0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.05 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.5IgDiWVqtE true 0.12/0.37 % Computer : n003.cluster.edu 0.12/0.37 % Model : x86_64 x86_64 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.37 % Memory : 8046.5625MB 0.12/0.37 % OS : Linux 6.8.0-71-generic 0.12/0.38 % CPULimit : 1440 0.12/0.38 % WCLimit : 180 0.12/0.38 % DateTime : Mon Jul 27 13:20:54 UTC 2026 0.12/0.38 % CPUTime : 0.12/0.38 % Running portfolio for 1440 s 0.12/0.38 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.12/0.38 % Number of cores: 8 0.12/0.38 % Python version: Python 3.12.3 0.12/0.39 % Running in HO mode 0.45/0.68 % Total configuration time : 828 0.45/0.68 % Estimated wc time : 1656 0.45/0.68 % Estimated cpu time (8 cpus) : 207.0 0.48/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.49/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.49/0.81 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.49/0.81 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.49/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.49/0.83 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.49/0.83 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.50/0.91 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 23.59/4.01 % Solved by lams/20_acsne_simpl.sh. 23.59/4.01 % done 3992 iterations in 3.064s 23.59/4.01 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 23.59/4.01 % SZS output start Refutation 23.59/4.01 thf(a_type, type, a: $tType). 23.59/4.01 thf(b_type, type, b: $tType). 23.59/4.01 thf('#sk7_type', type, '#sk7': a > b). 23.59/4.01 thf('#sk15_type', type, '#sk15': a). 23.59/4.01 thf('#sk8_type', type, '#sk8': a > b). 23.59/4.01 thf('#sk11_type', type, '#sk11': a > b). 23.59/4.01 thf('#sk1_type', type, '#sk1': a > a > $o). 23.59/4.01 thf('#sk14_type', type, '#sk14': a). 23.59/4.01 thf('#form9_type', type, '#form9': $o). 23.59/4.01 thf('#sk10_type', type, '#sk10': a > b). 23.59/4.01 thf('#sk17_type', type, '#sk17': a). 23.59/4.01 thf('#sk4_type', type, '#sk4': a > b > b > $o). 23.59/4.01 thf('#sk13_type', type, '#sk13': a > b). 23.59/4.01 thf('#sk19_type', type, '#sk19': a). 23.59/4.01 thf('#sk21_type', type, '#sk21': a). 23.59/4.01 thf('#_fresh_sk6_type', type, '#_fresh_sk6': a > b). 23.59/4.01 thf('#sk18_type', type, '#sk18': a). 23.59/4.01 thf('#sk3_type', type, '#sk3': a > b > b > $o). 23.59/4.01 thf('#form20_type', type, '#form20': $o). 23.59/4.01 thf('#sk2_type', type, '#sk2': a > a > $o). 23.59/4.01 thf('#sk22_type', type, '#sk22': a). 23.59/4.01 thf('#sk16_type', type, '#sk16': a). 23.59/4.01 thf('#form12_type', type, '#form12': $o). 23.59/4.01 thf('#_fresh_sk5_type', type, '#_fresh_sk5': a > b). 23.59/4.01 thf(cTHM517_pme, conjecture, 23.59/4.01 (![Xp:( a > a > $o ),Xq:( a > a > $o ),Xr:( a > b > b > $o ), 23.59/4.01 Xs:( a > b > b > $o )]: 23.59/4.01 ( ( ( ![Xx:a,Xy:a]: ( ( Xp @ Xx @ Xy ) => ( Xp @ Xy @ Xx ) ) ) & 23.59/4.01 ( ![Xx:a,Xy:a,Xz:a]: 23.59/4.01 ( ( ( Xp @ Xy @ Xz ) & ( Xp @ Xx @ Xy ) ) => ( Xp @ Xx @ Xz ) ) ) & 23.59/4.01 ( ( Xp ) = ( Xq ) ) ) => 23.59/4.01 ( ( ![Xx:a,Xy:a]: 23.59/4.01 ( ( Xp @ Xx @ Xy ) => 23.59/4.01 ( ( ![Xx0:b,Xy0:b]: 23.59/4.01 ( ( Xr @ Xx @ Xx0 @ Xy0 ) => ( Xr @ Xx @ Xy0 @ Xx0 ) ) ) & 23.59/4.01 ( ( Xr @ Xx ) = ( Xr @ Xy ) ) & 23.59/4.01 ( ![Xx0:b,Xy0:b,Xz:b]: 23.59/4.01 ( ( ( Xr @ Xx @ Xx0 @ Xy0 ) & ( Xr @ Xx @ Xy0 @ Xz ) ) => 23.59/4.01 ( Xr @ Xx @ Xx0 @ Xz ) ) ) ) ) ) => 23.59/4.01 ( ( ![Xx:a]: 23.59/4.01 ( ( Xp @ Xx @ Xx ) => 23.59/4.01 ( ( ![Xx0:b,Xy:b]: 23.59/4.01 ( ( Xr @ Xx @ Xx0 @ Xy ) => ( Xr @ Xx @ Xy @ Xx0 ) ) ) & 23.59/4.01 ( ( Xr @ Xx ) = ( Xs @ Xx ) ) & 23.59/4.01 ( ![Xx0:b,Xy:b,Xz:b]: 23.59/4.01 ( ( ( Xr @ Xx @ Xy @ Xz ) & ( Xr @ Xx @ Xx0 @ Xy ) ) => 23.59/4.01 ( Xr @ Xx @ Xx0 @ Xz ) ) ) ) ) ) => 23.59/4.01 ( ( ![Xx:( a > b ),Xy:( a > b )]: 23.59/4.01 ( ( ![Xx0:a,Xy0:a]: 23.59/4.01 ( ( Xp @ Xx0 @ Xy0 ) => 23.59/4.01 ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) ) ) => 23.59/4.01 ( ![Xx0:a,Xy0:a]: 23.59/4.01 ( ( Xp @ Xx0 @ Xy0 ) => 23.59/4.01 ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xy0 ) ) ) ) ) ) & 23.59/4.01 ( ( ^[Xf:( a > b ),Xg:( a > b )]: 23.59/4.01 ( ![Xx:a,Xy:a]: 23.59/4.01 ( ( Xp @ Xx @ Xy ) => 23.59/4.01 ( Xr @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) ) = 23.59/4.01 ( ^[Xf:( a > b ),Xg:( a > b )]: 23.59/4.01 ( ![Xx:a,Xy:a]: 23.59/4.01 ( ( Xq @ Xx @ Xy ) => 23.59/4.01 ( Xs @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) ) ) & 23.59/4.01 ( ![Xx:( a > b ),Xy:( a > b ),Xz:( a > b )]: 23.59/4.01 ( ( ( ![Xx0:a,Xy0:a]: 23.59/4.01 ( ( Xp @ Xx0 @ Xy0 ) => 23.59/4.01 ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xy0 ) ) ) ) & 23.59/4.01 ( ![Xx0:a,Xy0:a]: 23.59/4.01 ( ( Xp @ Xx0 @ Xy0 ) => 23.59/4.01 ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) ) ) ) => 23.59/4.01 ( ![Xx0:a,Xy0:a]: 23.59/4.01 ( ( Xp @ Xx0 @ Xy0 ) => 23.59/4.01 ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xy0 ) ) ) ) ) ) ) ) ) ))). 23.59/4.01 thf(zf_stmt_0, negated_conjecture, 23.59/4.01 (~( ![Xp:( a > a > $o ),Xq:( a > a > $o ),Xr:( a > b > b > $o ), 23.59/4.01 Xs:( a > b > b > $o )]: 23.59/4.01 ( ( ( ![Xx:a,Xy:a]: ( ( Xp @ Xx @ Xy ) => ( Xp @ Xy @ Xx ) ) ) & 23.59/4.01 ( ![Xx:a,Xy:a,Xz:a]: 23.59/4.01 ( ( ( Xp @ Xy @ Xz ) & ( Xp @ Xx @ Xy ) ) => ( Xp @ Xx @ Xz ) ) ) & 23.59/4.01 ( ( Xp ) = ( Xq ) ) ) => 23.59/4.01 ( ( ![Xx:a,Xy:a]: 23.59/4.01 ( ( Xp @ Xx @ Xy ) => 23.59/4.01 ( ( ![Xx0:b,Xy0:b]: 23.59/4.01 ( ( Xr @ Xx @ Xx0 @ Xy0 ) => ( Xr @ Xx @ Xy0 @ Xx0 ) ) ) & 23.59/4.01 ( ( Xr @ Xx ) = ( Xr @ Xy ) ) & 23.59/4.01 ( ![Xx0:b,Xy0:b,Xz:b]: 23.59/4.01 ( ( ( Xr @ Xx @ Xx0 @ Xy0 ) & ( Xr @ Xx @ Xy0 @ Xz ) ) => 23.59/4.01 ( Xr @ Xx @ Xx0 @ Xz ) ) ) ) ) ) => 23.59/4.01 ( ( ![Xx:a]: 23.59/4.01 ( ( Xp @ Xx @ Xx ) => 23.59/4.01 ( ( ![Xx0:b,Xy:b]: 23.59/4.01 ( ( Xr @ Xx @ Xx0 @ Xy ) => ( Xr @ Xx @ Xy @ Xx0 ) ) ) & 23.59/4.01 ( ( Xr @ Xx ) = ( Xs @ Xx ) ) & 23.59/4.01 ( ![Xx0:b,Xy:b,Xz:b]: 23.59/4.01 ( ( ( Xr @ Xx @ Xy @ Xz ) & ( Xr @ Xx @ Xx0 @ Xy ) ) => 23.59/4.01 ( Xr @ Xx @ Xx0 @ Xz ) ) ) ) ) ) => 23.59/4.01 ( ( ![Xx:( a > b ),Xy:( a > b )]: 23.59/4.01 ( ( ![Xx0:a,Xy0:a]: 23.59/4.01 ( ( Xp @ Xx0 @ Xy0 ) => 23.59/4.01 ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) ) ) => 23.59/4.01 ( ![Xx0:a,Xy0:a]: 23.59/4.01 ( ( Xp @ Xx0 @ Xy0 ) => 23.59/4.01 ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xy0 ) ) ) ) ) ) & 23.59/4.01 ( ( ^[Xf:( a > b ),Xg:( a > b )]: 23.59/4.01 ( ![Xx:a,Xy:a]: 23.59/4.01 ( ( Xp @ Xx @ Xy ) => 23.59/4.01 ( Xr @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) ) = 23.59/4.01 ( ^[Xf:( a > b ),Xg:( a > b )]: 23.59/4.01 ( ![Xx:a,Xy:a]: 23.59/4.01 ( ( Xq @ Xx @ Xy ) => 23.59/4.01 ( Xs @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) ) ) & 23.59/4.01 ( ![Xx:( a > b ),Xy:( a > b ),Xz:( a > b )]: 23.59/4.01 ( ( ( ![Xx0:a,Xy0:a]: 23.59/4.01 ( ( Xp @ Xx0 @ Xy0 ) => 23.59/4.01 ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xy0 ) ) ) ) & 23.59/4.01 ( ![Xx0:a,Xy0:a]: 23.59/4.01 ( ( Xp @ Xx0 @ Xy0 ) => 23.59/4.01 ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) ) ) ) => 23.59/4.01 ( ![Xx0:a,Xy0:a]: 23.59/4.01 ( ( Xp @ Xx0 @ Xy0 ) => 23.59/4.01 ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xy0 ) ) ) ) ) ) ) ) ) ) )), 23.59/4.01 inference('cnf.neg', [status(esa)], [cTHM517_pme])). 23.59/4.01 thf(zip_derived_cl0, plain, 23.59/4.01 (~ (((!!) @ (^[Y0 : a > a > $o]: 23.59/4.01 (((!!) @ (^[Y1 : a > a > $o]: 23.59/4.01 (((!!) @ (^[Y2 : a > b > b > $o]: 23.59/4.01 (((!!) @ (^[Y3 : a > b > b > $o]: 23.59/4.01 (((((((!!) @ ( 23.59/4.01 ^[Y4 : a]: 23.59/4.01 (((!!) @ ( 23.59/4.01 ^[Y5 : a]: 23.59/4.01 (( 23.59/4.01 (Y0 @ 23.59/4.01 Y4 @ 23.59/4.01 Y5) => 23.59/4.01 (Y0 @ 23.59/4.01 Y5 @ Y4))))))))) & 23.59/4.01 (((!!) @ ( 23.59/4.01 ^[Y4 : a]: 23.59/4.01 (((!!) @ ( 23.59/4.01 ^[Y5 : a]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y6 : a]: 23.59/4.01 (( 23.59/4.01 (( 23.59/4.01 (Y0 @ 23.59/4.01 Y5 @ 23.59/4.01 Y6) & 23.59/4.01 (Y0 @ 23.59/4.01 Y4 @ Y5))) => 23.59/4.01 (Y0 @ 23.59/4.01 Y4 @ Y6)))))))))))) & 23.59/4.01 (((Y0) = (Y1))))) => 23.59/4.01 (((((!!) @ ( 23.59/4.01 ^[Y4 : a]: 23.59/4.01 (((!!) @ ( 23.59/4.01 ^[Y5 : a]: 23.59/4.01 (( 23.59/4.01 (Y0 @ 23.59/4.01 Y4 @ 23.59/4.01 Y5) => 23.59/4.01 (( 23.59/4.01 ( 23.59/4.01 ( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y6 : b]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y7 : b]: 23.59/4.01 (( 23.59/4.01 (Y2 @ 23.59/4.01 Y4 @ 23.59/4.01 Y6 @ 23.59/4.01 Y7) => 23.59/4.01 (Y2 @ 23.59/4.01 Y4 @ 23.59/4.01 Y7 @ Y6))))))))) & 23.59/4.01 ( 23.59/4.01 ( 23.59/4.01 (Y2 @ 23.59/4.01 Y4) = 23.59/4.01 (Y2 @ Y5))) & 23.59/4.01 ( 23.59/4.01 ( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y6 : b]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y7 : b]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y8 : b]: 23.59/4.01 (( 23.59/4.01 (( 23.59/4.01 (Y2 @ 23.59/4.01 Y4 @ 23.59/4.01 Y6 @ 23.59/4.01 Y7) & 23.59/4.01 (Y2 @ 23.59/4.01 Y4 @ 23.59/4.01 Y7 @ Y8))) => 23.59/4.01 (Y2 @ 23.59/4.01 Y4 @ 23.59/4.01 Y6 @ Y8)))))))))))))))))))))) => 23.59/4.01 (((((!!) @ ( 23.59/4.01 ^[Y4 : a]: 23.59/4.01 (((Y0 @ 23.59/4.01 Y4 @ 23.59/4.01 Y4) => 23.59/4.01 (( 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y5 : b]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y6 : b]: 23.59/4.01 (( 23.59/4.01 (Y2 @ 23.59/4.01 Y4 @ 23.59/4.01 Y5 @ 23.59/4.01 Y6) => 23.59/4.01 (Y2 @ 23.59/4.01 Y4 @ 23.59/4.01 Y6 @ Y5))))))))) & 23.59/4.01 (( 23.59/4.01 (Y2 @ 23.59/4.01 Y4) = 23.59/4.01 (Y3 @ Y4))) & 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y5 : b]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y6 : b]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y7 : b]: 23.59/4.01 (( 23.59/4.01 (( 23.59/4.01 (Y2 @ 23.59/4.01 Y4 @ 23.59/4.01 Y6 @ 23.59/4.01 Y7) & 23.59/4.01 (Y2 @ 23.59/4.01 Y4 @ 23.59/4.01 Y5 @ Y6))) => 23.59/4.01 (Y2 @ 23.59/4.01 Y4 @ 23.59/4.01 Y5 @ Y7))))))))))))))))))) => 23.59/4.01 (((((!!) @ ( 23.59/4.01 ^[Y4 : a > b]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y5 : a > b]: 23.59/4.01 (( 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y6 : a]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y7 : a]: 23.59/4.01 (( 23.59/4.01 (Y0 @ 23.59/4.01 Y6 @ 23.59/4.01 Y7) => 23.59/4.01 (Y2 @ 23.59/4.01 Y6 @ 23.59/4.01 ( 23.59/4.01 Y4 @ Y6) @ 23.59/4.01 ( 23.59/4.01 Y5 @ Y7)))))))))) => 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y6 : a]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y7 : a]: 23.59/4.01 (( 23.59/4.01 (Y0 @ 23.59/4.01 Y6 @ 23.59/4.01 Y7) => 23.59/4.01 (Y2 @ 23.59/4.01 Y6 @ 23.59/4.01 ( 23.59/4.01 Y5 @ Y6) @ 23.59/4.01 ( 23.59/4.01 Y4 @ Y7)))))))))))))))))) & 23.59/4.01 ((((^[Y4 : a > b, 23.59/4.01 Y5 : a > b]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y6 : a]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y7 : a]: 23.59/4.01 (( 23.59/4.01 (Y0 @ 23.59/4.01 Y6 @ 23.59/4.01 Y7) => 23.59/4.01 (Y2 @ 23.59/4.01 Y6 @ 23.59/4.01 ( 23.59/4.01 Y4 @ Y6) @ 23.59/4.01 ( 23.59/4.01 Y5 @ Y7)))))))))))) = 23.59/4.01 ((^[Y4 : a > b, 23.59/4.01 Y5 : a > b]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y6 : a]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y7 : a]: 23.59/4.01 (( 23.59/4.01 (Y1 @ 23.59/4.01 Y6 @ 23.59/4.01 Y7) => 23.59/4.01 (Y3 @ 23.59/4.01 Y6 @ 23.59/4.01 ( 23.59/4.01 Y4 @ Y6) @ 23.59/4.01 ( 23.59/4.01 Y5 @ Y7)))))))))))))) & 23.59/4.01 (((!!) @ ( 23.59/4.01 ^[Y4 : a > b]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y5 : a > b]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y6 : a > b]: 23.59/4.01 (( 23.59/4.01 (( 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y7 : a]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y8 : a]: 23.59/4.01 (( 23.59/4.01 (Y0 @ 23.59/4.01 Y7 @ 23.59/4.01 Y8) => 23.59/4.01 (Y2 @ 23.59/4.01 Y7 @ 23.59/4.01 ( 23.59/4.01 Y5 @ Y7) @ 23.59/4.01 ( 23.59/4.01 Y6 @ Y8)))))))))) & 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y7 : a]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y8 : a]: 23.59/4.01 (( 23.59/4.01 (Y0 @ 23.59/4.01 Y7 @ 23.59/4.01 Y8) => 23.59/4.01 (Y2 @ 23.59/4.01 Y7 @ 23.59/4.01 ( 23.59/4.01 Y4 @ Y7) @ 23.59/4.01 ( 23.59/4.01 Y5 @ Y8)))))))))))) => 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y7 : a]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y8 : a]: 23.59/4.01 (( 23.59/4.01 (Y0 @ 23.59/4.01 Y7 @ 23.59/4.01 Y8) => 23.59/4.01 (Y2 @ 23.59/4.01 Y7 @ 23.59/4.01 ( 23.59/4.01 Y4 @ Y7) @ 23.59/4.01 ( 23.59/4.01 Y6 @ Y8)))))))))))))))))))))))))))))))))))))))))), 23.59/4.01 inference('cnf', [status(esa)], [zf_stmt_0])). 23.59/4.01 thf(zip_derived_cl1, plain, 23.59/4.01 (~ (((!!) @ (^[Y0 : a > a > $o]: 23.59/4.01 (((!!) @ (^[Y1 : a > b > b > $o]: 23.59/4.01 (((!!) @ (^[Y2 : a > b > b > $o]: 23.59/4.01 (((((((!!) @ (^[Y3 : a]: 23.59/4.01 (((!!) @ ( 23.59/4.01 ^[Y4 : a]: 23.59/4.01 ((('#sk1' @ 23.59/4.01 Y3 @ Y4) => 23.59/4.01 ('#sk1' @ 23.59/4.01 Y4 @ Y3))))))))) & 23.59/4.01 (((!!) @ (^[Y3 : a]: 23.59/4.01 (((!!) @ ( 23.59/4.01 ^[Y4 : a]: 23.59/4.01 (((!!) @ ( 23.59/4.01 ^[Y5 : a]: 23.59/4.01 (( 23.59/4.01 (( 23.59/4.01 ('#sk1' @ 23.59/4.01 Y4 @ 23.59/4.01 Y5) & 23.59/4.01 ('#sk1' @ 23.59/4.01 Y3 @ Y4))) => 23.59/4.01 ('#sk1' @ 23.59/4.01 Y3 @ Y5)))))))))))) & 23.59/4.01 ((('#sk1') = (Y0))))) => 23.59/4.01 (((((!!) @ (^[Y3 : a]: 23.59/4.01 (((!!) @ ( 23.59/4.01 ^[Y4 : a]: 23.59/4.01 ((('#sk1' @ 23.59/4.01 Y3 @ Y4) => 23.59/4.01 (((( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y5 : b]: 23.59/4.01 (( 23.59/4.01 (!!) @ ( 23.59/4.01 ^[Y6 : b]: 23.59/4.01 (( 23.59/4.01 (Y1 @ 23.59/4.01 Y3 @ 23.59/4.01 Y5 @ 23.59/4.01 Y6) => 23.59/4.01 (Y1 @ 23.59/4.01 Y3 @ 23.59/4.02 Y6 @ Y5))))))))) & 23.59/4.02 (( 23.59/4.02 (Y1 @ 23.59/4.02 Y3) = 23.59/4.02 (Y1 @ Y4))) & 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : b]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y6 : b]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y7 : b]: 23.59/4.02 (( 23.59/4.02 (( 23.59/4.02 (Y1 @ 23.59/4.02 Y3 @ 23.59/4.02 Y5 @ 23.59/4.02 Y6) & 23.59/4.02 (Y1 @ 23.59/4.02 Y3 @ 23.59/4.02 Y6 @ Y7))) => 23.59/4.02 (Y1 @ 23.59/4.02 Y3 @ 23.59/4.02 Y5 @ Y7)))))))))))))))))))))) => 23.59/4.02 (((((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ Y3) => 23.59/4.02 (((((!!) @ ( 23.59/4.02 ^[Y4 : b]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : b]: 23.59/4.02 (( 23.59/4.02 (Y1 @ 23.59/4.02 Y3 @ 23.59/4.02 Y4 @ 23.59/4.02 Y5) => 23.59/4.02 (Y1 @ 23.59/4.02 Y3 @ 23.59/4.02 Y5 @ Y4))))))))) & 23.59/4.02 (((Y1 @ 23.59/4.02 Y3) = 23.59/4.02 (Y2 @ Y3))) & 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : b]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : b]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y6 : b]: 23.59/4.02 (( 23.59/4.02 (( 23.59/4.02 (Y1 @ 23.59/4.02 Y3 @ 23.59/4.02 Y5 @ 23.59/4.02 Y6) & 23.59/4.02 (Y1 @ 23.59/4.02 Y3 @ 23.59/4.02 Y4 @ Y5))) => 23.59/4.02 (Y1 @ 23.59/4.02 Y3 @ 23.59/4.02 Y4 @ Y6))))))))))))))))))) => 23.59/4.02 (((((!!) @ (^[Y3 : a > b]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a > b]: 23.59/4.02 (( 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : a]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y6 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y5 @ 23.59/4.02 Y6) => 23.59/4.02 (Y1 @ 23.59/4.02 Y5 @ 23.59/4.02 ( 23.59/4.02 Y3 @ Y5) @ 23.59/4.02 ( 23.59/4.02 Y4 @ Y6)))))))))) => 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : a]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y6 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y5 @ 23.59/4.02 Y6) => 23.59/4.02 (Y1 @ 23.59/4.02 Y5 @ 23.59/4.02 ( 23.59/4.02 Y4 @ Y5) @ 23.59/4.02 ( 23.59/4.02 Y3 @ Y6)))))))))))))))))) & 23.59/4.02 ((((^[Y3 : a > b, 23.59/4.02 Y4 : a > b]: 23.59/4.02 (((!!) @ (^[Y5 : a]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y6 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y5 @ 23.59/4.02 Y6) => 23.59/4.02 (Y1 @ 23.59/4.02 Y5 @ 23.59/4.02 ( 23.59/4.02 Y3 @ Y5) @ 23.59/4.02 ( 23.59/4.02 Y4 @ Y6)))))))))))) = 23.59/4.02 ((^[Y3 : a > b, 23.59/4.02 Y4 : a > b]: 23.59/4.02 (((!!) @ (^[Y5 : a]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y6 : a]: 23.59/4.02 (( 23.59/4.02 (Y0 @ 23.59/4.02 Y5 @ 23.59/4.02 Y6) => 23.59/4.02 (Y2 @ 23.59/4.02 Y5 @ 23.59/4.02 ( 23.59/4.02 Y3 @ Y5) @ 23.59/4.02 ( 23.59/4.02 Y4 @ Y6)))))))))))))) & 23.59/4.02 (((!!) @ (^[Y3 : a > b]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a > b]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : a > b]: 23.59/4.02 (( 23.59/4.02 (( 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y6 : a]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y7 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y6 @ 23.59/4.02 Y7) => 23.59/4.02 (Y1 @ 23.59/4.02 Y6 @ 23.59/4.02 ( 23.59/4.02 Y4 @ Y6) @ 23.59/4.02 ( 23.59/4.02 Y5 @ Y7)))))))))) & 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y6 : a]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y7 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y6 @ 23.59/4.02 Y7) => 23.59/4.02 (Y1 @ 23.59/4.02 Y6 @ 23.59/4.02 ( 23.59/4.02 Y3 @ Y6) @ 23.59/4.02 ( 23.59/4.02 Y4 @ Y7)))))))))))) => 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y6 : a]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y7 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y6 @ 23.59/4.02 Y7) => 23.59/4.02 (Y1 @ 23.59/4.02 Y6 @ 23.59/4.02 ( 23.59/4.02 Y3 @ Y6) @ 23.59/4.02 ( 23.59/4.02 Y5 @ Y7))))))))))))))))))))))))))))))))))))))), 23.59/4.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 23.59/4.02 thf(zip_derived_cl2, plain, 23.59/4.02 (~ (((!!) @ (^[Y0 : a > b > b > $o]: 23.59/4.02 (((!!) @ (^[Y1 : a > b > b > $o]: 23.59/4.02 (((((((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ 23.59/4.02 Y3) => 23.59/4.02 ('#sk1' @ Y3 @ 23.59/4.02 Y2))))))))) & 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((((('#sk1' @ 23.59/4.02 Y3 @ Y4) & 23.59/4.02 ('#sk1' @ 23.59/4.02 Y2 @ Y3))) => 23.59/4.02 ('#sk1' @ 23.59/4.02 Y2 @ Y4)))))))))))) & 23.59/4.02 ((('#sk1') = ('#sk2'))))) => 23.59/4.02 (((((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ 23.59/4.02 Y3) => 23.59/4.02 (((((!!) @ ( 23.59/4.02 ^[Y4 : b]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : b]: 23.59/4.02 (( 23.59/4.02 (Y0 @ 23.59/4.02 Y2 @ 23.59/4.02 Y4 @ 23.59/4.02 Y5) => 23.59/4.02 (Y0 @ 23.59/4.02 Y2 @ 23.59/4.02 Y5 @ Y4))))))))) & 23.59/4.02 (((Y0 @ Y2) = 23.59/4.02 (Y0 @ Y3))) & 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : b]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : b]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y6 : b]: 23.59/4.02 (( 23.59/4.02 (( 23.59/4.02 (Y0 @ 23.59/4.02 Y2 @ 23.59/4.02 Y4 @ 23.59/4.02 Y5) & 23.59/4.02 (Y0 @ 23.59/4.02 Y2 @ 23.59/4.02 Y5 @ Y6))) => 23.59/4.02 (Y0 @ 23.59/4.02 Y2 @ 23.59/4.02 Y4 @ Y6)))))))))))))))))))))) => 23.59/4.02 (((((!!) @ (^[Y2 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ Y2) => 23.59/4.02 (((((!!) @ (^[Y3 : b]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : b]: 23.59/4.02 (( 23.59/4.02 (Y0 @ 23.59/4.02 Y2 @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 (Y0 @ 23.59/4.02 Y2 @ 23.59/4.02 Y4 @ Y3))))))))) & 23.59/4.02 (((Y0 @ Y2) = (Y1 @ Y2))) & 23.59/4.02 (((!!) @ (^[Y3 : b]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : b]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : b]: 23.59/4.02 (( 23.59/4.02 (( 23.59/4.02 (Y0 @ 23.59/4.02 Y2 @ 23.59/4.02 Y4 @ 23.59/4.02 Y5) & 23.59/4.02 (Y0 @ 23.59/4.02 Y2 @ 23.59/4.02 Y3 @ Y4))) => 23.59/4.02 (Y0 @ 23.59/4.02 Y2 @ 23.59/4.02 Y3 @ Y5))))))))))))))))))) => 23.59/4.02 (((((!!) @ (^[Y2 : a > b]: 23.59/4.02 (((!!) @ (^[Y3 : a > b]: 23.59/4.02 (((((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y4 @ 23.59/4.02 Y5) => 23.59/4.02 (Y0 @ 23.59/4.02 Y4 @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4) @ 23.59/4.02 ( 23.59/4.02 Y3 @ Y5)))))))))) => 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y4 @ 23.59/4.02 Y5) => 23.59/4.02 (Y0 @ 23.59/4.02 Y4 @ 23.59/4.02 ( 23.59/4.02 Y3 @ Y4) @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y5)))))))))))))))))) & 23.59/4.02 ((((^[Y2 : a > b,Y3 : a > b]: 23.59/4.02 (((!!) @ (^[Y4 : a]: 23.59/4.02 (((!!) @ (^[Y5 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y4 @ 23.59/4.02 Y5) => 23.59/4.02 (Y0 @ 23.59/4.02 Y4 @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4) @ 23.59/4.02 ( 23.59/4.02 Y3 @ Y5)))))))))))) = 23.59/4.02 ((^[Y2 : a > b,Y3 : a > b]: 23.59/4.02 (((!!) @ (^[Y4 : a]: 23.59/4.02 (((!!) @ (^[Y5 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk2' @ 23.59/4.02 Y4 @ 23.59/4.02 Y5) => 23.59/4.02 (Y1 @ 23.59/4.02 Y4 @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4) @ 23.59/4.02 ( 23.59/4.02 Y3 @ Y5)))))))))))))) & 23.59/4.02 (((!!) @ (^[Y2 : a > b]: 23.59/4.02 (((!!) @ (^[Y3 : a > b]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a > b]: 23.59/4.02 (( 23.59/4.02 (( 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : a]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y6 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y5 @ 23.59/4.02 Y6) => 23.59/4.02 (Y0 @ 23.59/4.02 Y5 @ 23.59/4.02 ( 23.59/4.02 Y3 @ Y5) @ 23.59/4.02 ( 23.59/4.02 Y4 @ Y6)))))))))) & 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : a]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y6 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y5 @ 23.59/4.02 Y6) => 23.59/4.02 (Y0 @ 23.59/4.02 Y5 @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y5) @ 23.59/4.02 ( 23.59/4.02 Y3 @ Y6)))))))))))) => 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : a]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y6 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y5 @ 23.59/4.02 Y6) => 23.59/4.02 (Y0 @ 23.59/4.02 Y5 @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y5) @ 23.59/4.02 ( 23.59/4.02 Y4 @ Y6)))))))))))))))))))))))))))))))))))), 23.59/4.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 23.59/4.02 thf(zip_derived_cl3, plain, 23.59/4.02 (~ (((!!) @ (^[Y0 : a > b > b > $o]: 23.59/4.02 (((((((!!) @ (^[Y1 : a]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 ((('#sk1' @ Y1 @ Y2) => 23.59/4.02 ('#sk1' @ Y2 @ Y1))))))))) & 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((((('#sk1' @ 23.59/4.02 Y2 @ Y3) & 23.59/4.02 ('#sk1' @ 23.59/4.02 Y1 @ Y2))) => 23.59/4.02 ('#sk1' @ Y1 @ 23.59/4.02 Y3)))))))))))) & 23.59/4.02 ((('#sk1') = ('#sk2'))))) => 23.59/4.02 (((((!!) @ (^[Y1 : a]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 ((('#sk1' @ Y1 @ Y2) => 23.59/4.02 (((((!!) @ (^[Y3 : b]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : b]: 23.59/4.02 (( 23.59/4.02 ('#sk3' @ 23.59/4.02 Y1 @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y1 @ 23.59/4.02 Y4 @ Y3))))))))) & 23.59/4.02 ((('#sk3' @ Y1) = 23.59/4.02 ('#sk3' @ Y2))) & 23.59/4.02 (((!!) @ (^[Y3 : b]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : b]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : b]: 23.59/4.02 (( 23.59/4.02 (( 23.59/4.02 ('#sk3' @ 23.59/4.02 Y1 @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) & 23.59/4.02 ('#sk3' @ 23.59/4.02 Y1 @ 23.59/4.02 Y4 @ Y5))) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y1 @ 23.59/4.02 Y3 @ Y5)))))))))))))))))))))) => 23.59/4.02 (((((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk1' @ Y1 @ Y1) => 23.59/4.02 (((((!!) @ (^[Y2 : b]: 23.59/4.02 (((!!) @ (^[Y3 : b]: 23.59/4.02 ((('#sk3' @ 23.59/4.02 Y1 @ Y2 @ 23.59/4.02 Y3) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y1 @ Y3 @ 23.59/4.02 Y2))))))))) & 23.59/4.02 ((('#sk3' @ Y1) = (Y0 @ Y1))) & 23.59/4.02 (((!!) @ (^[Y2 : b]: 23.59/4.02 (((!!) @ (^[Y3 : b]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : b]: 23.59/4.02 (( 23.59/4.02 (( 23.59/4.02 ('#sk3' @ 23.59/4.02 Y1 @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) & 23.59/4.02 ('#sk3' @ 23.59/4.02 Y1 @ 23.59/4.02 Y2 @ Y3))) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y1 @ 23.59/4.02 Y2 @ Y4))))))))))))))))))) => 23.59/4.02 (((((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a > b]: 23.59/4.02 (((((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4)))))))))) => 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y4)))))))))))))))))) & 23.59/4.02 ((((^[Y1 : a > b,Y2 : a > b]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ (^[Y4 : a]: 23.59/4.02 ((('#sk1' @ Y3 @ 23.59/4.02 Y4) => ('#sk3' @ 23.59/4.02 Y3 @ (Y1 @ Y3) @ 23.59/4.02 (Y2 @ Y4)))))))))))) = 23.59/4.02 ((^[Y1 : a > b,Y2 : a > b]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ (^[Y4 : a]: 23.59/4.02 ((('#sk2' @ Y3 @ 23.59/4.02 Y4) => (Y0 @ Y3 @ 23.59/4.02 (Y1 @ Y3) @ 23.59/4.02 (Y2 @ Y4)))))))))))))) & 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a > b]: 23.59/4.02 (((!!) @ (^[Y3 : a > b]: 23.59/4.02 (((((( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y4 @ 23.59/4.02 Y5) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y4 @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4) @ 23.59/4.02 ( 23.59/4.02 Y3 @ Y5)))))))))) & 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y4 @ 23.59/4.02 Y5) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y4 @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y4) @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y5)))))))))))) => 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y5 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y4 @ 23.59/4.02 Y5) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y4 @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y4) @ 23.59/4.02 ( 23.59/4.02 Y3 @ Y5))))))))))))))))))))))))))))))))), 23.59/4.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 23.59/4.02 thf(zip_derived_cl4, plain, 23.59/4.02 (~ (((((((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y1) => ('#sk1' @ Y1 @ Y0))))))))) & 23.59/4.02 (((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 ((((('#sk1' @ Y1 @ Y2) & 23.59/4.02 ('#sk1' @ Y0 @ Y1))) => 23.59/4.02 ('#sk1' @ Y0 @ Y2)))))))))))) & 23.59/4.02 ((('#sk1') = ('#sk2'))))) => 23.59/4.02 (((((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y1) => 23.59/4.02 (((((!!) @ (^[Y2 : b]: 23.59/4.02 (((!!) @ (^[Y3 : b]: 23.59/4.02 ((('#sk3' @ 23.59/4.02 Y0 @ Y2 @ 23.59/4.02 Y3) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y0 @ Y3 @ 23.59/4.02 Y2))))))))) & 23.59/4.02 ((('#sk3' @ Y0) = ('#sk3' @ Y1))) & 23.59/4.02 (((!!) @ (^[Y2 : b]: 23.59/4.02 (((!!) @ (^[Y3 : b]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : b]: 23.59/4.02 (( 23.59/4.02 (( 23.59/4.02 ('#sk3' @ 23.59/4.02 Y0 @ 23.59/4.02 Y2 @ 23.59/4.02 Y3) & 23.59/4.02 ('#sk3' @ 23.59/4.02 Y0 @ 23.59/4.02 Y3 @ Y4))) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y0 @ 23.59/4.02 Y2 @ Y4)))))))))))))))))))))) => 23.59/4.02 (((((!!) @ (^[Y0 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y0) => 23.59/4.02 (((((!!) @ (^[Y1 : b]: 23.59/4.02 (((!!) @ (^[Y2 : b]: 23.59/4.02 ((('#sk3' @ Y0 @ Y1 @ 23.59/4.02 Y2) => ('#sk3' @ Y0 @ 23.59/4.02 Y2 @ Y1))))))))) & 23.59/4.02 ((('#sk3' @ Y0) = ('#sk4' @ Y0))) & 23.59/4.02 (((!!) @ (^[Y1 : b]: 23.59/4.02 (((!!) @ (^[Y2 : b]: 23.59/4.02 (((!!) @ (^[Y3 : b]: 23.59/4.02 (((( 23.59/4.02 ('#sk3' @ 23.59/4.02 Y0 @ Y2 @ 23.59/4.02 Y3) & 23.59/4.02 ('#sk3' @ 23.59/4.02 Y0 @ Y1 @ 23.59/4.02 Y2))) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y0 @ Y1 @ 23.59/4.02 Y3))))))))))))))))))) => 23.59/4.02 (((((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y2 @ 23.59/4.02 Y3) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y2 @ 23.59/4.02 (Y0 @ Y2) @ 23.59/4.02 (Y1 @ Y3)))))))))) => 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y2 @ 23.59/4.02 Y3) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y2 @ 23.59/4.02 (Y1 @ Y2) @ 23.59/4.02 (Y0 @ Y3)))))))))))))))))) & 23.59/4.02 ((((^[Y0 : a > b,Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ Y3) => 23.59/4.02 ('#sk3' @ Y2 @ (Y0 @ Y2) @ 23.59/4.02 (Y1 @ Y3)))))))))))) = 23.59/4.02 ((^[Y0 : a > b,Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk2' @ Y2 @ Y3) => 23.59/4.02 ('#sk4' @ Y2 @ (Y0 @ Y2) @ 23.59/4.02 (Y1 @ Y3)))))))))))))) & 23.59/4.02 (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a > b]: 23.59/4.02 (((((((!!) @ (^[Y3 : a]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4)))))))))) & 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (( 23.59/4.02 (!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y0 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y4)))))))))))) => 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y0 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4)))))))))))))))))))))))))))))), 23.59/4.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 23.59/4.02 thf(zip_derived_cl6, plain, 23.59/4.02 (~ (((((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y1) => 23.59/4.02 (((((!!) @ (^[Y2 : b]: 23.59/4.02 (((!!) @ (^[Y3 : b]: 23.59/4.02 ((('#sk3' @ 23.59/4.02 Y0 @ Y2 @ 23.59/4.02 Y3) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y0 @ Y3 @ Y2))))))))) & 23.59/4.02 ((('#sk3' @ Y0) = ('#sk3' @ Y1))) & 23.59/4.02 (((!!) @ (^[Y2 : b]: 23.59/4.02 (((!!) @ (^[Y3 : b]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : b]: 23.59/4.02 (((( 23.59/4.02 ('#sk3' @ 23.59/4.02 Y0 @ Y2 @ 23.59/4.02 Y3) & 23.59/4.02 ('#sk3' @ 23.59/4.02 Y0 @ Y3 @ 23.59/4.02 Y4))) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y0 @ Y2 @ 23.59/4.02 Y4)))))))))))))))))))))) => 23.59/4.02 (((((!!) @ (^[Y0 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y0) => 23.59/4.02 (((((!!) @ (^[Y1 : b]: 23.59/4.02 (((!!) @ (^[Y2 : b]: 23.59/4.02 ((('#sk3' @ Y0 @ Y1 @ 23.59/4.02 Y2) => ('#sk3' @ Y0 @ 23.59/4.02 Y2 @ Y1))))))))) & 23.59/4.02 ((('#sk3' @ Y0) = ('#sk4' @ Y0))) & 23.59/4.02 (((!!) @ (^[Y1 : b]: 23.59/4.02 (((!!) @ (^[Y2 : b]: 23.59/4.02 (((!!) @ (^[Y3 : b]: 23.59/4.02 ((((('#sk3' @ 23.59/4.02 Y0 @ Y2 @ 23.59/4.02 Y3) & 23.59/4.02 ('#sk3' @ 23.59/4.02 Y0 @ Y1 @ 23.59/4.02 Y2))) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y0 @ Y1 @ 23.59/4.02 Y3))))))))))))))))))) => 23.59/4.02 (((((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y2 @ Y3) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y2 @ 23.59/4.02 (Y0 @ Y2) @ 23.59/4.02 (Y1 @ Y3)))))))))) => 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y2 @ Y3) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y2 @ 23.59/4.02 (Y1 @ Y2) @ 23.59/4.02 (Y0 @ Y3)))))))))))))))))) & 23.59/4.02 ((((^[Y0 : a > b,Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ Y3) => ('#sk3' @ 23.59/4.02 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))) = 23.59/4.02 ((^[Y0 : a > b,Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk2' @ Y2 @ Y3) => ('#sk4' @ 23.59/4.02 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))))) & 23.59/4.02 (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a > b]: 23.59/4.02 (((((((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4)))))))))) & 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y0 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y4)))))))))))) => 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y0 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4)))))))))))))))))))))))))))), 23.59/4.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 23.59/4.02 thf(zip_derived_cl11, plain, 23.59/4.02 (~ (((((!!) @ (^[Y0 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y0) => 23.59/4.02 (((((!!) @ (^[Y1 : b]: 23.59/4.02 (((!!) @ (^[Y2 : b]: 23.59/4.02 ((('#sk3' @ Y0 @ Y1 @ Y2) => 23.59/4.02 ('#sk3' @ Y0 @ Y2 @ Y1))))))))) & 23.59/4.02 ((('#sk3' @ Y0) = ('#sk4' @ Y0))) & 23.59/4.02 (((!!) @ (^[Y1 : b]: 23.59/4.02 (((!!) @ (^[Y2 : b]: 23.59/4.02 (((!!) @ (^[Y3 : b]: 23.59/4.02 ((((('#sk3' @ 23.59/4.02 Y0 @ Y2 @ 23.59/4.02 Y3) & 23.59/4.02 ('#sk3' @ 23.59/4.02 Y0 @ Y1 @ 23.59/4.02 Y2))) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y0 @ Y1 @ Y3))))))))))))))))))) => 23.59/4.02 (((((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y2 @ Y3) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y2 @ 23.59/4.02 (Y0 @ Y2) @ 23.59/4.02 (Y1 @ Y3)))))))))) => 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y2 @ Y3) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y2 @ 23.59/4.02 (Y1 @ Y2) @ 23.59/4.02 (Y0 @ Y3)))))))))))))))))) & 23.59/4.02 ((((^[Y0 : a > b,Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ Y3) => ('#sk3' @ 23.59/4.02 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))) = 23.59/4.02 ((^[Y0 : a > b,Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk2' @ Y2 @ Y3) => ('#sk4' @ 23.59/4.02 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))))) & 23.59/4.02 (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a > b]: 23.59/4.02 (((((((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4)))))))))) & 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 (( 23.59/4.02 ('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y0 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y4)))))))))))) => 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 (Y0 @ Y3) @ 23.59/4.02 (Y2 @ Y4)))))))))))))))))))))))))), 23.59/4.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 23.59/4.02 thf(zip_derived_cl18, plain, 23.59/4.02 (~ (((((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ 23.59/4.02 Y3) => 23.59/4.02 ('#sk3' @ Y2 @ 23.59/4.02 (Y0 @ Y2) @ 23.59/4.02 (Y1 @ Y3)))))))))) => 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ 23.59/4.02 Y3) => 23.59/4.02 ('#sk3' @ Y2 @ 23.59/4.02 (Y1 @ Y2) @ 23.59/4.02 (Y0 @ Y3)))))))))))))))))) & 23.59/4.02 ((((^[Y0 : a > b,Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ Y3) => ('#sk3' @ 23.59/4.02 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))) = 23.59/4.02 ((^[Y0 : a > b,Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk2' @ Y2 @ Y3) => ('#sk4' @ 23.59/4.02 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))))) & 23.59/4.02 (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a > b]: 23.59/4.02 (((((((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 (Y1 @ Y3) @ 23.59/4.02 (Y2 @ Y4)))))))))) & 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 (Y0 @ Y3) @ 23.59/4.02 (Y1 @ Y4)))))))))))) => 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 (Y0 @ Y3) @ 23.59/4.02 (Y2 @ Y4)))))))))))))))))))))))), 23.59/4.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 23.59/4.02 thf(zip_derived_cl23, plain, 23.59/4.02 ((~ (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ 23.59/4.02 Y3) => ('#sk3' @ 23.59/4.02 Y2 @ (Y0 @ Y2) @ 23.59/4.02 (Y1 @ Y3)))))))))) => 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ 23.59/4.02 Y3) => ('#sk3' @ 23.59/4.02 Y2 @ (Y1 @ Y2) @ 23.59/4.02 (Y0 @ Y3)))))))))))))))))) 23.59/4.02 | ~ ((((^[Y0 : a > b,Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ Y3) => ('#sk3' @ 23.59/4.02 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))) = 23.59/4.02 ((^[Y0 : a > b,Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk2' @ Y2 @ Y3) => ('#sk4' @ 23.59/4.02 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))))) 23.59/4.02 | ~ (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a > b]: 23.59/4.02 (((((((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4)))))))))) & 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y0 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y4)))))))))))) => 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 (Y0 @ Y3) @ 23.59/4.02 (Y2 @ Y4))))))))))))))))))))))), 23.59/4.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])). 23.59/4.02 thf(zip_derived_cl28, plain, 23.59/4.02 ((~ (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ 23.59/4.02 Y3) => ('#sk3' @ 23.59/4.02 Y2 @ (Y0 @ Y2) @ 23.59/4.02 (Y1 @ Y3)))))))))) => 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ 23.59/4.02 Y3) => ('#sk3' @ 23.59/4.02 Y2 @ (Y1 @ Y2) @ 23.59/4.02 (Y0 @ Y3)))))))))))))))))) 23.59/4.02 | (((^[Y0 : a > b,Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ Y3) => ('#sk3' @ Y2 @ 23.59/4.02 (Y0 @ Y2) @ (Y1 @ Y3)))))))))))) 23.59/4.02 != ((^[Y0 : a > b,Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk2' @ Y2 @ Y3) => ('#sk4' @ 23.59/4.02 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))))))))) 23.59/4.02 | ~ (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a > b]: 23.59/4.02 (((((((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4)))))))))) & 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y0 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y4)))))))))))) => 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 (Y0 @ Y3) @ 23.59/4.02 (Y2 @ Y4))))))))))))))))))))))), 23.59/4.02 inference('simplify nested equalities', [status(thm)], [zip_derived_cl23])). 23.59/4.02 thf(zip_derived_cl29, plain, 23.59/4.02 ((~ (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ 23.59/4.02 Y3) => ('#sk3' @ 23.59/4.02 Y2 @ (Y0 @ Y2) @ 23.59/4.02 (Y1 @ Y3)))))))))) => 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ 23.59/4.02 Y3) => ('#sk3' @ 23.59/4.02 Y2 @ (Y1 @ Y2) @ 23.59/4.02 (Y0 @ Y3)))))))))))))))))) 23.59/4.02 | (((^[Y0 : a > b,Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ Y3) => ('#sk3' @ Y2 @ 23.59/4.02 (Y0 @ Y2) @ (Y1 @ Y3))))))))))) @ 23.59/4.02 '#_fresh_sk5' @ '#_fresh_sk6') 23.59/4.02 != ((^[Y0 : a > b,Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk2' @ Y2 @ Y3) => ('#sk4' @ 23.59/4.02 Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))))))) @ 23.59/4.02 '#_fresh_sk5' @ '#_fresh_sk6')) 23.59/4.02 | ~ (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a > b]: 23.59/4.02 (((((((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4)))))))))) & 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y0 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y4)))))))))))) => 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 (Y0 @ Y3) @ 23.59/4.02 (Y2 @ Y4))))))))))))))))))))))), 23.59/4.02 inference('neg_ext_simpl', [status(thm)], [zip_derived_cl28])). 23.59/4.02 thf(zip_derived_cl30, plain, 23.59/4.02 ((~ (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ 23.59/4.02 Y3) => ('#sk3' @ 23.59/4.02 Y2 @ (Y0 @ Y2) @ 23.59/4.02 (Y1 @ Y3)))))))))) => 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ 23.59/4.02 Y3) => ('#sk3' @ 23.59/4.02 Y2 @ (Y1 @ Y2) @ 23.59/4.02 (Y0 @ Y3)))))))))))))))))) 23.59/4.02 | ((((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.02 ('#_fresh_sk5' @ Y0) @ 23.59/4.02 ('#_fresh_sk6' @ Y1)))))))))) 23.59/4.02 != (((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.02 ('#_fresh_sk5' @ Y0) @ 23.59/4.02 ('#_fresh_sk6' @ Y1))))))))))) 23.59/4.02 | ~ (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a > b]: 23.59/4.02 (((((((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4)))))))))) & 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y0 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y4)))))))))))) => 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 (Y0 @ Y3) @ 23.59/4.02 (Y2 @ Y4))))))))))))))))))))))), 23.59/4.02 inference('ho_norm', [status(thm)], [zip_derived_cl29])). 23.59/4.02 thf(zip_derived_cl31, plain, 23.59/4.02 ((~ (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((((!!) @ (^[Y1 : a]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 ((('#sk1' @ Y1 @ Y2) => 23.59/4.02 ('#sk3' @ Y1 @ 23.59/4.02 ('#sk7' @ Y1) @ (Y0 @ Y2)))))))))) => 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 ((('#sk1' @ Y1 @ Y2) => 23.59/4.02 ('#sk3' @ Y1 @ (Y0 @ Y1) @ 23.59/4.02 ('#sk7' @ Y2))))))))))))))) 23.59/4.02 | ~ (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a > b]: 23.59/4.02 (((((((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4)))))))))) & 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y0 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y4)))))))))))) => 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 (Y0 @ Y3) @ 23.59/4.02 (Y2 @ Y4))))))))))))))))))))) 23.59/4.02 | ((((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.02 ('#_fresh_sk5' @ Y0) @ 23.59/4.02 ('#_fresh_sk6' @ Y1)))))))))) 23.59/4.02 != (((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.02 ('#_fresh_sk5' @ Y0) @ 23.59/4.02 ('#_fresh_sk6' @ Y1))))))))))))), 23.59/4.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])). 23.59/4.02 thf(zip_derived_cl39, plain, 23.59/4.02 ((~ (((((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.02 ('#sk7' @ Y0) @ ('#sk8' @ Y1)))))))))) => 23.59/4.02 (((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.02 ('#sk8' @ Y0) @ ('#sk7' @ Y1)))))))))))) 23.59/4.02 | ((((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.02 ('#_fresh_sk5' @ Y0) @ 23.59/4.02 ('#_fresh_sk6' @ Y1)))))))))) 23.59/4.02 != (((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.02 ('#_fresh_sk5' @ Y0) @ 23.59/4.02 ('#_fresh_sk6' @ Y1))))))))))) 23.59/4.02 | ~ (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a > b]: 23.59/4.02 (((((((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4)))))))))) & 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y0 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y4)))))))))))) => 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 (Y0 @ Y3) @ 23.59/4.02 (Y2 @ Y4))))))))))))))))))))))), 23.59/4.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl31])). 23.59/4.02 thf(zip_derived_cl49, plain, 23.59/4.02 (( (((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.02 ('#sk7' @ Y0) @ ('#sk8' @ Y1)))))))))) 23.59/4.02 | ~ (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a > b]: 23.59/4.02 (((((((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4)))))))))) & 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y0 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y4)))))))))))) => 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 (Y0 @ Y3) @ 23.59/4.02 (Y2 @ Y4))))))))))))))))))))) 23.59/4.02 | ((((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.02 ('#_fresh_sk5' @ Y0) @ 23.59/4.02 ('#_fresh_sk6' @ Y1)))))))))) 23.59/4.02 != (((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.02 ('#_fresh_sk5' @ Y0) @ 23.59/4.02 ('#_fresh_sk6' @ Y1))))))))))))), 23.59/4.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 23.59/4.02 thf(zip_derived_cl55, plain, 23.59/4.02 (( ('#form9') 23.59/4.02 | ~ (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a > b]: 23.59/4.02 (((((((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4)))))))))) & 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y0 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y4)))))))))))) => 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 (Y0 @ Y3) @ 23.59/4.02 (Y2 @ Y4))))))))))))))))))))))), 23.59/4.02 define([status(thm)])). 23.59/4.02 thf(zip_derived_cl56, plain, 23.59/4.02 ((~ (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((((((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ 23.59/4.02 Y3) => 23.59/4.02 ('#sk3' @ Y2 @ 23.59/4.02 (Y0 @ Y2) @ 23.59/4.02 (Y1 @ Y3)))))))))) & 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ 23.59/4.02 Y3) => 23.59/4.02 ('#sk3' @ Y2 @ 23.59/4.02 ('#sk10' @ Y2) @ 23.59/4.02 (Y0 @ Y3)))))))))))) => 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 ((('#sk1' @ Y2 @ 23.59/4.02 Y3) => ('#sk3' @ 23.59/4.02 Y2 @ 23.59/4.02 ('#sk10' @ Y2) @ 23.59/4.02 (Y1 @ Y3)))))))))))))))))) 23.59/4.02 | ('#form9'))), 23.59/4.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl55])). 23.59/4.02 thf(zip_derived_cl64, plain, 23.59/4.02 ((~ (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((((((!!) @ (^[Y1 : a]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 ((('#sk1' @ Y1 @ Y2) => 23.59/4.02 ('#sk3' @ Y1 @ 23.59/4.02 ('#sk11' @ Y1) @ (Y0 @ Y2)))))))))) & 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 ((('#sk1' @ Y1 @ Y2) => 23.59/4.02 ('#sk3' @ Y1 @ 23.59/4.02 ('#sk10' @ Y1) @ 23.59/4.02 ('#sk11' @ Y2)))))))))))) => 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 (((!!) @ (^[Y2 : a]: 23.59/4.02 ((('#sk1' @ Y1 @ Y2) => 23.59/4.02 ('#sk3' @ Y1 @ 23.59/4.02 ('#sk10' @ Y1) @ (Y0 @ Y2))))))))))))))) 23.59/4.02 | ('#form9'))), 23.59/4.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl56])). 23.59/4.02 thf(zip_derived_cl72, plain, 23.59/4.02 ((~ (((((((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.02 ('#sk11' @ Y0) @ ('#sk13' @ Y1)))))))))) & 23.59/4.02 (((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.02 ('#sk10' @ Y0) @ ('#sk11' @ Y1)))))))))))) => 23.59/4.02 (((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.02 ('#sk10' @ Y0) @ ('#sk13' @ Y1)))))))))))) 23.59/4.02 | ('#form9'))), 23.59/4.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl64])). 23.59/4.02 thf(zip_derived_cl80, plain, 23.59/4.02 ((~ (((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.02 ('#sk10' @ Y0) @ ('#sk13' @ Y1)))))))))) 23.59/4.02 | ('#form9'))), 23.59/4.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl72])). 23.59/4.02 thf(zip_derived_cl87, plain, 23.59/4.02 ((~ (((!!) @ (^[Y0 : a]: 23.59/4.02 ((('#sk1' @ '#sk18' @ Y0) => ('#sk3' @ '#sk18' @ 23.59/4.02 ('#sk10' @ '#sk18') @ ('#sk13' @ Y0))))))) 23.59/4.02 | ('#form9'))), 23.59/4.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl80])). 23.59/4.02 thf(zip_derived_cl95, plain, 23.59/4.02 ((~ ((('#sk1' @ '#sk18' @ '#sk19') => ('#sk3' @ '#sk18' @ 23.59/4.02 ('#sk10' @ '#sk18') @ ('#sk13' @ '#sk19')))) 23.59/4.02 | ('#form9'))), 23.59/4.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl87])). 23.59/4.02 thf(zip_derived_cl106, plain, 23.59/4.02 ((~ ('#sk3' @ '#sk18' @ ('#sk10' @ '#sk18') @ ('#sk13' @ '#sk19')) 23.59/4.02 | ('#form9'))), 23.59/4.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])). 23.59/4.02 thf(zip_derived_cl49, plain, 23.59/4.02 (( (((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.02 ('#sk7' @ Y0) @ ('#sk8' @ Y1)))))))))) 23.59/4.02 | ~ (((!!) @ (^[Y0 : a > b]: 23.59/4.02 (((!!) @ (^[Y1 : a > b]: 23.59/4.02 (((!!) @ (^[Y2 : a > b]: 23.59/4.02 (((((((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y2 @ Y4)))))))))) & 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ 23.59/4.02 Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 ( 23.59/4.02 Y0 @ Y3) @ 23.59/4.02 ( 23.59/4.02 Y1 @ Y4)))))))))))) => 23.59/4.02 (((!!) @ (^[Y3 : a]: 23.59/4.02 (((!!) @ ( 23.59/4.02 ^[Y4 : a]: 23.59/4.02 ((('#sk1' @ 23.59/4.02 Y3 @ Y4) => 23.59/4.02 ('#sk3' @ 23.59/4.02 Y3 @ 23.59/4.02 (Y0 @ Y3) @ 23.59/4.02 (Y2 @ Y4))))))))))))))))))))) 23.59/4.02 | ((((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.02 ('#_fresh_sk5' @ Y0) @ 23.59/4.02 ('#_fresh_sk6' @ Y1)))))))))) 23.59/4.02 != (((!!) @ (^[Y0 : a]: 23.59/4.02 (((!!) @ (^[Y1 : a]: 23.59/4.02 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.02 ('#_fresh_sk5' @ Y0) @ 23.59/4.02 ('#_fresh_sk6' @ Y1))))))))))))), 23.59/4.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 23.59/4.02 thf(zip_derived_cl55, plain, 23.59/4.02 (( ('#form9') 23.59/4.03 | ~ (((!!) @ (^[Y0 : a > b]: 23.59/4.03 (((!!) @ (^[Y1 : a > b]: 23.59/4.03 (((!!) @ (^[Y2 : a > b]: 23.59/4.03 (((((((!!) @ (^[Y3 : a]: 23.59/4.03 (((!!) @ ( 23.59/4.03 ^[Y4 : a]: 23.59/4.03 ((('#sk1' @ 23.59/4.03 Y3 @ 23.59/4.03 Y4) => 23.59/4.03 ('#sk3' @ 23.59/4.03 Y3 @ 23.59/4.03 ( 23.59/4.03 Y1 @ Y3) @ 23.59/4.03 ( 23.59/4.03 Y2 @ Y4)))))))))) & 23.59/4.03 (((!!) @ (^[Y3 : a]: 23.59/4.03 (((!!) @ ( 23.59/4.03 ^[Y4 : a]: 23.59/4.03 ((('#sk1' @ 23.59/4.03 Y3 @ 23.59/4.03 Y4) => 23.59/4.03 ('#sk3' @ 23.59/4.03 Y3 @ 23.59/4.03 ( 23.59/4.03 Y0 @ Y3) @ 23.59/4.03 ( 23.59/4.03 Y1 @ Y4)))))))))))) => 23.59/4.03 (((!!) @ (^[Y3 : a]: 23.59/4.03 (((!!) @ ( 23.59/4.03 ^[Y4 : a]: 23.59/4.03 ((('#sk1' @ 23.59/4.03 Y3 @ Y4) => 23.59/4.03 ('#sk3' @ 23.59/4.03 Y3 @ 23.59/4.03 (Y0 @ Y3) @ 23.59/4.03 (Y2 @ Y4))))))))))))))))))))))), 23.59/4.03 define([status(thm)])). 23.59/4.03 thf(zip_derived_cl57, plain, 23.59/4.03 ((~ ('#form9') 23.59/4.03 | ((((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))) 23.59/4.03 != (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1))))))))))) 23.59/4.03 | (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.03 ('#sk7' @ Y0) @ ('#sk8' @ Y1)))))))))))), 23.59/4.03 inference('renaming', [status(thm)], [zip_derived_cl49, zip_derived_cl55])). 23.59/4.03 thf(zip_derived_cl63, plain, 23.59/4.03 (![X2 : a]: 23.59/4.03 ( (((!!) @ (^[Y0 : a]: 23.59/4.03 ((('#sk1' @ X2 @ Y0) => ('#sk3' @ X2 @ ('#sk7' @ X2) @ 23.59/4.03 ('#sk8' @ Y0))))))) 23.59/4.03 | ((((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))) 23.59/4.03 != (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ 23.59/4.03 Y0 @ ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1))))))))))) 23.59/4.03 | ~ ('#form9'))), 23.59/4.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 23.59/4.03 thf(zip_derived_cl50, plain, 23.59/4.03 ((~ (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.03 ('#sk8' @ Y0) @ ('#sk7' @ Y1)))))))))) 23.59/4.03 | ~ (((!!) @ (^[Y0 : a > b]: 23.59/4.03 (((!!) @ (^[Y1 : a > b]: 23.59/4.03 (((!!) @ (^[Y2 : a > b]: 23.59/4.03 (((((((!!) @ (^[Y3 : a]: 23.59/4.03 (((!!) @ ( 23.59/4.03 ^[Y4 : a]: 23.59/4.03 ((('#sk1' @ 23.59/4.03 Y3 @ 23.59/4.03 Y4) => 23.59/4.03 ('#sk3' @ 23.59/4.03 Y3 @ 23.59/4.03 ( 23.59/4.03 Y1 @ Y3) @ 23.59/4.03 ( 23.59/4.03 Y2 @ Y4)))))))))) & 23.59/4.03 (((!!) @ (^[Y3 : a]: 23.59/4.03 (((!!) @ ( 23.59/4.03 ^[Y4 : a]: 23.59/4.03 ((('#sk1' @ 23.59/4.03 Y3 @ 23.59/4.03 Y4) => 23.59/4.03 ('#sk3' @ 23.59/4.03 Y3 @ 23.59/4.03 ( 23.59/4.03 Y0 @ Y3) @ 23.59/4.03 ( 23.59/4.03 Y1 @ Y4)))))))))))) => 23.59/4.03 (((!!) @ (^[Y3 : a]: 23.59/4.03 (((!!) @ ( 23.59/4.03 ^[Y4 : a]: 23.59/4.03 ((('#sk1' @ 23.59/4.03 Y3 @ Y4) => 23.59/4.03 ('#sk3' @ 23.59/4.03 Y3 @ 23.59/4.03 (Y0 @ Y3) @ 23.59/4.03 (Y2 @ Y4))))))))))))))))))))) 23.59/4.03 | ((((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))) 23.59/4.03 != (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1))))))))))))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 23.59/4.03 thf(zip_derived_cl55, plain, 23.59/4.03 (( ('#form9') 23.59/4.03 | ~ (((!!) @ (^[Y0 : a > b]: 23.59/4.03 (((!!) @ (^[Y1 : a > b]: 23.59/4.03 (((!!) @ (^[Y2 : a > b]: 23.59/4.03 (((((((!!) @ (^[Y3 : a]: 23.59/4.03 (((!!) @ ( 23.59/4.03 ^[Y4 : a]: 23.59/4.03 ((('#sk1' @ 23.59/4.03 Y3 @ 23.59/4.03 Y4) => 23.59/4.03 ('#sk3' @ 23.59/4.03 Y3 @ 23.59/4.03 ( 23.59/4.03 Y1 @ Y3) @ 23.59/4.03 ( 23.59/4.03 Y2 @ Y4)))))))))) & 23.59/4.03 (((!!) @ (^[Y3 : a]: 23.59/4.03 (((!!) @ ( 23.59/4.03 ^[Y4 : a]: 23.59/4.03 ((('#sk1' @ 23.59/4.03 Y3 @ 23.59/4.03 Y4) => 23.59/4.03 ('#sk3' @ 23.59/4.03 Y3 @ 23.59/4.03 ( 23.59/4.03 Y0 @ Y3) @ 23.59/4.03 ( 23.59/4.03 Y1 @ Y4)))))))))))) => 23.59/4.03 (((!!) @ (^[Y3 : a]: 23.59/4.03 (((!!) @ ( 23.59/4.03 ^[Y4 : a]: 23.59/4.03 ((('#sk1' @ 23.59/4.03 Y3 @ Y4) => 23.59/4.03 ('#sk3' @ 23.59/4.03 Y3 @ 23.59/4.03 (Y0 @ Y3) @ 23.59/4.03 (Y2 @ Y4))))))))))))))))))))))), 23.59/4.03 define([status(thm)])). 23.59/4.03 thf(zip_derived_cl58, plain, 23.59/4.03 ((~ ('#form9') 23.59/4.03 | ((((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))) 23.59/4.03 != (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1))))))))))) 23.59/4.03 | ~ (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.03 ('#sk8' @ Y0) @ ('#sk7' @ Y1)))))))))))), 23.59/4.03 inference('renaming', [status(thm)], [zip_derived_cl50, zip_derived_cl55])). 23.59/4.03 thf(zip_derived_cl65, plain, 23.59/4.03 (( ('#form12') 23.59/4.03 | ~ (((((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))) <=> 23.59/4.03 (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))))))), 23.59/4.03 define([status(thm)])). 23.59/4.03 thf(zip_derived_cl71, plain, 23.59/4.03 (![X2 : a]: 23.59/4.03 (~ ('#form12') 23.59/4.03 | ~ ('#form9') 23.59/4.03 | (((!!) @ (^[Y0 : a]: 23.59/4.03 ((('#sk1' @ X2 @ Y0) => ('#sk3' @ X2 @ 23.59/4.03 ('#sk7' @ X2) @ ('#sk8' @ Y0))))))))), 23.59/4.03 inference('renaming', [status(thm)], [zip_derived_cl63, zip_derived_cl65])). 23.59/4.03 thf(zip_derived_cl78, plain, 23.59/4.03 (![X2 : a, X4 : a]: 23.59/4.03 ( ((('#sk1' @ X2 @ X4) => ('#sk3' @ X2 @ ('#sk7' @ X2) @ 23.59/4.03 ('#sk8' @ X4)))) 23.59/4.03 | ~ ('#form9') 23.59/4.03 | ~ ('#form12'))), 23.59/4.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl71])). 23.59/4.03 thf(zip_derived_cl84, plain, 23.59/4.03 (![X2 : a, X4 : a]: 23.59/4.03 (~ ('#sk1' @ X2 @ X4) 23.59/4.03 | ('#sk3' @ X2 @ ('#sk7' @ X2) @ ('#sk8' @ X4)) 23.59/4.03 | ~ ('#form12') 23.59/4.03 | ~ ('#form9'))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 23.59/4.03 thf(zip_derived_cl10, plain, 23.59/4.03 ( (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => 23.59/4.03 (((((!!) @ (^[Y2 : b]: 23.59/4.03 (((!!) @ (^[Y3 : b]: 23.59/4.03 ((('#sk3' @ Y0 @ 23.59/4.03 Y2 @ Y3) => 23.59/4.03 ('#sk3' @ Y0 @ 23.59/4.03 Y3 @ Y2))))))))) & 23.59/4.03 ((('#sk3' @ Y0) = ('#sk3' @ Y1))) & 23.59/4.03 (((!!) @ (^[Y2 : b]: 23.59/4.03 (((!!) @ (^[Y3 : b]: 23.59/4.03 (((!!) @ (^[Y4 : b]: 23.59/4.03 (( 23.59/4.03 (( 23.59/4.03 ('#sk3' @ 23.59/4.03 Y0 @ 23.59/4.03 Y2 @ 23.59/4.03 Y3) & 23.59/4.03 ('#sk3' @ 23.59/4.03 Y0 @ 23.59/4.03 Y3 @ Y4))) => 23.59/4.03 ('#sk3' @ 23.59/4.03 Y0 @ 23.59/4.03 Y2 @ Y4))))))))))))))))))))))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 23.59/4.03 thf(zip_derived_cl16, plain, 23.59/4.03 (![X2 : a]: 23.59/4.03 (((!!) @ (^[Y0 : a]: 23.59/4.03 ((('#sk1' @ X2 @ Y0) => 23.59/4.03 (((((!!) @ (^[Y1 : b]: 23.59/4.03 (((!!) @ (^[Y2 : b]: 23.59/4.03 ((('#sk3' @ X2 @ Y1 @ Y2) => 23.59/4.03 ('#sk3' @ X2 @ Y2 @ Y1))))))))) & 23.59/4.03 ((('#sk3' @ X2) = ('#sk3' @ Y0))) & 23.59/4.03 (((!!) @ (^[Y1 : b]: 23.59/4.03 (((!!) @ (^[Y2 : b]: 23.59/4.03 (((!!) @ (^[Y3 : b]: 23.59/4.03 ((((('#sk3' @ 23.59/4.03 X2 @ Y1 @ 23.59/4.03 Y2) & 23.59/4.03 ('#sk3' @ 23.59/4.03 X2 @ Y2 @ Y3))) => 23.59/4.03 ('#sk3' @ X2 @ 23.59/4.03 Y1 @ Y3)))))))))))))))))))), 23.59/4.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 23.59/4.03 thf(zip_derived_cl21, plain, 23.59/4.03 (![X2 : a, X4 : a]: 23.59/4.03 ((('#sk1' @ X2 @ X4) => 23.59/4.03 (((((!!) @ (^[Y0 : b]: 23.59/4.03 (((!!) @ (^[Y1 : b]: 23.59/4.03 ((('#sk3' @ X2 @ Y0 @ Y1) => ('#sk3' @ 23.59/4.03 X2 @ Y1 @ Y0))))))))) & 23.59/4.03 ((('#sk3' @ X2) = ('#sk3' @ X4))) & 23.59/4.03 (((!!) @ (^[Y0 : b]: 23.59/4.03 (((!!) @ (^[Y1 : b]: 23.59/4.03 (((!!) @ (^[Y2 : b]: 23.59/4.03 ((((('#sk3' @ X2 @ Y0 @ Y1) & 23.59/4.03 ('#sk3' @ X2 @ Y1 @ Y2))) => 23.59/4.03 ('#sk3' @ X2 @ Y0 @ Y2))))))))))))))))), 23.59/4.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 23.59/4.03 thf(zip_derived_cl26, plain, 23.59/4.03 (![X2 : a, X4 : a]: 23.59/4.03 (~ ('#sk1' @ X2 @ X4) 23.59/4.03 | (((((!!) @ (^[Y0 : b]: 23.59/4.03 (((!!) @ (^[Y1 : b]: 23.59/4.03 ((('#sk3' @ X2 @ Y0 @ Y1) => ('#sk3' @ 23.59/4.03 X2 @ Y1 @ Y0))))))))) & 23.59/4.03 ((('#sk3' @ X2) = ('#sk3' @ X4))) & 23.59/4.03 (((!!) @ (^[Y0 : b]: 23.59/4.03 (((!!) @ (^[Y1 : b]: 23.59/4.03 (((!!) @ (^[Y2 : b]: 23.59/4.03 ((((('#sk3' @ X2 @ Y0 @ 23.59/4.03 Y1) & ('#sk3' @ X2 @ 23.59/4.03 Y1 @ Y2))) => 23.59/4.03 ('#sk3' @ X2 @ Y0 @ Y2)))))))))))))))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 23.59/4.03 thf(zip_derived_cl33, plain, 23.59/4.03 (![X2 : a, X4 : a]: 23.59/4.03 ( (((!!) @ (^[Y0 : b]: 23.59/4.03 (((!!) @ (^[Y1 : b]: 23.59/4.03 ((('#sk3' @ X2 @ Y0 @ Y1) => ('#sk3' @ X2 @ 23.59/4.03 Y1 @ Y0))))))))) 23.59/4.03 | ~ ('#sk1' @ X2 @ X4))), 23.59/4.03 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 23.59/4.03 thf(zip_derived_cl41, plain, 23.59/4.03 (![X2 : a, X4 : a, X6 : b]: 23.59/4.03 ( (((!!) @ (^[Y0 : b]: 23.59/4.03 ((('#sk3' @ X2 @ X6 @ Y0) => ('#sk3' @ X2 @ Y0 @ X6)))))) 23.59/4.03 | ~ ('#sk1' @ X2 @ X4))), 23.59/4.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl33])). 23.59/4.03 thf(zip_derived_cl51, plain, 23.59/4.03 (![X2 : a, X4 : a, X6 : b, X8 : b]: 23.59/4.03 ( ((('#sk3' @ X2 @ X6 @ X8) => ('#sk3' @ X2 @ X8 @ X6))) 23.59/4.03 | ~ ('#sk1' @ X2 @ X4))), 23.59/4.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 23.59/4.03 thf(zip_derived_cl59, plain, 23.59/4.03 (![X2 : a, X4 : a, X6 : b, X8 : b]: 23.59/4.03 (~ ('#sk3' @ X2 @ X6 @ X8) 23.59/4.03 | ('#sk3' @ X2 @ X8 @ X6) 23.59/4.03 | ~ ('#sk1' @ X2 @ X4))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 23.59/4.03 thf(zip_derived_cl331, plain, 23.59/4.03 (![X0 : a, X1 : a, X2 : a]: 23.59/4.03 (~ ('#form9') 23.59/4.03 | ~ ('#form12') 23.59/4.03 | ~ ('#sk1' @ X1 @ X0) 23.59/4.03 | ~ ('#sk1' @ X1 @ X2) 23.59/4.03 | ('#sk3' @ X1 @ ('#sk8' @ X0) @ ('#sk7' @ X1)))), 23.59/4.03 inference('sup-', [status(thm)], [zip_derived_cl84, zip_derived_cl59])). 23.59/4.03 thf(zip_derived_cl2919, plain, 23.59/4.03 (![X0 : a, X1 : a]: 23.59/4.03 (~ ('#form9') 23.59/4.03 | ~ ('#form12') 23.59/4.03 | ('#sk3' @ X0 @ ('#sk8' @ X1) @ ('#sk7' @ X0)) 23.59/4.03 | ~ ('#sk1' @ X0 @ X1))), 23.59/4.03 inference('condensation', [status(thm)], [zip_derived_cl331])). 23.59/4.03 thf(zip_derived_cl58, plain, 23.59/4.03 ((~ ('#form9') 23.59/4.03 | ((((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))) 23.59/4.03 != (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1))))))))))) 23.59/4.03 | ~ (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.03 ('#sk8' @ Y0) @ ('#sk7' @ Y1)))))))))))), 23.59/4.03 inference('renaming', [status(thm)], [zip_derived_cl50, zip_derived_cl55])). 23.59/4.03 thf(zip_derived_cl65, plain, 23.59/4.03 (( ('#form12') 23.59/4.03 | ~ (((((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))) <=> 23.59/4.03 (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))))))), 23.59/4.03 define([status(thm)])). 23.59/4.03 thf(zip_derived_cl68, plain, 23.59/4.03 ((~ ('#form12') 23.59/4.03 | ~ (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.03 ('#sk8' @ Y0) @ ('#sk7' @ Y1)))))))))) 23.59/4.03 | ~ ('#form9'))), 23.59/4.03 inference('renaming', [status(thm)], [zip_derived_cl58, zip_derived_cl65])). 23.59/4.03 thf(zip_derived_cl73, plain, 23.59/4.03 ((~ (((!!) @ (^[Y0 : a]: 23.59/4.03 ((('#sk1' @ '#sk14' @ Y0) => ('#sk3' @ '#sk14' @ 23.59/4.03 ('#sk8' @ '#sk14') @ ('#sk7' @ Y0))))))) 23.59/4.03 | ~ ('#form9') 23.59/4.03 | ~ ('#form12'))), 23.59/4.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl68])). 23.59/4.03 thf(zip_derived_cl81, plain, 23.59/4.03 ((~ ((('#sk1' @ '#sk14' @ '#sk16') => ('#sk3' @ '#sk14' @ 23.59/4.03 ('#sk8' @ '#sk14') @ ('#sk7' @ '#sk16')))) 23.59/4.03 | ~ ('#form12') 23.59/4.03 | ~ ('#form9'))), 23.59/4.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl73])). 23.59/4.03 thf(zip_derived_cl88, plain, 23.59/4.03 (( ('#sk1' @ '#sk14' @ '#sk16') | ~ ('#form9') | ~ ('#form12'))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 23.59/4.03 thf(zip_derived_cl5, plain, 23.59/4.03 ( (((((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk1' @ Y1 @ Y0))))))))) & 23.59/4.03 (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 (((!!) @ (^[Y2 : a]: 23.59/4.03 ((((('#sk1' @ Y1 @ Y2) & 23.59/4.03 ('#sk1' @ Y0 @ Y1))) => 23.59/4.03 ('#sk1' @ Y0 @ Y2)))))))))))) & 23.59/4.03 ((('#sk1') = ('#sk2')))))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 23.59/4.03 thf(zip_derived_cl7, plain, 23.59/4.03 ( (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk1' @ Y1 @ Y0)))))))))), 23.59/4.03 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl5])). 23.59/4.03 thf(zip_derived_cl12, plain, 23.59/4.03 (![X2 : a]: 23.59/4.03 (((!!) @ (^[Y0 : a]: ((('#sk1' @ X2 @ Y0) => ('#sk1' @ Y0 @ X2))))))), 23.59/4.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 23.59/4.03 thf(zip_derived_cl19, plain, 23.59/4.03 (![X2 : a, X4 : a]: ((('#sk1' @ X2 @ X4) => ('#sk1' @ X4 @ X2)))), 23.59/4.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])). 23.59/4.03 thf(zip_derived_cl24, plain, 23.59/4.03 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 23.59/4.03 thf(zip_derived_cl130, plain, 23.59/4.03 ((~ ('#form12') | ~ ('#form9') | ('#sk1' @ '#sk16' @ '#sk14'))), 23.59/4.03 inference('sup-', [status(thm)], [zip_derived_cl88, zip_derived_cl24])). 23.59/4.03 thf(zip_derived_cl34, plain, 23.59/4.03 (![X2 : a, X4 : a]: 23.59/4.03 ( ((('#sk3' @ X2) = ('#sk3' @ X4))) | ~ ('#sk1' @ X2 @ X4))), 23.59/4.03 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 23.59/4.03 thf(zip_derived_cl42, plain, 23.59/4.03 (![X2 : a, X4 : a]: 23.59/4.03 ((('#sk3' @ X2) = ('#sk3' @ X4)) | ~ ('#sk1' @ X2 @ X4))), 23.59/4.03 inference('simplify nested equalities', [status(thm)], [zip_derived_cl34])). 23.59/4.03 thf(zip_derived_cl43, plain, 23.59/4.03 (![X2 : a, X4 : a, X6 : b, X7 : b]: 23.59/4.03 ((('#sk3' @ X2 @ X6 @ X7) = ('#sk3' @ X4 @ X6 @ X7)) 23.59/4.03 | ~ ('#sk1' @ X2 @ X4))), 23.59/4.03 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl42])). 23.59/4.03 thf(zip_derived_cl214, plain, 23.59/4.03 (![X0 : b, X1 : b]: 23.59/4.03 (~ ('#form9') 23.59/4.03 | ~ ('#form12') 23.59/4.03 | (('#sk3' @ '#sk16' @ X1 @ X0) = ('#sk3' @ '#sk14' @ X1 @ X0)))), 23.59/4.03 inference('sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl43])). 23.59/4.03 thf(zip_derived_cl89, plain, 23.59/4.03 ((~ ('#sk3' @ '#sk14' @ ('#sk8' @ '#sk14') @ ('#sk7' @ '#sk16')) 23.59/4.03 | ~ ('#form9') 23.59/4.03 | ~ ('#form12'))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 23.59/4.03 thf(zip_derived_cl996, plain, 23.59/4.03 ((~ ('#sk3' @ '#sk16' @ ('#sk8' @ '#sk14') @ ('#sk7' @ '#sk16')) 23.59/4.03 | ~ ('#form12') 23.59/4.03 | ~ ('#form9') 23.59/4.03 | ~ ('#form12') 23.59/4.03 | ~ ('#form9'))), 23.59/4.03 inference('sup-', [status(thm)], [zip_derived_cl214, zip_derived_cl89])). 23.59/4.03 thf(zip_derived_cl1017, plain, 23.59/4.03 ((~ ('#form9') 23.59/4.03 | ~ ('#form12') 23.59/4.03 | ~ ('#sk3' @ '#sk16' @ ('#sk8' @ '#sk14') @ ('#sk7' @ '#sk16')))), 23.59/4.03 inference('simplify', [status(thm)], [zip_derived_cl996])). 23.59/4.03 thf(zip_derived_cl2938, plain, 23.59/4.03 ((~ ('#sk1' @ '#sk16' @ '#sk14') 23.59/4.03 | ~ ('#form12') 23.59/4.03 | ~ ('#form9') 23.59/4.03 | ~ ('#form12') 23.59/4.03 | ~ ('#form9'))), 23.59/4.03 inference('sup-', [status(thm)], [zip_derived_cl2919, zip_derived_cl1017])). 23.59/4.03 thf(zip_derived_cl2996, plain, 23.59/4.03 ((~ ('#form9') | ~ ('#form12') | ~ ('#sk1' @ '#sk16' @ '#sk14'))), 23.59/4.03 inference('simplify', [status(thm)], [zip_derived_cl2938])). 23.59/4.03 thf(zip_derived_cl130, plain, 23.59/4.03 ((~ ('#form12') | ~ ('#form9') | ('#sk1' @ '#sk16' @ '#sk14'))), 23.59/4.03 inference('sup-', [status(thm)], [zip_derived_cl88, zip_derived_cl24])). 23.59/4.03 thf(zip_derived_cl3022, plain, ((~ ('#form12') | ~ ('#form9'))), 23.59/4.03 inference('clc', [status(thm)], [zip_derived_cl2996, zip_derived_cl130])). 23.59/4.03 thf(zip_derived_cl65, plain, 23.59/4.03 (( ('#form12') 23.59/4.03 | ~ (((((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))) <=> 23.59/4.03 (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))))))), 23.59/4.03 define([status(thm)])). 23.59/4.03 thf(zip_derived_cl67, plain, 23.59/4.03 ((~ (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))) 23.59/4.03 | ~ (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))) 23.59/4.03 | ('#form12'))), 23.59/4.03 inference('lazy_cnf_xor', [status(thm)], [zip_derived_cl65])). 23.59/4.03 thf(zip_derived_cl74, plain, 23.59/4.03 ((~ (((!!) @ (^[Y0 : a]: 23.59/4.03 ((('#sk1' @ '#sk15' @ Y0) => ('#sk3' @ '#sk15' @ 23.59/4.03 ('#_fresh_sk5' @ '#sk15') @ ('#_fresh_sk6' @ Y0))))))) 23.59/4.03 | ('#form12') 23.59/4.03 | ~ (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))))), 23.59/4.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl67])). 23.59/4.03 thf(zip_derived_cl82, plain, 23.59/4.03 ((~ ((('#sk1' @ '#sk15' @ '#sk17') => ('#sk3' @ '#sk15' @ 23.59/4.03 ('#_fresh_sk5' @ '#sk15') @ ('#_fresh_sk6' @ '#sk17')))) 23.59/4.03 | ~ (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))) 23.59/4.03 | ('#form12'))), 23.59/4.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl74])). 23.59/4.03 thf(zip_derived_cl90, plain, 23.59/4.03 (( ('#sk1' @ '#sk15' @ '#sk17') 23.59/4.03 | ('#form12') 23.59/4.03 | ~ (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 23.59/4.03 thf(zip_derived_cl96, plain, 23.59/4.03 (( ('#form20') 23.59/4.03 | ~ (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))))), 23.59/4.03 define([status(thm)])). 23.59/4.03 thf(zip_derived_cl97, plain, 23.59/4.03 ((~ (((!!) @ (^[Y0 : a]: 23.59/4.03 ((('#sk2' @ '#sk21' @ Y0) => ('#sk4' @ '#sk21' @ 23.59/4.03 ('#_fresh_sk5' @ '#sk21') @ ('#_fresh_sk6' @ Y0))))))) 23.59/4.03 | ('#form20'))), 23.59/4.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 23.59/4.03 thf(zip_derived_cl107, plain, 23.59/4.03 ((~ ((('#sk2' @ '#sk21' @ '#sk22') => ('#sk4' @ '#sk21' @ 23.59/4.03 ('#_fresh_sk5' @ '#sk21') @ ('#_fresh_sk6' @ '#sk22')))) 23.59/4.03 | ('#form20'))), 23.59/4.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl97])). 23.59/4.03 thf(zip_derived_cl111, plain, 23.59/4.03 (( ('#sk2' @ '#sk21' @ '#sk22') | ('#form20'))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])). 23.59/4.03 thf(zip_derived_cl9, plain, ( ((('#sk1') = ('#sk2')))), 23.59/4.03 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl5])). 23.59/4.03 thf(zip_derived_cl14, plain, ((('#sk1') = ('#sk2'))), 23.59/4.03 inference('simplify nested equalities', [status(thm)], [zip_derived_cl9])). 23.59/4.03 thf(zip_derived_cl15, plain, 23.59/4.03 (![X2 : a, X3 : a]: (('#sk1' @ X2 @ X3) = ('#sk2' @ X2 @ X3))), 23.59/4.03 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl14])). 23.59/4.03 thf(zip_derived_cl114, plain, 23.59/4.03 (![X2 : a, X3 : a]: ( ('#sk1' @ X2 @ X3) | ~ ('#sk2' @ X2 @ X3))), 23.59/4.03 inference('eq_elim', [status(thm)], [zip_derived_cl15])). 23.59/4.03 thf(zip_derived_cl143, plain, 23.59/4.03 (( ('#form20') | ('#sk1' @ '#sk21' @ '#sk22'))), 23.59/4.03 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl114])). 23.59/4.03 thf(zip_derived_cl65, plain, 23.59/4.03 (( ('#form12') 23.59/4.03 | ~ (((((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))) <=> 23.59/4.03 (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))))))), 23.59/4.03 define([status(thm)])). 23.59/4.03 thf(zip_derived_cl66, plain, 23.59/4.03 (( (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ ('#_fresh_sk6' @ Y1)))))))))) 23.59/4.03 | (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))) 23.59/4.03 | ('#form12'))), 23.59/4.03 inference('lazy_cnf_xor', [status(thm)], [zip_derived_cl65])). 23.59/4.03 thf(zip_derived_cl75, plain, 23.59/4.03 (![X2 : a]: 23.59/4.03 ( (((!!) @ (^[Y0 : a]: 23.59/4.03 ((('#sk1' @ X2 @ Y0) => ('#sk3' @ X2 @ 23.59/4.03 ('#_fresh_sk5' @ X2) @ ('#_fresh_sk6' @ Y0))))))) 23.59/4.03 | ('#form12') 23.59/4.03 | (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))))), 23.59/4.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl66])). 23.59/4.03 thf(zip_derived_cl83, plain, 23.59/4.03 (![X2 : a, X4 : a]: 23.59/4.03 ( ((('#sk1' @ X2 @ X4) => ('#sk3' @ X2 @ ('#_fresh_sk5' @ X2) @ 23.59/4.03 ('#_fresh_sk6' @ X4)))) 23.59/4.03 | (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))) 23.59/4.03 | ('#form12'))), 23.59/4.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl75])). 23.59/4.03 thf(zip_derived_cl92, plain, 23.59/4.03 (![X2 : a, X4 : a]: 23.59/4.03 (~ ('#sk1' @ X2 @ X4) 23.59/4.03 | ('#sk3' @ X2 @ ('#_fresh_sk5' @ X2) @ ('#_fresh_sk6' @ X4)) 23.59/4.03 | ('#form12') 23.59/4.03 | (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl83])). 23.59/4.03 thf(zip_derived_cl92, plain, 23.59/4.03 (![X2 : a, X4 : a]: 23.59/4.03 (~ ('#sk1' @ X2 @ X4) 23.59/4.03 | ('#sk3' @ X2 @ ('#_fresh_sk5' @ X2) @ ('#_fresh_sk6' @ X4)) 23.59/4.03 | ('#form12') 23.59/4.03 | (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl83])). 23.59/4.03 thf(zip_derived_cl100, plain, 23.59/4.03 ((~ ('#form20') 23.59/4.03 | (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))))), 23.59/4.03 define([status(thm)])). 23.59/4.03 thf(zip_derived_cl96, plain, 23.59/4.03 (( ('#form20') 23.59/4.03 | ~ (((!!) @ (^[Y0 : a]: 23.59/4.03 (((!!) @ (^[Y1 : a]: 23.59/4.03 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.03 ('#_fresh_sk5' @ Y0) @ 23.59/4.03 ('#_fresh_sk6' @ Y1)))))))))))), 23.59/4.03 define([status(thm)])). 23.59/4.03 thf(zip_derived_cl102, plain, 23.59/4.03 (![X2 : a, X4 : a]: 23.59/4.03 ( ('#form20') 23.59/4.03 | ('#form12') 23.59/4.03 | ('#sk3' @ X2 @ ('#_fresh_sk5' @ X2) @ ('#_fresh_sk6' @ X4)) 23.59/4.03 | ~ ('#sk1' @ X2 @ X4))), 23.59/4.03 inference('renaming', [status(thm)], 23.59/4.03 [zip_derived_cl92, zip_derived_cl100, zip_derived_cl96])). 23.59/4.03 thf(zip_derived_cl459, plain, 23.59/4.03 (( ('#form20') 23.59/4.03 | ('#sk3' @ '#sk21' @ ('#_fresh_sk5' @ '#sk21') @ 23.59/4.03 ('#_fresh_sk6' @ '#sk22')) 23.59/4.03 | ('#form12') 23.59/4.03 | ('#form20'))), 23.59/4.03 inference('sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl102])). 23.59/4.03 thf(zip_derived_cl481, plain, 23.59/4.03 (( ('#form12') 23.59/4.03 | ('#sk3' @ '#sk21' @ ('#_fresh_sk5' @ '#sk21') @ 23.59/4.03 ('#_fresh_sk6' @ '#sk22')) 23.59/4.03 | ('#form20'))), 23.59/4.03 inference('simplify', [status(thm)], [zip_derived_cl459])). 23.59/4.03 thf(zip_derived_cl111, plain, 23.59/4.03 (( ('#sk2' @ '#sk21' @ '#sk22') | ('#form20'))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])). 23.59/4.03 thf(zip_derived_cl15, plain, 23.59/4.03 (![X2 : a, X3 : a]: (('#sk1' @ X2 @ X3) = ('#sk2' @ X2 @ X3))), 23.59/4.03 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl14])). 23.59/4.03 thf(zip_derived_cl24, plain, 23.59/4.03 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 23.59/4.03 thf(zip_derived_cl120, plain, 23.59/4.03 (![X0 : a, X1 : a]: (~ ('#sk2' @ X1 @ X0) | ('#sk1' @ X0 @ X1))), 23.59/4.03 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl24])). 23.59/4.03 thf(zip_derived_cl142, plain, 23.59/4.03 (( ('#form20') | ('#sk1' @ '#sk22' @ '#sk21'))), 23.59/4.03 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl120])). 23.59/4.03 thf(zip_derived_cl43, plain, 23.59/4.03 (![X2 : a, X4 : a, X6 : b, X7 : b]: 23.59/4.03 ((('#sk3' @ X2 @ X6 @ X7) = ('#sk3' @ X4 @ X6 @ X7)) 23.59/4.03 | ~ ('#sk1' @ X2 @ X4))), 23.59/4.03 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl42])). 23.59/4.03 thf(zip_derived_cl210, plain, 23.59/4.03 (![X0 : b, X1 : b]: 23.59/4.03 ( ('#form20') 23.59/4.03 | (('#sk3' @ '#sk22' @ X1 @ X0) = ('#sk3' @ '#sk21' @ X1 @ X0)))), 23.59/4.03 inference('sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl43])). 23.59/4.03 thf(zip_derived_cl210, plain, 23.59/4.03 (![X0 : b, X1 : b]: 23.59/4.03 ( ('#form20') 23.59/4.03 | (('#sk3' @ '#sk22' @ X1 @ X0) = ('#sk3' @ '#sk21' @ X1 @ X0)))), 23.59/4.03 inference('sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl43])). 23.59/4.03 thf(zip_derived_cl17, plain, 23.59/4.03 ( (((!!) @ (^[Y0 : a]: 23.59/4.03 ((('#sk1' @ Y0 @ Y0) => 23.59/4.03 (((((!!) @ (^[Y1 : b]: 23.59/4.03 (((!!) @ (^[Y2 : b]: 23.59/4.03 ((('#sk3' @ Y0 @ Y1 @ Y2) => 23.59/4.03 ('#sk3' @ Y0 @ Y2 @ Y1))))))))) & 23.59/4.03 ((('#sk3' @ Y0) = ('#sk4' @ Y0))) & 23.59/4.03 (((!!) @ (^[Y1 : b]: 23.59/4.03 (((!!) @ (^[Y2 : b]: 23.59/4.03 (((!!) @ (^[Y3 : b]: 23.59/4.03 ((((('#sk3' @ Y0 @ 23.59/4.03 Y2 @ Y3) & 23.59/4.03 ('#sk3' @ Y0 @ 23.59/4.03 Y1 @ Y2))) => 23.59/4.03 ('#sk3' @ Y0 @ 23.59/4.03 Y1 @ Y3)))))))))))))))))))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 23.59/4.03 thf(zip_derived_cl22, plain, 23.59/4.03 (![X2 : a]: 23.59/4.03 ((('#sk1' @ X2 @ X2) => 23.59/4.03 (((((!!) @ (^[Y0 : b]: 23.59/4.03 (((!!) @ (^[Y1 : b]: 23.59/4.03 ((('#sk3' @ X2 @ Y0 @ Y1) => ('#sk3' @ 23.59/4.03 X2 @ Y1 @ Y0))))))))) & 23.59/4.03 ((('#sk3' @ X2) = ('#sk4' @ X2))) & 23.59/4.03 (((!!) @ (^[Y0 : b]: 23.59/4.03 (((!!) @ (^[Y1 : b]: 23.59/4.03 (((!!) @ (^[Y2 : b]: 23.59/4.03 ((((('#sk3' @ X2 @ Y1 @ Y2) & 23.59/4.03 ('#sk3' @ X2 @ Y0 @ Y1))) => 23.59/4.03 ('#sk3' @ X2 @ Y0 @ Y2))))))))))))))))), 23.59/4.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 23.59/4.03 thf(zip_derived_cl27, plain, 23.59/4.03 (![X2 : a]: 23.59/4.03 (~ ('#sk1' @ X2 @ X2) 23.59/4.03 | (((((!!) @ (^[Y0 : b]: 23.59/4.03 (((!!) @ (^[Y1 : b]: 23.59/4.03 ((('#sk3' @ X2 @ Y0 @ Y1) => ('#sk3' @ 23.59/4.03 X2 @ Y1 @ Y0))))))))) & 23.59/4.03 ((('#sk3' @ X2) = ('#sk4' @ X2))) & 23.59/4.03 (((!!) @ (^[Y0 : b]: 23.59/4.03 (((!!) @ (^[Y1 : b]: 23.59/4.03 (((!!) @ (^[Y2 : b]: 23.59/4.03 ((((('#sk3' @ X2 @ Y1 @ 23.59/4.03 Y2) & ('#sk3' @ X2 @ 23.59/4.03 Y0 @ Y1))) => 23.59/4.03 ('#sk3' @ X2 @ Y0 @ Y2)))))))))))))))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 23.59/4.03 thf(zip_derived_cl37, plain, 23.59/4.03 (![X2 : a]: ( ((('#sk3' @ X2) = ('#sk4' @ X2))) | ~ ('#sk1' @ X2 @ X2))), 23.59/4.03 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl27])). 23.59/4.03 thf(zip_derived_cl46, plain, 23.59/4.03 (![X2 : a]: ((('#sk3' @ X2) = ('#sk4' @ X2)) | ~ ('#sk1' @ X2 @ X2))), 23.59/4.03 inference('simplify nested equalities', [status(thm)], [zip_derived_cl37])). 23.59/4.03 thf(zip_derived_cl47, plain, 23.59/4.03 (![X2 : a, X4 : b, X5 : b]: 23.59/4.03 ((('#sk3' @ X2 @ X4 @ X5) = ('#sk4' @ X2 @ X4 @ X5)) 23.59/4.03 | ~ ('#sk1' @ X2 @ X2))), 23.59/4.03 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl46])). 23.59/4.03 thf(zip_derived_cl112, plain, 23.59/4.03 ((~ ('#sk4' @ '#sk21' @ ('#_fresh_sk5' @ '#sk21') @ 23.59/4.03 ('#_fresh_sk6' @ '#sk22')) 23.59/4.03 | ('#form20'))), 23.59/4.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])). 23.59/4.03 thf(zip_derived_cl253, plain, 23.59/4.03 ((~ ('#sk3' @ '#sk21' @ ('#_fresh_sk5' @ '#sk21') @ 23.59/4.03 ('#_fresh_sk6' @ '#sk22')) 23.59/4.03 | ~ ('#sk1' @ '#sk21' @ '#sk21') 23.59/4.03 | ('#form20'))), 23.59/4.03 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl112])). 23.59/4.03 thf(zip_derived_cl426, plain, 23.59/4.03 ((~ ('#sk3' @ '#sk22' @ ('#_fresh_sk5' @ '#sk21') @ 23.59/4.03 ('#_fresh_sk6' @ '#sk22')) 23.59/4.03 | ('#form20') 23.59/4.03 | ('#form20') 23.59/4.03 | ~ ('#sk1' @ '#sk21' @ '#sk21'))), 23.59/4.03 inference('sup-', [status(thm)], [zip_derived_cl210, zip_derived_cl253])). 23.59/4.03 thf(zip_derived_cl432, plain, 23.59/4.03 ((~ ('#sk1' @ '#sk21' @ '#sk21') 23.59/4.03 | ('#form20') 23.59/4.03 | ~ ('#sk3' @ '#sk22' @ ('#_fresh_sk5' @ '#sk21') @ 23.59/4.03 ('#_fresh_sk6' @ '#sk22')))), 23.59/4.03 inference('simplify', [status(thm)], [zip_derived_cl426])). 23.59/4.03 thf(zip_derived_cl774, plain, 23.59/4.03 ((~ ('#sk3' @ '#sk21' @ ('#_fresh_sk5' @ '#sk21') @ 23.59/4.03 ('#_fresh_sk6' @ '#sk22')) 23.59/4.03 | ('#form20') 23.59/4.03 | ('#form20') 23.59/4.03 | ~ ('#sk1' @ '#sk21' @ '#sk21'))), 23.59/4.03 inference('sup-', [status(thm)], [zip_derived_cl210, zip_derived_cl432])). 23.59/4.03 thf(zip_derived_cl780, plain, 23.59/4.03 ((~ ('#sk1' @ '#sk21' @ '#sk21') 23.59/4.04 | ('#form20') 23.59/4.04 | ~ ('#sk3' @ '#sk21' @ ('#_fresh_sk5' @ '#sk21') @ 23.59/4.04 ('#_fresh_sk6' @ '#sk22')))), 23.59/4.04 inference('simplify', [status(thm)], [zip_derived_cl774])). 23.59/4.04 thf(zip_derived_cl143, plain, 23.59/4.04 (( ('#form20') | ('#sk1' @ '#sk21' @ '#sk22'))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl114])). 23.59/4.04 thf(zip_derived_cl142, plain, 23.59/4.04 (( ('#form20') | ('#sk1' @ '#sk22' @ '#sk21'))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl120])). 23.59/4.04 thf(zip_derived_cl8, plain, 23.59/4.04 ( (((!!) @ (^[Y0 : a]: 23.59/4.04 (((!!) @ (^[Y1 : a]: 23.59/4.04 (((!!) @ (^[Y2 : a]: 23.59/4.04 ((((('#sk1' @ Y1 @ Y2) & ('#sk1' @ 23.59/4.04 Y0 @ Y1))) => 23.59/4.04 ('#sk1' @ Y0 @ Y2))))))))))))), 23.59/4.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl5])). 23.59/4.04 thf(zip_derived_cl13, plain, 23.59/4.04 (![X2 : a]: 23.59/4.04 (((!!) @ (^[Y0 : a]: 23.59/4.04 (((!!) @ (^[Y1 : a]: 23.59/4.04 ((((('#sk1' @ Y0 @ Y1) & ('#sk1' @ X2 @ Y0))) => 23.59/4.04 ('#sk1' @ X2 @ Y1)))))))))), 23.59/4.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 23.59/4.04 thf(zip_derived_cl20, plain, 23.59/4.04 (![X2 : a, X4 : a]: 23.59/4.04 (((!!) @ (^[Y0 : a]: 23.59/4.04 ((((('#sk1' @ X4 @ Y0) & ('#sk1' @ X2 @ X4))) => 23.59/4.04 ('#sk1' @ X2 @ Y0))))))), 23.59/4.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 23.59/4.04 thf(zip_derived_cl25, plain, 23.59/4.04 (![X2 : a, X4 : a, X6 : a]: 23.59/4.04 ((((('#sk1' @ X4 @ X6) & ('#sk1' @ X2 @ X4))) => ('#sk1' @ X2 @ X6)))), 23.59/4.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])). 23.59/4.04 thf(zip_derived_cl32, plain, 23.59/4.04 (![X2 : a, X4 : a, X6 : a]: 23.59/4.04 (~ ((('#sk1' @ X4 @ X6) & ('#sk1' @ X2 @ X4))) | ('#sk1' @ X2 @ X6))), 23.59/4.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 23.59/4.04 thf(zip_derived_cl40, plain, 23.59/4.04 (![X2 : a, X4 : a, X6 : a]: 23.59/4.04 (~ ('#sk1' @ X4 @ X6) | ~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X2 @ X6))), 23.59/4.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl32])). 23.59/4.04 thf(zip_derived_cl172, plain, 23.59/4.04 (![X0 : a]: 23.59/4.04 ( ('#form20') | ('#sk1' @ X0 @ '#sk21') | ~ ('#sk1' @ X0 @ '#sk22'))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl40])). 23.59/4.04 thf(zip_derived_cl801, plain, 23.59/4.04 (( ('#form20') | ('#sk1' @ '#sk21' @ '#sk21') | ('#form20'))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl172])). 23.59/4.04 thf(zip_derived_cl805, plain, 23.59/4.04 (( ('#sk1' @ '#sk21' @ '#sk21') | ('#form20'))), 23.59/4.04 inference('simplify', [status(thm)], [zip_derived_cl801])). 23.59/4.04 thf(zip_derived_cl850, plain, 23.59/4.04 ((~ ('#sk3' @ '#sk21' @ ('#_fresh_sk5' @ '#sk21') @ 23.59/4.04 ('#_fresh_sk6' @ '#sk22')) 23.59/4.04 | ('#form20'))), 23.59/4.04 inference('clc', [status(thm)], [zip_derived_cl780, zip_derived_cl805])). 23.59/4.04 thf(zip_derived_cl4302, plain, (( ('#form20') | ('#form12'))), 23.59/4.04 inference('clc', [status(thm)], [zip_derived_cl481, zip_derived_cl850])). 23.59/4.04 thf(zip_derived_cl90, plain, 23.59/4.04 (( ('#sk1' @ '#sk15' @ '#sk17') 23.59/4.04 | ('#form12') 23.59/4.04 | ~ (((!!) @ (^[Y0 : a]: 23.59/4.04 (((!!) @ (^[Y1 : a]: 23.59/4.04 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.04 ('#_fresh_sk5' @ Y0) @ 23.59/4.04 ('#_fresh_sk6' @ Y1)))))))))))), 23.59/4.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 23.59/4.04 thf(zip_derived_cl96, plain, 23.59/4.04 (( ('#form20') 23.59/4.04 | ~ (((!!) @ (^[Y0 : a]: 23.59/4.04 (((!!) @ (^[Y1 : a]: 23.59/4.04 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.04 ('#_fresh_sk5' @ Y0) @ 23.59/4.04 ('#_fresh_sk6' @ Y1)))))))))))), 23.59/4.04 define([status(thm)])). 23.59/4.04 thf(zip_derived_cl98, plain, 23.59/4.04 ((~ ('#form20') | ('#form12') | ('#sk1' @ '#sk15' @ '#sk17'))), 23.59/4.04 inference('renaming', [status(thm)], [zip_derived_cl90, zip_derived_cl96])). 23.59/4.04 thf(zip_derived_cl98, plain, 23.59/4.04 ((~ ('#form20') | ('#form12') | ('#sk1' @ '#sk15' @ '#sk17'))), 23.59/4.04 inference('renaming', [status(thm)], [zip_derived_cl90, zip_derived_cl96])). 23.59/4.04 thf(zip_derived_cl24, plain, 23.59/4.04 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 23.59/4.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 23.59/4.04 thf(zip_derived_cl398, plain, 23.59/4.04 (( ('#form12') | ~ ('#form20') | ('#sk1' @ '#sk17' @ '#sk15'))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl98, zip_derived_cl24])). 23.59/4.04 thf(zip_derived_cl40, plain, 23.59/4.04 (![X2 : a, X4 : a, X6 : a]: 23.59/4.04 (~ ('#sk1' @ X4 @ X6) | ~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X2 @ X6))), 23.59/4.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl32])). 23.59/4.04 thf(zip_derived_cl406, plain, 23.59/4.04 (![X0 : a]: 23.59/4.04 (~ ('#form20') 23.59/4.04 | ('#form12') 23.59/4.04 | ('#sk1' @ X0 @ '#sk15') 23.59/4.04 | ~ ('#sk1' @ X0 @ '#sk17'))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl398, zip_derived_cl40])). 23.59/4.04 thf(zip_derived_cl1501, plain, 23.59/4.04 (( ('#form12') 23.59/4.04 | ~ ('#form20') 23.59/4.04 | ('#sk1' @ '#sk15' @ '#sk15') 23.59/4.04 | ('#form12') 23.59/4.04 | ~ ('#form20'))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl98, zip_derived_cl406])). 23.59/4.04 thf(zip_derived_cl1505, plain, 23.59/4.04 (( ('#sk1' @ '#sk15' @ '#sk15') | ~ ('#form20') | ('#form12'))), 23.59/4.04 inference('simplify', [status(thm)], [zip_derived_cl1501])). 23.59/4.04 thf(zip_derived_cl100, plain, 23.59/4.04 ((~ ('#form20') 23.59/4.04 | (((!!) @ (^[Y0 : a]: 23.59/4.04 (((!!) @ (^[Y1 : a]: 23.59/4.04 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.04 ('#_fresh_sk5' @ Y0) @ 23.59/4.04 ('#_fresh_sk6' @ Y1)))))))))))), 23.59/4.04 define([status(thm)])). 23.59/4.04 thf(zip_derived_cl101, plain, 23.59/4.04 (![X2 : a]: 23.59/4.04 ( (((!!) @ (^[Y0 : a]: 23.59/4.04 ((('#sk2' @ X2 @ Y0) => ('#sk4' @ X2 @ 23.59/4.04 ('#_fresh_sk5' @ X2) @ ('#_fresh_sk6' @ Y0))))))) 23.59/4.04 | ~ ('#form20'))), 23.59/4.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl100])). 23.59/4.04 thf(zip_derived_cl108, plain, 23.59/4.04 (![X2 : a, X4 : a]: 23.59/4.04 ( ((('#sk2' @ X2 @ X4) => ('#sk4' @ X2 @ ('#_fresh_sk5' @ X2) @ 23.59/4.04 ('#_fresh_sk6' @ X4)))) 23.59/4.04 | ~ ('#form20'))), 23.59/4.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl101])). 23.59/4.04 thf(zip_derived_cl113, plain, 23.59/4.04 (![X2 : a, X4 : a]: 23.59/4.04 (~ ('#sk2' @ X2 @ X4) 23.59/4.04 | ('#sk4' @ X2 @ ('#_fresh_sk5' @ X2) @ ('#_fresh_sk6' @ X4)) 23.59/4.04 | ~ ('#form20'))), 23.59/4.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 23.59/4.04 thf(zip_derived_cl47, plain, 23.59/4.04 (![X2 : a, X4 : b, X5 : b]: 23.59/4.04 ((('#sk3' @ X2 @ X4 @ X5) = ('#sk4' @ X2 @ X4 @ X5)) 23.59/4.04 | ~ ('#sk1' @ X2 @ X2))), 23.59/4.04 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl46])). 23.59/4.04 thf(zip_derived_cl91, plain, 23.59/4.04 ((~ ('#sk3' @ '#sk15' @ ('#_fresh_sk5' @ '#sk15') @ 23.59/4.04 ('#_fresh_sk6' @ '#sk17')) 23.59/4.04 | ('#form12') 23.59/4.04 | ~ (((!!) @ (^[Y0 : a]: 23.59/4.04 (((!!) @ (^[Y1 : a]: 23.59/4.04 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.04 ('#_fresh_sk5' @ Y0) @ 23.59/4.04 ('#_fresh_sk6' @ Y1)))))))))))), 23.59/4.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 23.59/4.04 thf(zip_derived_cl96, plain, 23.59/4.04 (( ('#form20') 23.59/4.04 | ~ (((!!) @ (^[Y0 : a]: 23.59/4.04 (((!!) @ (^[Y1 : a]: 23.59/4.04 ((('#sk2' @ Y0 @ Y1) => ('#sk4' @ Y0 @ 23.59/4.04 ('#_fresh_sk5' @ Y0) @ 23.59/4.04 ('#_fresh_sk6' @ Y1)))))))))))), 23.59/4.04 define([status(thm)])). 23.59/4.04 thf(zip_derived_cl99, plain, 23.59/4.04 ((~ ('#form20') 23.59/4.04 | ('#form12') 23.59/4.04 | ~ ('#sk3' @ '#sk15' @ ('#_fresh_sk5' @ '#sk15') @ 23.59/4.04 ('#_fresh_sk6' @ '#sk17')))), 23.59/4.04 inference('renaming', [status(thm)], [zip_derived_cl91, zip_derived_cl96])). 23.59/4.04 thf(zip_derived_cl251, plain, 23.59/4.04 ((~ ('#sk4' @ '#sk15' @ ('#_fresh_sk5' @ '#sk15') @ 23.59/4.04 ('#_fresh_sk6' @ '#sk17')) 23.59/4.04 | ~ ('#sk1' @ '#sk15' @ '#sk15') 23.59/4.04 | ('#form12') 23.59/4.04 | ~ ('#form20'))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl99])). 23.59/4.04 thf(zip_derived_cl936, plain, 23.59/4.04 ((~ ('#form20') 23.59/4.04 | ~ ('#sk2' @ '#sk15' @ '#sk17') 23.59/4.04 | ~ ('#form20') 23.59/4.04 | ('#form12') 23.59/4.04 | ~ ('#sk1' @ '#sk15' @ '#sk15'))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl113, zip_derived_cl251])). 23.59/4.04 thf(zip_derived_cl942, plain, 23.59/4.04 ((~ ('#sk1' @ '#sk15' @ '#sk15') 23.59/4.04 | ('#form12') 23.59/4.04 | ~ ('#sk2' @ '#sk15' @ '#sk17') 23.59/4.04 | ~ ('#form20'))), 23.59/4.04 inference('simplify', [status(thm)], [zip_derived_cl936])). 23.59/4.04 thf(zip_derived_cl98, plain, 23.59/4.04 ((~ ('#form20') | ('#form12') | ('#sk1' @ '#sk15' @ '#sk17'))), 23.59/4.04 inference('renaming', [status(thm)], [zip_derived_cl90, zip_derived_cl96])). 23.59/4.04 thf(zip_derived_cl15, plain, 23.59/4.04 (![X2 : a, X3 : a]: (('#sk1' @ X2 @ X3) = ('#sk2' @ X2 @ X3))), 23.59/4.04 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl14])). 23.59/4.04 thf(zip_derived_cl115, plain, 23.59/4.04 (![X2 : a, X3 : a]: (~ ('#sk1' @ X2 @ X3) | ('#sk2' @ X2 @ X3))), 23.59/4.04 inference('eq_elim', [status(thm)], [zip_derived_cl15])). 23.59/4.04 thf(zip_derived_cl399, plain, 23.59/4.04 (( ('#form12') | ~ ('#form20') | ('#sk2' @ '#sk15' @ '#sk17'))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl98, zip_derived_cl115])). 23.59/4.04 thf(zip_derived_cl950, plain, 23.59/4.04 ((~ ('#form20') | ('#form12') | ~ ('#sk1' @ '#sk15' @ '#sk15'))), 23.59/4.04 inference('clc', [status(thm)], [zip_derived_cl942, zip_derived_cl399])). 23.59/4.04 thf(zip_derived_cl1529, plain, (( ('#form12') | ~ ('#form20'))), 23.59/4.04 inference('clc', [status(thm)], [zip_derived_cl1505, zip_derived_cl950])). 23.59/4.04 thf(zip_derived_cl4303, plain, ( ('#form12')), 23.59/4.04 inference('clc', [status(thm)], [zip_derived_cl4302, zip_derived_cl1529])). 23.59/4.04 thf(zip_derived_cl4304, plain, (~ ('#form9')), 23.59/4.04 inference('demod', [status(thm)], 23.59/4.04 [zip_derived_cl3022, zip_derived_cl4303])). 23.59/4.04 thf(zip_derived_cl4306, plain, 23.59/4.04 (~ ('#sk3' @ '#sk18' @ ('#sk10' @ '#sk18') @ ('#sk13' @ '#sk19'))), 23.59/4.04 inference('demod', [status(thm)], [zip_derived_cl106, zip_derived_cl4304])). 23.59/4.04 thf(zip_derived_cl105, plain, 23.59/4.04 (( ('#sk1' @ '#sk18' @ '#sk19') | ('#form9'))), 23.59/4.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])). 23.59/4.04 thf(zip_derived_cl24, plain, 23.59/4.04 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 23.59/4.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 23.59/4.04 thf(zip_derived_cl136, plain, 23.59/4.04 (( ('#form9') | ('#sk1' @ '#sk19' @ '#sk18'))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl24])). 23.59/4.04 thf(zip_derived_cl105, plain, 23.59/4.04 (( ('#sk1' @ '#sk18' @ '#sk19') | ('#form9'))), 23.59/4.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])). 23.59/4.04 thf(zip_derived_cl40, plain, 23.59/4.04 (![X2 : a, X4 : a, X6 : a]: 23.59/4.04 (~ ('#sk1' @ X4 @ X6) | ~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X2 @ X6))), 23.59/4.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl32])). 23.59/4.04 thf(zip_derived_cl161, plain, 23.59/4.04 (![X0 : a]: 23.59/4.04 ( ('#form9') | ('#sk1' @ X0 @ '#sk19') | ~ ('#sk1' @ X0 @ '#sk18'))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl40])). 23.59/4.04 thf(zip_derived_cl729, plain, 23.59/4.04 (( ('#form9') | ('#sk1' @ '#sk19' @ '#sk19') | ('#form9'))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl161])). 23.59/4.04 thf(zip_derived_cl735, plain, 23.59/4.04 (( ('#sk1' @ '#sk19' @ '#sk19') | ('#form9'))), 23.59/4.04 inference('simplify', [status(thm)], [zip_derived_cl729])). 23.59/4.04 thf(zip_derived_cl79, plain, 23.59/4.04 (( (((((!!) @ (^[Y0 : a]: 23.59/4.04 (((!!) @ (^[Y1 : a]: 23.59/4.04 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.04 ('#sk11' @ Y0) @ ('#sk13' @ Y1)))))))))) & 23.59/4.04 (((!!) @ (^[Y0 : a]: 23.59/4.04 (((!!) @ (^[Y1 : a]: 23.59/4.04 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.04 ('#sk10' @ Y0) @ ('#sk11' @ Y1)))))))))))) 23.59/4.04 | ('#form9'))), 23.59/4.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl72])). 23.59/4.04 thf(zip_derived_cl85, plain, 23.59/4.04 (( (((!!) @ (^[Y0 : a]: 23.59/4.04 (((!!) @ (^[Y1 : a]: 23.59/4.04 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.04 ('#sk11' @ Y0) @ ('#sk13' @ Y1)))))))))) 23.59/4.04 | ('#form9'))), 23.59/4.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl79])). 23.59/4.04 thf(zip_derived_cl93, plain, 23.59/4.04 (![X2 : a]: 23.59/4.04 ( (((!!) @ (^[Y0 : a]: 23.59/4.04 ((('#sk1' @ X2 @ Y0) => ('#sk3' @ X2 @ ('#sk11' @ X2) @ 23.59/4.04 ('#sk13' @ Y0))))))) 23.59/4.04 | ('#form9'))), 23.59/4.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 23.59/4.04 thf(zip_derived_cl103, plain, 23.59/4.04 (![X2 : a, X4 : a]: 23.59/4.04 ( ((('#sk1' @ X2 @ X4) => ('#sk3' @ X2 @ ('#sk11' @ X2) @ 23.59/4.04 ('#sk13' @ X4)))) 23.59/4.04 | ('#form9'))), 23.59/4.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl93])). 23.59/4.04 thf(zip_derived_cl109, plain, 23.59/4.04 (![X2 : a, X4 : a]: 23.59/4.04 (~ ('#sk1' @ X2 @ X4) 23.59/4.04 | ('#sk3' @ X2 @ ('#sk11' @ X2) @ ('#sk13' @ X4)) 23.59/4.04 | ('#form9'))), 23.59/4.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])). 23.59/4.04 thf(zip_derived_cl742, plain, 23.59/4.04 (( ('#form9') 23.59/4.04 | ('#form9') 23.59/4.04 | ('#sk3' @ '#sk19' @ ('#sk11' @ '#sk19') @ ('#sk13' @ '#sk19')))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl735, zip_derived_cl109])). 23.59/4.04 thf(zip_derived_cl759, plain, 23.59/4.04 (( ('#sk3' @ '#sk19' @ ('#sk11' @ '#sk19') @ ('#sk13' @ '#sk19')) 23.59/4.04 | ('#form9'))), 23.59/4.04 inference('simplify', [status(thm)], [zip_derived_cl742])). 23.59/4.04 thf(zip_derived_cl136, plain, 23.59/4.04 (( ('#form9') | ('#sk1' @ '#sk19' @ '#sk18'))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl24])). 23.59/4.04 thf(zip_derived_cl43, plain, 23.59/4.04 (![X2 : a, X4 : a, X6 : b, X7 : b]: 23.59/4.04 ((('#sk3' @ X2 @ X6 @ X7) = ('#sk3' @ X4 @ X6 @ X7)) 23.59/4.04 | ~ ('#sk1' @ X2 @ X4))), 23.59/4.04 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl42])). 23.59/4.04 thf(zip_derived_cl212, plain, 23.59/4.04 (![X0 : b, X1 : b]: 23.59/4.04 ( ('#form9') 23.59/4.04 | (('#sk3' @ '#sk19' @ X1 @ X0) = ('#sk3' @ '#sk18' @ X1 @ X0)))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl43])). 23.59/4.04 thf(zip_derived_cl1074, plain, 23.59/4.04 (( ('#sk3' @ '#sk18' @ ('#sk11' @ '#sk19') @ ('#sk13' @ '#sk19')) 23.59/4.04 | ('#form9') 23.59/4.04 | ('#form9'))), 23.59/4.04 inference('sup+', [status(thm)], [zip_derived_cl759, zip_derived_cl212])). 23.59/4.04 thf(zip_derived_cl1082, plain, 23.59/4.04 (( ('#form9') 23.59/4.04 | ('#sk3' @ '#sk18' @ ('#sk11' @ '#sk19') @ ('#sk13' @ '#sk19')))), 23.59/4.04 inference('simplify', [status(thm)], [zip_derived_cl1074])). 23.59/4.04 thf(zip_derived_cl4304, plain, (~ ('#form9')), 23.59/4.04 inference('demod', [status(thm)], 23.59/4.04 [zip_derived_cl3022, zip_derived_cl4303])). 23.59/4.04 thf(zip_derived_cl4345, plain, 23.59/4.04 ( ('#sk3' @ '#sk18' @ ('#sk11' @ '#sk19') @ ('#sk13' @ '#sk19'))), 23.59/4.04 inference('demod', [status(thm)], 23.59/4.04 [zip_derived_cl1082, zip_derived_cl4304])). 23.59/4.04 thf(zip_derived_cl105, plain, 23.59/4.04 (( ('#sk1' @ '#sk18' @ '#sk19') | ('#form9'))), 23.59/4.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])). 23.59/4.04 thf(zip_derived_cl86, plain, 23.59/4.04 (( (((!!) @ (^[Y0 : a]: 23.59/4.04 (((!!) @ (^[Y1 : a]: 23.59/4.04 ((('#sk1' @ Y0 @ Y1) => ('#sk3' @ Y0 @ 23.59/4.04 ('#sk10' @ Y0) @ ('#sk11' @ Y1)))))))))) 23.59/4.04 | ('#form9'))), 23.59/4.04 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl79])). 23.59/4.04 thf(zip_derived_cl94, plain, 23.59/4.04 (![X2 : a]: 23.59/4.04 ( (((!!) @ (^[Y0 : a]: 23.59/4.04 ((('#sk1' @ X2 @ Y0) => ('#sk3' @ X2 @ ('#sk10' @ X2) @ 23.59/4.04 ('#sk11' @ Y0))))))) 23.59/4.04 | ('#form9'))), 23.59/4.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl86])). 23.59/4.04 thf(zip_derived_cl104, plain, 23.59/4.04 (![X2 : a, X4 : a]: 23.59/4.04 ( ((('#sk1' @ X2 @ X4) => ('#sk3' @ X2 @ ('#sk10' @ X2) @ 23.59/4.04 ('#sk11' @ X4)))) 23.59/4.04 | ('#form9'))), 23.59/4.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])). 23.59/4.04 thf(zip_derived_cl110, plain, 23.59/4.04 (![X2 : a, X4 : a]: 23.59/4.04 (~ ('#sk1' @ X2 @ X4) 23.59/4.04 | ('#sk3' @ X2 @ ('#sk10' @ X2) @ ('#sk11' @ X4)) 23.59/4.04 | ('#form9'))), 23.59/4.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl104])). 23.59/4.04 thf(zip_derived_cl575, plain, 23.59/4.04 (( ('#form9') 23.59/4.04 | ('#form9') 23.59/4.04 | ('#sk3' @ '#sk18' @ ('#sk10' @ '#sk18') @ ('#sk11' @ '#sk19')))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl110])). 23.59/4.04 thf(zip_derived_cl595, plain, 23.59/4.04 (( ('#sk3' @ '#sk18' @ ('#sk10' @ '#sk18') @ ('#sk11' @ '#sk19')) 23.59/4.04 | ('#form9'))), 23.59/4.04 inference('simplify', [status(thm)], [zip_derived_cl575])). 23.59/4.04 thf(zip_derived_cl47, plain, 23.59/4.04 (![X2 : a, X4 : b, X5 : b]: 23.59/4.04 ((('#sk3' @ X2 @ X4 @ X5) = ('#sk4' @ X2 @ X4 @ X5)) 23.59/4.04 | ~ ('#sk1' @ X2 @ X2))), 23.59/4.04 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl46])). 23.59/4.04 thf(zip_derived_cl601, plain, 23.59/4.04 (( ('#sk4' @ '#sk18' @ ('#sk10' @ '#sk18') @ ('#sk11' @ '#sk19')) 23.59/4.04 | ('#form9') 23.59/4.04 | ~ ('#sk1' @ '#sk18' @ '#sk18'))), 23.59/4.04 inference('sup+', [status(thm)], [zip_derived_cl595, zip_derived_cl47])). 23.59/4.04 thf(zip_derived_cl105, plain, 23.59/4.04 (( ('#sk1' @ '#sk18' @ '#sk19') | ('#form9'))), 23.59/4.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])). 23.59/4.04 thf(zip_derived_cl136, plain, 23.59/4.04 (( ('#form9') | ('#sk1' @ '#sk19' @ '#sk18'))), 23.59/4.04 inference('sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl24])). 23.59/4.04 thf(zip_derived_cl40, plain, 23.59/4.04 (![X2 : a, X4 : a, X6 : a]: 23.59/4.05 (~ ('#sk1' @ X4 @ X6) | ~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X2 @ X6))), 23.59/4.05 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl32])). 23.59/4.05 thf(zip_derived_cl160, plain, 23.59/4.05 (![X0 : a]: 23.59/4.05 ( ('#form9') | ('#sk1' @ X0 @ '#sk18') | ~ ('#sk1' @ X0 @ '#sk19'))), 23.59/4.05 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl40])). 23.59/4.05 thf(zip_derived_cl682, plain, 23.59/4.05 (( ('#form9') | ('#sk1' @ '#sk18' @ '#sk18') | ('#form9'))), 23.59/4.05 inference('sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl160])). 23.59/4.05 thf(zip_derived_cl686, plain, 23.59/4.05 (( ('#sk1' @ '#sk18' @ '#sk18') | ('#form9'))), 23.59/4.05 inference('simplify', [status(thm)], [zip_derived_cl682])). 23.59/4.05 thf(zip_derived_cl1880, plain, 23.59/4.05 (( ('#form9') 23.59/4.05 | ('#sk4' @ '#sk18' @ ('#sk10' @ '#sk18') @ ('#sk11' @ '#sk19')))), 23.59/4.05 inference('clc', [status(thm)], [zip_derived_cl601, zip_derived_cl686])). 23.59/4.05 thf(zip_derived_cl4304, plain, (~ ('#form9')), 23.59/4.05 inference('demod', [status(thm)], 23.59/4.05 [zip_derived_cl3022, zip_derived_cl4303])). 23.59/4.05 thf(zip_derived_cl4347, plain, 23.59/4.05 ( ('#sk4' @ '#sk18' @ ('#sk10' @ '#sk18') @ ('#sk11' @ '#sk19'))), 23.59/4.05 inference('demod', [status(thm)], 23.59/4.05 [zip_derived_cl1880, zip_derived_cl4304])). 23.59/4.05 thf(zip_derived_cl47, plain, 23.59/4.05 (![X2 : a, X4 : b, X5 : b]: 23.59/4.05 ((('#sk3' @ X2 @ X4 @ X5) = ('#sk4' @ X2 @ X4 @ X5)) 23.59/4.05 | ~ ('#sk1' @ X2 @ X2))), 23.59/4.05 inference('arg_cong_simpl', [status(thm)], [zip_derived_cl46])). 23.59/4.05 thf(zip_derived_cl35, plain, 23.59/4.05 (![X2 : a, X4 : a]: 23.59/4.05 ( (((!!) @ (^[Y0 : b]: 23.59/4.05 (((!!) @ (^[Y1 : b]: 23.59/4.05 (((!!) @ (^[Y2 : b]: 23.59/4.05 ((((('#sk3' @ X2 @ Y0 @ Y1) & 23.59/4.05 ('#sk3' @ X2 @ Y1 @ Y2))) => 23.59/4.05 ('#sk3' @ X2 @ Y0 @ Y2)))))))))))) 23.59/4.05 | ~ ('#sk1' @ X2 @ X4))), 23.59/4.05 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 23.59/4.05 thf(zip_derived_cl44, plain, 23.59/4.05 (![X2 : a, X4 : a, X6 : b]: 23.59/4.05 ( (((!!) @ (^[Y0 : b]: 23.59/4.05 (((!!) @ (^[Y1 : b]: 23.59/4.05 ((((('#sk3' @ X2 @ X6 @ Y0) & ('#sk3' @ 23.59/4.05 X2 @ Y0 @ Y1))) => 23.59/4.05 ('#sk3' @ X2 @ X6 @ Y1))))))))) 23.59/4.05 | ~ ('#sk1' @ X2 @ X4))), 23.59/4.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl35])). 23.59/4.05 thf(zip_derived_cl52, plain, 23.59/4.05 (![X2 : a, X4 : a, X6 : b, X8 : b]: 23.59/4.05 ( (((!!) @ (^[Y0 : b]: 23.59/4.05 ((((('#sk3' @ X2 @ X6 @ X8) & ('#sk3' @ X2 @ X8 @ Y0))) => 23.59/4.05 ('#sk3' @ X2 @ X6 @ Y0)))))) 23.59/4.05 | ~ ('#sk1' @ X2 @ X4))), 23.59/4.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl44])). 23.59/4.05 thf(zip_derived_cl60, plain, 23.59/4.05 (![X2 : a, X4 : a, X6 : b, X8 : b, X10 : b]: 23.59/4.05 ( ((((('#sk3' @ X2 @ X6 @ X8) & ('#sk3' @ X2 @ X8 @ X10))) => 23.59/4.05 ('#sk3' @ X2 @ X6 @ X10))) 23.59/4.05 | ~ ('#sk1' @ X2 @ X4))), 23.59/4.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl52])). 23.59/4.05 thf(zip_derived_cl69, plain, 23.59/4.05 (![X2 : a, X4 : a, X6 : b, X8 : b, X10 : b]: 23.59/4.05 (~ ((('#sk3' @ X2 @ X6 @ X8) & ('#sk3' @ X2 @ X8 @ X10))) 23.59/4.05 | ('#sk3' @ X2 @ X6 @ X10) 23.59/4.05 | ~ ('#sk1' @ X2 @ X4))), 23.59/4.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl60])). 23.59/4.05 thf(zip_derived_cl76, plain, 23.59/4.05 (![X2 : a, X4 : a, X6 : b, X8 : b, X10 : b]: 23.59/4.05 (~ ('#sk3' @ X2 @ X6 @ X8) 23.59/4.05 | ~ ('#sk3' @ X2 @ X8 @ X10) 23.59/4.05 | ~ ('#sk1' @ X2 @ X4) 23.59/4.05 | ('#sk3' @ X2 @ X6 @ X10))), 23.59/4.05 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 23.59/4.05 thf(zip_derived_cl306, plain, 23.59/4.05 (![X0 : b, X1 : b, X2 : a, X3 : b, X4 : a]: 23.59/4.05 (~ ('#sk4' @ X2 @ X1 @ X0) 23.59/4.05 | ~ ('#sk1' @ X2 @ X2) 23.59/4.05 | ('#sk3' @ X2 @ X1 @ X3) 23.59/4.05 | ~ ('#sk1' @ X2 @ X4) 23.59/4.05 | ~ ('#sk3' @ X2 @ X0 @ X3))), 23.59/4.05 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl76])). 23.59/4.05 thf(zip_derived_cl1989, plain, 23.59/4.05 (![X0 : b, X1 : b, X2 : a, X3 : b]: 23.59/4.05 (~ ('#sk4' @ X2 @ X1 @ X0) 23.59/4.05 | ~ ('#sk1' @ X2 @ X2) 23.59/4.05 | ('#sk3' @ X2 @ X1 @ X3) 23.59/4.05 | ~ ('#sk3' @ X2 @ X0 @ X3))), 23.59/4.05 inference('condensation', [status(thm)], [zip_derived_cl306])). 23.59/4.05 thf(zip_derived_cl5656, plain, 23.59/4.05 (![X0 : b]: 23.59/4.05 (~ ('#sk3' @ '#sk18' @ ('#sk11' @ '#sk19') @ X0) 23.59/4.05 | ('#sk3' @ '#sk18' @ ('#sk10' @ '#sk18') @ X0) 23.59/4.05 | ~ ('#sk1' @ '#sk18' @ '#sk18'))), 23.59/4.05 inference('sup-', [status(thm)], [zip_derived_cl4347, zip_derived_cl1989])). 23.59/4.05 thf(zip_derived_cl686, plain, 23.59/4.05 (( ('#sk1' @ '#sk18' @ '#sk18') | ('#form9'))), 23.59/4.05 inference('simplify', [status(thm)], [zip_derived_cl682])). 23.59/4.05 thf(zip_derived_cl4304, plain, (~ ('#form9')), 23.59/4.05 inference('demod', [status(thm)], 23.59/4.05 [zip_derived_cl3022, zip_derived_cl4303])). 23.59/4.05 thf(zip_derived_cl4329, plain, ( ('#sk1' @ '#sk18' @ '#sk18')), 23.59/4.05 inference('demod', [status(thm)], [zip_derived_cl686, zip_derived_cl4304])). 23.59/4.05 thf(zip_derived_cl5679, plain, 23.59/4.05 (![X0 : b]: 23.59/4.05 (~ ('#sk3' @ '#sk18' @ ('#sk11' @ '#sk19') @ X0) 23.59/4.05 | ('#sk3' @ '#sk18' @ ('#sk10' @ '#sk18') @ X0))), 23.59/4.05 inference('demod', [status(thm)], 23.59/4.05 [zip_derived_cl5656, zip_derived_cl4329])). 23.59/4.05 thf(zip_derived_cl12206, plain, 23.59/4.05 ( ('#sk3' @ '#sk18' @ ('#sk10' @ '#sk18') @ ('#sk13' @ '#sk19'))), 23.59/4.05 inference('sup-', [status(thm)], [zip_derived_cl4345, zip_derived_cl5679])). 23.59/4.05 thf(zip_derived_cl12333, plain, ($false), 23.59/4.05 inference('demod', [status(thm)], 23.59/4.05 [zip_derived_cl4306, zip_derived_cl12206])). 23.59/4.05 23.59/4.05 % SZS output end Refutation 23.59/4.05 23.59/4.05 23.59/4.05 % Terminating... 23.59/4.05 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 24.90/4.13 % Runner terminated. 21.07/4.17 % Zipperpin 1.5 exiting 21.07/4.20 EOF