0.05/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.E8hzPRdkOI true 0.10/0.31 % Computer : n029.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 1440 0.10/0.31 % WCLimit : 180 0.10/0.31 % DateTime : Mon Jul 3 11:04:57 EDT 2023 0.10/0.31 % CPUTime : 0.10/0.31 % Running portfolio for 1440 s 0.15/0.31 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.15/0.31 % Number of cores: 8 0.15/0.31 % Python version: Python 3.6.8 0.15/0.32 % Running in HO mode 0.44/0.59 % Total configuration time : 828 0.44/0.59 % Estimated wc time : 1656 0.44/0.59 % Estimated cpu time (8 cpus) : 207.0 0.46/0.68 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.46/0.68 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.46/0.68 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.46/0.68 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.46/0.68 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.46/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.46/0.69 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.46/0.69 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 238.22/30.72 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 351.46/45.77 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 351.46/45.77 % Solved by lams/30_b.l.sh. 351.46/45.77 % done 277 iterations in 14.782s 351.46/45.77 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 351.46/45.77 % SZS output start Refutation 351.46/45.77 thf(a_type, type, a: $tType). 351.46/45.77 thf('#sk109_type', type, '#sk109': a > a > (a > $o) > a). 351.46/45.77 thf('#sk28_type', type, '#sk28': a > a). 351.46/45.77 thf('#form127_type', type, '#form127': a > (a > $o) > $o). 351.46/45.77 thf('#form24_type', type, '#form24': $o). 351.46/45.77 thf('#sk27_type', type, '#sk27': a). 351.46/45.77 thf('#sk128_type', type, '#sk128': a > (a > $o) > a). 351.46/45.77 thf('#sk7_type', type, '#sk7': a). 351.46/45.77 thf('#sk45_type', type, '#sk45': a > a > $o). 351.46/45.77 thf('#sk64_type', type, '#sk64': a > a > a > $o). 351.46/45.77 thf('#form72_type', type, '#form72': a > $o). 351.46/45.77 thf('#sk30_type', type, '#sk30': a). 351.46/45.77 thf('#form44_type', type, '#form44': a > (a > $o) > $o). 351.46/45.77 thf('#sk2_type', type, '#sk2': a > a > a). 351.46/45.77 thf('#form26_type', type, '#form26': $o). 351.46/45.77 thf('#sk32_type', type, '#sk32': a > a > $o). 351.46/45.77 thf('#form31_type', type, '#form31': a > $o). 351.46/45.77 thf('#sk51_type', type, '#sk51': a > (a > $o) > a). 351.46/45.77 thf('#sk63_type', type, '#sk63': a > (a > $o) > a). 351.46/45.77 thf('#sk33_type', type, '#sk33': a > a > $o). 351.46/45.77 thf('#sk6_type', type, '#sk6': a > $o). 351.46/45.77 thf('#sk29_type', type, '#sk29': a > a). 351.46/45.77 thf('#sk25_type', type, '#sk25': a). 351.46/45.77 thf('#sk3_type', type, '#sk3': a > a). 351.46/45.77 thf('#sk4_type', type, '#sk4': a > a). 351.46/45.77 thf('#sk18_type', type, '#sk18': (a > $o) > a). 351.46/45.77 thf('#sk40_type', type, '#sk40': a > a > a). 351.46/45.77 thf('#sk1_type', type, '#sk1': a). 351.46/45.77 thf('#sk5_type', type, '#sk5': a > $o). 351.46/45.77 thf(cPU_X238A_pme, conjecture, 351.46/45.77 (![Z:a,P:( a > a > a ),L:( a > a ),R:( a > a ),F:( a > $o )]: 351.46/45.77 ( ( ( ( L @ Z ) = ( Z ) ) & ( ( R @ Z ) = ( Z ) ) & 351.46/45.77 ( ![Xx:a,Xy:a]: ( ( L @ ( P @ Xx @ Xy ) ) = ( Xx ) ) ) & 351.46/45.77 ( ![Xx:a,Xy:a]: ( ( R @ ( P @ Xx @ Xy ) ) = ( Xy ) ) ) & 351.46/45.77 ( ![X:( a > $o )]: 351.46/45.77 ( ( ?[Xt:a]: 351.46/45.77 ( ( X @ Xt ) & ( ![Xu:a]: ( ( X @ Xu ) => ( X @ ( L @ Xu ) ) ) ) ) ) => 351.46/45.77 ( X @ Z ) ) ) & 351.46/45.77 ( ![Xt:a]: 351.46/45.77 ( ( ( Xt ) = ( P @ ( L @ Xt ) @ ( R @ Xt ) ) ) <=> 351.46/45.77 ( ( Xt ) != ( Z ) ) ) ) ) => 351.46/45.77 ( ![X:( a > $o ),Xz:a]: 351.46/45.77 ( ( ?[Xx:a]: 351.46/45.77 ( ( ![Xx_6:a]: 351.46/45.77 ( ( ![X0:( a > $o )]: 351.46/45.77 ( ( ( ![Xz0:a]: ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) & 351.46/45.77 ( X0 @ Xx ) ) => 351.46/45.77 ( ?[Xv:a]: ( ( X0 @ Xv ) & ( ( R @ Xv ) = ( Xx_6 ) ) ) ) ) ) => 351.46/45.77 ( X @ Xx_6 ) ) ) & 351.46/45.77 ( ?[Xx_8:a]: 351.46/45.77 ( ( ![Xx_7:a]: 351.46/45.77 ( ( ![X0:( a > $o )]: 351.46/45.77 ( ( ( ![Xz0:a]: 351.46/45.77 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) & 351.46/45.77 ( X0 @ Xx_8 ) ) => 351.46/45.77 ( ?[Xv:a]: 351.46/45.77 ( ( ( R @ Xv ) = ( Xx_7 ) ) & ( X0 @ Xv ) ) ) ) ) => 351.46/45.77 ( ![X0:( a > $o )]: 351.46/45.77 ( ( ( X0 @ Xx ) & 351.46/45.77 ( ![Xz0:a]: 351.46/45.77 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) ) => 351.46/45.77 ( ?[Xv:a]: 351.46/45.77 ( ( ( R @ Xv ) = ( Xx_7 ) ) & ( X0 @ Xv ) ) ) ) ) ) ) & 351.46/45.77 ( F @ ( P @ Xx_8 @ Xz ) ) ) ) ) ) <=> 351.46/45.77 ( ?[Xx:a]: 351.46/45.77 ( ( F @ ( P @ Xx @ Xz ) ) & 351.46/45.77 ( ![Xx_5:a]: 351.46/45.77 ( ( ![X0:( a > $o )]: 351.46/45.77 ( ( ( ![Xz0:a]: ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) & 351.46/45.77 ( X0 @ Xx ) ) => 351.46/45.77 ( ?[Xv:a]: ( ( ( R @ Xv ) = ( Xx_5 ) ) & ( X0 @ Xv ) ) ) ) ) => 351.46/45.77 ( X @ Xx_5 ) ) ) ) ) ) ) ))). 351.46/45.77 thf(zf_stmt_0, negated_conjecture, 351.46/45.77 (~( ![Z:a,P:( a > a > a ),L:( a > a ),R:( a > a ),F:( a > $o )]: 351.46/45.77 ( ( ( ( L @ Z ) = ( Z ) ) & ( ( R @ Z ) = ( Z ) ) & 351.46/45.77 ( ![Xx:a,Xy:a]: ( ( L @ ( P @ Xx @ Xy ) ) = ( Xx ) ) ) & 351.46/45.77 ( ![Xx:a,Xy:a]: ( ( R @ ( P @ Xx @ Xy ) ) = ( Xy ) ) ) & 351.46/45.77 ( ![X:( a > $o )]: 351.46/45.77 ( ( ?[Xt:a]: 351.46/45.77 ( ( X @ Xt ) & 351.46/45.77 ( ![Xu:a]: ( ( X @ Xu ) => ( X @ ( L @ Xu ) ) ) ) ) ) => 351.46/45.77 ( X @ Z ) ) ) & 351.46/45.77 ( ![Xt:a]: 351.46/45.77 ( ( ( Xt ) = ( P @ ( L @ Xt ) @ ( R @ Xt ) ) ) <=> 351.46/45.77 ( ( Xt ) != ( Z ) ) ) ) ) => 351.46/45.77 ( ![X:( a > $o ),Xz:a]: 351.46/45.77 ( ( ?[Xx:a]: 351.46/45.77 ( ( ![Xx_6:a]: 351.46/45.77 ( ( ![X0:( a > $o )]: 351.46/45.77 ( ( ( ![Xz0:a]: 351.46/45.77 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) & 351.46/45.77 ( X0 @ Xx ) ) => 351.46/45.77 ( ?[Xv:a]: 351.46/45.77 ( ( X0 @ Xv ) & ( ( R @ Xv ) = ( Xx_6 ) ) ) ) ) ) => 351.46/45.77 ( X @ Xx_6 ) ) ) & 351.46/45.77 ( ?[Xx_8:a]: 351.46/45.77 ( ( ![Xx_7:a]: 351.46/45.77 ( ( ![X0:( a > $o )]: 351.46/45.77 ( ( ( ![Xz0:a]: 351.46/45.77 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) & 351.46/45.77 ( X0 @ Xx_8 ) ) => 351.46/45.77 ( ?[Xv:a]: 351.46/45.77 ( ( ( R @ Xv ) = ( Xx_7 ) ) & ( X0 @ Xv ) ) ) ) ) => 351.46/45.77 ( ![X0:( a > $o )]: 351.46/45.77 ( ( ( X0 @ Xx ) & 351.46/45.77 ( ![Xz0:a]: 351.46/45.77 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) ) => 351.46/45.77 ( ?[Xv:a]: 351.46/45.77 ( ( ( R @ Xv ) = ( Xx_7 ) ) & ( X0 @ Xv ) ) ) ) ) ) ) & 351.46/45.77 ( F @ ( P @ Xx_8 @ Xz ) ) ) ) ) ) <=> 351.46/45.77 ( ?[Xx:a]: 351.46/45.77 ( ( F @ ( P @ Xx @ Xz ) ) & 351.46/45.77 ( ![Xx_5:a]: 351.46/45.77 ( ( ![X0:( a > $o )]: 351.46/45.77 ( ( ( ![Xz0:a]: 351.46/45.77 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) & 351.46/45.77 ( X0 @ Xx ) ) => 351.46/45.77 ( ?[Xv:a]: 351.46/45.77 ( ( ( R @ Xv ) = ( Xx_5 ) ) & ( X0 @ Xv ) ) ) ) ) => 351.46/45.77 ( X @ Xx_5 ) ) ) ) ) ) ) ) )), 351.46/45.77 inference('cnf.neg', [status(esa)], [cPU_X238A_pme])). 351.46/45.77 thf(zip_derived_cl0, plain, 351.46/45.77 (~ (((!!) @ (^[Y0 : a]: 351.46/45.77 (((!!) @ (^[Y1 : a > a > a]: 351.46/45.77 (((!!) @ (^[Y2 : a > a]: 351.46/45.77 (((!!) @ (^[Y3 : a > a]: 351.46/45.77 (((!!) @ (^[Y4 : a > $o]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 ( 351.46/45.77 ( 351.46/45.77 (Y2 @ 351.46/45.77 Y0) = 351.46/45.77 (Y0))) & 351.46/45.77 ( 351.46/45.77 ( 351.46/45.77 (Y3 @ 351.46/45.77 Y0) = 351.46/45.77 (Y0))) & 351.46/45.77 ( 351.46/45.77 ( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y5 : a]: 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y6 : a]: 351.46/45.77 (( 351.46/45.77 (Y2 @ 351.46/45.77 ( 351.46/45.77 Y1 @ 351.46/45.77 Y5 @ Y6)) = 351.46/45.77 (Y5))))))))) & 351.46/45.77 ( 351.46/45.77 ( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y5 : a]: 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y6 : a]: 351.46/45.77 (( 351.46/45.77 (Y3 @ 351.46/45.77 ( 351.46/45.77 Y1 @ 351.46/45.77 Y5 @ Y6)) = 351.46/45.77 (Y6))))))))) & 351.46/45.77 ( 351.46/45.77 ( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y5 : a > $o]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (??) @ ( 351.46/45.77 ^[Y6 : a]: 351.46/45.77 (( 351.46/45.77 (Y5 @ 351.46/45.77 Y6) & 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y7 : a]: 351.46/45.77 (( 351.46/45.77 (Y5 @ 351.46/45.77 Y7) => 351.46/45.77 (Y5 @ 351.46/45.77 ( 351.46/45.77 Y2 @ Y7)))))))))))) => 351.46/45.77 (Y5 @ Y0)))))) & 351.46/45.77 ( 351.46/45.77 ( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y5 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (Y5) = 351.46/45.77 (Y1 @ 351.46/45.77 ( 351.46/45.77 Y2 @ Y5) @ 351.46/45.77 ( 351.46/45.77 Y3 @ Y5)))) <=> 351.46/45.77 (( 351.46/45.77 (Y5) != 351.46/45.77 (Y0)))))))))) => 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y5 : a > $o]: 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y6 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (??) @ ( 351.46/45.77 ^[Y7 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y8 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y9 : a > $o]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y10 : a]: 351.46/45.77 (( 351.46/45.77 (Y9 @ 351.46/45.77 Y10) => 351.46/45.77 (Y9 @ 351.46/45.77 ( 351.46/45.77 Y2 @ Y10))))))) & 351.46/45.77 (Y9 @ Y7))) => 351.46/45.77 (( 351.46/45.77 (??) @ ( 351.46/45.77 ^[Y10 : a]: 351.46/45.77 (( 351.46/45.77 (Y9 @ 351.46/45.77 Y10) & 351.46/45.77 (( 351.46/45.77 (Y3 @ 351.46/45.77 Y10) = 351.46/45.77 (Y8))))))))))))) => 351.46/45.77 (Y5 @ Y8)))))) & 351.46/45.77 (( 351.46/45.77 (??) @ ( 351.46/45.77 ^[Y8 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y9 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y10 : a > $o]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y11 : a]: 351.46/45.77 (( 351.46/45.77 (Y10 @ 351.46/45.77 Y11) => 351.46/45.77 (Y10 @ 351.46/45.77 ( 351.46/45.77 Y2 @ Y11))))))) & 351.46/45.77 (Y10 @ 351.46/45.77 Y8))) => 351.46/45.77 (( 351.46/45.77 (??) @ ( 351.46/45.77 ^[Y11 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (Y3 @ 351.46/45.77 Y11) = 351.46/45.77 (Y9))) & 351.46/45.77 (Y10 @ 351.46/45.77 Y11))))))))))) => 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y10 : a > $o]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (Y10 @ 351.46/45.77 Y7) & 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y11 : a]: 351.46/45.77 (( 351.46/45.77 (Y10 @ 351.46/45.77 Y11) => 351.46/45.77 (Y10 @ 351.46/45.77 ( 351.46/45.77 Y2 @ Y11))))))))) => 351.46/45.77 (( 351.46/45.77 (??) @ ( 351.46/45.77 ^[Y11 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (Y3 @ 351.46/45.77 Y11) = 351.46/45.77 (Y9))) & 351.46/45.77 (Y10 @ 351.46/45.77 Y11)))))))))))))))) & 351.46/45.77 (Y4 @ 351.46/45.77 ( 351.46/45.77 Y1 @ 351.46/45.77 Y8 @ Y6)))))))))))) <=> 351.46/45.77 (( 351.46/45.77 (??) @ ( 351.46/45.77 ^[Y7 : a]: 351.46/45.77 (( 351.46/45.77 (Y4 @ 351.46/45.77 ( 351.46/45.77 Y1 @ 351.46/45.77 Y7 @ Y6)) & 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y8 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y9 : a > $o]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y10 : a]: 351.46/45.77 (( 351.46/45.77 (Y9 @ 351.46/45.77 Y10) => 351.46/45.77 (Y9 @ 351.46/45.77 ( 351.46/45.77 Y2 @ Y10))))))) & 351.46/45.77 (Y9 @ Y7))) => 351.46/45.77 (( 351.46/45.77 (??) @ ( 351.46/45.77 ^[Y10 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (Y3 @ 351.46/45.77 Y10) = 351.46/45.77 (Y8))) & 351.46/45.77 (Y9 @ 351.46/45.77 Y10))))))))))) => 351.46/45.77 (Y5 @ Y8))))))))))))))))))))))))))))))))))))), 351.46/45.77 inference('cnf', [status(esa)], [zf_stmt_0])). 351.46/45.77 thf(zip_derived_cl1, plain, 351.46/45.77 (~ (((!!) @ (^[Y0 : a > a > a]: 351.46/45.77 (((!!) @ (^[Y1 : a > a]: 351.46/45.77 (((!!) @ (^[Y2 : a > a]: 351.46/45.77 (((!!) @ (^[Y3 : a > $o]: 351.46/45.77 (((((((Y1 @ '#sk1') = 351.46/45.77 ('#sk1'))) & 351.46/45.77 (((Y2 @ '#sk1') = 351.46/45.77 ('#sk1'))) & 351.46/45.77 (((!!) @ ( 351.46/45.77 ^[Y4 : a]: 351.46/45.77 (((!!) @ ( 351.46/45.77 ^[Y5 : a]: 351.46/45.77 (( 351.46/45.77 (Y1 @ 351.46/45.77 ( 351.46/45.77 Y0 @ 351.46/45.77 Y4 @ Y5)) = 351.46/45.77 (Y4))))))))) & 351.46/45.77 (((!!) @ ( 351.46/45.77 ^[Y4 : a]: 351.46/45.77 (((!!) @ ( 351.46/45.77 ^[Y5 : a]: 351.46/45.77 (( 351.46/45.77 (Y2 @ 351.46/45.77 ( 351.46/45.77 Y0 @ 351.46/45.77 Y4 @ Y5)) = 351.46/45.77 (Y5))))))))) & 351.46/45.77 (((!!) @ ( 351.46/45.77 ^[Y4 : a > $o]: 351.46/45.77 (((((??) @ ( 351.46/45.77 ^[Y5 : a]: 351.46/45.77 (( 351.46/45.77 (Y4 @ 351.46/45.77 Y5) & 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y6 : a]: 351.46/45.77 (( 351.46/45.77 (Y4 @ 351.46/45.77 Y6) => 351.46/45.77 (Y4 @ 351.46/45.77 ( 351.46/45.77 Y1 @ Y6)))))))))))) => 351.46/45.77 (Y4 @ 351.46/45.77 '#sk1')))))) & 351.46/45.77 (((!!) @ ( 351.46/45.77 ^[Y4 : a]: 351.46/45.77 (((((Y4) = 351.46/45.77 (Y0 @ 351.46/45.77 (Y1 @ Y4) @ 351.46/45.77 (Y2 @ Y4)))) <=> 351.46/45.77 (((Y4) != 351.46/45.77 ('#sk1')))))))))) => 351.46/45.77 (((!!) @ (^[Y4 : a > $o]: 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y5 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (??) @ ( 351.46/45.77 ^[Y6 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y7 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y8 : a > $o]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y9 : a]: 351.46/45.77 (( 351.46/45.77 (Y8 @ 351.46/45.77 Y9) => 351.46/45.77 (Y8 @ 351.46/45.77 ( 351.46/45.77 Y1 @ Y9))))))) & 351.46/45.77 (Y8 @ Y6))) => 351.46/45.77 (( 351.46/45.77 (??) @ ( 351.46/45.77 ^[Y9 : a]: 351.46/45.77 (( 351.46/45.77 (Y8 @ 351.46/45.77 Y9) & 351.46/45.77 (( 351.46/45.77 (Y2 @ 351.46/45.77 Y9) = 351.46/45.77 (Y7))))))))))))) => 351.46/45.77 (Y4 @ Y7)))))) & 351.46/45.77 (( 351.46/45.77 (??) @ ( 351.46/45.77 ^[Y7 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y8 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y9 : a > $o]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y10 : a]: 351.46/45.77 (( 351.46/45.77 (Y9 @ 351.46/45.77 Y10) => 351.46/45.77 (Y9 @ 351.46/45.77 ( 351.46/45.77 Y1 @ Y10))))))) & 351.46/45.77 (Y9 @ Y7))) => 351.46/45.77 (( 351.46/45.77 (??) @ ( 351.46/45.77 ^[Y10 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (Y2 @ 351.46/45.77 Y10) = 351.46/45.77 (Y8))) & 351.46/45.77 (Y9 @ 351.46/45.77 Y10))))))))))) => 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y9 : a > $o]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (Y9 @ 351.46/45.77 Y6) & 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y10 : a]: 351.46/45.77 (( 351.46/45.77 (Y9 @ 351.46/45.77 Y10) => 351.46/45.77 (Y9 @ 351.46/45.77 ( 351.46/45.77 Y1 @ Y10))))))))) => 351.46/45.77 (( 351.46/45.77 (??) @ ( 351.46/45.77 ^[Y10 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (Y2 @ 351.46/45.77 Y10) = 351.46/45.77 (Y8))) & 351.46/45.77 (Y9 @ 351.46/45.77 Y10)))))))))))))))) & 351.46/45.77 (Y3 @ 351.46/45.77 ( 351.46/45.77 Y0 @ 351.46/45.77 Y7 @ Y5)))))))))))) <=> 351.46/45.77 (( 351.46/45.77 (??) @ ( 351.46/45.77 ^[Y6 : a]: 351.46/45.77 (( 351.46/45.77 (Y3 @ 351.46/45.77 ( 351.46/45.77 Y0 @ 351.46/45.77 Y6 @ Y5)) & 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y7 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y8 : a > $o]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y9 : a]: 351.46/45.77 (( 351.46/45.77 (Y8 @ 351.46/45.77 Y9) => 351.46/45.77 (Y8 @ 351.46/45.77 ( 351.46/45.77 Y1 @ Y9))))))) & 351.46/45.77 (Y8 @ Y6))) => 351.46/45.77 (( 351.46/45.77 (??) @ ( 351.46/45.77 ^[Y9 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (Y2 @ 351.46/45.77 Y9) = 351.46/45.77 (Y7))) & 351.46/45.77 (Y8 @ Y9))))))))))) => 351.46/45.77 (Y4 @ Y7)))))))))))))))))))))))))))))))))), 351.46/45.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 351.46/45.77 thf(zip_derived_cl2, plain, 351.46/45.77 (~ (((!!) @ (^[Y0 : a > a]: 351.46/45.77 (((!!) @ (^[Y1 : a > a]: 351.46/45.77 (((!!) @ (^[Y2 : a > $o]: 351.46/45.77 (((((((Y0 @ '#sk1') = ('#sk1'))) & 351.46/45.77 (((Y1 @ '#sk1') = ('#sk1'))) & 351.46/45.77 (((!!) @ (^[Y3 : a]: 351.46/45.77 (((!!) @ ( 351.46/45.77 ^[Y4 : a]: 351.46/45.77 (((Y0 @ 351.46/45.77 ('#sk2' @ 351.46/45.77 Y3 @ Y4)) = 351.46/45.77 (Y3))))))))) & 351.46/45.77 (((!!) @ (^[Y3 : a]: 351.46/45.77 (((!!) @ ( 351.46/45.77 ^[Y4 : a]: 351.46/45.77 (((Y1 @ 351.46/45.77 ('#sk2' @ 351.46/45.77 Y3 @ Y4)) = 351.46/45.77 (Y4))))))))) & 351.46/45.77 (((!!) @ (^[Y3 : a > $o]: 351.46/45.77 (((((??) @ ( 351.46/45.77 ^[Y4 : a]: 351.46/45.77 (((Y3 @ 351.46/45.77 Y4) & 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y5 : a]: 351.46/45.77 (( 351.46/45.77 (Y3 @ 351.46/45.77 Y5) => 351.46/45.77 (Y3 @ 351.46/45.77 ( 351.46/45.77 Y0 @ Y5)))))))))))) => 351.46/45.77 (Y3 @ '#sk1')))))) & 351.46/45.77 (((!!) @ (^[Y3 : a]: 351.46/45.77 (((((Y3) = 351.46/45.77 ('#sk2' @ 351.46/45.77 (Y0 @ Y3) @ 351.46/45.77 (Y1 @ Y3)))) <=> 351.46/45.77 (((Y3) != 351.46/45.77 ('#sk1')))))))))) => 351.46/45.77 (((!!) @ (^[Y3 : a > $o]: 351.46/45.77 (((!!) @ (^[Y4 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (??) @ ( 351.46/45.77 ^[Y5 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y6 : a]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y7 : a > $o]: 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (( 351.46/45.77 (!!) @ ( 351.46/45.77 ^[Y8 : a]: 351.46/45.77 (( 351.46/45.77 (Y7 @ 351.46/45.77 Y8) => 351.46/45.77 (Y7 @ 351.46/45.77 ( 351.46/45.77 Y0 @ Y8))))))) & 351.46/45.77 (Y7 @ Y5))) => 351.46/45.77 (( 351.46/45.77 (??) @ ( 351.46/45.77 ^[Y8 : a]: 351.46/45.77 (( 351.46/45.77 (Y7 @ 351.46/45.77 Y8) & 351.46/45.77 (( 351.46/45.77 (Y1 @ 351.46/45.77 Y8) = 351.46/45.77 (Y6))))))))))))) => 351.46/45.77 (Y3 @ Y6)))))) & 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y6 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y7 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y8 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y9 : a]: 351.46/45.78 (( 351.46/45.78 (Y8 @ 351.46/45.78 Y9) => 351.46/45.78 (Y8 @ 351.46/45.78 ( 351.46/45.78 Y0 @ Y9))))))) & 351.46/45.78 (Y8 @ Y6))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y9 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (Y1 @ 351.46/45.78 Y9) = 351.46/45.78 (Y7))) & 351.46/45.78 (Y8 @ Y9))))))))))) => 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y8 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (Y8 @ 351.46/45.78 Y5) & 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y9 : a]: 351.46/45.78 (( 351.46/45.78 (Y8 @ 351.46/45.78 Y9) => 351.46/45.78 (Y8 @ 351.46/45.78 ( 351.46/45.78 Y0 @ Y9))))))))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y9 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (Y1 @ 351.46/45.78 Y9) = 351.46/45.78 (Y7))) & 351.46/45.78 (Y8 @ Y9)))))))))))))))) & 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk2' @ 351.46/45.78 Y6 @ Y4)))))))))))) <=> 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y5 : a]: 351.46/45.78 (( 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk2' @ 351.46/45.78 Y5 @ Y4)) & 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y6 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y7 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y8 : a]: 351.46/45.78 (( 351.46/45.78 (Y7 @ 351.46/45.78 Y8) => 351.46/45.78 (Y7 @ 351.46/45.78 ( 351.46/45.78 Y0 @ Y8))))))) & 351.46/45.78 (Y7 @ Y5))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y8 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (Y1 @ 351.46/45.78 Y8) = 351.46/45.78 (Y6))) & 351.46/45.78 (Y7 @ Y8))))))))))) => 351.46/45.78 (Y3 @ Y6))))))))))))))))))))))))))))))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 351.46/45.78 thf(zip_derived_cl3, plain, 351.46/45.78 (~ (((!!) @ (^[Y0 : a > a]: 351.46/45.78 (((!!) @ (^[Y1 : a > $o]: 351.46/45.78 ((((((('#sk3' @ '#sk1') = ('#sk1'))) & 351.46/45.78 (((Y0 @ '#sk1') = ('#sk1'))) & 351.46/45.78 (((!!) @ (^[Y2 : a]: 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 ((('#sk3' @ 351.46/45.78 ('#sk2' @ Y2 @ 351.46/45.78 Y3)) = 351.46/45.78 (Y2))))))))) & 351.46/45.78 (((!!) @ (^[Y2 : a]: 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y0 @ 351.46/45.78 ('#sk2' @ Y2 @ 351.46/45.78 Y3)) = 351.46/45.78 (Y3))))))))) & 351.46/45.78 (((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((??) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ Y3) & 351.46/45.78 (((!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (Y2 @ 351.46/45.78 Y4) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4)))))))))))) => 351.46/45.78 (Y2 @ '#sk1')))))) & 351.46/45.78 (((!!) @ (^[Y2 : a]: 351.46/45.78 (((((Y2) = ('#sk2' @ 351.46/45.78 ('#sk3' @ Y2) @ (Y0 @ Y2)))) <=> 351.46/45.78 (((Y2) != ('#sk1')))))))))) => 351.46/45.78 (((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 (((((??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (((((!!) @ ( 351.46/45.78 ^[Y5 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y6 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y7 : a]: 351.46/45.78 (( 351.46/45.78 (Y6 @ 351.46/45.78 Y7) => 351.46/45.78 (Y6 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y7))))))) & 351.46/45.78 (Y6 @ Y4))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y7 : a]: 351.46/45.78 (( 351.46/45.78 (Y6 @ 351.46/45.78 Y7) & 351.46/45.78 (( 351.46/45.78 (Y0 @ 351.46/45.78 Y7) = 351.46/45.78 (Y5))))))))))))) => 351.46/45.78 (Y2 @ Y5)))))) & 351.46/45.78 (((??) @ ( 351.46/45.78 ^[Y5 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y6 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y7 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y8 : a]: 351.46/45.78 (( 351.46/45.78 (Y7 @ 351.46/45.78 Y8) => 351.46/45.78 (Y7 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y8))))))) & 351.46/45.78 (Y7 @ Y5))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y8 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (Y0 @ 351.46/45.78 Y8) = 351.46/45.78 (Y6))) & 351.46/45.78 (Y7 @ Y8))))))))))) => 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y7 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (Y7 @ 351.46/45.78 Y4) & 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y8 : a]: 351.46/45.78 (( 351.46/45.78 (Y7 @ 351.46/45.78 Y8) => 351.46/45.78 (Y7 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y8))))))))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y8 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (Y0 @ 351.46/45.78 Y8) = 351.46/45.78 (Y6))) & 351.46/45.78 (Y7 @ Y8)))))))))))))))) & 351.46/45.78 (Y1 @ 351.46/45.78 ( 351.46/45.78 '#sk2' @ 351.46/45.78 Y5 @ Y3)))))))))))) <=> 351.46/45.78 (((??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (((Y1 @ 351.46/45.78 ('#sk2' @ 351.46/45.78 Y4 @ Y3)) & 351.46/45.78 (((!!) @ ( 351.46/45.78 ^[Y5 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y6 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y7 : a]: 351.46/45.78 (( 351.46/45.78 (Y6 @ 351.46/45.78 Y7) => 351.46/45.78 (Y6 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y7))))))) & 351.46/45.78 (Y6 @ Y4))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y7 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (Y0 @ 351.46/45.78 Y7) = 351.46/45.78 (Y5))) & 351.46/45.78 (Y6 @ Y7))))))))))) => 351.46/45.78 (Y2 @ Y5)))))))))))))))))))))))))))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 351.46/45.78 thf(zip_derived_cl4, plain, 351.46/45.78 (~ (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 ((((((('#sk3' @ '#sk1') = ('#sk1'))) & 351.46/45.78 ((('#sk4' @ '#sk1') = ('#sk1'))) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((!!) @ (^[Y2 : a]: 351.46/45.78 ((('#sk3' @ 351.46/45.78 ('#sk2' @ Y1 @ Y2)) = (Y1))))))))) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((!!) @ (^[Y2 : a]: 351.46/45.78 ((('#sk4' @ 351.46/45.78 ('#sk2' @ Y1 @ Y2)) = (Y2))))))))) & 351.46/45.78 (((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((??) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y1 @ Y3) => 351.46/45.78 (Y1 @ 351.46/45.78 ('#sk3' @ Y3)))))))))))) => 351.46/45.78 (Y1 @ '#sk1')))))) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((Y1) = ('#sk2' @ ('#sk3' @ Y1) @ 351.46/45.78 ('#sk4' @ Y1)))) <=> 351.46/45.78 (((Y1) != ('#sk1')))))))))) => 351.46/45.78 (((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((!!) @ (^[Y2 : a]: 351.46/45.78 (((((??) @ (^[Y3 : a]: 351.46/45.78 (((((!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (((( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y5 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y6 : a]: 351.46/45.78 (( 351.46/45.78 (Y5 @ 351.46/45.78 Y6) => 351.46/45.78 (Y5 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y6))))))) & 351.46/45.78 (Y5 @ Y3))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y6 : a]: 351.46/45.78 (( 351.46/45.78 (Y5 @ 351.46/45.78 Y6) & 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y6) = 351.46/45.78 (Y4))))))))))))) => 351.46/45.78 (Y1 @ Y4)))))) & 351.46/45.78 (((??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (((( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y5 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y6 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y7 : a]: 351.46/45.78 (( 351.46/45.78 (Y6 @ 351.46/45.78 Y7) => 351.46/45.78 (Y6 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y7))))))) & 351.46/45.78 (Y6 @ Y4))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y7 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y7) = 351.46/45.78 (Y5))) & 351.46/45.78 (Y6 @ Y7))))))))))) => 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y6 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (Y6 @ 351.46/45.78 Y3) & 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y7 : a]: 351.46/45.78 (( 351.46/45.78 (Y6 @ 351.46/45.78 Y7) => 351.46/45.78 (Y6 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y7))))))))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y7 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y7) = 351.46/45.78 (Y5))) & 351.46/45.78 (Y6 @ Y7)))))))))))))))) & 351.46/45.78 (Y0 @ 351.46/45.78 ('#sk2' @ 351.46/45.78 Y4 @ Y2)))))))))))) <=> 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((Y0 @ 351.46/45.78 ('#sk2' @ Y3 @ 351.46/45.78 Y2)) & 351.46/45.78 (((!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (((( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y5 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y6 : a]: 351.46/45.78 (( 351.46/45.78 (Y5 @ 351.46/45.78 Y6) => 351.46/45.78 (Y5 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y6))))))) & 351.46/45.78 (Y5 @ Y3))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y6 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y6) = 351.46/45.78 (Y4))) & 351.46/45.78 (Y5 @ Y6))))))))))) => 351.46/45.78 (Y1 @ Y4))))))))))))))))))))))))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 351.46/45.78 thf(zip_derived_cl5, plain, 351.46/45.78 (~ ((((((('#sk3' @ '#sk1') = ('#sk1'))) & 351.46/45.78 ((('#sk4' @ '#sk1') = ('#sk1'))) & 351.46/45.78 (((!!) @ (^[Y0 : a]: 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 ((('#sk3' @ ('#sk2' @ Y0 @ Y1)) = (Y0))))))))) & 351.46/45.78 (((!!) @ (^[Y0 : a]: 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 ((('#sk4' @ ('#sk2' @ Y0 @ Y1)) = (Y1))))))))) & 351.46/45.78 (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((??) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) & 351.46/45.78 (((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y0 @ Y2) => (Y0 @ 351.46/45.78 ('#sk3' @ Y2)))))))))))) => 351.46/45.78 (Y0 @ '#sk1')))))) & 351.46/45.78 (((!!) @ (^[Y0 : a]: 351.46/45.78 (((((Y0) = ('#sk2' @ ('#sk3' @ Y0) @ ('#sk4' @ Y0)))) <=> 351.46/45.78 (((Y0) != ('#sk1')))))))))) => 351.46/45.78 (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((??) @ (^[Y2 : a]: 351.46/45.78 (((((!!) @ (^[Y3 : a]: 351.46/45.78 (((((!!) @ ( 351.46/45.78 ^[Y4 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y5 : a]: 351.46/45.78 (( 351.46/45.78 (Y4 @ 351.46/45.78 Y5) => 351.46/45.78 (Y4 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y5))))))) & 351.46/45.78 (Y4 @ Y2))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y5 : a]: 351.46/45.78 (( 351.46/45.78 (Y4 @ 351.46/45.78 Y5) & 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y5) = 351.46/45.78 (Y3))))))))))))) => 351.46/45.78 (Y0 @ Y3)))))) & 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((((!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y5 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y6 : a]: 351.46/45.78 (( 351.46/45.78 (Y5 @ 351.46/45.78 Y6) => 351.46/45.78 (Y5 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y6))))))) & 351.46/45.78 (Y5 @ Y3))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y6 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y6) = 351.46/45.78 (Y4))) & 351.46/45.78 (Y5 @ Y6))))))))))) => 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y5 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (Y5 @ 351.46/45.78 Y2) & 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y6 : a]: 351.46/45.78 (( 351.46/45.78 (Y5 @ 351.46/45.78 Y6) => 351.46/45.78 (Y5 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y6))))))))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y6 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y6) = 351.46/45.78 (Y4))) & 351.46/45.78 (Y5 @ Y6)))))))))))))))) & 351.46/45.78 ('#sk5' @ 351.46/45.78 ('#sk2' @ 351.46/45.78 Y3 @ Y1)))))))))))) <=> 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 ((('#sk5' @ 351.46/45.78 ('#sk2' @ Y2 @ Y1)) & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 (((((!!) @ ( 351.46/45.78 ^[Y4 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y5 : a]: 351.46/45.78 (( 351.46/45.78 (Y4 @ 351.46/45.78 Y5) => 351.46/45.78 (Y4 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y5))))))) & 351.46/45.78 (Y4 @ Y2))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y5 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y5) = 351.46/45.78 (Y3))) & 351.46/45.78 (Y4 @ Y5))))))))))) => 351.46/45.78 (Y0 @ Y3)))))))))))))))))))))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl4])). 351.46/45.78 thf(zip_derived_cl7, plain, 351.46/45.78 (~ (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((??) @ (^[Y2 : a]: 351.46/45.78 (((((!!) @ (^[Y3 : a]: 351.46/45.78 (((((!!) @ ( 351.46/45.78 ^[Y4 : a > $o]: 351.46/45.78 (((( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y5 : a]: 351.46/45.78 (( 351.46/45.78 (Y4 @ 351.46/45.78 Y5) => 351.46/45.78 (Y4 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y5))))))) & 351.46/45.78 (Y4 @ Y2))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y5 : a]: 351.46/45.78 (( 351.46/45.78 (Y4 @ 351.46/45.78 Y5) & 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y5) = 351.46/45.78 (Y3))))))))))))) => 351.46/45.78 (Y0 @ Y3)))))) & 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((((!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (((( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y5 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y6 : a]: 351.46/45.78 (( 351.46/45.78 (Y5 @ 351.46/45.78 Y6) => 351.46/45.78 (Y5 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y6))))))) & 351.46/45.78 (Y5 @ Y3))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y6 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y6) = 351.46/45.78 (Y4))) & 351.46/45.78 (Y5 @ Y6))))))))))) => 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y5 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (Y5 @ 351.46/45.78 Y2) & 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y6 : a]: 351.46/45.78 (( 351.46/45.78 (Y5 @ 351.46/45.78 Y6) => 351.46/45.78 (Y5 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y6))))))))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y6 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y6) = 351.46/45.78 (Y4))) & 351.46/45.78 (Y5 @ Y6)))))))))))))))) & 351.46/45.78 ('#sk5' @ 351.46/45.78 ('#sk2' @ Y3 @ 351.46/45.78 Y1)))))))))))) <=> 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 ((('#sk5' @ 351.46/45.78 ('#sk2' @ Y2 @ Y1)) & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 (((((!!) @ ( 351.46/45.78 ^[Y4 : a > $o]: 351.46/45.78 (((( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y5 : a]: 351.46/45.78 (( 351.46/45.78 (Y4 @ 351.46/45.78 Y5) => 351.46/45.78 (Y4 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y5))))))) & 351.46/45.78 (Y4 @ Y2))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y5 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y5) = 351.46/45.78 (Y3))) & 351.46/45.78 (Y4 @ Y5))))))))))) => 351.46/45.78 (Y0 @ Y3)))))))))))))))))))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 351.46/45.78 thf(zip_derived_cl14, plain, 351.46/45.78 (~ (((!!) @ (^[Y0 : a]: 351.46/45.78 (((((??) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a]: 351.46/45.78 (((((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((((((!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))) & 351.46/45.78 (Y3 @ Y1))) => 351.46/45.78 (((??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) & 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))))))))))))) => 351.46/45.78 ('#sk6' @ Y2)))))) & 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 (((((!!) @ (^[Y3 : a]: 351.46/45.78 (((((!!) @ ( 351.46/45.78 ^[Y4 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y5 : a]: 351.46/45.78 (( 351.46/45.78 (Y4 @ 351.46/45.78 Y5) => 351.46/45.78 (Y4 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y5))))))) & 351.46/45.78 (Y4 @ Y2))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y5 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y5) = 351.46/45.78 (Y3))) & 351.46/45.78 (Y4 @ Y5))))))))))) => 351.46/45.78 (((!!) @ ( 351.46/45.78 ^[Y4 : a > $o]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 (Y4 @ 351.46/45.78 Y1) & 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y5 : a]: 351.46/45.78 (( 351.46/45.78 (Y4 @ 351.46/45.78 Y5) => 351.46/45.78 (Y4 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y5))))))))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y5 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y5) = 351.46/45.78 (Y3))) & 351.46/45.78 (Y4 @ Y5)))))))))))))))) & 351.46/45.78 ('#sk5' @ 351.46/45.78 ('#sk2' @ Y2 @ Y0)))))))))))) <=> 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y1 @ Y0)) & 351.46/45.78 (((!!) @ (^[Y2 : a]: 351.46/45.78 (((((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((((((!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))) & 351.46/45.78 (Y3 @ Y1))) => 351.46/45.78 (((??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))) & 351.46/45.78 (Y3 @ Y4))))))))))) => 351.46/45.78 ('#sk6' @ Y2))))))))))))))))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl7])). 351.46/45.78 thf(zip_derived_cl21, plain, 351.46/45.78 (~ (((((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ('#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ Y3) & 351.46/45.78 ((('#sk4' @ 351.46/45.78 Y3) = (Y1))))))))))))) => 351.46/45.78 ('#sk6' @ Y1)))))) & 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a]: 351.46/45.78 (((((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((((( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))) & 351.46/45.78 (Y3 @ Y1))) => 351.46/45.78 (((??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))) & 351.46/45.78 (Y3 @ Y4))))))))))) => 351.46/45.78 (((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((((Y3 @ 351.46/45.78 Y0) & 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))))) => 351.46/45.78 (((??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))) & 351.46/45.78 (Y3 @ Y4)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y1 @ '#sk7')))))))))))) <=> 351.46/45.78 (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ('#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 ('#sk6' @ Y1)))))))))))))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl14])). 351.46/45.78 thf(zip_derived_cl26, plain, 351.46/45.78 (((((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ('#sk3' @ Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ Y3) & 351.46/45.78 ((('#sk4' @ 351.46/45.78 Y3) = (Y1))))))))))))) => 351.46/45.78 ('#sk6' @ Y1)))))) & 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a]: 351.46/45.78 (((((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((((((!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))) & 351.46/45.78 (Y3 @ Y1))) => 351.46/45.78 (((??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))) & 351.46/45.78 (Y3 @ Y4))))))))))) => 351.46/45.78 (((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((((Y3 @ Y0) & 351.46/45.78 (((!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))))) => 351.46/45.78 (((??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))) & 351.46/45.78 (Y3 @ Y4)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y1 @ '#sk7')))))))))))) 351.46/45.78 != (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 ('#sk6' @ Y1))))))))))))), 351.46/45.78 inference('simplify nested equalities', [status(thm)], [zip_derived_cl21])). 351.46/45.78 thf(zip_derived_cl35, plain, 351.46/45.78 (( ('#form24') 351.46/45.78 | ~ (((((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) & 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))))))))))))) => 351.46/45.78 ('#sk6' @ Y1)))))) & 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a]: 351.46/45.78 (((((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))) & 351.46/45.78 (Y3 @ Y1))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))) & 351.46/45.78 (Y3 @ Y4))))))))))) => 351.46/45.78 (((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((( 351.46/45.78 (Y3 @ 351.46/45.78 Y0) & 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))) & 351.46/45.78 (Y3 @ Y4)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y1 @ '#sk7')))))))))))) <=> 351.46/45.78 (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 ('#sk6' @ Y1))))))))))))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl36, plain, 351.46/45.78 (( (((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ('#sk3' @ Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ Y3) & 351.46/45.78 ((('#sk4' @ 351.46/45.78 Y3) = (Y1))))))))))))) => 351.46/45.78 ('#sk6' @ Y1)))))) & 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a]: 351.46/45.78 (((((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((((((!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))) & 351.46/45.78 (Y3 @ Y1))) => 351.46/45.78 (((??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))) & 351.46/45.78 (Y3 @ Y4))))))))))) => 351.46/45.78 (((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((((Y3 @ Y0) & 351.46/45.78 (((!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))))) => 351.46/45.78 (((??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))) & 351.46/45.78 (Y3 @ Y4)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y1 @ '#sk7')))))))))))) 351.46/45.78 | (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ('#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 ('#sk6' @ Y1))))))))))) 351.46/45.78 | ('#form24'))), 351.46/45.78 inference('lazy_cnf_xor', [status(thm)], [zip_derived_cl35])). 351.46/45.78 thf(zip_derived_cl40, plain, 351.46/45.78 (( (((((!!) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))) & 351.46/45.78 (Y1 @ '#sk25'))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) & 351.46/45.78 ((('#sk4' @ Y2) = (Y0))))))))))))) => 351.46/45.78 ('#sk6' @ Y0)))))) & 351.46/45.78 (((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ('#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 (((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((Y2 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ('#sk3' @ 351.46/45.78 Y3))))))))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = (Y1))) & 351.46/45.78 (Y2 @ Y3)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))) 351.46/45.78 | ('#form24') 351.46/45.78 | (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ('#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 ('#sk6' @ Y1))))))))))))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl36])). 351.46/45.78 thf(zip_derived_cl40, plain, 351.46/45.78 (( (((((!!) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))) & 351.46/45.78 (Y1 @ '#sk25'))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) & 351.46/45.78 ((('#sk4' @ Y2) = (Y0))))))))))))) => 351.46/45.78 ('#sk6' @ Y0)))))) & 351.46/45.78 (((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ('#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 (((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((Y2 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ('#sk3' @ 351.46/45.78 Y3))))))))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = (Y1))) & 351.46/45.78 (Y2 @ Y3)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))) 351.46/45.78 | ('#form24') 351.46/45.78 | (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ('#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 ('#sk6' @ Y1))))))))))))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl36])). 351.46/45.78 thf(zip_derived_cl44, plain, 351.46/45.78 ((~ ('#form26') 351.46/45.78 | (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ('#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 ('#sk6' @ Y1))))))))))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl35, plain, 351.46/45.78 (( ('#form24') 351.46/45.78 | ~ (((((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) & 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))))))))))))) => 351.46/45.78 ('#sk6' @ Y1)))))) & 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a]: 351.46/45.78 (((((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))) & 351.46/45.78 (Y3 @ Y1))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))) & 351.46/45.78 (Y3 @ Y4))))))))))) => 351.46/45.78 (((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((( 351.46/45.78 (Y3 @ 351.46/45.78 Y0) & 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))) & 351.46/45.78 (Y3 @ Y4)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y1 @ '#sk7')))))))))))) <=> 351.46/45.78 (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 ('#sk6' @ Y1))))))))))))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl37, plain, 351.46/45.78 ((~ (((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ('#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ Y3) & 351.46/45.78 ((('#sk4' @ 351.46/45.78 Y3) = (Y1))))))))))))) => 351.46/45.78 ('#sk6' @ Y1)))))) & 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a]: 351.46/45.78 (((((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((((((!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))) & 351.46/45.78 (Y3 @ Y1))) => 351.46/45.78 (((??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))) & 351.46/45.78 (Y3 @ Y4))))))))))) => 351.46/45.78 (((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((((Y3 @ Y0) & 351.46/45.78 (((!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))))) => 351.46/45.78 (((??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))) & 351.46/45.78 (Y3 @ Y4)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y1 @ '#sk7')))))))))))) 351.46/45.78 | ~ (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 ('#sk6' @ Y1))))))))))) 351.46/45.78 | ('#form24'))), 351.46/45.78 inference('lazy_cnf_xor', [status(thm)], [zip_derived_cl35])). 351.46/45.78 thf(zip_derived_cl39, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ (((((!!) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))) & 351.46/45.78 (Y1 @ X2))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) & 351.46/45.78 ((('#sk4' @ Y2) = (Y0))))))))))))) => 351.46/45.78 ('#sk6' @ Y0)))))) & 351.46/45.78 (((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 (((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((Y2 @ X2) & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))) 351.46/45.78 | ('#form24') 351.46/45.78 | ~ (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 ('#sk6' @ Y1))))))))))))), 351.46/45.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 351.46/45.78 thf(zip_derived_cl41, plain, 351.46/45.78 (( ('#form26') 351.46/45.78 | ~ (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 ('#sk6' @ Y1))))))))))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl46, plain, 351.46/45.78 (( ('#form26') 351.46/45.78 | ('#form24') 351.46/45.78 | (((((!!) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))) & 351.46/45.78 (Y1 @ '#sk25'))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) & 351.46/45.78 ((('#sk4' @ Y2) = (Y0))))))))))))) => 351.46/45.78 ('#sk6' @ Y0)))))) & 351.46/45.78 (((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 (((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((Y2 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 (( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = (Y1))) & 351.46/45.78 (Y2 @ Y3)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))))), 351.46/45.78 inference('renaming', [status(thm)], 351.46/45.78 [zip_derived_cl40, zip_derived_cl44, zip_derived_cl41])). 351.46/45.78 thf(zip_derived_cl50, plain, 351.46/45.78 (( (((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ('#sk3' @ Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 (((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((Y2 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ('#sk3' @ Y3))))))))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = (Y1))) & 351.46/45.78 (Y2 @ Y3)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))) 351.46/45.78 | ('#form24') 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 351.46/45.78 thf(zip_derived_cl56, plain, 351.46/45.78 (( (((((!!) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))) & 351.46/45.78 (Y1 @ '#sk30'))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 ((((('#sk4' @ Y2) = (Y0))) & 351.46/45.78 (Y1 @ Y2))))))))))) => 351.46/45.78 (((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((Y1 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 ((((('#sk4' @ Y2) = (Y0))) & 351.46/45.78 (Y1 @ Y2)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ '#sk30' @ '#sk7')))) 351.46/45.78 | ('#form26') 351.46/45.78 | ('#form24'))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl50])). 351.46/45.78 thf(zip_derived_cl64, plain, 351.46/45.78 (( ('#sk5' @ ('#sk2' @ '#sk30' @ '#sk7')) | ('#form24') | ('#form26'))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl56])). 351.46/45.78 thf(zip_derived_cl26, plain, 351.46/45.78 (((((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ('#sk3' @ Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ Y3) & 351.46/45.78 ((('#sk4' @ 351.46/45.78 Y3) = (Y1))))))))))))) => 351.46/45.78 ('#sk6' @ Y1)))))) & 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a]: 351.46/45.78 (((((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((((((!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))) & 351.46/45.78 (Y3 @ Y1))) => 351.46/45.78 (((??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))) & 351.46/45.78 (Y3 @ Y4))))))))))) => 351.46/45.78 (((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((((Y3 @ Y0) & 351.46/45.78 (((!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))))) => 351.46/45.78 (((??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))) & 351.46/45.78 (Y3 @ Y4)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y1 @ '#sk7')))))))))))) 351.46/45.78 != (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 ('#sk6' @ Y1))))))))))))), 351.46/45.78 inference('simplify nested equalities', [status(thm)], [zip_derived_cl21])). 351.46/45.78 thf(zip_derived_cl35, plain, 351.46/45.78 (( ('#form24') 351.46/45.78 | ~ (((((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) & 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))))))))))))) => 351.46/45.78 ('#sk6' @ Y1)))))) & 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a]: 351.46/45.78 (((((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((( 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))) & 351.46/45.78 (Y3 @ Y1))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))) & 351.46/45.78 (Y3 @ Y4))))))))))) => 351.46/45.78 (((!!) @ (^[Y3 : a > $o]: 351.46/45.78 (((( 351.46/45.78 (Y3 @ 351.46/45.78 Y0) & 351.46/45.78 (( 351.46/45.78 (!!) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (Y3 @ 351.46/45.78 Y4) => 351.46/45.78 (Y3 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y4))))))))) => 351.46/45.78 (( 351.46/45.78 (??) @ ( 351.46/45.78 ^[Y4 : a]: 351.46/45.78 (( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y4) = 351.46/45.78 (Y2))) & 351.46/45.78 (Y3 @ Y4)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y1 @ '#sk7')))))))))))) <=> 351.46/45.78 (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 ('#sk6' @ Y1))))))))))))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl38, plain, (~ ('#form24')), 351.46/45.78 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 351.46/45.78 thf(zip_derived_cl161, plain, 351.46/45.78 (( ('#sk5' @ ('#sk2' @ '#sk30' @ '#sk7')) | ('#form26'))), 351.46/45.78 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl38])). 351.46/45.78 thf(zip_derived_cl41, plain, 351.46/45.78 (( ('#form26') 351.46/45.78 | ~ (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 ('#sk6' @ Y1))))))))))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl42, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ ((('#sk5' @ ('#sk2' @ X2 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))) & 351.46/45.78 (Y1 @ X2))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 ((((('#sk4' @ Y2) = (Y0))) & 351.46/45.78 (Y1 @ Y2))))))))))) => 351.46/45.78 ('#sk6' @ Y0)))))))) 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 351.46/45.78 thf(zip_derived_cl48, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')) 351.46/45.78 | ~ (((!!) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))) & 351.46/45.78 (Y1 @ X2))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 ((((('#sk4' @ Y2) = (Y0))) & 351.46/45.78 (Y1 @ Y2))))))))))) => 351.46/45.78 ('#sk6' @ Y0)))))) 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl42])). 351.46/45.78 thf(zip_derived_cl54, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ (((((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 351.46/45.78 (Y0 @ X2))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = ('#sk29' @ X2))) & 351.46/45.78 (Y0 @ Y1))))))))))) => 351.46/45.78 ('#sk6' @ ('#sk29' @ X2)))) 351.46/45.78 | ('#form26') 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl48])). 351.46/45.78 thf(zip_derived_cl61, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ ('#sk6' @ ('#sk29' @ X2)) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')) 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl54])). 351.46/45.78 thf(zip_derived_cl1265, plain, 351.46/45.78 (( ('#form26') | ('#form26') | ~ ('#sk6' @ ('#sk29' @ '#sk30')))), 351.46/45.78 inference('sup-', [status(thm)], [zip_derived_cl161, zip_derived_cl61])). 351.46/45.78 thf(zip_derived_cl1283, plain, 351.46/45.78 ((~ ('#sk6' @ ('#sk29' @ '#sk30')) | ('#form26'))), 351.46/45.78 inference('simplify', [status(thm)], [zip_derived_cl1265])). 351.46/45.78 thf(zip_derived_cl63, plain, 351.46/45.78 (( (((!!) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))) & 351.46/45.78 (Y1 @ '#sk30'))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 ((((('#sk4' @ Y2) = (Y0))) & 351.46/45.78 (Y1 @ Y2))))))))))) => 351.46/45.78 (((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((Y1 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 ((((('#sk4' @ Y2) = (Y0))) & 351.46/45.78 (Y1 @ Y2)))))))))))))))) 351.46/45.78 | ('#form24') 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl56])). 351.46/45.78 thf(zip_derived_cl72, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( (((((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 351.46/45.78 (Y0 @ '#sk30'))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))) => 351.46/45.78 (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((Y0 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))))) 351.46/45.78 | ('#form26') 351.46/45.78 | ('#form24'))), 351.46/45.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 351.46/45.78 thf(zip_derived_cl79, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 351.46/45.78 (Y0 @ '#sk30'))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))) 351.46/45.78 | (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((Y0 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))) 351.46/45.78 | ('#form24') 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl72])). 351.46/45.78 thf(zip_derived_cl92, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ (((((((!!) @ (^[Y0 : a]: 351.46/45.78 ((('#sk45' @ X2 @ Y0) => ('#sk45' @ X2 @ 351.46/45.78 ('#sk3' @ Y0))))))) & 351.46/45.78 ('#sk45' @ X2 @ '#sk30'))) => 351.46/45.78 (((??) @ (^[Y0 : a]: 351.46/45.78 ((((('#sk4' @ Y0) = (X2))) & ('#sk45' @ X2 @ Y0)))))))) 351.46/45.78 | ('#form26') 351.46/45.78 | ('#form24') 351.46/45.78 | (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((Y0 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl79])). 351.46/45.78 thf(zip_derived_cl103, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ (((??) @ (^[Y0 : a]: 351.46/45.78 ((((('#sk4' @ Y0) = (X2))) & ('#sk45' @ X2 @ Y0)))))) 351.46/45.78 | (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((Y0 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))) 351.46/45.78 | ('#form24') 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])). 351.46/45.78 thf(zip_derived_cl117, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ ('#form72' @ X2) 351.46/45.78 | (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((Y0 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl118, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( (((((X4 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))))) => 351.46/45.78 (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))))) 351.46/45.78 | ~ ('#form72' @ X2))), 351.46/45.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl117])). 351.46/45.78 thf(zip_derived_cl130, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ (((X4 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))))) 351.46/45.78 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))) 351.46/45.78 | ~ ('#form72' @ X2))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl118])). 351.46/45.78 thf(zip_derived_cl137, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ (X4 @ '#sk25') 351.46/45.78 | ~ (((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) 351.46/45.78 | ~ ('#form72' @ X2) 351.46/45.78 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl130])). 351.46/45.78 thf(zip_derived_cl144, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ (((X4 @ ('#sk18' @ X4)) => (X4 @ ('#sk3' @ ('#sk18' @ X4))))) 351.46/45.78 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))) 351.46/45.78 | ~ ('#form72' @ X2) 351.46/45.78 | ~ (X4 @ '#sk25'))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl137])). 351.46/45.78 thf(zip_derived_cl149, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( (X4 @ ('#sk18' @ X4)) 351.46/45.78 | ~ (X4 @ '#sk25') 351.46/45.78 | ~ ('#form72' @ X2) 351.46/45.78 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl144])). 351.46/45.78 thf(zip_derived_cl152, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ ('#form127' @ X2 @ X4) 351.46/45.78 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl153, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( ((((('#sk4' @ ('#sk128' @ X2 @ X4)) = (X2))) & (X4 @ 351.46/45.78 ('#sk128' @ X2 @ X4)))) 351.46/45.78 | ~ ('#form127' @ X2 @ X4))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl152])). 351.46/45.78 thf(zip_derived_cl157, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( (X4 @ ('#sk128' @ X2 @ X4)) | ~ ('#form127' @ X2 @ X4))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl153])). 351.46/45.78 thf(zip_derived_cl149, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( (X4 @ ('#sk18' @ X4)) 351.46/45.78 | ~ (X4 @ '#sk25') 351.46/45.78 | ~ ('#form72' @ X2) 351.46/45.78 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl144])). 351.46/45.78 thf(zip_derived_cl152, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ ('#form127' @ X2 @ X4) 351.46/45.78 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl154, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( ('#form127' @ X2 @ X4) 351.46/45.78 | ~ ('#form72' @ X2) 351.46/45.78 | ~ (X4 @ '#sk25') 351.46/45.78 | (X4 @ ('#sk18' @ X4)))), 351.46/45.78 inference('renaming', [status(thm)], 351.46/45.78 [zip_derived_cl149, zip_derived_cl152])). 351.46/45.78 thf(zip_derived_cl156, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( ((('#sk4' @ ('#sk128' @ X2 @ X4)) = (X2))) 351.46/45.78 | ~ ('#form127' @ X2 @ X4))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl153])). 351.46/45.78 thf(zip_derived_cl159, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ((('#sk4' @ ('#sk128' @ X2 @ X4)) = (X2)) | ~ ('#form127' @ X2 @ X4))), 351.46/45.78 inference('simplify nested equalities', [status(thm)], 351.46/45.78 [zip_derived_cl156])). 351.46/45.78 thf(zip_derived_cl49, plain, 351.46/45.78 (( (((!!) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))) & 351.46/45.78 (Y1 @ '#sk25'))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) & 351.46/45.78 ((('#sk4' @ Y2) = (Y0))))))))))))) => 351.46/45.78 ('#sk6' @ Y0)))))) 351.46/45.78 | ('#form24') 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 351.46/45.78 thf(zip_derived_cl55, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( (((((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 351.46/45.78 (Y0 @ '#sk25'))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X2))))))))))))) => 351.46/45.78 ('#sk6' @ X2))) 351.46/45.78 | ('#form26') 351.46/45.78 | ('#form24'))), 351.46/45.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl49])). 351.46/45.78 thf(zip_derived_cl62, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 351.46/45.78 (Y0 @ '#sk25'))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X2))))))))))))) 351.46/45.78 | ('#sk6' @ X2) 351.46/45.78 | ('#form24') 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 351.46/45.78 thf(zip_derived_cl71, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ (((((((!!) @ (^[Y0 : a]: 351.46/45.78 ((('#sk32' @ X2 @ Y0) => ('#sk32' @ X2 @ 351.46/45.78 ('#sk3' @ Y0))))))) & 351.46/45.78 ('#sk32' @ X2 @ '#sk25'))) => 351.46/45.78 (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk32' @ X2 @ Y0) & ((('#sk4' @ Y0) = (X2)))))))))) 351.46/45.78 | ('#form26') 351.46/45.78 | ('#form24') 351.46/45.78 | ('#sk6' @ X2))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl62])). 351.46/45.78 thf(zip_derived_cl78, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk32' @ X2 @ Y0) & ((('#sk4' @ Y0) = (X2)))))))) 351.46/45.78 | ('#sk6' @ X2) 351.46/45.78 | ('#form24') 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 351.46/45.78 thf(zip_derived_cl91, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 (~ ((('#sk32' @ X2 @ X4) & ((('#sk4' @ X4) = (X2))))) 351.46/45.78 | ('#form26') 351.46/45.78 | ('#form24') 351.46/45.78 | ('#sk6' @ X2))), 351.46/45.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl78])). 351.46/45.78 thf(zip_derived_cl101, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 (~ ('#sk32' @ X2 @ X4) 351.46/45.78 | ~ ((('#sk4' @ X4) = (X2))) 351.46/45.78 | ('#sk6' @ X2) 351.46/45.78 | ('#form24') 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl91])). 351.46/45.78 thf(zip_derived_cl114, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 (~ ('#sk32' @ X2 @ X4) 351.46/45.78 | (('#sk4' @ X4) != (X2)) 351.46/45.78 | ('#sk6' @ X2) 351.46/45.78 | ('#form24') 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('simplify nested equalities', [status(thm)], 351.46/45.78 [zip_derived_cl101])). 351.46/45.78 thf(zip_derived_cl115, plain, 351.46/45.78 (![X4 : a]: 351.46/45.78 ( ('#form26') 351.46/45.78 | ('#form24') 351.46/45.78 | ('#sk6' @ ('#sk4' @ X4)) 351.46/45.78 | ~ ('#sk32' @ ('#sk4' @ X4) @ X4))), 351.46/45.78 inference('simplify', [status(thm)], [zip_derived_cl114])). 351.46/45.78 thf(zip_derived_cl38, plain, (~ ('#form24')), 351.46/45.78 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 351.46/45.78 thf(zip_derived_cl162, plain, 351.46/45.78 (![X4 : a]: 351.46/45.78 ( ('#form26') 351.46/45.78 | ('#sk6' @ ('#sk4' @ X4)) 351.46/45.78 | ~ ('#sk32' @ ('#sk4' @ X4) @ X4))), 351.46/45.78 inference('demod', [status(thm)], [zip_derived_cl115, zip_derived_cl38])). 351.46/45.78 thf(zip_derived_cl77, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( (((((!!) @ (^[Y0 : a]: 351.46/45.78 ((('#sk32' @ X2 @ Y0) => ('#sk32' @ X2 @ 351.46/45.78 ('#sk3' @ Y0))))))) & 351.46/45.78 ('#sk32' @ X2 @ '#sk25'))) 351.46/45.78 | ('#sk6' @ X2) 351.46/45.78 | ('#form24') 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 351.46/45.78 thf(zip_derived_cl77, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( (((((!!) @ (^[Y0 : a]: 351.46/45.78 ((('#sk32' @ X2 @ Y0) => ('#sk32' @ X2 @ 351.46/45.78 ('#sk3' @ Y0))))))) & 351.46/45.78 ('#sk32' @ X2 @ '#sk25'))) 351.46/45.78 | ('#sk6' @ X2) 351.46/45.78 | ('#form24') 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 351.46/45.78 thf(zip_derived_cl87, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ ('#form44' @ X2 @ X4) 351.46/45.78 | (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl60, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 351.46/45.78 (Y0 @ X2))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = ('#sk29' @ X2))) & 351.46/45.78 (Y0 @ Y1))))))))))) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')) 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl54])). 351.46/45.78 thf(zip_derived_cl70, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( (((((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))) => 351.46/45.78 (((??) @ (^[Y0 : a]: 351.46/45.78 ((((('#sk4' @ Y0) = ('#sk29' @ X2))) & (X4 @ Y0)))))))) 351.46/45.78 | ('#form26') 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')))), 351.46/45.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl60])). 351.46/45.78 thf(zip_derived_cl76, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))) 351.46/45.78 | (((??) @ (^[Y0 : a]: 351.46/45.78 ((((('#sk4' @ Y0) = ('#sk29' @ X2))) & (X4 @ Y0)))))) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')) 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl70])). 351.46/45.78 thf(zip_derived_cl84, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( ('#form44' @ X2 @ X4) 351.46/45.78 | ~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl90, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( ('#form44' @ '#sk25' @ ('#sk32' @ X2)) 351.46/45.78 | ('#form26') 351.46/45.78 | ('#form24') 351.46/45.78 | ('#sk6' @ X2))), 351.46/45.78 inference('renaming', [status(thm)], 351.46/45.78 [zip_derived_cl77, zip_derived_cl87, zip_derived_cl84])). 351.46/45.78 thf(zip_derived_cl38, plain, (~ ('#form24')), 351.46/45.78 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 351.46/45.78 thf(zip_derived_cl163, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( ('#form44' @ '#sk25' @ ('#sk32' @ X2)) 351.46/45.78 | ('#form26') 351.46/45.78 | ('#sk6' @ X2))), 351.46/45.78 inference('demod', [status(thm)], [zip_derived_cl90, zip_derived_cl38])). 351.46/45.78 thf(zip_derived_cl87, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ ('#form44' @ X2 @ X4) 351.46/45.78 | (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl88, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( (((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) 351.46/45.78 | ~ ('#form44' @ X2 @ X4))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl87])). 351.46/45.78 thf(zip_derived_cl100, plain, 351.46/45.78 (![X2 : a, X4 : a > $o, X6 : a]: 351.46/45.78 ( (((X4 @ X6) => (X4 @ ('#sk3' @ X6)))) | ~ ('#form44' @ X2 @ X4))), 351.46/45.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl88])). 351.46/45.78 thf(zip_derived_cl113, plain, 351.46/45.78 (![X2 : a, X4 : a > $o, X6 : a]: 351.46/45.78 (~ (X4 @ X6) | (X4 @ ('#sk3' @ X6)) | ~ ('#form44' @ X2 @ X4))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 351.46/45.78 thf(zip_derived_cl161, plain, 351.46/45.78 (( ('#sk5' @ ('#sk2' @ '#sk30' @ '#sk7')) | ('#form26'))), 351.46/45.78 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl38])). 351.46/45.78 thf(zip_derived_cl150, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ (X4 @ ('#sk3' @ ('#sk18' @ X4))) 351.46/45.78 | ~ (X4 @ '#sk25') 351.46/45.78 | ~ ('#form72' @ X2) 351.46/45.78 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl144])). 351.46/45.78 thf(zip_derived_cl152, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ ('#form127' @ X2 @ X4) 351.46/45.78 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl155, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( ('#form127' @ X2 @ (^[Y0 : a]: (X4 @ Y0))) 351.46/45.78 | ~ ('#form72' @ X2) 351.46/45.78 | ~ (X4 @ '#sk25') 351.46/45.78 | ~ (X4 @ ('#sk3' @ ('#sk18' @ X4))))), 351.46/45.78 inference('renaming', [status(thm)], 351.46/45.78 [zip_derived_cl150, zip_derived_cl152])). 351.46/45.78 thf(zip_derived_cl158, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( ('#form127' @ X2 @ X4) 351.46/45.78 | ~ ('#form72' @ X2) 351.46/45.78 | ~ (X4 @ '#sk25') 351.46/45.78 | ~ (X4 @ ('#sk3' @ ('#sk18' @ X4))))), 351.46/45.78 inference('ho_norm', [status(thm)], [zip_derived_cl155])). 351.46/45.78 thf(zip_derived_cl89, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: ( (X4 @ X2) | ~ ('#form44' @ X2 @ X4))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl87])). 351.46/45.78 thf(zip_derived_cl44, plain, 351.46/45.78 ((~ ('#form26') 351.46/45.78 | (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ('#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 ('#sk6' @ Y1))))))))))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl45, plain, 351.46/45.78 (( ((('#sk5' @ ('#sk2' @ '#sk27' @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))) & 351.46/45.78 (Y1 @ '#sk27'))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 ((((('#sk4' @ Y2) = (Y0))) & 351.46/45.78 (Y1 @ Y2))))))))))) => 351.46/45.78 ('#sk6' @ Y0)))))))) 351.46/45.78 | ~ ('#form26'))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl44])). 351.46/45.78 thf(zip_derived_cl51, plain, 351.46/45.78 (( ('#sk5' @ ('#sk2' @ '#sk27' @ '#sk7')) | ~ ('#form26'))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl45])). 351.46/45.78 thf(zip_derived_cl102, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( (((((!!) @ (^[Y0 : a]: 351.46/45.78 ((('#sk45' @ X2 @ Y0) => ('#sk45' @ X2 @ 351.46/45.78 ('#sk3' @ Y0))))))) & 351.46/45.78 ('#sk45' @ X2 @ '#sk30'))) 351.46/45.78 | (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((Y0 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))) 351.46/45.78 | ('#form24') 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])). 351.46/45.78 thf(zip_derived_cl87, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ ('#form44' @ X2 @ X4) 351.46/45.78 | (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl84, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( ('#form44' @ X2 @ X4) 351.46/45.78 | ~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl116, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( ('#form44' @ '#sk30' @ ('#sk45' @ X2)) 351.46/45.78 | ('#form26') 351.46/45.78 | ('#form24') 351.46/45.78 | (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((Y0 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))))), 351.46/45.78 inference('renaming', [status(thm)], 351.46/45.78 [zip_derived_cl102, zip_derived_cl87, zip_derived_cl84])). 351.46/45.78 thf(zip_derived_cl117, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ ('#form72' @ X2) 351.46/45.78 | (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((Y0 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl128, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( ('#form72' @ X2) 351.46/45.78 | ('#form24') 351.46/45.78 | ('#form26') 351.46/45.78 | ('#form44' @ '#sk30' @ ('#sk45' @ X2)))), 351.46/45.78 inference('renaming', [status(thm)], 351.46/45.78 [zip_derived_cl116, zip_derived_cl117])). 351.46/45.78 thf(zip_derived_cl38, plain, (~ ('#form24')), 351.46/45.78 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 351.46/45.78 thf(zip_derived_cl165, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( ('#form72' @ X2) 351.46/45.78 | ('#form26') 351.46/45.78 | ('#form44' @ '#sk30' @ ('#sk45' @ X2)))), 351.46/45.78 inference('demod', [status(thm)], [zip_derived_cl128, zip_derived_cl38])). 351.46/45.78 thf(zip_derived_cl52, plain, 351.46/45.78 (( (((!!) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))) & 351.46/45.78 (Y1 @ '#sk27'))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 ((((('#sk4' @ Y2) = (Y0))) & 351.46/45.78 (Y1 @ Y2))))))))))) => 351.46/45.78 ('#sk6' @ Y0)))))) 351.46/45.78 | ~ ('#form26'))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl45])). 351.46/45.78 thf(zip_derived_cl57, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( (((((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 351.46/45.78 (Y0 @ '#sk27'))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))) => 351.46/45.78 ('#sk6' @ X2))) 351.46/45.78 | ~ ('#form26'))), 351.46/45.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl52])). 351.46/45.78 thf(zip_derived_cl65, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 351.46/45.78 (Y0 @ '#sk27'))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))) 351.46/45.78 | ('#sk6' @ X2) 351.46/45.78 | ~ ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 351.46/45.78 thf(zip_derived_cl73, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ (((((((!!) @ (^[Y0 : a]: 351.46/45.78 ((('#sk33' @ X2 @ Y0) => ('#sk33' @ X2 @ 351.46/45.78 ('#sk3' @ Y0))))))) & 351.46/45.78 ('#sk33' @ X2 @ '#sk27'))) => 351.46/45.78 (((??) @ (^[Y0 : a]: 351.46/45.78 ((((('#sk4' @ Y0) = (X2))) & ('#sk33' @ X2 @ Y0)))))))) 351.46/45.78 | ~ ('#form26') 351.46/45.78 | ('#sk6' @ X2))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl65])). 351.46/45.78 thf(zip_derived_cl80, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( (((((!!) @ (^[Y0 : a]: 351.46/45.78 ((('#sk33' @ X2 @ Y0) => ('#sk33' @ X2 @ 351.46/45.78 ('#sk3' @ Y0))))))) & 351.46/45.78 ('#sk33' @ X2 @ '#sk27'))) 351.46/45.78 | ('#sk6' @ X2) 351.46/45.78 | ~ ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 351.46/45.78 thf(zip_derived_cl87, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ ('#form44' @ X2 @ X4) 351.46/45.78 | (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl84, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( ('#form44' @ X2 @ X4) 351.46/45.78 | ~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl93, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( ('#form44' @ '#sk27' @ ('#sk33' @ X2)) 351.46/45.78 | ~ ('#form26') 351.46/45.78 | ('#sk6' @ X2))), 351.46/45.78 inference('renaming', [status(thm)], 351.46/45.78 [zip_derived_cl80, zip_derived_cl87, zip_derived_cl84])). 351.46/45.78 thf(zip_derived_cl76, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))) 351.46/45.78 | (((??) @ (^[Y0 : a]: 351.46/45.78 ((((('#sk4' @ Y0) = ('#sk29' @ X2))) & (X4 @ Y0)))))) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')) 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl70])). 351.46/45.78 thf(zip_derived_cl84, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( ('#form44' @ X2 @ X4) 351.46/45.78 | ~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl86, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ ('#form44' @ X2 @ X4) 351.46/45.78 | ('#form26') 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')) 351.46/45.78 | (((??) @ (^[Y0 : a]: 351.46/45.78 ((((('#sk4' @ Y0) = ('#sk29' @ X2))) & (X4 @ Y0)))))))), 351.46/45.78 inference('renaming', [status(thm)], [zip_derived_cl76, zip_derived_cl84])). 351.46/45.78 thf(zip_derived_cl98, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( ((((('#sk4' @ ('#sk51' @ X2 @ X4)) = ('#sk29' @ X2))) & (X4 @ 351.46/45.78 ('#sk51' @ X2 @ X4)))) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')) 351.46/45.78 | ('#form26') 351.46/45.78 | ~ ('#form44' @ X2 @ X4))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl86])). 351.46/45.78 thf(zip_derived_cl110, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( (X4 @ ('#sk51' @ X2 @ X4)) 351.46/45.78 | ~ ('#form44' @ X2 @ X4) 351.46/45.78 | ('#form26') 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl98])). 351.46/45.78 thf(zip_derived_cl39, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ (((((!!) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))) & 351.46/45.78 (Y1 @ X2))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) & 351.46/45.78 ((('#sk4' @ Y2) = (Y0))))))))))))) => 351.46/45.78 ('#sk6' @ Y0)))))) & 351.46/45.78 (((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 (((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((Y2 @ X2) & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))) 351.46/45.78 | ('#form24') 351.46/45.78 | ~ (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 ('#sk6' @ Y1))))))))))))), 351.46/45.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 351.46/45.78 thf(zip_derived_cl41, plain, 351.46/45.78 (( ('#form26') 351.46/45.78 | ~ (((??) @ (^[Y0 : a]: 351.46/45.78 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (((Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ((((('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 ('#sk6' @ Y1))))))))))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl43, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ ('#form26') 351.46/45.78 | ('#form24') 351.46/45.78 | ~ (((((!!) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))) & 351.46/45.78 (Y1 @ X2))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) & 351.46/45.78 ((('#sk4' @ Y2) = 351.46/45.78 (Y0))))))))))))) => 351.46/45.78 ('#sk6' @ Y0)))))) & 351.46/45.78 (((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 (( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 (((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((Y2 @ X2) & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 (( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))))), 351.46/45.78 inference('renaming', [status(thm)], [zip_derived_cl39, zip_derived_cl41])). 351.46/45.78 thf(zip_derived_cl47, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ (((!!) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))) & 351.46/45.78 (Y1 @ X2))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) & 351.46/45.78 ((('#sk4' @ Y2) = (Y0))))))))))))) => 351.46/45.78 ('#sk6' @ Y0)))))) 351.46/45.78 | ~ (((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 (((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((Y2 @ X2) & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))) 351.46/45.78 | ('#form24') 351.46/45.78 | ~ ('#form26'))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl43])). 351.46/45.78 thf(zip_derived_cl53, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ (((((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 351.46/45.78 (Y0 @ X2))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) & 351.46/45.78 ((('#sk4' @ Y1) = ('#sk28' @ X2))))))))))))) => 351.46/45.78 ('#sk6' @ ('#sk28' @ X2)))) 351.46/45.78 | ~ ('#form26') 351.46/45.78 | ('#form24') 351.46/45.78 | ~ (((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 (((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((Y2 @ X2) & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 351.46/45.78 thf(zip_derived_cl58, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 351.46/45.78 (Y0 @ X2))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) & 351.46/45.78 ((('#sk4' @ Y1) = ('#sk28' @ X2))))))))))))) 351.46/45.78 | ~ (((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 (((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((Y2 @ X2) & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))) 351.46/45.78 | ('#form24') 351.46/45.78 | ~ ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 351.46/45.78 thf(zip_derived_cl58, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 351.46/45.78 (Y0 @ X2))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) & 351.46/45.78 ((('#sk4' @ Y1) = ('#sk28' @ X2))))))))))))) 351.46/45.78 | ~ (((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 (((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((Y2 @ X2) & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))) 351.46/45.78 | ('#form24') 351.46/45.78 | ~ ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 351.46/45.78 thf(zip_derived_cl66, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( ('#form31' @ X2) 351.46/45.78 | ~ (((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 (((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((Y2 @ X2) & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl68, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ ('#form31' @ X2) 351.46/45.78 | ~ ('#form26') 351.46/45.78 | ('#form24') 351.46/45.78 | (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 351.46/45.78 (Y0 @ X2))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) & 351.46/45.78 ((('#sk4' @ Y1) = ('#sk28' @ X2))))))))))))))), 351.46/45.78 inference('renaming', [status(thm)], [zip_derived_cl58, zip_derived_cl66])). 351.46/45.78 thf(zip_derived_cl74, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( (((((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))) => 351.46/45.78 (((??) @ (^[Y0 : a]: 351.46/45.78 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk28' @ X2)))))))))) 351.46/45.78 | ('#form24') 351.46/45.78 | ~ ('#form26') 351.46/45.78 | ~ ('#form31' @ X2))), 351.46/45.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl68])). 351.46/45.78 thf(zip_derived_cl82, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))) 351.46/45.78 | (((??) @ (^[Y0 : a]: 351.46/45.78 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk28' @ X2)))))))) 351.46/45.78 | ~ ('#form31' @ X2) 351.46/45.78 | ~ ('#form26') 351.46/45.78 | ('#form24'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])). 351.46/45.78 thf(zip_derived_cl87, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ ('#form44' @ X2 @ X4) 351.46/45.78 | (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl84, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( ('#form44' @ X2 @ X4) 351.46/45.78 | ~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl95, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ ('#form44' @ X2 @ (^[Y0 : a]: (X4 @ Y0))) 351.46/45.78 | ('#form24') 351.46/45.78 | ~ ('#form26') 351.46/45.78 | ~ ('#form31' @ X2) 351.46/45.78 | (((??) @ (^[Y0 : a]: 351.46/45.78 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk28' @ X2)))))))))), 351.46/45.78 inference('renaming', [status(thm)], 351.46/45.78 [zip_derived_cl82, zip_derived_cl87, zip_derived_cl84])). 351.46/45.78 thf(zip_derived_cl105, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ ('#form44' @ X2 @ X4) 351.46/45.78 | ('#form24') 351.46/45.78 | ~ ('#form26') 351.46/45.78 | ~ ('#form31' @ X2) 351.46/45.78 | (((??) @ (^[Y0 : a]: 351.46/45.78 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk28' @ X2)))))))))), 351.46/45.78 inference('ho_norm', [status(thm)], [zip_derived_cl95])). 351.46/45.78 thf(zip_derived_cl106, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( (((X4 @ ('#sk63' @ X2 @ X4)) & 351.46/45.78 ((('#sk4' @ ('#sk63' @ X2 @ X4)) = ('#sk28' @ X2))))) 351.46/45.78 | ~ ('#form31' @ X2) 351.46/45.78 | ~ ('#form26') 351.46/45.78 | ('#form24') 351.46/45.78 | ~ ('#form44' @ X2 @ X4))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl105])). 351.46/45.78 thf(zip_derived_cl122, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( (X4 @ ('#sk63' @ X2 @ X4)) 351.46/45.78 | ~ ('#form44' @ X2 @ X4) 351.46/45.78 | ('#form24') 351.46/45.78 | ~ ('#form26') 351.46/45.78 | ~ ('#form31' @ X2))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])). 351.46/45.78 thf(zip_derived_cl38, plain, (~ ('#form24')), 351.46/45.78 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 351.46/45.78 thf(zip_derived_cl167, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( (X4 @ ('#sk63' @ X2 @ X4)) 351.46/45.78 | ~ ('#form44' @ X2 @ X4) 351.46/45.78 | ~ ('#form26') 351.46/45.78 | ~ ('#form31' @ X2))), 351.46/45.78 inference('demod', [status(thm)], [zip_derived_cl122, zip_derived_cl38])). 351.46/45.78 thf(zip_derived_cl66, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( ('#form31' @ X2) 351.46/45.78 | ~ (((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 (((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((Y2 @ X2) & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl67, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 (~ (((((!!) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))) & 351.46/45.78 (Y1 @ X4))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 ((((('#sk4' @ Y2) = (Y0))) & 351.46/45.78 (Y1 @ Y2))))))))))) => 351.46/45.78 (((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((Y1 @ X2) & 351.46/45.78 (((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 ((((('#sk4' @ Y2) = (Y0))) & 351.46/45.78 (Y1 @ Y2)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))) 351.46/45.78 | ('#form31' @ X2))), 351.46/45.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl66])). 351.46/45.78 thf(zip_derived_cl75, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 (~ (((!!) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))) & 351.46/45.78 (Y1 @ X4))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 ((((('#sk4' @ Y2) = (Y0))) & 351.46/45.78 (Y1 @ Y2))))))))))) => 351.46/45.78 (((!!) @ (^[Y1 : a > $o]: 351.46/45.78 (((((Y1 @ X2) & 351.46/45.78 (((!!) @ (^[Y2 : a]: 351.46/45.78 (((Y1 @ Y2) => (Y1 @ 351.46/45.78 ('#sk3' @ Y2))))))))) => 351.46/45.78 (((??) @ (^[Y2 : a]: 351.46/45.78 ((((('#sk4' @ Y2) = (Y0))) & 351.46/45.78 (Y1 @ Y2)))))))))))))))) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 351.46/45.78 | ('#form31' @ X2))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl67])). 351.46/45.78 thf(zip_derived_cl83, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 (~ (((((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 351.46/45.78 (Y0 @ X4))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = ('#sk40' @ X2 @ X4))) & 351.46/45.78 (Y0 @ Y1))))))))))) => 351.46/45.78 (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((Y0 @ X2) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = ('#sk40' @ X2 @ X4))) & 351.46/45.78 (Y0 @ Y1))))))))))))) 351.46/45.78 | ('#form31' @ X2) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl75])). 351.46/45.78 thf(zip_derived_cl97, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 (~ (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((Y0 @ X2) & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = ('#sk40' @ X2 @ X4))) & 351.46/45.78 (Y0 @ Y1))))))))))) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 351.46/45.78 | ('#form31' @ X2))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl83])). 351.46/45.78 thf(zip_derived_cl108, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 (~ ((((('#sk64' @ X2 @ X4 @ X2) & 351.46/45.78 (((!!) @ (^[Y0 : a]: 351.46/45.78 ((('#sk64' @ X2 @ X4 @ Y0) => ('#sk64' @ X2 @ X4 @ 351.46/45.78 ('#sk3' @ Y0))))))))) => 351.46/45.78 (((??) @ (^[Y0 : a]: 351.46/45.78 ((((('#sk4' @ Y0) = ('#sk40' @ X2 @ X4))) & 351.46/45.78 ('#sk64' @ X2 @ X4 @ Y0)))))))) 351.46/45.78 | ('#form31' @ X2) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl97])). 351.46/45.78 thf(zip_derived_cl125, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 ( ((('#sk64' @ X2 @ X4 @ X2) & 351.46/45.78 (((!!) @ (^[Y0 : a]: 351.46/45.78 ((('#sk64' @ X2 @ X4 @ Y0) => ('#sk64' @ X2 @ X4 @ 351.46/45.78 ('#sk3' @ Y0))))))))) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 351.46/45.78 | ('#form31' @ X2))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 351.46/45.78 thf(zip_derived_cl133, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 ( ('#sk64' @ X2 @ X4 @ X2) 351.46/45.78 | ('#form31' @ X2) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl125])). 351.46/45.78 thf(zip_derived_cl109, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( ((('#sk4' @ ('#sk51' @ X2 @ X4)) = ('#sk29' @ X2))) 351.46/45.78 | ~ ('#form44' @ X2 @ X4) 351.46/45.78 | ('#form26') 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl98])). 351.46/45.78 thf(zip_derived_cl127, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ((('#sk4' @ ('#sk51' @ X2 @ X4)) = ('#sk29' @ X2)) 351.46/45.78 | ~ ('#form44' @ X2 @ X4) 351.46/45.78 | ('#form26') 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')))), 351.46/45.78 inference('simplify nested equalities', [status(thm)], 351.46/45.78 [zip_derived_cl109])). 351.46/45.78 thf(zip_derived_cl103, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ (((??) @ (^[Y0 : a]: 351.46/45.78 ((((('#sk4' @ Y0) = (X2))) & ('#sk45' @ X2 @ Y0)))))) 351.46/45.78 | (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((Y0 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))) 351.46/45.78 | ('#form24') 351.46/45.78 | ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])). 351.46/45.78 thf(zip_derived_cl117, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ ('#form72' @ X2) 351.46/45.78 | (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((Y0 @ '#sk25') & 351.46/45.78 (((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl119, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( ('#form72' @ X2) 351.46/45.78 | ('#form26') 351.46/45.78 | ('#form24') 351.46/45.78 | ~ (((??) @ (^[Y0 : a]: 351.46/45.78 ((((('#sk4' @ Y0) = (X2))) & ('#sk45' @ X2 @ Y0)))))))), 351.46/45.78 inference('renaming', [status(thm)], 351.46/45.78 [zip_derived_cl103, zip_derived_cl117])). 351.46/45.78 thf(zip_derived_cl129, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 (~ ((((('#sk4' @ X4) = (X2))) & ('#sk45' @ X2 @ X4))) 351.46/45.78 | ('#form24') 351.46/45.78 | ('#form26') 351.46/45.78 | ('#form72' @ X2))), 351.46/45.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl119])). 351.46/45.78 thf(zip_derived_cl136, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 (~ ((('#sk4' @ X4) = (X2))) 351.46/45.78 | ~ ('#sk45' @ X2 @ X4) 351.46/45.78 | ('#form72' @ X2) 351.46/45.78 | ('#form26') 351.46/45.78 | ('#form24'))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl129])). 351.46/45.78 thf(zip_derived_cl142, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 ((('#sk4' @ X4) != (X2)) 351.46/45.78 | ~ ('#sk45' @ X2 @ X4) 351.46/45.78 | ('#form72' @ X2) 351.46/45.78 | ('#form26') 351.46/45.78 | ('#form24'))), 351.46/45.78 inference('simplify nested equalities', [status(thm)], 351.46/45.78 [zip_derived_cl136])). 351.46/45.78 thf(zip_derived_cl143, plain, 351.46/45.78 (![X4 : a]: 351.46/45.78 ( ('#form24') 351.46/45.78 | ('#form26') 351.46/45.78 | ('#form72' @ ('#sk4' @ X4)) 351.46/45.78 | ~ ('#sk45' @ ('#sk4' @ X4) @ X4))), 351.46/45.78 inference('simplify', [status(thm)], [zip_derived_cl142])). 351.46/45.78 thf(zip_derived_cl38, plain, (~ ('#form24')), 351.46/45.78 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 351.46/45.78 thf(zip_derived_cl164, plain, 351.46/45.78 (![X4 : a]: 351.46/45.78 ( ('#form26') 351.46/45.78 | ('#form72' @ ('#sk4' @ X4)) 351.46/45.78 | ~ ('#sk45' @ ('#sk4' @ X4) @ X4))), 351.46/45.78 inference('demod', [status(thm)], [zip_derived_cl143, zip_derived_cl38])). 351.46/45.78 thf(zip_derived_cl59, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ ('#sk6' @ ('#sk28' @ X2)) 351.46/45.78 | ~ (((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 (((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((Y2 @ X2) & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))) 351.46/45.78 | ('#form24') 351.46/45.78 | ~ ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 351.46/45.78 thf(zip_derived_cl66, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 ( ('#form31' @ X2) 351.46/45.78 | ~ (((??) @ (^[Y0 : a]: 351.46/45.78 (((((!!) @ (^[Y1 : a]: 351.46/45.78 (((((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))) & 351.46/45.78 (Y2 @ Y0))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3))))))))))) => 351.46/45.78 (((!!) @ (^[Y2 : a > $o]: 351.46/45.78 (((((Y2 @ X2) & 351.46/45.78 (((!!) @ (^[Y3 : a]: 351.46/45.78 ( 351.46/45.78 ( 351.46/45.78 (Y2 @ 351.46/45.78 Y3) => 351.46/45.78 (Y2 @ 351.46/45.78 ( 351.46/45.78 '#sk3' @ 351.46/45.78 Y3))))))))) => 351.46/45.78 (((??) @ (^[Y3 : a]: 351.46/45.78 (((( 351.46/45.78 ('#sk4' @ 351.46/45.78 Y3) = 351.46/45.78 (Y1))) & 351.46/45.78 (Y2 @ Y3)))))))))))))))) & 351.46/45.78 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl69, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ ('#form31' @ X2) 351.46/45.78 | ~ ('#form26') 351.46/45.78 | ('#form24') 351.46/45.78 | ~ ('#sk6' @ ('#sk28' @ X2)))), 351.46/45.78 inference('renaming', [status(thm)], [zip_derived_cl59, zip_derived_cl66])). 351.46/45.78 thf(zip_derived_cl38, plain, (~ ('#form24')), 351.46/45.78 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 351.46/45.78 thf(zip_derived_cl160, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ ('#form31' @ X2) | ~ ('#form26') | ~ ('#sk6' @ ('#sk28' @ X2)))), 351.46/45.78 inference('demod', [status(thm)], [zip_derived_cl69, zip_derived_cl38])). 351.46/45.78 thf(zip_derived_cl123, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( ((('#sk4' @ ('#sk63' @ X2 @ X4)) = ('#sk28' @ X2))) 351.46/45.78 | ~ ('#form44' @ X2 @ X4) 351.46/45.78 | ('#form24') 351.46/45.78 | ~ ('#form26') 351.46/45.78 | ~ ('#form31' @ X2))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])). 351.46/45.78 thf(zip_derived_cl131, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ((('#sk4' @ ('#sk63' @ X2 @ X4)) = ('#sk28' @ X2)) 351.46/45.78 | ~ ('#form44' @ X2 @ X4) 351.46/45.78 | ('#form24') 351.46/45.78 | ~ ('#form26') 351.46/45.78 | ~ ('#form31' @ X2))), 351.46/45.78 inference('simplify nested equalities', [status(thm)], 351.46/45.78 [zip_derived_cl123])). 351.46/45.78 thf(zip_derived_cl38, plain, (~ ('#form24')), 351.46/45.78 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 351.46/45.78 thf(zip_derived_cl166, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ((('#sk4' @ ('#sk63' @ X2 @ X4)) = ('#sk28' @ X2)) 351.46/45.78 | ~ ('#form44' @ X2 @ X4) 351.46/45.78 | ~ ('#form26') 351.46/45.78 | ~ ('#form31' @ X2))), 351.46/45.78 inference('demod', [status(thm)], [zip_derived_cl131, zip_derived_cl38])). 351.46/45.78 thf(zip_derived_cl81, plain, 351.46/45.78 (![X2 : a]: 351.46/45.78 (~ (((??) @ (^[Y0 : a]: 351.46/45.78 ((((('#sk4' @ Y0) = (X2))) & ('#sk33' @ X2 @ Y0)))))) 351.46/45.78 | ('#sk6' @ X2) 351.46/45.78 | ~ ('#form26'))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 351.46/45.78 thf(zip_derived_cl94, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 (~ ((((('#sk4' @ X4) = (X2))) & ('#sk33' @ X2 @ X4))) 351.46/45.78 | ~ ('#form26') 351.46/45.78 | ('#sk6' @ X2))), 351.46/45.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl81])). 351.46/45.78 thf(zip_derived_cl104, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 (~ ((('#sk4' @ X4) = (X2))) 351.46/45.78 | ~ ('#sk33' @ X2 @ X4) 351.46/45.78 | ('#sk6' @ X2) 351.46/45.78 | ~ ('#form26'))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl94])). 351.46/45.78 thf(zip_derived_cl120, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 ((('#sk4' @ X4) != (X2)) 351.46/45.78 | ~ ('#sk33' @ X2 @ X4) 351.46/45.78 | ('#sk6' @ X2) 351.46/45.78 | ~ ('#form26'))), 351.46/45.78 inference('simplify nested equalities', [status(thm)], 351.46/45.78 [zip_derived_cl104])). 351.46/45.78 thf(zip_derived_cl121, plain, 351.46/45.78 (![X4 : a]: 351.46/45.78 (~ ('#form26') 351.46/45.78 | ('#sk6' @ ('#sk4' @ X4)) 351.46/45.78 | ~ ('#sk33' @ ('#sk4' @ X4) @ X4))), 351.46/45.78 inference('simplify', [status(thm)], [zip_derived_cl120])). 351.46/45.78 thf(zip_derived_cl84, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( ('#form44' @ X2 @ X4) 351.46/45.78 | ~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl85, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ (((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) 351.46/45.78 | ~ (X4 @ X2) 351.46/45.78 | ('#form44' @ X2 @ X4))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl84])). 351.46/45.78 thf(zip_derived_cl99, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ (((X4 @ ('#sk18' @ X4)) => (X4 @ ('#sk3' @ ('#sk18' @ X4))))) 351.46/45.78 | ('#form44' @ X2 @ X4) 351.46/45.78 | ~ (X4 @ X2))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl85])). 351.46/45.78 thf(zip_derived_cl111, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( (X4 @ ('#sk18' @ X4)) | ~ (X4 @ X2) | ('#form44' @ X2 @ X4))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl99])). 351.46/45.78 thf(zip_derived_cl134, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 ( (((!!) @ (^[Y0 : a]: 351.46/45.78 ((('#sk64' @ X2 @ X4 @ Y0) => ('#sk64' @ X2 @ X4 @ 351.46/45.78 ('#sk3' @ Y0))))))) 351.46/45.78 | ('#form31' @ X2) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl125])). 351.46/45.78 thf(zip_derived_cl140, plain, 351.46/45.78 (![X2 : a, X4 : a, X6 : a]: 351.46/45.78 ( ((('#sk64' @ X2 @ X4 @ X6) => ('#sk64' @ X2 @ X4 @ ('#sk3' @ X6)))) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 351.46/45.78 | ('#form31' @ X2))), 351.46/45.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl134])). 351.46/45.78 thf(zip_derived_cl147, plain, 351.46/45.78 (![X2 : a, X4 : a, X6 : a]: 351.46/45.78 (~ ('#sk64' @ X2 @ X4 @ X6) 351.46/45.78 | ('#sk64' @ X2 @ X4 @ ('#sk3' @ X6)) 351.46/45.78 | ('#form31' @ X2) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl140])). 351.46/45.78 thf(zip_derived_cl112, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ (X4 @ ('#sk3' @ ('#sk18' @ X4))) 351.46/45.78 | ~ (X4 @ X2) 351.46/45.78 | ('#form44' @ X2 @ X4))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl99])). 351.46/45.78 thf(zip_derived_cl96, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 ( (((!!) @ (^[Y0 : a > $o]: 351.46/45.78 (((((((!!) @ (^[Y1 : a]: 351.46/45.78 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 351.46/45.78 (Y0 @ X4))) => 351.46/45.78 (((??) @ (^[Y1 : a]: 351.46/45.78 ((((('#sk4' @ Y1) = ('#sk40' @ X2 @ X4))) & 351.46/45.78 (Y0 @ Y1))))))))))) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 351.46/45.78 | ('#form31' @ X2))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl83])). 351.46/45.78 thf(zip_derived_cl107, plain, 351.46/45.78 (![X2 : a, X4 : a, X6 : a > $o]: 351.46/45.78 ( (((((((!!) @ (^[Y0 : a]: (((X6 @ Y0) => (X6 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X6 @ X4))) => 351.46/45.78 (((??) @ (^[Y0 : a]: 351.46/45.78 ((((('#sk4' @ Y0) = ('#sk40' @ X2 @ X4))) & (X6 @ Y0)))))))) 351.46/45.78 | ('#form31' @ X2) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 351.46/45.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl96])). 351.46/45.78 thf(zip_derived_cl124, plain, 351.46/45.78 (![X2 : a, X4 : a, X6 : a > $o]: 351.46/45.78 (~ (((((!!) @ (^[Y0 : a]: (((X6 @ Y0) => (X6 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X6 @ X4))) 351.46/45.78 | (((??) @ (^[Y0 : a]: 351.46/45.78 ((((('#sk4' @ Y0) = ('#sk40' @ X2 @ X4))) & (X6 @ Y0)))))) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 351.46/45.78 | ('#form31' @ X2))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])). 351.46/45.78 thf(zip_derived_cl87, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 (~ ('#form44' @ X2 @ X4) 351.46/45.78 | (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl84, plain, 351.46/45.78 (![X2 : a, X4 : a > $o]: 351.46/45.78 ( ('#form44' @ X2 @ X4) 351.46/45.78 | ~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 351.46/45.78 (X4 @ X2))))), 351.46/45.78 define([status(thm)])). 351.46/45.78 thf(zip_derived_cl132, plain, 351.46/45.78 (![X2 : a, X4 : a, X6 : a > $o]: 351.46/45.78 (~ ('#form44' @ X4 @ (^[Y0 : a]: (X6 @ Y0))) 351.46/45.78 | ('#form31' @ X2) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 351.46/45.78 | (((??) @ (^[Y0 : a]: 351.46/45.78 ((((('#sk4' @ Y0) = ('#sk40' @ X2 @ X4))) & (X6 @ Y0)))))))), 351.46/45.78 inference('renaming', [status(thm)], 351.46/45.78 [zip_derived_cl124, zip_derived_cl87, zip_derived_cl84])). 351.46/45.78 thf(zip_derived_cl138, plain, 351.46/45.78 (![X2 : a, X4 : a, X6 : a > $o]: 351.46/45.78 (~ ('#form44' @ X4 @ X6) 351.46/45.78 | ('#form31' @ X2) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 351.46/45.78 | (((??) @ (^[Y0 : a]: 351.46/45.78 ((((('#sk4' @ Y0) = ('#sk40' @ X2 @ X4))) & (X6 @ Y0)))))))), 351.46/45.78 inference('ho_norm', [status(thm)], [zip_derived_cl132])). 351.46/45.78 thf(zip_derived_cl139, plain, 351.46/45.78 (![X2 : a, X4 : a, X6 : a > $o]: 351.46/45.78 ( ((((('#sk4' @ ('#sk109' @ X2 @ X4 @ X6)) = ('#sk40' @ X2 @ X4))) & 351.46/45.78 (X6 @ ('#sk109' @ X2 @ X4 @ X6)))) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 351.46/45.78 | ('#form31' @ X2) 351.46/45.78 | ~ ('#form44' @ X4 @ X6))), 351.46/45.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl138])). 351.46/45.78 thf(zip_derived_cl145, plain, 351.46/45.78 (![X2 : a, X4 : a, X6 : a > $o]: 351.46/45.78 ( ((('#sk4' @ ('#sk109' @ X2 @ X4 @ X6)) = ('#sk40' @ X2 @ X4))) 351.46/45.78 | ~ ('#form44' @ X4 @ X6) 351.46/45.78 | ('#form31' @ X2) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl139])). 351.46/45.78 thf(zip_derived_cl151, plain, 351.46/45.78 (![X2 : a, X4 : a, X6 : a > $o]: 351.46/45.78 ((('#sk4' @ ('#sk109' @ X2 @ X4 @ X6)) = ('#sk40' @ X2 @ X4)) 351.46/45.78 | ~ ('#form44' @ X4 @ X6) 351.46/45.78 | ('#form31' @ X2) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 351.46/45.78 inference('simplify nested equalities', [status(thm)], 351.46/45.78 [zip_derived_cl145])). 351.46/45.78 thf(zip_derived_cl146, plain, 351.46/45.78 (![X2 : a, X4 : a, X6 : a > $o]: 351.46/45.78 ( (X6 @ ('#sk109' @ X2 @ X4 @ X6)) 351.46/45.78 | ~ ('#form44' @ X4 @ X6) 351.46/45.78 | ('#form31' @ X2) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl139])). 351.46/45.78 thf(zip_derived_cl126, plain, 351.46/45.78 (![X2 : a, X4 : a]: 351.46/45.78 (~ (((??) @ (^[Y0 : a]: 351.46/45.78 ((((('#sk4' @ Y0) = ('#sk40' @ X2 @ X4))) & ('#sk64' @ 351.46/45.78 X2 @ X4 @ Y0)))))) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 351.46/45.78 | ('#form31' @ X2))), 351.46/45.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 351.46/45.78 thf(zip_derived_cl135, plain, 351.46/45.78 (![X2 : a, X4 : a, X6 : a]: 351.46/45.78 (~ ((((('#sk4' @ X6) = ('#sk40' @ X2 @ X4))) & ('#sk64' @ X2 @ X4 @ 351.46/45.78 X6))) 351.46/45.78 | ('#form31' @ X2) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 351.46/45.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl126])). 351.46/45.78 thf(zip_derived_cl141, plain, 351.46/45.78 (![X2 : a, X4 : a, X6 : a]: 351.46/45.78 (~ ((('#sk4' @ X6) = ('#sk40' @ X2 @ X4))) 351.46/45.78 | ~ ('#sk64' @ X2 @ X4 @ X6) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 351.46/45.78 | ('#form31' @ X2))), 351.46/45.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl135])). 351.46/45.78 thf(zip_derived_cl148, plain, 351.46/45.78 (![X2 : a, X4 : a, X6 : a]: 351.46/45.78 ((('#sk4' @ X6) != ('#sk40' @ X2 @ X4)) 351.46/45.78 | ~ ('#sk64' @ X2 @ X4 @ X6) 351.46/45.78 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 351.46/45.78 | ('#form31' @ X2))), 351.46/45.78 inference('simplify nested equalities', [status(thm)], 351.46/45.78 [zip_derived_cl141])). 351.46/45.78 thf(zip_derived_cl10715, plain, ($false), 351.46/45.78 inference('eprover', [status(thm)], 351.46/45.78 [zip_derived_cl1283, zip_derived_cl157, zip_derived_cl154, 351.46/45.78 zip_derived_cl159, zip_derived_cl162, zip_derived_cl163, 351.46/45.78 zip_derived_cl113, zip_derived_cl161, zip_derived_cl158, 351.46/45.78 zip_derived_cl89, zip_derived_cl51, zip_derived_cl165, 351.46/45.78 zip_derived_cl93, zip_derived_cl110, zip_derived_cl167, 351.46/45.78 zip_derived_cl133, zip_derived_cl127, zip_derived_cl164, 351.46/45.78 zip_derived_cl160, zip_derived_cl166, zip_derived_cl121, 351.46/45.78 zip_derived_cl111, zip_derived_cl147, zip_derived_cl112, 351.46/45.78 zip_derived_cl151, zip_derived_cl146, zip_derived_cl148])). 351.46/45.78 351.46/45.78 % SZS output end Refutation 351.46/45.78 351.46/45.78 351.46/45.78 % Terminating... 352.18/46.00 % Runner terminated. 352.24/46.04 % Zipperpin 1.5 exiting 352.24/46.05 EOF