0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.G8dyWKU033 true 0.15/0.35 % Computer : n023.cluster.edu 0.15/0.35 % Model : x86_64 x86_64 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.35 % Memory : 8042.1875MB 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.35 % CPULimit : 960 0.15/0.35 % WCLimit : 120 0.15/0.35 % DateTime : Tue Aug 9 07:17:58 EDT 2022 0.15/0.36 % CPUTime : 0.15/0.36 % Running portfolio for 960 s 0.15/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.15/0.36 % Number of cores: 8 0.15/0.36 % Python version: Python 3.6.8 0.15/0.36 % Running in HO mode 0.51/0.67 % Total configuration time : 828 0.51/0.67 % Estimated wc time : 1656 0.51/0.67 % Estimated cpu time (8 cpus) : 207.0 0.51/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.51/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.51/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.51/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.51/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.51/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.51/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.53/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 12.21/2.17 % Solved by lams/20_acsne_simpl.sh. 12.21/2.17 % done 3453 iterations in 1.343s 12.21/2.17 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 12.21/2.17 % SZS output start Refutation 12.21/2.17 thf(a_type, type, a: $tType). 12.21/2.17 thf(b_type, type, b: $tType). 12.21/2.17 thf('#_fresh_sk6_type', type, '#_fresh_sk6': a > b). 12.21/2.17 thf('#sk14_type', type, '#sk14': a). 12.21/2.17 thf('#sk7_type', type, '#sk7': a > b). 12.21/2.17 thf('#sk10_type', type, '#sk10': a > b). 12.21/2.17 thf('#sk13_type', type, '#sk13': a > b). 12.21/2.17 thf('#sk22_type', type, '#sk22': a). 12.21/2.17 thf('#sk8_type', type, '#sk8': a > b). 12.21/2.17 thf('#form9_type', type, '#form9': $o). 12.21/2.17 thf('#sk16_type', type, '#sk16': a). 12.21/2.17 thf('#sk3_type', type, '#sk3': a > b > b > $o). 12.21/2.17 thf('#form12_type', type, '#form12': $o). 12.21/2.17 thf('#sk18_type', type, '#sk18': a). 12.21/2.17 thf('#form20_type', type, '#form20': $o). 12.21/2.17 thf('#_fresh_sk5_type', type, '#_fresh_sk5': a > b). 12.21/2.17 thf('#sk17_type', type, '#sk17': a). 12.21/2.17 thf('#sk2_type', type, '#sk2': a > a > $o). 12.21/2.17 thf('#sk19_type', type, '#sk19': a). 12.21/2.17 thf('#sk1_type', type, '#sk1': a > a > $o). 12.21/2.17 thf('#sk21_type', type, '#sk21': a). 12.21/2.17 thf('#sk15_type', type, '#sk15': a). 12.21/2.17 thf('#sk11_type', type, '#sk11': a > b). 12.21/2.17 thf('#sk4_type', type, '#sk4': a > b > b > $o). 12.21/2.17 thf(cTHM517_pme, conjecture, 12.21/2.17 (![Xp:( a > a > $o ),Xq:( a > a > $o ),Xr:( a > b > b > $o ), 12.21/2.17 Xs:( a > b > b > $o )]: 12.21/2.17 ( ( ( ![Xx:a,Xy:a]: ( ( Xp @ Xx @ Xy ) => ( Xp @ Xy @ Xx ) ) ) & 12.21/2.17 ( ![Xx:a,Xy:a,Xz:a]: 12.21/2.17 ( ( ( Xp @ Xx @ Xy ) & ( Xp @ Xy @ Xz ) ) => ( Xp @ Xx @ Xz ) ) ) & 12.21/2.17 ( ( Xp ) = ( Xq ) ) ) => 12.21/2.17 ( ( ![Xx:a,Xy:a]: 12.21/2.17 ( ( Xp @ Xx @ Xy ) => 12.21/2.17 ( ( ![Xx0:b,Xy0:b,Xz:b]: 12.21/2.17 ( ( ( Xr @ Xx @ Xx0 @ Xy0 ) & ( Xr @ Xx @ Xy0 @ Xz ) ) => 12.21/2.17 ( Xr @ Xx @ Xx0 @ Xz ) ) ) & 12.21/2.17 ( ( Xr @ Xx ) = ( Xr @ Xy ) ) & 12.21/2.17 ( ![Xx0:b,Xy0:b]: 12.21/2.17 ( ( Xr @ Xx @ Xx0 @ Xy0 ) => ( Xr @ Xx @ Xy0 @ Xx0 ) ) ) ) ) ) => 12.21/2.17 ( ( ![Xx:a]: 12.21/2.17 ( ( Xp @ Xx @ Xx ) => 12.21/2.17 ( ( ![Xx0:b,Xy:b,Xz:b]: 12.21/2.17 ( ( ( Xr @ Xx @ Xx0 @ Xy ) & ( Xr @ Xx @ Xy @ Xz ) ) => 12.21/2.17 ( Xr @ Xx @ Xx0 @ Xz ) ) ) & 12.21/2.18 ( ( Xr @ Xx ) = ( Xs @ Xx ) ) & 12.21/2.18 ( ![Xx0:b,Xy:b]: 12.21/2.18 ( ( Xr @ Xx @ Xx0 @ Xy ) => ( Xr @ Xx @ Xy @ Xx0 ) ) ) ) ) ) => 12.21/2.18 ( ( ![Xx:( a > b ),Xy:( a > b )]: 12.21/2.18 ( ( ![Xx0:a,Xy0:a]: 12.21/2.18 ( ( Xp @ Xx0 @ Xy0 ) => 12.21/2.18 ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) ) ) => 12.21/2.18 ( ![Xx0:a,Xy0:a]: 12.21/2.18 ( ( Xp @ Xx0 @ Xy0 ) => 12.21/2.18 ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xy0 ) ) ) ) ) ) & 12.21/2.18 ( ( ^[Xf:( a > b ),Xg:( a > b )]: 12.21/2.18 ( ![Xx:a,Xy:a]: 12.21/2.18 ( ( Xp @ Xx @ Xy ) => 12.21/2.18 ( Xr @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) ) = 12.21/2.18 ( ^[Xf:( a > b ),Xg:( a > b )]: 12.21/2.18 ( ![Xx:a,Xy:a]: 12.21/2.18 ( ( Xq @ Xx @ Xy ) => 12.21/2.18 ( Xs @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) ) ) & 12.21/2.18 ( ![Xx:( a > b ),Xy:( a > b ),Xz:( a > b )]: 12.21/2.18 ( ( ( ![Xx0:a,Xy0:a]: 12.21/2.18 ( ( Xp @ Xx0 @ Xy0 ) => 12.21/2.18 ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) ) ) & 12.21/2.18 ( ![Xx0:a,Xy0:a]: 12.21/2.18 ( ( Xp @ Xx0 @ Xy0 ) => 12.21/2.18 ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xy0 ) ) ) ) ) => 12.21/2.18 ( ![Xx0:a,Xy0:a]: 12.21/2.18 ( ( Xp @ Xx0 @ Xy0 ) => 12.21/2.18 ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xy0 ) ) ) ) ) ) ) ) ) ))). 12.21/2.18 thf(zf_stmt_0, negated_conjecture, 12.21/2.18 (~( ![Xp:( a > a > $o ),Xq:( a > a > $o ),Xr:( a > b > b > $o ), 12.21/2.18 Xs:( a > b > b > $o )]: 12.21/2.18 ( ( ( ![Xx:a,Xy:a]: ( ( Xp @ Xx @ Xy ) => ( Xp @ Xy @ Xx ) ) ) & 12.21/2.18 ( ![Xx:a,Xy:a,Xz:a]: 12.21/2.18 ( ( ( Xp @ Xx @ Xy ) & ( Xp @ Xy @ Xz ) ) => ( Xp @ Xx @ Xz ) ) ) & 12.21/2.18 ( ( Xp ) = ( Xq ) ) ) => 12.21/2.18 ( ( ![Xx:a,Xy:a]: 12.21/2.18 ( ( Xp @ Xx @ Xy ) => 12.21/2.18 ( ( ![Xx0:b,Xy0:b,Xz:b]: 12.21/2.18 ( ( ( Xr @ Xx @ Xx0 @ Xy0 ) & ( Xr @ Xx @ Xy0 @ Xz ) ) => 12.21/2.18 ( Xr @ Xx @ Xx0 @ Xz ) ) ) & 12.21/2.18 ( ( Xr @ Xx ) = ( Xr @ Xy ) ) & 12.21/2.18 ( ![Xx0:b,Xy0:b]: 12.21/2.18 ( ( Xr @ Xx @ Xx0 @ Xy0 ) => ( Xr @ Xx @ Xy0 @ Xx0 ) ) ) ) ) ) => 12.21/2.18 ( ( ![Xx:a]: 12.21/2.18 ( ( Xp @ Xx @ Xx ) => 12.21/2.18 ( ( ![Xx0:b,Xy:b,Xz:b]: 12.21/2.18 ( ( ( Xr @ Xx @ Xx0 @ Xy ) & ( Xr @ Xx @ Xy @ Xz ) ) => 12.21/2.18 ( Xr @ Xx @ Xx0 @ Xz ) ) ) & 12.21/2.18 ( ( Xr @ Xx ) = ( Xs @ Xx ) ) & 12.21/2.18 ( ![Xx0:b,Xy:b]: 12.21/2.18 ( ( Xr @ Xx @ Xx0 @ Xy ) => ( Xr @ Xx @ Xy @ Xx0 ) ) ) ) ) ) => 12.21/2.18 ( ( ![Xx:( a > b ),Xy:( a > b )]: 12.21/2.18 ( ( ![Xx0:a,Xy0:a]: 12.21/2.18 ( ( Xp @ Xx0 @ Xy0 ) => 12.21/2.18 ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) ) ) => 12.21/2.18 ( ![Xx0:a,Xy0:a]: 12.21/2.18 ( ( Xp @ Xx0 @ Xy0 ) => 12.21/2.18 ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xy0 ) ) ) ) ) ) & 12.21/2.18 ( ( ^[Xf:( a > b ),Xg:( a > b )]: 12.21/2.18 ( ![Xx:a,Xy:a]: 12.21/2.18 ( ( Xp @ Xx @ Xy ) => 12.21/2.18 ( Xr @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) ) = 12.21/2.18 ( ^[Xf:( a > b ),Xg:( a > b )]: 12.21/2.18 ( ![Xx:a,Xy:a]: 12.21/2.18 ( ( Xq @ Xx @ Xy ) => 12.21/2.18 ( Xs @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) ) ) & 12.21/2.18 ( ![Xx:( a > b ),Xy:( a > b ),Xz:( a > b )]: 12.21/2.18 ( ( ( ![Xx0:a,Xy0:a]: 12.21/2.18 ( ( Xp @ Xx0 @ Xy0 ) => 12.21/2.18 ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) ) ) & 12.21/2.18 ( ![Xx0:a,Xy0:a]: 12.21/2.18 ( ( Xp @ Xx0 @ Xy0 ) => 12.21/2.18 ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xy0 ) ) ) ) ) => 12.21/2.18 ( ![Xx0:a,Xy0:a]: 12.21/2.18 ( ( Xp @ Xx0 @ Xy0 ) => 12.21/2.18 ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xy0 ) ) ) ) ) ) ) ) ) ) )), 12.21/2.18 inference('cnf.neg', [status(esa)], [cTHM517_pme])). 12.21/2.18 thf(zip_derived_cl0, plain, 12.21/2.18 (~ (((!!) @ (^[Y0 : a > a > $o]: 12.21/2.18 (((!!) @ (^[Y1 : a > a > $o]: 12.21/2.18 (((!!) @ (^[Y2 : a > b > b > $o]: 12.21/2.18 (((!!) @ (^[Y3 : a > b > b > $o]: 12.21/2.18 (((((((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 (Y0 @ 12.21/2.18 Y4 @ 12.21/2.18 Y5) => 12.21/2.18 (Y0 @ 12.21/2.18 Y5 @ Y4))))))))) & 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : a]: 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 (Y0 @ 12.21/2.18 Y4 @ 12.21/2.18 Y5) & 12.21/2.18 (Y0 @ 12.21/2.18 Y5 @ Y6))) => 12.21/2.18 (Y0 @ 12.21/2.18 Y4 @ Y6)))))))))))) & 12.21/2.18 (((Y0) = (Y1))))) => 12.21/2.18 (((((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 (Y0 @ 12.21/2.18 Y4 @ 12.21/2.18 Y5) => 12.21/2.18 (( 12.21/2.18 ( 12.21/2.18 ( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y7 : b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y8 : b]: 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 (Y2 @ 12.21/2.18 Y4 @ 12.21/2.18 Y6 @ 12.21/2.18 Y7) & 12.21/2.18 (Y2 @ 12.21/2.18 Y4 @ 12.21/2.18 Y7 @ Y8))) => 12.21/2.18 (Y2 @ 12.21/2.18 Y4 @ 12.21/2.18 Y6 @ Y8)))))))))))) & 12.21/2.18 ( 12.21/2.18 ( 12.21/2.18 (Y2 @ 12.21/2.18 Y4) = 12.21/2.18 (Y2 @ Y5))) & 12.21/2.18 ( 12.21/2.18 ( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y7 : b]: 12.21/2.18 (( 12.21/2.18 (Y2 @ 12.21/2.18 Y4 @ 12.21/2.18 Y6 @ 12.21/2.18 Y7) => 12.21/2.18 (Y2 @ 12.21/2.18 Y4 @ 12.21/2.18 Y7 @ Y6))))))))))))))))))) => 12.21/2.18 (((((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (((Y0 @ 12.21/2.18 Y4 @ 12.21/2.18 Y4) => 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y7 : b]: 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 (Y2 @ 12.21/2.18 Y4 @ 12.21/2.18 Y5 @ 12.21/2.18 Y6) & 12.21/2.18 (Y2 @ 12.21/2.18 Y4 @ 12.21/2.18 Y6 @ Y7))) => 12.21/2.18 (Y2 @ 12.21/2.18 Y4 @ 12.21/2.18 Y5 @ Y7)))))))))))) & 12.21/2.18 (( 12.21/2.18 (Y2 @ 12.21/2.18 Y4) = 12.21/2.18 (Y3 @ Y4))) & 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : b]: 12.21/2.18 (( 12.21/2.18 (Y2 @ 12.21/2.18 Y4 @ 12.21/2.18 Y5 @ 12.21/2.18 Y6) => 12.21/2.18 (Y2 @ 12.21/2.18 Y4 @ 12.21/2.18 Y6 @ Y5)))))))))))))))) => 12.21/2.18 (((((!!) @ ( 12.21/2.18 ^[Y4 : a > b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : a > b]: 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y7 : a]: 12.21/2.18 (( 12.21/2.18 (Y0 @ 12.21/2.18 Y6 @ 12.21/2.18 Y7) => 12.21/2.18 (Y2 @ 12.21/2.18 Y6 @ 12.21/2.18 ( 12.21/2.18 Y4 @ Y6) @ 12.21/2.18 ( 12.21/2.18 Y5 @ Y7)))))))))) => 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y7 : a]: 12.21/2.18 (( 12.21/2.18 (Y0 @ 12.21/2.18 Y6 @ 12.21/2.18 Y7) => 12.21/2.18 (Y2 @ 12.21/2.18 Y6 @ 12.21/2.18 ( 12.21/2.18 Y5 @ Y6) @ 12.21/2.18 ( 12.21/2.18 Y4 @ Y7)))))))))))))))))) & 12.21/2.18 ((((^[Y4 : a > b, 12.21/2.18 Y5 : a > b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y7 : a]: 12.21/2.18 (( 12.21/2.18 (Y0 @ 12.21/2.18 Y6 @ 12.21/2.18 Y7) => 12.21/2.18 (Y2 @ 12.21/2.18 Y6 @ 12.21/2.18 ( 12.21/2.18 Y4 @ Y6) @ 12.21/2.18 ( 12.21/2.18 Y5 @ Y7)))))))))))) = 12.21/2.18 ((^[Y4 : a > b, 12.21/2.18 Y5 : a > b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y7 : a]: 12.21/2.18 (( 12.21/2.18 (Y1 @ 12.21/2.18 Y6 @ 12.21/2.18 Y7) => 12.21/2.18 (Y3 @ 12.21/2.18 Y6 @ 12.21/2.18 ( 12.21/2.18 Y4 @ Y6) @ 12.21/2.18 ( 12.21/2.18 Y5 @ Y7)))))))))))))) & 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a > b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : a > b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : a > b]: 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y7 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y8 : a]: 12.21/2.18 (( 12.21/2.18 (Y0 @ 12.21/2.18 Y7 @ 12.21/2.18 Y8) => 12.21/2.18 (Y2 @ 12.21/2.18 Y7 @ 12.21/2.18 ( 12.21/2.18 Y4 @ Y7) @ 12.21/2.18 ( 12.21/2.18 Y5 @ Y8)))))))))) & 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y7 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y8 : a]: 12.21/2.18 (( 12.21/2.18 (Y0 @ 12.21/2.18 Y7 @ 12.21/2.18 Y8) => 12.21/2.18 (Y2 @ 12.21/2.18 Y7 @ 12.21/2.18 ( 12.21/2.18 Y5 @ Y7) @ 12.21/2.18 ( 12.21/2.18 Y6 @ Y8)))))))))))) => 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y7 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y8 : a]: 12.21/2.18 (( 12.21/2.18 (Y0 @ 12.21/2.18 Y7 @ 12.21/2.18 Y8) => 12.21/2.18 (Y2 @ 12.21/2.18 Y7 @ 12.21/2.18 ( 12.21/2.18 Y4 @ Y7) @ 12.21/2.18 ( 12.21/2.18 Y6 @ Y8)))))))))))))))))))))))))))))))))))))))))), 12.21/2.18 inference('cnf', [status(esa)], [zf_stmt_0])). 12.21/2.18 thf(zip_derived_cl1, plain, 12.21/2.18 (~ (((!!) @ (^[Y0 : a > a > $o]: 12.21/2.18 (((!!) @ (^[Y1 : a > b > b > $o]: 12.21/2.18 (((!!) @ (^[Y2 : a > b > b > $o]: 12.21/2.18 (((((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ Y4) => 12.21/2.18 ('#sk1' @ 12.21/2.18 Y4 @ Y3))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) & 12.21/2.18 ('#sk1' @ 12.21/2.18 Y4 @ Y5))) => 12.21/2.18 ('#sk1' @ 12.21/2.18 Y3 @ Y5)))))))))))) & 12.21/2.18 ((('#sk1') = (Y0))))) => 12.21/2.18 (((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ Y4) => 12.21/2.18 (((( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y7 : b]: 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 (Y1 @ 12.21/2.18 Y3 @ 12.21/2.18 Y5 @ 12.21/2.18 Y6) & 12.21/2.18 (Y1 @ 12.21/2.18 Y3 @ 12.21/2.18 Y6 @ Y7))) => 12.21/2.18 (Y1 @ 12.21/2.18 Y3 @ 12.21/2.18 Y5 @ Y7)))))))))))) & 12.21/2.18 (( 12.21/2.18 (Y1 @ 12.21/2.18 Y3) = 12.21/2.18 (Y1 @ Y4))) & 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : b]: 12.21/2.18 (( 12.21/2.18 (Y1 @ 12.21/2.18 Y3 @ 12.21/2.18 Y5 @ 12.21/2.18 Y6) => 12.21/2.18 (Y1 @ 12.21/2.18 Y3 @ 12.21/2.18 Y6 @ Y5))))))))))))))))))) => 12.21/2.18 (((((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ Y3) => 12.21/2.18 (((((!!) @ ( 12.21/2.18 ^[Y4 : b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : b]: 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 (Y1 @ 12.21/2.18 Y3 @ 12.21/2.18 Y4 @ 12.21/2.18 Y5) & 12.21/2.18 (Y1 @ 12.21/2.18 Y3 @ 12.21/2.18 Y5 @ Y6))) => 12.21/2.18 (Y1 @ 12.21/2.18 Y3 @ 12.21/2.18 Y4 @ Y6)))))))))))) & 12.21/2.18 (((Y1 @ 12.21/2.18 Y3) = 12.21/2.18 (Y2 @ Y3))) & 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : b]: 12.21/2.18 (( 12.21/2.18 (Y1 @ 12.21/2.18 Y3 @ 12.21/2.18 Y4 @ 12.21/2.18 Y5) => 12.21/2.18 (Y1 @ 12.21/2.18 Y3 @ 12.21/2.18 Y5 @ Y4)))))))))))))))) => 12.21/2.18 (((((!!) @ (^[Y3 : a > b]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a > b]: 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y5 @ 12.21/2.18 Y6) => 12.21/2.18 (Y1 @ 12.21/2.18 Y5 @ 12.21/2.18 ( 12.21/2.18 Y3 @ Y5) @ 12.21/2.18 ( 12.21/2.18 Y4 @ Y6)))))))))) => 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y5 @ 12.21/2.18 Y6) => 12.21/2.18 (Y1 @ 12.21/2.18 Y5 @ 12.21/2.18 ( 12.21/2.18 Y4 @ Y5) @ 12.21/2.18 ( 12.21/2.18 Y3 @ Y6)))))))))))))))))) & 12.21/2.18 ((((^[Y3 : a > b, 12.21/2.18 Y4 : a > b]: 12.21/2.18 (((!!) @ (^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y5 @ 12.21/2.18 Y6) => 12.21/2.18 (Y1 @ 12.21/2.18 Y5 @ 12.21/2.18 ( 12.21/2.18 Y3 @ Y5) @ 12.21/2.18 ( 12.21/2.18 Y4 @ Y6)))))))))))) = 12.21/2.18 ((^[Y3 : a > b, 12.21/2.18 Y4 : a > b]: 12.21/2.18 (((!!) @ (^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : a]: 12.21/2.18 (( 12.21/2.18 (Y0 @ 12.21/2.18 Y5 @ 12.21/2.18 Y6) => 12.21/2.18 (Y2 @ 12.21/2.18 Y5 @ 12.21/2.18 ( 12.21/2.18 Y3 @ Y5) @ 12.21/2.18 ( 12.21/2.18 Y4 @ Y6)))))))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a > b]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a > b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : a > b]: 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y7 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y6 @ 12.21/2.18 Y7) => 12.21/2.18 (Y1 @ 12.21/2.18 Y6 @ 12.21/2.18 ( 12.21/2.18 Y3 @ Y6) @ 12.21/2.18 ( 12.21/2.18 Y4 @ Y7)))))))))) & 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y7 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y6 @ 12.21/2.18 Y7) => 12.21/2.18 (Y1 @ 12.21/2.18 Y6 @ 12.21/2.18 ( 12.21/2.18 Y4 @ Y6) @ 12.21/2.18 ( 12.21/2.18 Y5 @ Y7)))))))))))) => 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y7 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y6 @ 12.21/2.18 Y7) => 12.21/2.18 (Y1 @ 12.21/2.18 Y6 @ 12.21/2.18 ( 12.21/2.18 Y3 @ Y6) @ 12.21/2.18 ( 12.21/2.18 Y5 @ Y7))))))))))))))))))))))))))))))))))))))), 12.21/2.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 12.21/2.18 thf(zip_derived_cl2, plain, 12.21/2.18 (~ (((!!) @ (^[Y0 : a > b > b > $o]: 12.21/2.18 (((!!) @ (^[Y1 : a > b > b > $o]: 12.21/2.18 (((((((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ 12.21/2.18 Y3) => 12.21/2.18 ('#sk1' @ Y3 @ 12.21/2.18 Y2))))))))) & 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((((('#sk1' @ 12.21/2.18 Y2 @ Y3) & 12.21/2.18 ('#sk1' @ 12.21/2.18 Y3 @ Y4))) => 12.21/2.18 ('#sk1' @ 12.21/2.18 Y2 @ Y4)))))))))))) & 12.21/2.18 ((('#sk1') = ('#sk2'))))) => 12.21/2.18 (((((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ 12.21/2.18 Y3) => 12.21/2.18 (((((!!) @ ( 12.21/2.18 ^[Y4 : b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : b]: 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 (Y0 @ 12.21/2.18 Y2 @ 12.21/2.18 Y4 @ 12.21/2.18 Y5) & 12.21/2.18 (Y0 @ 12.21/2.18 Y2 @ 12.21/2.18 Y5 @ Y6))) => 12.21/2.18 (Y0 @ 12.21/2.18 Y2 @ 12.21/2.18 Y4 @ Y6)))))))))))) & 12.21/2.18 (((Y0 @ Y2) = 12.21/2.18 (Y0 @ Y3))) & 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : b]: 12.21/2.18 (( 12.21/2.18 (Y0 @ 12.21/2.18 Y2 @ 12.21/2.18 Y4 @ 12.21/2.18 Y5) => 12.21/2.18 (Y0 @ 12.21/2.18 Y2 @ 12.21/2.18 Y5 @ Y4))))))))))))))))))) => 12.21/2.18 (((((!!) @ (^[Y2 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ Y2) => 12.21/2.18 (((((!!) @ (^[Y3 : b]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : b]: 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 (Y0 @ 12.21/2.18 Y2 @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) & 12.21/2.18 (Y0 @ 12.21/2.18 Y2 @ 12.21/2.18 Y4 @ Y5))) => 12.21/2.18 (Y0 @ 12.21/2.18 Y2 @ 12.21/2.18 Y3 @ Y5)))))))))))) & 12.21/2.18 (((Y0 @ Y2) = (Y1 @ Y2))) & 12.21/2.18 (((!!) @ (^[Y3 : b]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : b]: 12.21/2.18 (( 12.21/2.18 (Y0 @ 12.21/2.18 Y2 @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 (Y0 @ 12.21/2.18 Y2 @ 12.21/2.18 Y4 @ Y3)))))))))))))))) => 12.21/2.18 (((((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((!!) @ (^[Y3 : a > b]: 12.21/2.18 (((((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y4 @ 12.21/2.18 Y5) => 12.21/2.18 (Y0 @ 12.21/2.18 Y4 @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4) @ 12.21/2.18 ( 12.21/2.18 Y3 @ Y5)))))))))) => 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y4 @ 12.21/2.18 Y5) => 12.21/2.18 (Y0 @ 12.21/2.18 Y4 @ 12.21/2.18 ( 12.21/2.18 Y3 @ Y4) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y5)))))))))))))))))) & 12.21/2.18 ((((^[Y2 : a > b,Y3 : a > b]: 12.21/2.18 (((!!) @ (^[Y4 : a]: 12.21/2.18 (((!!) @ (^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y4 @ 12.21/2.18 Y5) => 12.21/2.18 (Y0 @ 12.21/2.18 Y4 @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4) @ 12.21/2.18 ( 12.21/2.18 Y3 @ Y5)))))))))))) = 12.21/2.18 ((^[Y2 : a > b,Y3 : a > b]: 12.21/2.18 (((!!) @ (^[Y4 : a]: 12.21/2.18 (((!!) @ (^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk2' @ 12.21/2.18 Y4 @ 12.21/2.18 Y5) => 12.21/2.18 (Y1 @ 12.21/2.18 Y4 @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4) @ 12.21/2.18 ( 12.21/2.18 Y3 @ Y5)))))))))))))) & 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((!!) @ (^[Y3 : a > b]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a > b]: 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y5 @ 12.21/2.18 Y6) => 12.21/2.18 (Y0 @ 12.21/2.18 Y5 @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y5) @ 12.21/2.18 ( 12.21/2.18 Y3 @ Y6)))))))))) & 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y5 @ 12.21/2.18 Y6) => 12.21/2.18 (Y0 @ 12.21/2.18 Y5 @ 12.21/2.18 ( 12.21/2.18 Y3 @ Y5) @ 12.21/2.18 ( 12.21/2.18 Y4 @ Y6)))))))))))) => 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y6 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y5 @ 12.21/2.18 Y6) => 12.21/2.18 (Y0 @ 12.21/2.18 Y5 @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y5) @ 12.21/2.18 ( 12.21/2.18 Y4 @ Y6)))))))))))))))))))))))))))))))))))), 12.21/2.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 12.21/2.18 thf(zip_derived_cl3, plain, 12.21/2.18 (~ (((!!) @ (^[Y0 : a > b > b > $o]: 12.21/2.18 (((((((!!) @ (^[Y1 : a]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 ((('#sk1' @ Y1 @ Y2) => 12.21/2.18 ('#sk1' @ Y2 @ Y1))))))))) & 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((((('#sk1' @ 12.21/2.18 Y1 @ Y2) & 12.21/2.18 ('#sk1' @ 12.21/2.18 Y2 @ Y3))) => 12.21/2.18 ('#sk1' @ Y1 @ 12.21/2.18 Y3)))))))))))) & 12.21/2.18 ((('#sk1') = ('#sk2'))))) => 12.21/2.18 (((((!!) @ (^[Y1 : a]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 ((('#sk1' @ Y1 @ Y2) => 12.21/2.18 (((((!!) @ (^[Y3 : b]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : b]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : b]: 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 ('#sk3' @ 12.21/2.18 Y1 @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) & 12.21/2.18 ('#sk3' @ 12.21/2.18 Y1 @ 12.21/2.18 Y4 @ Y5))) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y1 @ 12.21/2.18 Y3 @ Y5)))))))))))) & 12.21/2.18 ((('#sk3' @ Y1) = 12.21/2.18 ('#sk3' @ Y2))) & 12.21/2.18 (((!!) @ (^[Y3 : b]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : b]: 12.21/2.18 (( 12.21/2.18 ('#sk3' @ 12.21/2.18 Y1 @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y1 @ 12.21/2.18 Y4 @ Y3))))))))))))))))))) => 12.21/2.18 (((((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y1 @ Y1) => 12.21/2.18 (((((!!) @ (^[Y2 : b]: 12.21/2.18 (((!!) @ (^[Y3 : b]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : b]: 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 ('#sk3' @ 12.21/2.18 Y1 @ 12.21/2.18 Y2 @ 12.21/2.18 Y3) & 12.21/2.18 ('#sk3' @ 12.21/2.18 Y1 @ 12.21/2.18 Y3 @ Y4))) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y1 @ 12.21/2.18 Y2 @ Y4)))))))))))) & 12.21/2.18 ((('#sk3' @ Y1) = (Y0 @ Y1))) & 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 (((!!) @ (^[Y3 : b]: 12.21/2.18 ((('#sk3' @ 12.21/2.18 Y1 @ Y2 @ 12.21/2.18 Y3) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y1 @ Y3 @ 12.21/2.18 Y2)))))))))))))))) => 12.21/2.18 (((((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))) => 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4)))))))))))))))))) & 12.21/2.18 ((((^[Y1 : a > b,Y2 : a > b]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ (^[Y4 : a]: 12.21/2.18 ((('#sk1' @ Y3 @ 12.21/2.18 Y4) => ('#sk3' @ 12.21/2.18 Y3 @ (Y1 @ Y3) @ 12.21/2.18 (Y2 @ Y4)))))))))))) = 12.21/2.18 ((^[Y1 : a > b,Y2 : a > b]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ (^[Y4 : a]: 12.21/2.18 ((('#sk2' @ Y3 @ 12.21/2.18 Y4) => (Y0 @ Y3 @ 12.21/2.18 (Y1 @ Y3) @ 12.21/2.18 (Y2 @ Y4)))))))))))))) & 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((!!) @ (^[Y3 : a > b]: 12.21/2.18 (((((( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y4 @ 12.21/2.18 Y5) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y4 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y5)))))))))) & 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y4 @ 12.21/2.18 Y5) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y4 @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4) @ 12.21/2.18 ( 12.21/2.18 Y3 @ Y5)))))))))))) => 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y5 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y4 @ 12.21/2.18 Y5) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y4 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4) @ 12.21/2.18 ( 12.21/2.18 Y3 @ Y5))))))))))))))))))))))))))))))))), 12.21/2.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 12.21/2.18 thf(zip_derived_cl4, plain, 12.21/2.18 (~ (((((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk1' @ Y1 @ Y0))))))))) & 12.21/2.18 (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 ((((('#sk1' @ Y0 @ Y1) & 12.21/2.18 ('#sk1' @ Y1 @ Y2))) => 12.21/2.18 ('#sk1' @ Y0 @ Y2)))))))))))) & 12.21/2.18 ((('#sk1') = ('#sk2'))))) => 12.21/2.18 (((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => 12.21/2.18 (((((!!) @ (^[Y2 : b]: 12.21/2.18 (((!!) @ (^[Y3 : b]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : b]: 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ 12.21/2.18 Y2 @ 12.21/2.18 Y3) & 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ 12.21/2.18 Y3 @ Y4))) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ 12.21/2.18 Y2 @ Y4)))))))))))) & 12.21/2.18 ((('#sk3' @ Y0) = ('#sk3' @ Y1))) & 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 (((!!) @ (^[Y3 : b]: 12.21/2.18 ((('#sk3' @ 12.21/2.18 Y0 @ Y2 @ 12.21/2.18 Y3) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ Y3 @ 12.21/2.18 Y2))))))))))))))))))) => 12.21/2.18 (((((!!) @ (^[Y0 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y0) => 12.21/2.18 (((((!!) @ (^[Y1 : b]: 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 (((!!) @ (^[Y3 : b]: 12.21/2.18 (((( 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ Y1 @ 12.21/2.18 Y2) & 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ Y2 @ 12.21/2.18 Y3))) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ Y1 @ 12.21/2.18 Y3)))))))))))) & 12.21/2.18 ((('#sk3' @ Y0) = ('#sk4' @ Y0))) & 12.21/2.18 (((!!) @ (^[Y1 : b]: 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 ((('#sk3' @ Y0 @ Y1 @ 12.21/2.18 Y2) => ('#sk3' @ Y0 @ 12.21/2.18 Y2 @ Y1)))))))))))))))) => 12.21/2.18 (((((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y2 @ 12.21/2.18 Y3) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y2 @ 12.21/2.18 (Y0 @ Y2) @ 12.21/2.18 (Y1 @ Y3)))))))))) => 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y2 @ 12.21/2.18 Y3) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y2 @ 12.21/2.18 (Y1 @ Y2) @ 12.21/2.18 (Y0 @ Y3)))))))))))))))))) & 12.21/2.18 ((((^[Y0 : a > b,Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ Y3) => 12.21/2.18 ('#sk3' @ Y2 @ (Y0 @ Y2) @ 12.21/2.18 (Y1 @ Y3)))))))))))) = 12.21/2.18 ((^[Y0 : a > b,Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk2' @ Y2 @ Y3) => 12.21/2.18 ('#sk4' @ Y2 @ (Y0 @ Y2) @ 12.21/2.18 (Y1 @ Y3)))))))))))))) & 12.21/2.18 (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y3 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y0 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4)))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (( 12.21/2.18 (!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))))) => 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y0 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))))))))))))))))))))))), 12.21/2.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 12.21/2.18 thf(zip_derived_cl6, plain, 12.21/2.18 (~ (((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => 12.21/2.18 (((((!!) @ (^[Y2 : b]: 12.21/2.18 (((!!) @ (^[Y3 : b]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : b]: 12.21/2.18 (((( 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ Y2 @ 12.21/2.18 Y3) & 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ Y3 @ 12.21/2.18 Y4))) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ Y2 @ 12.21/2.18 Y4)))))))))))) & 12.21/2.18 ((('#sk3' @ Y0) = ('#sk3' @ Y1))) & 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 (((!!) @ (^[Y3 : b]: 12.21/2.18 ((('#sk3' @ 12.21/2.18 Y0 @ Y2 @ 12.21/2.18 Y3) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ Y3 @ Y2))))))))))))))))))) => 12.21/2.18 (((((!!) @ (^[Y0 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y0) => 12.21/2.18 (((((!!) @ (^[Y1 : b]: 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 (((!!) @ (^[Y3 : b]: 12.21/2.18 ((((('#sk3' @ 12.21/2.18 Y0 @ Y1 @ 12.21/2.18 Y2) & 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ Y2 @ 12.21/2.18 Y3))) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ Y1 @ 12.21/2.18 Y3)))))))))))) & 12.21/2.18 ((('#sk3' @ Y0) = ('#sk4' @ Y0))) & 12.21/2.18 (((!!) @ (^[Y1 : b]: 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 ((('#sk3' @ Y0 @ Y1 @ 12.21/2.18 Y2) => ('#sk3' @ Y0 @ 12.21/2.18 Y2 @ Y1)))))))))))))))) => 12.21/2.18 (((((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y2 @ Y3) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y2 @ 12.21/2.18 (Y0 @ Y2) @ 12.21/2.18 (Y1 @ Y3)))))))))) => 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y2 @ Y3) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y2 @ 12.21/2.18 (Y1 @ Y2) @ 12.21/2.18 (Y0 @ Y3)))))))))))))))))) & 12.21/2.18 ((((^[Y0 : a > b,Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ Y3) => ('#sk3' @ 12.21/2.18 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))) = 12.21/2.18 ((^[Y0 : a > b,Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk2' @ Y2 @ Y3) => ('#sk4' @ 12.21/2.18 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))))) & 12.21/2.18 (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y0 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4)))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))))) => 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y0 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))))))))))))))))))))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 12.21/2.18 thf(zip_derived_cl11, plain, 12.21/2.18 (~ (((((!!) @ (^[Y0 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y0) => 12.21/2.18 (((((!!) @ (^[Y1 : b]: 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 (((!!) @ (^[Y3 : b]: 12.21/2.18 ((((('#sk3' @ 12.21/2.18 Y0 @ Y1 @ 12.21/2.18 Y2) & 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ Y2 @ 12.21/2.18 Y3))) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ Y1 @ Y3)))))))))))) & 12.21/2.18 ((('#sk3' @ Y0) = ('#sk4' @ Y0))) & 12.21/2.18 (((!!) @ (^[Y1 : b]: 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 ((('#sk3' @ Y0 @ Y1 @ Y2) => 12.21/2.18 ('#sk3' @ Y0 @ Y2 @ Y1)))))))))))))))) => 12.21/2.18 (((((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y2 @ Y3) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y2 @ 12.21/2.18 (Y0 @ Y2) @ 12.21/2.18 (Y1 @ Y3)))))))))) => 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y2 @ Y3) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y2 @ 12.21/2.18 (Y1 @ Y2) @ 12.21/2.18 (Y0 @ Y3)))))))))))))))))) & 12.21/2.18 ((((^[Y0 : a > b,Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ Y3) => ('#sk3' @ 12.21/2.18 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))) = 12.21/2.18 ((^[Y0 : a > b,Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk2' @ Y2 @ Y3) => ('#sk4' @ 12.21/2.18 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))))) & 12.21/2.18 (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y0 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4)))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 (( 12.21/2.18 ('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))))) => 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 (Y0 @ Y3) @ 12.21/2.18 (Y2 @ Y4)))))))))))))))))))))))))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 12.21/2.18 thf(zip_derived_cl18, plain, 12.21/2.18 (~ (((((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ 12.21/2.18 Y3) => 12.21/2.18 ('#sk3' @ Y2 @ 12.21/2.18 (Y0 @ Y2) @ 12.21/2.18 (Y1 @ Y3)))))))))) => 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ 12.21/2.18 Y3) => 12.21/2.18 ('#sk3' @ Y2 @ 12.21/2.18 (Y1 @ Y2) @ 12.21/2.18 (Y0 @ Y3)))))))))))))))))) & 12.21/2.18 ((((^[Y0 : a > b,Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ Y3) => ('#sk3' @ 12.21/2.18 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))) = 12.21/2.18 ((^[Y0 : a > b,Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk2' @ Y2 @ Y3) => ('#sk4' @ 12.21/2.18 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))))) & 12.21/2.18 (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 (Y0 @ Y3) @ 12.21/2.18 (Y1 @ Y4)))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 (Y1 @ Y3) @ 12.21/2.18 (Y2 @ Y4)))))))))))) => 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 (Y0 @ Y3) @ 12.21/2.18 (Y2 @ Y4)))))))))))))))))))))))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 12.21/2.18 thf(zip_derived_cl23, plain, 12.21/2.18 ((~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ 12.21/2.18 Y3) => ('#sk3' @ 12.21/2.18 Y2 @ (Y0 @ Y2) @ 12.21/2.18 (Y1 @ Y3)))))))))) => 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ 12.21/2.18 Y3) => ('#sk3' @ 12.21/2.18 Y2 @ (Y1 @ Y2) @ 12.21/2.18 (Y0 @ Y3)))))))))))))))))) 12.21/2.18 | ~ ((((^[Y0 : a > b,Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ Y3) => ('#sk3' @ 12.21/2.18 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))) = 12.21/2.18 ((^[Y0 : a > b,Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk2' @ Y2 @ Y3) => ('#sk4' @ 12.21/2.18 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))))) 12.21/2.18 | ~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y0 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4)))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))))) => 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 (Y0 @ Y3) @ 12.21/2.18 (Y2 @ Y4))))))))))))))))))))))), 12.21/2.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])). 12.21/2.18 thf(zip_derived_cl28, plain, 12.21/2.18 ((~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ 12.21/2.18 Y3) => ('#sk3' @ 12.21/2.18 Y2 @ (Y0 @ Y2) @ 12.21/2.18 (Y1 @ Y3)))))))))) => 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ 12.21/2.18 Y3) => ('#sk3' @ 12.21/2.18 Y2 @ (Y1 @ Y2) @ 12.21/2.18 (Y0 @ Y3)))))))))))))))))) 12.21/2.18 | (((^[Y0 : a > b,Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ Y3) => ('#sk3' @ Y2 @ 12.21/2.18 (Y0 @ Y2) @ (Y1 @ Y3)))))))))))) 12.21/2.18 != ((^[Y0 : a > b,Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk2' @ Y2 @ Y3) => ('#sk4' @ 12.21/2.18 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))))))))) 12.21/2.18 | ~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y0 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4)))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))))) => 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 (Y0 @ Y3) @ 12.21/2.18 (Y2 @ Y4))))))))))))))))))))))), 12.21/2.18 inference('simplify nested equalities', [status(thm)], [zip_derived_cl23])). 12.21/2.18 thf(zip_derived_cl29, plain, 12.21/2.18 ((~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ 12.21/2.18 Y3) => ('#sk3' @ 12.21/2.18 Y2 @ (Y0 @ Y2) @ 12.21/2.18 (Y1 @ Y3)))))))))) => 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ 12.21/2.18 Y3) => ('#sk3' @ 12.21/2.18 Y2 @ (Y1 @ Y2) @ 12.21/2.18 (Y0 @ Y3)))))))))))))))))) 12.21/2.18 | (((^[Y0 : a > b,Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ Y3) => ('#sk3' @ Y2 @ 12.21/2.18 (Y0 @ Y2) @ (Y1 @ Y3))))))))))) @ 12.21/2.18 '#_fresh_sk5' @ '#_fresh_sk6') 12.21/2.18 != ((^[Y0 : a > b,Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk2' @ Y2 @ Y3) => ('#sk4' @ 12.21/2.18 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))))))) @ 12.21/2.18 '#_fresh_sk5' @ '#_fresh_sk6')) 12.21/2.18 | ~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y0 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4)))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))))) => 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 (Y0 @ Y3) @ 12.21/2.18 (Y2 @ Y4))))))))))))))))))))))), 12.21/2.18 inference('neg_ext_simpl', [status(thm)], [zip_derived_cl28])). 12.21/2.18 thf(zip_derived_cl30, plain, 12.21/2.18 ((~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ 12.21/2.18 Y3) => ('#sk3' @ 12.21/2.18 Y2 @ (Y0 @ Y2) @ 12.21/2.18 (Y1 @ Y3)))))))))) => 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ 12.21/2.18 Y3) => ('#sk3' @ 12.21/2.18 Y2 @ (Y1 @ Y2) @ 12.21/2.18 (Y0 @ Y3)))))))))))))))))) 12.21/2.18 | ((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) 12.21/2.18 != (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1))))))))))) 12.21/2.18 | ~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y0 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4)))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))))) => 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 (Y0 @ Y3) @ 12.21/2.18 (Y2 @ Y4))))))))))))))))))))))), 12.21/2.18 inference('ho_norm', [status(thm)], [zip_derived_cl29])). 12.21/2.18 thf(zip_derived_cl31, plain, 12.21/2.18 ((~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((((!!) @ (^[Y1 : a]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 ((('#sk1' @ Y1 @ Y2) => 12.21/2.18 ('#sk3' @ Y1 @ 12.21/2.18 ('#sk7' @ Y1) @ (Y0 @ Y2)))))))))) => 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 ((('#sk1' @ Y1 @ Y2) => 12.21/2.18 ('#sk3' @ Y1 @ (Y0 @ Y1) @ 12.21/2.18 ('#sk7' @ Y2))))))))))))))) 12.21/2.18 | ~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y0 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4)))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))))) => 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 (Y0 @ Y3) @ 12.21/2.18 (Y2 @ Y4))))))))))))))))))))) 12.21/2.18 | ((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) 12.21/2.18 != (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1))))))))))))), 12.21/2.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])). 12.21/2.18 thf(zip_derived_cl39, plain, 12.21/2.18 ((~ (((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#sk7' @ Y0) @ ('#sk8' @ Y1)))))))))) => 12.21/2.18 (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#sk8' @ Y0) @ ('#sk7' @ Y1)))))))))))) 12.21/2.18 | ((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) 12.21/2.18 != (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1))))))))))) 12.21/2.18 | ~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y0 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4)))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))))) => 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 (Y0 @ Y3) @ 12.21/2.18 (Y2 @ Y4))))))))))))))))))))))), 12.21/2.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl31])). 12.21/2.18 thf(zip_derived_cl49, plain, 12.21/2.18 (( (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#sk7' @ Y0) @ ('#sk8' @ Y1)))))))))) 12.21/2.18 | ~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y0 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4)))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))))) => 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 (Y0 @ Y3) @ 12.21/2.18 (Y2 @ Y4))))))))))))))))))))) 12.21/2.18 | ((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) 12.21/2.18 != (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1))))))))))))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 12.21/2.18 thf(zip_derived_cl55, plain, 12.21/2.18 (( ('#form9') 12.21/2.18 | ~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y0 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4)))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))))) => 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 (Y0 @ Y3) @ 12.21/2.18 (Y2 @ Y4))))))))))))))))))))))), 12.21/2.18 define([status(thm)])). 12.21/2.18 thf(zip_derived_cl56, plain, 12.21/2.18 ((~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ 12.21/2.18 Y3) => 12.21/2.18 ('#sk3' @ Y2 @ 12.21/2.18 ('#sk10' @ Y2) @ 12.21/2.18 (Y0 @ Y3)))))))))) & 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ 12.21/2.18 Y3) => 12.21/2.18 ('#sk3' @ Y2 @ 12.21/2.18 (Y0 @ Y2) @ 12.21/2.18 (Y1 @ Y3)))))))))))) => 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 ((('#sk1' @ Y2 @ 12.21/2.18 Y3) => ('#sk3' @ 12.21/2.18 Y2 @ 12.21/2.18 ('#sk10' @ Y2) @ 12.21/2.18 (Y1 @ Y3)))))))))))))))))) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl55])). 12.21/2.18 thf(zip_derived_cl64, plain, 12.21/2.18 ((~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y1 : a]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 ((('#sk1' @ Y1 @ Y2) => 12.21/2.18 ('#sk3' @ Y1 @ 12.21/2.18 ('#sk10' @ Y1) @ 12.21/2.18 ('#sk11' @ Y2)))))))))) & 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 ((('#sk1' @ Y1 @ Y2) => 12.21/2.18 ('#sk3' @ Y1 @ 12.21/2.18 ('#sk11' @ Y1) @ (Y0 @ Y2)))))))))))) => 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 ((('#sk1' @ Y1 @ Y2) => 12.21/2.18 ('#sk3' @ Y1 @ 12.21/2.18 ('#sk10' @ Y1) @ (Y0 @ Y2))))))))))))))) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl56])). 12.21/2.18 thf(zip_derived_cl72, plain, 12.21/2.18 ((~ (((((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#sk10' @ Y0) @ ('#sk11' @ Y1)))))))))) & 12.21/2.18 (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#sk11' @ Y0) @ ('#sk13' @ Y1)))))))))))) => 12.21/2.18 (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#sk10' @ Y0) @ ('#sk13' @ Y1)))))))))))) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl64])). 12.21/2.18 thf(zip_derived_cl80, plain, 12.21/2.18 ((~ (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#sk10' @ Y0) @ ('#sk13' @ Y1)))))))))) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl72])). 12.21/2.18 thf(zip_derived_cl87, plain, 12.21/2.18 ((~ (((!!) @ (^[Y0 : a]: 12.21/2.18 ((('#sk1' @ '#sk18' @ Y0) => ('#sk3' @ '#sk18' @ 12.21/2.18 ('#sk10' @ '#sk18') @ ('#sk13' @ Y0))))))) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl80])). 12.21/2.18 thf(zip_derived_cl95, plain, 12.21/2.18 ((~ ((('#sk1' @ '#sk18' @ '#sk19') => ('#sk3' @ '#sk18' @ 12.21/2.18 ('#sk10' @ '#sk18') @ ('#sk13' @ '#sk19')))) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl87])). 12.21/2.18 thf(zip_derived_cl106, plain, 12.21/2.18 ((~ ('#sk3' @ '#sk18' @ ('#sk10' @ '#sk18') @ ('#sk13' @ '#sk19')) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])). 12.21/2.18 thf(zip_derived_cl49, plain, 12.21/2.18 (( (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#sk7' @ Y0) @ ('#sk8' @ Y1)))))))))) 12.21/2.18 | ~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y0 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4)))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))))) => 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 (Y0 @ Y3) @ 12.21/2.18 (Y2 @ Y4))))))))))))))))))))) 12.21/2.18 | ((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) 12.21/2.18 != (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1))))))))))))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 12.21/2.18 thf(zip_derived_cl55, plain, 12.21/2.18 (( ('#form9') 12.21/2.18 | ~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y0 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4)))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))))) => 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 (Y0 @ Y3) @ 12.21/2.18 (Y2 @ Y4))))))))))))))))))))))), 12.21/2.18 define([status(thm)])). 12.21/2.18 thf(zip_derived_cl57, plain, 12.21/2.18 ((~ ('#form9') 12.21/2.18 | ((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) 12.21/2.18 != (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1))))))))))) 12.21/2.18 | (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#sk7' @ Y0) @ ('#sk8' @ Y1)))))))))))), 12.21/2.18 inference('renaming', [status(thm)], [zip_derived_cl49, zip_derived_cl55])). 12.21/2.18 thf(zip_derived_cl63, plain, 12.21/2.18 (![X2 : a]: 12.21/2.18 ( (((!!) @ (^[Y0 : a]: 12.21/2.18 ((('#sk1' @ X2 @ Y0) => ('#sk3' @ X2 @ ('#sk7' @ X2) @ 12.21/2.18 ('#sk8' @ Y0))))))) 12.21/2.18 | ((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) 12.21/2.18 != (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ 12.21/2.18 Y0 @ ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1))))))))))) 12.21/2.18 | ~ ('#form9'))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 12.21/2.18 thf(zip_derived_cl50, plain, 12.21/2.18 ((~ (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#sk8' @ Y0) @ ('#sk7' @ Y1)))))))))) 12.21/2.18 | ~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y0 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4)))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))))) => 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 (Y0 @ Y3) @ 12.21/2.18 (Y2 @ Y4))))))))))))))))))))) 12.21/2.18 | ((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) 12.21/2.18 != (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1))))))))))))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 12.21/2.18 thf(zip_derived_cl55, plain, 12.21/2.18 (( ('#form9') 12.21/2.18 | ~ (((!!) @ (^[Y0 : a > b]: 12.21/2.18 (((!!) @ (^[Y1 : a > b]: 12.21/2.18 (((!!) @ (^[Y2 : a > b]: 12.21/2.18 (((((((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y0 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y4)))))))))) & 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ 12.21/2.18 Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 ( 12.21/2.18 Y1 @ Y3) @ 12.21/2.18 ( 12.21/2.18 Y2 @ Y4)))))))))))) => 12.21/2.18 (((!!) @ (^[Y3 : a]: 12.21/2.18 (((!!) @ ( 12.21/2.18 ^[Y4 : a]: 12.21/2.18 ((('#sk1' @ 12.21/2.18 Y3 @ Y4) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y3 @ 12.21/2.18 (Y0 @ Y3) @ 12.21/2.18 (Y2 @ Y4))))))))))))))))))))))), 12.21/2.18 define([status(thm)])). 12.21/2.18 thf(zip_derived_cl58, plain, 12.21/2.18 ((~ ('#form9') 12.21/2.18 | ((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) 12.21/2.18 != (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1))))))))))) 12.21/2.18 | ~ (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#sk8' @ Y0) @ ('#sk7' @ Y1)))))))))))), 12.21/2.18 inference('renaming', [status(thm)], [zip_derived_cl50, zip_derived_cl55])). 12.21/2.18 thf(zip_derived_cl65, plain, 12.21/2.18 (( ('#form12') 12.21/2.18 | ~ (((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) <=> 12.21/2.18 (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))))))), 12.21/2.18 define([status(thm)])). 12.21/2.18 thf(zip_derived_cl71, plain, 12.21/2.18 (![X2 : a]: 12.21/2.18 (~ ('#form12') 12.21/2.18 | ~ ('#form9') 12.21/2.18 | (((!!) @ (^[Y0 : a]: 12.21/2.18 ((('#sk1' @ X2 @ Y0) => ('#sk3' @ X2 @ 12.21/2.18 ('#sk7' @ X2) @ ('#sk8' @ Y0))))))))), 12.21/2.18 inference('renaming', [status(thm)], [zip_derived_cl63, zip_derived_cl65])). 12.21/2.18 thf(zip_derived_cl78, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 ( ((('#sk1' @ X2 @ X4) => ('#sk3' @ X2 @ ('#sk7' @ X2) @ 12.21/2.18 ('#sk8' @ X4)))) 12.21/2.18 | ~ ('#form9') 12.21/2.18 | ~ ('#form12'))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl71])). 12.21/2.18 thf(zip_derived_cl84, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 (~ ('#sk1' @ X2 @ X4) 12.21/2.18 | ('#sk3' @ X2 @ ('#sk7' @ X2) @ ('#sk8' @ X4)) 12.21/2.18 | ~ ('#form12') 12.21/2.18 | ~ ('#form9'))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 12.21/2.18 thf(zip_derived_cl10, plain, 12.21/2.18 ( (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => 12.21/2.18 (((((!!) @ (^[Y2 : b]: 12.21/2.18 (((!!) @ (^[Y3 : b]: 12.21/2.18 (((!!) @ (^[Y4 : b]: 12.21/2.18 (( 12.21/2.18 (( 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ 12.21/2.18 Y2 @ 12.21/2.18 Y3) & 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ 12.21/2.18 Y3 @ Y4))) => 12.21/2.18 ('#sk3' @ 12.21/2.18 Y0 @ 12.21/2.18 Y2 @ Y4)))))))))))) & 12.21/2.18 ((('#sk3' @ Y0) = ('#sk3' @ Y1))) & 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 (((!!) @ (^[Y3 : b]: 12.21/2.18 ((('#sk3' @ Y0 @ 12.21/2.18 Y2 @ Y3) => 12.21/2.18 ('#sk3' @ Y0 @ 12.21/2.18 Y3 @ Y2)))))))))))))))))))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 12.21/2.18 thf(zip_derived_cl16, plain, 12.21/2.18 (![X2 : a]: 12.21/2.18 (((!!) @ (^[Y0 : a]: 12.21/2.18 ((('#sk1' @ X2 @ Y0) => 12.21/2.18 (((((!!) @ (^[Y1 : b]: 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 (((!!) @ (^[Y3 : b]: 12.21/2.18 ((((('#sk3' @ 12.21/2.18 X2 @ Y1 @ 12.21/2.18 Y2) & 12.21/2.18 ('#sk3' @ 12.21/2.18 X2 @ Y2 @ Y3))) => 12.21/2.18 ('#sk3' @ X2 @ 12.21/2.18 Y1 @ Y3)))))))))))) & 12.21/2.18 ((('#sk3' @ X2) = ('#sk3' @ Y0))) & 12.21/2.18 (((!!) @ (^[Y1 : b]: 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 ((('#sk3' @ X2 @ Y1 @ Y2) => 12.21/2.18 ('#sk3' @ X2 @ Y2 @ Y1))))))))))))))))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 12.21/2.18 thf(zip_derived_cl21, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 ((('#sk1' @ X2 @ X4) => 12.21/2.18 (((((!!) @ (^[Y0 : b]: 12.21/2.18 (((!!) @ (^[Y1 : b]: 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 ((((('#sk3' @ X2 @ Y0 @ Y1) & 12.21/2.18 ('#sk3' @ X2 @ Y1 @ Y2))) => 12.21/2.18 ('#sk3' @ X2 @ Y0 @ Y2)))))))))))) & 12.21/2.18 ((('#sk3' @ X2) = ('#sk3' @ X4))) & 12.21/2.18 (((!!) @ (^[Y0 : b]: 12.21/2.18 (((!!) @ (^[Y1 : b]: 12.21/2.18 ((('#sk3' @ X2 @ Y0 @ Y1) => ('#sk3' @ 12.21/2.18 X2 @ Y1 @ Y0)))))))))))))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 12.21/2.18 thf(zip_derived_cl26, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 (~ ('#sk1' @ X2 @ X4) 12.21/2.18 | (((((!!) @ (^[Y0 : b]: 12.21/2.18 (((!!) @ (^[Y1 : b]: 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 ((((('#sk3' @ X2 @ Y0 @ 12.21/2.18 Y1) & ('#sk3' @ X2 @ 12.21/2.18 Y1 @ Y2))) => 12.21/2.18 ('#sk3' @ X2 @ Y0 @ Y2)))))))))))) & 12.21/2.18 ((('#sk3' @ X2) = ('#sk3' @ X4))) & 12.21/2.18 (((!!) @ (^[Y0 : b]: 12.21/2.18 (((!!) @ (^[Y1 : b]: 12.21/2.18 ((('#sk3' @ X2 @ Y0 @ Y1) => ('#sk3' @ 12.21/2.18 X2 @ Y1 @ Y0))))))))))))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 12.21/2.18 thf(zip_derived_cl35, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 ( (((!!) @ (^[Y0 : b]: 12.21/2.18 (((!!) @ (^[Y1 : b]: 12.21/2.18 ((('#sk3' @ X2 @ Y0 @ Y1) => ('#sk3' @ X2 @ 12.21/2.18 Y1 @ Y0))))))))) 12.21/2.18 | ~ ('#sk1' @ X2 @ X4))), 12.21/2.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 12.21/2.18 thf(zip_derived_cl44, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : b]: 12.21/2.18 ( (((!!) @ (^[Y0 : b]: 12.21/2.18 ((('#sk3' @ X2 @ X6 @ Y0) => ('#sk3' @ X2 @ Y0 @ X6)))))) 12.21/2.18 | ~ ('#sk1' @ X2 @ X4))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl35])). 12.21/2.18 thf(zip_derived_cl52, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : b, X8 : b]: 12.21/2.18 ( ((('#sk3' @ X2 @ X6 @ X8) => ('#sk3' @ X2 @ X8 @ X6))) 12.21/2.18 | ~ ('#sk1' @ X2 @ X4))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl44])). 12.21/2.18 thf(zip_derived_cl60, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : b, X8 : b]: 12.21/2.18 (~ ('#sk3' @ X2 @ X6 @ X8) 12.21/2.18 | ('#sk3' @ X2 @ X8 @ X6) 12.21/2.18 | ~ ('#sk1' @ X2 @ X4))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 12.21/2.18 thf(zip_derived_cl331, plain, 12.21/2.18 (![X0 : a, X1 : a, X2 : a]: 12.21/2.18 (~ ('#form9') 12.21/2.18 | ~ ('#form12') 12.21/2.18 | ~ ('#sk1' @ X1 @ X0) 12.21/2.18 | ~ ('#sk1' @ X1 @ X2) 12.21/2.18 | ('#sk3' @ X1 @ ('#sk8' @ X0) @ ('#sk7' @ X1)))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl84, zip_derived_cl60])). 12.21/2.18 thf(zip_derived_cl2847, plain, 12.21/2.18 (![X0 : a, X1 : a]: 12.21/2.18 (~ ('#form9') 12.21/2.18 | ~ ('#form12') 12.21/2.18 | ('#sk3' @ X0 @ ('#sk8' @ X1) @ ('#sk7' @ X0)) 12.21/2.18 | ~ ('#sk1' @ X0 @ X1))), 12.21/2.18 inference('condensation', [status(thm)], [zip_derived_cl331])). 12.21/2.18 thf(zip_derived_cl58, plain, 12.21/2.18 ((~ ('#form9') 12.21/2.18 | ((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) 12.21/2.18 != (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1))))))))))) 12.21/2.18 | ~ (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#sk8' @ Y0) @ ('#sk7' @ Y1)))))))))))), 12.21/2.18 inference('renaming', [status(thm)], [zip_derived_cl50, zip_derived_cl55])). 12.21/2.18 thf(zip_derived_cl65, plain, 12.21/2.18 (( ('#form12') 12.21/2.18 | ~ (((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) <=> 12.21/2.18 (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))))))), 12.21/2.18 define([status(thm)])). 12.21/2.18 thf(zip_derived_cl68, plain, 12.21/2.18 ((~ ('#form12') 12.21/2.18 | ~ (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#sk8' @ Y0) @ ('#sk7' @ Y1)))))))))) 12.21/2.18 | ~ ('#form9'))), 12.21/2.18 inference('renaming', [status(thm)], [zip_derived_cl58, zip_derived_cl65])). 12.21/2.18 thf(zip_derived_cl73, plain, 12.21/2.18 ((~ (((!!) @ (^[Y0 : a]: 12.21/2.18 ((('#sk1' @ '#sk14' @ Y0) => ('#sk3' @ '#sk14' @ 12.21/2.18 ('#sk8' @ '#sk14') @ ('#sk7' @ Y0))))))) 12.21/2.18 | ~ ('#form9') 12.21/2.18 | ~ ('#form12'))), 12.21/2.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl68])). 12.21/2.18 thf(zip_derived_cl81, plain, 12.21/2.18 ((~ ((('#sk1' @ '#sk14' @ '#sk16') => ('#sk3' @ '#sk14' @ 12.21/2.18 ('#sk8' @ '#sk14') @ ('#sk7' @ '#sk16')))) 12.21/2.18 | ~ ('#form12') 12.21/2.18 | ~ ('#form9'))), 12.21/2.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl73])). 12.21/2.18 thf(zip_derived_cl88, plain, 12.21/2.18 (( ('#sk1' @ '#sk14' @ '#sk16') | ~ ('#form9') | ~ ('#form12'))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 12.21/2.18 thf(zip_derived_cl5, plain, 12.21/2.18 ( (((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk1' @ Y1 @ Y0))))))))) & 12.21/2.18 (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 ((((('#sk1' @ Y0 @ Y1) & 12.21/2.18 ('#sk1' @ Y1 @ Y2))) => 12.21/2.18 ('#sk1' @ Y0 @ Y2)))))))))))) & 12.21/2.18 ((('#sk1') = ('#sk2')))))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 12.21/2.18 thf(zip_derived_cl7, plain, 12.21/2.18 ( (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk1' @ Y1 @ Y0)))))))))), 12.21/2.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl5])). 12.21/2.18 thf(zip_derived_cl12, plain, 12.21/2.18 (![X2 : a]: 12.21/2.18 (((!!) @ (^[Y0 : a]: ((('#sk1' @ X2 @ Y0) => ('#sk1' @ Y0 @ X2))))))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 12.21/2.18 thf(zip_derived_cl19, plain, 12.21/2.18 (![X2 : a, X4 : a]: ((('#sk1' @ X2 @ X4) => ('#sk1' @ X4 @ X2)))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])). 12.21/2.18 thf(zip_derived_cl24, plain, 12.21/2.18 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 12.21/2.18 thf(zip_derived_cl130, plain, 12.21/2.18 ((~ ('#form12') | ~ ('#form9') | ('#sk1' @ '#sk16' @ '#sk14'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl88, zip_derived_cl24])). 12.21/2.18 thf(zip_derived_cl34, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 ( ((('#sk3' @ X2) = ('#sk3' @ X4))) | ~ ('#sk1' @ X2 @ X4))), 12.21/2.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 12.21/2.18 thf(zip_derived_cl42, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 ((('#sk3' @ X2) = ('#sk3' @ X4)) | ~ ('#sk1' @ X2 @ X4))), 12.21/2.18 inference('simplify nested equalities', [status(thm)], [zip_derived_cl34])). 12.21/2.18 thf(zip_derived_cl43, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : b, X7 : b]: 12.21/2.18 ((('#sk3' @ X2 @ X6 @ X7) = ('#sk3' @ X4 @ X6 @ X7)) 12.21/2.18 | ~ ('#sk1' @ X2 @ X4))), 12.21/2.18 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl42])). 12.21/2.18 thf(zip_derived_cl214, plain, 12.21/2.18 (![X0 : b, X1 : b]: 12.21/2.18 (~ ('#form9') 12.21/2.18 | ~ ('#form12') 12.21/2.18 | (('#sk3' @ '#sk16' @ X1 @ X0) = ('#sk3' @ '#sk14' @ X1 @ X0)))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl43])). 12.21/2.18 thf(zip_derived_cl89, plain, 12.21/2.18 ((~ ('#sk3' @ '#sk14' @ ('#sk8' @ '#sk14') @ ('#sk7' @ '#sk16')) 12.21/2.18 | ~ ('#form9') 12.21/2.18 | ~ ('#form12'))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 12.21/2.18 thf(zip_derived_cl879, plain, 12.21/2.18 ((~ ('#sk3' @ '#sk16' @ ('#sk8' @ '#sk14') @ ('#sk7' @ '#sk16')) 12.21/2.18 | ~ ('#form12') 12.21/2.18 | ~ ('#form9') 12.21/2.18 | ~ ('#form12') 12.21/2.18 | ~ ('#form9'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl214, zip_derived_cl89])). 12.21/2.18 thf(zip_derived_cl900, plain, 12.21/2.18 ((~ ('#form9') 12.21/2.18 | ~ ('#form12') 12.21/2.18 | ~ ('#sk3' @ '#sk16' @ ('#sk8' @ '#sk14') @ ('#sk7' @ '#sk16')))), 12.21/2.18 inference('simplify', [status(thm)], [zip_derived_cl879])). 12.21/2.18 thf(zip_derived_cl2866, plain, 12.21/2.18 ((~ ('#sk1' @ '#sk16' @ '#sk14') 12.21/2.18 | ~ ('#form12') 12.21/2.18 | ~ ('#form9') 12.21/2.18 | ~ ('#form12') 12.21/2.18 | ~ ('#form9'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl2847, zip_derived_cl900])). 12.21/2.18 thf(zip_derived_cl2922, plain, 12.21/2.18 ((~ ('#form9') | ~ ('#form12') | ~ ('#sk1' @ '#sk16' @ '#sk14'))), 12.21/2.18 inference('simplify', [status(thm)], [zip_derived_cl2866])). 12.21/2.18 thf(zip_derived_cl130, plain, 12.21/2.18 ((~ ('#form12') | ~ ('#form9') | ('#sk1' @ '#sk16' @ '#sk14'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl88, zip_derived_cl24])). 12.21/2.18 thf(zip_derived_cl2946, plain, ((~ ('#form12') | ~ ('#form9'))), 12.21/2.18 inference('clc', [status(thm)], [zip_derived_cl2922, zip_derived_cl130])). 12.21/2.18 thf(zip_derived_cl65, plain, 12.21/2.18 (( ('#form12') 12.21/2.18 | ~ (((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) <=> 12.21/2.18 (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))))))), 12.21/2.18 define([status(thm)])). 12.21/2.18 thf(zip_derived_cl67, plain, 12.21/2.18 ((~ (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) 12.21/2.18 | ~ (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) 12.21/2.18 | ('#form12'))), 12.21/2.18 inference('lazy_cnf_xor', [status(thm)], [zip_derived_cl65])). 12.21/2.18 thf(zip_derived_cl74, plain, 12.21/2.18 ((~ (((!!) @ (^[Y0 : a]: 12.21/2.18 ((('#sk1' @ '#sk15' @ Y0) => ('#sk3' @ '#sk15' @ 12.21/2.18 ('#_fresh_sk5' @ '#sk15') @ ('#_fresh_sk6' @ Y0))))))) 12.21/2.18 | ('#form12') 12.21/2.18 | ~ (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))))), 12.21/2.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl67])). 12.21/2.18 thf(zip_derived_cl82, plain, 12.21/2.18 ((~ ((('#sk1' @ '#sk15' @ '#sk17') => ('#sk3' @ '#sk15' @ 12.21/2.18 ('#_fresh_sk5' @ '#sk15') @ ('#_fresh_sk6' @ '#sk17')))) 12.21/2.18 | ~ (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) 12.21/2.18 | ('#form12'))), 12.21/2.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl74])). 12.21/2.18 thf(zip_derived_cl90, plain, 12.21/2.18 (( ('#sk1' @ '#sk15' @ '#sk17') 12.21/2.18 | ('#form12') 12.21/2.18 | ~ (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 12.21/2.18 thf(zip_derived_cl96, plain, 12.21/2.18 (( ('#form20') 12.21/2.18 | ~ (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))))), 12.21/2.18 define([status(thm)])). 12.21/2.18 thf(zip_derived_cl97, plain, 12.21/2.18 ((~ (((!!) @ (^[Y0 : a]: 12.21/2.18 ((('#sk2' @ '#sk21' @ Y0) => ('#sk4' @ '#sk21' @ 12.21/2.18 ('#_fresh_sk5' @ '#sk21') @ ('#_fresh_sk6' @ Y0))))))) 12.21/2.18 | ('#form20'))), 12.21/2.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 12.21/2.18 thf(zip_derived_cl107, plain, 12.21/2.18 ((~ ((('#sk2' @ '#sk21' @ '#sk22') => ('#sk4' @ '#sk21' @ 12.21/2.18 ('#_fresh_sk5' @ '#sk21') @ ('#_fresh_sk6' @ '#sk22')))) 12.21/2.18 | ('#form20'))), 12.21/2.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl97])). 12.21/2.18 thf(zip_derived_cl111, plain, 12.21/2.18 (( ('#sk2' @ '#sk21' @ '#sk22') | ('#form20'))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])). 12.21/2.18 thf(zip_derived_cl9, plain, ( ((('#sk1') = ('#sk2')))), 12.21/2.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl5])). 12.21/2.18 thf(zip_derived_cl14, plain, ((('#sk1') = ('#sk2'))), 12.21/2.18 inference('simplify nested equalities', [status(thm)], [zip_derived_cl9])). 12.21/2.18 thf(zip_derived_cl15, plain, 12.21/2.18 (![X2 : a, X3 : a]: (('#sk1' @ X2 @ X3) = ('#sk2' @ X2 @ X3))), 12.21/2.18 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl14])). 12.21/2.18 thf(zip_derived_cl114, plain, 12.21/2.18 (![X2 : a, X3 : a]: ( ('#sk1' @ X2 @ X3) | ~ ('#sk2' @ X2 @ X3))), 12.21/2.18 inference('eq_elim', [status(thm)], [zip_derived_cl15])). 12.21/2.18 thf(zip_derived_cl143, plain, 12.21/2.18 (( ('#form20') | ('#sk1' @ '#sk21' @ '#sk22'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl114])). 12.21/2.18 thf(zip_derived_cl65, plain, 12.21/2.18 (( ('#form12') 12.21/2.18 | ~ (((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) <=> 12.21/2.18 (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))))))), 12.21/2.18 define([status(thm)])). 12.21/2.18 thf(zip_derived_cl66, plain, 12.21/2.18 (( (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ ('#_fresh_sk6' @ Y1)))))))))) 12.21/2.18 | (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) 12.21/2.18 | ('#form12'))), 12.21/2.18 inference('lazy_cnf_xor', [status(thm)], [zip_derived_cl65])). 12.21/2.18 thf(zip_derived_cl75, plain, 12.21/2.18 (![X2 : a]: 12.21/2.18 ( (((!!) @ (^[Y0 : a]: 12.21/2.18 ((('#sk1' @ X2 @ Y0) => ('#sk3' @ X2 @ 12.21/2.18 ('#_fresh_sk5' @ X2) @ ('#_fresh_sk6' @ Y0))))))) 12.21/2.18 | ('#form12') 12.21/2.18 | (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl66])). 12.21/2.18 thf(zip_derived_cl83, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 ( ((('#sk1' @ X2 @ X4) => ('#sk3' @ X2 @ ('#_fresh_sk5' @ X2) @ 12.21/2.18 ('#_fresh_sk6' @ X4)))) 12.21/2.18 | (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))) 12.21/2.18 | ('#form12'))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl75])). 12.21/2.18 thf(zip_derived_cl92, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 (~ ('#sk1' @ X2 @ X4) 12.21/2.18 | ('#sk3' @ X2 @ ('#_fresh_sk5' @ X2) @ ('#_fresh_sk6' @ X4)) 12.21/2.18 | ('#form12') 12.21/2.18 | (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl83])). 12.21/2.18 thf(zip_derived_cl92, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 (~ ('#sk1' @ X2 @ X4) 12.21/2.18 | ('#sk3' @ X2 @ ('#_fresh_sk5' @ X2) @ ('#_fresh_sk6' @ X4)) 12.21/2.18 | ('#form12') 12.21/2.18 | (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl83])). 12.21/2.18 thf(zip_derived_cl100, plain, 12.21/2.18 ((~ ('#form20') 12.21/2.18 | (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))))), 12.21/2.18 define([status(thm)])). 12.21/2.18 thf(zip_derived_cl96, plain, 12.21/2.18 (( ('#form20') 12.21/2.18 | ~ (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))))), 12.21/2.18 define([status(thm)])). 12.21/2.18 thf(zip_derived_cl102, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 ( ('#form20') 12.21/2.18 | ('#form12') 12.21/2.18 | ('#sk3' @ X2 @ ('#_fresh_sk5' @ X2) @ ('#_fresh_sk6' @ X4)) 12.21/2.18 | ~ ('#sk1' @ X2 @ X4))), 12.21/2.18 inference('renaming', [status(thm)], 12.21/2.18 [zip_derived_cl92, zip_derived_cl100, zip_derived_cl96])). 12.21/2.18 thf(zip_derived_cl439, plain, 12.21/2.18 (( ('#form20') 12.21/2.18 | ('#sk3' @ '#sk21' @ ('#_fresh_sk5' @ '#sk21') @ 12.21/2.18 ('#_fresh_sk6' @ '#sk22')) 12.21/2.18 | ('#form12') 12.21/2.18 | ('#form20'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl102])). 12.21/2.18 thf(zip_derived_cl461, plain, 12.21/2.18 (( ('#form12') 12.21/2.18 | ('#sk3' @ '#sk21' @ ('#_fresh_sk5' @ '#sk21') @ 12.21/2.18 ('#_fresh_sk6' @ '#sk22')) 12.21/2.18 | ('#form20'))), 12.21/2.18 inference('simplify', [status(thm)], [zip_derived_cl439])). 12.21/2.18 thf(zip_derived_cl111, plain, 12.21/2.18 (( ('#sk2' @ '#sk21' @ '#sk22') | ('#form20'))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])). 12.21/2.18 thf(zip_derived_cl15, plain, 12.21/2.18 (![X2 : a, X3 : a]: (('#sk1' @ X2 @ X3) = ('#sk2' @ X2 @ X3))), 12.21/2.18 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl14])). 12.21/2.18 thf(zip_derived_cl24, plain, 12.21/2.18 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 12.21/2.18 thf(zip_derived_cl120, plain, 12.21/2.18 (![X0 : a, X1 : a]: (~ ('#sk2' @ X1 @ X0) | ('#sk1' @ X0 @ X1))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl24])). 12.21/2.18 thf(zip_derived_cl142, plain, 12.21/2.18 (( ('#form20') | ('#sk1' @ '#sk22' @ '#sk21'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl120])). 12.21/2.18 thf(zip_derived_cl43, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : b, X7 : b]: 12.21/2.18 ((('#sk3' @ X2 @ X6 @ X7) = ('#sk3' @ X4 @ X6 @ X7)) 12.21/2.18 | ~ ('#sk1' @ X2 @ X4))), 12.21/2.18 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl42])). 12.21/2.18 thf(zip_derived_cl210, plain, 12.21/2.18 (![X0 : b, X1 : b]: 12.21/2.18 ( ('#form20') 12.21/2.18 | (('#sk3' @ '#sk22' @ X1 @ X0) = ('#sk3' @ '#sk21' @ X1 @ X0)))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl43])). 12.21/2.18 thf(zip_derived_cl210, plain, 12.21/2.18 (![X0 : b, X1 : b]: 12.21/2.18 ( ('#form20') 12.21/2.18 | (('#sk3' @ '#sk22' @ X1 @ X0) = ('#sk3' @ '#sk21' @ X1 @ X0)))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl43])). 12.21/2.18 thf(zip_derived_cl17, plain, 12.21/2.18 ( (((!!) @ (^[Y0 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y0) => 12.21/2.18 (((((!!) @ (^[Y1 : b]: 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 (((!!) @ (^[Y3 : b]: 12.21/2.18 ((((('#sk3' @ Y0 @ 12.21/2.18 Y1 @ Y2) & 12.21/2.18 ('#sk3' @ Y0 @ 12.21/2.18 Y2 @ Y3))) => 12.21/2.18 ('#sk3' @ Y0 @ 12.21/2.18 Y1 @ Y3)))))))))))) & 12.21/2.18 ((('#sk3' @ Y0) = ('#sk4' @ Y0))) & 12.21/2.18 (((!!) @ (^[Y1 : b]: 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 ((('#sk3' @ Y0 @ Y1 @ Y2) => 12.21/2.18 ('#sk3' @ Y0 @ Y2 @ Y1))))))))))))))))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 12.21/2.18 thf(zip_derived_cl22, plain, 12.21/2.18 (![X2 : a]: 12.21/2.18 ((('#sk1' @ X2 @ X2) => 12.21/2.18 (((((!!) @ (^[Y0 : b]: 12.21/2.18 (((!!) @ (^[Y1 : b]: 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 ((((('#sk3' @ X2 @ Y0 @ Y1) & 12.21/2.18 ('#sk3' @ X2 @ Y1 @ Y2))) => 12.21/2.18 ('#sk3' @ X2 @ Y0 @ Y2)))))))))))) & 12.21/2.18 ((('#sk3' @ X2) = ('#sk4' @ X2))) & 12.21/2.18 (((!!) @ (^[Y0 : b]: 12.21/2.18 (((!!) @ (^[Y1 : b]: 12.21/2.18 ((('#sk3' @ X2 @ Y0 @ Y1) => ('#sk3' @ 12.21/2.18 X2 @ Y1 @ Y0)))))))))))))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 12.21/2.18 thf(zip_derived_cl27, plain, 12.21/2.18 (![X2 : a]: 12.21/2.18 (~ ('#sk1' @ X2 @ X2) 12.21/2.18 | (((((!!) @ (^[Y0 : b]: 12.21/2.18 (((!!) @ (^[Y1 : b]: 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 ((((('#sk3' @ X2 @ Y0 @ 12.21/2.18 Y1) & ('#sk3' @ X2 @ 12.21/2.18 Y1 @ Y2))) => 12.21/2.18 ('#sk3' @ X2 @ Y0 @ Y2)))))))))))) & 12.21/2.18 ((('#sk3' @ X2) = ('#sk4' @ X2))) & 12.21/2.18 (((!!) @ (^[Y0 : b]: 12.21/2.18 (((!!) @ (^[Y1 : b]: 12.21/2.18 ((('#sk3' @ X2 @ Y0 @ Y1) => ('#sk3' @ 12.21/2.18 X2 @ Y1 @ Y0))))))))))))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 12.21/2.18 thf(zip_derived_cl37, plain, 12.21/2.18 (![X2 : a]: ( ((('#sk3' @ X2) = ('#sk4' @ X2))) | ~ ('#sk1' @ X2 @ X2))), 12.21/2.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl27])). 12.21/2.18 thf(zip_derived_cl46, plain, 12.21/2.18 (![X2 : a]: ((('#sk3' @ X2) = ('#sk4' @ X2)) | ~ ('#sk1' @ X2 @ X2))), 12.21/2.18 inference('simplify nested equalities', [status(thm)], [zip_derived_cl37])). 12.21/2.18 thf(zip_derived_cl47, plain, 12.21/2.18 (![X2 : a, X4 : b, X5 : b]: 12.21/2.18 ((('#sk3' @ X2 @ X4 @ X5) = ('#sk4' @ X2 @ X4 @ X5)) 12.21/2.18 | ~ ('#sk1' @ X2 @ X2))), 12.21/2.18 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl46])). 12.21/2.18 thf(zip_derived_cl112, plain, 12.21/2.18 ((~ ('#sk4' @ '#sk21' @ ('#_fresh_sk5' @ '#sk21') @ 12.21/2.18 ('#_fresh_sk6' @ '#sk22')) 12.21/2.18 | ('#form20'))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])). 12.21/2.18 thf(zip_derived_cl253, plain, 12.21/2.18 ((~ ('#sk3' @ '#sk21' @ ('#_fresh_sk5' @ '#sk21') @ 12.21/2.18 ('#_fresh_sk6' @ '#sk22')) 12.21/2.18 | ~ ('#sk1' @ '#sk21' @ '#sk21') 12.21/2.18 | ('#form20'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl112])). 12.21/2.18 thf(zip_derived_cl496, plain, 12.21/2.18 ((~ ('#sk3' @ '#sk22' @ ('#_fresh_sk5' @ '#sk21') @ 12.21/2.18 ('#_fresh_sk6' @ '#sk22')) 12.21/2.18 | ('#form20') 12.21/2.18 | ('#form20') 12.21/2.18 | ~ ('#sk1' @ '#sk21' @ '#sk21'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl210, zip_derived_cl253])). 12.21/2.18 thf(zip_derived_cl502, plain, 12.21/2.18 ((~ ('#sk1' @ '#sk21' @ '#sk21') 12.21/2.18 | ('#form20') 12.21/2.18 | ~ ('#sk3' @ '#sk22' @ ('#_fresh_sk5' @ '#sk21') @ 12.21/2.18 ('#_fresh_sk6' @ '#sk22')))), 12.21/2.18 inference('simplify', [status(thm)], [zip_derived_cl496])). 12.21/2.18 thf(zip_derived_cl47, plain, 12.21/2.18 (![X2 : a, X4 : b, X5 : b]: 12.21/2.18 ((('#sk3' @ X2 @ X4 @ X5) = ('#sk4' @ X2 @ X4 @ X5)) 12.21/2.18 | ~ ('#sk1' @ X2 @ X2))), 12.21/2.18 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl46])). 12.21/2.18 thf(zip_derived_cl761, plain, 12.21/2.18 ((~ ('#sk4' @ '#sk22' @ ('#_fresh_sk5' @ '#sk21') @ 12.21/2.18 ('#_fresh_sk6' @ '#sk22')) 12.21/2.18 | ('#form20') 12.21/2.18 | ~ ('#sk1' @ '#sk21' @ '#sk21') 12.21/2.18 | ~ ('#sk1' @ '#sk22' @ '#sk22'))), 12.21/2.18 inference('sup+', [status(thm)], [zip_derived_cl502, zip_derived_cl47])). 12.21/2.18 thf(zip_derived_cl142, plain, 12.21/2.18 (( ('#form20') | ('#sk1' @ '#sk22' @ '#sk21'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl120])). 12.21/2.18 thf(zip_derived_cl143, plain, 12.21/2.18 (( ('#form20') | ('#sk1' @ '#sk21' @ '#sk22'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl114])). 12.21/2.18 thf(zip_derived_cl8, plain, 12.21/2.18 ( (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 (((!!) @ (^[Y2 : a]: 12.21/2.18 ((((('#sk1' @ Y0 @ Y1) & ('#sk1' @ 12.21/2.18 Y1 @ Y2))) => 12.21/2.18 ('#sk1' @ Y0 @ Y2))))))))))))), 12.21/2.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl5])). 12.21/2.18 thf(zip_derived_cl13, plain, 12.21/2.18 (![X2 : a]: 12.21/2.18 (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((((('#sk1' @ X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 12.21/2.18 ('#sk1' @ X2 @ Y1)))))))))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 12.21/2.18 thf(zip_derived_cl20, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 (((!!) @ (^[Y0 : a]: 12.21/2.18 ((((('#sk1' @ X2 @ X4) & ('#sk1' @ X4 @ Y0))) => 12.21/2.18 ('#sk1' @ X2 @ Y0))))))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 12.21/2.18 thf(zip_derived_cl25, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : a]: 12.21/2.18 ((((('#sk1' @ X2 @ X4) & ('#sk1' @ X4 @ X6))) => ('#sk1' @ X2 @ X6)))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])). 12.21/2.18 thf(zip_derived_cl32, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : a]: 12.21/2.18 (~ ((('#sk1' @ X2 @ X4) & ('#sk1' @ X4 @ X6))) | ('#sk1' @ X2 @ X6))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 12.21/2.18 thf(zip_derived_cl40, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : a]: 12.21/2.18 (~ ('#sk1' @ X2 @ X4) | ~ ('#sk1' @ X4 @ X6) | ('#sk1' @ X2 @ X6))), 12.21/2.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl32])). 12.21/2.18 thf(zip_derived_cl180, plain, 12.21/2.18 (![X0 : a]: 12.21/2.18 ( ('#form20') | ('#sk1' @ '#sk21' @ X0) | ~ ('#sk1' @ '#sk22' @ X0))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl40])). 12.21/2.18 thf(zip_derived_cl820, plain, 12.21/2.18 (( ('#form20') | ('#sk1' @ '#sk21' @ '#sk21') | ('#form20'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl180])). 12.21/2.18 thf(zip_derived_cl826, plain, 12.21/2.18 (( ('#sk1' @ '#sk21' @ '#sk21') | ('#form20'))), 12.21/2.18 inference('simplify', [status(thm)], [zip_derived_cl820])). 12.21/2.18 thf(zip_derived_cl1445, plain, 12.21/2.18 ((~ ('#sk1' @ '#sk22' @ '#sk22') 12.21/2.18 | ('#form20') 12.21/2.18 | ~ ('#sk4' @ '#sk22' @ ('#_fresh_sk5' @ '#sk21') @ 12.21/2.18 ('#_fresh_sk6' @ '#sk22')))), 12.21/2.18 inference('clc', [status(thm)], [zip_derived_cl761, zip_derived_cl826])). 12.21/2.18 thf(zip_derived_cl143, plain, 12.21/2.18 (( ('#form20') | ('#sk1' @ '#sk21' @ '#sk22'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl114])). 12.21/2.18 thf(zip_derived_cl142, plain, 12.21/2.18 (( ('#form20') | ('#sk1' @ '#sk22' @ '#sk21'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl120])). 12.21/2.18 thf(zip_derived_cl40, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : a]: 12.21/2.18 (~ ('#sk1' @ X2 @ X4) | ~ ('#sk1' @ X4 @ X6) | ('#sk1' @ X2 @ X6))), 12.21/2.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl32])). 12.21/2.18 thf(zip_derived_cl172, plain, 12.21/2.18 (![X0 : a]: 12.21/2.18 ( ('#form20') | ('#sk1' @ '#sk22' @ X0) | ~ ('#sk1' @ '#sk21' @ X0))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl40])). 12.21/2.18 thf(zip_derived_cl788, plain, 12.21/2.18 (( ('#form20') | ('#sk1' @ '#sk22' @ '#sk22') | ('#form20'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl172])). 12.21/2.18 thf(zip_derived_cl792, plain, 12.21/2.18 (( ('#sk1' @ '#sk22' @ '#sk22') | ('#form20'))), 12.21/2.18 inference('simplify', [status(thm)], [zip_derived_cl788])). 12.21/2.18 thf(zip_derived_cl1446, plain, 12.21/2.18 ((~ ('#sk4' @ '#sk22' @ ('#_fresh_sk5' @ '#sk21') @ 12.21/2.18 ('#_fresh_sk6' @ '#sk22')) 12.21/2.18 | ('#form20'))), 12.21/2.18 inference('clc', [status(thm)], [zip_derived_cl1445, zip_derived_cl792])). 12.21/2.18 thf(zip_derived_cl47, plain, 12.21/2.18 (![X2 : a, X4 : b, X5 : b]: 12.21/2.18 ((('#sk3' @ X2 @ X4 @ X5) = ('#sk4' @ X2 @ X4 @ X5)) 12.21/2.18 | ~ ('#sk1' @ X2 @ X2))), 12.21/2.18 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl46])). 12.21/2.18 thf(zip_derived_cl1447, plain, 12.21/2.18 ((~ ('#sk3' @ '#sk22' @ ('#_fresh_sk5' @ '#sk21') @ 12.21/2.18 ('#_fresh_sk6' @ '#sk22')) 12.21/2.18 | ('#form20') 12.21/2.18 | ~ ('#sk1' @ '#sk22' @ '#sk22'))), 12.21/2.18 inference('sup+', [status(thm)], [zip_derived_cl1446, zip_derived_cl47])). 12.21/2.18 thf(zip_derived_cl792, plain, 12.21/2.18 (( ('#sk1' @ '#sk22' @ '#sk22') | ('#form20'))), 12.21/2.18 inference('simplify', [status(thm)], [zip_derived_cl788])). 12.21/2.18 thf(zip_derived_cl1451, plain, 12.21/2.18 (( ('#form20') 12.21/2.18 | ~ ('#sk3' @ '#sk22' @ ('#_fresh_sk5' @ '#sk21') @ 12.21/2.18 ('#_fresh_sk6' @ '#sk22')))), 12.21/2.18 inference('clc', [status(thm)], [zip_derived_cl1447, zip_derived_cl792])). 12.21/2.18 thf(zip_derived_cl1454, plain, 12.21/2.18 ((~ ('#sk3' @ '#sk21' @ ('#_fresh_sk5' @ '#sk21') @ 12.21/2.18 ('#_fresh_sk6' @ '#sk22')) 12.21/2.18 | ('#form20') 12.21/2.18 | ('#form20'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl210, zip_derived_cl1451])). 12.21/2.18 thf(zip_derived_cl1460, plain, 12.21/2.18 (( ('#form20') 12.21/2.18 | ~ ('#sk3' @ '#sk21' @ ('#_fresh_sk5' @ '#sk21') @ 12.21/2.18 ('#_fresh_sk6' @ '#sk22')))), 12.21/2.18 inference('simplify', [status(thm)], [zip_derived_cl1454])). 12.21/2.18 thf(zip_derived_cl4256, plain, (( ('#form20') | ('#form12'))), 12.21/2.18 inference('clc', [status(thm)], [zip_derived_cl461, zip_derived_cl1460])). 12.21/2.18 thf(zip_derived_cl90, plain, 12.21/2.18 (( ('#sk1' @ '#sk15' @ '#sk17') 12.21/2.18 | ('#form12') 12.21/2.18 | ~ (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 12.21/2.18 thf(zip_derived_cl96, plain, 12.21/2.18 (( ('#form20') 12.21/2.18 | ~ (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))))), 12.21/2.18 define([status(thm)])). 12.21/2.18 thf(zip_derived_cl98, plain, 12.21/2.18 ((~ ('#form20') | ('#form12') | ('#sk1' @ '#sk15' @ '#sk17'))), 12.21/2.18 inference('renaming', [status(thm)], [zip_derived_cl90, zip_derived_cl96])). 12.21/2.18 thf(zip_derived_cl24, plain, 12.21/2.18 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 12.21/2.18 thf(zip_derived_cl402, plain, 12.21/2.18 (( ('#form12') | ~ ('#form20') | ('#sk1' @ '#sk17' @ '#sk15'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl98, zip_derived_cl24])). 12.21/2.18 thf(zip_derived_cl98, plain, 12.21/2.18 ((~ ('#form20') | ('#form12') | ('#sk1' @ '#sk15' @ '#sk17'))), 12.21/2.18 inference('renaming', [status(thm)], [zip_derived_cl90, zip_derived_cl96])). 12.21/2.18 thf(zip_derived_cl40, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : a]: 12.21/2.18 (~ ('#sk1' @ X2 @ X4) | ~ ('#sk1' @ X4 @ X6) | ('#sk1' @ X2 @ X6))), 12.21/2.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl32])). 12.21/2.18 thf(zip_derived_cl401, plain, 12.21/2.18 (![X0 : a]: 12.21/2.18 ( ('#form12') 12.21/2.18 | ~ ('#form20') 12.21/2.18 | ('#sk1' @ '#sk15' @ X0) 12.21/2.18 | ~ ('#sk1' @ '#sk17' @ X0))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl98, zip_derived_cl40])). 12.21/2.18 thf(zip_derived_cl1369, plain, 12.21/2.18 ((~ ('#form20') 12.21/2.18 | ('#form12') 12.21/2.18 | ('#sk1' @ '#sk15' @ '#sk15') 12.21/2.18 | ~ ('#form20') 12.21/2.18 | ('#form12'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl402, zip_derived_cl401])). 12.21/2.18 thf(zip_derived_cl1371, plain, 12.21/2.18 (( ('#sk1' @ '#sk15' @ '#sk15') | ('#form12') | ~ ('#form20'))), 12.21/2.18 inference('simplify', [status(thm)], [zip_derived_cl1369])). 12.21/2.18 thf(zip_derived_cl100, plain, 12.21/2.18 ((~ ('#form20') 12.21/2.18 | (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))))), 12.21/2.18 define([status(thm)])). 12.21/2.18 thf(zip_derived_cl101, plain, 12.21/2.18 (![X2 : a]: 12.21/2.18 ( (((!!) @ (^[Y0 : a]: 12.21/2.18 ((('#sk2' @ X2 @ Y0) => ('#sk4' @ X2 @ 12.21/2.18 ('#_fresh_sk5' @ X2) @ ('#_fresh_sk6' @ Y0))))))) 12.21/2.18 | ~ ('#form20'))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl100])). 12.21/2.18 thf(zip_derived_cl108, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 ( ((('#sk2' @ X2 @ X4) => ('#sk4' @ X2 @ ('#_fresh_sk5' @ X2) @ 12.21/2.18 ('#_fresh_sk6' @ X4)))) 12.21/2.18 | ~ ('#form20'))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl101])). 12.21/2.18 thf(zip_derived_cl113, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 (~ ('#sk2' @ X2 @ X4) 12.21/2.18 | ('#sk4' @ X2 @ ('#_fresh_sk5' @ X2) @ ('#_fresh_sk6' @ X4)) 12.21/2.18 | ~ ('#form20'))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 12.21/2.18 thf(zip_derived_cl47, plain, 12.21/2.18 (![X2 : a, X4 : b, X5 : b]: 12.21/2.18 ((('#sk3' @ X2 @ X4 @ X5) = ('#sk4' @ X2 @ X4 @ X5)) 12.21/2.18 | ~ ('#sk1' @ X2 @ X2))), 12.21/2.18 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl46])). 12.21/2.18 thf(zip_derived_cl91, plain, 12.21/2.18 ((~ ('#sk3' @ '#sk15' @ ('#_fresh_sk5' @ '#sk15') @ 12.21/2.18 ('#_fresh_sk6' @ '#sk17')) 12.21/2.18 | ('#form12') 12.21/2.18 | ~ (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 12.21/2.18 thf(zip_derived_cl96, plain, 12.21/2.18 (( ('#form20') 12.21/2.18 | ~ (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 12.21/2.18 ('#_fresh_sk5' @ Y0) @ 12.21/2.18 ('#_fresh_sk6' @ Y1)))))))))))), 12.21/2.18 define([status(thm)])). 12.21/2.18 thf(zip_derived_cl99, plain, 12.21/2.18 ((~ ('#form20') 12.21/2.18 | ('#form12') 12.21/2.18 | ~ ('#sk3' @ '#sk15' @ ('#_fresh_sk5' @ '#sk15') @ 12.21/2.18 ('#_fresh_sk6' @ '#sk17')))), 12.21/2.18 inference('renaming', [status(thm)], [zip_derived_cl91, zip_derived_cl96])). 12.21/2.18 thf(zip_derived_cl251, plain, 12.21/2.18 ((~ ('#sk4' @ '#sk15' @ ('#_fresh_sk5' @ '#sk15') @ 12.21/2.18 ('#_fresh_sk6' @ '#sk17')) 12.21/2.18 | ~ ('#sk1' @ '#sk15' @ '#sk15') 12.21/2.18 | ('#form12') 12.21/2.18 | ~ ('#form20'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl99])). 12.21/2.18 thf(zip_derived_cl852, plain, 12.21/2.18 ((~ ('#form20') 12.21/2.18 | ~ ('#sk2' @ '#sk15' @ '#sk17') 12.21/2.18 | ~ ('#form20') 12.21/2.18 | ('#form12') 12.21/2.18 | ~ ('#sk1' @ '#sk15' @ '#sk15'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl113, zip_derived_cl251])). 12.21/2.18 thf(zip_derived_cl858, plain, 12.21/2.18 ((~ ('#sk1' @ '#sk15' @ '#sk15') 12.21/2.18 | ('#form12') 12.21/2.18 | ~ ('#sk2' @ '#sk15' @ '#sk17') 12.21/2.18 | ~ ('#form20'))), 12.21/2.18 inference('simplify', [status(thm)], [zip_derived_cl852])). 12.21/2.18 thf(zip_derived_cl98, plain, 12.21/2.18 ((~ ('#form20') | ('#form12') | ('#sk1' @ '#sk15' @ '#sk17'))), 12.21/2.18 inference('renaming', [status(thm)], [zip_derived_cl90, zip_derived_cl96])). 12.21/2.18 thf(zip_derived_cl15, plain, 12.21/2.18 (![X2 : a, X3 : a]: (('#sk1' @ X2 @ X3) = ('#sk2' @ X2 @ X3))), 12.21/2.18 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl14])). 12.21/2.18 thf(zip_derived_cl115, plain, 12.21/2.18 (![X2 : a, X3 : a]: (~ ('#sk1' @ X2 @ X3) | ('#sk2' @ X2 @ X3))), 12.21/2.18 inference('eq_elim', [status(thm)], [zip_derived_cl15])). 12.21/2.18 thf(zip_derived_cl403, plain, 12.21/2.18 (( ('#form12') | ~ ('#form20') | ('#sk2' @ '#sk15' @ '#sk17'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl98, zip_derived_cl115])). 12.21/2.18 thf(zip_derived_cl866, plain, 12.21/2.18 ((~ ('#form20') | ('#form12') | ~ ('#sk1' @ '#sk15' @ '#sk15'))), 12.21/2.18 inference('clc', [status(thm)], [zip_derived_cl858, zip_derived_cl403])). 12.21/2.18 thf(zip_derived_cl1381, plain, ((~ ('#form20') | ('#form12'))), 12.21/2.18 inference('clc', [status(thm)], [zip_derived_cl1371, zip_derived_cl866])). 12.21/2.18 thf(zip_derived_cl4257, plain, ( ('#form12')), 12.21/2.18 inference('clc', [status(thm)], [zip_derived_cl4256, zip_derived_cl1381])). 12.21/2.18 thf(zip_derived_cl4258, plain, (~ ('#form9')), 12.21/2.18 inference('demod', [status(thm)], 12.21/2.18 [zip_derived_cl2946, zip_derived_cl4257])). 12.21/2.18 thf(zip_derived_cl4260, plain, 12.21/2.18 (~ ('#sk3' @ '#sk18' @ ('#sk10' @ '#sk18') @ ('#sk13' @ '#sk19'))), 12.21/2.18 inference('demod', [status(thm)], [zip_derived_cl106, zip_derived_cl4258])). 12.21/2.18 thf(zip_derived_cl105, plain, 12.21/2.18 (( ('#sk1' @ '#sk18' @ '#sk19') | ('#form9'))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])). 12.21/2.18 thf(zip_derived_cl105, plain, 12.21/2.18 (( ('#sk1' @ '#sk18' @ '#sk19') | ('#form9'))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])). 12.21/2.18 thf(zip_derived_cl24, plain, 12.21/2.18 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 12.21/2.18 thf(zip_derived_cl136, plain, 12.21/2.18 (( ('#form9') | ('#sk1' @ '#sk19' @ '#sk18'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl24])). 12.21/2.18 thf(zip_derived_cl40, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : a]: 12.21/2.18 (~ ('#sk1' @ X2 @ X4) | ~ ('#sk1' @ X4 @ X6) | ('#sk1' @ X2 @ X6))), 12.21/2.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl32])). 12.21/2.18 thf(zip_derived_cl160, plain, 12.21/2.18 (![X0 : a]: 12.21/2.18 ( ('#form9') | ('#sk1' @ '#sk19' @ X0) | ~ ('#sk1' @ '#sk18' @ X0))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl40])). 12.21/2.18 thf(zip_derived_cl682, plain, 12.21/2.18 (( ('#form9') | ('#sk1' @ '#sk19' @ '#sk19') | ('#form9'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl160])). 12.21/2.18 thf(zip_derived_cl686, plain, 12.21/2.18 (( ('#sk1' @ '#sk19' @ '#sk19') | ('#form9'))), 12.21/2.18 inference('simplify', [status(thm)], [zip_derived_cl682])). 12.21/2.18 thf(zip_derived_cl79, plain, 12.21/2.18 (( (((((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#sk10' @ Y0) @ ('#sk11' @ Y1)))))))))) & 12.21/2.18 (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#sk11' @ Y0) @ ('#sk13' @ Y1)))))))))))) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl72])). 12.21/2.18 thf(zip_derived_cl86, plain, 12.21/2.18 (( (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#sk11' @ Y0) @ ('#sk13' @ Y1)))))))))) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl79])). 12.21/2.18 thf(zip_derived_cl94, plain, 12.21/2.18 (![X2 : a]: 12.21/2.18 ( (((!!) @ (^[Y0 : a]: 12.21/2.18 ((('#sk1' @ X2 @ Y0) => ('#sk3' @ X2 @ ('#sk11' @ X2) @ 12.21/2.18 ('#sk13' @ Y0))))))) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl86])). 12.21/2.18 thf(zip_derived_cl104, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 ( ((('#sk1' @ X2 @ X4) => ('#sk3' @ X2 @ ('#sk11' @ X2) @ 12.21/2.18 ('#sk13' @ X4)))) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])). 12.21/2.18 thf(zip_derived_cl110, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 (~ ('#sk1' @ X2 @ X4) 12.21/2.18 | ('#sk3' @ X2 @ ('#sk11' @ X2) @ ('#sk13' @ X4)) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl104])). 12.21/2.18 thf(zip_derived_cl688, plain, 12.21/2.18 (( ('#form9') 12.21/2.18 | ('#form9') 12.21/2.18 | ('#sk3' @ '#sk19' @ ('#sk11' @ '#sk19') @ ('#sk13' @ '#sk19')))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl686, zip_derived_cl110])). 12.21/2.18 thf(zip_derived_cl703, plain, 12.21/2.18 (( ('#sk3' @ '#sk19' @ ('#sk11' @ '#sk19') @ ('#sk13' @ '#sk19')) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('simplify', [status(thm)], [zip_derived_cl688])). 12.21/2.18 thf(zip_derived_cl136, plain, 12.21/2.18 (( ('#form9') | ('#sk1' @ '#sk19' @ '#sk18'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl24])). 12.21/2.18 thf(zip_derived_cl43, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : b, X7 : b]: 12.21/2.18 ((('#sk3' @ X2 @ X6 @ X7) = ('#sk3' @ X4 @ X6 @ X7)) 12.21/2.18 | ~ ('#sk1' @ X2 @ X4))), 12.21/2.18 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl42])). 12.21/2.18 thf(zip_derived_cl212, plain, 12.21/2.18 (![X0 : b, X1 : b]: 12.21/2.18 ( ('#form9') 12.21/2.18 | (('#sk3' @ '#sk19' @ X1 @ X0) = ('#sk3' @ '#sk18' @ X1 @ X0)))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl43])). 12.21/2.18 thf(zip_derived_cl1143, plain, 12.21/2.18 (( ('#sk3' @ '#sk18' @ ('#sk11' @ '#sk19') @ ('#sk13' @ '#sk19')) 12.21/2.18 | ('#form9') 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('sup+', [status(thm)], [zip_derived_cl703, zip_derived_cl212])). 12.21/2.18 thf(zip_derived_cl1155, plain, 12.21/2.18 (( ('#form9') 12.21/2.18 | ('#sk3' @ '#sk18' @ ('#sk11' @ '#sk19') @ ('#sk13' @ '#sk19')))), 12.21/2.18 inference('simplify', [status(thm)], [zip_derived_cl1143])). 12.21/2.18 thf(zip_derived_cl4258, plain, (~ ('#form9')), 12.21/2.18 inference('demod', [status(thm)], 12.21/2.18 [zip_derived_cl2946, zip_derived_cl4257])). 12.21/2.18 thf(zip_derived_cl4295, plain, 12.21/2.18 ( ('#sk3' @ '#sk18' @ ('#sk11' @ '#sk19') @ ('#sk13' @ '#sk19'))), 12.21/2.18 inference('demod', [status(thm)], 12.21/2.18 [zip_derived_cl1155, zip_derived_cl4258])). 12.21/2.18 thf(zip_derived_cl105, plain, 12.21/2.18 (( ('#sk1' @ '#sk18' @ '#sk19') | ('#form9'))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])). 12.21/2.18 thf(zip_derived_cl85, plain, 12.21/2.18 (( (((!!) @ (^[Y0 : a]: 12.21/2.18 (((!!) @ (^[Y1 : a]: 12.21/2.18 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 12.21/2.18 ('#sk10' @ Y0) @ ('#sk11' @ Y1)))))))))) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl79])). 12.21/2.18 thf(zip_derived_cl93, plain, 12.21/2.18 (![X2 : a]: 12.21/2.18 ( (((!!) @ (^[Y0 : a]: 12.21/2.18 ((('#sk1' @ X2 @ Y0) => ('#sk3' @ X2 @ ('#sk10' @ X2) @ 12.21/2.18 ('#sk11' @ Y0))))))) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 12.21/2.18 thf(zip_derived_cl103, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 ( ((('#sk1' @ X2 @ X4) => ('#sk3' @ X2 @ ('#sk10' @ X2) @ 12.21/2.18 ('#sk11' @ X4)))) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl93])). 12.21/2.18 thf(zip_derived_cl109, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 (~ ('#sk1' @ X2 @ X4) 12.21/2.18 | ('#sk3' @ X2 @ ('#sk10' @ X2) @ ('#sk11' @ X4)) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])). 12.21/2.18 thf(zip_derived_cl513, plain, 12.21/2.18 (( ('#form9') 12.21/2.18 | ('#form9') 12.21/2.18 | ('#sk3' @ '#sk18' @ ('#sk10' @ '#sk18') @ ('#sk11' @ '#sk19')))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl109])). 12.21/2.18 thf(zip_derived_cl533, plain, 12.21/2.18 (( ('#sk3' @ '#sk18' @ ('#sk10' @ '#sk18') @ ('#sk11' @ '#sk19')) 12.21/2.18 | ('#form9'))), 12.21/2.18 inference('simplify', [status(thm)], [zip_derived_cl513])). 12.21/2.18 thf(zip_derived_cl47, plain, 12.21/2.18 (![X2 : a, X4 : b, X5 : b]: 12.21/2.18 ((('#sk3' @ X2 @ X4 @ X5) = ('#sk4' @ X2 @ X4 @ X5)) 12.21/2.18 | ~ ('#sk1' @ X2 @ X2))), 12.21/2.18 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl46])). 12.21/2.18 thf(zip_derived_cl547, plain, 12.21/2.18 (( ('#sk4' @ '#sk18' @ ('#sk10' @ '#sk18') @ ('#sk11' @ '#sk19')) 12.21/2.18 | ('#form9') 12.21/2.18 | ~ ('#sk1' @ '#sk18' @ '#sk18'))), 12.21/2.18 inference('sup+', [status(thm)], [zip_derived_cl533, zip_derived_cl47])). 12.21/2.18 thf(zip_derived_cl136, plain, 12.21/2.18 (( ('#form9') | ('#sk1' @ '#sk19' @ '#sk18'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl24])). 12.21/2.18 thf(zip_derived_cl105, plain, 12.21/2.18 (( ('#sk1' @ '#sk18' @ '#sk19') | ('#form9'))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])). 12.21/2.18 thf(zip_derived_cl40, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : a]: 12.21/2.18 (~ ('#sk1' @ X2 @ X4) | ~ ('#sk1' @ X4 @ X6) | ('#sk1' @ X2 @ X6))), 12.21/2.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl32])). 12.21/2.18 thf(zip_derived_cl161, plain, 12.21/2.18 (![X0 : a]: 12.21/2.18 ( ('#form9') | ('#sk1' @ '#sk18' @ X0) | ~ ('#sk1' @ '#sk19' @ X0))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl40])). 12.21/2.18 thf(zip_derived_cl723, plain, 12.21/2.18 (( ('#form9') | ('#sk1' @ '#sk18' @ '#sk18') | ('#form9'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl161])). 12.21/2.18 thf(zip_derived_cl729, plain, 12.21/2.18 (( ('#sk1' @ '#sk18' @ '#sk18') | ('#form9'))), 12.21/2.18 inference('simplify', [status(thm)], [zip_derived_cl723])). 12.21/2.18 thf(zip_derived_cl1659, plain, 12.21/2.18 (( ('#form9') 12.21/2.18 | ('#sk4' @ '#sk18' @ ('#sk10' @ '#sk18') @ ('#sk11' @ '#sk19')))), 12.21/2.18 inference('clc', [status(thm)], [zip_derived_cl547, zip_derived_cl729])). 12.21/2.18 thf(zip_derived_cl4258, plain, (~ ('#form9')), 12.21/2.18 inference('demod', [status(thm)], 12.21/2.18 [zip_derived_cl2946, zip_derived_cl4257])). 12.21/2.18 thf(zip_derived_cl4299, plain, 12.21/2.18 ( ('#sk4' @ '#sk18' @ ('#sk10' @ '#sk18') @ ('#sk11' @ '#sk19'))), 12.21/2.18 inference('demod', [status(thm)], 12.21/2.18 [zip_derived_cl1659, zip_derived_cl4258])). 12.21/2.18 thf(zip_derived_cl47, plain, 12.21/2.18 (![X2 : a, X4 : b, X5 : b]: 12.21/2.18 ((('#sk3' @ X2 @ X4 @ X5) = ('#sk4' @ X2 @ X4 @ X5)) 12.21/2.18 | ~ ('#sk1' @ X2 @ X2))), 12.21/2.18 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl46])). 12.21/2.18 thf(zip_derived_cl33, plain, 12.21/2.18 (![X2 : a, X4 : a]: 12.21/2.18 ( (((!!) @ (^[Y0 : b]: 12.21/2.18 (((!!) @ (^[Y1 : b]: 12.21/2.18 (((!!) @ (^[Y2 : b]: 12.21/2.18 ((((('#sk3' @ X2 @ Y0 @ Y1) & 12.21/2.18 ('#sk3' @ X2 @ Y1 @ Y2))) => 12.21/2.18 ('#sk3' @ X2 @ Y0 @ Y2)))))))))))) 12.21/2.18 | ~ ('#sk1' @ X2 @ X4))), 12.21/2.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 12.21/2.18 thf(zip_derived_cl41, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : b]: 12.21/2.18 ( (((!!) @ (^[Y0 : b]: 12.21/2.18 (((!!) @ (^[Y1 : b]: 12.21/2.18 ((((('#sk3' @ X2 @ X6 @ Y0) & ('#sk3' @ 12.21/2.18 X2 @ Y0 @ Y1))) => 12.21/2.18 ('#sk3' @ X2 @ X6 @ Y1))))))))) 12.21/2.18 | ~ ('#sk1' @ X2 @ X4))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl33])). 12.21/2.18 thf(zip_derived_cl51, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : b, X8 : b]: 12.21/2.18 ( (((!!) @ (^[Y0 : b]: 12.21/2.18 ((((('#sk3' @ X2 @ X6 @ X8) & ('#sk3' @ X2 @ X8 @ Y0))) => 12.21/2.18 ('#sk3' @ X2 @ X6 @ Y0)))))) 12.21/2.18 | ~ ('#sk1' @ X2 @ X4))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 12.21/2.18 thf(zip_derived_cl59, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : b, X8 : b, X10 : b]: 12.21/2.18 ( ((((('#sk3' @ X2 @ X6 @ X8) & ('#sk3' @ X2 @ X8 @ X10))) => 12.21/2.18 ('#sk3' @ X2 @ X6 @ X10))) 12.21/2.18 | ~ ('#sk1' @ X2 @ X4))), 12.21/2.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl51])). 12.21/2.18 thf(zip_derived_cl69, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : b, X8 : b, X10 : b]: 12.21/2.18 (~ ((('#sk3' @ X2 @ X6 @ X8) & ('#sk3' @ X2 @ X8 @ X10))) 12.21/2.18 | ('#sk3' @ X2 @ X6 @ X10) 12.21/2.18 | ~ ('#sk1' @ X2 @ X4))), 12.21/2.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl59])). 12.21/2.18 thf(zip_derived_cl76, plain, 12.21/2.18 (![X2 : a, X4 : a, X6 : b, X8 : b, X10 : b]: 12.21/2.18 (~ ('#sk3' @ X2 @ X6 @ X8) 12.21/2.18 | ~ ('#sk3' @ X2 @ X8 @ X10) 12.21/2.18 | ~ ('#sk1' @ X2 @ X4) 12.21/2.18 | ('#sk3' @ X2 @ X6 @ X10))), 12.21/2.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 12.21/2.18 thf(zip_derived_cl306, plain, 12.21/2.18 (![X0 : b, X1 : b, X2 : a, X3 : b, X4 : a]: 12.21/2.18 (~ ('#sk4' @ X2 @ X1 @ X0) 12.21/2.18 | ~ ('#sk1' @ X2 @ X2) 12.21/2.18 | ('#sk3' @ X2 @ X1 @ X3) 12.21/2.18 | ~ ('#sk1' @ X2 @ X4) 12.21/2.18 | ~ ('#sk3' @ X2 @ X0 @ X3))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl76])). 12.21/2.18 thf(zip_derived_cl1740, plain, 12.21/2.18 (![X0 : b, X1 : b, X2 : a, X3 : b]: 12.21/2.18 (~ ('#sk4' @ X2 @ X1 @ X0) 12.21/2.18 | ~ ('#sk1' @ X2 @ X2) 12.21/2.18 | ('#sk3' @ X2 @ X1 @ X3) 12.21/2.18 | ~ ('#sk3' @ X2 @ X0 @ X3))), 12.21/2.18 inference('condensation', [status(thm)], [zip_derived_cl306])). 12.21/2.18 thf(zip_derived_cl5569, plain, 12.21/2.18 (![X0 : b]: 12.21/2.18 (~ ('#sk3' @ '#sk18' @ ('#sk11' @ '#sk19') @ X0) 12.21/2.18 | ('#sk3' @ '#sk18' @ ('#sk10' @ '#sk18') @ X0) 12.21/2.18 | ~ ('#sk1' @ '#sk18' @ '#sk18'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl4299, zip_derived_cl1740])). 12.21/2.18 thf(zip_derived_cl729, plain, 12.21/2.18 (( ('#sk1' @ '#sk18' @ '#sk18') | ('#form9'))), 12.21/2.18 inference('simplify', [status(thm)], [zip_derived_cl723])). 12.21/2.18 thf(zip_derived_cl4258, plain, (~ ('#form9')), 12.21/2.18 inference('demod', [status(thm)], 12.21/2.18 [zip_derived_cl2946, zip_derived_cl4257])). 12.21/2.18 thf(zip_derived_cl4289, plain, ( ('#sk1' @ '#sk18' @ '#sk18')), 12.21/2.18 inference('demod', [status(thm)], [zip_derived_cl729, zip_derived_cl4258])). 12.21/2.18 thf(zip_derived_cl5592, plain, 12.21/2.18 (![X0 : b]: 12.21/2.18 (~ ('#sk3' @ '#sk18' @ ('#sk11' @ '#sk19') @ X0) 12.21/2.18 | ('#sk3' @ '#sk18' @ ('#sk10' @ '#sk18') @ X0))), 12.21/2.18 inference('demod', [status(thm)], 12.21/2.18 [zip_derived_cl5569, zip_derived_cl4289])). 12.21/2.18 thf(zip_derived_cl10152, plain, 12.21/2.18 ( ('#sk3' @ '#sk18' @ ('#sk10' @ '#sk18') @ ('#sk13' @ '#sk19'))), 12.21/2.18 inference('sup-', [status(thm)], [zip_derived_cl4295, zip_derived_cl5592])). 12.21/2.18 thf(zip_derived_cl10170, plain, ($false), 12.21/2.18 inference('demod', [status(thm)], 12.21/2.18 [zip_derived_cl4260, zip_derived_cl10152])). 12.21/2.18 12.21/2.18 % SZS output end Refutation 12.21/2.18 12.21/2.18 12.21/2.18 % Terminating... 12.21/2.18 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 13.46/2.35 % Runner terminated. 13.46/2.36 % Zipperpin 1.5 exiting 13.46/2.36 EOF