0.05/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.BD4Fo6bpsn true 0.14/0.35 % Computer : n025.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 1440 0.14/0.35 % WCLimit : 180 0.14/0.35 % DateTime : Mon Jul 3 04:55:38 EDT 2023 0.14/0.35 % CPUTime : 0.14/0.35 % Running portfolio for 1440 s 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.36 % Number of cores: 8 0.14/0.36 % Python version: Python 3.6.8 0.14/0.36 % Running in HO mode 0.54/0.65 % Total configuration time : 828 0.54/0.65 % Estimated wc time : 1656 0.54/0.65 % Estimated cpu time (8 cpus) : 207.0 0.56/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.57/0.77 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.57/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.57/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.57/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.57/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.57/0.81 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.57/0.82 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 50.22/7.10 % Solved by lams/20_acsne_simpl.sh. 50.22/7.10 % done 818 iterations in 6.089s 50.22/7.10 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 50.22/7.10 % SZS output start Refutation 50.22/7.10 thf(a_type, type, a: $tType). 50.22/7.10 thf('#sk60_type', type, '#sk60': (a > $o) > a). 50.22/7.10 thf('#form254_type', type, '#form254': (a > $o) > $o). 50.22/7.10 thf('#sk6_type', type, '#sk6': a). 50.22/7.10 thf('#sk143_type', type, '#sk143': (a > $o) > a). 50.22/7.10 thf('#form19_type', type, '#form19': $o). 50.22/7.10 thf('#sk97_type', type, '#sk97': (a > $o) > a). 50.22/7.10 thf('#sk5_type', type, '#sk5': a > $o). 50.22/7.10 thf('#form14_type', type, '#form14': $o). 50.22/7.10 thf('#sk255_type', type, '#sk255': (a > $o) > a). 50.22/7.10 thf('#sk4_type', type, '#sk4': a). 50.22/7.10 thf('#form117_type', type, '#form117': (a > $o) > $o). 50.22/7.10 thf('#sk56_type', type, '#sk56': (a > $o) > a). 50.22/7.10 thf('#sk15_type', type, '#sk15': a). 50.22/7.10 thf('#form9_type', type, '#form9': $o). 50.22/7.10 thf('#sk138_type', type, '#sk138': (a > $o) > a). 50.22/7.10 thf('#sk23_type', type, '#sk23': a). 50.22/7.10 thf('#form96_type', type, '#form96': (a > $o) > $o). 50.22/7.10 thf('#sk107_type', type, '#sk107': (a > $o) > a). 50.22/7.10 thf('#sk8_type', type, '#sk8': a > $o). 50.22/7.10 thf('#form264_type', type, '#form264': (a > $o) > $o). 50.22/7.10 thf('#sk43_type', type, '#sk43': a > $o). 50.22/7.10 thf('#sk187_type', type, '#sk187': (a > $o) > a). 50.22/7.10 thf('#sk118_type', type, '#sk118': (a > $o) > a). 50.22/7.10 thf('#sk265_type', type, '#sk265': (a > $o) > a). 50.22/7.10 thf('#sk3_type', type, '#sk3': a). 50.22/7.10 thf('#sk7_type', type, '#sk7': a). 50.22/7.10 thf('#sk1_type', type, '#sk1': a > a > $o). 50.22/7.10 thf('#sk42_type', type, '#sk42': (a > $o) > a). 50.22/7.10 thf('#sk50_type', type, '#sk50': (a > $o) > a). 50.22/7.10 thf('#sk2_type', type, '#sk2': a > a > $o). 50.22/7.10 thf('#sk65_type', type, '#sk65': (a > $o) > a). 50.22/7.10 thf('#sk10_type', type, '#sk10': a). 50.22/7.10 thf(cTHM251H_pme, conjecture, 50.22/7.10 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 50.22/7.10 ( ( ( ![Xx0:a,Xy0:a]: 50.22/7.10 ( ( ( ![Xq:( a > $o )]: 50.22/7.10 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 50.22/7.10 ( ![Xu:a,Xv:a]: 50.22/7.10 ( ( ( Xq @ Xu ) & ( R @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) ) => 50.22/7.10 ( Xq @ Xy0 ) ) ) | 50.22/7.10 ( ![Xq:( a > $o )]: 50.22/7.10 ( ( ( ![Xu:a,Xv:a]: 50.22/7.10 ( ( ( Xq @ Xu ) & ( S @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) & 50.22/7.10 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 50.22/7.10 ( Xq @ Xy0 ) ) ) ) => 50.22/7.10 ( ![Xq:( a > $o )]: 50.22/7.10 ( ( ( ![Xu:a,Xv:a]: 50.22/7.10 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 50.22/7.10 ( Xq @ Xv ) ) ) & 50.22/7.10 ( ![Xw:a]: 50.22/7.10 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 50.22/7.10 ( Xq @ Xy0 ) ) ) ) ) & 50.22/7.10 ( ![Xx0:a,Xy0:a,Xz:a]: 50.22/7.10 ( ( ( ![Xq:( a > $o )]: 50.22/7.10 ( ( ( ![Xu:a,Xv:a]: 50.22/7.10 ( ( ( Xq @ Xu ) & ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 50.22/7.10 ( Xq @ Xv ) ) ) & 50.22/7.10 ( ![Xw:a]: 50.22/7.10 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 50.22/7.10 ( Xq @ Xy0 ) ) ) & 50.22/7.10 ( ![Xq:( a > $o )]: 50.22/7.10 ( ( ( ![Xu:a,Xv:a]: 50.22/7.10 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 50.22/7.10 ( Xq @ Xv ) ) ) & 50.22/7.10 ( ![Xw:a]: 50.22/7.10 ( ( ( S @ Xy0 @ Xw ) | ( R @ Xy0 @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 50.22/7.10 ( Xq @ Xz ) ) ) ) => 50.22/7.10 ( ![Xq:( a > $o )]: 50.22/7.10 ( ( ( ![Xu:a,Xv:a]: 50.22/7.10 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 50.22/7.10 ( Xq @ Xv ) ) ) & 50.22/7.10 ( ![Xw:a]: 50.22/7.10 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 50.22/7.10 ( Xq @ Xz ) ) ) ) ) & 50.22/7.10 ( ~( ![Xq:( a > $o )]: 50.22/7.10 ( ( ( ![Xu:a,Xv:a]: 50.22/7.10 ( ( ( Xq @ Xu ) & ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 50.22/7.10 ( Xq @ Xv ) ) ) & 50.22/7.10 ( ![Xw:a]: 50.22/7.10 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 50.22/7.10 ( Xq @ Xy ) ) ) ) ) | 50.22/7.10 ( ![Xq:( a > $o )]: 50.22/7.10 ( ( ( ![Xu:a,Xv:a]: 50.22/7.10 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 50.22/7.10 ( Xq @ Xv ) ) ) & 50.22/7.10 ( ![Xw:a]: 50.22/7.10 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 50.22/7.10 ( Xq @ Xy ) ) ) ))). 50.22/7.10 thf(zf_stmt_0, negated_conjecture, 50.22/7.10 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 50.22/7.10 ( ( ( ![Xx0:a,Xy0:a]: 50.22/7.10 ( ( ( ![Xq:( a > $o )]: 50.22/7.10 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 50.22/7.10 ( ![Xu:a,Xv:a]: 50.22/7.10 ( ( ( Xq @ Xu ) & ( R @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) ) => 50.22/7.10 ( Xq @ Xy0 ) ) ) | 50.22/7.10 ( ![Xq:( a > $o )]: 50.22/7.10 ( ( ( ![Xu:a,Xv:a]: 50.22/7.10 ( ( ( Xq @ Xu ) & ( S @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) & 50.22/7.10 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 50.22/7.10 ( Xq @ Xy0 ) ) ) ) => 50.22/7.10 ( ![Xq:( a > $o )]: 50.22/7.10 ( ( ( ![Xu:a,Xv:a]: 50.22/7.10 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 50.22/7.10 ( Xq @ Xv ) ) ) & 50.22/7.10 ( ![Xw:a]: 50.22/7.10 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 50.22/7.10 ( Xq @ Xw ) ) ) ) => 50.22/7.10 ( Xq @ Xy0 ) ) ) ) ) & 50.22/7.10 ( ![Xx0:a,Xy0:a,Xz:a]: 50.22/7.10 ( ( ( ![Xq:( a > $o )]: 50.22/7.10 ( ( ( ![Xu:a,Xv:a]: 50.22/7.10 ( ( ( Xq @ Xu ) & 50.22/7.10 ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 50.22/7.10 ( Xq @ Xv ) ) ) & 50.22/7.10 ( ![Xw:a]: 50.22/7.10 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 50.22/7.10 ( Xq @ Xw ) ) ) ) => 50.22/7.10 ( Xq @ Xy0 ) ) ) & 50.22/7.10 ( ![Xq:( a > $o )]: 50.22/7.10 ( ( ( ![Xu:a,Xv:a]: 50.22/7.10 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & 50.22/7.10 ( Xq @ Xu ) ) => 50.22/7.10 ( Xq @ Xv ) ) ) & 50.22/7.10 ( ![Xw:a]: 50.22/7.10 ( ( ( S @ Xy0 @ Xw ) | ( R @ Xy0 @ Xw ) ) => 50.22/7.10 ( Xq @ Xw ) ) ) ) => 50.22/7.10 ( Xq @ Xz ) ) ) ) => 50.22/7.10 ( ![Xq:( a > $o )]: 50.22/7.10 ( ( ( ![Xu:a,Xv:a]: 50.22/7.10 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 50.22/7.10 ( Xq @ Xv ) ) ) & 50.22/7.10 ( ![Xw:a]: 50.22/7.10 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 50.22/7.10 ( Xq @ Xw ) ) ) ) => 50.22/7.10 ( Xq @ Xz ) ) ) ) ) & 50.22/7.10 ( ~( ![Xq:( a > $o )]: 50.22/7.10 ( ( ( ![Xu:a,Xv:a]: 50.22/7.10 ( ( ( Xq @ Xu ) & ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 50.22/7.10 ( Xq @ Xv ) ) ) & 50.22/7.10 ( ![Xw:a]: 50.22/7.10 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 50.22/7.10 ( Xq @ Xy ) ) ) ) ) | 50.22/7.10 ( ![Xq:( a > $o )]: 50.22/7.10 ( ( ( ![Xu:a,Xv:a]: 50.22/7.10 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 50.22/7.10 ( Xq @ Xv ) ) ) & 50.22/7.10 ( ![Xw:a]: 50.22/7.10 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 50.22/7.10 ( Xq @ Xy ) ) ) ) )), 50.22/7.10 inference('cnf.neg', [status(esa)], [cTHM251H_pme])). 50.22/7.10 thf(zip_derived_cl0, plain, 50.22/7.10 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.22/7.10 (((!!) @ (^[Y1 : a > a > $o]: 50.22/7.10 (((!!) @ (^[Y2 : a]: 50.22/7.10 (((!!) @ (^[Y3 : a]: 50.22/7.10 (((((((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (Y0 @ 50.22/7.10 Y4 @ 50.22/7.10 Y7) => 50.22/7.10 (Y6 @ Y7)))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y8 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y6 @ 50.22/7.10 Y7) & 50.22/7.10 (Y0 @ 50.22/7.10 Y7 @ Y8))) => 50.22/7.10 (Y6 @ Y8))))))))))) => 50.22/7.10 (Y6 @ Y5)))))) | 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y8 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y6 @ 50.22/7.10 Y7) & 50.22/7.10 (Y1 @ 50.22/7.10 Y7 @ Y8))) => 50.22/7.10 (Y6 @ Y8))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (Y1 @ 50.22/7.10 Y4 @ 50.22/7.10 Y7) => 50.22/7.10 (Y6 @ Y7)))))))) => 50.22/7.10 (Y6 @ Y5)))))))) => 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y8 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y1 @ 50.22/7.10 Y7 @ 50.22/7.10 Y8) | 50.22/7.10 (Y0 @ 50.22/7.10 Y7 @ Y8))) & 50.22/7.10 (Y6 @ Y7))) => 50.22/7.10 (Y6 @ Y8))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y1 @ 50.22/7.10 Y4 @ 50.22/7.10 Y7) | 50.22/7.10 (Y0 @ 50.22/7.10 Y4 @ Y7))) => 50.22/7.10 (Y6 @ Y7)))))))) => 50.22/7.10 (Y6 @ Y5)))))))))))))) & 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y8 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y9 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y7 @ 50.22/7.10 Y8) & 50.22/7.10 (( 50.22/7.10 (Y1 @ 50.22/7.10 Y8 @ 50.22/7.10 Y9) | 50.22/7.10 (Y0 @ 50.22/7.10 Y8 @ Y9))))) => 50.22/7.10 (Y7 @ Y9))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y8 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y0 @ 50.22/7.10 Y4 @ 50.22/7.10 Y8) | 50.22/7.10 (Y1 @ 50.22/7.10 Y4 @ Y8))) => 50.22/7.10 (Y7 @ Y8)))))))) => 50.22/7.10 (Y7 @ Y5)))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y8 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y9 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y1 @ 50.22/7.10 Y8 @ 50.22/7.10 Y9) | 50.22/7.10 (Y0 @ 50.22/7.10 Y8 @ Y9))) & 50.22/7.10 (Y7 @ Y8))) => 50.22/7.10 (Y7 @ Y9))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y8 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y1 @ 50.22/7.10 Y5 @ 50.22/7.10 Y8) | 50.22/7.10 (Y0 @ 50.22/7.10 Y5 @ Y8))) => 50.22/7.10 (Y7 @ Y8)))))))) => 50.22/7.10 (Y7 @ Y6)))))))) => 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y8 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y9 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y1 @ 50.22/7.10 Y8 @ 50.22/7.10 Y9) | 50.22/7.10 (Y0 @ 50.22/7.10 Y8 @ Y9))) & 50.22/7.10 (Y7 @ Y8))) => 50.22/7.10 (Y7 @ Y9))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y8 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y0 @ 50.22/7.10 Y4 @ 50.22/7.10 Y8) | 50.22/7.10 (Y1 @ 50.22/7.10 Y4 @ Y8))) => 50.22/7.10 (Y7 @ Y8)))))))) => 50.22/7.10 (Y7 @ Y6))))))))))))))))) & 50.22/7.10 (((~) @ (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y4 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y4 @ 50.22/7.10 Y5) & 50.22/7.10 (( 50.22/7.10 (Y1 @ 50.22/7.10 Y5 @ 50.22/7.10 Y6) | 50.22/7.10 (Y0 @ 50.22/7.10 Y5 @ Y6))))) => 50.22/7.10 (Y4 @ Y6))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y1 @ 50.22/7.10 Y2 @ 50.22/7.10 Y5) | 50.22/7.10 (Y0 @ 50.22/7.10 Y2 @ Y5))) => 50.22/7.10 (Y4 @ Y5)))))))) => 50.22/7.10 (Y4 @ Y3)))))))))) | 50.22/7.10 (((!!) @ (^[Y4 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y0 @ 50.22/7.10 Y5 @ 50.22/7.10 Y6) | 50.22/7.10 (Y1 @ 50.22/7.10 Y5 @ Y6))) & 50.22/7.10 (Y4 @ Y5))) => 50.22/7.10 (Y4 @ Y6))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y1 @ 50.22/7.10 Y2 @ 50.22/7.10 Y5) | 50.22/7.10 (Y0 @ 50.22/7.10 Y2 @ Y5))) => 50.22/7.10 (Y4 @ Y5)))))))) => 50.22/7.10 (Y4 @ Y3))))))))))))))))))))), 50.22/7.10 inference('cnf', [status(esa)], [zf_stmt_0])). 50.22/7.10 thf(zip_derived_cl1, plain, 50.22/7.10 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.22/7.10 (((!!) @ (^[Y1 : a]: 50.22/7.10 (((!!) @ (^[Y2 : a]: 50.22/7.10 (((((((!!) @ (^[Y3 : a]: 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (((((( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 ('#sk1' @ 50.22/7.10 Y3 @ 50.22/7.10 Y6) => 50.22/7.10 (Y5 @ Y6)))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y5 @ 50.22/7.10 Y6) & 50.22/7.10 ('#sk1' @ 50.22/7.10 Y6 @ Y7))) => 50.22/7.10 (Y5 @ Y7))))))))))) => 50.22/7.10 (Y5 @ Y4)))))) | 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y5 @ 50.22/7.10 Y6) & 50.22/7.10 (Y0 @ 50.22/7.10 Y6 @ Y7))) => 50.22/7.10 (Y5 @ Y7))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (Y0 @ 50.22/7.10 Y3 @ 50.22/7.10 Y6) => 50.22/7.10 (Y5 @ Y6)))))))) => 50.22/7.10 (Y5 @ Y4)))))))) => 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y5 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y0 @ 50.22/7.10 Y6 @ 50.22/7.10 Y7) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y6 @ Y7))) & 50.22/7.10 (Y5 @ Y6))) => 50.22/7.10 (Y5 @ Y7))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y0 @ 50.22/7.10 Y3 @ 50.22/7.10 Y6) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y3 @ Y6))) => 50.22/7.10 (Y5 @ Y6)))))))) => 50.22/7.10 (Y5 @ Y4)))))))))))))) & 50.22/7.10 (((!!) @ (^[Y3 : a]: 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y8 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y6 @ 50.22/7.10 Y7) & 50.22/7.10 (( 50.22/7.10 (Y0 @ 50.22/7.10 Y7 @ 50.22/7.10 Y8) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y7 @ Y8))))) => 50.22/7.10 (Y6 @ Y8))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk1' @ 50.22/7.10 Y3 @ 50.22/7.10 Y7) | 50.22/7.10 (Y0 @ 50.22/7.10 Y3 @ Y7))) => 50.22/7.10 (Y6 @ Y7)))))))) => 50.22/7.10 (Y6 @ Y4)))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y8 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y0 @ 50.22/7.10 Y7 @ 50.22/7.10 Y8) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y7 @ Y8))) & 50.22/7.10 (Y6 @ Y7))) => 50.22/7.10 (Y6 @ Y8))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y0 @ 50.22/7.10 Y4 @ 50.22/7.10 Y7) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y4 @ Y7))) => 50.22/7.10 (Y6 @ Y7)))))))) => 50.22/7.10 (Y6 @ Y5)))))))) => 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y8 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y0 @ 50.22/7.10 Y7 @ 50.22/7.10 Y8) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y7 @ Y8))) & 50.22/7.10 (Y6 @ Y7))) => 50.22/7.10 (Y6 @ Y8))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk1' @ 50.22/7.10 Y3 @ 50.22/7.10 Y7) | 50.22/7.10 (Y0 @ 50.22/7.10 Y3 @ Y7))) => 50.22/7.10 (Y6 @ Y7)))))))) => 50.22/7.10 (Y6 @ Y5))))))))))))))))) & 50.22/7.10 (((~) @ (((!!) @ (^[Y3 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y3 @ 50.22/7.10 Y4) & 50.22/7.10 (( 50.22/7.10 (Y0 @ 50.22/7.10 Y4 @ 50.22/7.10 Y5) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y4 @ Y5))))) => 50.22/7.10 (Y3 @ Y5))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y0 @ 50.22/7.10 Y1 @ 50.22/7.10 Y4) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y1 @ Y4))) => 50.22/7.10 (Y3 @ Y4)))))))) => 50.22/7.10 (Y3 @ Y2)))))))))) | 50.22/7.10 (((!!) @ (^[Y3 : a > $o]: 50.22/7.10 (((((((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk1' @ 50.22/7.10 Y4 @ 50.22/7.10 Y5) | 50.22/7.10 (Y0 @ 50.22/7.10 Y4 @ Y5))) & 50.22/7.10 (Y3 @ Y4))) => 50.22/7.10 (Y3 @ Y5))))))))) & 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (((( 50.22/7.10 (Y0 @ 50.22/7.10 Y1 @ Y4) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y1 @ Y4))) => 50.22/7.10 (Y3 @ Y4)))))))) => 50.22/7.10 (Y3 @ Y2)))))))))))))))))), 50.22/7.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 50.22/7.10 thf(zip_derived_cl2, plain, 50.22/7.10 (~ (((!!) @ (^[Y0 : a]: 50.22/7.10 (((!!) @ (^[Y1 : a]: 50.22/7.10 (((((((!!) @ (^[Y2 : a]: 50.22/7.10 (((!!) @ (^[Y3 : a]: 50.22/7.10 (((((((!!) @ ( 50.22/7.10 ^[Y4 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 ('#sk1' @ 50.22/7.10 Y2 @ 50.22/7.10 Y5) => 50.22/7.10 (Y4 @ Y5)))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y4 @ 50.22/7.10 Y5) & 50.22/7.10 ('#sk1' @ 50.22/7.10 Y5 @ Y6))) => 50.22/7.10 (Y4 @ Y6))))))))))) => 50.22/7.10 (Y4 @ Y3)))))) | 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y4 @ 50.22/7.10 Y5) & 50.22/7.10 ('#sk2' @ 50.22/7.10 Y5 @ Y6))) => 50.22/7.10 (Y4 @ Y6))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y2 @ 50.22/7.10 Y5) => 50.22/7.10 (Y4 @ Y5)))))))) => 50.22/7.10 (Y4 @ Y3)))))))) => 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a > $o]: 50.22/7.10 (((( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y5 @ 50.22/7.10 Y6) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y5 @ Y6))) & 50.22/7.10 (Y4 @ Y5))) => 50.22/7.10 (Y4 @ Y6))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y2 @ 50.22/7.10 Y5) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y2 @ Y5))) => 50.22/7.10 (Y4 @ Y5)))))))) => 50.22/7.10 (Y4 @ Y3)))))))))))))) & 50.22/7.10 (((!!) @ (^[Y2 : a]: 50.22/7.10 (((!!) @ (^[Y3 : a]: 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (((((( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y5 @ 50.22/7.10 Y6) & 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y6 @ 50.22/7.10 Y7) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y6 @ Y7))))) => 50.22/7.10 (Y5 @ Y7))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk1' @ 50.22/7.10 Y2 @ 50.22/7.10 Y6) | 50.22/7.10 ('#sk2' @ 50.22/7.10 Y2 @ Y6))) => 50.22/7.10 (Y5 @ Y6)))))))) => 50.22/7.10 (Y5 @ Y3)))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y6 @ 50.22/7.10 Y7) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y6 @ Y7))) & 50.22/7.10 (Y5 @ Y6))) => 50.22/7.10 (Y5 @ Y7))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y3 @ 50.22/7.10 Y6) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y3 @ Y6))) => 50.22/7.10 (Y5 @ Y6)))))))) => 50.22/7.10 (Y5 @ Y4)))))))) => 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y5 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y7 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y6 @ 50.22/7.10 Y7) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y6 @ Y7))) & 50.22/7.10 (Y5 @ Y6))) => 50.22/7.10 (Y5 @ Y7))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk1' @ 50.22/7.10 Y2 @ 50.22/7.10 Y6) | 50.22/7.10 ('#sk2' @ 50.22/7.10 Y2 @ Y6))) => 50.22/7.10 (Y5 @ Y6)))))))) => 50.22/7.10 (Y5 @ Y4))))))))))))))))) & 50.22/7.10 (((~) @ (((!!) @ (^[Y2 : a > $o]: 50.22/7.10 (((((((!!) @ ( 50.22/7.10 ^[Y3 : a]: 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y2 @ 50.22/7.10 Y3) & 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y3 @ 50.22/7.10 Y4) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y3 @ Y4))))) => 50.22/7.10 (Y2 @ Y4))))))))) & 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y3 : a]: 50.22/7.10 ((((('#sk2' @ 50.22/7.10 Y0 @ Y3) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y0 @ Y3))) => 50.22/7.10 (Y2 @ Y3)))))))) => 50.22/7.10 (Y2 @ Y1)))))))))) | 50.22/7.10 (((!!) @ (^[Y2 : a > $o]: 50.22/7.10 (((((((!!) @ (^[Y3 : a]: 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (((( 50.22/7.10 (( 50.22/7.10 ('#sk1' @ 50.22/7.10 Y3 @ Y4) | 50.22/7.10 ('#sk2' @ 50.22/7.10 Y3 @ Y4))) & 50.22/7.10 (Y2 @ Y3))) => 50.22/7.10 (Y2 @ Y4))))))))) & 50.22/7.10 (((!!) @ (^[Y3 : a]: 50.22/7.10 ((((('#sk2' @ 50.22/7.10 Y0 @ Y3) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y0 @ Y3))) => 50.22/7.10 (Y2 @ Y3)))))))) => 50.22/7.10 (Y2 @ Y1))))))))))))))), 50.22/7.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 50.22/7.10 thf(zip_derived_cl3, plain, 50.22/7.10 (~ (((!!) @ (^[Y0 : a]: 50.22/7.10 (((((((!!) @ (^[Y1 : a]: 50.22/7.10 (((!!) @ (^[Y2 : a]: 50.22/7.10 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.10 (((((( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 ('#sk1' @ 50.22/7.10 Y1 @ 50.22/7.10 Y4) => 50.22/7.10 (Y3 @ Y4)))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y3 @ 50.22/7.10 Y4) & 50.22/7.10 ('#sk1' @ 50.22/7.10 Y4 @ Y5))) => 50.22/7.10 (Y3 @ Y5))))))))))) => 50.22/7.10 (Y3 @ Y2)))))) | 50.22/7.10 (((!!) @ (^[Y3 : a > $o]: 50.22/7.10 (((((( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y3 @ 50.22/7.10 Y4) & 50.22/7.10 ('#sk2' @ 50.22/7.10 Y4 @ Y5))) => 50.22/7.10 (Y3 @ Y5))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y1 @ 50.22/7.10 Y4) => 50.22/7.10 (Y3 @ Y4)))))))) => 50.22/7.10 (Y3 @ Y2)))))))) => 50.22/7.10 (((!!) @ (^[Y3 : a > $o]: 50.22/7.10 (((((((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y4 @ 50.22/7.10 Y5) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y4 @ Y5))) & 50.22/7.10 (Y3 @ Y4))) => 50.22/7.10 (Y3 @ Y5))))))))) & 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y1 @ 50.22/7.10 Y4) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y1 @ Y4))) => 50.22/7.10 (Y3 @ Y4)))))))) => 50.22/7.10 (Y3 @ Y2)))))))))))))) & 50.22/7.10 (((!!) @ (^[Y1 : a]: 50.22/7.10 (((!!) @ (^[Y2 : a]: 50.22/7.10 (((!!) @ (^[Y3 : a]: 50.22/7.10 (((((((!!) @ ( 50.22/7.10 ^[Y4 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y4 @ 50.22/7.10 Y5) & 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y5 @ 50.22/7.10 Y6) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y5 @ Y6))))) => 50.22/7.10 (Y4 @ Y6))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk1' @ 50.22/7.10 Y1 @ 50.22/7.10 Y5) | 50.22/7.10 ('#sk2' @ 50.22/7.10 Y1 @ Y5))) => 50.22/7.10 (Y4 @ Y5)))))))) => 50.22/7.10 (Y4 @ Y2)))))) & 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a > $o]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y5 @ 50.22/7.10 Y6) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y5 @ Y6))) & 50.22/7.10 (Y4 @ Y5))) => 50.22/7.10 (Y4 @ Y6))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y2 @ 50.22/7.10 Y5) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y2 @ Y5))) => 50.22/7.10 (Y4 @ Y5)))))))) => 50.22/7.10 (Y4 @ Y3)))))))) => 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a > $o]: 50.22/7.10 (((( 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y6 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y5 @ 50.22/7.10 Y6) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y5 @ Y6))) & 50.22/7.10 (Y4 @ Y5))) => 50.22/7.10 (Y4 @ Y6))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk1' @ 50.22/7.10 Y1 @ 50.22/7.10 Y5) | 50.22/7.10 ('#sk2' @ 50.22/7.10 Y1 @ Y5))) => 50.22/7.10 (Y4 @ Y5)))))))) => 50.22/7.10 (Y4 @ Y3))))))))))))))))) & 50.22/7.10 (((~) @ (((!!) @ (^[Y1 : a > $o]: 50.22/7.10 (((((((!!) @ (^[Y2 : a]: 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y3 : a]: 50.22/7.10 (((((Y1 @ 50.22/7.10 Y2) & 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y2 @ Y3) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y2 @ Y3))))) => 50.22/7.10 (Y1 @ Y3))))))))) & 50.22/7.10 (((!!) @ (^[Y2 : a]: 50.22/7.10 ((((('#sk2' @ 50.22/7.10 '#sk3' @ Y2) | 50.22/7.10 ('#sk1' @ 50.22/7.10 '#sk3' @ Y2))) => 50.22/7.10 (Y1 @ Y2)))))))) => 50.22/7.10 (Y1 @ Y0)))))))))) | 50.22/7.10 (((!!) @ (^[Y1 : a > $o]: 50.22/7.10 (((((((!!) @ (^[Y2 : a]: 50.22/7.10 (((!!) @ (^[Y3 : a]: 50.22/7.10 ((((((('#sk1' @ 50.22/7.10 Y2 @ Y3) | 50.22/7.10 ('#sk2' @ 50.22/7.10 Y2 @ Y3))) & 50.22/7.10 (Y1 @ Y2))) => 50.22/7.10 (Y1 @ Y3))))))))) & 50.22/7.10 (((!!) @ (^[Y2 : a]: 50.22/7.10 ((((('#sk2' @ '#sk3' @ Y2) | 50.22/7.10 ('#sk1' @ '#sk3' @ Y2))) => 50.22/7.10 (Y1 @ Y2)))))))) => 50.22/7.10 (Y1 @ Y0)))))))))))), 50.22/7.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 50.22/7.10 thf(zip_derived_cl4, plain, 50.22/7.10 (~ (((((((!!) @ (^[Y0 : a]: 50.22/7.10 (((!!) @ (^[Y1 : a]: 50.22/7.10 (((((((!!) @ (^[Y2 : a > $o]: 50.22/7.10 (((((((!!) @ (^[Y3 : a]: 50.22/7.10 (( 50.22/7.10 ('#sk1' @ 50.22/7.10 Y0 @ 50.22/7.10 Y3) => 50.22/7.10 (Y2 @ Y3)))))) & 50.22/7.10 (((!!) @ (^[Y3 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y2 @ 50.22/7.10 Y3) & 50.22/7.10 ('#sk1' @ 50.22/7.10 Y3 @ Y4))) => 50.22/7.10 (Y2 @ Y4))))))))))) => 50.22/7.10 (Y2 @ Y1)))))) | 50.22/7.10 (((!!) @ (^[Y2 : a > $o]: 50.22/7.10 (((((((!!) @ (^[Y3 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y2 @ 50.22/7.10 Y3) & 50.22/7.10 ('#sk2' @ 50.22/7.10 Y3 @ Y4))) => 50.22/7.10 (Y2 @ Y4))))))))) & 50.22/7.10 (((!!) @ (^[Y3 : a]: 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y0 @ 50.22/7.10 Y3) => 50.22/7.10 (Y2 @ Y3)))))))) => 50.22/7.10 (Y2 @ Y1)))))))) => 50.22/7.10 (((!!) @ (^[Y2 : a > $o]: 50.22/7.10 (((((((!!) @ (^[Y3 : a]: 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y3 @ 50.22/7.10 Y4) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y3 @ Y4))) & 50.22/7.10 (Y2 @ Y3))) => 50.22/7.10 (Y2 @ Y4))))))))) & 50.22/7.10 (((!!) @ (^[Y3 : a]: 50.22/7.10 (((( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y0 @ Y3) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y0 @ Y3))) => 50.22/7.10 (Y2 @ Y3)))))))) => 50.22/7.10 (Y2 @ Y1)))))))))))))) & 50.22/7.10 (((!!) @ (^[Y0 : a]: 50.22/7.10 (((!!) @ (^[Y1 : a]: 50.22/7.10 (((!!) @ (^[Y2 : a]: 50.22/7.10 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.10 (((((( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y3 @ 50.22/7.10 Y4) & 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y4 @ 50.22/7.10 Y5) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y4 @ Y5))))) => 50.22/7.10 (Y3 @ Y5))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk1' @ 50.22/7.10 Y0 @ 50.22/7.10 Y4) | 50.22/7.10 ('#sk2' @ 50.22/7.10 Y0 @ Y4))) => 50.22/7.10 (Y3 @ Y4)))))))) => 50.22/7.10 (Y3 @ Y1)))))) & 50.22/7.10 (((!!) @ (^[Y3 : a > $o]: 50.22/7.10 (((((( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y4 @ 50.22/7.10 Y5) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y4 @ Y5))) & 50.22/7.10 (Y3 @ Y4))) => 50.22/7.10 (Y3 @ Y5))))))))) & 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y1 @ 50.22/7.10 Y4) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y1 @ Y4))) => 50.22/7.10 (Y3 @ Y4)))))))) => 50.22/7.10 (Y3 @ Y2)))))))) => 50.22/7.10 (((!!) @ (^[Y3 : a > $o]: 50.22/7.10 (((((((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y4 @ 50.22/7.10 Y5) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y4 @ Y5))) & 50.22/7.10 (Y3 @ Y4))) => 50.22/7.10 (Y3 @ Y5))))))))) & 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk1' @ 50.22/7.10 Y0 @ 50.22/7.10 Y4) | 50.22/7.10 ('#sk2' @ 50.22/7.10 Y0 @ Y4))) => 50.22/7.10 (Y3 @ Y4)))))))) => 50.22/7.10 (Y3 @ Y2))))))))))))))))) & 50.22/7.10 (((~) @ (((!!) @ (^[Y0 : a > $o]: 50.22/7.10 (((((((!!) @ (^[Y1 : a]: 50.22/7.10 (((!!) @ (^[Y2 : a]: 50.22/7.10 (((((Y0 @ Y1) & 50.22/7.10 ((('#sk2' @ 50.22/7.10 Y1 @ Y2) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y1 @ Y2))))) => 50.22/7.10 (Y0 @ Y2))))))))) & 50.22/7.10 (((!!) @ (^[Y1 : a]: 50.22/7.10 ((((('#sk2' @ '#sk3' @ Y1) | 50.22/7.10 ('#sk1' @ '#sk3' @ Y1))) => 50.22/7.10 (Y0 @ Y1)))))))) => 50.22/7.10 (Y0 @ '#sk4')))))))))) | 50.22/7.10 (((!!) @ (^[Y0 : a > $o]: 50.22/7.10 (((((((!!) @ (^[Y1 : a]: 50.22/7.10 (((!!) @ (^[Y2 : a]: 50.22/7.10 ((((((('#sk1' @ Y1 @ Y2) | 50.22/7.10 ('#sk2' @ Y1 @ Y2))) & 50.22/7.10 (Y0 @ Y1))) => 50.22/7.10 (Y0 @ Y2))))))))) & 50.22/7.10 (((!!) @ (^[Y1 : a]: 50.22/7.10 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.22/7.10 '#sk3' @ Y1))) => 50.22/7.10 (Y0 @ Y1)))))))) => 50.22/7.10 (Y0 @ '#sk4'))))))))), 50.22/7.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 50.22/7.10 thf(zip_derived_cl6, plain, 50.22/7.10 (~ (((!!) @ (^[Y0 : a > $o]: 50.22/7.10 (((((((!!) @ (^[Y1 : a]: 50.22/7.10 (((!!) @ (^[Y2 : a]: 50.22/7.10 ((((((('#sk1' @ Y1 @ Y2) | 50.22/7.10 ('#sk2' @ Y1 @ Y2))) & 50.22/7.10 (Y0 @ Y1))) => 50.22/7.10 (Y0 @ Y2))))))))) & 50.22/7.10 (((!!) @ (^[Y1 : a]: 50.22/7.10 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.22/7.10 '#sk3' @ Y1))) => 50.22/7.10 (Y0 @ Y1)))))))) => 50.22/7.10 (Y0 @ '#sk4'))))))), 50.22/7.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 50.22/7.10 thf(zip_derived_cl8, plain, 50.22/7.10 (~ (((((((!!) @ (^[Y0 : a]: 50.22/7.10 (((!!) @ (^[Y1 : a]: 50.22/7.10 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 50.22/7.10 Y1))) & 50.22/7.10 ('#sk5' @ Y0))) => 50.22/7.10 ('#sk5' @ Y1))))))))) & 50.22/7.10 (((!!) @ (^[Y0 : a]: 50.22/7.10 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.22/7.10 ('#sk5' @ Y0)))))))) => 50.22/7.10 ('#sk5' @ '#sk4')))), 50.22/7.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 50.22/7.10 thf(zip_derived_cl10, plain, 50.22/7.10 ( (((((!!) @ (^[Y0 : a]: 50.22/7.10 (((!!) @ (^[Y1 : a]: 50.22/7.10 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 50.22/7.10 ('#sk5' @ Y0))) => 50.22/7.10 ('#sk5' @ Y1))))))))) & 50.22/7.10 (((!!) @ (^[Y0 : a]: 50.22/7.10 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.22/7.10 ('#sk5' @ Y0))))))))), 50.22/7.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 50.22/7.10 thf(zip_derived_cl13, plain, 50.22/7.10 ( (((!!) @ (^[Y0 : a]: 50.22/7.10 (((!!) @ (^[Y1 : a]: 50.22/7.10 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 50.22/7.10 ('#sk5' @ Y0))) => 50.22/7.10 ('#sk5' @ Y1)))))))))), 50.22/7.10 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 50.22/7.10 thf(zip_derived_cl17, plain, 50.22/7.10 (![X2 : a]: 50.22/7.10 (((!!) @ (^[Y0 : a]: 50.22/7.10 ((((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) & 50.22/7.10 ('#sk5' @ X2))) => 50.22/7.10 ('#sk5' @ Y0))))))), 50.22/7.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 50.22/7.10 thf(zip_derived_cl21, plain, 50.22/7.10 (![X2 : a, X4 : a]: 50.22/7.10 ((((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk5' @ X2))) => 50.22/7.10 ('#sk5' @ X4)))), 50.22/7.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 50.22/7.10 thf(zip_derived_cl29, plain, 50.22/7.10 (![X2 : a, X4 : a]: 50.22/7.10 (~ ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk5' @ X2))) 50.22/7.10 | ('#sk5' @ X4))), 50.22/7.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 50.22/7.10 thf(zip_derived_cl39, plain, 50.22/7.10 (![X2 : a, X4 : a]: 50.22/7.10 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 50.22/7.10 | ~ ('#sk5' @ X2) 50.22/7.10 | ('#sk5' @ X4))), 50.22/7.10 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl29])). 50.22/7.10 thf(zip_derived_cl49, plain, 50.22/7.10 (![X2 : a, X4 : a]: 50.22/7.10 (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 50.22/7.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 50.22/7.10 thf(zip_derived_cl50, plain, 50.22/7.10 (![X2 : a, X4 : a]: 50.22/7.10 (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 50.22/7.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 50.22/7.10 thf(zip_derived_cl5, plain, 50.22/7.10 (~ (((((!!) @ (^[Y0 : a]: 50.22/7.10 (((!!) @ (^[Y1 : a]: 50.22/7.10 (((((((!!) @ (^[Y2 : a > $o]: 50.22/7.10 (((((((!!) @ (^[Y3 : a]: 50.22/7.10 ((('#sk1' @ 50.22/7.10 Y0 @ 50.22/7.10 Y3) => 50.22/7.10 (Y2 @ Y3)))))) & 50.22/7.10 (((!!) @ (^[Y3 : a]: 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y2 @ 50.22/7.10 Y3) & 50.22/7.10 ('#sk1' @ 50.22/7.10 Y3 @ Y4))) => 50.22/7.10 (Y2 @ Y4))))))))))) => 50.22/7.10 (Y2 @ Y1)))))) | 50.22/7.10 (((!!) @ (^[Y2 : a > $o]: 50.22/7.10 (((((((!!) @ (^[Y3 : a]: 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y2 @ 50.22/7.10 Y3) & 50.22/7.10 ('#sk2' @ 50.22/7.10 Y3 @ Y4))) => 50.22/7.10 (Y2 @ Y4))))))))) & 50.22/7.10 (((!!) @ (^[Y3 : a]: 50.22/7.10 ((('#sk2' @ 50.22/7.10 Y0 @ 50.22/7.10 Y3) => 50.22/7.10 (Y2 @ Y3)))))))) => 50.22/7.10 (Y2 @ Y1)))))))) => 50.22/7.10 (((!!) @ (^[Y2 : a > $o]: 50.22/7.10 (((((((!!) @ (^[Y3 : a]: 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y3 @ 50.22/7.10 Y4) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y3 @ Y4))) & 50.22/7.10 (Y2 @ Y3))) => 50.22/7.10 (Y2 @ Y4))))))))) & 50.22/7.10 (((!!) @ (^[Y3 : a]: 50.22/7.10 ((((('#sk2' @ 50.22/7.10 Y0 @ Y3) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y0 @ Y3))) => 50.22/7.10 (Y2 @ Y3)))))))) => 50.22/7.10 (Y2 @ Y1)))))))))))))) & 50.22/7.10 (((!!) @ (^[Y0 : a]: 50.22/7.10 (((!!) @ (^[Y1 : a]: 50.22/7.10 (((!!) @ (^[Y2 : a]: 50.22/7.10 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.10 (((((((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (Y3 @ 50.22/7.10 Y4) & 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y4 @ 50.22/7.10 Y5) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y4 @ Y5))))) => 50.22/7.10 (Y3 @ Y5))))))))) & 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk1' @ 50.22/7.10 Y0 @ 50.22/7.10 Y4) | 50.22/7.10 ('#sk2' @ 50.22/7.10 Y0 @ Y4))) => 50.22/7.10 (Y3 @ Y4)))))))) => 50.22/7.10 (Y3 @ Y1)))))) & 50.22/7.10 (((!!) @ (^[Y3 : a > $o]: 50.22/7.10 (((((((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y4 @ 50.22/7.10 Y5) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y4 @ Y5))) & 50.22/7.10 (Y3 @ Y4))) => 50.22/7.10 (Y3 @ Y5))))))))) & 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y1 @ 50.22/7.10 Y4) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y1 @ Y4))) => 50.22/7.10 (Y3 @ Y4)))))))) => 50.22/7.10 (Y3 @ Y2)))))))) => 50.22/7.10 (((!!) @ (^[Y3 : a > $o]: 50.22/7.10 (((((((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (!!) @ ( 50.22/7.10 ^[Y5 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y4 @ 50.22/7.10 Y5) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y4 @ Y5))) & 50.22/7.10 (Y3 @ Y4))) => 50.22/7.10 (Y3 @ Y5))))))))) & 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (( 50.22/7.10 (( 50.22/7.10 ('#sk1' @ 50.22/7.10 Y0 @ 50.22/7.10 Y4) | 50.22/7.10 ('#sk2' @ 50.22/7.10 Y0 @ Y4))) => 50.22/7.10 (Y3 @ Y4)))))))) => 50.22/7.10 (Y3 @ Y2))))))))))))))))) & 50.22/7.10 (((~) @ (((!!) @ (^[Y0 : a > $o]: 50.22/7.10 (((((((!!) @ (^[Y1 : a]: 50.22/7.10 (((!!) @ (^[Y2 : a]: 50.22/7.10 (((((Y0 @ Y1) & 50.22/7.10 ((('#sk2' @ 50.22/7.10 Y1 @ Y2) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y1 @ Y2))))) => 50.22/7.10 (Y0 @ Y2))))))))) & 50.22/7.10 (((!!) @ (^[Y1 : a]: 50.22/7.10 ((((('#sk2' @ '#sk3' @ Y1) | 50.22/7.10 ('#sk1' @ '#sk3' @ Y1))) => 50.22/7.10 (Y0 @ Y1)))))))) => 50.22/7.10 (Y0 @ '#sk4'))))))))))), 50.22/7.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 50.22/7.10 thf(zip_derived_cl7, plain, 50.22/7.10 ((~ (((!!) @ (^[Y0 : a]: 50.22/7.10 (((!!) @ (^[Y1 : a]: 50.22/7.10 (((((((!!) @ (^[Y2 : a > $o]: 50.22/7.10 (((((((!!) @ (^[Y3 : a]: 50.22/7.10 ((('#sk1' @ 50.22/7.10 Y0 @ Y3) => 50.22/7.10 (Y2 @ Y3)))))) & 50.22/7.10 (((!!) @ (^[Y3 : a]: 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 ( 50.22/7.10 ( 50.22/7.10 (( 50.22/7.10 (Y2 @ 50.22/7.10 Y3) & 50.22/7.10 ('#sk1' @ 50.22/7.10 Y3 @ Y4))) => 50.22/7.10 (Y2 @ Y4))))))))))) => 50.22/7.10 (Y2 @ Y1)))))) | 50.22/7.10 (((!!) @ (^[Y2 : a > $o]: 50.22/7.10 (((((((!!) @ (^[Y3 : a]: 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 ( 50.22/7.10 ( 50.22/7.10 (( 50.22/7.10 (Y2 @ 50.22/7.10 Y3) & 50.22/7.10 ('#sk2' @ 50.22/7.10 Y3 @ Y4))) => 50.22/7.10 (Y2 @ Y4))))))))) & 50.22/7.10 (((!!) @ (^[Y3 : a]: 50.22/7.10 ((('#sk2' @ 50.22/7.10 Y0 @ Y3) => 50.22/7.10 (Y2 @ Y3)))))))) => 50.22/7.10 (Y2 @ Y1)))))))) => 50.22/7.10 (((!!) @ (^[Y2 : a > $o]: 50.22/7.10 (((((((!!) @ (^[Y3 : a]: 50.22/7.10 (((!!) @ ( 50.22/7.10 ^[Y4 : a]: 50.22/7.10 (((( 50.22/7.10 (( 50.22/7.10 ('#sk2' @ 50.22/7.10 Y3 @ 50.22/7.10 Y4) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y3 @ Y4))) & 50.22/7.10 (Y2 @ Y3))) => 50.22/7.10 (Y2 @ Y4))))))))) & 50.22/7.10 (((!!) @ (^[Y3 : a]: 50.22/7.10 ((((('#sk2' @ 50.22/7.10 Y0 @ Y3) | 50.22/7.10 ('#sk1' @ 50.22/7.10 Y0 @ Y3))) => 50.22/7.10 (Y2 @ Y3)))))))) => 50.22/7.10 (Y2 @ Y1)))))))))))))) 50.22/7.10 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.10 (((!!) @ (^[Y1 : a]: 50.22/7.10 (((!!) @ (^[Y2 : a]: 50.22/7.10 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))) 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk3' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk4')))))))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl5])). 50.22/7.11 thf(zip_derived_cl9, plain, 50.22/7.11 ((~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((((((!!) @ (^[Y1 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y2 : a]: 50.22/7.11 ((('#sk1' @ '#sk6' @ 50.22/7.11 Y2) => (Y1 @ Y2)))))) & 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((!!) @ (^[Y3 : a]: 50.22/7.11 (((((Y1 @ 50.22/7.11 Y2) & 50.22/7.11 ('#sk1' @ 50.22/7.11 Y2 @ Y3))) => 50.22/7.11 (Y1 @ Y3))))))))))) => 50.22/7.11 (Y1 @ Y0)))))) | 50.22/7.11 (((!!) @ (^[Y1 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y2 : a]: 50.22/7.11 (((!!) @ (^[Y3 : a]: 50.22/7.11 (((((Y1 @ 50.22/7.11 Y2) & 50.22/7.11 ('#sk2' @ 50.22/7.11 Y2 @ Y3))) => 50.22/7.11 (Y1 @ Y3))))))))) & 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 ((('#sk2' @ '#sk6' @ 50.22/7.11 Y2) => (Y1 @ Y2)))))))) => 50.22/7.11 (Y1 @ Y0)))))))) => 50.22/7.11 (((!!) @ (^[Y1 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y2 : a]: 50.22/7.11 (((!!) @ (^[Y3 : a]: 50.22/7.11 ((((((('#sk2' @ 50.22/7.11 Y2 @ 50.22/7.11 Y3) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y2 @ Y3))) & 50.22/7.11 (Y1 @ Y2))) => 50.22/7.11 (Y1 @ Y3))))))))) & 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 ((((('#sk2' @ '#sk6' @ 50.22/7.11 Y2) | ('#sk1' @ 50.22/7.11 '#sk6' @ Y2))) => 50.22/7.11 (Y1 @ Y2)))))))) => 50.22/7.11 (Y1 @ Y0))))))))))) 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk3' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk4')))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl7])). 50.22/7.11 thf(zip_derived_cl12, plain, 50.22/7.11 ((~ (((((((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ('#sk1' @ Y1 @ Y2))) => 50.22/7.11 (Y0 @ Y2))))))))))) => 50.22/7.11 (Y0 @ '#sk7')))))) | 50.22/7.11 (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ('#sk2' @ Y1 @ Y2))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk7')))))))) => 50.22/7.11 (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 ((((((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))) & 50.22/7.11 (Y0 @ Y1))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk6' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk7')))))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))) 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk3' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk4')))))))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl9])). 50.22/7.11 thf(zip_derived_cl15, plain, 50.22/7.11 (( (((((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & ('#sk1' @ 50.22/7.11 Y1 @ Y2))) => 50.22/7.11 (Y0 @ Y2))))))))))) => 50.22/7.11 (Y0 @ '#sk7')))))) | 50.22/7.11 (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & ('#sk2' @ 50.22/7.11 Y1 @ Y2))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk7')))))))) 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk3' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk4')))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])). 50.22/7.11 thf(zip_derived_cl19, plain, 50.22/7.11 (( (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & ('#sk1' @ 50.22/7.11 Y1 @ Y2))) => 50.22/7.11 (Y0 @ Y2))))))))))) => 50.22/7.11 (Y0 @ '#sk7')))))) 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & ('#sk2' @ 50.22/7.11 Y1 @ Y2))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk7')))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))) 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk3' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk4')))))))), 50.22/7.11 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl15])). 50.22/7.11 thf(zip_derived_cl23, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.22/7.11 (X2 @ Y1))))))))))) => 50.22/7.11 (X2 @ '#sk7'))) 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y1) | 50.22/7.11 ('#sk1' @ '#sk3' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk4')))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))) 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & ('#sk2' @ 50.22/7.11 Y1 @ Y2))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk7')))))))), 50.22/7.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 50.22/7.11 thf(zip_derived_cl32, plain, 50.22/7.11 ((~ ('#form14') 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk3' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk4')))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl33, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( (((((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((((X2 @ Y0) & 50.22/7.11 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.22/7.11 Y0 @ Y1))))) => 50.22/7.11 (X2 @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))) => 50.22/7.11 (X2 @ '#sk4'))) 50.22/7.11 | ~ ('#form14'))), 50.22/7.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 50.22/7.11 thf(zip_derived_cl35, plain, 50.22/7.11 (( (((((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk5' @ Y0) & 50.22/7.11 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.22/7.11 Y1))))) => 50.22/7.11 ('#sk5' @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.22/7.11 ('#sk5' @ Y0)))))))) => 50.22/7.11 ('#sk5' @ '#sk4'))) 50.22/7.11 | ~ ('#form14'))), 50.22/7.11 inference('triggered_bool_instantiation', [status(thm)], 50.22/7.11 [zip_derived_cl33])). 50.22/7.11 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk4')), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 50.22/7.11 thf(zip_derived_cl262, plain, 50.22/7.11 (( (((((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk5' @ Y0) & 50.22/7.11 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.22/7.11 Y1))))) => 50.22/7.11 ('#sk5' @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.22/7.11 ('#sk5' @ Y0)))))))) => 50.22/7.11 ($false))) 50.22/7.11 | ~ ('#form14'))), 50.22/7.11 inference('demod', [status(thm)], [zip_derived_cl35, zip_derived_cl11])). 50.22/7.11 thf(zip_derived_cl263, plain, 50.22/7.11 (( (((~) @ (((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk5' @ Y0) & 50.22/7.11 ((('#sk2' @ Y0 @ Y1) | 50.22/7.11 ('#sk1' @ Y0 @ Y1))))) => 50.22/7.11 ('#sk5' @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ 50.22/7.11 Y0))) => 50.22/7.11 ('#sk5' @ Y0)))))))))) 50.22/7.11 | ~ ('#form14'))), 50.22/7.11 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl262])). 50.22/7.11 thf(zip_derived_cl264, plain, 50.22/7.11 ((~ (((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk5' @ Y0) & 50.22/7.11 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.22/7.11 Y1))))) => 50.22/7.11 ('#sk5' @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.22/7.11 ('#sk5' @ Y0)))))))) 50.22/7.11 | ~ ('#form14'))), 50.22/7.11 inference('simplify nested equalities', [status(thm)], 50.22/7.11 [zip_derived_cl263])). 50.22/7.11 thf(zip_derived_cl265, plain, 50.22/7.11 ((~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk5' @ Y0) & 50.22/7.11 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))))) => 50.22/7.11 ('#sk5' @ Y1))))))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.22/7.11 ('#sk5' @ Y0)))))) 50.22/7.11 | ~ ('#form14'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl264])). 50.22/7.11 thf(zip_derived_cl33, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( (((((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((((X2 @ Y0) & 50.22/7.11 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.22/7.11 Y0 @ Y1))))) => 50.22/7.11 (X2 @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))) => 50.22/7.11 (X2 @ '#sk4'))) 50.22/7.11 | ~ ('#form14'))), 50.22/7.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 50.22/7.11 thf(zip_derived_cl45, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((((X2 @ Y0) & 50.22/7.11 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.22/7.11 Y0 @ Y1))))) => 50.22/7.11 (X2 @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))) 50.22/7.11 | (X2 @ '#sk4') 50.22/7.11 | ~ ('#form14'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])). 50.22/7.11 thf(zip_derived_cl53, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((((X2 @ Y0) & 50.22/7.11 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.22/7.11 Y1))))) => 50.22/7.11 (X2 @ Y1))))))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))) 50.22/7.11 | ~ ('#form14') 50.22/7.11 | (X2 @ '#sk4'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl45])). 50.22/7.11 thf(zip_derived_cl60, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((((X2 @ ('#sk42' @ X2)) & 50.22/7.11 ((('#sk2' @ ('#sk42' @ X2) @ Y0) | ('#sk1' @ 50.22/7.11 ('#sk42' @ X2) @ Y0))))) => 50.22/7.11 (X2 @ Y0)))))) 50.22/7.11 | (X2 @ '#sk4') 50.22/7.11 | ~ ('#form14') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl53])). 50.22/7.11 thf(zip_derived_cl71, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (((((X2 @ ('#sk42' @ X2)) & 50.22/7.11 ((('#sk2' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) | ('#sk1' @ 50.22/7.11 ('#sk42' @ X2) @ ('#sk56' @ X2)))))) => 50.22/7.11 (X2 @ ('#sk56' @ X2)))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))) 50.22/7.11 | ~ ('#form14') 50.22/7.11 | (X2 @ '#sk4'))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl60])). 50.22/7.11 thf(zip_derived_cl87, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (X2 @ ('#sk56' @ X2)) 50.22/7.11 | (X2 @ '#sk4') 50.22/7.11 | ~ ('#form14') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 50.22/7.11 thf(zip_derived_cl101, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#form96' @ X2) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl266, plain, 50.22/7.11 ((~ ('#form96' @ '#sk5') 50.22/7.11 | ~ ('#form14') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk5' @ Y0) & 50.22/7.11 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.22/7.11 Y1))))) => 50.22/7.11 ('#sk5' @ Y1))))))))))), 50.22/7.11 inference('renaming', [status(thm)], 50.22/7.11 [zip_derived_cl265, zip_derived_cl101])). 50.22/7.11 thf(zip_derived_cl267, plain, 50.22/7.11 ((~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk5' @ ('#sk42' @ '#sk5')) & 50.22/7.11 ((('#sk2' @ ('#sk42' @ '#sk5') @ Y0) | ('#sk1' @ 50.22/7.11 ('#sk42' @ '#sk5') @ Y0))))) => 50.22/7.11 ('#sk5' @ Y0)))))) 50.22/7.11 | ~ ('#form14') 50.22/7.11 | ~ ('#form96' @ '#sk5'))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl266])). 50.22/7.11 thf(zip_derived_cl268, plain, 50.22/7.11 ((~ ((((('#sk5' @ ('#sk42' @ '#sk5')) & 50.22/7.11 ((('#sk2' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) | ('#sk1' @ 50.22/7.11 ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')))))) => 50.22/7.11 ('#sk5' @ ('#sk56' @ '#sk5')))) 50.22/7.11 | ~ ('#form96' @ '#sk5') 50.22/7.11 | ~ ('#form14'))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl267])). 50.22/7.11 thf(zip_derived_cl270, plain, 50.22/7.11 ((~ ('#sk5' @ ('#sk56' @ '#sk5')) 50.22/7.11 | ~ ('#form14') 50.22/7.11 | ~ ('#form96' @ '#sk5'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl268])). 50.22/7.11 thf(zip_derived_cl269, plain, 50.22/7.11 (( ((('#sk5' @ ('#sk42' @ '#sk5')) & 50.22/7.11 ((('#sk2' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) | ('#sk1' @ 50.22/7.11 ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')))))) 50.22/7.11 | ~ ('#form14') 50.22/7.11 | ~ ('#form96' @ '#sk5'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl268])). 50.22/7.11 thf(zip_derived_cl271, plain, 50.22/7.11 (( ('#sk5' @ ('#sk42' @ '#sk5')) | ~ ('#form96' @ '#sk5') | ~ ('#form14'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl269])). 50.22/7.11 thf(zip_derived_cl272, plain, 50.22/7.11 (( ((('#sk2' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) | ('#sk1' @ 50.22/7.11 ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')))) 50.22/7.11 | ~ ('#form96' @ '#sk5') 50.22/7.11 | ~ ('#form14'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl269])). 50.22/7.11 thf(zip_derived_cl273, plain, 50.22/7.11 (( ('#sk2' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) 50.22/7.11 | ('#sk1' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) 50.22/7.11 | ~ ('#form14') 50.22/7.11 | ~ ('#form96' @ '#sk5'))), 50.22/7.11 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl272])). 50.22/7.11 thf(zip_derived_cl23, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.22/7.11 (X2 @ Y1))))))))))) => 50.22/7.11 (X2 @ '#sk7'))) 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y1) | 50.22/7.11 ('#sk1' @ '#sk3' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk4')))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))) 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & ('#sk2' @ 50.22/7.11 Y1 @ Y2))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk7')))))))), 50.22/7.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 50.22/7.11 thf(zip_derived_cl32, plain, 50.22/7.11 ((~ ('#form14') 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk3' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk4')))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl36, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#form14') 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & ('#sk2' @ 50.22/7.11 Y1 @ Y2))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk7')))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))) 50.22/7.11 | (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.22/7.11 (X2 @ Y1))))))))))) => 50.22/7.11 (X2 @ '#sk7'))))), 50.22/7.11 inference('renaming', [status(thm)], [zip_derived_cl23, zip_derived_cl32])). 50.22/7.11 thf(zip_derived_cl40, plain, 50.22/7.11 ((~ ('#form19') 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & ('#sk2' @ 50.22/7.11 Y1 @ Y2))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk7')))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl41, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( (((((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.22/7.11 (X2 @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) => 50.22/7.11 (X2 @ '#sk7'))) 50.22/7.11 | ~ ('#form19'))), 50.22/7.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl40])). 50.22/7.11 thf(zip_derived_cl52, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.22/7.11 (X2 @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) 50.22/7.11 | (X2 @ '#sk7') 50.22/7.11 | ~ ('#form19'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])). 50.22/7.11 thf(zip_derived_cl59, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.22/7.11 (X2 @ Y1))))))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 50.22/7.11 | ~ ('#form19') 50.22/7.11 | (X2 @ '#sk7'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl52])). 50.22/7.11 thf(zip_derived_cl70, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((((X2 @ ('#sk50' @ X2)) & ('#sk2' @ ('#sk50' @ X2) @ 50.22/7.11 Y0))) => 50.22/7.11 (X2 @ Y0)))))) 50.22/7.11 | (X2 @ '#sk7') 50.22/7.11 | ~ ('#form19') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl59])). 50.22/7.11 thf(zip_derived_cl85, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (((((X2 @ ('#sk50' @ X2)) & ('#sk2' @ ('#sk50' @ X2) @ 50.22/7.11 ('#sk65' @ X2)))) => 50.22/7.11 (X2 @ ('#sk65' @ X2)))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 50.22/7.11 | ~ ('#form19') 50.22/7.11 | (X2 @ '#sk7'))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl70])). 50.22/7.11 thf(zip_derived_cl98, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (X2 @ ('#sk65' @ X2)) 50.22/7.11 | (X2 @ '#sk7') 50.22/7.11 | ~ ('#form19') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl85])). 50.22/7.11 thf(zip_derived_cl98, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (X2 @ ('#sk65' @ X2)) 50.22/7.11 | (X2 @ '#sk7') 50.22/7.11 | ~ ('#form19') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl85])). 50.22/7.11 thf(zip_derived_cl113, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#form117' @ X2) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl115, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ ('#form117' @ X2) 50.22/7.11 | ~ ('#form19') 50.22/7.11 | (X2 @ '#sk7') 50.22/7.11 | ~ (X2 @ ('#sk65' @ X2)))), 50.22/7.11 inference('renaming', [status(thm)], 50.22/7.11 [zip_derived_cl98, zip_derived_cl113])). 50.22/7.11 thf(zip_derived_cl101, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#form96' @ X2) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl102, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ ((((('#sk2' @ '#sk3' @ ('#sk97' @ X2)) | ('#sk1' @ '#sk3' @ 50.22/7.11 ('#sk97' @ X2)))) => 50.22/7.11 (X2 @ ('#sk97' @ X2)))) 50.22/7.11 | ('#form96' @ X2))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl101])). 50.22/7.11 thf(zip_derived_cl118, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ((('#sk2' @ '#sk3' @ ('#sk97' @ X2)) | ('#sk1' @ '#sk3' @ 50.22/7.11 ('#sk97' @ X2)))) 50.22/7.11 | ('#form96' @ X2))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])). 50.22/7.11 thf(zip_derived_cl135, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#sk2' @ '#sk3' @ ('#sk97' @ X2)) 50.22/7.11 | ('#sk1' @ '#sk3' @ ('#sk97' @ X2)) 50.22/7.11 | ('#form96' @ X2))), 50.22/7.11 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl118])). 50.22/7.11 thf(zip_derived_cl119, plain, 50.22/7.11 (![X2 : a > $o]: (~ (X2 @ ('#sk97' @ X2)) | ('#form96' @ X2))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])). 50.22/7.11 thf(zip_derived_cl16, plain, 50.22/7.11 ((~ (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 ((((((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))) & 50.22/7.11 (Y0 @ Y1))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk6' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk7')))))) 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk3' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk4')))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])). 50.22/7.11 thf(zip_derived_cl20, plain, 50.22/7.11 ((~ (((((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.22/7.11 Y0 @ Y1))) & 50.22/7.11 ('#sk8' @ Y0))) => 50.22/7.11 ('#sk8' @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.22/7.11 ('#sk8' @ Y0)))))))) => 50.22/7.11 ('#sk8' @ '#sk7'))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))) 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk3' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk4')))))))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl16])). 50.22/7.11 thf(zip_derived_cl20, plain, 50.22/7.11 ((~ (((((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.22/7.11 Y0 @ Y1))) & 50.22/7.11 ('#sk8' @ Y0))) => 50.22/7.11 ('#sk8' @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.22/7.11 ('#sk8' @ Y0)))))))) => 50.22/7.11 ('#sk8' @ '#sk7'))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))) 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk3' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk4')))))))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl16])). 50.22/7.11 thf(zip_derived_cl26, plain, 50.22/7.11 (( ('#form9') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl28, plain, 50.22/7.11 ((~ ('#form9') 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk3' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk4')))))) 50.22/7.11 | ~ (((((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.22/7.11 Y0 @ Y1))) & 50.22/7.11 ('#sk8' @ Y0))) => 50.22/7.11 ('#sk8' @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.22/7.11 ('#sk8' @ Y0)))))))) => 50.22/7.11 ('#sk8' @ '#sk7'))))), 50.22/7.11 inference('renaming', [status(thm)], [zip_derived_cl20, zip_derived_cl26])). 50.22/7.11 thf(zip_derived_cl32, plain, 50.22/7.11 ((~ ('#form14') 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk3' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk4')))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl37, plain, 50.22/7.11 (( ('#form14') 50.22/7.11 | ~ (((((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.22/7.11 Y0 @ Y1))) & 50.22/7.11 ('#sk8' @ Y0))) => 50.22/7.11 ('#sk8' @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.22/7.11 ('#sk8' @ Y0)))))))) => 50.22/7.11 ('#sk8' @ '#sk7'))) 50.22/7.11 | ~ ('#form9'))), 50.22/7.11 inference('renaming', [status(thm)], [zip_derived_cl28, zip_derived_cl32])). 50.22/7.11 thf(zip_derived_cl47, plain, 50.22/7.11 ((~ ('#sk8' @ '#sk7') | ~ ('#form9') | ('#form14'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 50.22/7.11 thf(zip_derived_cl46, plain, 50.22/7.11 (( (((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.22/7.11 Y1))) & 50.22/7.11 ('#sk8' @ Y0))) => 50.22/7.11 ('#sk8' @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.22/7.11 ('#sk8' @ Y0)))))))) 50.22/7.11 | ~ ('#form9') 50.22/7.11 | ('#form14'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 50.22/7.11 thf(zip_derived_cl54, plain, 50.22/7.11 (( (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 50.22/7.11 ('#sk8' @ Y0))) => 50.22/7.11 ('#sk8' @ Y1))))))))) 50.22/7.11 | ('#form14') 50.22/7.11 | ~ ('#form9'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 50.22/7.11 thf(zip_derived_cl61, plain, 50.22/7.11 (![X2 : a]: 50.22/7.11 ( (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) & 50.22/7.11 ('#sk8' @ X2))) => 50.22/7.11 ('#sk8' @ Y0)))))) 50.22/7.11 | ~ ('#form9') 50.22/7.11 | ('#form14'))), 50.22/7.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl54])). 50.22/7.11 thf(zip_derived_cl72, plain, 50.22/7.11 (![X2 : a, X4 : a]: 50.22/7.11 ( ((((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk8' @ X2))) => 50.22/7.11 ('#sk8' @ X4))) 50.22/7.11 | ('#form14') 50.22/7.11 | ~ ('#form9'))), 50.22/7.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl61])). 50.22/7.11 thf(zip_derived_cl88, plain, 50.22/7.11 (![X2 : a, X4 : a]: 50.22/7.11 (~ ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk8' @ X2))) 50.22/7.11 | ('#sk8' @ X4) 50.22/7.11 | ~ ('#form9') 50.22/7.11 | ('#form14'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl72])). 50.22/7.11 thf(zip_derived_cl104, plain, 50.22/7.11 (![X2 : a, X4 : a]: 50.22/7.11 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 50.22/7.11 | ~ ('#sk8' @ X2) 50.22/7.11 | ('#form14') 50.22/7.11 | ~ ('#form9') 50.22/7.11 | ('#sk8' @ X4))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl88])). 50.22/7.11 thf(zip_derived_cl120, plain, 50.22/7.11 (![X2 : a, X4 : a]: 50.22/7.11 (~ ('#sk2' @ X2 @ X4) 50.22/7.11 | ('#sk8' @ X4) 50.22/7.11 | ~ ('#form9') 50.22/7.11 | ('#form14') 50.22/7.11 | ~ ('#sk8' @ X2))), 50.22/7.11 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl104])). 50.22/7.11 thf(zip_derived_cl14, plain, 50.22/7.11 ( (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 50.22/7.11 ('#sk5' @ Y0))))))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 50.22/7.11 thf(zip_derived_cl18, plain, 50.22/7.11 (![X2 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ X2) | ('#sk1' @ '#sk3' @ X2))) => ('#sk5' @ 50.22/7.11 X2)))), 50.22/7.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 50.22/7.11 thf(zip_derived_cl22, plain, 50.22/7.11 (![X2 : a]: 50.22/7.11 (~ ((('#sk2' @ '#sk3' @ X2) | ('#sk1' @ '#sk3' @ X2))) 50.22/7.11 | ('#sk5' @ X2))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 50.22/7.11 thf(zip_derived_cl31, plain, 50.22/7.11 (![X2 : a]: (~ ('#sk1' @ '#sk3' @ X2) | ('#sk5' @ X2))), 50.22/7.11 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl22])). 50.22/7.11 thf(zip_derived_cl30, plain, 50.22/7.11 (![X2 : a]: (~ ('#sk2' @ '#sk3' @ X2) | ('#sk5' @ X2))), 50.22/7.11 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl22])). 50.22/7.11 thf(zip_derived_cl97, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( (((X2 @ ('#sk50' @ X2)) & ('#sk2' @ ('#sk50' @ X2) @ ('#sk65' @ X2)))) 50.22/7.11 | (X2 @ '#sk7') 50.22/7.11 | ~ ('#form19') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl85])). 50.22/7.11 thf(zip_derived_cl111, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( (X2 @ ('#sk50' @ X2)) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 50.22/7.11 | ~ ('#form19') 50.22/7.11 | (X2 @ '#sk7'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl97])). 50.22/7.11 thf(zip_derived_cl113, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#form117' @ X2) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl128, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ ('#form117' @ (^[Y0 : a]: (X2 @ Y0))) 50.22/7.11 | (X2 @ '#sk7') 50.22/7.11 | ~ ('#form19') 50.22/7.11 | (X2 @ ('#sk50' @ X2)))), 50.22/7.11 inference('renaming', [status(thm)], 50.22/7.11 [zip_derived_cl111, zip_derived_cl113])). 50.22/7.11 thf(zip_derived_cl145, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ ('#form117' @ X2) 50.22/7.11 | (X2 @ '#sk7') 50.22/7.11 | ~ ('#form19') 50.22/7.11 | (X2 @ ('#sk50' @ X2)))), 50.22/7.11 inference('ho_norm', [status(thm)], [zip_derived_cl128])). 50.22/7.11 thf(zip_derived_cl113, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#form117' @ X2) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl114, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ ((('#sk2' @ '#sk6' @ ('#sk118' @ X2)) => (X2 @ ('#sk118' @ X2)))) 50.22/7.11 | ('#form117' @ X2))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl113])). 50.22/7.11 thf(zip_derived_cl130, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#sk2' @ '#sk6' @ ('#sk118' @ X2)) | ('#form117' @ X2))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl114])). 50.22/7.11 thf(zip_derived_cl131, plain, 50.22/7.11 (![X2 : a > $o]: (~ (X2 @ ('#sk118' @ X2)) | ('#form117' @ X2))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl114])). 50.22/7.11 thf(zip_derived_cl112, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#sk2' @ ('#sk50' @ X2) @ ('#sk65' @ X2)) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 50.22/7.11 | ~ ('#form19') 50.22/7.11 | (X2 @ '#sk7'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl97])). 50.22/7.11 thf(zip_derived_cl113, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#form117' @ X2) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl129, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ ('#form117' @ (^[Y0 : a]: (X2 @ Y0))) 50.22/7.11 | (X2 @ '#sk7') 50.22/7.11 | ~ ('#form19') 50.22/7.11 | ('#sk2' @ ('#sk50' @ X2) @ ('#sk65' @ X2)))), 50.22/7.11 inference('renaming', [status(thm)], 50.22/7.11 [zip_derived_cl112, zip_derived_cl113])). 50.22/7.11 thf(zip_derived_cl146, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ ('#form117' @ X2) 50.22/7.11 | (X2 @ '#sk7') 50.22/7.11 | ~ ('#form19') 50.22/7.11 | ('#sk2' @ ('#sk50' @ X2) @ ('#sk65' @ X2)))), 50.22/7.11 inference('ho_norm', [status(thm)], [zip_derived_cl129])). 50.22/7.11 thf(zip_derived_cl55, plain, 50.22/7.11 (( (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 50.22/7.11 ('#sk8' @ Y0)))))) 50.22/7.11 | ('#form14') 50.22/7.11 | ~ ('#form9'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 50.22/7.11 thf(zip_derived_cl62, plain, 50.22/7.11 (![X2 : a]: 50.22/7.11 ( ((((('#sk2' @ '#sk6' @ X2) | ('#sk1' @ '#sk6' @ X2))) => ('#sk8' @ 50.22/7.11 X2))) 50.22/7.11 | ~ ('#form9') 50.22/7.11 | ('#form14'))), 50.22/7.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl55])). 50.22/7.11 thf(zip_derived_cl73, plain, 50.22/7.11 (![X2 : a]: 50.22/7.11 (~ ((('#sk2' @ '#sk6' @ X2) | ('#sk1' @ '#sk6' @ X2))) 50.22/7.11 | ('#sk8' @ X2) 50.22/7.11 | ('#form14') 50.22/7.11 | ~ ('#form9'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 50.22/7.11 thf(zip_derived_cl89, plain, 50.22/7.11 (![X2 : a]: 50.22/7.11 (~ ('#sk2' @ '#sk6' @ X2) 50.22/7.11 | ~ ('#form9') 50.22/7.11 | ('#form14') 50.22/7.11 | ('#sk8' @ X2))), 50.22/7.11 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl73])). 50.22/7.11 thf(zip_derived_cl23, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.22/7.11 (X2 @ Y1))))))))))) => 50.22/7.11 (X2 @ '#sk7'))) 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y1) | 50.22/7.11 ('#sk1' @ '#sk3' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk4')))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))) 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & ('#sk2' @ 50.22/7.11 Y1 @ Y2))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk7')))))))), 50.22/7.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 50.22/7.11 thf(zip_derived_cl24, plain, 50.22/7.11 (( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.22/7.11 ('#sk8' @ Y1))))))))))) => 50.22/7.11 ('#sk8' @ '#sk7'))) 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk3' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk4')))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))) 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & ('#sk2' @ 50.22/7.11 Y1 @ Y2))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk7')))))))), 50.22/7.11 inference('triggered_bool_instantiation', [status(thm)], 50.22/7.11 [zip_derived_cl23])). 50.22/7.11 thf(zip_derived_cl32, plain, 50.22/7.11 ((~ ('#form14') 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk3' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk4')))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl202, plain, 50.22/7.11 (( ('#form14') 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & ('#sk2' @ 50.22/7.11 Y1 @ Y2))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk7')))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))) 50.22/7.11 | (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.22/7.11 ('#sk8' @ Y1))))))))))) => 50.22/7.11 ('#sk8' @ '#sk7'))))), 50.22/7.11 inference('renaming', [status(thm)], [zip_derived_cl24, zip_derived_cl32])). 50.22/7.11 thf(zip_derived_cl40, plain, 50.22/7.11 ((~ ('#form19') 50.22/7.11 | (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & ('#sk2' @ 50.22/7.11 Y1 @ Y2))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk7')))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl203, plain, 50.22/7.11 (( ('#form19') 50.22/7.11 | (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.22/7.11 ('#sk8' @ Y1))))))))))) => 50.22/7.11 ('#sk8' @ '#sk7'))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))) 50.22/7.11 | ('#form14'))), 50.22/7.11 inference('renaming', [status(thm)], 50.22/7.11 [zip_derived_cl202, zip_derived_cl40])). 50.22/7.11 thf(zip_derived_cl26, plain, 50.22/7.11 (( ('#form9') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl204, plain, 50.22/7.11 ((~ ('#form9') 50.22/7.11 | ('#form14') 50.22/7.11 | (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.22/7.11 ('#sk8' @ Y1))))))))))) => 50.22/7.11 ('#sk8' @ '#sk7'))) 50.22/7.11 | ('#form19'))), 50.22/7.11 inference('renaming', [status(thm)], 50.22/7.11 [zip_derived_cl203, zip_derived_cl26])). 50.22/7.11 thf(zip_derived_cl205, plain, 50.22/7.11 ((~ (((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.22/7.11 ('#sk8' @ Y1))))))))))) 50.22/7.11 | ('#sk8' @ '#sk7') 50.22/7.11 | ('#form19') 50.22/7.11 | ('#form14') 50.22/7.11 | ~ ('#form9'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl204])). 50.22/7.11 thf(zip_derived_cl47, plain, 50.22/7.11 ((~ ('#sk8' @ '#sk7') | ~ ('#form9') | ('#form14'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 50.22/7.11 thf(zip_derived_cl206, plain, 50.22/7.11 ((~ ('#form9') 50.22/7.11 | ('#form14') 50.22/7.11 | ('#form19') 50.22/7.11 | ~ (((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.22/7.11 ('#sk8' @ Y1))))))))))))), 50.22/7.11 inference('clc', [status(thm)], [zip_derived_cl205, zip_derived_cl47])). 50.22/7.11 thf(zip_derived_cl207, plain, 50.22/7.11 ((~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.22/7.11 ('#sk8' @ Y1))))))))) 50.22/7.11 | ('#form19') 50.22/7.11 | ('#form14') 50.22/7.11 | ~ ('#form9'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl206])). 50.22/7.11 thf(zip_derived_cl208, plain, 50.22/7.11 ((~ ((('#sk1' @ '#sk6' @ ('#sk60' @ '#sk8')) => ('#sk8' @ 50.22/7.11 ('#sk60' @ '#sk8')))) 50.22/7.11 | ~ ('#form9') 50.22/7.11 | ('#form14') 50.22/7.11 | ('#form19') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.22/7.11 ('#sk8' @ Y1))))))))))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl207])). 50.22/7.11 thf(zip_derived_cl210, plain, 50.22/7.11 ((~ ('#sk8' @ ('#sk60' @ '#sk8')) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.22/7.11 ('#sk8' @ Y1))))))))) 50.22/7.11 | ('#form19') 50.22/7.11 | ('#form14') 50.22/7.11 | ~ ('#form9'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl208])). 50.22/7.11 thf(zip_derived_cl212, plain, 50.22/7.11 ((~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk8' @ ('#sk107' @ '#sk8')) & ('#sk1' @ 50.22/7.11 ('#sk107' @ '#sk8') @ Y0))) => 50.22/7.11 ('#sk8' @ Y0)))))) 50.22/7.11 | ~ ('#form9') 50.22/7.11 | ('#form14') 50.22/7.11 | ('#form19') 50.22/7.11 | ~ ('#sk8' @ ('#sk60' @ '#sk8')))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl210])). 50.22/7.11 thf(zip_derived_cl214, plain, 50.22/7.11 ((~ ((((('#sk8' @ ('#sk107' @ '#sk8')) & ('#sk1' @ ('#sk107' @ '#sk8') @ 50.22/7.11 ('#sk143' @ '#sk8')))) => 50.22/7.11 ('#sk8' @ ('#sk143' @ '#sk8')))) 50.22/7.11 | ~ ('#sk8' @ ('#sk60' @ '#sk8')) 50.22/7.11 | ('#form19') 50.22/7.11 | ('#form14') 50.22/7.11 | ~ ('#form9'))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl212])). 50.22/7.11 thf(zip_derived_cl218, plain, 50.22/7.11 ((~ ('#sk8' @ ('#sk143' @ '#sk8')) 50.22/7.11 | ~ ('#form9') 50.22/7.11 | ('#form14') 50.22/7.11 | ('#form19') 50.22/7.11 | ~ ('#sk8' @ ('#sk60' @ '#sk8')))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl214])). 50.22/7.11 thf(zip_derived_cl217, plain, 50.22/7.11 (( ((('#sk8' @ ('#sk107' @ '#sk8')) & ('#sk1' @ ('#sk107' @ '#sk8') @ 50.22/7.11 ('#sk143' @ '#sk8')))) 50.22/7.11 | ~ ('#form9') 50.22/7.11 | ('#form14') 50.22/7.11 | ('#form19') 50.22/7.11 | ~ ('#sk8' @ ('#sk60' @ '#sk8')))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl214])). 50.22/7.11 thf(zip_derived_cl221, plain, 50.22/7.11 (( ('#sk8' @ ('#sk107' @ '#sk8')) 50.22/7.11 | ~ ('#sk8' @ ('#sk60' @ '#sk8')) 50.22/7.11 | ('#form19') 50.22/7.11 | ('#form14') 50.22/7.11 | ~ ('#form9'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl217])). 50.22/7.11 thf(zip_derived_cl222, plain, 50.22/7.11 (( ('#sk1' @ ('#sk107' @ '#sk8') @ ('#sk143' @ '#sk8')) 50.22/7.11 | ~ ('#sk8' @ ('#sk60' @ '#sk8')) 50.22/7.11 | ('#form19') 50.22/7.11 | ('#form14') 50.22/7.11 | ~ ('#form9'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl217])). 50.22/7.11 thf(zip_derived_cl209, plain, 50.22/7.11 (( ('#sk1' @ '#sk6' @ ('#sk60' @ '#sk8')) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 50.22/7.11 ('#sk8' @ Y1))))))))) 50.22/7.11 | ('#form19') 50.22/7.11 | ('#form14') 50.22/7.11 | ~ ('#form9'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl208])). 50.22/7.11 thf(zip_derived_cl211, plain, 50.22/7.11 ((~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk8' @ ('#sk107' @ '#sk8')) & ('#sk1' @ 50.22/7.11 ('#sk107' @ '#sk8') @ Y0))) => 50.22/7.11 ('#sk8' @ Y0)))))) 50.22/7.11 | ~ ('#form9') 50.22/7.11 | ('#form14') 50.22/7.11 | ('#form19') 50.22/7.11 | ('#sk1' @ '#sk6' @ ('#sk60' @ '#sk8')))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl209])). 50.22/7.11 thf(zip_derived_cl213, plain, 50.22/7.11 ((~ ((((('#sk8' @ ('#sk107' @ '#sk8')) & ('#sk1' @ ('#sk107' @ '#sk8') @ 50.22/7.11 ('#sk143' @ '#sk8')))) => 50.22/7.11 ('#sk8' @ ('#sk143' @ '#sk8')))) 50.22/7.11 | ('#sk1' @ '#sk6' @ ('#sk60' @ '#sk8')) 50.22/7.11 | ('#form19') 50.22/7.11 | ('#form14') 50.22/7.11 | ~ ('#form9'))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl211])). 50.22/7.11 thf(zip_derived_cl216, plain, 50.22/7.11 ((~ ('#sk8' @ ('#sk143' @ '#sk8')) 50.22/7.11 | ~ ('#form9') 50.22/7.11 | ('#form14') 50.22/7.11 | ('#form19') 50.22/7.11 | ('#sk1' @ '#sk6' @ ('#sk60' @ '#sk8')))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl213])). 50.22/7.11 thf(zip_derived_cl215, plain, 50.22/7.11 (( ((('#sk8' @ ('#sk107' @ '#sk8')) & ('#sk1' @ ('#sk107' @ '#sk8') @ 50.22/7.11 ('#sk143' @ '#sk8')))) 50.22/7.11 | ~ ('#form9') 50.22/7.11 | ('#form14') 50.22/7.11 | ('#form19') 50.22/7.11 | ('#sk1' @ '#sk6' @ ('#sk60' @ '#sk8')))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl213])). 50.22/7.11 thf(zip_derived_cl219, plain, 50.22/7.11 (( ('#sk8' @ ('#sk107' @ '#sk8')) 50.22/7.11 | ('#sk1' @ '#sk6' @ ('#sk60' @ '#sk8')) 50.22/7.11 | ('#form19') 50.22/7.11 | ('#form14') 50.22/7.11 | ~ ('#form9'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl215])). 50.22/7.11 thf(zip_derived_cl220, plain, 50.22/7.11 (( ('#sk1' @ ('#sk107' @ '#sk8') @ ('#sk143' @ '#sk8')) 50.22/7.11 | ('#sk1' @ '#sk6' @ ('#sk60' @ '#sk8')) 50.22/7.11 | ('#form19') 50.22/7.11 | ('#form14') 50.22/7.11 | ~ ('#form9'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl215])). 50.22/7.11 thf(zip_derived_cl90, plain, 50.22/7.11 (![X2 : a]: 50.22/7.11 (~ ('#sk1' @ '#sk6' @ X2) 50.22/7.11 | ~ ('#form9') 50.22/7.11 | ('#form14') 50.22/7.11 | ('#sk8' @ X2))), 50.22/7.11 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl73])). 50.22/7.11 thf(zip_derived_cl26, plain, 50.22/7.11 (( ('#form9') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (Y3 @ 50.22/7.11 Y4) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y1)))))) & 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y1 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y1 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2)))))))) => 50.22/7.11 (((!!) @ (^[Y3 : a > $o]: 50.22/7.11 (((((((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (!!) @ ( 50.22/7.11 ^[Y5 : a]: 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y4 @ 50.22/7.11 Y5) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y4 @ Y5))) & 50.22/7.11 (Y3 @ Y4))) => 50.22/7.11 (Y3 @ Y5))))))))) & 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (( 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk2' @ 50.22/7.11 Y0 @ Y4))) => 50.22/7.11 (Y3 @ Y4)))))))) => 50.22/7.11 (Y3 @ Y2))))))))))))))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl27, plain, 50.22/7.11 ((~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((((((!!) @ (^[Y2 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y3 : a]: 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (( 50.22/7.11 (Y2 @ 50.22/7.11 Y3) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y3 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y3 @ Y4))))) => 50.22/7.11 (Y2 @ Y4))))))))) & 50.22/7.11 (((!!) @ (^[Y3 : a]: 50.22/7.11 ((((('#sk1' @ 50.22/7.11 '#sk10' @ 50.22/7.11 Y3) | 50.22/7.11 ('#sk2' @ 50.22/7.11 '#sk10' @ 50.22/7.11 Y3))) => 50.22/7.11 (Y2 @ Y3)))))))) => 50.22/7.11 (Y2 @ Y0)))))) & 50.22/7.11 (((!!) @ (^[Y2 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y3 : a]: 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 ( 50.22/7.11 ( 50.22/7.11 (( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y3 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y3 @ Y4))) & 50.22/7.11 (Y2 @ Y3))) => 50.22/7.11 (Y2 @ Y4))))))))) & 50.22/7.11 (((!!) @ (^[Y3 : a]: 50.22/7.11 ((((('#sk2' @ 50.22/7.11 Y0 @ 50.22/7.11 Y3) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y0 @ Y3))) => 50.22/7.11 (Y2 @ Y3)))))))) => 50.22/7.11 (Y2 @ Y1)))))))) => 50.22/7.11 (((!!) @ (^[Y2 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y3 : a]: 50.22/7.11 (((!!) @ ( 50.22/7.11 ^[Y4 : a]: 50.22/7.11 (((( 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y3 @ 50.22/7.11 Y4) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y3 @ Y4))) & 50.22/7.11 (Y2 @ Y3))) => 50.22/7.11 (Y2 @ Y4))))))))) & 50.22/7.11 (((!!) @ (^[Y3 : a]: 50.22/7.11 ((((('#sk1' @ 50.22/7.11 '#sk10' @ 50.22/7.11 Y3) | 50.22/7.11 ('#sk2' @ 50.22/7.11 '#sk10' @ 50.22/7.11 Y3))) => 50.22/7.11 (Y2 @ Y3)))))))) => 50.22/7.11 (Y2 @ Y1)))))))))))))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl26])). 50.22/7.11 thf(zip_derived_cl38, plain, 50.22/7.11 ((~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((((((!!) @ (^[Y1 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y2 : a]: 50.22/7.11 (((!!) @ (^[Y3 : a]: 50.22/7.11 (((((Y1 @ 50.22/7.11 Y2) & 50.22/7.11 (( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y2 @ 50.22/7.11 Y3) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y2 @ Y3))))) => 50.22/7.11 (Y1 @ Y3))))))))) & 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ 50.22/7.11 Y2) | ('#sk2' @ 50.22/7.11 '#sk10' @ Y2))) => 50.22/7.11 (Y1 @ Y2)))))))) => 50.22/7.11 (Y1 @ '#sk15')))))) & 50.22/7.11 (((!!) @ (^[Y1 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y2 : a]: 50.22/7.11 (((!!) @ (^[Y3 : a]: 50.22/7.11 (((((( 50.22/7.11 ('#sk2' @ 50.22/7.11 Y2 @ 50.22/7.11 Y3) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y2 @ Y3))) & 50.22/7.11 (Y1 @ Y2))) => 50.22/7.11 (Y1 @ Y3))))))))) & 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 ((((('#sk2' @ '#sk15' @ 50.22/7.11 Y2) | ('#sk1' @ 50.22/7.11 '#sk15' @ Y2))) => 50.22/7.11 (Y1 @ Y2)))))))) => 50.22/7.11 (Y1 @ Y0)))))))) => 50.22/7.11 (((!!) @ (^[Y1 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y2 : a]: 50.22/7.11 (((!!) @ (^[Y3 : a]: 50.22/7.11 ((((((('#sk2' @ 50.22/7.11 Y2 @ 50.22/7.11 Y3) | 50.22/7.11 ('#sk1' @ 50.22/7.11 Y2 @ Y3))) & 50.22/7.11 (Y1 @ Y2))) => 50.22/7.11 (Y1 @ Y3))))))))) & 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ 50.22/7.11 Y2) | ('#sk2' @ 50.22/7.11 '#sk10' @ Y2))) => 50.22/7.11 (Y1 @ Y2)))))))) => 50.22/7.11 (Y1 @ Y0))))))))))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl27])). 50.22/7.11 thf(zip_derived_cl48, plain, 50.22/7.11 ((~ (((((((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ 50.22/7.11 Y2) | ('#sk1' @ 50.22/7.11 Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y1) | 50.22/7.11 ('#sk2' @ '#sk10' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk15')))))) & 50.22/7.11 (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 ((((((('#sk2' @ Y1 @ 50.22/7.11 Y2) | ('#sk1' @ 50.22/7.11 Y1 @ Y2))) & 50.22/7.11 (Y0 @ Y1))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk15' @ Y1) | 50.22/7.11 ('#sk1' @ '#sk15' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk23')))))))) => 50.22/7.11 (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 ((((((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))) & 50.22/7.11 (Y0 @ Y1))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y1) | 50.22/7.11 ('#sk2' @ '#sk10' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk23')))))))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl38])). 50.22/7.11 thf(zip_derived_cl56, plain, 50.22/7.11 (( (((((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y1) | ('#sk2' @ 50.22/7.11 '#sk10' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk15')))))) & 50.22/7.11 (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 ((((((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))) & 50.22/7.11 (Y0 @ Y1))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk15' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk15' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk23')))))))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 50.22/7.11 thf(zip_derived_cl64, plain, 50.22/7.11 (( (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 ((((((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))) & 50.22/7.11 (Y0 @ Y1))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk2' @ '#sk15' @ Y1) | ('#sk1' @ 50.22/7.11 '#sk15' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk23')))))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl56])). 50.22/7.11 thf(zip_derived_cl78, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( (((((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.22/7.11 Y0 @ Y1))) & 50.22/7.11 (X2 @ Y0))) => 50.22/7.11 (X2 @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ 50.22/7.11 Y0))) => 50.22/7.11 (X2 @ Y0)))))))) => 50.22/7.11 (X2 @ '#sk23'))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl64])). 50.22/7.11 thf(zip_derived_cl79, plain, 50.22/7.11 (( (((((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.22/7.11 Y1))) & 50.22/7.11 ('#sk43' @ Y0))) => 50.22/7.11 ('#sk43' @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 50.22/7.11 ('#sk43' @ Y0)))))))) => 50.22/7.11 ('#sk43' @ '#sk23'))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('triggered_bool_instantiation', [status(thm)], 50.22/7.11 [zip_derived_cl78])). 50.22/7.11 thf(zip_derived_cl334, plain, 50.22/7.11 ((~ (((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.22/7.11 Y1))) & 50.22/7.11 ('#sk43' @ Y0))) => 50.22/7.11 ('#sk43' @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 50.22/7.11 ('#sk43' @ Y0)))))))) 50.22/7.11 | ('#sk43' @ '#sk23') 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])). 50.22/7.11 thf(zip_derived_cl57, plain, 50.22/7.11 ((~ (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 ((((((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))) & 50.22/7.11 (Y0 @ Y1))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y1) | ('#sk2' @ 50.22/7.11 '#sk10' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk23')))))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 50.22/7.11 thf(zip_derived_cl68, plain, 50.22/7.11 ((~ (((((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.22/7.11 Y0 @ Y1))) & 50.22/7.11 ('#sk43' @ Y0))) => 50.22/7.11 ('#sk43' @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.22/7.11 ('#sk43' @ Y0)))))))) => 50.22/7.11 ('#sk43' @ '#sk23'))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl57])). 50.22/7.11 thf(zip_derived_cl83, plain, ((~ ('#sk43' @ '#sk23') | ('#form9'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 50.22/7.11 thf(zip_derived_cl335, plain, 50.22/7.11 (( ('#form9') 50.22/7.11 | ~ (((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.22/7.11 Y0 @ Y1))) & 50.22/7.11 ('#sk43' @ Y0))) => 50.22/7.11 ('#sk43' @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 50.22/7.11 ('#sk43' @ Y0)))))))))), 50.22/7.11 inference('clc', [status(thm)], [zip_derived_cl334, zip_derived_cl83])). 50.22/7.11 thf(zip_derived_cl336, plain, 50.22/7.11 ((~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 50.22/7.11 ('#sk43' @ Y0))) => 50.22/7.11 ('#sk43' @ Y1))))))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 50.22/7.11 ('#sk43' @ Y0)))))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl335])). 50.22/7.11 thf(zip_derived_cl78, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( (((((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.22/7.11 Y0 @ Y1))) & 50.22/7.11 (X2 @ Y0))) => 50.22/7.11 (X2 @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ 50.22/7.11 Y0))) => 50.22/7.11 (X2 @ Y0)))))))) => 50.22/7.11 (X2 @ '#sk23'))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl64])). 50.22/7.11 thf(zip_derived_cl92, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.22/7.11 Y0 @ Y1))) & 50.22/7.11 (X2 @ Y0))) => 50.22/7.11 (X2 @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))) 50.22/7.11 | (X2 @ '#sk23') 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 50.22/7.11 thf(zip_derived_cl106, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.22/7.11 Y1))) & 50.22/7.11 (X2 @ Y0))) => 50.22/7.11 (X2 @ Y1))))))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))) 50.22/7.11 | ('#form9') 50.22/7.11 | (X2 @ '#sk23'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl92])). 50.22/7.11 thf(zip_derived_cl123, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((((('#sk2' @ ('#sk138' @ X2) @ Y0) | ('#sk1' @ 50.22/7.11 ('#sk138' @ X2) @ Y0))) & 50.22/7.11 (X2 @ ('#sk138' @ X2)))) => 50.22/7.11 (X2 @ Y0)))))) 50.22/7.11 | (X2 @ '#sk23') 50.22/7.11 | ('#form9') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl106])). 50.22/7.11 thf(zip_derived_cl137, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ ((((((('#sk2' @ ('#sk138' @ X2) @ ('#sk187' @ X2)) | ('#sk1' @ 50.22/7.11 ('#sk138' @ X2) @ ('#sk187' @ X2)))) & 50.22/7.11 (X2 @ ('#sk138' @ X2)))) => 50.22/7.11 (X2 @ ('#sk187' @ X2)))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))) 50.22/7.11 | ('#form9') 50.22/7.11 | (X2 @ '#sk23'))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl123])). 50.22/7.11 thf(zip_derived_cl150, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (X2 @ ('#sk187' @ X2)) 50.22/7.11 | (X2 @ '#sk23') 50.22/7.11 | ('#form9') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])). 50.22/7.11 thf(zip_derived_cl163, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#form264' @ X2) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl337, plain, 50.22/7.11 ((~ ('#form264' @ '#sk43') 50.22/7.11 | ('#form9') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.22/7.11 Y1))) & 50.22/7.11 ('#sk43' @ Y0))) => 50.22/7.11 ('#sk43' @ Y1))))))))))), 50.22/7.11 inference('renaming', [status(thm)], 50.22/7.11 [zip_derived_cl336, zip_derived_cl163])). 50.22/7.11 thf(zip_derived_cl338, plain, 50.22/7.11 ((~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((((('#sk2' @ ('#sk138' @ '#sk43') @ Y0) | ('#sk1' @ 50.22/7.11 ('#sk138' @ '#sk43') @ Y0))) & 50.22/7.11 ('#sk43' @ ('#sk138' @ '#sk43')))) => 50.22/7.11 ('#sk43' @ Y0)))))) 50.22/7.11 | ('#form9') 50.22/7.11 | ~ ('#form264' @ '#sk43'))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl337])). 50.22/7.11 thf(zip_derived_cl339, plain, 50.22/7.11 ((~ ((((((('#sk2' @ ('#sk138' @ '#sk43') @ ('#sk187' @ '#sk43')) | 50.22/7.11 ('#sk1' @ ('#sk138' @ '#sk43') @ ('#sk187' @ '#sk43')))) & 50.22/7.11 ('#sk43' @ ('#sk138' @ '#sk43')))) => 50.22/7.11 ('#sk43' @ ('#sk187' @ '#sk43')))) 50.22/7.11 | ~ ('#form264' @ '#sk43') 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl338])). 50.22/7.11 thf(zip_derived_cl341, plain, 50.22/7.11 ((~ ('#sk43' @ ('#sk187' @ '#sk43')) 50.22/7.11 | ('#form9') 50.22/7.11 | ~ ('#form264' @ '#sk43'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl339])). 50.22/7.11 thf(zip_derived_cl121, plain, 50.22/7.11 (![X2 : a, X4 : a]: 50.22/7.11 (~ ('#sk1' @ X2 @ X4) 50.22/7.11 | ('#sk8' @ X4) 50.22/7.11 | ~ ('#form9') 50.22/7.11 | ('#form14') 50.22/7.11 | ~ ('#sk8' @ X2))), 50.22/7.11 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl104])). 50.22/7.11 thf(zip_derived_cl340, plain, 50.22/7.11 (( ((((('#sk2' @ ('#sk138' @ '#sk43') @ ('#sk187' @ '#sk43')) | 50.22/7.11 ('#sk1' @ ('#sk138' @ '#sk43') @ ('#sk187' @ '#sk43')))) & 50.22/7.11 ('#sk43' @ ('#sk138' @ '#sk43')))) 50.22/7.11 | ('#form9') 50.22/7.11 | ~ ('#form264' @ '#sk43'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl339])). 50.22/7.11 thf(zip_derived_cl343, plain, 50.22/7.11 (( ('#sk43' @ ('#sk138' @ '#sk43')) 50.22/7.11 | ~ ('#form264' @ '#sk43') 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl340])). 50.22/7.11 thf(zip_derived_cl342, plain, 50.22/7.11 (( ((('#sk2' @ ('#sk138' @ '#sk43') @ ('#sk187' @ '#sk43')) | ('#sk1' @ 50.22/7.11 ('#sk138' @ '#sk43') @ ('#sk187' @ '#sk43')))) 50.22/7.11 | ~ ('#form264' @ '#sk43') 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl340])). 50.22/7.11 thf(zip_derived_cl344, plain, 50.22/7.11 (( ('#sk2' @ ('#sk138' @ '#sk43') @ ('#sk187' @ '#sk43')) 50.22/7.11 | ('#sk1' @ ('#sk138' @ '#sk43') @ ('#sk187' @ '#sk43')) 50.22/7.11 | ('#form9') 50.22/7.11 | ~ ('#form264' @ '#sk43'))), 50.22/7.11 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl342])). 50.22/7.11 thf(zip_derived_cl163, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#form264' @ X2) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl164, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ ((((('#sk2' @ '#sk15' @ ('#sk265' @ X2)) | ('#sk1' @ '#sk15' @ 50.22/7.11 ('#sk265' @ X2)))) => 50.22/7.11 (X2 @ ('#sk265' @ X2)))) 50.22/7.11 | ('#form264' @ X2))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl163])). 50.22/7.11 thf(zip_derived_cl175, plain, 50.22/7.11 (![X2 : a > $o]: (~ (X2 @ ('#sk265' @ X2)) | ('#form264' @ X2))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])). 50.22/7.11 thf(zip_derived_cl174, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ((('#sk2' @ '#sk15' @ ('#sk265' @ X2)) | ('#sk1' @ '#sk15' @ 50.22/7.11 ('#sk265' @ X2)))) 50.22/7.11 | ('#form264' @ X2))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])). 50.22/7.11 thf(zip_derived_cl183, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#sk2' @ '#sk15' @ ('#sk265' @ X2)) 50.22/7.11 | ('#sk1' @ '#sk15' @ ('#sk265' @ X2)) 50.22/7.11 | ('#form264' @ X2))), 50.22/7.11 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl174])). 50.22/7.11 thf(zip_derived_cl63, plain, 50.22/7.11 (( (((!!) @ (^[Y0 : a > $o]: 50.22/7.11 (((((((!!) @ (^[Y1 : a]: 50.22/7.11 (((!!) @ (^[Y2 : a]: 50.22/7.11 (((((Y0 @ Y1) & 50.22/7.11 ((('#sk2' @ Y1 @ Y2) | 50.22/7.11 ('#sk1' @ Y1 @ Y2))))) => 50.22/7.11 (Y0 @ Y2))))))))) & 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y1) | ('#sk2' @ 50.22/7.11 '#sk10' @ Y1))) => 50.22/7.11 (Y0 @ Y1)))))))) => 50.22/7.11 (Y0 @ '#sk15')))))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl56])). 50.22/7.11 thf(zip_derived_cl74, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( (((((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((((X2 @ Y0) & 50.22/7.11 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.22/7.11 Y0 @ Y1))))) => 50.22/7.11 (X2 @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ 50.22/7.11 Y0))) => 50.22/7.11 (X2 @ Y0)))))))) => 50.22/7.11 (X2 @ '#sk15'))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 50.22/7.11 thf(zip_derived_cl91, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((((X2 @ Y0) & 50.22/7.11 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 50.22/7.11 Y0 @ Y1))))) => 50.22/7.11 (X2 @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))) 50.22/7.11 | (X2 @ '#sk15') 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])). 50.22/7.11 thf(zip_derived_cl105, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 (((((X2 @ Y0) & 50.22/7.11 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.22/7.11 Y1))))) => 50.22/7.11 (X2 @ Y1))))))))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))) 50.22/7.11 | ('#form9') 50.22/7.11 | (X2 @ '#sk15'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl91])). 50.22/7.11 thf(zip_derived_cl122, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (((!!) @ (^[Y0 : a]: 50.22/7.11 (((((X2 @ ('#sk42' @ X2)) & 50.22/7.11 ((('#sk2' @ ('#sk42' @ X2) @ Y0) | ('#sk1' @ 50.22/7.11 ('#sk42' @ X2) @ Y0))))) => 50.22/7.11 (X2 @ Y0)))))) 50.22/7.11 | (X2 @ '#sk15') 50.22/7.11 | ('#form9') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl105])). 50.22/7.11 thf(zip_derived_cl136, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (((((X2 @ ('#sk42' @ X2)) & 50.22/7.11 ((('#sk2' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) | ('#sk1' @ 50.22/7.11 ('#sk42' @ X2) @ ('#sk56' @ X2)))))) => 50.22/7.11 (X2 @ ('#sk56' @ X2)))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))) 50.22/7.11 | ('#form9') 50.22/7.11 | (X2 @ '#sk15'))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl122])). 50.22/7.11 thf(zip_derived_cl148, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (X2 @ ('#sk56' @ X2)) 50.22/7.11 | (X2 @ '#sk15') 50.22/7.11 | ('#form9') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl136])). 50.22/7.11 thf(zip_derived_cl148, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ (X2 @ ('#sk56' @ X2)) 50.22/7.11 | (X2 @ '#sk15') 50.22/7.11 | ('#form9') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl136])). 50.22/7.11 thf(zip_derived_cl158, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#form254' @ X2) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl160, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ ('#form254' @ X2) 50.22/7.11 | ('#form9') 50.22/7.11 | (X2 @ '#sk15') 50.22/7.11 | ~ (X2 @ ('#sk56' @ X2)))), 50.22/7.11 inference('renaming', [status(thm)], 50.22/7.11 [zip_derived_cl148, zip_derived_cl158])). 50.22/7.11 thf(zip_derived_cl82, plain, 50.22/7.11 (( (((((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.22/7.11 Y1))) & 50.22/7.11 ('#sk43' @ Y0))) => 50.22/7.11 ('#sk43' @ Y1))))))))) & 50.22/7.11 (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.22/7.11 ('#sk43' @ Y0)))))))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 50.22/7.11 thf(zip_derived_cl93, plain, 50.22/7.11 (( (((!!) @ (^[Y0 : a]: 50.22/7.11 (((!!) @ (^[Y1 : a]: 50.22/7.11 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 50.22/7.11 ('#sk43' @ Y0))) => 50.22/7.11 ('#sk43' @ Y1))))))))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl82])). 50.22/7.11 thf(zip_derived_cl107, plain, 50.22/7.11 (![X2 : a]: 50.22/7.11 ( (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) & 50.22/7.11 ('#sk43' @ X2))) => 50.22/7.11 ('#sk43' @ Y0)))))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl93])). 50.22/7.11 thf(zip_derived_cl124, plain, 50.22/7.11 (![X2 : a, X4 : a]: 50.22/7.11 ( ((((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk43' @ X2))) => 50.22/7.11 ('#sk43' @ X4))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl107])). 50.22/7.11 thf(zip_derived_cl138, plain, 50.22/7.11 (![X2 : a, X4 : a]: 50.22/7.11 (~ ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk43' @ X2))) 50.22/7.11 | ('#sk43' @ X4) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl124])). 50.22/7.11 thf(zip_derived_cl151, plain, 50.22/7.11 (![X2 : a, X4 : a]: 50.22/7.11 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 50.22/7.11 | ~ ('#sk43' @ X2) 50.22/7.11 | ('#form9') 50.22/7.11 | ('#sk43' @ X4))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl138])). 50.22/7.11 thf(zip_derived_cl167, plain, 50.22/7.11 (![X2 : a, X4 : a]: 50.22/7.11 (~ ('#sk1' @ X2 @ X4) 50.22/7.11 | ('#sk43' @ X4) 50.22/7.11 | ('#form9') 50.22/7.11 | ~ ('#sk43' @ X2))), 50.22/7.11 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl151])). 50.22/7.11 thf(zip_derived_cl166, plain, 50.22/7.11 (![X2 : a, X4 : a]: 50.22/7.11 (~ ('#sk2' @ X2 @ X4) 50.22/7.11 | ('#sk43' @ X4) 50.22/7.11 | ('#form9') 50.22/7.11 | ~ ('#sk43' @ X2))), 50.22/7.11 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl151])). 50.22/7.11 thf(zip_derived_cl147, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( (((X2 @ ('#sk42' @ X2)) & 50.22/7.11 ((('#sk2' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) | ('#sk1' @ 50.22/7.11 ('#sk42' @ X2) @ ('#sk56' @ X2)))))) 50.22/7.11 | (X2 @ '#sk15') 50.22/7.11 | ('#form9') 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl136])). 50.22/7.11 thf(zip_derived_cl156, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( (X2 @ ('#sk42' @ X2)) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))) 50.22/7.11 | ('#form9') 50.22/7.11 | (X2 @ '#sk15'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl147])). 50.22/7.11 thf(zip_derived_cl158, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#form254' @ X2) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl168, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ ('#form254' @ (^[Y0 : a]: (X2 @ Y0))) 50.22/7.11 | (X2 @ '#sk15') 50.22/7.11 | ('#form9') 50.22/7.11 | (X2 @ ('#sk42' @ X2)))), 50.22/7.11 inference('renaming', [status(thm)], 50.22/7.11 [zip_derived_cl156, zip_derived_cl158])). 50.22/7.11 thf(zip_derived_cl176, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ ('#form254' @ X2) 50.22/7.11 | (X2 @ '#sk15') 50.22/7.11 | ('#form9') 50.22/7.11 | (X2 @ ('#sk42' @ X2)))), 50.22/7.11 inference('ho_norm', [status(thm)], [zip_derived_cl168])). 50.22/7.11 thf(zip_derived_cl157, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ((('#sk2' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) | ('#sk1' @ 50.22/7.11 ('#sk42' @ X2) @ ('#sk56' @ X2)))) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))) 50.22/7.11 | ('#form9') 50.22/7.11 | (X2 @ '#sk15'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl147])). 50.22/7.11 thf(zip_derived_cl158, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#form254' @ X2) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl169, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ ('#form254' @ (^[Y0 : a]: (X2 @ Y0))) 50.22/7.11 | (X2 @ '#sk15') 50.22/7.11 | ('#form9') 50.22/7.11 | ((('#sk2' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) | ('#sk1' @ 50.22/7.11 ('#sk42' @ X2) @ ('#sk56' @ X2)))))), 50.22/7.11 inference('renaming', [status(thm)], 50.22/7.11 [zip_derived_cl157, zip_derived_cl158])). 50.22/7.11 thf(zip_derived_cl177, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ ('#form254' @ X2) 50.22/7.11 | (X2 @ '#sk15') 50.22/7.11 | ('#form9') 50.22/7.11 | ((('#sk2' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) | ('#sk1' @ 50.22/7.11 ('#sk42' @ X2) @ ('#sk56' @ X2)))))), 50.22/7.11 inference('ho_norm', [status(thm)], [zip_derived_cl169])). 50.22/7.11 thf(zip_derived_cl178, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#sk2' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) 50.22/7.11 | ('#sk1' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) 50.22/7.11 | ('#form9') 50.22/7.11 | (X2 @ '#sk15') 50.22/7.11 | ~ ('#form254' @ X2))), 50.22/7.11 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl177])). 50.22/7.11 thf(zip_derived_cl158, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#form254' @ X2) 50.22/7.11 | ~ (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.22/7.11 (X2 @ Y0)))))))), 50.22/7.11 define([status(thm)])). 50.22/7.11 thf(zip_derived_cl159, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 (~ ((((('#sk1' @ '#sk10' @ ('#sk255' @ X2)) | ('#sk2' @ '#sk10' @ 50.22/7.11 ('#sk255' @ X2)))) => 50.22/7.11 (X2 @ ('#sk255' @ X2)))) 50.22/7.11 | ('#form254' @ X2))), 50.22/7.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl158])). 50.22/7.11 thf(zip_derived_cl170, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ((('#sk1' @ '#sk10' @ ('#sk255' @ X2)) | ('#sk2' @ '#sk10' @ 50.22/7.11 ('#sk255' @ X2)))) 50.22/7.11 | ('#form254' @ X2))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])). 50.22/7.11 thf(zip_derived_cl179, plain, 50.22/7.11 (![X2 : a > $o]: 50.22/7.11 ( ('#sk1' @ '#sk10' @ ('#sk255' @ X2)) 50.22/7.11 | ('#sk2' @ '#sk10' @ ('#sk255' @ X2)) 50.22/7.11 | ('#form254' @ X2))), 50.22/7.11 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl170])). 50.22/7.11 thf(zip_derived_cl171, plain, 50.22/7.11 (![X2 : a > $o]: (~ (X2 @ ('#sk255' @ X2)) | ('#form254' @ X2))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])). 50.22/7.11 thf(zip_derived_cl94, plain, 50.22/7.11 (( (((!!) @ (^[Y0 : a]: 50.22/7.11 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 50.22/7.11 ('#sk43' @ Y0)))))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl82])). 50.22/7.11 thf(zip_derived_cl108, plain, 50.22/7.11 (![X2 : a]: 50.22/7.11 ( ((((('#sk1' @ '#sk10' @ X2) | ('#sk2' @ '#sk10' @ X2))) => 50.22/7.11 ('#sk43' @ X2))) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])). 50.22/7.11 thf(zip_derived_cl125, plain, 50.22/7.11 (![X2 : a]: 50.22/7.11 (~ ((('#sk1' @ '#sk10' @ X2) | ('#sk2' @ '#sk10' @ X2))) 50.22/7.11 | ('#sk43' @ X2) 50.22/7.11 | ('#form9'))), 50.22/7.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 50.22/7.11 thf(zip_derived_cl139, plain, 50.22/7.11 (![X2 : a]: (~ ('#sk1' @ '#sk10' @ X2) | ('#form9') | ('#sk43' @ X2))), 50.22/7.11 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl125])). 50.22/7.11 thf(zip_derived_cl140, plain, 50.22/7.11 (![X2 : a]: (~ ('#sk2' @ '#sk10' @ X2) | ('#form9') | ('#sk43' @ X2))), 50.22/7.11 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl125])). 50.22/7.11 thf(zip_derived_cl9126, plain, ($false), 50.22/7.11 inference('eprover', [status(thm)], 50.22/7.11 [zip_derived_cl49, zip_derived_cl50, zip_derived_cl270, 50.22/7.11 zip_derived_cl271, zip_derived_cl273, zip_derived_cl115, 50.22/7.11 zip_derived_cl135, zip_derived_cl119, zip_derived_cl47, 50.22/7.11 zip_derived_cl120, zip_derived_cl31, zip_derived_cl30, 50.22/7.11 zip_derived_cl145, zip_derived_cl130, zip_derived_cl131, 50.22/7.11 zip_derived_cl146, zip_derived_cl89, zip_derived_cl218, 50.22/7.11 zip_derived_cl221, zip_derived_cl222, zip_derived_cl216, 50.22/7.11 zip_derived_cl219, zip_derived_cl220, zip_derived_cl90, 50.22/7.11 zip_derived_cl341, zip_derived_cl121, zip_derived_cl343, 50.22/7.11 zip_derived_cl344, zip_derived_cl175, zip_derived_cl183, 50.22/7.11 zip_derived_cl160, zip_derived_cl167, zip_derived_cl166, 50.22/7.11 zip_derived_cl176, zip_derived_cl178, zip_derived_cl179, 50.22/7.11 zip_derived_cl171, zip_derived_cl139, zip_derived_cl140])). 50.22/7.11 50.22/7.11 % SZS output end Refutation 50.22/7.11 50.22/7.11 50.22/7.12 % Terminating... 50.83/7.19 % Runner terminated. 50.83/7.20 % Zipperpin 1.5 exiting 50.83/7.21 EOF