ Y0) & ((('#sk4' @ Y0) = ('#sk32' @ X2 @ X4)))))))))), 345.35/44.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 345.35/44.48 thf(zip_derived_cl145, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.48 (~ ('#form92' @ X2 @ X4 @ X6) 345.35/44.48 | (((??) @ (^[Y0 : a]: 345.35/44.48 (((X6 @ Y0) & ((('#sk4' @ Y0) = ('#sk32' @ X2 @ X4)))))))))), 345.35/44.48 define([status(thm)])). 345.35/44.48 thf(zip_derived_cl147, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.48 ( ('#form92' @ X2 @ X4 @ X6) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ('#form24') 345.35/44.48 | ~ (X6 @ X4) 345.35/44.48 | (X6 @ ('#sk18' @ X6)))), 345.35/44.48 inference('renaming', [status(thm)], 345.35/44.48 [zip_derived_cl136, zip_derived_cl145])). 345.35/44.48 thf(zip_derived_cl38, plain, (~ ('#form24')), 345.35/44.48 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 345.35/44.48 thf(zip_derived_cl171, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.48 ( ('#form92' @ X2 @ X4 @ X6) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ~ (X6 @ X4) 345.35/44.48 | (X6 @ ('#sk18' @ X6)))), 345.35/44.48 inference('demod', [status(thm)], [zip_derived_cl147, zip_derived_cl38])). 345.35/44.48 thf(zip_derived_cl116, plain, 345.35/44.48 (![X2 : a, X4 : a]: 345.35/44.48 ( (((!!) @ (^[Y0 : a]: 345.35/44.48 ((('#sk40' @ X2 @ X4 @ Y0) => ('#sk40' @ X2 @ X4 @ 345.35/44.48 ('#sk3' @ Y0))))))) 345.35/44.48 | ('#form24') 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 345.35/44.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl101])). 345.35/44.48 thf(zip_derived_cl128, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a]: 345.35/44.48 ( ((('#sk40' @ X2 @ X4 @ X6) => ('#sk40' @ X2 @ X4 @ ('#sk3' @ X6)))) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ('#form24'))), 345.35/44.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl116])). 345.35/44.48 thf(zip_derived_cl138, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a]: 345.35/44.48 (~ ('#sk40' @ X2 @ X4 @ X6) 345.35/44.48 | ('#sk40' @ X2 @ X4 @ ('#sk3' @ X6)) 345.35/44.48 | ('#form24') 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 345.35/44.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl128])). 345.35/44.48 thf(zip_derived_cl38, plain, (~ ('#form24')), 345.35/44.48 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 345.35/44.48 thf(zip_derived_cl170, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a]: 345.35/44.48 (~ ('#sk40' @ X2 @ X4 @ X6) 345.35/44.48 | ('#sk40' @ X2 @ X4 @ ('#sk3' @ X6)) 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 345.35/44.48 inference('demod', [status(thm)], [zip_derived_cl138, zip_derived_cl38])). 345.35/44.48 thf(zip_derived_cl137, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.48 (~ (X6 @ ('#sk3' @ ('#sk18' @ X6))) 345.35/44.48 | ~ (X6 @ X4) 345.35/44.48 | ('#form24') 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.48 | (((??) @ (^[Y0 : a]: 345.35/44.48 (((X6 @ Y0) & ((('#sk4' @ Y0) = ('#sk32' @ X2 @ X4)))))))))), 345.35/44.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 345.35/44.48 thf(zip_derived_cl145, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.48 (~ ('#form92' @ X2 @ X4 @ X6) 345.35/44.48 | (((??) @ (^[Y0 : a]: 345.35/44.48 (((X6 @ Y0) & ((('#sk4' @ Y0) = ('#sk32' @ X2 @ X4)))))))))), 345.35/44.48 define([status(thm)])). 345.35/44.48 thf(zip_derived_cl148, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.48 ( ('#form92' @ X2 @ X4 @ (^[Y0 : a]: (X6 @ Y0))) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ('#form24') 345.35/44.48 | ~ (X6 @ X4) 345.35/44.48 | ~ (X6 @ ('#sk3' @ ('#sk18' @ X6))))), 345.35/44.48 inference('renaming', [status(thm)], 345.35/44.48 [zip_derived_cl137, zip_derived_cl145])). 345.35/44.48 thf(zip_derived_cl153, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.48 ( ('#form92' @ X2 @ X4 @ X6) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ('#form24') 345.35/44.48 | ~ (X6 @ X4) 345.35/44.48 | ~ (X6 @ ('#sk3' @ ('#sk18' @ X6))))), 345.35/44.48 inference('ho_norm', [status(thm)], [zip_derived_cl148])). 345.35/44.48 thf(zip_derived_cl38, plain, (~ ('#form24')), 345.35/44.48 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 345.35/44.48 thf(zip_derived_cl172, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.48 ( ('#form92' @ X2 @ X4 @ X6) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ~ (X6 @ X4) 345.35/44.48 | ~ (X6 @ ('#sk3' @ ('#sk18' @ X6))))), 345.35/44.48 inference('demod', [status(thm)], [zip_derived_cl153, zip_derived_cl38])). 345.35/44.48 thf(zip_derived_cl145, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.48 (~ ('#form92' @ X2 @ X4 @ X6) 345.35/44.48 | (((??) @ (^[Y0 : a]: 345.35/44.48 (((X6 @ Y0) & ((('#sk4' @ Y0) = ('#sk32' @ X2 @ X4)))))))))), 345.35/44.48 define([status(thm)])). 345.35/44.48 thf(zip_derived_cl146, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.48 ( (((X6 @ ('#sk93' @ X2 @ X4 @ X6)) & 345.35/44.48 ((('#sk4' @ ('#sk93' @ X2 @ X4 @ X6)) = ('#sk32' @ X2 @ X4))))) 345.35/44.48 | ~ ('#form92' @ X2 @ X4 @ X6))), 345.35/44.48 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl145])). 345.35/44.48 thf(zip_derived_cl152, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.48 ( ((('#sk4' @ ('#sk93' @ X2 @ X4 @ X6)) = ('#sk32' @ X2 @ X4))) 345.35/44.48 | ~ ('#form92' @ X2 @ X4 @ X6))), 345.35/44.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl146])). 345.35/44.48 thf(zip_derived_cl158, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.48 ((('#sk4' @ ('#sk93' @ X2 @ X4 @ X6)) = ('#sk32' @ X2 @ X4)) 345.35/44.48 | ~ ('#form92' @ X2 @ X4 @ X6))), 345.35/44.48 inference('simplify nested equalities', [status(thm)], 345.35/44.48 [zip_derived_cl152])). 345.35/44.48 thf(zip_derived_cl151, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a > $o]: 345.35/44.48 ( (X6 @ ('#sk93' @ X2 @ X4 @ X6)) | ~ ('#form92' @ X2 @ X4 @ X6))), 345.35/44.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl146])). 345.35/44.48 thf(zip_derived_cl102, plain, 345.35/44.48 (![X2 : a, X4 : a]: 345.35/44.48 (~ (((??) @ (^[Y0 : a]: 345.35/44.48 ((('#sk40' @ X2 @ X4 @ Y0) & 345.35/44.48 ((('#sk4' @ Y0) = ('#sk32' @ X2 @ X4)))))))) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ('#form24'))), 345.35/44.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])). 345.35/44.48 thf(zip_derived_cl118, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a]: 345.35/44.48 (~ ((('#sk40' @ X2 @ X4 @ X6) & 345.35/44.48 ((('#sk4' @ X6) = ('#sk32' @ X2 @ X4))))) 345.35/44.48 | ('#form24') 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 345.35/44.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl102])). 345.35/44.48 thf(zip_derived_cl129, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a]: 345.35/44.48 (~ ('#sk40' @ X2 @ X4 @ X6) 345.35/44.48 | ~ ((('#sk4' @ X6) = ('#sk32' @ X2 @ X4))) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ('#form24'))), 345.35/44.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl118])). 345.35/44.48 thf(zip_derived_cl139, plain, 345.35/44.48 (![X2 : a, X4 : a, X6 : a]: 345.35/44.48 (~ ('#sk40' @ X2 @ X4 @ X6) 345.35/44.48 | (('#sk4' @ X6) != ('#sk32' @ X2 @ X4)) 345.35/44.48 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.48 | ~ ('#form28' @ X2) 345.35/44.48 | ~ ('#form26') 345.35/44.48 | ('#form24'))), 345.35/44.48 inference('simplify nested equalities', [status(thm)], 345.35/44.48 [zip_derived_cl129])). 345.35/44.48 thf(zip_derived_cl38, plain, (~ ('#form24')), 345.35/44.48 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 345.35/44.49 thf(zip_derived_cl167, plain, 345.35/44.49 (![X2 : a, X4 : a, X6 : a]: 345.35/44.49 (~ ('#sk40' @ X2 @ X4 @ X6) 345.35/44.49 | (('#sk4' @ X6) != ('#sk32' @ X2 @ X4)) 345.35/44.49 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 345.35/44.49 | ~ ('#form28' @ X2) 345.35/44.49 | ~ ('#form26'))), 345.35/44.49 inference('demod', [status(thm)], [zip_derived_cl139, zip_derived_cl38])). 345.35/44.49 thf(zip_derived_cl13240, plain, ($false), 345.35/44.49 inference('eprover', [status(thm)], 345.35/44.49 [zip_derived_cl15, zip_derived_cl23, zip_derived_cl32, 345.35/44.49 zip_derived_cl164, zip_derived_cl163, zip_derived_cl161, 345.35/44.49 zip_derived_cl34, zip_derived_cl156, zip_derived_cl159, 345.35/44.49 zip_derived_cl29, zip_derived_cl886, zip_derived_cl165, 345.35/44.49 zip_derived_cl162, zip_derived_cl105, zip_derived_cl84, 345.35/44.49 zip_derived_cl107, zip_derived_cl52, zip_derived_cl88, 345.35/44.49 zip_derived_cl64, zip_derived_cl169, zip_derived_cl121, 345.35/44.49 zip_derived_cl112, zip_derived_cl132, zip_derived_cl130, 345.35/44.49 zip_derived_cl166, zip_derived_cl56, zip_derived_cl168, 345.35/44.49 zip_derived_cl140, zip_derived_cl114, zip_derived_cl171, 345.35/44.49 zip_derived_cl170, zip_derived_cl172, zip_derived_cl158, 345.35/44.49 zip_derived_cl151, zip_derived_cl167])). 345.35/44.49 345.35/44.49 % SZS output end Refutation 345.35/44.49 345.35/44.49 345.35/44.49 % Terminating... 345.39/44.57 % Runner terminated. 345.39/44.58 % Zipperpin 1.5 exiting 345.39/44.60 EOF