0.00/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.10 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.NoWwsVDrR8 true 0.08/0.28 % Computer : n021.cluster.edu 0.08/0.28 % Model : x86_64 x86_64 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.08/0.28 % Memory : 8042.1875MB 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64 0.08/0.28 % CPULimit : 1440 0.08/0.28 % WCLimit : 180 0.08/0.28 % DateTime : Mon Jul 3 10:48:37 EDT 2023 0.08/0.28 % CPUTime : 0.08/0.28 % Running portfolio for 1440 s 0.08/0.28 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.08/0.28 % Number of cores: 8 0.08/0.29 % Python version: Python 3.6.8 0.12/0.29 % Running in HO mode 0.13/0.57 % Total configuration time : 828 0.13/0.57 % Estimated wc time : 1656 0.13/0.57 % Estimated cpu time (8 cpus) : 207.0 0.13/0.59 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.13/0.59 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 1.08/0.62 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 1.10/0.63 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 1.10/0.63 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 1.10/0.63 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 1.10/0.64 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 1.10/0.64 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 237.60/30.43 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 344.16/44.52 % Solved by lams/30_b.l.sh. 344.16/44.52 % done 445 iterations in 13.950s 344.16/44.52 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 344.16/44.52 % SZS output start Refutation 344.16/44.52 thf(a_type, type, a: $tType). 344.16/44.52 thf('#sk109_type', type, '#sk109': a > a > (a > $o) > a). 344.16/44.52 thf('#sk28_type', type, '#sk28': a > a). 344.16/44.52 thf('#form127_type', type, '#form127': a > (a > $o) > $o). 344.16/44.52 thf('#form24_type', type, '#form24': $o). 344.16/44.52 thf('#sk27_type', type, '#sk27': a). 344.16/44.52 thf('#sk128_type', type, '#sk128': a > (a > $o) > a). 344.16/44.52 thf('#sk7_type', type, '#sk7': a). 344.16/44.52 thf('#sk45_type', type, '#sk45': a > a > $o). 344.16/44.52 thf('#sk64_type', type, '#sk64': a > a > a > $o). 344.16/44.52 thf('#form72_type', type, '#form72': a > $o). 344.16/44.52 thf('#sk30_type', type, '#sk30': a). 344.16/44.52 thf('#form44_type', type, '#form44': a > (a > $o) > $o). 344.16/44.52 thf('#sk2_type', type, '#sk2': a > a > a). 344.16/44.52 thf('#form26_type', type, '#form26': $o). 344.16/44.52 thf('#sk32_type', type, '#sk32': a > a > $o). 344.16/44.52 thf('#form31_type', type, '#form31': a > $o). 344.16/44.52 thf('#sk51_type', type, '#sk51': a > (a > $o) > a). 344.16/44.52 thf('#sk63_type', type, '#sk63': a > (a > $o) > a). 344.16/44.52 thf('#sk33_type', type, '#sk33': a > a > $o). 344.16/44.52 thf('#sk6_type', type, '#sk6': a > $o). 344.16/44.52 thf('#sk29_type', type, '#sk29': a > a). 344.16/44.52 thf('#sk25_type', type, '#sk25': a). 344.16/44.52 thf('#sk3_type', type, '#sk3': a > a). 344.16/44.52 thf('#sk4_type', type, '#sk4': a > a). 344.16/44.52 thf('#sk18_type', type, '#sk18': (a > $o) > a). 344.16/44.52 thf('#sk40_type', type, '#sk40': a > a > a). 344.16/44.52 thf('#sk1_type', type, '#sk1': a). 344.16/44.52 thf('#sk5_type', type, '#sk5': a > $o). 344.16/44.52 thf(cPU_X238A_pme, conjecture, 344.16/44.52 (![Z:a,P:( a > a > a ),L:( a > a ),R:( a > a ),F:( a > $o )]: 344.16/44.52 ( ( ( ( L @ Z ) = ( Z ) ) & ( ( R @ Z ) = ( Z ) ) & 344.16/44.52 ( ![Xx:a,Xy:a]: ( ( L @ ( P @ Xx @ Xy ) ) = ( Xx ) ) ) & 344.16/44.52 ( ![Xx:a,Xy:a]: ( ( R @ ( P @ Xx @ Xy ) ) = ( Xy ) ) ) & 344.16/44.52 ( ![X:( a > $o )]: 344.16/44.52 ( ( ?[Xt:a]: 344.16/44.52 ( ( X @ Xt ) & ( ![Xu:a]: ( ( X @ Xu ) => ( X @ ( L @ Xu ) ) ) ) ) ) => 344.16/44.52 ( X @ Z ) ) ) & 344.16/44.52 ( ![Xt:a]: 344.16/44.52 ( ( ( Xt ) = ( P @ ( L @ Xt ) @ ( R @ Xt ) ) ) <=> 344.16/44.52 ( ( Xt ) != ( Z ) ) ) ) ) => 344.16/44.52 ( ![X:( a > $o ),Xz:a]: 344.16/44.52 ( ( ?[Xx:a]: 344.16/44.52 ( ( ![Xx_6:a]: 344.16/44.52 ( ( ![X0:( a > $o )]: 344.16/44.52 ( ( ( ![Xz0:a]: ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) & 344.16/44.52 ( X0 @ Xx ) ) => 344.16/44.52 ( ?[Xv:a]: ( ( X0 @ Xv ) & ( ( R @ Xv ) = ( Xx_6 ) ) ) ) ) ) => 344.16/44.52 ( X @ Xx_6 ) ) ) & 344.16/44.52 ( ?[Xx_8:a]: 344.16/44.52 ( ( ![Xx_7:a]: 344.16/44.52 ( ( ![X0:( a > $o )]: 344.16/44.52 ( ( ( ![Xz0:a]: 344.16/44.52 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) & 344.16/44.52 ( X0 @ Xx_8 ) ) => 344.16/44.52 ( ?[Xv:a]: 344.16/44.52 ( ( ( R @ Xv ) = ( Xx_7 ) ) & ( X0 @ Xv ) ) ) ) ) => 344.16/44.52 ( ![X0:( a > $o )]: 344.16/44.52 ( ( ( X0 @ Xx ) & 344.16/44.52 ( ![Xz0:a]: 344.16/44.52 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) ) => 344.16/44.52 ( ?[Xv:a]: 344.16/44.52 ( ( ( R @ Xv ) = ( Xx_7 ) ) & ( X0 @ Xv ) ) ) ) ) ) ) & 344.16/44.52 ( F @ ( P @ Xx_8 @ Xz ) ) ) ) ) ) <=> 344.16/44.52 ( ?[Xx:a]: 344.16/44.52 ( ( F @ ( P @ Xx @ Xz ) ) & 344.16/44.52 ( ![Xx_5:a]: 344.16/44.52 ( ( ![X0:( a > $o )]: 344.16/44.52 ( ( ( ![Xz0:a]: ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) & 344.16/44.52 ( X0 @ Xx ) ) => 344.16/44.52 ( ?[Xv:a]: ( ( ( R @ Xv ) = ( Xx_5 ) ) & ( X0 @ Xv ) ) ) ) ) => 344.16/44.52 ( X @ Xx_5 ) ) ) ) ) ) ) ))). 344.16/44.52 thf(zf_stmt_0, negated_conjecture, 344.16/44.52 (~( ![Z:a,P:( a > a > a ),L:( a > a ),R:( a > a ),F:( a > $o )]: 344.16/44.52 ( ( ( ( L @ Z ) = ( Z ) ) & ( ( R @ Z ) = ( Z ) ) & 344.16/44.52 ( ![Xx:a,Xy:a]: ( ( L @ ( P @ Xx @ Xy ) ) = ( Xx ) ) ) & 344.16/44.52 ( ![Xx:a,Xy:a]: ( ( R @ ( P @ Xx @ Xy ) ) = ( Xy ) ) ) & 344.16/44.52 ( ![X:( a > $o )]: 344.16/44.52 ( ( ?[Xt:a]: 344.16/44.52 ( ( X @ Xt ) & 344.16/44.52 ( ![Xu:a]: ( ( X @ Xu ) => ( X @ ( L @ Xu ) ) ) ) ) ) => 344.16/44.52 ( X @ Z ) ) ) & 344.16/44.52 ( ![Xt:a]: 344.16/44.52 ( ( ( Xt ) = ( P @ ( L @ Xt ) @ ( R @ Xt ) ) ) <=> 344.16/44.52 ( ( Xt ) != ( Z ) ) ) ) ) => 344.16/44.52 ( ![X:( a > $o ),Xz:a]: 344.16/44.52 ( ( ?[Xx:a]: 344.16/44.52 ( ( ![Xx_6:a]: 344.16/44.52 ( ( ![X0:( a > $o )]: 344.16/44.52 ( ( ( ![Xz0:a]: 344.16/44.52 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) & 344.16/44.52 ( X0 @ Xx ) ) => 344.16/44.52 ( ?[Xv:a]: 344.16/44.52 ( ( X0 @ Xv ) & ( ( R @ Xv ) = ( Xx_6 ) ) ) ) ) ) => 344.16/44.52 ( X @ Xx_6 ) ) ) & 344.16/44.52 ( ?[Xx_8:a]: 344.16/44.52 ( ( ![Xx_7:a]: 344.16/44.52 ( ( ![X0:( a > $o )]: 344.16/44.52 ( ( ( ![Xz0:a]: 344.16/44.52 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) & 344.16/44.52 ( X0 @ Xx_8 ) ) => 344.16/44.52 ( ?[Xv:a]: 344.16/44.52 ( ( ( R @ Xv ) = ( Xx_7 ) ) & ( X0 @ Xv ) ) ) ) ) => 344.16/44.52 ( ![X0:( a > $o )]: 344.16/44.52 ( ( ( X0 @ Xx ) & 344.16/44.52 ( ![Xz0:a]: 344.16/44.52 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) ) => 344.16/44.52 ( ?[Xv:a]: 344.16/44.52 ( ( ( R @ Xv ) = ( Xx_7 ) ) & ( X0 @ Xv ) ) ) ) ) ) ) & 344.16/44.52 ( F @ ( P @ Xx_8 @ Xz ) ) ) ) ) ) <=> 344.16/44.52 ( ?[Xx:a]: 344.16/44.52 ( ( F @ ( P @ Xx @ Xz ) ) & 344.16/44.52 ( ![Xx_5:a]: 344.16/44.52 ( ( ![X0:( a > $o )]: 344.16/44.52 ( ( ( ![Xz0:a]: 344.16/44.52 ( ( X0 @ Xz0 ) => ( X0 @ ( L @ Xz0 ) ) ) ) & 344.16/44.52 ( X0 @ Xx ) ) => 344.16/44.52 ( ?[Xv:a]: 344.16/44.52 ( ( ( R @ Xv ) = ( Xx_5 ) ) & ( X0 @ Xv ) ) ) ) ) => 344.16/44.52 ( X @ Xx_5 ) ) ) ) ) ) ) ) )), 344.16/44.52 inference('cnf.neg', [status(esa)], [cPU_X238A_pme])). 344.16/44.52 thf(zip_derived_cl0, plain, 344.16/44.52 (~ (((!!) @ (^[Y0 : a]: 344.16/44.52 (((!!) @ (^[Y1 : a > a > a]: 344.16/44.52 (((!!) @ (^[Y2 : a > a]: 344.16/44.52 (((!!) @ (^[Y3 : a > a]: 344.16/44.52 (((!!) @ (^[Y4 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 ( 344.16/44.52 ( 344.16/44.52 (Y2 @ 344.16/44.52 Y0) = 344.16/44.52 (Y0))) & 344.16/44.52 ( 344.16/44.52 ( 344.16/44.52 (Y3 @ 344.16/44.52 Y0) = 344.16/44.52 (Y0))) & 344.16/44.52 ( 344.16/44.52 ( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (Y2 @ 344.16/44.52 ( 344.16/44.52 Y1 @ 344.16/44.52 Y5 @ Y6)) = 344.16/44.52 (Y5))))))))) & 344.16/44.52 ( 344.16/44.52 ( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (Y3 @ 344.16/44.52 ( 344.16/44.52 Y1 @ 344.16/44.52 Y5 @ Y6)) = 344.16/44.52 (Y6))))))))) & 344.16/44.52 ( 344.16/44.52 ( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (Y5 @ 344.16/44.52 Y6) & 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y7 : a]: 344.16/44.52 (( 344.16/44.52 (Y5 @ 344.16/44.52 Y7) => 344.16/44.52 (Y5 @ 344.16/44.52 ( 344.16/44.52 Y2 @ Y7)))))))))))) => 344.16/44.52 (Y5 @ Y0)))))) & 344.16/44.52 ( 344.16/44.52 ( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y5) = 344.16/44.52 (Y1 @ 344.16/44.52 ( 344.16/44.52 Y2 @ Y5) @ 344.16/44.52 ( 344.16/44.52 Y3 @ Y5)))) <=> 344.16/44.52 (( 344.16/44.52 (Y5) != 344.16/44.52 (Y0)))))))))) => 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a > $o]: 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y7 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y8 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y9 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y10 : a]: 344.16/44.52 (( 344.16/44.52 (Y9 @ 344.16/44.52 Y10) => 344.16/44.52 (Y9 @ 344.16/44.52 ( 344.16/44.52 Y2 @ Y10))))))) & 344.16/44.52 (Y9 @ Y7))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y10 : a]: 344.16/44.52 (( 344.16/44.52 (Y9 @ 344.16/44.52 Y10) & 344.16/44.52 (( 344.16/44.52 (Y3 @ 344.16/44.52 Y10) = 344.16/44.52 (Y8))))))))))))) => 344.16/44.52 (Y5 @ Y8)))))) & 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y8 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y9 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y10 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y11 : a]: 344.16/44.52 (( 344.16/44.52 (Y10 @ 344.16/44.52 Y11) => 344.16/44.52 (Y10 @ 344.16/44.52 ( 344.16/44.52 Y2 @ Y11))))))) & 344.16/44.52 (Y10 @ 344.16/44.52 Y8))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y11 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y3 @ 344.16/44.52 Y11) = 344.16/44.52 (Y9))) & 344.16/44.52 (Y10 @ 344.16/44.52 Y11))))))))))) => 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y10 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y10 @ 344.16/44.52 Y7) & 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y11 : a]: 344.16/44.52 (( 344.16/44.52 (Y10 @ 344.16/44.52 Y11) => 344.16/44.52 (Y10 @ 344.16/44.52 ( 344.16/44.52 Y2 @ Y11))))))))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y11 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y3 @ 344.16/44.52 Y11) = 344.16/44.52 (Y9))) & 344.16/44.52 (Y10 @ 344.16/44.52 Y11)))))))))))))))) & 344.16/44.52 (Y4 @ 344.16/44.52 ( 344.16/44.52 Y1 @ 344.16/44.52 Y8 @ Y6)))))))))))) <=> 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y7 : a]: 344.16/44.52 (( 344.16/44.52 (Y4 @ 344.16/44.52 ( 344.16/44.52 Y1 @ 344.16/44.52 Y7 @ Y6)) & 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y8 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y9 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y10 : a]: 344.16/44.52 (( 344.16/44.52 (Y9 @ 344.16/44.52 Y10) => 344.16/44.52 (Y9 @ 344.16/44.52 ( 344.16/44.52 Y2 @ Y10))))))) & 344.16/44.52 (Y9 @ Y7))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y10 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y3 @ 344.16/44.52 Y10) = 344.16/44.52 (Y8))) & 344.16/44.52 (Y9 @ 344.16/44.52 Y10))))))))))) => 344.16/44.52 (Y5 @ Y8))))))))))))))))))))))))))))))))))))), 344.16/44.52 inference('cnf', [status(esa)], [zf_stmt_0])). 344.16/44.52 thf(zip_derived_cl1, plain, 344.16/44.52 (~ (((!!) @ (^[Y0 : a > a > a]: 344.16/44.52 (((!!) @ (^[Y1 : a > a]: 344.16/44.52 (((!!) @ (^[Y2 : a > a]: 344.16/44.52 (((!!) @ (^[Y3 : a > $o]: 344.16/44.52 (((((((Y1 @ '#sk1') = 344.16/44.52 ('#sk1'))) & 344.16/44.52 (((Y2 @ '#sk1') = 344.16/44.52 ('#sk1'))) & 344.16/44.52 (((!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (((!!) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (Y1 @ 344.16/44.52 ( 344.16/44.52 Y0 @ 344.16/44.52 Y4 @ Y5)) = 344.16/44.52 (Y4))))))))) & 344.16/44.52 (((!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (((!!) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (Y2 @ 344.16/44.52 ( 344.16/44.52 Y0 @ 344.16/44.52 Y4 @ Y5)) = 344.16/44.52 (Y5))))))))) & 344.16/44.52 (((!!) @ ( 344.16/44.52 ^[Y4 : a > $o]: 344.16/44.52 (((((??) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (Y4 @ 344.16/44.52 Y5) & 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (Y4 @ 344.16/44.52 Y6) => 344.16/44.52 (Y4 @ 344.16/44.52 ( 344.16/44.52 Y1 @ Y6)))))))))))) => 344.16/44.52 (Y4 @ 344.16/44.52 '#sk1')))))) & 344.16/44.52 (((!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (((((Y4) = 344.16/44.52 (Y0 @ 344.16/44.52 (Y1 @ Y4) @ 344.16/44.52 (Y2 @ Y4)))) <=> 344.16/44.52 (((Y4) != 344.16/44.52 ('#sk1')))))))))) => 344.16/44.52 (((!!) @ (^[Y4 : a > $o]: 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y7 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y8 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y9 : a]: 344.16/44.52 (( 344.16/44.52 (Y8 @ 344.16/44.52 Y9) => 344.16/44.52 (Y8 @ 344.16/44.52 ( 344.16/44.52 Y1 @ Y9))))))) & 344.16/44.52 (Y8 @ Y6))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y9 : a]: 344.16/44.52 (( 344.16/44.52 (Y8 @ 344.16/44.52 Y9) & 344.16/44.52 (( 344.16/44.52 (Y2 @ 344.16/44.52 Y9) = 344.16/44.52 (Y7))))))))))))) => 344.16/44.52 (Y4 @ Y7)))))) & 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y7 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y8 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y9 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y10 : a]: 344.16/44.52 (( 344.16/44.52 (Y9 @ 344.16/44.52 Y10) => 344.16/44.52 (Y9 @ 344.16/44.52 ( 344.16/44.52 Y1 @ Y10))))))) & 344.16/44.52 (Y9 @ Y7))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y10 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y2 @ 344.16/44.52 Y10) = 344.16/44.52 (Y8))) & 344.16/44.52 (Y9 @ 344.16/44.52 Y10))))))))))) => 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y9 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y9 @ 344.16/44.52 Y6) & 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y10 : a]: 344.16/44.52 (( 344.16/44.52 (Y9 @ 344.16/44.52 Y10) => 344.16/44.52 (Y9 @ 344.16/44.52 ( 344.16/44.52 Y1 @ Y10))))))))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y10 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y2 @ 344.16/44.52 Y10) = 344.16/44.52 (Y8))) & 344.16/44.52 (Y9 @ 344.16/44.52 Y10)))))))))))))))) & 344.16/44.52 (Y3 @ 344.16/44.52 ( 344.16/44.52 Y0 @ 344.16/44.52 Y7 @ Y5)))))))))))) <=> 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (Y3 @ 344.16/44.52 ( 344.16/44.52 Y0 @ 344.16/44.52 Y6 @ Y5)) & 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y7 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y8 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y9 : a]: 344.16/44.52 (( 344.16/44.52 (Y8 @ 344.16/44.52 Y9) => 344.16/44.52 (Y8 @ 344.16/44.52 ( 344.16/44.52 Y1 @ Y9))))))) & 344.16/44.52 (Y8 @ Y6))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y9 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y2 @ 344.16/44.52 Y9) = 344.16/44.52 (Y7))) & 344.16/44.52 (Y8 @ Y9))))))))))) => 344.16/44.52 (Y4 @ Y7)))))))))))))))))))))))))))))))))), 344.16/44.52 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 344.16/44.52 thf(zip_derived_cl2, plain, 344.16/44.52 (~ (((!!) @ (^[Y0 : a > a]: 344.16/44.52 (((!!) @ (^[Y1 : a > a]: 344.16/44.52 (((!!) @ (^[Y2 : a > $o]: 344.16/44.52 (((((((Y0 @ '#sk1') = ('#sk1'))) & 344.16/44.52 (((Y1 @ '#sk1') = ('#sk1'))) & 344.16/44.52 (((!!) @ (^[Y3 : a]: 344.16/44.52 (((!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (((Y0 @ 344.16/44.52 ('#sk2' @ 344.16/44.52 Y3 @ Y4)) = 344.16/44.52 (Y3))))))))) & 344.16/44.52 (((!!) @ (^[Y3 : a]: 344.16/44.52 (((!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (((Y1 @ 344.16/44.52 ('#sk2' @ 344.16/44.52 Y3 @ Y4)) = 344.16/44.52 (Y4))))))))) & 344.16/44.52 (((!!) @ (^[Y3 : a > $o]: 344.16/44.52 (((((??) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (((Y3 @ 344.16/44.52 Y4) & 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (Y3 @ 344.16/44.52 Y5) => 344.16/44.52 (Y3 @ 344.16/44.52 ( 344.16/44.52 Y0 @ Y5)))))))))))) => 344.16/44.52 (Y3 @ '#sk1')))))) & 344.16/44.52 (((!!) @ (^[Y3 : a]: 344.16/44.52 (((((Y3) = 344.16/44.52 ('#sk2' @ 344.16/44.52 (Y0 @ Y3) @ 344.16/44.52 (Y1 @ Y3)))) <=> 344.16/44.52 (((Y3) != 344.16/44.52 ('#sk1')))))))))) => 344.16/44.52 (((!!) @ (^[Y3 : a > $o]: 344.16/44.52 (((!!) @ (^[Y4 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y7 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y8 : a]: 344.16/44.52 (( 344.16/44.52 (Y7 @ 344.16/44.52 Y8) => 344.16/44.52 (Y7 @ 344.16/44.52 ( 344.16/44.52 Y0 @ Y8))))))) & 344.16/44.52 (Y7 @ Y5))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y8 : a]: 344.16/44.52 (( 344.16/44.52 (Y7 @ 344.16/44.52 Y8) & 344.16/44.52 (( 344.16/44.52 (Y1 @ 344.16/44.52 Y8) = 344.16/44.52 (Y6))))))))))))) => 344.16/44.52 (Y3 @ Y6)))))) & 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y7 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y8 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y9 : a]: 344.16/44.52 (( 344.16/44.52 (Y8 @ 344.16/44.52 Y9) => 344.16/44.52 (Y8 @ 344.16/44.52 ( 344.16/44.52 Y0 @ Y9))))))) & 344.16/44.52 (Y8 @ Y6))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y9 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y1 @ 344.16/44.52 Y9) = 344.16/44.52 (Y7))) & 344.16/44.52 (Y8 @ Y9))))))))))) => 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y8 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y8 @ 344.16/44.52 Y5) & 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y9 : a]: 344.16/44.52 (( 344.16/44.52 (Y8 @ 344.16/44.52 Y9) => 344.16/44.52 (Y8 @ 344.16/44.52 ( 344.16/44.52 Y0 @ Y9))))))))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y9 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y1 @ 344.16/44.52 Y9) = 344.16/44.52 (Y7))) & 344.16/44.52 (Y8 @ Y9)))))))))))))))) & 344.16/44.52 (Y2 @ 344.16/44.52 ( 344.16/44.52 '#sk2' @ 344.16/44.52 Y6 @ Y4)))))))))))) <=> 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (Y2 @ 344.16/44.52 ( 344.16/44.52 '#sk2' @ 344.16/44.52 Y5 @ Y4)) & 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y7 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y8 : a]: 344.16/44.52 (( 344.16/44.52 (Y7 @ 344.16/44.52 Y8) => 344.16/44.52 (Y7 @ 344.16/44.52 ( 344.16/44.52 Y0 @ Y8))))))) & 344.16/44.52 (Y7 @ Y5))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y8 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y1 @ 344.16/44.52 Y8) = 344.16/44.52 (Y6))) & 344.16/44.52 (Y7 @ Y8))))))))))) => 344.16/44.52 (Y3 @ Y6))))))))))))))))))))))))))))))), 344.16/44.52 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 344.16/44.52 thf(zip_derived_cl3, plain, 344.16/44.52 (~ (((!!) @ (^[Y0 : a > a]: 344.16/44.52 (((!!) @ (^[Y1 : a > $o]: 344.16/44.52 ((((((('#sk3' @ '#sk1') = ('#sk1'))) & 344.16/44.52 (((Y0 @ '#sk1') = ('#sk1'))) & 344.16/44.52 (((!!) @ (^[Y2 : a]: 344.16/44.52 (((!!) @ (^[Y3 : a]: 344.16/44.52 ((('#sk3' @ 344.16/44.52 ('#sk2' @ Y2 @ 344.16/44.52 Y3)) = 344.16/44.52 (Y2))))))))) & 344.16/44.52 (((!!) @ (^[Y2 : a]: 344.16/44.52 (((!!) @ (^[Y3 : a]: 344.16/44.52 (((Y0 @ 344.16/44.52 ('#sk2' @ Y2 @ 344.16/44.52 Y3)) = 344.16/44.52 (Y3))))))))) & 344.16/44.52 (((!!) @ (^[Y2 : a > $o]: 344.16/44.52 (((((??) @ (^[Y3 : a]: 344.16/44.52 (((Y2 @ Y3) & 344.16/44.52 (((!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (( 344.16/44.52 (Y2 @ 344.16/44.52 Y4) => 344.16/44.52 (Y2 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y4)))))))))))) => 344.16/44.52 (Y2 @ '#sk1')))))) & 344.16/44.52 (((!!) @ (^[Y2 : a]: 344.16/44.52 (((((Y2) = ('#sk2' @ 344.16/44.52 ('#sk3' @ Y2) @ (Y0 @ Y2)))) <=> 344.16/44.52 (((Y2) != ('#sk1')))))))))) => 344.16/44.52 (((!!) @ (^[Y2 : a > $o]: 344.16/44.52 (((!!) @ (^[Y3 : a]: 344.16/44.52 (((((??) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (((((!!) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y6 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y7 : a]: 344.16/44.52 (( 344.16/44.52 (Y6 @ 344.16/44.52 Y7) => 344.16/44.52 (Y6 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y7))))))) & 344.16/44.52 (Y6 @ Y4))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y7 : a]: 344.16/44.52 (( 344.16/44.52 (Y6 @ 344.16/44.52 Y7) & 344.16/44.52 (( 344.16/44.52 (Y0 @ 344.16/44.52 Y7) = 344.16/44.52 (Y5))))))))))))) => 344.16/44.52 (Y2 @ Y5)))))) & 344.16/44.52 (((??) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y7 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y8 : a]: 344.16/44.52 (( 344.16/44.52 (Y7 @ 344.16/44.52 Y8) => 344.16/44.52 (Y7 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y8))))))) & 344.16/44.52 (Y7 @ Y5))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y8 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y0 @ 344.16/44.52 Y8) = 344.16/44.52 (Y6))) & 344.16/44.52 (Y7 @ Y8))))))))))) => 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y7 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y7 @ 344.16/44.52 Y4) & 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y8 : a]: 344.16/44.52 (( 344.16/44.52 (Y7 @ 344.16/44.52 Y8) => 344.16/44.52 (Y7 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y8))))))))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y8 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y0 @ 344.16/44.52 Y8) = 344.16/44.52 (Y6))) & 344.16/44.52 (Y7 @ Y8)))))))))))))))) & 344.16/44.52 (Y1 @ 344.16/44.52 ( 344.16/44.52 '#sk2' @ 344.16/44.52 Y5 @ Y3)))))))))))) <=> 344.16/44.52 (((??) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (((Y1 @ 344.16/44.52 ('#sk2' @ 344.16/44.52 Y4 @ Y3)) & 344.16/44.52 (((!!) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y6 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y7 : a]: 344.16/44.52 (( 344.16/44.52 (Y6 @ 344.16/44.52 Y7) => 344.16/44.52 (Y6 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y7))))))) & 344.16/44.52 (Y6 @ Y4))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y7 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y0 @ 344.16/44.52 Y7) = 344.16/44.52 (Y5))) & 344.16/44.52 (Y6 @ Y7))))))))))) => 344.16/44.52 (Y2 @ Y5)))))))))))))))))))))))))))), 344.16/44.52 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 344.16/44.52 thf(zip_derived_cl4, plain, 344.16/44.52 (~ (((!!) @ (^[Y0 : a > $o]: 344.16/44.52 ((((((('#sk3' @ '#sk1') = ('#sk1'))) & 344.16/44.52 ((('#sk4' @ '#sk1') = ('#sk1'))) & 344.16/44.52 (((!!) @ (^[Y1 : a]: 344.16/44.52 (((!!) @ (^[Y2 : a]: 344.16/44.52 ((('#sk3' @ 344.16/44.52 ('#sk2' @ Y1 @ Y2)) = (Y1))))))))) & 344.16/44.52 (((!!) @ (^[Y1 : a]: 344.16/44.52 (((!!) @ (^[Y2 : a]: 344.16/44.52 ((('#sk4' @ 344.16/44.52 ('#sk2' @ Y1 @ Y2)) = (Y2))))))))) & 344.16/44.52 (((!!) @ (^[Y1 : a > $o]: 344.16/44.52 (((((??) @ (^[Y2 : a]: 344.16/44.52 (((Y1 @ Y2) & 344.16/44.52 (((!!) @ (^[Y3 : a]: 344.16/44.52 (((Y1 @ Y3) => 344.16/44.52 (Y1 @ 344.16/44.52 ('#sk3' @ Y3)))))))))))) => 344.16/44.52 (Y1 @ '#sk1')))))) & 344.16/44.52 (((!!) @ (^[Y1 : a]: 344.16/44.52 (((((Y1) = ('#sk2' @ ('#sk3' @ Y1) @ 344.16/44.52 ('#sk4' @ Y1)))) <=> 344.16/44.52 (((Y1) != ('#sk1')))))))))) => 344.16/44.52 (((!!) @ (^[Y1 : a > $o]: 344.16/44.52 (((!!) @ (^[Y2 : a]: 344.16/44.52 (((((??) @ (^[Y3 : a]: 344.16/44.52 (((((!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (((( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (Y5 @ 344.16/44.52 Y6) => 344.16/44.52 (Y5 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y6))))))) & 344.16/44.52 (Y5 @ Y3))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (Y5 @ 344.16/44.52 Y6) & 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y6) = 344.16/44.52 (Y4))))))))))))) => 344.16/44.52 (Y1 @ Y4)))))) & 344.16/44.52 (((??) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (((( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y6 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y7 : a]: 344.16/44.52 (( 344.16/44.52 (Y6 @ 344.16/44.52 Y7) => 344.16/44.52 (Y6 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y7))))))) & 344.16/44.52 (Y6 @ Y4))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y7 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y7) = 344.16/44.52 (Y5))) & 344.16/44.52 (Y6 @ Y7))))))))))) => 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y6 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y6 @ 344.16/44.52 Y3) & 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y7 : a]: 344.16/44.52 (( 344.16/44.52 (Y6 @ 344.16/44.52 Y7) => 344.16/44.52 (Y6 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y7))))))))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y7 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y7) = 344.16/44.52 (Y5))) & 344.16/44.52 (Y6 @ Y7)))))))))))))))) & 344.16/44.52 (Y0 @ 344.16/44.52 ('#sk2' @ 344.16/44.52 Y4 @ Y2)))))))))))) <=> 344.16/44.52 (((??) @ (^[Y3 : a]: 344.16/44.52 (((Y0 @ 344.16/44.52 ('#sk2' @ Y3 @ 344.16/44.52 Y2)) & 344.16/44.52 (((!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (((( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (Y5 @ 344.16/44.52 Y6) => 344.16/44.52 (Y5 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y6))))))) & 344.16/44.52 (Y5 @ Y3))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y6) = 344.16/44.52 (Y4))) & 344.16/44.52 (Y5 @ Y6))))))))))) => 344.16/44.52 (Y1 @ Y4))))))))))))))))))))))))), 344.16/44.52 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 344.16/44.52 thf(zip_derived_cl5, plain, 344.16/44.52 (~ ((((((('#sk3' @ '#sk1') = ('#sk1'))) & 344.16/44.52 ((('#sk4' @ '#sk1') = ('#sk1'))) & 344.16/44.52 (((!!) @ (^[Y0 : a]: 344.16/44.52 (((!!) @ (^[Y1 : a]: 344.16/44.52 ((('#sk3' @ ('#sk2' @ Y0 @ Y1)) = (Y0))))))))) & 344.16/44.52 (((!!) @ (^[Y0 : a]: 344.16/44.52 (((!!) @ (^[Y1 : a]: 344.16/44.52 ((('#sk4' @ ('#sk2' @ Y0 @ Y1)) = (Y1))))))))) & 344.16/44.52 (((!!) @ (^[Y0 : a > $o]: 344.16/44.52 (((((??) @ (^[Y1 : a]: 344.16/44.52 (((Y0 @ Y1) & 344.16/44.52 (((!!) @ (^[Y2 : a]: 344.16/44.52 (((Y0 @ Y2) => (Y0 @ 344.16/44.52 ('#sk3' @ Y2)))))))))))) => 344.16/44.52 (Y0 @ '#sk1')))))) & 344.16/44.52 (((!!) @ (^[Y0 : a]: 344.16/44.52 (((((Y0) = ('#sk2' @ ('#sk3' @ Y0) @ ('#sk4' @ Y0)))) <=> 344.16/44.52 (((Y0) != ('#sk1')))))))))) => 344.16/44.52 (((!!) @ (^[Y0 : a > $o]: 344.16/44.52 (((!!) @ (^[Y1 : a]: 344.16/44.52 (((((??) @ (^[Y2 : a]: 344.16/44.52 (((((!!) @ (^[Y3 : a]: 344.16/44.52 (((((!!) @ ( 344.16/44.52 ^[Y4 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (Y4 @ 344.16/44.52 Y5) => 344.16/44.52 (Y4 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y5))))))) & 344.16/44.52 (Y4 @ Y2))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (Y4 @ 344.16/44.52 Y5) & 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y5) = 344.16/44.52 (Y3))))))))))))) => 344.16/44.52 (Y0 @ Y3)))))) & 344.16/44.52 (((??) @ (^[Y3 : a]: 344.16/44.52 (((((!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (Y5 @ 344.16/44.52 Y6) => 344.16/44.52 (Y5 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y6))))))) & 344.16/44.52 (Y5 @ Y3))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y6) = 344.16/44.52 (Y4))) & 344.16/44.52 (Y5 @ Y6))))))))))) => 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y5 @ 344.16/44.52 Y2) & 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (Y5 @ 344.16/44.52 Y6) => 344.16/44.52 (Y5 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y6))))))))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y6) = 344.16/44.52 (Y4))) & 344.16/44.52 (Y5 @ Y6)))))))))))))))) & 344.16/44.52 ('#sk5' @ 344.16/44.52 ('#sk2' @ 344.16/44.52 Y3 @ Y1)))))))))))) <=> 344.16/44.52 (((??) @ (^[Y2 : a]: 344.16/44.52 ((('#sk5' @ 344.16/44.52 ('#sk2' @ Y2 @ Y1)) & 344.16/44.52 (((!!) @ (^[Y3 : a]: 344.16/44.52 (((((!!) @ ( 344.16/44.52 ^[Y4 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (Y4 @ 344.16/44.52 Y5) => 344.16/44.52 (Y4 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y5))))))) & 344.16/44.52 (Y4 @ Y2))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y5) = 344.16/44.52 (Y3))) & 344.16/44.52 (Y4 @ Y5))))))))))) => 344.16/44.52 (Y0 @ Y3)))))))))))))))))))))), 344.16/44.52 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl4])). 344.16/44.52 thf(zip_derived_cl7, plain, 344.16/44.52 (~ (((!!) @ (^[Y0 : a > $o]: 344.16/44.52 (((!!) @ (^[Y1 : a]: 344.16/44.52 (((((??) @ (^[Y2 : a]: 344.16/44.52 (((((!!) @ (^[Y3 : a]: 344.16/44.52 (((((!!) @ ( 344.16/44.52 ^[Y4 : a > $o]: 344.16/44.52 (((( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (Y4 @ 344.16/44.52 Y5) => 344.16/44.52 (Y4 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y5))))))) & 344.16/44.52 (Y4 @ Y2))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (Y4 @ 344.16/44.52 Y5) & 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y5) = 344.16/44.52 (Y3))))))))))))) => 344.16/44.52 (Y0 @ Y3)))))) & 344.16/44.52 (((??) @ (^[Y3 : a]: 344.16/44.52 (((((!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (((( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (Y5 @ 344.16/44.52 Y6) => 344.16/44.52 (Y5 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y6))))))) & 344.16/44.52 (Y5 @ Y3))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y6) = 344.16/44.52 (Y4))) & 344.16/44.52 (Y5 @ Y6))))))))))) => 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y5 @ 344.16/44.52 Y2) & 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (Y5 @ 344.16/44.52 Y6) => 344.16/44.52 (Y5 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y6))))))))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y6 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y6) = 344.16/44.52 (Y4))) & 344.16/44.52 (Y5 @ Y6)))))))))))))))) & 344.16/44.52 ('#sk5' @ 344.16/44.52 ('#sk2' @ Y3 @ 344.16/44.52 Y1)))))))))))) <=> 344.16/44.52 (((??) @ (^[Y2 : a]: 344.16/44.52 ((('#sk5' @ 344.16/44.52 ('#sk2' @ Y2 @ Y1)) & 344.16/44.52 (((!!) @ (^[Y3 : a]: 344.16/44.52 (((((!!) @ ( 344.16/44.52 ^[Y4 : a > $o]: 344.16/44.52 (((( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (Y4 @ 344.16/44.52 Y5) => 344.16/44.52 (Y4 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y5))))))) & 344.16/44.52 (Y4 @ Y2))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y5) = 344.16/44.52 (Y3))) & 344.16/44.52 (Y4 @ Y5))))))))))) => 344.16/44.52 (Y0 @ Y3)))))))))))))))))))), 344.16/44.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 344.16/44.52 thf(zip_derived_cl14, plain, 344.16/44.52 (~ (((!!) @ (^[Y0 : a]: 344.16/44.52 (((((??) @ (^[Y1 : a]: 344.16/44.52 (((((!!) @ (^[Y2 : a]: 344.16/44.52 (((((!!) @ (^[Y3 : a > $o]: 344.16/44.52 (((((((!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (( 344.16/44.52 (Y3 @ 344.16/44.52 Y4) => 344.16/44.52 (Y3 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y4))))))) & 344.16/44.52 (Y3 @ Y1))) => 344.16/44.52 (((??) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (( 344.16/44.52 (Y3 @ 344.16/44.52 Y4) & 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y4) = 344.16/44.52 (Y2))))))))))))) => 344.16/44.52 ('#sk6' @ Y2)))))) & 344.16/44.52 (((??) @ (^[Y2 : a]: 344.16/44.52 (((((!!) @ (^[Y3 : a]: 344.16/44.52 (((((!!) @ ( 344.16/44.52 ^[Y4 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (Y4 @ 344.16/44.52 Y5) => 344.16/44.52 (Y4 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y5))))))) & 344.16/44.52 (Y4 @ Y2))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y5) = 344.16/44.52 (Y3))) & 344.16/44.52 (Y4 @ Y5))))))))))) => 344.16/44.52 (((!!) @ ( 344.16/44.52 ^[Y4 : a > $o]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 (Y4 @ 344.16/44.52 Y1) & 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (Y4 @ 344.16/44.52 Y5) => 344.16/44.52 (Y4 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y5))))))))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y5 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y5) = 344.16/44.52 (Y3))) & 344.16/44.52 (Y4 @ Y5)))))))))))))))) & 344.16/44.52 ('#sk5' @ 344.16/44.52 ('#sk2' @ Y2 @ Y0)))))))))))) <=> 344.16/44.52 (((??) @ (^[Y1 : a]: 344.16/44.52 ((('#sk5' @ ('#sk2' @ Y1 @ Y0)) & 344.16/44.52 (((!!) @ (^[Y2 : a]: 344.16/44.52 (((((!!) @ (^[Y3 : a > $o]: 344.16/44.52 (((((((!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (( 344.16/44.52 (Y3 @ 344.16/44.52 Y4) => 344.16/44.52 (Y3 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y4))))))) & 344.16/44.52 (Y3 @ Y1))) => 344.16/44.52 (((??) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y4) = 344.16/44.52 (Y2))) & 344.16/44.52 (Y3 @ Y4))))))))))) => 344.16/44.52 ('#sk6' @ Y2))))))))))))))))), 344.16/44.52 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl7])). 344.16/44.52 thf(zip_derived_cl21, plain, 344.16/44.52 (~ (((((??) @ (^[Y0 : a]: 344.16/44.52 (((((!!) @ (^[Y1 : a]: 344.16/44.52 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thf(zip_derived_cl26, plain, 344.16/44.52 (((((??) @ (^[Y0 : a]: 344.16/44.52 (((((!!) @ (^[Y1 : a]: 344.16/44.52 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.52 (((((((!!) @ (^[Y3 : a]: 344.16/44.52 (((Y2 @ Y3) => 344.16/44.52 (Y2 @ 344.16/44.52 ('#sk3' @ Y3))))))) & 344.16/44.52 (Y2 @ Y0))) => 344.16/44.52 (((??) @ (^[Y3 : a]: 344.16/44.52 (((Y2 @ Y3) & 344.16/44.52 ((('#sk4' @ 344.16/44.52 Y3) = (Y1))))))))))))) => 344.16/44.52 ('#sk6' @ Y1)))))) & 344.16/44.52 (((??) @ (^[Y1 : a]: 344.16/44.52 (((((!!) @ (^[Y2 : a]: 344.16/44.52 (((((!!) @ (^[Y3 : a > $o]: 344.16/44.52 (((((((!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 ( 344.16/44.52 ( 344.16/44.52 (Y3 @ 344.16/44.52 Y4) => 344.16/44.52 (Y3 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y4))))))) & 344.16/44.52 (Y3 @ Y1))) => 344.16/44.52 (((??) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (((( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y4) = 344.16/44.52 (Y2))) & 344.16/44.52 (Y3 @ Y4))))))))))) => 344.16/44.52 (((!!) @ (^[Y3 : a > $o]: 344.16/44.52 (((((Y3 @ Y0) & 344.16/44.52 (((!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 ( 344.16/44.52 ( 344.16/44.52 (Y3 @ 344.16/44.52 Y4) => 344.16/44.52 (Y3 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y4))))))))) => 344.16/44.52 (((??) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (((( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y4) = 344.16/44.52 (Y2))) & 344.16/44.52 (Y3 @ Y4)))))))))))))))) & 344.16/44.52 ('#sk5' @ ('#sk2' @ Y1 @ '#sk7')))))))))))) 344.16/44.52 != (((??) @ (^[Y0 : a]: 344.16/44.52 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 344.16/44.52 (((!!) @ (^[Y1 : a]: 344.16/44.52 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.52 (((((((!!) @ (^[Y3 : a]: 344.16/44.52 (((Y2 @ 344.16/44.52 Y3) => 344.16/44.52 (Y2 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y3))))))) & 344.16/44.52 (Y2 @ Y0))) => 344.16/44.52 (((??) @ (^[Y3 : a]: 344.16/44.52 ((((('#sk4' @ 344.16/44.52 Y3) = 344.16/44.52 (Y1))) & 344.16/44.52 (Y2 @ Y3))))))))))) => 344.16/44.52 ('#sk6' @ Y1))))))))))))), 344.16/44.52 inference('simplify nested equalities', [status(thm)], [zip_derived_cl21])). 344.16/44.52 thf(zip_derived_cl35, plain, 344.16/44.52 (( ('#form24') 344.16/44.52 | ~ (((((??) @ (^[Y0 : a]: 344.16/44.52 (((((!!) @ (^[Y1 : a]: 344.16/44.52 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.52 (((((((!!) @ (^[Y3 : a]: 344.16/44.52 ( 344.16/44.52 ( 344.16/44.52 (Y2 @ 344.16/44.52 Y3) => 344.16/44.52 (Y2 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y3))))))) & 344.16/44.52 (Y2 @ Y0))) => 344.16/44.52 (((??) @ (^[Y3 : a]: 344.16/44.52 (((Y2 @ 344.16/44.52 Y3) & 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y3) = 344.16/44.52 (Y1))))))))))))) => 344.16/44.52 ('#sk6' @ Y1)))))) & 344.16/44.52 (((??) @ (^[Y1 : a]: 344.16/44.52 (((((!!) @ (^[Y2 : a]: 344.16/44.52 (((((!!) @ (^[Y3 : a > $o]: 344.16/44.52 (((( 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (( 344.16/44.52 (Y3 @ 344.16/44.52 Y4) => 344.16/44.52 (Y3 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y4))))))) & 344.16/44.52 (Y3 @ Y1))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y4) = 344.16/44.52 (Y2))) & 344.16/44.52 (Y3 @ Y4))))))))))) => 344.16/44.52 (((!!) @ (^[Y3 : a > $o]: 344.16/44.52 (((( 344.16/44.52 (Y3 @ 344.16/44.52 Y0) & 344.16/44.52 (( 344.16/44.52 (!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (( 344.16/44.52 (Y3 @ 344.16/44.52 Y4) => 344.16/44.52 (Y3 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y4))))))))) => 344.16/44.52 (( 344.16/44.52 (??) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y4) = 344.16/44.52 (Y2))) & 344.16/44.52 (Y3 @ Y4)))))))))))))))) & 344.16/44.52 ('#sk5' @ ('#sk2' @ Y1 @ '#sk7')))))))))))) <=> 344.16/44.52 (((??) @ (^[Y0 : a]: 344.16/44.52 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 344.16/44.52 (((!!) @ (^[Y1 : a]: 344.16/44.52 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.52 (((((((!!) @ (^[Y3 : a]: 344.16/44.52 ( 344.16/44.52 ( 344.16/44.52 (Y2 @ 344.16/44.52 Y3) => 344.16/44.52 (Y2 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y3))))))) & 344.16/44.52 (Y2 @ Y0))) => 344.16/44.52 (((??) @ (^[Y3 : a]: 344.16/44.52 (((( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y3) = 344.16/44.52 (Y1))) & 344.16/44.52 (Y2 @ Y3))))))))))) => 344.16/44.52 ('#sk6' @ Y1))))))))))))))), 344.16/44.52 define([status(thm)])). 344.16/44.52 thf(zip_derived_cl36, plain, 344.16/44.52 (( (((??) @ (^[Y0 : a]: 344.16/44.52 (((((!!) @ (^[Y1 : a]: 344.16/44.52 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.52 (((((((!!) @ (^[Y3 : a]: 344.16/44.52 (((Y2 @ Y3) => 344.16/44.52 (Y2 @ 344.16/44.52 ('#sk3' @ Y3))))))) & 344.16/44.52 (Y2 @ Y0))) => 344.16/44.52 (((??) @ (^[Y3 : a]: 344.16/44.52 (((Y2 @ Y3) & 344.16/44.52 ((('#sk4' @ 344.16/44.52 Y3) = (Y1))))))))))))) => 344.16/44.52 ('#sk6' @ Y1)))))) & 344.16/44.52 (((??) @ (^[Y1 : a]: 344.16/44.52 (((((!!) @ (^[Y2 : a]: 344.16/44.52 (((((!!) @ (^[Y3 : a > $o]: 344.16/44.52 (((((((!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (( 344.16/44.52 (Y3 @ 344.16/44.52 Y4) => 344.16/44.52 (Y3 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y4))))))) & 344.16/44.52 (Y3 @ Y1))) => 344.16/44.52 (((??) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y4) = 344.16/44.52 (Y2))) & 344.16/44.52 (Y3 @ Y4))))))))))) => 344.16/44.52 (((!!) @ (^[Y3 : a > $o]: 344.16/44.52 (((((Y3 @ Y0) & 344.16/44.52 (((!!) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (( 344.16/44.52 (Y3 @ 344.16/44.52 Y4) => 344.16/44.52 (Y3 @ 344.16/44.52 ( 344.16/44.52 '#sk3' @ 344.16/44.52 Y4))))))))) => 344.16/44.52 (((??) @ ( 344.16/44.52 ^[Y4 : a]: 344.16/44.52 (( 344.16/44.52 (( 344.16/44.52 ('#sk4' @ 344.16/44.52 Y4) = 344.16/44.52 (Y2))) & 344.16/44.52 (Y3 @ Y4)))))))))))))))) & 344.16/44.52 ('#sk5' @ ('#sk2' @ Y1 @ '#sk7')))))))))))) 344.16/44.52 | (((??) @ (^[Y0 : a]: 344.16/44.52 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 344.16/44.52 (((!!) @ (^[Y1 : a]: 344.16/44.52 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.52 (((((((!!) @ (^[Y3 : a]: 344.16/44.52 (((Y2 @ 344.16/44.52 Y3) => 344.16/44.52 (Y2 @ 344.16/44.52 ('#sk3' @ 344.16/44.52 Y3))))))) & 344.16/44.52 (Y2 @ Y0))) => 344.16/44.52 (((??) @ (^[Y3 : a]: 344.16/44.52 ((((('#sk4' @ 344.16/44.52 Y3) = (Y1))) & 344.16/44.52 (Y2 @ Y3))))))))))) => 344.16/44.52 ('#sk6' @ Y1))))))))))) 344.16/44.52 | ('#form24'))), 344.16/44.52 inference('lazy_cnf_xor', [status(thm)], [zip_derived_cl35])). 344.16/44.52 thf(zip_derived_cl40, plain, 344.16/44.52 (( (((((!!) @ (^[Y0 : a]: 344.16/44.52 (((((!!) @ (^[Y1 : a > $o]: 344.16/44.52 (((((((!!) @ (^[Y2 : a]: 344.16/44.52 (((Y1 @ Y2) => (Y1 @ 344.16/44.52 ('#sk3' @ Y2))))))) & 344.16/44.52 (Y1 @ '#sk25'))) => 344.16/44.52 (((??) @ (^[Y2 : a]: 344.16/44.52 (((Y1 @ Y2) & 344.16/44.52 ((('#sk4' @ Y2) = (Y0))))))))))))) => 344.16/44.52 ('#sk6' @ Y0)))))) & 344.16/44.52 (((??) @ (^[Y0 : a]: 344.16/44.52 (((((!!) @ (^[Y1 : a]: 344.16/44.52 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.52 (((((((!!) @ (^[Y3 : a]: 344.16/44.52 (((Y2 @ 344.16/44.52 Y3) => 344.16/44.52 (Y2 @ 344.16/44.52 ('#sk3' @ 344.16/44.52 Y3))))))) & 344.16/44.52 (Y2 @ Y0))) => 344.16/44.52 (((??) @ (^[Y3 : a]: 344.16/44.52 ((((('#sk4' @ 344.16/44.52 Y3) = (Y1))) & 344.16/44.52 (Y2 @ Y3))))))))))) => 344.16/44.52 (((!!) @ (^[Y2 : a > $o]: 344.16/44.52 (((((Y2 @ '#sk25') & 344.16/44.52 (((!!) @ (^[Y3 : a]: 344.16/44.52 (((Y2 @ 344.16/44.52 Y3) => 344.16/44.52 (Y2 @ 344.16/44.52 ('#sk3' @ 344.16/44.52 Y3))))))))) => 344.16/44.52 (((??) @ (^[Y3 : a]: 344.16/44.52 ((((('#sk4' @ 344.16/44.52 Y3) = (Y1))) & 344.16/44.52 (Y2 @ Y3)))))))))))))))) & 344.16/44.52 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))) 344.16/44.52 | ('#form24') 344.16/44.52 | (((??) @ (^[Y0 : a]: 344.16/44.52 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 344.16/44.52 (((!!) @ (^[Y1 : a]: 344.16/44.52 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ('#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 ((((('#sk4' @ 344.16/44.53 Y3) = (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 ('#sk6' @ Y1))))))))))))), 344.16/44.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl36])). 344.16/44.53 thf(zip_derived_cl40, plain, 344.16/44.53 (( (((((!!) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))) & 344.16/44.53 (Y1 @ '#sk25'))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) & 344.16/44.53 ((('#sk4' @ Y2) = (Y0))))))))))))) => 344.16/44.53 ('#sk6' @ Y0)))))) & 344.16/44.53 (((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ('#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 ((((('#sk4' @ 344.16/44.53 Y3) = (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 (((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((Y2 @ '#sk25') & 344.16/44.53 (((!!) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ('#sk3' @ 344.16/44.53 Y3))))))))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 ((((('#sk4' @ 344.16/44.53 Y3) = (Y1))) & 344.16/44.53 (Y2 @ Y3)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))) 344.16/44.53 | ('#form24') 344.16/44.53 | (((??) @ (^[Y0 : a]: 344.16/44.53 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ('#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 ((((('#sk4' @ 344.16/44.53 Y3) = (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 ('#sk6' @ Y1))))))))))))), 344.16/44.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl36])). 344.16/44.53 thf(zip_derived_cl44, plain, 344.16/44.53 ((~ ('#form26') 344.16/44.53 | (((??) @ (^[Y0 : a]: 344.16/44.53 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ('#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 ((((('#sk4' @ 344.16/44.53 Y3) = (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 ('#sk6' @ Y1))))))))))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl35, plain, 344.16/44.53 (( ('#form24') 344.16/44.53 | ~ (((((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ 344.16/44.53 Y3) & 344.16/44.53 (( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))))))))))))) => 344.16/44.53 ('#sk6' @ Y1)))))) & 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a]: 344.16/44.53 (((((!!) @ (^[Y3 : a > $o]: 344.16/44.53 (((( 344.16/44.53 (( 344.16/44.53 (!!) @ ( 344.16/44.53 ^[Y4 : a]: 344.16/44.53 (( 344.16/44.53 (Y3 @ 344.16/44.53 Y4) => 344.16/44.53 (Y3 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y4))))))) & 344.16/44.53 (Y3 @ Y1))) => 344.16/44.53 (( 344.16/44.53 (??) @ ( 344.16/44.53 ^[Y4 : a]: 344.16/44.53 (( 344.16/44.53 (( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y4) = 344.16/44.53 (Y2))) & 344.16/44.53 (Y3 @ Y4))))))))))) => 344.16/44.53 (((!!) @ (^[Y3 : a > $o]: 344.16/44.53 (((( 344.16/44.53 (Y3 @ 344.16/44.53 Y0) & 344.16/44.53 (( 344.16/44.53 (!!) @ ( 344.16/44.53 ^[Y4 : a]: 344.16/44.53 (( 344.16/44.53 (Y3 @ 344.16/44.53 Y4) => 344.16/44.53 (Y3 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y4))))))))) => 344.16/44.53 (( 344.16/44.53 (??) @ ( 344.16/44.53 ^[Y4 : a]: 344.16/44.53 (( 344.16/44.53 (( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y4) = 344.16/44.53 (Y2))) & 344.16/44.53 (Y3 @ Y4)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y1 @ '#sk7')))))))))))) <=> 344.16/44.53 (((??) @ (^[Y0 : a]: 344.16/44.53 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 ('#sk6' @ Y1))))))))))))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl37, plain, 344.16/44.53 ((~ (((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ('#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ Y3) & 344.16/44.53 ((('#sk4' @ 344.16/44.53 Y3) = (Y1))))))))))))) => 344.16/44.53 ('#sk6' @ Y1)))))) & 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a]: 344.16/44.53 (((((!!) @ (^[Y3 : a > $o]: 344.16/44.53 (((((((!!) @ ( 344.16/44.53 ^[Y4 : a]: 344.16/44.53 (( 344.16/44.53 (Y3 @ 344.16/44.53 Y4) => 344.16/44.53 (Y3 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y4))))))) & 344.16/44.53 (Y3 @ Y1))) => 344.16/44.53 (((??) @ ( 344.16/44.53 ^[Y4 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y4) = 344.16/44.53 (Y2))) & 344.16/44.53 (Y3 @ Y4))))))))))) => 344.16/44.53 (((!!) @ (^[Y3 : a > $o]: 344.16/44.53 (((((Y3 @ Y0) & 344.16/44.53 (((!!) @ ( 344.16/44.53 ^[Y4 : a]: 344.16/44.53 (( 344.16/44.53 (Y3 @ 344.16/44.53 Y4) => 344.16/44.53 (Y3 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y4))))))))) => 344.16/44.53 (((??) @ ( 344.16/44.53 ^[Y4 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y4) = 344.16/44.53 (Y2))) & 344.16/44.53 (Y3 @ Y4)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y1 @ '#sk7')))))))))))) 344.16/44.53 | ~ (((??) @ (^[Y0 : a]: 344.16/44.53 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 ((((('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 ('#sk6' @ Y1))))))))))) 344.16/44.53 | ('#form24'))), 344.16/44.53 inference('lazy_cnf_xor', [status(thm)], [zip_derived_cl35])). 344.16/44.53 thf(zip_derived_cl39, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ (((((!!) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))) & 344.16/44.53 (Y1 @ X2))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) & 344.16/44.53 ((('#sk4' @ Y2) = (Y0))))))))))))) => 344.16/44.53 ('#sk6' @ Y0)))))) & 344.16/44.53 (((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 (((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((Y2 @ X2) & 344.16/44.53 (((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))) 344.16/44.53 | ('#form24') 344.16/44.53 | ~ (((??) @ (^[Y0 : a]: 344.16/44.53 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 ('#sk6' @ Y1))))))))))))), 344.16/44.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 344.16/44.53 thf(zip_derived_cl41, plain, 344.16/44.53 (( ('#form26') 344.16/44.53 | ~ (((??) @ (^[Y0 : a]: 344.16/44.53 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 ((((('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 ('#sk6' @ Y1))))))))))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl46, plain, 344.16/44.53 (( ('#form26') 344.16/44.53 | ('#form24') 344.16/44.53 | (((((!!) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))) & 344.16/44.53 (Y1 @ '#sk25'))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) & 344.16/44.53 ((('#sk4' @ Y2) = (Y0))))))))))))) => 344.16/44.53 ('#sk6' @ Y0)))))) & 344.16/44.53 (((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 (( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 (((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((Y2 @ '#sk25') & 344.16/44.53 (((!!) @ (^[Y3 : a]: 344.16/44.53 (( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = (Y1))) & 344.16/44.53 (Y2 @ Y3)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))))), 344.16/44.53 inference('renaming', [status(thm)], 344.16/44.53 [zip_derived_cl40, zip_derived_cl44, zip_derived_cl41])). 344.16/44.53 thf(zip_derived_cl50, plain, 344.16/44.53 (( (((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ('#sk3' @ Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 ((((('#sk4' @ 344.16/44.53 Y3) = (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 (((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((Y2 @ '#sk25') & 344.16/44.53 (((!!) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ('#sk3' @ Y3))))))))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 ((((('#sk4' @ 344.16/44.53 Y3) = (Y1))) & 344.16/44.53 (Y2 @ Y3)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))) 344.16/44.53 | ('#form24') 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 344.16/44.53 thf(zip_derived_cl56, plain, 344.16/44.53 (( (((((!!) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))) & 344.16/44.53 (Y1 @ '#sk30'))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 ((((('#sk4' @ Y2) = (Y0))) & 344.16/44.53 (Y1 @ Y2))))))))))) => 344.16/44.53 (((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((Y1 @ '#sk25') & 344.16/44.53 (((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 ((((('#sk4' @ Y2) = (Y0))) & 344.16/44.53 (Y1 @ Y2)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ '#sk30' @ '#sk7')))) 344.16/44.53 | ('#form26') 344.16/44.53 | ('#form24'))), 344.16/44.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl50])). 344.16/44.53 thf(zip_derived_cl64, plain, 344.16/44.53 (( ('#sk5' @ ('#sk2' @ '#sk30' @ '#sk7')) | ('#form24') | ('#form26'))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl56])). 344.16/44.53 thf(zip_derived_cl26, plain, 344.16/44.53 (((((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ('#sk3' @ Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ Y3) & 344.16/44.53 ((('#sk4' @ 344.16/44.53 Y3) = (Y1))))))))))))) => 344.16/44.53 ('#sk6' @ Y1)))))) & 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a]: 344.16/44.53 (((((!!) @ (^[Y3 : a > $o]: 344.16/44.53 (((((((!!) @ ( 344.16/44.53 ^[Y4 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y3 @ 344.16/44.53 Y4) => 344.16/44.53 (Y3 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y4))))))) & 344.16/44.53 (Y3 @ Y1))) => 344.16/44.53 (((??) @ ( 344.16/44.53 ^[Y4 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y4) = 344.16/44.53 (Y2))) & 344.16/44.53 (Y3 @ Y4))))))))))) => 344.16/44.53 (((!!) @ (^[Y3 : a > $o]: 344.16/44.53 (((((Y3 @ Y0) & 344.16/44.53 (((!!) @ ( 344.16/44.53 ^[Y4 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y3 @ 344.16/44.53 Y4) => 344.16/44.53 (Y3 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y4))))))))) => 344.16/44.53 (((??) @ ( 344.16/44.53 ^[Y4 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y4) = 344.16/44.53 (Y2))) & 344.16/44.53 (Y3 @ Y4)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y1 @ '#sk7')))))))))))) 344.16/44.53 != (((??) @ (^[Y0 : a]: 344.16/44.53 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 ((((('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 ('#sk6' @ Y1))))))))))))), 344.16/44.53 inference('simplify nested equalities', [status(thm)], [zip_derived_cl21])). 344.16/44.53 thf(zip_derived_cl35, plain, 344.16/44.53 (( ('#form24') 344.16/44.53 | ~ (((((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ 344.16/44.53 Y3) & 344.16/44.53 (( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))))))))))))) => 344.16/44.53 ('#sk6' @ Y1)))))) & 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a]: 344.16/44.53 (((((!!) @ (^[Y3 : a > $o]: 344.16/44.53 (((( 344.16/44.53 (( 344.16/44.53 (!!) @ ( 344.16/44.53 ^[Y4 : a]: 344.16/44.53 (( 344.16/44.53 (Y3 @ 344.16/44.53 Y4) => 344.16/44.53 (Y3 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y4))))))) & 344.16/44.53 (Y3 @ Y1))) => 344.16/44.53 (( 344.16/44.53 (??) @ ( 344.16/44.53 ^[Y4 : a]: 344.16/44.53 (( 344.16/44.53 (( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y4) = 344.16/44.53 (Y2))) & 344.16/44.53 (Y3 @ Y4))))))))))) => 344.16/44.53 (((!!) @ (^[Y3 : a > $o]: 344.16/44.53 (((( 344.16/44.53 (Y3 @ 344.16/44.53 Y0) & 344.16/44.53 (( 344.16/44.53 (!!) @ ( 344.16/44.53 ^[Y4 : a]: 344.16/44.53 (( 344.16/44.53 (Y3 @ 344.16/44.53 Y4) => 344.16/44.53 (Y3 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y4))))))))) => 344.16/44.53 (( 344.16/44.53 (??) @ ( 344.16/44.53 ^[Y4 : a]: 344.16/44.53 (( 344.16/44.53 (( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y4) = 344.16/44.53 (Y2))) & 344.16/44.53 (Y3 @ Y4)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y1 @ '#sk7')))))))))))) <=> 344.16/44.53 (((??) @ (^[Y0 : a]: 344.16/44.53 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 ('#sk6' @ Y1))))))))))))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl38, plain, (~ ('#form24')), 344.16/44.53 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 344.16/44.53 thf(zip_derived_cl161, plain, 344.16/44.53 (( ('#sk5' @ ('#sk2' @ '#sk30' @ '#sk7')) | ('#form26'))), 344.16/44.53 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl38])). 344.16/44.53 thf(zip_derived_cl41, plain, 344.16/44.53 (( ('#form26') 344.16/44.53 | ~ (((??) @ (^[Y0 : a]: 344.16/44.53 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 ((((('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 ('#sk6' @ Y1))))))))))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl42, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ ((('#sk5' @ ('#sk2' @ X2 @ '#sk7')) & 344.16/44.53 (((!!) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))) & 344.16/44.53 (Y1 @ X2))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 ((((('#sk4' @ Y2) = (Y0))) & 344.16/44.53 (Y1 @ Y2))))))))))) => 344.16/44.53 ('#sk6' @ Y0)))))))) 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 344.16/44.53 thf(zip_derived_cl48, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')) 344.16/44.53 | ~ (((!!) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))) & 344.16/44.53 (Y1 @ X2))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 ((((('#sk4' @ Y2) = (Y0))) & 344.16/44.53 (Y1 @ Y2))))))))))) => 344.16/44.53 ('#sk6' @ Y0)))))) 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl42])). 344.16/44.53 thf(zip_derived_cl54, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ (((((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 344.16/44.53 (Y0 @ X2))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = ('#sk29' @ X2))) & 344.16/44.53 (Y0 @ Y1))))))))))) => 344.16/44.53 ('#sk6' @ ('#sk29' @ X2)))) 344.16/44.53 | ('#form26') 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')))), 344.16/44.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl48])). 344.16/44.53 thf(zip_derived_cl61, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ ('#sk6' @ ('#sk29' @ X2)) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')) 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl54])). 344.16/44.53 thf(zip_derived_cl1265, plain, 344.16/44.53 (( ('#form26') | ('#form26') | ~ ('#sk6' @ ('#sk29' @ '#sk30')))), 344.16/44.53 inference('sup-', [status(thm)], [zip_derived_cl161, zip_derived_cl61])). 344.16/44.53 thf(zip_derived_cl1283, plain, 344.16/44.53 ((~ ('#sk6' @ ('#sk29' @ '#sk30')) | ('#form26'))), 344.16/44.53 inference('simplify', [status(thm)], [zip_derived_cl1265])). 344.16/44.53 thf(zip_derived_cl63, plain, 344.16/44.53 (( (((!!) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))) & 344.16/44.53 (Y1 @ '#sk30'))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 ((((('#sk4' @ Y2) = (Y0))) & 344.16/44.53 (Y1 @ Y2))))))))))) => 344.16/44.53 (((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((Y1 @ '#sk25') & 344.16/44.53 (((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 ((((('#sk4' @ Y2) = (Y0))) & 344.16/44.53 (Y1 @ Y2)))))))))))))))) 344.16/44.53 | ('#form24') 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl56])). 344.16/44.53 thf(zip_derived_cl72, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( (((((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 344.16/44.53 (Y0 @ '#sk30'))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))) => 344.16/44.53 (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((Y0 @ '#sk25') & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))))) 344.16/44.53 | ('#form26') 344.16/44.53 | ('#form24'))), 344.16/44.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 344.16/44.53 thf(zip_derived_cl79, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 344.16/44.53 (Y0 @ '#sk30'))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))) 344.16/44.53 | (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((Y0 @ '#sk25') & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))) 344.16/44.53 | ('#form24') 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl72])). 344.16/44.53 thf(zip_derived_cl92, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ (((((((!!) @ (^[Y0 : a]: 344.16/44.53 ((('#sk45' @ X2 @ Y0) => ('#sk45' @ X2 @ 344.16/44.53 ('#sk3' @ Y0))))))) & 344.16/44.53 ('#sk45' @ X2 @ '#sk30'))) => 344.16/44.53 (((??) @ (^[Y0 : a]: 344.16/44.53 ((((('#sk4' @ Y0) = (X2))) & ('#sk45' @ X2 @ Y0)))))))) 344.16/44.53 | ('#form26') 344.16/44.53 | ('#form24') 344.16/44.53 | (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((Y0 @ '#sk25') & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))))), 344.16/44.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl79])). 344.16/44.53 thf(zip_derived_cl103, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ (((??) @ (^[Y0 : a]: 344.16/44.53 ((((('#sk4' @ Y0) = (X2))) & ('#sk45' @ X2 @ Y0)))))) 344.16/44.53 | (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((Y0 @ '#sk25') & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))) 344.16/44.53 | ('#form24') 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])). 344.16/44.53 thf(zip_derived_cl117, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ ('#form72' @ X2) 344.16/44.53 | (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((Y0 @ '#sk25') & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl118, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( (((((X4 @ '#sk25') & 344.16/44.53 (((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))))) => 344.16/44.53 (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))))) 344.16/44.53 | ~ ('#form72' @ X2))), 344.16/44.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl117])). 344.16/44.53 thf(zip_derived_cl130, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ (((X4 @ '#sk25') & 344.16/44.53 (((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))))) 344.16/44.53 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))) 344.16/44.53 | ~ ('#form72' @ X2))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl118])). 344.16/44.53 thf(zip_derived_cl137, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ (X4 @ '#sk25') 344.16/44.53 | ~ (((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) 344.16/44.53 | ~ ('#form72' @ X2) 344.16/44.53 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl130])). 344.16/44.53 thf(zip_derived_cl144, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ (((X4 @ ('#sk18' @ X4)) => (X4 @ ('#sk3' @ ('#sk18' @ X4))))) 344.16/44.53 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))) 344.16/44.53 | ~ ('#form72' @ X2) 344.16/44.53 | ~ (X4 @ '#sk25'))), 344.16/44.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl137])). 344.16/44.53 thf(zip_derived_cl149, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( (X4 @ ('#sk18' @ X4)) 344.16/44.53 | ~ (X4 @ '#sk25') 344.16/44.53 | ~ ('#form72' @ X2) 344.16/44.53 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl144])). 344.16/44.53 thf(zip_derived_cl152, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ ('#form127' @ X2 @ X4) 344.16/44.53 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl153, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( ((((('#sk4' @ ('#sk128' @ X2 @ X4)) = (X2))) & (X4 @ 344.16/44.53 ('#sk128' @ X2 @ X4)))) 344.16/44.53 | ~ ('#form127' @ X2 @ X4))), 344.16/44.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl152])). 344.16/44.53 thf(zip_derived_cl157, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( (X4 @ ('#sk128' @ X2 @ X4)) | ~ ('#form127' @ X2 @ X4))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl153])). 344.16/44.53 thf(zip_derived_cl149, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( (X4 @ ('#sk18' @ X4)) 344.16/44.53 | ~ (X4 @ '#sk25') 344.16/44.53 | ~ ('#form72' @ X2) 344.16/44.53 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl144])). 344.16/44.53 thf(zip_derived_cl152, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ ('#form127' @ X2 @ X4) 344.16/44.53 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl154, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( ('#form127' @ X2 @ X4) 344.16/44.53 | ~ ('#form72' @ X2) 344.16/44.53 | ~ (X4 @ '#sk25') 344.16/44.53 | (X4 @ ('#sk18' @ X4)))), 344.16/44.53 inference('renaming', [status(thm)], 344.16/44.53 [zip_derived_cl149, zip_derived_cl152])). 344.16/44.53 thf(zip_derived_cl156, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( ((('#sk4' @ ('#sk128' @ X2 @ X4)) = (X2))) 344.16/44.53 | ~ ('#form127' @ X2 @ X4))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl153])). 344.16/44.53 thf(zip_derived_cl159, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ((('#sk4' @ ('#sk128' @ X2 @ X4)) = (X2)) | ~ ('#form127' @ X2 @ X4))), 344.16/44.53 inference('simplify nested equalities', [status(thm)], 344.16/44.53 [zip_derived_cl156])). 344.16/44.53 thf(zip_derived_cl49, plain, 344.16/44.53 (( (((!!) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))) & 344.16/44.53 (Y1 @ '#sk25'))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) & 344.16/44.53 ((('#sk4' @ Y2) = (Y0))))))))))))) => 344.16/44.53 ('#sk6' @ Y0)))))) 344.16/44.53 | ('#form24') 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 344.16/44.53 thf(zip_derived_cl55, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( (((((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 344.16/44.53 (Y0 @ '#sk25'))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X2))))))))))))) => 344.16/44.53 ('#sk6' @ X2))) 344.16/44.53 | ('#form26') 344.16/44.53 | ('#form24'))), 344.16/44.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl49])). 344.16/44.53 thf(zip_derived_cl62, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 344.16/44.53 (Y0 @ '#sk25'))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) & ((('#sk4' @ Y1) = (X2))))))))))))) 344.16/44.53 | ('#sk6' @ X2) 344.16/44.53 | ('#form24') 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 344.16/44.53 thf(zip_derived_cl71, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ (((((((!!) @ (^[Y0 : a]: 344.16/44.53 ((('#sk32' @ X2 @ Y0) => ('#sk32' @ X2 @ 344.16/44.53 ('#sk3' @ Y0))))))) & 344.16/44.53 ('#sk32' @ X2 @ '#sk25'))) => 344.16/44.53 (((??) @ (^[Y0 : a]: 344.16/44.53 ((('#sk32' @ X2 @ Y0) & ((('#sk4' @ Y0) = (X2)))))))))) 344.16/44.53 | ('#form26') 344.16/44.53 | ('#form24') 344.16/44.53 | ('#sk6' @ X2))), 344.16/44.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl62])). 344.16/44.53 thf(zip_derived_cl78, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ (((??) @ (^[Y0 : a]: 344.16/44.53 ((('#sk32' @ X2 @ Y0) & ((('#sk4' @ Y0) = (X2)))))))) 344.16/44.53 | ('#sk6' @ X2) 344.16/44.53 | ('#form24') 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 344.16/44.53 thf(zip_derived_cl91, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 (~ ((('#sk32' @ X2 @ X4) & ((('#sk4' @ X4) = (X2))))) 344.16/44.53 | ('#form26') 344.16/44.53 | ('#form24') 344.16/44.53 | ('#sk6' @ X2))), 344.16/44.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl78])). 344.16/44.53 thf(zip_derived_cl101, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 (~ ('#sk32' @ X2 @ X4) 344.16/44.53 | ~ ((('#sk4' @ X4) = (X2))) 344.16/44.53 | ('#sk6' @ X2) 344.16/44.53 | ('#form24') 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl91])). 344.16/44.53 thf(zip_derived_cl114, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 (~ ('#sk32' @ X2 @ X4) 344.16/44.53 | (('#sk4' @ X4) != (X2)) 344.16/44.53 | ('#sk6' @ X2) 344.16/44.53 | ('#form24') 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('simplify nested equalities', [status(thm)], 344.16/44.53 [zip_derived_cl101])). 344.16/44.53 thf(zip_derived_cl115, plain, 344.16/44.53 (![X4 : a]: 344.16/44.53 ( ('#form26') 344.16/44.53 | ('#form24') 344.16/44.53 | ('#sk6' @ ('#sk4' @ X4)) 344.16/44.53 | ~ ('#sk32' @ ('#sk4' @ X4) @ X4))), 344.16/44.53 inference('simplify', [status(thm)], [zip_derived_cl114])). 344.16/44.53 thf(zip_derived_cl38, plain, (~ ('#form24')), 344.16/44.53 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 344.16/44.53 thf(zip_derived_cl162, plain, 344.16/44.53 (![X4 : a]: 344.16/44.53 ( ('#form26') 344.16/44.53 | ('#sk6' @ ('#sk4' @ X4)) 344.16/44.53 | ~ ('#sk32' @ ('#sk4' @ X4) @ X4))), 344.16/44.53 inference('demod', [status(thm)], [zip_derived_cl115, zip_derived_cl38])). 344.16/44.53 thf(zip_derived_cl77, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( (((((!!) @ (^[Y0 : a]: 344.16/44.53 ((('#sk32' @ X2 @ Y0) => ('#sk32' @ X2 @ 344.16/44.53 ('#sk3' @ Y0))))))) & 344.16/44.53 ('#sk32' @ X2 @ '#sk25'))) 344.16/44.53 | ('#sk6' @ X2) 344.16/44.53 | ('#form24') 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 344.16/44.53 thf(zip_derived_cl77, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( (((((!!) @ (^[Y0 : a]: 344.16/44.53 ((('#sk32' @ X2 @ Y0) => ('#sk32' @ X2 @ 344.16/44.53 ('#sk3' @ Y0))))))) & 344.16/44.53 ('#sk32' @ X2 @ '#sk25'))) 344.16/44.53 | ('#sk6' @ X2) 344.16/44.53 | ('#form24') 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 344.16/44.53 thf(zip_derived_cl87, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ ('#form44' @ X2 @ X4) 344.16/44.53 | (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl60, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 344.16/44.53 (Y0 @ X2))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = ('#sk29' @ X2))) & 344.16/44.53 (Y0 @ Y1))))))))))) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')) 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl54])). 344.16/44.53 thf(zip_derived_cl70, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( (((((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))) => 344.16/44.53 (((??) @ (^[Y0 : a]: 344.16/44.53 ((((('#sk4' @ Y0) = ('#sk29' @ X2))) & (X4 @ Y0)))))))) 344.16/44.53 | ('#form26') 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')))), 344.16/44.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl60])). 344.16/44.53 thf(zip_derived_cl76, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))) 344.16/44.53 | (((??) @ (^[Y0 : a]: 344.16/44.53 ((((('#sk4' @ Y0) = ('#sk29' @ X2))) & (X4 @ Y0)))))) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')) 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl70])). 344.16/44.53 thf(zip_derived_cl84, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( ('#form44' @ X2 @ X4) 344.16/44.53 | ~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl90, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( ('#form44' @ '#sk25' @ ('#sk32' @ X2)) 344.16/44.53 | ('#form26') 344.16/44.53 | ('#form24') 344.16/44.53 | ('#sk6' @ X2))), 344.16/44.53 inference('renaming', [status(thm)], 344.16/44.53 [zip_derived_cl77, zip_derived_cl87, zip_derived_cl84])). 344.16/44.53 thf(zip_derived_cl38, plain, (~ ('#form24')), 344.16/44.53 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 344.16/44.53 thf(zip_derived_cl163, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( ('#form44' @ '#sk25' @ ('#sk32' @ X2)) 344.16/44.53 | ('#form26') 344.16/44.53 | ('#sk6' @ X2))), 344.16/44.53 inference('demod', [status(thm)], [zip_derived_cl90, zip_derived_cl38])). 344.16/44.53 thf(zip_derived_cl87, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ ('#form44' @ X2 @ X4) 344.16/44.53 | (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl88, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( (((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) 344.16/44.53 | ~ ('#form44' @ X2 @ X4))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl87])). 344.16/44.53 thf(zip_derived_cl100, plain, 344.16/44.53 (![X2 : a, X4 : a > $o, X6 : a]: 344.16/44.53 ( (((X4 @ X6) => (X4 @ ('#sk3' @ X6)))) | ~ ('#form44' @ X2 @ X4))), 344.16/44.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl88])). 344.16/44.53 thf(zip_derived_cl113, plain, 344.16/44.53 (![X2 : a, X4 : a > $o, X6 : a]: 344.16/44.53 (~ (X4 @ X6) | (X4 @ ('#sk3' @ X6)) | ~ ('#form44' @ X2 @ X4))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 344.16/44.53 thf(zip_derived_cl161, plain, 344.16/44.53 (( ('#sk5' @ ('#sk2' @ '#sk30' @ '#sk7')) | ('#form26'))), 344.16/44.53 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl38])). 344.16/44.53 thf(zip_derived_cl150, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ (X4 @ ('#sk3' @ ('#sk18' @ X4))) 344.16/44.53 | ~ (X4 @ '#sk25') 344.16/44.53 | ~ ('#form72' @ X2) 344.16/44.53 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl144])). 344.16/44.53 thf(zip_derived_cl152, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ ('#form127' @ X2 @ X4) 344.16/44.53 | (((??) @ (^[Y0 : a]: ((((('#sk4' @ Y0) = (X2))) & (X4 @ Y0)))))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl155, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( ('#form127' @ X2 @ (^[Y0 : a]: (X4 @ Y0))) 344.16/44.53 | ~ ('#form72' @ X2) 344.16/44.53 | ~ (X4 @ '#sk25') 344.16/44.53 | ~ (X4 @ ('#sk3' @ ('#sk18' @ X4))))), 344.16/44.53 inference('renaming', [status(thm)], 344.16/44.53 [zip_derived_cl150, zip_derived_cl152])). 344.16/44.53 thf(zip_derived_cl158, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( ('#form127' @ X2 @ X4) 344.16/44.53 | ~ ('#form72' @ X2) 344.16/44.53 | ~ (X4 @ '#sk25') 344.16/44.53 | ~ (X4 @ ('#sk3' @ ('#sk18' @ X4))))), 344.16/44.53 inference('ho_norm', [status(thm)], [zip_derived_cl155])). 344.16/44.53 thf(zip_derived_cl89, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: ( (X4 @ X2) | ~ ('#form44' @ X2 @ X4))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl87])). 344.16/44.53 thf(zip_derived_cl44, plain, 344.16/44.53 ((~ ('#form26') 344.16/44.53 | (((??) @ (^[Y0 : a]: 344.16/44.53 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ('#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 ((((('#sk4' @ 344.16/44.53 Y3) = (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 ('#sk6' @ Y1))))))))))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl45, plain, 344.16/44.53 (( ((('#sk5' @ ('#sk2' @ '#sk27' @ '#sk7')) & 344.16/44.53 (((!!) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))) & 344.16/44.53 (Y1 @ '#sk27'))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 ((((('#sk4' @ Y2) = (Y0))) & 344.16/44.53 (Y1 @ Y2))))))))))) => 344.16/44.53 ('#sk6' @ Y0)))))))) 344.16/44.53 | ~ ('#form26'))), 344.16/44.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl44])). 344.16/44.53 thf(zip_derived_cl51, plain, 344.16/44.53 (( ('#sk5' @ ('#sk2' @ '#sk27' @ '#sk7')) | ~ ('#form26'))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl45])). 344.16/44.53 thf(zip_derived_cl102, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( (((((!!) @ (^[Y0 : a]: 344.16/44.53 ((('#sk45' @ X2 @ Y0) => ('#sk45' @ X2 @ 344.16/44.53 ('#sk3' @ Y0))))))) & 344.16/44.53 ('#sk45' @ X2 @ '#sk30'))) 344.16/44.53 | (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((Y0 @ '#sk25') & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))) 344.16/44.53 | ('#form24') 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])). 344.16/44.53 thf(zip_derived_cl87, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ ('#form44' @ X2 @ X4) 344.16/44.53 | (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl84, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( ('#form44' @ X2 @ X4) 344.16/44.53 | ~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl116, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( ('#form44' @ '#sk30' @ ('#sk45' @ X2)) 344.16/44.53 | ('#form26') 344.16/44.53 | ('#form24') 344.16/44.53 | (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((Y0 @ '#sk25') & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))))), 344.16/44.53 inference('renaming', [status(thm)], 344.16/44.53 [zip_derived_cl102, zip_derived_cl87, zip_derived_cl84])). 344.16/44.53 thf(zip_derived_cl117, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ ('#form72' @ X2) 344.16/44.53 | (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((Y0 @ '#sk25') & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl128, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( ('#form72' @ X2) 344.16/44.53 | ('#form24') 344.16/44.53 | ('#form26') 344.16/44.53 | ('#form44' @ '#sk30' @ ('#sk45' @ X2)))), 344.16/44.53 inference('renaming', [status(thm)], 344.16/44.53 [zip_derived_cl116, zip_derived_cl117])). 344.16/44.53 thf(zip_derived_cl38, plain, (~ ('#form24')), 344.16/44.53 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 344.16/44.53 thf(zip_derived_cl165, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( ('#form72' @ X2) 344.16/44.53 | ('#form26') 344.16/44.53 | ('#form44' @ '#sk30' @ ('#sk45' @ X2)))), 344.16/44.53 inference('demod', [status(thm)], [zip_derived_cl128, zip_derived_cl38])). 344.16/44.53 thf(zip_derived_cl52, plain, 344.16/44.53 (( (((!!) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))) & 344.16/44.53 (Y1 @ '#sk27'))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 ((((('#sk4' @ Y2) = (Y0))) & 344.16/44.53 (Y1 @ Y2))))))))))) => 344.16/44.53 ('#sk6' @ Y0)))))) 344.16/44.53 | ~ ('#form26'))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl45])). 344.16/44.53 thf(zip_derived_cl57, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( (((((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 344.16/44.53 (Y0 @ '#sk27'))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))) => 344.16/44.53 ('#sk6' @ X2))) 344.16/44.53 | ~ ('#form26'))), 344.16/44.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl52])). 344.16/44.53 thf(zip_derived_cl65, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 344.16/44.53 (Y0 @ '#sk27'))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))) 344.16/44.53 | ('#sk6' @ X2) 344.16/44.53 | ~ ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 344.16/44.53 thf(zip_derived_cl73, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ (((((((!!) @ (^[Y0 : a]: 344.16/44.53 ((('#sk33' @ X2 @ Y0) => ('#sk33' @ X2 @ 344.16/44.53 ('#sk3' @ Y0))))))) & 344.16/44.53 ('#sk33' @ X2 @ '#sk27'))) => 344.16/44.53 (((??) @ (^[Y0 : a]: 344.16/44.53 ((((('#sk4' @ Y0) = (X2))) & ('#sk33' @ X2 @ Y0)))))))) 344.16/44.53 | ~ ('#form26') 344.16/44.53 | ('#sk6' @ X2))), 344.16/44.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl65])). 344.16/44.53 thf(zip_derived_cl80, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( (((((!!) @ (^[Y0 : a]: 344.16/44.53 ((('#sk33' @ X2 @ Y0) => ('#sk33' @ X2 @ 344.16/44.53 ('#sk3' @ Y0))))))) & 344.16/44.53 ('#sk33' @ X2 @ '#sk27'))) 344.16/44.53 | ('#sk6' @ X2) 344.16/44.53 | ~ ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 344.16/44.53 thf(zip_derived_cl87, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ ('#form44' @ X2 @ X4) 344.16/44.53 | (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl84, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( ('#form44' @ X2 @ X4) 344.16/44.53 | ~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl93, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( ('#form44' @ '#sk27' @ ('#sk33' @ X2)) 344.16/44.53 | ~ ('#form26') 344.16/44.53 | ('#sk6' @ X2))), 344.16/44.53 inference('renaming', [status(thm)], 344.16/44.53 [zip_derived_cl80, zip_derived_cl87, zip_derived_cl84])). 344.16/44.53 thf(zip_derived_cl76, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))) 344.16/44.53 | (((??) @ (^[Y0 : a]: 344.16/44.53 ((((('#sk4' @ Y0) = ('#sk29' @ X2))) & (X4 @ Y0)))))) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')) 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl70])). 344.16/44.53 thf(zip_derived_cl84, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( ('#form44' @ X2 @ X4) 344.16/44.53 | ~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl86, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ ('#form44' @ X2 @ X4) 344.16/44.53 | ('#form26') 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')) 344.16/44.53 | (((??) @ (^[Y0 : a]: 344.16/44.53 ((((('#sk4' @ Y0) = ('#sk29' @ X2))) & (X4 @ Y0)))))))), 344.16/44.53 inference('renaming', [status(thm)], [zip_derived_cl76, zip_derived_cl84])). 344.16/44.53 thf(zip_derived_cl98, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( ((((('#sk4' @ ('#sk51' @ X2 @ X4)) = ('#sk29' @ X2))) & (X4 @ 344.16/44.53 ('#sk51' @ X2 @ X4)))) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')) 344.16/44.53 | ('#form26') 344.16/44.53 | ~ ('#form44' @ X2 @ X4))), 344.16/44.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl86])). 344.16/44.53 thf(zip_derived_cl110, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( (X4 @ ('#sk51' @ X2 @ X4)) 344.16/44.53 | ~ ('#form44' @ X2 @ X4) 344.16/44.53 | ('#form26') 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl98])). 344.16/44.53 thf(zip_derived_cl39, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ (((((!!) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))) & 344.16/44.53 (Y1 @ X2))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) & 344.16/44.53 ((('#sk4' @ Y2) = (Y0))))))))))))) => 344.16/44.53 ('#sk6' @ Y0)))))) & 344.16/44.53 (((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 (((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((Y2 @ X2) & 344.16/44.53 (((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))) 344.16/44.53 | ('#form24') 344.16/44.53 | ~ (((??) @ (^[Y0 : a]: 344.16/44.53 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 ('#sk6' @ Y1))))))))))))), 344.16/44.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 344.16/44.53 thf(zip_derived_cl41, plain, 344.16/44.53 (( ('#form26') 344.16/44.53 | ~ (((??) @ (^[Y0 : a]: 344.16/44.53 ((('#sk5' @ ('#sk2' @ Y0 @ '#sk7')) & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 (((Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 ((((('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 ('#sk6' @ Y1))))))))))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl43, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ ('#form26') 344.16/44.53 | ('#form24') 344.16/44.53 | ~ (((((!!) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))) & 344.16/44.53 (Y1 @ X2))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) & 344.16/44.53 ((('#sk4' @ Y2) = 344.16/44.53 (Y0))))))))))))) => 344.16/44.53 ('#sk6' @ Y0)))))) & 344.16/44.53 (((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 (( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 (((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((Y2 @ X2) & 344.16/44.53 (((!!) @ (^[Y3 : a]: 344.16/44.53 (( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))))), 344.16/44.53 inference('renaming', [status(thm)], [zip_derived_cl39, zip_derived_cl41])). 344.16/44.53 thf(zip_derived_cl47, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ (((!!) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))) & 344.16/44.53 (Y1 @ X2))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) & 344.16/44.53 ((('#sk4' @ Y2) = (Y0))))))))))))) => 344.16/44.53 ('#sk6' @ Y0)))))) 344.16/44.53 | ~ (((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 (((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((Y2 @ X2) & 344.16/44.53 (((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))) 344.16/44.53 | ('#form24') 344.16/44.53 | ~ ('#form26'))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl43])). 344.16/44.53 thf(zip_derived_cl53, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ (((((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 344.16/44.53 (Y0 @ X2))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) & 344.16/44.53 ((('#sk4' @ Y1) = ('#sk28' @ X2))))))))))))) => 344.16/44.53 ('#sk6' @ ('#sk28' @ X2)))) 344.16/44.53 | ~ ('#form26') 344.16/44.53 | ('#form24') 344.16/44.53 | ~ (((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 (((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((Y2 @ X2) & 344.16/44.53 (((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 344.16/44.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 344.16/44.53 thf(zip_derived_cl58, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 344.16/44.53 (Y0 @ X2))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) & 344.16/44.53 ((('#sk4' @ Y1) = ('#sk28' @ X2))))))))))))) 344.16/44.53 | ~ (((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 (((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((Y2 @ X2) & 344.16/44.53 (((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))) 344.16/44.53 | ('#form24') 344.16/44.53 | ~ ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 344.16/44.53 thf(zip_derived_cl58, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 344.16/44.53 (Y0 @ X2))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) & 344.16/44.53 ((('#sk4' @ Y1) = ('#sk28' @ X2))))))))))))) 344.16/44.53 | ~ (((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 (((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((Y2 @ X2) & 344.16/44.53 (((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))) 344.16/44.53 | ('#form24') 344.16/44.53 | ~ ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 344.16/44.53 thf(zip_derived_cl66, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( ('#form31' @ X2) 344.16/44.53 | ~ (((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 (((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((Y2 @ X2) & 344.16/44.53 (((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl68, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ ('#form31' @ X2) 344.16/44.53 | ~ ('#form26') 344.16/44.53 | ('#form24') 344.16/44.53 | (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 344.16/44.53 (Y0 @ X2))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) & 344.16/44.53 ((('#sk4' @ Y1) = ('#sk28' @ X2))))))))))))))), 344.16/44.53 inference('renaming', [status(thm)], [zip_derived_cl58, zip_derived_cl66])). 344.16/44.53 thf(zip_derived_cl74, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( (((((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))) => 344.16/44.53 (((??) @ (^[Y0 : a]: 344.16/44.53 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk28' @ X2)))))))))) 344.16/44.53 | ('#form24') 344.16/44.53 | ~ ('#form26') 344.16/44.53 | ~ ('#form31' @ X2))), 344.16/44.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl68])). 344.16/44.53 thf(zip_derived_cl82, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))) 344.16/44.53 | (((??) @ (^[Y0 : a]: 344.16/44.53 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk28' @ X2)))))))) 344.16/44.53 | ~ ('#form31' @ X2) 344.16/44.53 | ~ ('#form26') 344.16/44.53 | ('#form24'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])). 344.16/44.53 thf(zip_derived_cl87, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ ('#form44' @ X2 @ X4) 344.16/44.53 | (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl84, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( ('#form44' @ X2 @ X4) 344.16/44.53 | ~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl95, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ ('#form44' @ X2 @ (^[Y0 : a]: (X4 @ Y0))) 344.16/44.53 | ('#form24') 344.16/44.53 | ~ ('#form26') 344.16/44.53 | ~ ('#form31' @ X2) 344.16/44.53 | (((??) @ (^[Y0 : a]: 344.16/44.53 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk28' @ X2)))))))))), 344.16/44.53 inference('renaming', [status(thm)], 344.16/44.53 [zip_derived_cl82, zip_derived_cl87, zip_derived_cl84])). 344.16/44.53 thf(zip_derived_cl105, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ ('#form44' @ X2 @ X4) 344.16/44.53 | ('#form24') 344.16/44.53 | ~ ('#form26') 344.16/44.53 | ~ ('#form31' @ X2) 344.16/44.53 | (((??) @ (^[Y0 : a]: 344.16/44.53 (((X4 @ Y0) & ((('#sk4' @ Y0) = ('#sk28' @ X2)))))))))), 344.16/44.53 inference('ho_norm', [status(thm)], [zip_derived_cl95])). 344.16/44.53 thf(zip_derived_cl106, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( (((X4 @ ('#sk63' @ X2 @ X4)) & 344.16/44.53 ((('#sk4' @ ('#sk63' @ X2 @ X4)) = ('#sk28' @ X2))))) 344.16/44.53 | ~ ('#form31' @ X2) 344.16/44.53 | ~ ('#form26') 344.16/44.53 | ('#form24') 344.16/44.53 | ~ ('#form44' @ X2 @ X4))), 344.16/44.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl105])). 344.16/44.53 thf(zip_derived_cl122, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( (X4 @ ('#sk63' @ X2 @ X4)) 344.16/44.53 | ~ ('#form44' @ X2 @ X4) 344.16/44.53 | ('#form24') 344.16/44.53 | ~ ('#form26') 344.16/44.53 | ~ ('#form31' @ X2))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])). 344.16/44.53 thf(zip_derived_cl38, plain, (~ ('#form24')), 344.16/44.53 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 344.16/44.53 thf(zip_derived_cl167, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( (X4 @ ('#sk63' @ X2 @ X4)) 344.16/44.53 | ~ ('#form44' @ X2 @ X4) 344.16/44.53 | ~ ('#form26') 344.16/44.53 | ~ ('#form31' @ X2))), 344.16/44.53 inference('demod', [status(thm)], [zip_derived_cl122, zip_derived_cl38])). 344.16/44.53 thf(zip_derived_cl66, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( ('#form31' @ X2) 344.16/44.53 | ~ (((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 (((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((Y2 @ X2) & 344.16/44.53 (((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl67, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 (~ (((((!!) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))) & 344.16/44.53 (Y1 @ X4))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 ((((('#sk4' @ Y2) = (Y0))) & 344.16/44.53 (Y1 @ Y2))))))))))) => 344.16/44.53 (((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((Y1 @ X2) & 344.16/44.53 (((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 ((((('#sk4' @ Y2) = (Y0))) & 344.16/44.53 (Y1 @ Y2)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))) 344.16/44.53 | ('#form31' @ X2))), 344.16/44.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl66])). 344.16/44.53 thf(zip_derived_cl75, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 (~ (((!!) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))) & 344.16/44.53 (Y1 @ X4))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 ((((('#sk4' @ Y2) = (Y0))) & 344.16/44.53 (Y1 @ Y2))))))))))) => 344.16/44.53 (((!!) @ (^[Y1 : a > $o]: 344.16/44.53 (((((Y1 @ X2) & 344.16/44.53 (((!!) @ (^[Y2 : a]: 344.16/44.53 (((Y1 @ Y2) => (Y1 @ 344.16/44.53 ('#sk3' @ Y2))))))))) => 344.16/44.53 (((??) @ (^[Y2 : a]: 344.16/44.53 ((((('#sk4' @ Y2) = (Y0))) & 344.16/44.53 (Y1 @ Y2)))))))))))))))) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 344.16/44.53 | ('#form31' @ X2))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl67])). 344.16/44.53 thf(zip_derived_cl83, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 (~ (((((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 344.16/44.53 (Y0 @ X4))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = ('#sk40' @ X2 @ X4))) & 344.16/44.53 (Y0 @ Y1))))))))))) => 344.16/44.53 (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((Y0 @ X2) & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = ('#sk40' @ X2 @ X4))) & 344.16/44.53 (Y0 @ Y1))))))))))))) 344.16/44.53 | ('#form31' @ X2) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 344.16/44.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl75])). 344.16/44.53 thf(zip_derived_cl97, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 (~ (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((Y0 @ X2) & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = ('#sk40' @ X2 @ X4))) & 344.16/44.53 (Y0 @ Y1))))))))))) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 344.16/44.53 | ('#form31' @ X2))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl83])). 344.16/44.53 thf(zip_derived_cl108, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 (~ ((((('#sk64' @ X2 @ X4 @ X2) & 344.16/44.53 (((!!) @ (^[Y0 : a]: 344.16/44.53 ((('#sk64' @ X2 @ X4 @ Y0) => ('#sk64' @ X2 @ X4 @ 344.16/44.53 ('#sk3' @ Y0))))))))) => 344.16/44.53 (((??) @ (^[Y0 : a]: 344.16/44.53 ((((('#sk4' @ Y0) = ('#sk40' @ X2 @ X4))) & 344.16/44.53 ('#sk64' @ X2 @ X4 @ Y0)))))))) 344.16/44.53 | ('#form31' @ X2) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 344.16/44.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl97])). 344.16/44.53 thf(zip_derived_cl125, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 ( ((('#sk64' @ X2 @ X4 @ X2) & 344.16/44.53 (((!!) @ (^[Y0 : a]: 344.16/44.53 ((('#sk64' @ X2 @ X4 @ Y0) => ('#sk64' @ X2 @ X4 @ 344.16/44.53 ('#sk3' @ Y0))))))))) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 344.16/44.53 | ('#form31' @ X2))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 344.16/44.53 thf(zip_derived_cl133, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 ( ('#sk64' @ X2 @ X4 @ X2) 344.16/44.53 | ('#form31' @ X2) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl125])). 344.16/44.53 thf(zip_derived_cl109, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( ((('#sk4' @ ('#sk51' @ X2 @ X4)) = ('#sk29' @ X2))) 344.16/44.53 | ~ ('#form44' @ X2 @ X4) 344.16/44.53 | ('#form26') 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl98])). 344.16/44.53 thf(zip_derived_cl127, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ((('#sk4' @ ('#sk51' @ X2 @ X4)) = ('#sk29' @ X2)) 344.16/44.53 | ~ ('#form44' @ X2 @ X4) 344.16/44.53 | ('#form26') 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X2 @ '#sk7')))), 344.16/44.53 inference('simplify nested equalities', [status(thm)], 344.16/44.53 [zip_derived_cl109])). 344.16/44.53 thf(zip_derived_cl103, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ (((??) @ (^[Y0 : a]: 344.16/44.53 ((((('#sk4' @ Y0) = (X2))) & ('#sk45' @ X2 @ Y0)))))) 344.16/44.53 | (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((Y0 @ '#sk25') & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))) 344.16/44.53 | ('#form24') 344.16/44.53 | ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])). 344.16/44.53 thf(zip_derived_cl117, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ ('#form72' @ X2) 344.16/44.53 | (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((Y0 @ '#sk25') & 344.16/44.53 (((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = (X2))) & (Y0 @ Y1))))))))))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl119, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( ('#form72' @ X2) 344.16/44.53 | ('#form26') 344.16/44.53 | ('#form24') 344.16/44.53 | ~ (((??) @ (^[Y0 : a]: 344.16/44.53 ((((('#sk4' @ Y0) = (X2))) & ('#sk45' @ X2 @ Y0)))))))), 344.16/44.53 inference('renaming', [status(thm)], 344.16/44.53 [zip_derived_cl103, zip_derived_cl117])). 344.16/44.53 thf(zip_derived_cl129, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 (~ ((((('#sk4' @ X4) = (X2))) & ('#sk45' @ X2 @ X4))) 344.16/44.53 | ('#form24') 344.16/44.53 | ('#form26') 344.16/44.53 | ('#form72' @ X2))), 344.16/44.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl119])). 344.16/44.53 thf(zip_derived_cl136, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 (~ ((('#sk4' @ X4) = (X2))) 344.16/44.53 | ~ ('#sk45' @ X2 @ X4) 344.16/44.53 | ('#form72' @ X2) 344.16/44.53 | ('#form26') 344.16/44.53 | ('#form24'))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl129])). 344.16/44.53 thf(zip_derived_cl142, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 ((('#sk4' @ X4) != (X2)) 344.16/44.53 | ~ ('#sk45' @ X2 @ X4) 344.16/44.53 | ('#form72' @ X2) 344.16/44.53 | ('#form26') 344.16/44.53 | ('#form24'))), 344.16/44.53 inference('simplify nested equalities', [status(thm)], 344.16/44.53 [zip_derived_cl136])). 344.16/44.53 thf(zip_derived_cl143, plain, 344.16/44.53 (![X4 : a]: 344.16/44.53 ( ('#form24') 344.16/44.53 | ('#form26') 344.16/44.53 | ('#form72' @ ('#sk4' @ X4)) 344.16/44.53 | ~ ('#sk45' @ ('#sk4' @ X4) @ X4))), 344.16/44.53 inference('simplify', [status(thm)], [zip_derived_cl142])). 344.16/44.53 thf(zip_derived_cl38, plain, (~ ('#form24')), 344.16/44.53 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 344.16/44.53 thf(zip_derived_cl164, plain, 344.16/44.53 (![X4 : a]: 344.16/44.53 ( ('#form26') 344.16/44.53 | ('#form72' @ ('#sk4' @ X4)) 344.16/44.53 | ~ ('#sk45' @ ('#sk4' @ X4) @ X4))), 344.16/44.53 inference('demod', [status(thm)], [zip_derived_cl143, zip_derived_cl38])). 344.16/44.53 thf(zip_derived_cl59, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ ('#sk6' @ ('#sk28' @ X2)) 344.16/44.53 | ~ (((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 (((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((Y2 @ X2) & 344.16/44.53 (((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))) 344.16/44.53 | ('#form24') 344.16/44.53 | ~ ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 344.16/44.53 thf(zip_derived_cl66, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 ( ('#form31' @ X2) 344.16/44.53 | ~ (((??) @ (^[Y0 : a]: 344.16/44.53 (((((!!) @ (^[Y1 : a]: 344.16/44.53 (((((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))) & 344.16/44.53 (Y2 @ Y0))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3))))))))))) => 344.16/44.53 (((!!) @ (^[Y2 : a > $o]: 344.16/44.53 (((((Y2 @ X2) & 344.16/44.53 (((!!) @ (^[Y3 : a]: 344.16/44.53 ( 344.16/44.53 ( 344.16/44.53 (Y2 @ 344.16/44.53 Y3) => 344.16/44.53 (Y2 @ 344.16/44.53 ( 344.16/44.53 '#sk3' @ 344.16/44.53 Y3))))))))) => 344.16/44.53 (((??) @ (^[Y3 : a]: 344.16/44.53 (((( 344.16/44.53 ('#sk4' @ 344.16/44.53 Y3) = 344.16/44.53 (Y1))) & 344.16/44.53 (Y2 @ Y3)))))))))))))))) & 344.16/44.53 ('#sk5' @ ('#sk2' @ Y0 @ '#sk7'))))))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl69, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ ('#form31' @ X2) 344.16/44.53 | ~ ('#form26') 344.16/44.53 | ('#form24') 344.16/44.53 | ~ ('#sk6' @ ('#sk28' @ X2)))), 344.16/44.53 inference('renaming', [status(thm)], [zip_derived_cl59, zip_derived_cl66])). 344.16/44.53 thf(zip_derived_cl38, plain, (~ ('#form24')), 344.16/44.53 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 344.16/44.53 thf(zip_derived_cl160, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ ('#form31' @ X2) | ~ ('#form26') | ~ ('#sk6' @ ('#sk28' @ X2)))), 344.16/44.53 inference('demod', [status(thm)], [zip_derived_cl69, zip_derived_cl38])). 344.16/44.53 thf(zip_derived_cl123, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( ((('#sk4' @ ('#sk63' @ X2 @ X4)) = ('#sk28' @ X2))) 344.16/44.53 | ~ ('#form44' @ X2 @ X4) 344.16/44.53 | ('#form24') 344.16/44.53 | ~ ('#form26') 344.16/44.53 | ~ ('#form31' @ X2))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])). 344.16/44.53 thf(zip_derived_cl131, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ((('#sk4' @ ('#sk63' @ X2 @ X4)) = ('#sk28' @ X2)) 344.16/44.53 | ~ ('#form44' @ X2 @ X4) 344.16/44.53 | ('#form24') 344.16/44.53 | ~ ('#form26') 344.16/44.53 | ~ ('#form31' @ X2))), 344.16/44.53 inference('simplify nested equalities', [status(thm)], 344.16/44.53 [zip_derived_cl123])). 344.16/44.53 thf(zip_derived_cl38, plain, (~ ('#form24')), 344.16/44.53 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl35])). 344.16/44.53 thf(zip_derived_cl166, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ((('#sk4' @ ('#sk63' @ X2 @ X4)) = ('#sk28' @ X2)) 344.16/44.53 | ~ ('#form44' @ X2 @ X4) 344.16/44.53 | ~ ('#form26') 344.16/44.53 | ~ ('#form31' @ X2))), 344.16/44.53 inference('demod', [status(thm)], [zip_derived_cl131, zip_derived_cl38])). 344.16/44.53 thf(zip_derived_cl81, plain, 344.16/44.53 (![X2 : a]: 344.16/44.53 (~ (((??) @ (^[Y0 : a]: 344.16/44.53 ((((('#sk4' @ Y0) = (X2))) & ('#sk33' @ X2 @ Y0)))))) 344.16/44.53 | ('#sk6' @ X2) 344.16/44.53 | ~ ('#form26'))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 344.16/44.53 thf(zip_derived_cl94, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 (~ ((((('#sk4' @ X4) = (X2))) & ('#sk33' @ X2 @ X4))) 344.16/44.53 | ~ ('#form26') 344.16/44.53 | ('#sk6' @ X2))), 344.16/44.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl81])). 344.16/44.53 thf(zip_derived_cl104, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 (~ ((('#sk4' @ X4) = (X2))) 344.16/44.53 | ~ ('#sk33' @ X2 @ X4) 344.16/44.53 | ('#sk6' @ X2) 344.16/44.53 | ~ ('#form26'))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl94])). 344.16/44.53 thf(zip_derived_cl120, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 ((('#sk4' @ X4) != (X2)) 344.16/44.53 | ~ ('#sk33' @ X2 @ X4) 344.16/44.53 | ('#sk6' @ X2) 344.16/44.53 | ~ ('#form26'))), 344.16/44.53 inference('simplify nested equalities', [status(thm)], 344.16/44.53 [zip_derived_cl104])). 344.16/44.53 thf(zip_derived_cl121, plain, 344.16/44.53 (![X4 : a]: 344.16/44.53 (~ ('#form26') 344.16/44.53 | ('#sk6' @ ('#sk4' @ X4)) 344.16/44.53 | ~ ('#sk33' @ ('#sk4' @ X4) @ X4))), 344.16/44.53 inference('simplify', [status(thm)], [zip_derived_cl120])). 344.16/44.53 thf(zip_derived_cl84, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( ('#form44' @ X2 @ X4) 344.16/44.53 | ~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl85, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ (((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) 344.16/44.53 | ~ (X4 @ X2) 344.16/44.53 | ('#form44' @ X2 @ X4))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl84])). 344.16/44.53 thf(zip_derived_cl99, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ (((X4 @ ('#sk18' @ X4)) => (X4 @ ('#sk3' @ ('#sk18' @ X4))))) 344.16/44.53 | ('#form44' @ X2 @ X4) 344.16/44.53 | ~ (X4 @ X2))), 344.16/44.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl85])). 344.16/44.53 thf(zip_derived_cl111, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( (X4 @ ('#sk18' @ X4)) | ~ (X4 @ X2) | ('#form44' @ X2 @ X4))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl99])). 344.16/44.53 thf(zip_derived_cl134, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 ( (((!!) @ (^[Y0 : a]: 344.16/44.53 ((('#sk64' @ X2 @ X4 @ Y0) => ('#sk64' @ X2 @ X4 @ 344.16/44.53 ('#sk3' @ Y0))))))) 344.16/44.53 | ('#form31' @ X2) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl125])). 344.16/44.53 thf(zip_derived_cl140, plain, 344.16/44.53 (![X2 : a, X4 : a, X6 : a]: 344.16/44.53 ( ((('#sk64' @ X2 @ X4 @ X6) => ('#sk64' @ X2 @ X4 @ ('#sk3' @ X6)))) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 344.16/44.53 | ('#form31' @ X2))), 344.16/44.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl134])). 344.16/44.53 thf(zip_derived_cl147, plain, 344.16/44.53 (![X2 : a, X4 : a, X6 : a]: 344.16/44.53 (~ ('#sk64' @ X2 @ X4 @ X6) 344.16/44.53 | ('#sk64' @ X2 @ X4 @ ('#sk3' @ X6)) 344.16/44.53 | ('#form31' @ X2) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl140])). 344.16/44.53 thf(zip_derived_cl112, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ (X4 @ ('#sk3' @ ('#sk18' @ X4))) 344.16/44.53 | ~ (X4 @ X2) 344.16/44.53 | ('#form44' @ X2 @ X4))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl99])). 344.16/44.53 thf(zip_derived_cl96, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 ( (((!!) @ (^[Y0 : a > $o]: 344.16/44.53 (((((((!!) @ (^[Y1 : a]: 344.16/44.53 (((Y0 @ Y1) => (Y0 @ ('#sk3' @ Y1))))))) & 344.16/44.53 (Y0 @ X4))) => 344.16/44.53 (((??) @ (^[Y1 : a]: 344.16/44.53 ((((('#sk4' @ Y1) = ('#sk40' @ X2 @ X4))) & 344.16/44.53 (Y0 @ Y1))))))))))) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 344.16/44.53 | ('#form31' @ X2))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl83])). 344.16/44.53 thf(zip_derived_cl107, plain, 344.16/44.53 (![X2 : a, X4 : a, X6 : a > $o]: 344.16/44.53 ( (((((((!!) @ (^[Y0 : a]: (((X6 @ Y0) => (X6 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X6 @ X4))) => 344.16/44.53 (((??) @ (^[Y0 : a]: 344.16/44.53 ((((('#sk4' @ Y0) = ('#sk40' @ X2 @ X4))) & (X6 @ Y0)))))))) 344.16/44.53 | ('#form31' @ X2) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 344.16/44.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl96])). 344.16/44.53 thf(zip_derived_cl124, plain, 344.16/44.53 (![X2 : a, X4 : a, X6 : a > $o]: 344.16/44.53 (~ (((((!!) @ (^[Y0 : a]: (((X6 @ Y0) => (X6 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X6 @ X4))) 344.16/44.53 | (((??) @ (^[Y0 : a]: 344.16/44.53 ((((('#sk4' @ Y0) = ('#sk40' @ X2 @ X4))) & (X6 @ Y0)))))) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 344.16/44.53 | ('#form31' @ X2))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])). 344.16/44.53 thf(zip_derived_cl87, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 (~ ('#form44' @ X2 @ X4) 344.16/44.53 | (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl84, plain, 344.16/44.53 (![X2 : a, X4 : a > $o]: 344.16/44.53 ( ('#form44' @ X2 @ X4) 344.16/44.53 | ~ (((((!!) @ (^[Y0 : a]: (((X4 @ Y0) => (X4 @ ('#sk3' @ Y0))))))) & 344.16/44.53 (X4 @ X2))))), 344.16/44.53 define([status(thm)])). 344.16/44.53 thf(zip_derived_cl132, plain, 344.16/44.53 (![X2 : a, X4 : a, X6 : a > $o]: 344.16/44.53 (~ ('#form44' @ X4 @ (^[Y0 : a]: (X6 @ Y0))) 344.16/44.53 | ('#form31' @ X2) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 344.16/44.53 | (((??) @ (^[Y0 : a]: 344.16/44.53 ((((('#sk4' @ Y0) = ('#sk40' @ X2 @ X4))) & (X6 @ Y0)))))))), 344.16/44.53 inference('renaming', [status(thm)], 344.16/44.53 [zip_derived_cl124, zip_derived_cl87, zip_derived_cl84])). 344.16/44.53 thf(zip_derived_cl138, plain, 344.16/44.53 (![X2 : a, X4 : a, X6 : a > $o]: 344.16/44.53 (~ ('#form44' @ X4 @ X6) 344.16/44.53 | ('#form31' @ X2) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 344.16/44.53 | (((??) @ (^[Y0 : a]: 344.16/44.53 ((((('#sk4' @ Y0) = ('#sk40' @ X2 @ X4))) & (X6 @ Y0)))))))), 344.16/44.53 inference('ho_norm', [status(thm)], [zip_derived_cl132])). 344.16/44.53 thf(zip_derived_cl139, plain, 344.16/44.53 (![X2 : a, X4 : a, X6 : a > $o]: 344.16/44.53 ( ((((('#sk4' @ ('#sk109' @ X2 @ X4 @ X6)) = ('#sk40' @ X2 @ X4))) & 344.16/44.53 (X6 @ ('#sk109' @ X2 @ X4 @ X6)))) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 344.16/44.53 | ('#form31' @ X2) 344.16/44.53 | ~ ('#form44' @ X4 @ X6))), 344.16/44.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl138])). 344.16/44.53 thf(zip_derived_cl145, plain, 344.16/44.53 (![X2 : a, X4 : a, X6 : a > $o]: 344.16/44.53 ( ((('#sk4' @ ('#sk109' @ X2 @ X4 @ X6)) = ('#sk40' @ X2 @ X4))) 344.16/44.53 | ~ ('#form44' @ X4 @ X6) 344.16/44.53 | ('#form31' @ X2) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl139])). 344.16/44.53 thf(zip_derived_cl151, plain, 344.16/44.53 (![X2 : a, X4 : a, X6 : a > $o]: 344.16/44.53 ((('#sk4' @ ('#sk109' @ X2 @ X4 @ X6)) = ('#sk40' @ X2 @ X4)) 344.16/44.53 | ~ ('#form44' @ X4 @ X6) 344.16/44.53 | ('#form31' @ X2) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 344.16/44.53 inference('simplify nested equalities', [status(thm)], 344.16/44.53 [zip_derived_cl145])). 344.16/44.53 thf(zip_derived_cl146, plain, 344.16/44.53 (![X2 : a, X4 : a, X6 : a > $o]: 344.16/44.53 ( (X6 @ ('#sk109' @ X2 @ X4 @ X6)) 344.16/44.53 | ~ ('#form44' @ X4 @ X6) 344.16/44.53 | ('#form31' @ X2) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl139])). 344.16/44.53 thf(zip_derived_cl126, plain, 344.16/44.53 (![X2 : a, X4 : a]: 344.16/44.53 (~ (((??) @ (^[Y0 : a]: 344.16/44.53 ((((('#sk4' @ Y0) = ('#sk40' @ X2 @ X4))) & ('#sk64' @ 344.16/44.53 X2 @ X4 @ Y0)))))) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 344.16/44.53 | ('#form31' @ X2))), 344.16/44.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 344.16/44.53 thf(zip_derived_cl135, plain, 344.16/44.53 (![X2 : a, X4 : a, X6 : a]: 344.16/44.53 (~ ((((('#sk4' @ X6) = ('#sk40' @ X2 @ X4))) & ('#sk64' @ X2 @ X4 @ 344.16/44.53 X6))) 344.16/44.53 | ('#form31' @ X2) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')))), 344.16/44.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl126])). 344.16/44.53 thf(zip_derived_cl141, plain, 344.16/44.53 (![X2 : a, X4 : a, X6 : a]: 344.16/44.53 (~ ((('#sk4' @ X6) = ('#sk40' @ X2 @ X4))) 344.16/44.53 | ~ ('#sk64' @ X2 @ X4 @ X6) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 344.16/44.53 | ('#form31' @ X2))), 344.16/44.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl135])). 344.16/44.53 thf(zip_derived_cl148, plain, 344.16/44.53 (![X2 : a, X4 : a, X6 : a]: 344.16/44.53 ((('#sk4' @ X6) != ('#sk40' @ X2 @ X4)) 344.16/44.53 | ~ ('#sk64' @ X2 @ X4 @ X6) 344.16/44.53 | ~ ('#sk5' @ ('#sk2' @ X4 @ '#sk7')) 344.16/44.53 | ('#form31' @ X2))), 344.16/44.53 inference('simplify nested equalities', [status(thm)], 344.16/44.53 [zip_derived_cl141])). 344.16/44.53 thf(zip_derived_cl18397, plain, ($false), 344.16/44.53 inference('eprover', [status(thm)], 344.16/44.53 [zip_derived_cl1283, zip_derived_cl157, zip_derived_cl154, 344.16/44.53 zip_derived_cl159, zip_derived_cl162, zip_derived_cl163, 344.16/44.53 zip_derived_cl113, zip_derived_cl161, zip_derived_cl158, 344.16/44.53 zip_derived_cl89, zip_derived_cl51, zip_derived_cl165, 344.16/44.53 zip_derived_cl93, zip_derived_cl110, zip_derived_cl167, 344.16/44.53 zip_derived_cl133, zip_derived_cl127, zip_derived_cl164, 344.16/44.53 zip_derived_cl160, zip_derived_cl166, zip_derived_cl121, 344.16/44.53 zip_derived_cl111, zip_derived_cl147, zip_derived_cl112, 344.16/44.53 zip_derived_cl151, zip_derived_cl146, zip_derived_cl148])). 344.16/44.53 344.16/44.53 % SZS output end Refutation 344.16/44.53 344.16/44.53 344.16/44.53 % Terminating... 345.05/44.65 % Runner terminated. 345.05/44.65 % Zipperpin 1.5 exiting 345.05/44.65 EOF