0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.9fOaJKddQF true 0.13/0.34 % Computer : n008.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1200 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Jul 13 10:23:16 EDT 2021 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 120 s 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.49/0.62 % Total configuration time : 828 0.49/0.62 % Estimated wc time : 983 0.49/0.62 % Estimated cpu time (8 cpus) : 122.875 0.55/0.68 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 47s 0.55/0.70 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 47s 0.55/0.73 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 18s 0.55/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 47s 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 53s 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 41s 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 35s 31.65/4.61 % Solved by lams/20_acsne_simpl.sh. 31.65/4.61 % running E: timeout 13 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.9fOaJKddQF/e_inputc6bbdf --cpu-limit=11 --auto -s -p 31.65/4.61 % done 396 iterations in 3.780s 31.65/4.61 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 31.65/4.61 % SZS output start Refutation 31.65/4.61 thf(a_type, type, a: $tType). 31.65/4.61 thf('#sk179_type', type, '#sk179': (a > $o) > a). 31.65/4.61 thf('#form11_type', type, '#form11': $o). 31.65/4.61 thf('#sk12_type', type, '#sk12': a). 31.65/4.61 thf('#sk5_type', type, '#sk5': a > $o). 31.65/4.61 thf('#form81_type', type, '#form81': (a > $o) > $o). 31.65/4.61 thf('#sk27_type', type, '#sk27': (a > $o) > a). 31.65/4.61 thf('#sk4_type', type, '#sk4': a). 31.65/4.61 thf('#sk3_type', type, '#sk3': a). 31.65/4.61 thf('#form88_type', type, '#form88': (a > $o) > $o). 31.65/4.61 thf('#sk50_type', type, '#sk50': (a > $o) > a). 31.65/4.61 thf('#form231_type', type, '#form231': (a > $o) > $o). 31.65/4.61 thf('#sk8_type', type, '#sk8': a). 31.65/4.61 thf('#sk10_type', type, '#sk10': a). 31.65/4.61 thf('#form46_type', type, '#form46': $o). 31.65/4.61 thf('#sk7_type', type, '#sk7': a). 31.65/4.61 thf('#sk89_type', type, '#sk89': (a > $o) > a). 31.65/4.61 thf('#sk237_type', type, '#sk237': (a > $o) > a). 31.65/4.61 thf('#sk2_type', type, '#sk2': a > a > $o). 31.65/4.61 thf('#sk6_type', type, '#sk6': a). 31.65/4.61 thf('#sk20_type', type, '#sk20': a > $o). 31.65/4.61 thf('#sk16_type', type, '#sk16': a > $o). 31.65/4.61 thf('#sk1_type', type, '#sk1': a > a > $o). 31.65/4.61 thf('#sk125_type', type, '#sk125': (a > $o) > a). 31.65/4.61 thf('#sk39_type', type, '#sk39': (a > $o) > a). 31.65/4.61 thf('#sk129_type', type, '#sk129': (a > $o) > a). 31.65/4.61 thf('#form9_type', type, '#form9': $o). 31.65/4.61 thf('#sk82_type', type, '#sk82': (a > $o) > a). 31.65/4.61 thf('#sk214_type', type, '#sk214': (a > $o) > a). 31.65/4.61 thf('#sk232_type', type, '#sk232': (a > $o) > a). 31.65/4.61 thf('#sk61_type', type, '#sk61': (a > $o) > a). 31.65/4.61 thf('#sk133_type', type, '#sk133': (a > $o) > a). 31.65/4.61 thf(cTHM251D_pme, conjecture, 31.65/4.61 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 31.65/4.61 ( ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 31.65/4.61 ( ( ( ![Xq:( a > $o )]: 31.65/4.61 ( ( ( ![Xw:a]: 31.65/4.61 ( ( ( R @ Xy0 @ Xw ) | ( S @ Xy0 @ Xw ) ) => 31.65/4.61 ( Xq @ Xw ) ) ) & 31.65/4.61 ( ![Xu:a,Xv:a]: 31.65/4.61 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & 31.65/4.61 ( Xq @ Xu ) ) => 31.65/4.61 ( Xq @ Xv ) ) ) ) => 31.65/4.61 ( Xq @ Xz ) ) ) & 31.65/4.61 ( ![Xq:( a > $o )]: 31.65/4.61 ( ( ( ![Xw:a]: 31.65/4.61 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 31.65/4.61 ( Xq @ Xw ) ) ) & 31.65/4.61 ( ![Xu:a,Xv:a]: 31.65/4.61 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & 31.65/4.61 ( Xq @ Xu ) ) => 31.65/4.61 ( Xq @ Xv ) ) ) ) => 31.65/4.61 ( Xq @ Xy0 ) ) ) ) => 31.65/4.61 ( ![Xq:( a > $o )]: 31.65/4.61 ( ( ( ![Xw:a]: 31.65/4.61 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => ( Xq @ Xw ) ) ) & 31.65/4.61 ( ![Xu:a,Xv:a]: 31.65/4.61 ( ( ( Xq @ Xu ) & ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 31.65/4.61 ( Xq @ Xv ) ) ) ) => 31.65/4.61 ( Xq @ Xz ) ) ) ) ) & 31.65/4.61 ( ![Xx0:a,Xy0:a]: 31.65/4.61 ( ( ( ![Xq:( a > $o )]: 31.65/4.61 ( ( ( ![Xu:a,Xv:a]: 31.65/4.61 ( ( ( Xq @ Xu ) & ( S @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) & 31.65/4.61 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 31.65/4.61 ( Xq @ Xy0 ) ) ) | 31.65/4.61 ( ![Xq:( a > $o )]: 31.65/4.61 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 31.65/4.61 ( ![Xu:a,Xv:a]: 31.65/4.61 ( ( ( Xq @ Xu ) & ( R @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) ) => 31.65/4.61 ( Xq @ Xy0 ) ) ) ) => 31.65/4.61 ( ![Xq:( a > $o )]: 31.65/4.61 ( ( ( ![Xu:a,Xv:a]: 31.65/4.61 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 31.65/4.61 ( Xq @ Xv ) ) ) & 31.65/4.61 ( ![Xw:a]: 31.65/4.61 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 31.65/4.61 ( Xq @ Xy0 ) ) ) ) ) ) => 31.65/4.61 ( ![Xq:( a > $o )]: 31.65/4.61 ( ( ( ![Xu:a,Xv:a]: 31.65/4.61 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 31.65/4.61 ( Xq @ Xv ) ) ) & 31.65/4.61 ( ![Xw:a]: 31.65/4.61 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 31.65/4.61 ( Xq @ Xy ) ) ) ) => 31.65/4.61 ( ![Xq:( a > $o )]: 31.65/4.61 ( ( ( ![Xu:a,Xv:a]: 31.65/4.61 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 31.65/4.61 ( Xq @ Xv ) ) ) & 31.65/4.61 ( ![Xw:a]: 31.65/4.61 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 31.65/4.61 ( Xq @ Xy ) ) ) ))). 31.65/4.61 thf(zf_stmt_0, negated_conjecture, 31.65/4.61 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 31.65/4.61 ( ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 31.65/4.61 ( ( ( ![Xq:( a > $o )]: 31.65/4.61 ( ( ( ![Xw:a]: 31.65/4.61 ( ( ( R @ Xy0 @ Xw ) | ( S @ Xy0 @ Xw ) ) => 31.65/4.61 ( Xq @ Xw ) ) ) & 31.65/4.61 ( ![Xu:a,Xv:a]: 31.65/4.61 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & 31.65/4.61 ( Xq @ Xu ) ) => 31.65/4.61 ( Xq @ Xv ) ) ) ) => 31.65/4.61 ( Xq @ Xz ) ) ) & 31.65/4.61 ( ![Xq:( a > $o )]: 31.65/4.61 ( ( ( ![Xw:a]: 31.65/4.61 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 31.65/4.61 ( Xq @ Xw ) ) ) & 31.65/4.61 ( ![Xu:a,Xv:a]: 31.65/4.61 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & 31.65/4.61 ( Xq @ Xu ) ) => 31.65/4.61 ( Xq @ Xv ) ) ) ) => 31.65/4.61 ( Xq @ Xy0 ) ) ) ) => 31.65/4.61 ( ![Xq:( a > $o )]: 31.65/4.61 ( ( ( ![Xw:a]: 31.65/4.61 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 31.65/4.61 ( Xq @ Xw ) ) ) & 31.65/4.61 ( ![Xu:a,Xv:a]: 31.65/4.61 ( ( ( Xq @ Xu ) & 31.65/4.61 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 31.65/4.61 ( Xq @ Xv ) ) ) ) => 31.65/4.61 ( Xq @ Xz ) ) ) ) ) & 31.65/4.61 ( ![Xx0:a,Xy0:a]: 31.65/4.61 ( ( ( ![Xq:( a > $o )]: 31.65/4.61 ( ( ( ![Xu:a,Xv:a]: 31.65/4.61 ( ( ( Xq @ Xu ) & ( S @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) & 31.65/4.61 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 31.65/4.61 ( Xq @ Xy0 ) ) ) | 31.65/4.61 ( ![Xq:( a > $o )]: 31.65/4.61 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 31.65/4.61 ( ![Xu:a,Xv:a]: 31.65/4.61 ( ( ( Xq @ Xu ) & ( R @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) ) => 31.65/4.61 ( Xq @ Xy0 ) ) ) ) => 31.65/4.61 ( ![Xq:( a > $o )]: 31.65/4.61 ( ( ( ![Xu:a,Xv:a]: 31.65/4.61 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & 31.65/4.61 ( Xq @ Xu ) ) => 31.65/4.61 ( Xq @ Xv ) ) ) & 31.65/4.61 ( ![Xw:a]: 31.65/4.61 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 31.65/4.61 ( Xq @ Xw ) ) ) ) => 31.65/4.61 ( Xq @ Xy0 ) ) ) ) ) ) => 31.65/4.61 ( ![Xq:( a > $o )]: 31.65/4.61 ( ( ( ![Xu:a,Xv:a]: 31.65/4.61 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 31.65/4.61 ( Xq @ Xv ) ) ) & 31.65/4.61 ( ![Xw:a]: 31.65/4.61 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 31.65/4.61 ( Xq @ Xy ) ) ) ) => 31.65/4.61 ( ![Xq:( a > $o )]: 31.65/4.61 ( ( ( ![Xu:a,Xv:a]: 31.65/4.61 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 31.65/4.61 ( Xq @ Xv ) ) ) & 31.65/4.61 ( ![Xw:a]: 31.65/4.61 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 31.65/4.61 ( Xq @ Xy ) ) ) ) )), 31.65/4.61 inference('cnf.neg', [status(esa)], [cTHM251D_pme])). 31.65/4.61 thf(zip_derived_cl0, plain, 31.65/4.61 (~ (((!!) @ (^[Y0 : a > a > $o]: 31.65/4.61 (((!!) @ (^[Y1 : a > a > $o]: 31.65/4.61 (((!!) @ (^[Y2 : a]: 31.65/4.61 (((!!) @ (^[Y3 : a]: 31.65/4.61 (((((((((!!) @ ( 31.65/4.61 ^[Y4 : a]: 31.65/4.61 (((!!) @ ( 31.65/4.61 ^[Y5 : a]: 31.65/4.61 (( 31.65/4.61 (!!) @ ( 31.65/4.61 ^[Y6 : a]: 31.65/4.61 (( 31.65/4.61 (( 31.65/4.61 (( 31.65/4.61 (!!) @ ( 31.65/4.61 ^[Y7 : a > $o]: 31.65/4.61 (( 31.65/4.61 (( 31.65/4.61 (( 31.65/4.61 (!!) @ ( 31.65/4.61 ^[Y8 : a]: 31.65/4.61 (( 31.65/4.61 (( 31.65/4.61 (Y0 @ 31.65/4.61 Y5 @ 31.65/4.61 Y8) | 31.65/4.61 (Y1 @ 31.65/4.61 Y5 @ Y8))) => 31.65/4.61 (Y7 @ Y8)))))) & 31.65/4.61 (( 31.65/4.61 (!!) @ ( 31.65/4.61 ^[Y8 : a]: 31.65/4.61 (( 31.65/4.61 (!!) @ ( 31.65/4.61 ^[Y9 : a]: 31.65/4.61 (( 31.65/4.61 (( 31.65/4.61 (( 31.65/4.61 (Y0 @ 31.65/4.61 Y8 @ 31.65/4.61 Y9) | 31.65/4.61 (Y1 @ 31.65/4.61 Y8 @ Y9))) & 31.65/4.61 (Y7 @ Y8))) => 31.65/4.61 (Y7 @ Y9))))))))))) => 31.65/4.61 (Y7 @ Y6)))))) & 31.65/4.61 (( 31.65/4.61 (!!) @ ( 31.65/4.61 ^[Y7 : a > $o]: 31.65/4.61 (( 31.65/4.61 (( 31.65/4.61 (( 31.65/4.61 (!!) @ ( 31.65/4.61 ^[Y8 : a]: 31.65/4.61 (( 31.65/4.61 (( 31.65/4.61 (Y0 @ 31.65/4.61 Y4 @ 31.65/4.61 Y8) | 31.65/4.61 (Y1 @ 31.65/4.61 Y4 @ Y8))) => 31.65/4.61 (Y7 @ Y8)))))) & 31.65/4.61 (( 31.65/4.61 (!!) @ ( 31.65/4.61 ^[Y8 : a]: 31.65/4.61 (( 31.65/4.61 (!!) @ ( 31.65/4.61 ^[Y9 : a]: 31.65/4.61 (( 31.65/4.61 (( 31.65/4.61 (( 31.65/4.61 (Y0 @ 31.65/4.61 Y8 @ 31.65/4.61 Y9) | 31.65/4.61 (Y1 @ 31.65/4.61 Y8 @ Y9))) & 31.65/4.61 (Y7 @ Y8))) => 31.65/4.61 (Y7 @ Y9))))))))))) => 31.65/4.61 (Y7 @ Y5)))))))) => 31.65/4.61 (( 31.65/4.61 (!!) @ ( 31.65/4.61 ^[Y7 : a > $o]: 31.65/4.61 (( 31.65/4.61 (( 31.65/4.61 (( 31.65/4.61 (!!) @ ( 31.65/4.61 ^[Y8 : a]: 31.65/4.61 (( 31.65/4.61 (( 31.65/4.61 (Y1 @ 31.65/4.61 Y4 @ 31.65/4.61 Y8) | 31.65/4.61 (Y0 @ 31.65/4.61 Y4 @ Y8))) => 31.65/4.61 (Y7 @ Y8)))))) & 31.65/4.61 (( 31.65/4.61 (!!) @ ( 31.65/4.61 ^[Y8 : a]: 31.65/4.61 (( 31.65/4.61 (!!) @ ( 31.65/4.61 ^[Y9 : a]: 31.65/4.61 (( 31.65/4.62 (( 31.65/4.62 (Y7 @ 31.65/4.62 Y8) & 31.65/4.62 (( 31.65/4.62 (Y0 @ 31.65/4.62 Y8 @ 31.65/4.62 Y9) | 31.65/4.62 (Y1 @ 31.65/4.62 Y8 @ Y9))))) => 31.65/4.62 (Y7 @ Y9))))))))))) => 31.65/4.62 (Y7 @ Y6))))))))))))))))) & 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y8 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y6 @ 31.65/4.62 Y7) & 31.65/4.62 (Y1 @ 31.65/4.62 Y7 @ Y8))) => 31.65/4.62 (Y6 @ Y8))))))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (Y1 @ 31.65/4.62 Y4 @ 31.65/4.62 Y7) => 31.65/4.62 (Y6 @ Y7)))))))) => 31.65/4.62 (Y6 @ Y5)))))) | 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (Y0 @ 31.65/4.62 Y4 @ 31.65/4.62 Y7) => 31.65/4.62 (Y6 @ Y7)))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y8 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y6 @ 31.65/4.62 Y7) & 31.65/4.62 (Y0 @ 31.65/4.62 Y7 @ Y8))) => 31.65/4.62 (Y6 @ Y8))))))))))) => 31.65/4.62 (Y6 @ Y5)))))))) => 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y8 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y1 @ 31.65/4.62 Y7 @ 31.65/4.62 Y8) | 31.65/4.62 (Y0 @ 31.65/4.62 Y7 @ Y8))) & 31.65/4.62 (Y6 @ Y7))) => 31.65/4.62 (Y6 @ Y8))))))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y1 @ 31.65/4.62 Y4 @ 31.65/4.62 Y7) | 31.65/4.62 (Y0 @ 31.65/4.62 Y4 @ Y7))) => 31.65/4.62 (Y6 @ Y7)))))))) => 31.65/4.62 (Y6 @ Y5)))))))))))))))) => 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a > $o]: 31.65/4.62 (((((( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y1 @ 31.65/4.62 Y5 @ 31.65/4.62 Y6) | 31.65/4.62 (Y0 @ 31.65/4.62 Y5 @ Y6))) & 31.65/4.62 (Y4 @ Y5))) => 31.65/4.62 (Y4 @ Y6))))))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y0 @ 31.65/4.62 Y2 @ 31.65/4.62 Y5) | 31.65/4.62 (Y1 @ 31.65/4.62 Y2 @ Y5))) => 31.65/4.62 (Y4 @ Y5)))))))) => 31.65/4.62 (Y4 @ Y3)))))))) => 31.65/4.62 (((!!) @ (^[Y4 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y1 @ 31.65/4.62 Y5 @ 31.65/4.62 Y6) | 31.65/4.62 (Y0 @ 31.65/4.62 Y5 @ Y6))) & 31.65/4.62 (Y4 @ Y5))) => 31.65/4.62 (Y4 @ Y6))))))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y0 @ 31.65/4.62 Y2 @ 31.65/4.62 Y5) | 31.65/4.62 (Y1 @ 31.65/4.62 Y2 @ Y5))) => 31.65/4.62 (Y4 @ Y5)))))))) => 31.65/4.62 (Y4 @ Y3))))))))))))))))))))), 31.65/4.62 inference('cnf', [status(esa)], [zf_stmt_0])). 31.65/4.62 thf(zip_derived_cl1, plain, 31.65/4.62 (~ (((!!) @ (^[Y0 : a > a > $o]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y4 @ 31.65/4.62 Y7) | 31.65/4.62 (Y0 @ 31.65/4.62 Y4 @ Y7))) => 31.65/4.62 (Y6 @ Y7)))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y8 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y7 @ 31.65/4.62 Y8) | 31.65/4.62 (Y0 @ 31.65/4.62 Y7 @ Y8))) & 31.65/4.62 (Y6 @ Y7))) => 31.65/4.62 (Y6 @ Y8))))))))))) => 31.65/4.62 (Y6 @ Y5)))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ 31.65/4.62 Y7) | 31.65/4.62 (Y0 @ 31.65/4.62 Y3 @ Y7))) => 31.65/4.62 (Y6 @ Y7)))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y8 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y7 @ 31.65/4.62 Y8) | 31.65/4.62 (Y0 @ 31.65/4.62 Y7 @ Y8))) & 31.65/4.62 (Y6 @ Y7))) => 31.65/4.62 (Y6 @ Y8))))))))))) => 31.65/4.62 (Y6 @ Y4)))))))) => 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y0 @ 31.65/4.62 Y3 @ 31.65/4.62 Y7) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y7))) => 31.65/4.62 (Y6 @ Y7)))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y8 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y6 @ 31.65/4.62 Y7) & 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y7 @ 31.65/4.62 Y8) | 31.65/4.62 (Y0 @ 31.65/4.62 Y7 @ Y8))))) => 31.65/4.62 (Y6 @ Y8))))))))))) => 31.65/4.62 (Y6 @ Y5))))))))))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (((( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y5 @ 31.65/4.62 Y6) & 31.65/4.62 (Y0 @ 31.65/4.62 Y6 @ Y7))) => 31.65/4.62 (Y5 @ Y7))))))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (Y0 @ 31.65/4.62 Y3 @ 31.65/4.62 Y6) => 31.65/4.62 (Y5 @ Y6)))))))) => 31.65/4.62 (Y5 @ Y4)))))) | 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ 31.65/4.62 Y6) => 31.65/4.62 (Y5 @ Y6)))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y5 @ 31.65/4.62 Y6) & 31.65/4.62 ('#sk1' @ 31.65/4.62 Y6 @ Y7))) => 31.65/4.62 (Y5 @ Y7))))))))))) => 31.65/4.62 (Y5 @ Y4)))))))) => 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y0 @ 31.65/4.62 Y6 @ 31.65/4.62 Y7) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y6 @ Y7))) & 31.65/4.62 (Y5 @ Y6))) => 31.65/4.62 (Y5 @ Y7))))))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y0 @ 31.65/4.62 Y3 @ 31.65/4.62 Y6) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y6))) => 31.65/4.62 (Y5 @ Y6)))))))) => 31.65/4.62 (Y5 @ Y4)))))))))))))))) => 31.65/4.62 (((!!) @ (^[Y3 : a > $o]: 31.65/4.62 (((((((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y0 @ 31.65/4.62 Y4 @ 31.65/4.62 Y5) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y4 @ Y5))) & 31.65/4.62 (Y3 @ Y4))) => 31.65/4.62 (Y3 @ Y5))))))))) & 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y1 @ 31.65/4.62 Y4) | 31.65/4.62 (Y0 @ 31.65/4.62 Y1 @ Y4))) => 31.65/4.62 (Y3 @ Y4)))))))) => 31.65/4.62 (Y3 @ Y2)))))))) => 31.65/4.62 (((!!) @ (^[Y3 : a > $o]: 31.65/4.62 (((((((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y0 @ 31.65/4.62 Y4 @ 31.65/4.62 Y5) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y4 @ Y5))) & 31.65/4.62 (Y3 @ Y4))) => 31.65/4.62 (Y3 @ Y5))))))))) & 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (((( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y1 @ Y4) | 31.65/4.62 (Y0 @ 31.65/4.62 Y1 @ Y4))) => 31.65/4.62 (Y3 @ Y4)))))))) => 31.65/4.62 (Y3 @ Y2)))))))))))))))))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 31.65/4.62 thf(zip_derived_cl2, plain, 31.65/4.62 (~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((((((!!) @ (^[Y2 : a]: 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (((( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ 31.65/4.62 Y6) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ Y6))) => 31.65/4.62 (Y5 @ Y6)))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y6 @ 31.65/4.62 Y7) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y6 @ Y7))) & 31.65/4.62 (Y5 @ Y6))) => 31.65/4.62 (Y5 @ Y7))))))))))) => 31.65/4.62 (Y5 @ Y4)))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y2 @ 31.65/4.62 Y6) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y2 @ Y6))) => 31.65/4.62 (Y5 @ Y6)))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y6 @ 31.65/4.62 Y7) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y6 @ Y7))) & 31.65/4.62 (Y5 @ Y6))) => 31.65/4.62 (Y5 @ Y7))))))))))) => 31.65/4.62 (Y5 @ Y3)))))))) => 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y2 @ 31.65/4.62 Y6) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y2 @ Y6))) => 31.65/4.62 (Y5 @ Y6)))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y7 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y5 @ 31.65/4.62 Y6) & 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y6 @ 31.65/4.62 Y7) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y6 @ Y7))))) => 31.65/4.62 (Y5 @ Y7))))))))))) => 31.65/4.62 (Y5 @ Y4))))))))))))))))) & 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((((((!!) @ ( 31.65/4.62 ^[Y4 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y4 @ 31.65/4.62 Y5) & 31.65/4.62 ('#sk2' @ 31.65/4.62 Y5 @ Y6))) => 31.65/4.62 (Y4 @ Y6))))))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y2 @ 31.65/4.62 Y5) => 31.65/4.62 (Y4 @ Y5)))))))) => 31.65/4.62 (Y4 @ Y3)))))) | 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y2 @ 31.65/4.62 Y5) => 31.65/4.62 (Y4 @ Y5)))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y4 @ 31.65/4.62 Y5) & 31.65/4.62 ('#sk1' @ 31.65/4.62 Y5 @ Y6))) => 31.65/4.62 (Y4 @ Y6))))))))))) => 31.65/4.62 (Y4 @ Y3)))))))) => 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y5 @ 31.65/4.62 Y6) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y5 @ Y6))) & 31.65/4.62 (Y4 @ Y5))) => 31.65/4.62 (Y4 @ Y6))))))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y2 @ 31.65/4.62 Y5) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y2 @ Y5))) => 31.65/4.62 (Y4 @ Y5)))))))) => 31.65/4.62 (Y4 @ Y3)))))))))))))))) => 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) & 31.65/4.62 (Y2 @ Y3))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk1' @ 31.65/4.62 Y0 @ Y3) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y0 @ Y3))) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))))) => 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (((( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) & 31.65/4.62 (Y2 @ Y3))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk1' @ 31.65/4.62 Y0 @ Y3) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y0 @ Y3))) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1))))))))))))))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 31.65/4.62 thf(zip_derived_cl3, plain, 31.65/4.62 (~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((((((!!) @ ( 31.65/4.62 ^[Y4 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y2 @ 31.65/4.62 Y5) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y2 @ Y5))) => 31.65/4.62 (Y4 @ Y5)))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y5 @ 31.65/4.62 Y6) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y5 @ Y6))) & 31.65/4.62 (Y4 @ Y5))) => 31.65/4.62 (Y4 @ Y6))))))))))) => 31.65/4.62 (Y4 @ Y3)))))) & 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y1 @ 31.65/4.62 Y5) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y1 @ Y5))) => 31.65/4.62 (Y4 @ Y5)))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y6 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y5 @ 31.65/4.62 Y6) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y5 @ Y6))) & 31.65/4.62 (Y4 @ Y5))) => 31.65/4.62 (Y4 @ Y6))))))))))) => 31.65/4.62 (Y4 @ Y2)))))))) => 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a > $o]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y1 @ 31.65/4.62 Y5) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y1 @ Y5))) => 31.65/4.62 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31.65/4.62 (Y3 @ Y2)))))))))))))))) => 31.65/4.62 (((!!) @ (^[Y1 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y2 : a]: 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((((( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y2 @ Y3) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y2 @ Y3))) & 31.65/4.62 (Y1 @ Y2))) => 31.65/4.62 (Y1 @ Y3))))))))) & 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((('#sk1' @ '#sk3' @ 31.65/4.62 Y2) | ('#sk2' @ 31.65/4.62 '#sk3' @ Y2))) => 31.65/4.62 (Y1 @ Y2)))))))) => 31.65/4.62 (Y1 @ Y0)))))))) => 31.65/4.62 (((!!) @ (^[Y1 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y2 : a]: 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((((((('#sk2' @ 31.65/4.62 Y2 @ Y3) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y2 @ Y3))) & 31.65/4.62 (Y1 @ Y2))) => 31.65/4.62 (Y1 @ Y3))))))))) & 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((('#sk1' @ '#sk3' @ Y2) | 31.65/4.62 ('#sk2' @ '#sk3' @ Y2))) => 31.65/4.62 (Y1 @ Y2)))))))) => 31.65/4.62 (Y1 @ Y0)))))))))))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 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31.65/4.62 (Y3 @ Y4)))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y4 @ 31.65/4.62 Y5) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y4 @ Y5))) & 31.65/4.62 (Y3 @ Y4))) => 31.65/4.62 (Y3 @ Y5))))))))))) => 31.65/4.62 (Y3 @ Y1)))))))) => 31.65/4.62 (((!!) @ (^[Y3 : a > $o]: 31.65/4.62 (((((( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ Y4))) => 31.65/4.62 (Y3 @ Y4)))))) & 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y3 @ 31.65/4.62 Y4) & 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y4 @ 31.65/4.62 Y5) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y4 @ Y5))))) => 31.65/4.62 (Y3 @ Y5))))))))))) => 31.65/4.62 (Y3 @ Y2))))))))))))))))) & 31.65/4.62 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31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))))) => 31.65/4.62 (Y2 @ Y1)))))))) => 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) & 31.65/4.62 (Y2 @ Y3))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ Y3))) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))))))))))))) => 31.65/4.62 (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.62 ('#sk1' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk3' @ Y1) | 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31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y0 @ Y4))) => 31.65/4.62 (Y3 @ Y4)))))) & 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y4 @ 31.65/4.62 Y5) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y4 @ Y5))) & 31.65/4.62 (Y3 @ Y4))) => 31.65/4.62 (Y3 @ Y5))))))))))) => 31.65/4.62 (Y3 @ Y1)))))))) => 31.65/4.62 (((!!) @ (^[Y3 : a > $o]: 31.65/4.62 (((((((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ Y4))) => 31.65/4.62 (Y3 @ Y4)))))) & 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y3 @ 31.65/4.62 Y4) & 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y4 @ 31.65/4.62 Y5) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y4 @ Y5))))) => 31.65/4.62 (Y3 @ Y5))))))))))) => 31.65/4.62 (Y3 @ Y2))))))))))))))))) & 31.65/4.62 (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))) | 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk1' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))))) => 31.65/4.62 (Y2 @ Y1)))))))) => 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) & 31.65/4.62 (Y2 @ Y3))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ Y3))) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))))))))))))) 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.62 ('#sk1' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.65/4.62 '#sk3' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))))) => 31.65/4.62 (Y0 @ '#sk4')))))))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 31.65/4.62 thf(zip_derived_cl9, plain, 31.65/4.62 ((~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((((!!) @ (^[Y3 : a > $o]: 31.65/4.62 (((((((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y1 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y1 @ Y4))) => 31.65/4.62 (Y3 @ Y4)))))) & 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y4 @ 31.65/4.62 Y5) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y4 @ Y5))) & 31.65/4.62 (Y3 @ Y4))) => 31.65/4.62 (Y3 @ Y5))))))))))) => 31.65/4.62 (Y3 @ Y2)))))) & 31.65/4.62 (((!!) @ (^[Y3 : a > $o]: 31.65/4.62 (((((((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y0 @ Y4))) => 31.65/4.62 (Y3 @ Y4)))))) & 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y4 @ 31.65/4.62 Y5) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y4 @ Y5))) & 31.65/4.62 (Y3 @ Y4))) => 31.65/4.62 (Y3 @ Y5))))))))))) => 31.65/4.62 (Y3 @ Y1)))))))) => 31.65/4.62 (((!!) @ (^[Y3 : a > $o]: 31.65/4.62 (((((((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (((( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ Y4))) => 31.65/4.62 (Y3 @ Y4)))))) & 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y5 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y3 @ 31.65/4.62 Y4) & 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y4 @ 31.65/4.62 Y5) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y4 @ Y5))))) => 31.65/4.62 (Y3 @ Y5))))))))))) => 31.65/4.62 (Y3 @ Y2))))))))))))))))) 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))) | 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk1' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))))) => 31.65/4.62 (Y2 @ Y1)))))))) => 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) & 31.65/4.62 (Y2 @ Y3))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ Y3))) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))))))))))) 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.62 ('#sk1' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.65/4.62 '#sk3' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))))) => 31.65/4.62 (Y0 @ '#sk4')))))))), 31.65/4.62 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl7])). 31.65/4.62 thf(zip_derived_cl12, plain, 31.65/4.62 ((~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk1' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y0 @ Y3))) => 31.65/4.62 (Y2 @ Y3)))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ Y4))) & 31.65/4.62 (Y2 @ Y3))) => 31.65/4.62 (Y2 @ Y4))))))))))) => 31.65/4.62 (Y2 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk1' @ 31.65/4.62 '#sk6' @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk2' @ 31.65/4.62 '#sk6' @ 31.65/4.62 Y3))) => 31.65/4.62 (Y2 @ Y3)))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ Y4))) & 31.65/4.62 (Y2 @ Y3))) => 31.65/4.62 (Y2 @ Y4))))))))))) => 31.65/4.62 (Y2 @ Y0)))))))) => 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk2' @ 31.65/4.62 '#sk6' @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk1' @ 31.65/4.62 '#sk6' @ 31.65/4.62 Y3))) => 31.65/4.62 (Y2 @ Y3)))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (((( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 (( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ Y4))))) => 31.65/4.62 (Y2 @ Y4))))))))))) => 31.65/4.62 (Y2 @ Y1)))))))))))))) 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.62 ('#sk1' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.65/4.62 '#sk3' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))))) => 31.65/4.62 (Y0 @ '#sk4')))))) 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))) | 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk1' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))))) => 31.65/4.62 (Y2 @ Y1)))))))) => 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) & 31.65/4.62 (Y2 @ Y3))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ Y3))) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))))))))))))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl9])). 31.65/4.62 thf(zip_derived_cl15, plain, 31.65/4.62 ((~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((((((!!) @ (^[Y1 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y2 : a]: 31.65/4.62 ((((('#sk1' @ '#sk7' @ 31.65/4.62 Y2) | ('#sk2' @ 31.65/4.62 '#sk7' @ Y2))) => 31.65/4.62 (Y1 @ Y2)))))) & 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((((( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y2 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y2 @ Y3))) & 31.65/4.62 (Y1 @ Y2))) => 31.65/4.62 (Y1 @ Y3))))))))))) => 31.65/4.62 (Y1 @ Y0)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y2 : a]: 31.65/4.62 ((((('#sk1' @ '#sk6' @ 31.65/4.62 Y2) | ('#sk2' @ 31.65/4.62 '#sk6' @ Y2))) => 31.65/4.62 (Y1 @ Y2)))))) & 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((((( 31.65/4.62 ('#sk1' @ 31.65/4.62 Y2 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y2 @ Y3))) & 31.65/4.62 (Y1 @ Y2))) => 31.65/4.62 (Y1 @ Y3))))))))))) => 31.65/4.62 (Y1 @ '#sk7')))))))) => 31.65/4.62 (((!!) @ (^[Y1 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y2 : a]: 31.65/4.62 ((((('#sk2' @ '#sk6' @ 31.65/4.62 Y2) | ('#sk1' @ 31.65/4.62 '#sk6' @ Y2))) => 31.65/4.62 (Y1 @ Y2)))))) & 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((((Y1 @ Y2) & 31.65/4.62 ((('#sk1' @ 31.65/4.62 Y2 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk2' @ 31.65/4.62 Y2 @ Y3))))) => 31.65/4.62 (Y1 @ Y3))))))))))) => 31.65/4.62 (Y1 @ Y0))))))))))) 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : 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(((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk1' @ Y1 @ 31.65/4.62 Y2) | ('#sk2' @ 31.65/4.62 Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk8')))))) & 31.65/4.62 (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk6' @ Y1) | 31.65/4.62 ('#sk2' @ '#sk6' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk1' @ Y1 @ 31.65/4.62 Y2) | ('#sk2' @ 31.65/4.62 Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk7')))))))) => 31.65/4.62 (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 31.65/4.62 '#sk6' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & 31.65/4.62 ((('#sk1' @ Y1 @ Y2) | 31.65/4.62 ('#sk2' @ Y1 @ Y2))))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk8')))))))) 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.62 ('#sk1' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.65/4.62 '#sk3' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))))) => 31.65/4.62 (Y0 @ '#sk4')))))) 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))) | 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk1' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))))) => 31.65/4.62 (Y2 @ Y1)))))))) => 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) & 31.65/4.62 (Y2 @ Y3))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ Y3))) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))))))))))))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])). 31.65/4.62 thf(zip_derived_cl22, plain, 31.65/4.62 ((~ (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 31.65/4.62 '#sk6' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & 31.65/4.62 ((('#sk1' @ Y1 @ Y2) | 31.65/4.62 ('#sk2' @ Y1 @ Y2))))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk8')))))) 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))) | 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk1' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))))) => 31.65/4.62 (Y2 @ Y1)))))))) => 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) & 31.65/4.62 (Y2 @ Y3))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ Y3))) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))))))))))) 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.62 ('#sk1' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.65/4.62 '#sk3' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))))) => 31.65/4.62 (Y0 @ '#sk4')))))))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 31.65/4.62 thf(zip_derived_cl28, plain, 31.65/4.62 (( ('#form9') 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))) | 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk1' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))))) => 31.65/4.62 (Y2 @ Y1)))))))) => 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) & 31.65/4.62 (Y2 @ Y3))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ Y3))) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))))))))))))), 31.65/4.62 define([status(thm)])). 31.65/4.62 thf(zip_derived_cl29, plain, 31.65/4.62 ((~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((((((!!) @ (^[Y1 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y2 : a]: 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((((Y1 @ 31.65/4.62 Y2) & 31.65/4.62 ('#sk2' @ 31.65/4.62 Y2 @ Y3))) => 31.65/4.62 (Y1 @ Y3))))))))) & 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((('#sk2' @ '#sk10' @ 31.65/4.62 Y2) => (Y1 @ Y2)))))))) => 31.65/4.62 (Y1 @ Y0)))))) | 31.65/4.62 (((!!) @ (^[Y1 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y2 : a]: 31.65/4.62 ((('#sk1' @ '#sk10' @ 31.65/4.62 Y2) => (Y1 @ Y2)))))) & 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((((Y1 @ 31.65/4.62 Y2) & 31.65/4.62 ('#sk1' @ 31.65/4.62 Y2 @ Y3))) => 31.65/4.62 (Y1 @ Y3))))))))))) => 31.65/4.62 (Y1 @ Y0)))))))) => 31.65/4.62 (((!!) @ (^[Y1 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y2 : a]: 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((((((('#sk2' @ 31.65/4.62 Y2 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y2 @ Y3))) & 31.65/4.62 (Y1 @ Y2))) => 31.65/4.62 (Y1 @ Y3))))))))) & 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((('#sk2' @ '#sk10' @ 31.65/4.62 Y2) | ('#sk1' @ 31.65/4.62 '#sk10' @ Y2))) => 31.65/4.62 (Y1 @ Y2)))))))) => 31.65/4.62 (Y1 @ Y0))))))))))) 31.65/4.62 | ('#form9'))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl28])). 31.65/4.62 thf(zip_derived_cl38, plain, 31.65/4.62 ((~ (((((((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & 31.65/4.62 ('#sk2' @ Y1 @ Y2))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ 31.65/4.62 Y1)))))))) => 31.65/4.62 (Y0 @ '#sk12')))))) | 31.65/4.62 (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ 31.65/4.62 Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & 31.65/4.62 ('#sk1' @ Y1 @ Y2))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk12')))))))) => 31.65/4.62 (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.62 ('#sk1' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk2' @ '#sk10' @ Y1) | 31.65/4.62 ('#sk1' @ '#sk10' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))))) => 31.65/4.62 (Y0 @ '#sk12')))))))) 31.65/4.62 | ('#form9'))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl29])). 31.65/4.62 thf(zip_derived_cl46, plain, 31.65/4.62 (( (((((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & ('#sk2' @ 31.65/4.62 Y1 @ Y2))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))))) => 31.65/4.62 (Y0 @ '#sk12')))))) | 31.65/4.62 (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & ('#sk1' @ 31.65/4.62 Y1 @ Y2))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk12')))))))) 31.65/4.62 | ('#form9'))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 31.65/4.62 thf(zip_derived_cl57, plain, 31.65/4.62 (( (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & ('#sk2' @ 31.65/4.62 Y1 @ Y2))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))))) => 31.65/4.62 (Y0 @ '#sk12')))))) 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & ('#sk1' @ 31.65/4.62 Y1 @ Y2))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk12')))))) 31.65/4.62 | ('#form9'))), 31.65/4.62 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl46])). 31.65/4.62 thf(zip_derived_cl67, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 ( (((((((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 31.65/4.62 (X2 @ Y1))))))))) & 31.65/4.62 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 31.65/4.62 (X2 @ '#sk12'))) 31.65/4.62 | ('#form9') 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & ('#sk1' @ 31.65/4.62 Y1 @ Y2))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk12')))))))), 31.65/4.62 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 31.65/4.62 thf(zip_derived_cl78, plain, 31.65/4.62 ((~ ('#form46') 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & ('#sk1' @ 31.65/4.62 Y1 @ Y2))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk12')))))))), 31.65/4.62 define([status(thm)])). 31.65/4.62 thf(zip_derived_cl79, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 ( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) & 31.65/4.62 (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 31.65/4.62 (X2 @ Y1))))))))))) => 31.65/4.62 (X2 @ '#sk12'))) 31.65/4.62 | ~ ('#form46'))), 31.65/4.62 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl78])). 31.65/4.62 thf(zip_derived_cl93, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 (~ (((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) & 31.65/4.62 (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 31.65/4.62 (X2 @ Y1))))))))))) 31.65/4.62 | (X2 @ '#sk12') 31.65/4.62 | ~ ('#form46'))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])). 31.65/4.62 thf(zip_derived_cl110, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 (~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 31.65/4.62 (X2 @ Y1))))))))) 31.65/4.62 | ~ ('#form46') 31.65/4.62 | (X2 @ '#sk12'))), 31.65/4.62 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl93])). 31.65/4.62 thf(zip_derived_cl124, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 (~ ((('#sk1' @ '#sk10' @ ('#sk133' @ X2)) => (X2 @ ('#sk133' @ X2)))) 31.65/4.62 | (X2 @ '#sk12') 31.65/4.62 | ~ ('#form46') 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 31.65/4.62 (X2 @ Y1))))))))))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl110])). 31.65/4.62 thf(zip_derived_cl142, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 (~ (X2 @ ('#sk133' @ X2)) 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 31.65/4.62 (X2 @ Y1))))))))) 31.65/4.62 | ~ ('#form46') 31.65/4.62 | (X2 @ '#sk12'))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl124])). 31.65/4.62 thf(zip_derived_cl149, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 (~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((((X2 @ ('#sk214' @ X2)) & ('#sk1' @ 31.65/4.62 ('#sk214' @ X2) @ Y0))) => 31.65/4.62 (X2 @ Y0)))))) 31.65/4.62 | (X2 @ '#sk12') 31.65/4.62 | ~ ('#form46') 31.65/4.62 | ~ (X2 @ ('#sk133' @ X2)))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl142])). 31.65/4.62 thf(zip_derived_cl159, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 (~ (((((X2 @ ('#sk214' @ X2)) & ('#sk1' @ ('#sk214' @ X2) @ 31.65/4.62 ('#sk237' @ X2)))) => 31.65/4.62 (X2 @ ('#sk237' @ X2)))) 31.65/4.62 | ~ (X2 @ ('#sk133' @ X2)) 31.65/4.62 | ~ ('#form46') 31.65/4.62 | (X2 @ '#sk12'))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl149])). 31.65/4.62 thf(zip_derived_cl167, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 (~ (X2 @ ('#sk237' @ X2)) 31.65/4.62 | (X2 @ '#sk12') 31.65/4.62 | ~ ('#form46') 31.65/4.62 | ~ (X2 @ ('#sk133' @ X2)))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])). 31.65/4.62 thf(zip_derived_cl166, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 ( (((X2 @ ('#sk214' @ X2)) & ('#sk1' @ ('#sk214' @ X2) @ 31.65/4.62 ('#sk237' @ X2)))) 31.65/4.62 | (X2 @ '#sk12') 31.65/4.62 | ~ ('#form46') 31.65/4.62 | ~ (X2 @ ('#sk133' @ X2)))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])). 31.65/4.62 thf(zip_derived_cl173, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 ( ('#sk1' @ ('#sk214' @ X2) @ ('#sk237' @ X2)) 31.65/4.62 | ~ (X2 @ ('#sk133' @ X2)) 31.65/4.62 | ~ ('#form46') 31.65/4.62 | (X2 @ '#sk12'))), 31.65/4.62 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl166])). 31.65/4.62 thf(zip_derived_cl47, plain, 31.65/4.62 ((~ (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.62 ('#sk1' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk2' @ '#sk10' @ Y1) | ('#sk1' @ 31.65/4.62 '#sk10' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))))) => 31.65/4.62 (Y0 @ '#sk12')))))) 31.65/4.62 | ('#form9'))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 31.65/4.62 thf(zip_derived_cl61, plain, 31.65/4.62 ((~ (((((((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 31.65/4.62 Y0 @ Y1))) & 31.65/4.62 ('#sk20' @ Y0))) => 31.65/4.62 ('#sk20' @ Y1))))))))) & 31.65/4.62 (((!!) @ (^[Y0 : a]: 31.65/4.62 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 31.65/4.62 ('#sk20' @ Y0)))))))) => 31.65/4.62 ('#sk20' @ '#sk12'))) 31.65/4.62 | ('#form9'))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 31.65/4.62 thf(zip_derived_cl72, plain, ((~ ('#sk20' @ '#sk12') | ('#form9'))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 31.65/4.62 thf(zip_derived_cl141, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 ( ('#sk1' @ '#sk10' @ ('#sk133' @ X2)) 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 31.65/4.62 (X2 @ Y1))))))))) 31.65/4.62 | ~ ('#form46') 31.65/4.62 | (X2 @ '#sk12'))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl124])). 31.65/4.62 thf(zip_derived_cl148, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 (~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((((X2 @ ('#sk214' @ X2)) & ('#sk1' @ 31.65/4.62 ('#sk214' @ X2) @ Y0))) => 31.65/4.62 (X2 @ Y0)))))) 31.65/4.62 | (X2 @ '#sk12') 31.65/4.62 | ~ ('#form46') 31.65/4.62 | ('#sk1' @ '#sk10' @ ('#sk133' @ X2)))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl141])). 31.65/4.62 thf(zip_derived_cl158, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 (~ (((((X2 @ ('#sk214' @ X2)) & ('#sk1' @ ('#sk214' @ X2) @ 31.65/4.62 ('#sk237' @ X2)))) => 31.65/4.62 (X2 @ ('#sk237' @ X2)))) 31.65/4.62 | ('#sk1' @ '#sk10' @ ('#sk133' @ X2)) 31.65/4.62 | ~ ('#form46') 31.65/4.62 | (X2 @ '#sk12'))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl148])). 31.65/4.62 thf(zip_derived_cl165, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 (~ (X2 @ ('#sk237' @ X2)) 31.65/4.62 | (X2 @ '#sk12') 31.65/4.62 | ~ ('#form46') 31.65/4.62 | ('#sk1' @ '#sk10' @ ('#sk133' @ X2)))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])). 31.65/4.62 thf(zip_derived_cl172, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 ( (X2 @ ('#sk214' @ X2)) 31.65/4.62 | ~ (X2 @ ('#sk133' @ X2)) 31.65/4.62 | ~ ('#form46') 31.65/4.62 | (X2 @ '#sk12'))), 31.65/4.62 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl166])). 31.65/4.62 thf(zip_derived_cl164, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 ( (((X2 @ ('#sk214' @ X2)) & ('#sk1' @ ('#sk214' @ X2) @ 31.65/4.62 ('#sk237' @ X2)))) 31.65/4.62 | (X2 @ '#sk12') 31.65/4.62 | ~ ('#form46') 31.65/4.62 | ('#sk1' @ '#sk10' @ ('#sk133' @ X2)))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])). 31.65/4.62 thf(zip_derived_cl171, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 ( ('#sk1' @ ('#sk214' @ X2) @ ('#sk237' @ X2)) 31.65/4.62 | ('#sk1' @ '#sk10' @ ('#sk133' @ X2)) 31.65/4.62 | ~ ('#form46') 31.65/4.62 | (X2 @ '#sk12'))), 31.65/4.62 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl164])). 31.65/4.62 thf(zip_derived_cl71, plain, 31.65/4.62 (( (((((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.65/4.62 Y1))) & 31.65/4.62 ('#sk20' @ Y0))) => 31.65/4.62 ('#sk20' @ Y1))))))))) & 31.65/4.62 (((!!) @ (^[Y0 : a]: 31.65/4.62 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 31.65/4.62 ('#sk20' @ Y0)))))))) 31.65/4.62 | ('#form9'))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 31.65/4.62 thf(zip_derived_cl84, plain, 31.65/4.62 (( (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 31.65/4.62 ('#sk20' @ Y0))) => 31.65/4.62 ('#sk20' @ Y1))))))))) 31.65/4.62 | ('#form9'))), 31.65/4.62 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl71])). 31.65/4.62 thf(zip_derived_cl94, plain, 31.65/4.62 (![X2 : a]: 31.65/4.62 ( (((!!) @ (^[Y0 : a]: 31.65/4.62 ((((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) & 31.65/4.62 ('#sk20' @ X2))) => 31.65/4.62 ('#sk20' @ Y0)))))) 31.65/4.62 | ('#form9'))), 31.65/4.62 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl84])). 31.65/4.62 thf(zip_derived_cl111, plain, 31.65/4.62 (![X2 : a, X4 : a]: 31.65/4.62 ( ((((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk20' @ X2))) => 31.65/4.62 ('#sk20' @ X4))) 31.65/4.62 | ('#form9'))), 31.65/4.62 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])). 31.65/4.62 thf(zip_derived_cl125, plain, 31.65/4.62 (![X2 : a, X4 : a]: 31.65/4.62 (~ ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk20' @ X2))) 31.65/4.62 | ('#sk20' @ X4) 31.65/4.62 | ('#form9'))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl111])). 31.65/4.62 thf(zip_derived_cl143, plain, 31.65/4.62 (![X2 : a, X4 : a]: 31.65/4.62 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 31.65/4.62 | ~ ('#sk20' @ X2) 31.65/4.62 | ('#form9') 31.65/4.62 | ('#sk20' @ X4))), 31.65/4.62 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl125])). 31.65/4.62 thf(zip_derived_cl151, plain, 31.65/4.62 (![X2 : a, X4 : a]: 31.65/4.62 (~ ('#sk1' @ X2 @ X4) 31.65/4.62 | ('#sk20' @ X4) 31.65/4.62 | ('#form9') 31.65/4.62 | ~ ('#sk20' @ X2))), 31.65/4.62 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl143])). 31.65/4.62 thf(zip_derived_cl22, plain, 31.65/4.62 ((~ (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 31.65/4.62 '#sk6' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & 31.65/4.62 ((('#sk1' @ Y1 @ Y2) | 31.65/4.62 ('#sk2' @ Y1 @ Y2))))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk8')))))) 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))) | 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk1' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))))) => 31.65/4.62 (Y2 @ Y1)))))))) => 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) & 31.65/4.62 (Y2 @ Y3))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ Y3))) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))))))))))) 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.62 ('#sk1' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.65/4.62 '#sk3' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))))) => 31.65/4.62 (Y0 @ '#sk4')))))))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 31.65/4.62 thf(zip_derived_cl28, plain, 31.65/4.62 (( ('#form9') 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))) | 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk1' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))))) => 31.65/4.62 (Y2 @ Y1)))))))) => 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) & 31.65/4.62 (Y2 @ Y3))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ Y3))) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))))))))))))), 31.65/4.62 define([status(thm)])). 31.65/4.62 thf(zip_derived_cl30, plain, 31.65/4.62 ((~ ('#form9') 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.62 ('#sk1' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.65/4.62 '#sk3' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))))) => 31.65/4.62 (Y0 @ '#sk4')))))) 31.65/4.62 | ~ (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 31.65/4.62 '#sk6' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & 31.65/4.62 ((('#sk1' @ Y1 @ Y2) | 31.65/4.62 ('#sk2' @ Y1 @ Y2))))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk8')))))))), 31.65/4.62 inference('renaming', [status(thm)], [zip_derived_cl22, zip_derived_cl28])). 31.65/4.62 thf(zip_derived_cl21, plain, 31.65/4.62 (( (((((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk7' @ Y1) | ('#sk2' @ 31.65/4.62 '#sk7' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk1' @ Y1 @ Y2) | 31.65/4.62 ('#sk2' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk8')))))) & 31.65/4.62 (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk6' @ Y1) | ('#sk2' @ 31.65/4.62 '#sk6' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk1' @ Y1 @ Y2) | 31.65/4.62 ('#sk2' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk7')))))))) 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))) | 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk1' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))))) => 31.65/4.62 (Y2 @ Y1)))))))) => 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) & 31.65/4.62 (Y2 @ Y3))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ Y3))) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))))))))))) 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.62 ('#sk1' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.65/4.62 '#sk3' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))))) => 31.65/4.62 (Y0 @ '#sk4')))))))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 31.65/4.62 thf(zip_derived_cl26, plain, 31.65/4.62 (( (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk7' @ Y1) | ('#sk2' @ 31.65/4.62 '#sk7' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk1' @ Y1 @ Y2) | 31.65/4.62 ('#sk2' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk8')))))) 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.62 ('#sk1' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.65/4.62 '#sk3' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))))) => 31.65/4.62 (Y0 @ '#sk4')))))) 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))) | 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk1' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))))) => 31.65/4.62 (Y2 @ Y1)))))))) => 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) & 31.65/4.62 (Y2 @ Y3))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ Y3))) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))))))))))))), 31.65/4.62 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 31.65/4.62 thf(zip_derived_cl32, plain, 31.65/4.62 ((~ ('#form11') 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.62 ('#sk1' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.65/4.62 '#sk3' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))))) => 31.65/4.62 (Y0 @ '#sk4')))))))), 31.65/4.62 define([status(thm)])). 31.65/4.62 thf(zip_derived_cl37, plain, 31.65/4.62 (( ('#form11') 31.65/4.62 | ~ (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 31.65/4.62 '#sk6' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & 31.65/4.62 ((('#sk1' @ Y1 @ Y2) | 31.65/4.62 ('#sk2' @ Y1 @ Y2))))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk8')))))) 31.65/4.62 | ~ ('#form9'))), 31.65/4.62 inference('renaming', [status(thm)], [zip_derived_cl30, zip_derived_cl32])). 31.65/4.62 thf(zip_derived_cl45, plain, 31.65/4.62 ((~ (((((((!!) @ (^[Y0 : a]: 31.65/4.62 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.65/4.62 ('#sk16' @ Y0)))))) & 31.65/4.62 (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk16' @ Y0) & 31.65/4.62 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.65/4.62 Y0 @ Y1))))) => 31.65/4.62 ('#sk16' @ Y1))))))))))) => 31.65/4.62 ('#sk16' @ '#sk8'))) 31.65/4.62 | ~ ('#form9') 31.65/4.62 | ('#form11'))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl37])). 31.65/4.62 thf(zip_derived_cl56, plain, 31.65/4.62 ((~ ('#sk16' @ '#sk8') | ('#form11') | ~ ('#form9'))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 31.65/4.62 thf(zip_derived_cl85, plain, 31.65/4.62 (( (((!!) @ (^[Y0 : a]: 31.65/4.62 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 31.65/4.62 ('#sk20' @ Y0)))))) 31.65/4.62 | ('#form9'))), 31.65/4.62 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl71])). 31.65/4.62 thf(zip_derived_cl95, plain, 31.65/4.62 (![X2 : a]: 31.65/4.62 ( ((((('#sk2' @ '#sk10' @ X2) | ('#sk1' @ '#sk10' @ X2))) => 31.65/4.62 ('#sk20' @ X2))) 31.65/4.62 | ('#form9'))), 31.65/4.62 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 31.65/4.62 thf(zip_derived_cl112, plain, 31.65/4.62 (![X2 : a]: 31.65/4.62 (~ ((('#sk2' @ '#sk10' @ X2) | ('#sk1' @ '#sk10' @ X2))) 31.65/4.62 | ('#sk20' @ X2) 31.65/4.62 | ('#form9'))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])). 31.65/4.62 thf(zip_derived_cl127, plain, 31.65/4.62 (![X2 : a]: (~ ('#sk1' @ '#sk10' @ X2) | ('#form9') | ('#sk20' @ X2))), 31.65/4.62 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl112])). 31.65/4.62 thf(zip_derived_cl67, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 ( (((((((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 31.65/4.62 (X2 @ Y1))))))))) & 31.65/4.62 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 31.65/4.62 (X2 @ '#sk12'))) 31.65/4.62 | ('#form9') 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & ('#sk1' @ 31.65/4.62 Y1 @ Y2))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk12')))))))), 31.65/4.62 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 31.65/4.62 thf(zip_derived_cl68, plain, 31.65/4.62 (( (((((((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk20' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 31.65/4.62 ('#sk20' @ Y1))))))))) & 31.65/4.62 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))) => 31.65/4.62 ('#sk20' @ '#sk12'))) 31.65/4.62 | ('#form9') 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & ('#sk1' @ 31.65/4.62 Y1 @ Y2))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk12')))))))), 31.65/4.62 inference('triggered_bool_instantiation', [status(thm)], 31.65/4.62 [zip_derived_cl67])). 31.65/4.62 thf(zip_derived_cl78, plain, 31.65/4.62 ((~ ('#form46') 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & ('#sk1' @ 31.65/4.62 Y1 @ Y2))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk12')))))))), 31.65/4.62 define([status(thm)])). 31.65/4.62 thf(zip_derived_cl257, plain, 31.65/4.62 (( ('#form46') 31.65/4.62 | ('#form9') 31.65/4.62 | (((((((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk20' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 31.65/4.62 ('#sk20' @ Y1))))))))) & 31.65/4.62 (((!!) @ (^[Y0 : a]: 31.65/4.62 ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))) => 31.65/4.62 ('#sk20' @ '#sk12'))))), 31.65/4.62 inference('renaming', [status(thm)], [zip_derived_cl68, zip_derived_cl78])). 31.65/4.62 thf(zip_derived_cl258, plain, 31.65/4.62 ((~ (((((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk20' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 31.65/4.62 ('#sk20' @ Y1))))))))) & 31.65/4.62 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))) 31.65/4.62 | ('#sk20' @ '#sk12') 31.65/4.62 | ('#form9') 31.65/4.62 | ('#form46'))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl257])). 31.65/4.62 thf(zip_derived_cl72, plain, ((~ ('#sk20' @ '#sk12') | ('#form9'))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 31.65/4.62 thf(zip_derived_cl259, plain, 31.65/4.62 (( ('#form46') 31.65/4.62 | ('#form9') 31.65/4.62 | ~ (((((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk20' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 31.65/4.62 ('#sk20' @ Y1))))))))) & 31.65/4.62 (((!!) @ (^[Y0 : a]: 31.65/4.62 ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))))), 31.65/4.62 inference('clc', [status(thm)], [zip_derived_cl258, zip_derived_cl72])). 31.65/4.62 thf(zip_derived_cl260, plain, 31.65/4.62 ((~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk20' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 31.65/4.62 ('#sk20' @ Y1))))))))) 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))) 31.65/4.62 | ('#form9') 31.65/4.62 | ('#form46'))), 31.65/4.62 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl259])). 31.65/4.62 thf(zip_derived_cl67, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 ( (((((((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 31.65/4.62 (X2 @ Y1))))))))) & 31.65/4.62 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 31.65/4.62 (X2 @ '#sk12'))) 31.65/4.62 | ('#form9') 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & ('#sk1' @ 31.65/4.62 Y1 @ Y2))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk12')))))))), 31.65/4.62 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 31.65/4.62 thf(zip_derived_cl78, plain, 31.65/4.62 ((~ ('#form46') 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 (((((Y0 @ Y1) & ('#sk1' @ 31.65/4.62 Y1 @ Y2))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk12')))))))), 31.65/4.62 define([status(thm)])). 31.65/4.62 thf(zip_derived_cl83, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 ( ('#form46') 31.65/4.62 | ('#form9') 31.65/4.62 | (((((((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 31.65/4.62 (X2 @ Y1))))))))) & 31.65/4.62 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 31.65/4.62 (X2 @ '#sk12'))))), 31.65/4.62 inference('renaming', [status(thm)], [zip_derived_cl67, zip_derived_cl78])). 31.65/4.62 thf(zip_derived_cl92, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 (~ (((((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 31.65/4.62 (X2 @ Y1))))))))) & 31.65/4.62 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) 31.65/4.62 | (X2 @ '#sk12') 31.65/4.62 | ('#form9') 31.65/4.62 | ('#form46'))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl83])). 31.65/4.62 thf(zip_derived_cl109, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 (~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 31.65/4.62 (X2 @ Y1))))))))) 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 31.65/4.62 | ('#form46') 31.65/4.62 | ('#form9') 31.65/4.62 | (X2 @ '#sk12'))), 31.65/4.62 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl92])). 31.65/4.62 thf(zip_derived_cl123, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 (~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((((X2 @ ('#sk129' @ X2)) & ('#sk2' @ 31.65/4.62 ('#sk129' @ X2) @ Y0))) => 31.65/4.62 (X2 @ Y0)))))) 31.65/4.62 | (X2 @ '#sk12') 31.65/4.62 | ('#form9') 31.65/4.62 | ('#form46') 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl109])). 31.65/4.62 thf(zip_derived_cl140, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 (~ (((((X2 @ ('#sk129' @ X2)) & ('#sk2' @ ('#sk129' @ X2) @ 31.65/4.62 ('#sk179' @ X2)))) => 31.65/4.62 (X2 @ ('#sk179' @ X2)))) 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 31.65/4.62 | ('#form46') 31.65/4.62 | ('#form9') 31.65/4.62 | (X2 @ '#sk12'))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl123])). 31.65/4.62 thf(zip_derived_cl147, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 (~ (X2 @ ('#sk179' @ X2)) 31.65/4.62 | (X2 @ '#sk12') 31.65/4.62 | ('#form9') 31.65/4.62 | ('#form46') 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl140])). 31.65/4.62 thf(zip_derived_cl155, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 ( ('#form231' @ X2) 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 31.65/4.62 define([status(thm)])). 31.65/4.62 thf(zip_derived_cl261, plain, 31.65/4.62 ((~ ('#form231' @ '#sk20') 31.65/4.62 | ('#form46') 31.65/4.62 | ('#form9') 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk20' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 31.65/4.62 ('#sk20' @ Y1))))))))))), 31.65/4.62 inference('renaming', [status(thm)], 31.65/4.62 [zip_derived_cl260, zip_derived_cl155])). 31.65/4.62 thf(zip_derived_cl262, plain, 31.65/4.62 ((~ (((!!) @ (^[Y0 : a]: 31.65/4.62 ((((('#sk20' @ ('#sk129' @ '#sk20')) & ('#sk2' @ 31.65/4.62 ('#sk129' @ '#sk20') @ Y0))) => 31.65/4.62 ('#sk20' @ Y0)))))) 31.65/4.62 | ('#form9') 31.65/4.62 | ('#form46') 31.65/4.62 | ~ ('#form231' @ '#sk20'))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl261])). 31.65/4.62 thf(zip_derived_cl263, plain, 31.65/4.62 ((~ ((((('#sk20' @ ('#sk129' @ '#sk20')) & ('#sk2' @ 31.65/4.62 ('#sk129' @ '#sk20') @ ('#sk179' @ '#sk20')))) => 31.65/4.62 ('#sk20' @ ('#sk179' @ '#sk20')))) 31.65/4.62 | ~ ('#form231' @ '#sk20') 31.65/4.62 | ('#form46') 31.65/4.62 | ('#form9'))), 31.65/4.62 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl262])). 31.65/4.62 thf(zip_derived_cl264, plain, 31.65/4.62 (( ((('#sk20' @ ('#sk129' @ '#sk20')) & ('#sk2' @ ('#sk129' @ '#sk20') @ 31.65/4.62 ('#sk179' @ '#sk20')))) 31.65/4.62 | ('#form9') 31.65/4.62 | ('#form46') 31.65/4.62 | ~ ('#form231' @ '#sk20'))), 31.65/4.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl263])). 31.65/4.62 thf(zip_derived_cl266, plain, 31.65/4.62 (( ('#sk20' @ ('#sk129' @ '#sk20')) 31.65/4.62 | ~ ('#form231' @ '#sk20') 31.65/4.62 | ('#form46') 31.65/4.62 | ('#form9'))), 31.65/4.62 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl264])). 31.65/4.62 thf(zip_derived_cl170, plain, 31.65/4.62 (![X2 : a > $o]: 31.65/4.62 ( (X2 @ ('#sk214' @ X2)) 31.65/4.62 | ('#sk1' @ '#sk10' @ ('#sk133' @ X2)) 31.65/4.62 | ~ ('#form46') 31.65/4.62 | (X2 @ '#sk12'))), 31.65/4.62 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl164])). 31.65/4.62 thf(zip_derived_cl27, plain, 31.65/4.62 (( (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk6' @ Y1) | ('#sk2' @ 31.65/4.62 '#sk6' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk1' @ Y1 @ Y2) | 31.65/4.62 ('#sk2' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))))) => 31.65/4.62 (Y0 @ '#sk7')))))) 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.62 ('#sk1' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.65/4.62 '#sk3' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))))) => 31.65/4.62 (Y0 @ '#sk4')))))) 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))) | 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk1' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))))) => 31.65/4.62 (Y2 @ Y1)))))))) => 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) & 31.65/4.62 (Y2 @ Y3))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ Y3))) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))))))))))))), 31.65/4.62 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 31.65/4.62 thf(zip_derived_cl32, plain, 31.65/4.62 ((~ ('#form11') 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.62 (((!!) @ (^[Y2 : a]: 31.65/4.62 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.62 ('#sk1' @ Y1 @ Y2))) & 31.65/4.62 (Y0 @ Y1))) => 31.65/4.62 (Y0 @ Y2))))))))) & 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.65/4.62 '#sk3' @ Y1))) => 31.65/4.62 (Y0 @ Y1)))))))) => 31.65/4.62 (Y0 @ '#sk4')))))))), 31.65/4.62 define([status(thm)])). 31.65/4.62 thf(zip_derived_cl36, plain, 31.65/4.62 (( ('#form11') 31.65/4.62 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.62 (((!!) @ (^[Y1 : a]: 31.65/4.62 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))) | 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 ((('#sk1' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) => 31.65/4.62 (Y2 @ Y3)))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 (Y2 @ 31.65/4.62 Y3) & 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) => 31.65/4.62 (Y2 @ Y4))))))))))) => 31.65/4.62 (Y2 @ Y1)))))))) => 31.65/4.62 (((!!) @ (^[Y2 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y3 : a]: 31.65/4.62 (((!!) @ ( 31.65/4.62 ^[Y4 : a]: 31.65/4.62 ( 31.65/4.62 ( 31.65/4.62 (( 31.65/4.62 (( 31.65/4.62 ('#sk2' @ 31.65/4.62 Y3 @ 31.65/4.62 Y4) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y3 @ Y4))) & 31.65/4.62 (Y2 @ Y3))) => 31.65/4.62 (Y2 @ Y4))))))))) & 31.65/4.62 (((!!) @ (^[Y3 : a]: 31.65/4.62 ((((('#sk2' @ 31.65/4.62 Y0 @ 31.65/4.62 Y3) | 31.65/4.62 ('#sk1' @ 31.65/4.62 Y0 @ Y3))) => 31.65/4.62 (Y2 @ Y3)))))))) => 31.65/4.62 (Y2 @ Y1)))))))))))))) 31.65/4.62 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.62 (((((((!!) @ (^[Y1 : a]: 31.65/4.63 ((((('#sk1' @ '#sk6' @ Y1) | ('#sk2' @ 31.65/4.63 '#sk6' @ Y1))) => 31.65/4.63 (Y0 @ Y1)))))) & 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 (((!!) @ (^[Y2 : a]: 31.65/4.63 ((((((('#sk1' @ Y1 @ Y2) | 31.65/4.63 ('#sk2' @ Y1 @ Y2))) & 31.65/4.63 (Y0 @ Y1))) => 31.65/4.63 (Y0 @ Y2))))))))))) => 31.65/4.63 (Y0 @ '#sk7')))))))), 31.65/4.63 inference('renaming', [status(thm)], [zip_derived_cl27, zip_derived_cl32])). 31.65/4.63 thf(zip_derived_cl28, plain, 31.65/4.63 (( ('#form9') 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y3 : a]: 31.65/4.63 (((!!) @ ( 31.65/4.63 ^[Y4 : a]: 31.65/4.63 (( 31.65/4.63 (( 31.65/4.63 (Y2 @ 31.65/4.63 Y3) & 31.65/4.63 ('#sk2' @ 31.65/4.63 Y3 @ Y4))) => 31.65/4.63 (Y2 @ Y4))))))))) & 31.65/4.63 (((!!) @ (^[Y3 : a]: 31.65/4.63 ((('#sk2' @ 31.65/4.63 Y0 @ 31.65/4.63 Y3) => 31.65/4.63 (Y2 @ Y3)))))))) => 31.65/4.63 (Y2 @ Y1)))))) | 31.65/4.63 (((!!) @ (^[Y2 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y3 : a]: 31.65/4.63 ((('#sk1' @ 31.65/4.63 Y0 @ 31.65/4.63 Y3) => 31.65/4.63 (Y2 @ Y3)))))) & 31.65/4.63 (((!!) @ (^[Y3 : a]: 31.65/4.63 (((!!) @ ( 31.65/4.63 ^[Y4 : a]: 31.65/4.63 (( 31.65/4.63 (( 31.65/4.63 (Y2 @ 31.65/4.63 Y3) & 31.65/4.63 ('#sk1' @ 31.65/4.63 Y3 @ Y4))) => 31.65/4.63 (Y2 @ Y4))))))))))) => 31.65/4.63 (Y2 @ Y1)))))))) => 31.65/4.63 (((!!) @ (^[Y2 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y3 : a]: 31.65/4.63 (((!!) @ ( 31.65/4.63 ^[Y4 : a]: 31.65/4.63 ( 31.65/4.63 ( 31.65/4.63 (( 31.65/4.63 (( 31.65/4.63 ('#sk2' @ 31.65/4.63 Y3 @ 31.65/4.63 Y4) | 31.65/4.63 ('#sk1' @ 31.65/4.63 Y3 @ Y4))) & 31.65/4.63 (Y2 @ Y3))) => 31.65/4.63 (Y2 @ Y4))))))))) & 31.65/4.63 (((!!) @ (^[Y3 : a]: 31.65/4.63 ((((('#sk2' @ 31.65/4.63 Y0 @ 31.65/4.63 Y3) | 31.65/4.63 ('#sk1' @ 31.65/4.63 Y0 @ Y3))) => 31.65/4.63 (Y2 @ Y3)))))))) => 31.65/4.63 (Y2 @ Y1)))))))))))))))), 31.65/4.63 define([status(thm)])). 31.65/4.63 thf(zip_derived_cl43, plain, 31.65/4.63 ((~ ('#form9') 31.65/4.63 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y1 : a]: 31.65/4.63 ((((('#sk1' @ '#sk6' @ Y1) | ('#sk2' @ 31.65/4.63 '#sk6' @ Y1))) => 31.65/4.63 (Y0 @ Y1)))))) & 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 (((!!) @ (^[Y2 : a]: 31.65/4.63 ((((((('#sk1' @ Y1 @ Y2) | 31.65/4.63 ('#sk2' @ Y1 @ Y2))) & 31.65/4.63 (Y0 @ Y1))) => 31.65/4.63 (Y0 @ Y2))))))))))) => 31.65/4.63 (Y0 @ '#sk7')))))) 31.65/4.63 | ('#form11'))), 31.65/4.63 inference('renaming', [status(thm)], [zip_derived_cl36, zip_derived_cl28])). 31.65/4.63 thf(zip_derived_cl52, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( (((((((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 31.65/4.63 (X2 @ Y0)))))) & 31.65/4.63 (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))))) => 31.65/4.63 (X2 @ '#sk7'))) 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form9'))), 31.65/4.63 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 31.65/4.63 thf(zip_derived_cl64, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ (((((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 31.65/4.63 (X2 @ Y0)))))) & 31.65/4.63 (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))))) 31.65/4.63 | (X2 @ '#sk7') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#form11'))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 31.65/4.63 thf(zip_derived_cl75, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 31.65/4.63 (X2 @ Y0)))))) 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))) 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | (X2 @ '#sk7'))), 31.65/4.63 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl64])). 31.65/4.63 thf(zip_derived_cl89, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ ((((('#sk1' @ '#sk6' @ ('#sk61' @ X2)) | ('#sk2' @ '#sk6' @ 31.65/4.63 ('#sk61' @ X2)))) => 31.65/4.63 (X2 @ ('#sk61' @ X2)))) 31.65/4.63 | (X2 @ '#sk7') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#form11') 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))))), 31.65/4.63 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl75])). 31.65/4.63 thf(zip_derived_cl103, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( ('#form88' @ X2) 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))))), 31.65/4.63 define([status(thm)])). 31.65/4.63 thf(zip_derived_cl104, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((((('#sk1' @ ('#sk89' @ X2) @ Y0) | ('#sk2' @ 31.65/4.63 ('#sk89' @ X2) @ Y0))) & 31.65/4.63 (X2 @ ('#sk89' @ X2)))) => 31.65/4.63 (X2 @ Y0)))))) 31.65/4.63 | ('#form88' @ X2))), 31.65/4.63 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl103])). 31.65/4.63 thf(zip_derived_cl121, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ ((((((('#sk1' @ ('#sk89' @ X2) @ ('#sk125' @ X2)) | ('#sk2' @ 31.65/4.63 ('#sk89' @ X2) @ ('#sk125' @ X2)))) & 31.65/4.63 (X2 @ ('#sk89' @ X2)))) => 31.65/4.63 (X2 @ ('#sk125' @ X2)))) 31.65/4.63 | ('#form88' @ X2))), 31.65/4.63 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl104])). 31.65/4.63 thf(zip_derived_cl136, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( ((((('#sk1' @ ('#sk89' @ X2) @ ('#sk125' @ X2)) | ('#sk2' @ 31.65/4.63 ('#sk89' @ X2) @ ('#sk125' @ X2)))) & 31.65/4.63 (X2 @ ('#sk89' @ X2)))) 31.65/4.63 | ('#form88' @ X2))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl121])). 31.65/4.63 thf(zip_derived_cl145, plain, 31.65/4.63 (![X2 : a > $o]: ( (X2 @ ('#sk89' @ X2)) | ('#form88' @ X2))), 31.65/4.63 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl136])). 31.65/4.63 thf(zip_derived_cl265, plain, 31.65/4.63 ((~ ('#sk20' @ ('#sk179' @ '#sk20')) 31.65/4.63 | ('#form9') 31.65/4.63 | ('#form46') 31.65/4.63 | ~ ('#form231' @ '#sk20'))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl263])). 31.65/4.63 thf(zip_derived_cl137, plain, 31.65/4.63 (![X2 : a > $o]: (~ (X2 @ ('#sk125' @ X2)) | ('#form88' @ X2))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl121])). 31.65/4.63 thf(zip_derived_cl26, plain, 31.65/4.63 (( (((!!) @ (^[Y0 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y1 : a]: 31.65/4.63 ((((('#sk1' @ '#sk7' @ Y1) | ('#sk2' @ 31.65/4.63 '#sk7' @ Y1))) => 31.65/4.63 (Y0 @ Y1)))))) & 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 (((!!) @ (^[Y2 : a]: 31.65/4.63 ((((((('#sk1' @ Y1 @ Y2) | 31.65/4.63 ('#sk2' @ Y1 @ Y2))) & 31.65/4.63 (Y0 @ Y1))) => 31.65/4.63 (Y0 @ Y2))))))))))) => 31.65/4.63 (Y0 @ '#sk8')))))) 31.65/4.63 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y1 : a]: 31.65/4.63 (((!!) @ (^[Y2 : a]: 31.65/4.63 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.63 ('#sk1' @ Y1 @ Y2))) & 31.65/4.63 (Y0 @ Y1))) => 31.65/4.63 (Y0 @ Y2))))))))) & 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.65/4.63 '#sk3' @ Y1))) => 31.65/4.63 (Y0 @ Y1)))))))) => 31.65/4.63 (Y0 @ '#sk4')))))) 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y3 : a]: 31.65/4.63 (((!!) @ ( 31.65/4.63 ^[Y4 : a]: 31.65/4.63 (( 31.65/4.63 (( 31.65/4.63 (Y2 @ 31.65/4.63 Y3) & 31.65/4.63 ('#sk2' @ 31.65/4.63 Y3 @ Y4))) => 31.65/4.63 (Y2 @ Y4))))))))) & 31.65/4.63 (((!!) @ (^[Y3 : a]: 31.65/4.63 ((('#sk2' @ 31.65/4.63 Y0 @ 31.65/4.63 Y3) => 31.65/4.63 (Y2 @ Y3)))))))) => 31.65/4.63 (Y2 @ Y1)))))) | 31.65/4.63 (((!!) @ (^[Y2 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y3 : a]: 31.65/4.63 ((('#sk1' @ 31.65/4.63 Y0 @ 31.65/4.63 Y3) => 31.65/4.63 (Y2 @ Y3)))))) & 31.65/4.63 (((!!) @ (^[Y3 : a]: 31.65/4.63 (((!!) @ ( 31.65/4.63 ^[Y4 : a]: 31.65/4.63 (( 31.65/4.63 (( 31.65/4.63 (Y2 @ 31.65/4.63 Y3) & 31.65/4.63 ('#sk1' @ 31.65/4.63 Y3 @ Y4))) => 31.65/4.63 (Y2 @ Y4))))))))))) => 31.65/4.63 (Y2 @ Y1)))))))) => 31.65/4.63 (((!!) @ (^[Y2 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y3 : a]: 31.65/4.63 (((!!) @ ( 31.65/4.63 ^[Y4 : a]: 31.65/4.63 ( 31.65/4.63 ( 31.65/4.63 (( 31.65/4.63 (( 31.65/4.63 ('#sk2' @ 31.65/4.63 Y3 @ 31.65/4.63 Y4) | 31.65/4.63 ('#sk1' @ 31.65/4.63 Y3 @ Y4))) & 31.65/4.63 (Y2 @ Y3))) => 31.65/4.63 (Y2 @ Y4))))))))) & 31.65/4.63 (((!!) @ (^[Y3 : a]: 31.65/4.63 ((((('#sk2' @ 31.65/4.63 Y0 @ 31.65/4.63 Y3) | 31.65/4.63 ('#sk1' @ 31.65/4.63 Y0 @ Y3))) => 31.65/4.63 (Y2 @ Y3)))))))) => 31.65/4.63 (Y2 @ Y1)))))))))))))))), 31.65/4.63 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 31.65/4.63 thf(zip_derived_cl32, plain, 31.65/4.63 ((~ ('#form11') 31.65/4.63 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y1 : a]: 31.65/4.63 (((!!) @ (^[Y2 : a]: 31.65/4.63 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.63 ('#sk1' @ Y1 @ Y2))) & 31.65/4.63 (Y0 @ Y1))) => 31.65/4.63 (Y0 @ Y2))))))))) & 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.65/4.63 '#sk3' @ Y1))) => 31.65/4.63 (Y0 @ Y1)))))))) => 31.65/4.63 (Y0 @ '#sk4')))))))), 31.65/4.63 define([status(thm)])). 31.65/4.63 thf(zip_derived_cl35, plain, 31.65/4.63 (( ('#form11') 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y3 : a]: 31.65/4.63 (((!!) @ ( 31.65/4.63 ^[Y4 : a]: 31.65/4.63 (( 31.65/4.63 (( 31.65/4.63 (Y2 @ 31.65/4.63 Y3) & 31.65/4.63 ('#sk2' @ 31.65/4.63 Y3 @ Y4))) => 31.65/4.63 (Y2 @ Y4))))))))) & 31.65/4.63 (((!!) @ (^[Y3 : a]: 31.65/4.63 ((('#sk2' @ 31.65/4.63 Y0 @ 31.65/4.63 Y3) => 31.65/4.63 (Y2 @ Y3)))))))) => 31.65/4.63 (Y2 @ Y1)))))) | 31.65/4.63 (((!!) @ (^[Y2 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y3 : a]: 31.65/4.63 ((('#sk1' @ 31.65/4.63 Y0 @ 31.65/4.63 Y3) => 31.65/4.63 (Y2 @ Y3)))))) & 31.65/4.63 (((!!) @ (^[Y3 : a]: 31.65/4.63 (((!!) @ ( 31.65/4.63 ^[Y4 : a]: 31.65/4.63 (( 31.65/4.63 (( 31.65/4.63 (Y2 @ 31.65/4.63 Y3) & 31.65/4.63 ('#sk1' @ 31.65/4.63 Y3 @ Y4))) => 31.65/4.63 (Y2 @ Y4))))))))))) => 31.65/4.63 (Y2 @ Y1)))))))) => 31.65/4.63 (((!!) @ (^[Y2 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y3 : a]: 31.65/4.63 (((!!) @ ( 31.65/4.63 ^[Y4 : a]: 31.65/4.63 ( 31.65/4.63 ( 31.65/4.63 (( 31.65/4.63 (( 31.65/4.63 ('#sk2' @ 31.65/4.63 Y3 @ 31.65/4.63 Y4) | 31.65/4.63 ('#sk1' @ 31.65/4.63 Y3 @ Y4))) & 31.65/4.63 (Y2 @ Y3))) => 31.65/4.63 (Y2 @ Y4))))))))) & 31.65/4.63 (((!!) @ (^[Y3 : a]: 31.65/4.63 ((((('#sk2' @ 31.65/4.63 Y0 @ 31.65/4.63 Y3) | 31.65/4.63 ('#sk1' @ 31.65/4.63 Y0 @ Y3))) => 31.65/4.63 (Y2 @ Y3)))))))) => 31.65/4.63 (Y2 @ Y1)))))))))))))) 31.65/4.63 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y1 : a]: 31.65/4.63 ((((('#sk1' @ '#sk7' @ Y1) | ('#sk2' @ 31.65/4.63 '#sk7' @ Y1))) => 31.65/4.63 (Y0 @ Y1)))))) & 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 (((!!) @ (^[Y2 : a]: 31.65/4.63 ((((((('#sk1' @ Y1 @ Y2) | 31.65/4.63 ('#sk2' @ Y1 @ Y2))) & 31.65/4.63 (Y0 @ Y1))) => 31.65/4.63 (Y0 @ Y2))))))))))) => 31.65/4.63 (Y0 @ '#sk8')))))))), 31.65/4.63 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl32])). 31.65/4.63 thf(zip_derived_cl28, plain, 31.65/4.63 (( ('#form9') 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 (((((((!!) @ (^[Y2 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y3 : a]: 31.65/4.63 (((!!) @ ( 31.65/4.63 ^[Y4 : a]: 31.65/4.63 (( 31.65/4.63 (( 31.65/4.63 (Y2 @ 31.65/4.63 Y3) & 31.65/4.63 ('#sk2' @ 31.65/4.63 Y3 @ Y4))) => 31.65/4.63 (Y2 @ Y4))))))))) & 31.65/4.63 (((!!) @ (^[Y3 : a]: 31.65/4.63 ((('#sk2' @ 31.65/4.63 Y0 @ 31.65/4.63 Y3) => 31.65/4.63 (Y2 @ Y3)))))))) => 31.65/4.63 (Y2 @ Y1)))))) | 31.65/4.63 (((!!) @ (^[Y2 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y3 : a]: 31.65/4.63 ((('#sk1' @ 31.65/4.63 Y0 @ 31.65/4.63 Y3) => 31.65/4.63 (Y2 @ Y3)))))) & 31.65/4.63 (((!!) @ (^[Y3 : a]: 31.65/4.63 (((!!) @ ( 31.65/4.63 ^[Y4 : a]: 31.65/4.63 (( 31.65/4.63 (( 31.65/4.63 (Y2 @ 31.65/4.63 Y3) & 31.65/4.63 ('#sk1' @ 31.65/4.63 Y3 @ Y4))) => 31.65/4.63 (Y2 @ Y4))))))))))) => 31.65/4.63 (Y2 @ Y1)))))))) => 31.65/4.63 (((!!) @ (^[Y2 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y3 : a]: 31.65/4.63 (((!!) @ ( 31.65/4.63 ^[Y4 : a]: 31.65/4.63 ( 31.65/4.63 ( 31.65/4.63 (( 31.65/4.63 (( 31.65/4.63 ('#sk2' @ 31.65/4.63 Y3 @ 31.65/4.63 Y4) | 31.65/4.63 ('#sk1' @ 31.65/4.63 Y3 @ Y4))) & 31.65/4.63 (Y2 @ Y3))) => 31.65/4.63 (Y2 @ Y4))))))))) & 31.65/4.63 (((!!) @ (^[Y3 : a]: 31.65/4.63 ((((('#sk2' @ 31.65/4.63 Y0 @ 31.65/4.63 Y3) | 31.65/4.63 ('#sk1' @ 31.65/4.63 Y0 @ Y3))) => 31.65/4.63 (Y2 @ Y3)))))))) => 31.65/4.63 (Y2 @ Y1)))))))))))))))), 31.65/4.63 define([status(thm)])). 31.65/4.63 thf(zip_derived_cl41, plain, 31.65/4.63 ((~ ('#form9') 31.65/4.63 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y1 : a]: 31.65/4.63 ((((('#sk1' @ '#sk7' @ Y1) | ('#sk2' @ 31.65/4.63 '#sk7' @ Y1))) => 31.65/4.63 (Y0 @ Y1)))))) & 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 (((!!) @ (^[Y2 : a]: 31.65/4.63 ((((((('#sk1' @ Y1 @ Y2) | 31.65/4.63 ('#sk2' @ Y1 @ Y2))) & 31.65/4.63 (Y0 @ Y1))) => 31.65/4.63 (Y0 @ Y2))))))))))) => 31.65/4.63 (Y0 @ '#sk8')))))) 31.65/4.63 | ('#form11'))), 31.65/4.63 inference('renaming', [status(thm)], [zip_derived_cl35, zip_derived_cl28])). 31.65/4.63 thf(zip_derived_cl48, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( (((((((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk7' @ Y0) | ('#sk2' @ '#sk7' @ Y0))) => 31.65/4.63 (X2 @ Y0)))))) & 31.65/4.63 (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))))) => 31.65/4.63 (X2 @ '#sk8'))) 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form9'))), 31.65/4.63 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 31.65/4.63 thf(zip_derived_cl62, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ (((((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk7' @ Y0) | ('#sk2' @ '#sk7' @ Y0))) => 31.65/4.63 (X2 @ Y0)))))) & 31.65/4.63 (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))))) 31.65/4.63 | (X2 @ '#sk8') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#form11'))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 31.65/4.63 thf(zip_derived_cl73, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk7' @ Y0) | ('#sk2' @ '#sk7' @ Y0))) => 31.65/4.63 (X2 @ Y0)))))) 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))) 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | (X2 @ '#sk8'))), 31.65/4.63 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl62])). 31.65/4.63 thf(zip_derived_cl86, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ ((((('#sk1' @ '#sk7' @ ('#sk50' @ X2)) | ('#sk2' @ '#sk7' @ 31.65/4.63 ('#sk50' @ X2)))) => 31.65/4.63 (X2 @ ('#sk50' @ X2)))) 31.65/4.63 | (X2 @ '#sk8') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#form11') 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))))), 31.65/4.63 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl73])). 31.65/4.63 thf(zip_derived_cl97, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ (X2 @ ('#sk50' @ X2)) 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))) 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | (X2 @ '#sk8'))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl86])). 31.65/4.63 thf(zip_derived_cl103, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( ('#form88' @ X2) 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))))), 31.65/4.63 define([status(thm)])). 31.65/4.63 thf(zip_derived_cl114, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ ('#form88' @ (^[Y0 : a]: (X2 @ Y0))) 31.65/4.63 | (X2 @ '#sk8') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#form11') 31.65/4.63 | ~ (X2 @ ('#sk50' @ X2)))), 31.65/4.63 inference('renaming', [status(thm)], 31.65/4.63 [zip_derived_cl97, zip_derived_cl103])). 31.65/4.63 thf(zip_derived_cl130, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ ('#form88' @ X2) 31.65/4.63 | (X2 @ '#sk8') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#form11') 31.65/4.63 | ~ (X2 @ ('#sk50' @ X2)))), 31.65/4.63 inference('ho_norm', [status(thm)], [zip_derived_cl114])). 31.65/4.63 thf(zip_derived_cl144, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( ((('#sk1' @ ('#sk89' @ X2) @ ('#sk125' @ X2)) | ('#sk2' @ 31.65/4.63 ('#sk89' @ X2) @ ('#sk125' @ X2)))) 31.65/4.63 | ('#form88' @ X2))), 31.65/4.63 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl136])). 31.65/4.63 thf(zip_derived_cl152, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( ('#sk1' @ ('#sk89' @ X2) @ ('#sk125' @ X2)) 31.65/4.63 | ('#sk2' @ ('#sk89' @ X2) @ ('#sk125' @ X2)) 31.65/4.63 | ('#form88' @ X2))), 31.65/4.63 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl144])). 31.65/4.63 thf(zip_derived_cl89, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ ((((('#sk1' @ '#sk6' @ ('#sk61' @ X2)) | ('#sk2' @ '#sk6' @ 31.65/4.63 ('#sk61' @ X2)))) => 31.65/4.63 (X2 @ ('#sk61' @ X2)))) 31.65/4.63 | (X2 @ '#sk7') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#form11') 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))))), 31.65/4.63 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl75])). 31.65/4.63 thf(zip_derived_cl103, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( ('#form88' @ X2) 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))))), 31.65/4.63 define([status(thm)])). 31.65/4.63 thf(zip_derived_cl105, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ ('#form88' @ X2) 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | (X2 @ '#sk7') 31.65/4.63 | ~ ((((('#sk1' @ '#sk6' @ ('#sk61' @ X2)) | ('#sk2' @ '#sk6' @ 31.65/4.63 ('#sk61' @ X2)))) => 31.65/4.63 (X2 @ ('#sk61' @ X2)))))), 31.65/4.63 inference('renaming', [status(thm)], 31.65/4.63 [zip_derived_cl89, zip_derived_cl103])). 31.65/4.63 thf(zip_derived_cl120, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ (X2 @ ('#sk61' @ X2)) 31.65/4.63 | (X2 @ '#sk7') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form88' @ X2))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])). 31.65/4.63 thf(zip_derived_cl55, plain, 31.65/4.63 (( (((((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.65/4.63 ('#sk16' @ Y0)))))) & 31.65/4.63 (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((('#sk16' @ Y0) & 31.65/4.63 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 31.65/4.63 Y1))))) => 31.65/4.63 ('#sk16' @ Y1))))))))))) 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form9'))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 31.65/4.63 thf(zip_derived_cl66, plain, 31.65/4.63 (( (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((('#sk16' @ Y0) & 31.65/4.63 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 31.65/4.63 ('#sk16' @ Y1))))))))) 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#form11'))), 31.65/4.63 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 31.65/4.63 thf(zip_derived_cl77, plain, 31.65/4.63 (![X2 : a]: 31.65/4.63 ( (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk16' @ X2) & 31.65/4.63 ((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))))) => 31.65/4.63 ('#sk16' @ Y0)))))) 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form9'))), 31.65/4.63 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl66])). 31.65/4.63 thf(zip_derived_cl91, plain, 31.65/4.63 (![X2 : a, X4 : a]: 31.65/4.63 ( ((((('#sk16' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) => 31.65/4.63 ('#sk16' @ X4))) 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#form11'))), 31.65/4.63 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl77])). 31.65/4.63 thf(zip_derived_cl108, plain, 31.65/4.63 (![X2 : a, X4 : a]: 31.65/4.63 (~ ((('#sk16' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) 31.65/4.63 | ('#sk16' @ X4) 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form9'))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl91])). 31.65/4.63 thf(zip_derived_cl122, plain, 31.65/4.63 (![X2 : a, X4 : a]: 31.65/4.63 (~ ('#sk16' @ X2) 31.65/4.63 | ~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#form11') 31.65/4.63 | ('#sk16' @ X4))), 31.65/4.63 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl108])). 31.65/4.63 thf(zip_derived_cl139, plain, 31.65/4.63 (![X2 : a, X4 : a]: 31.65/4.63 (~ ('#sk2' @ X2 @ X4) 31.65/4.63 | ('#sk16' @ X4) 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ~ ('#sk16' @ X2))), 31.65/4.63 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl122])). 31.65/4.63 thf(zip_derived_cl267, plain, 31.65/4.63 (( ('#sk2' @ ('#sk129' @ '#sk20') @ ('#sk179' @ '#sk20')) 31.65/4.63 | ~ ('#form231' @ '#sk20') 31.65/4.63 | ('#form46') 31.65/4.63 | ('#form9'))), 31.65/4.63 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl264])). 31.65/4.63 thf(zip_derived_cl150, plain, 31.65/4.63 (![X2 : a, X4 : a]: 31.65/4.63 (~ ('#sk2' @ X2 @ X4) 31.65/4.63 | ('#sk20' @ X4) 31.65/4.63 | ('#form9') 31.65/4.63 | ~ ('#sk20' @ X2))), 31.65/4.63 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl143])). 31.65/4.63 thf(zip_derived_cl65, plain, 31.65/4.63 (( (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 31.65/4.63 ('#sk16' @ Y0)))))) 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#form11'))), 31.65/4.63 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 31.65/4.63 thf(zip_derived_cl76, plain, 31.65/4.63 (![X2 : a]: 31.65/4.63 ( ((((('#sk2' @ '#sk6' @ X2) | ('#sk1' @ '#sk6' @ X2))) => ('#sk16' @ 31.65/4.63 X2))) 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form9'))), 31.65/4.63 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl65])). 31.65/4.63 thf(zip_derived_cl90, plain, 31.65/4.63 (![X2 : a]: 31.65/4.63 (~ ((('#sk2' @ '#sk6' @ X2) | ('#sk1' @ '#sk6' @ X2))) 31.65/4.63 | ('#sk16' @ X2) 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#form11'))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl76])). 31.65/4.63 thf(zip_derived_cl106, plain, 31.65/4.63 (![X2 : a]: 31.65/4.63 (~ ('#sk2' @ '#sk6' @ X2) 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#sk16' @ X2))), 31.65/4.63 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl90])). 31.65/4.63 thf(zip_derived_cl96, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( ((('#sk1' @ '#sk7' @ ('#sk50' @ X2)) | ('#sk2' @ '#sk7' @ 31.65/4.63 ('#sk50' @ X2)))) 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))) 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | (X2 @ '#sk8'))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl86])). 31.65/4.63 thf(zip_derived_cl103, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( ('#form88' @ X2) 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))))), 31.65/4.63 define([status(thm)])). 31.65/4.63 thf(zip_derived_cl113, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ ('#form88' @ (^[Y0 : a]: (X2 @ Y0))) 31.65/4.63 | (X2 @ '#sk8') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#form11') 31.65/4.63 | ((('#sk1' @ '#sk7' @ ('#sk50' @ X2)) | ('#sk2' @ '#sk7' @ 31.65/4.63 ('#sk50' @ X2)))))), 31.65/4.63 inference('renaming', [status(thm)], 31.65/4.63 [zip_derived_cl96, zip_derived_cl103])). 31.65/4.63 thf(zip_derived_cl128, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ ('#form88' @ X2) 31.65/4.63 | (X2 @ '#sk8') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#form11') 31.65/4.63 | ((('#sk1' @ '#sk7' @ ('#sk50' @ X2)) | ('#sk2' @ '#sk7' @ 31.65/4.63 ('#sk50' @ X2)))))), 31.65/4.63 inference('ho_norm', [status(thm)], [zip_derived_cl113])). 31.65/4.63 thf(zip_derived_cl129, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( ('#sk1' @ '#sk7' @ ('#sk50' @ X2)) 31.65/4.63 | ('#sk2' @ '#sk7' @ ('#sk50' @ X2)) 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | (X2 @ '#sk8') 31.65/4.63 | ~ ('#form88' @ X2))), 31.65/4.63 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl128])). 31.65/4.63 thf(zip_derived_cl138, plain, 31.65/4.63 (![X2 : a, X4 : a]: 31.65/4.63 (~ ('#sk1' @ X2 @ X4) 31.65/4.63 | ('#sk16' @ X4) 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ~ ('#sk16' @ X2))), 31.65/4.63 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl122])). 31.65/4.63 thf(zip_derived_cl119, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( ((('#sk1' @ '#sk6' @ ('#sk61' @ X2)) | ('#sk2' @ '#sk6' @ 31.65/4.63 ('#sk61' @ X2)))) 31.65/4.63 | (X2 @ '#sk7') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form88' @ X2))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])). 31.65/4.63 thf(zip_derived_cl135, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( ('#sk1' @ '#sk6' @ ('#sk61' @ X2)) 31.65/4.63 | ('#sk2' @ '#sk6' @ ('#sk61' @ X2)) 31.65/4.63 | ~ ('#form88' @ X2) 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | (X2 @ '#sk7'))), 31.65/4.63 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl119])). 31.65/4.63 thf(zip_derived_cl107, plain, 31.65/4.63 (![X2 : a]: 31.65/4.63 (~ ('#sk1' @ '#sk6' @ X2) 31.65/4.63 | ('#form11') 31.65/4.63 | ~ ('#form9') 31.65/4.63 | ('#sk16' @ X2))), 31.65/4.63 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl90])). 31.65/4.63 thf(zip_derived_cl155, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( ('#form231' @ X2) 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 31.65/4.63 define([status(thm)])). 31.65/4.63 thf(zip_derived_cl156, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ ((('#sk2' @ '#sk10' @ ('#sk232' @ X2)) => (X2 @ ('#sk232' @ X2)))) 31.65/4.63 | ('#form231' @ X2))), 31.65/4.63 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl155])). 31.65/4.63 thf(zip_derived_cl162, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( ('#sk2' @ '#sk10' @ ('#sk232' @ X2)) | ('#form231' @ X2))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl156])). 31.65/4.63 thf(zip_derived_cl163, plain, 31.65/4.63 (![X2 : a > $o]: (~ (X2 @ ('#sk232' @ X2)) | ('#form231' @ X2))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl156])). 31.65/4.63 thf(zip_derived_cl126, plain, 31.65/4.63 (![X2 : a]: (~ ('#sk2' @ '#sk10' @ X2) | ('#form9') | ('#sk20' @ X2))), 31.65/4.63 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl112])). 31.65/4.63 thf(zip_derived_cl32, plain, 31.65/4.63 ((~ ('#form11') 31.65/4.63 | (((!!) @ (^[Y0 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y1 : a]: 31.65/4.63 (((!!) @ (^[Y2 : a]: 31.65/4.63 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.63 ('#sk1' @ Y1 @ Y2))) & 31.65/4.63 (Y0 @ Y1))) => 31.65/4.63 (Y0 @ Y2))))))))) & 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.65/4.63 '#sk3' @ Y1))) => 31.65/4.63 (Y0 @ Y1)))))))) => 31.65/4.63 (Y0 @ '#sk4')))))))), 31.65/4.63 define([status(thm)])). 31.65/4.63 thf(zip_derived_cl33, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( (((((((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))) & 31.65/4.63 (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.65/4.63 (X2 @ Y0)))))))) => 31.65/4.63 (X2 @ '#sk4'))) 31.65/4.63 | ~ ('#form11'))), 31.65/4.63 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 31.65/4.63 thf(zip_derived_cl42, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ (((((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))) & 31.65/4.63 (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.65/4.63 (X2 @ Y0)))))))) 31.65/4.63 | (X2 @ '#sk4') 31.65/4.63 | ~ ('#form11'))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])). 31.65/4.63 thf(zip_derived_cl51, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.65/4.63 Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))) 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.65/4.63 (X2 @ Y0)))))) 31.65/4.63 | ~ ('#form11') 31.65/4.63 | (X2 @ '#sk4'))), 31.65/4.63 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl42])). 31.65/4.63 thf(zip_derived_cl63, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((((('#sk2' @ ('#sk27' @ X2) @ Y0) | ('#sk1' @ 31.65/4.63 ('#sk27' @ X2) @ Y0))) & 31.65/4.63 (X2 @ ('#sk27' @ X2)))) => 31.65/4.63 (X2 @ Y0)))))) 31.65/4.63 | (X2 @ '#sk4') 31.65/4.63 | ~ ('#form11') 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.65/4.63 (X2 @ Y0)))))))), 31.65/4.63 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl51])). 31.65/4.63 thf(zip_derived_cl74, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ ((((((('#sk2' @ ('#sk27' @ X2) @ ('#sk39' @ X2)) | ('#sk1' @ 31.65/4.63 ('#sk27' @ X2) @ ('#sk39' @ X2)))) & 31.65/4.63 (X2 @ ('#sk27' @ X2)))) => 31.65/4.63 (X2 @ ('#sk39' @ X2)))) 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.65/4.63 (X2 @ Y0)))))) 31.65/4.63 | ~ ('#form11') 31.65/4.63 | (X2 @ '#sk4'))), 31.65/4.63 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl63])). 31.65/4.63 thf(zip_derived_cl88, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ (X2 @ ('#sk39' @ X2)) 31.65/4.63 | (X2 @ '#sk4') 31.65/4.63 | ~ ('#form11') 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.65/4.63 (X2 @ Y0)))))))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])). 31.65/4.63 thf(zip_derived_cl100, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( ('#form81' @ X2) 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.65/4.63 (X2 @ Y0)))))))), 31.65/4.63 define([status(thm)])). 31.65/4.63 thf(zip_derived_cl101, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 (~ ((((('#sk1' @ '#sk3' @ ('#sk82' @ X2)) | ('#sk2' @ '#sk3' @ 31.65/4.63 ('#sk82' @ X2)))) => 31.65/4.63 (X2 @ ('#sk82' @ X2)))) 31.65/4.63 | ('#form81' @ X2))), 31.65/4.63 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl100])). 31.65/4.63 thf(zip_derived_cl117, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( ((('#sk1' @ '#sk3' @ ('#sk82' @ X2)) | ('#sk2' @ '#sk3' @ 31.65/4.63 ('#sk82' @ X2)))) 31.65/4.63 | ('#form81' @ X2))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl101])). 31.65/4.63 thf(zip_derived_cl134, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( ('#sk1' @ '#sk3' @ ('#sk82' @ X2)) 31.65/4.63 | ('#sk2' @ '#sk3' @ ('#sk82' @ X2)) 31.65/4.63 | ('#form81' @ X2))), 31.65/4.63 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl117])). 31.65/4.63 thf(zip_derived_cl118, plain, 31.65/4.63 (![X2 : a > $o]: (~ (X2 @ ('#sk82' @ X2)) | ('#form81' @ X2))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl101])). 31.65/4.63 thf(zip_derived_cl33, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( (((((((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 31.65/4.63 Y0 @ Y1))) & 31.65/4.63 (X2 @ Y0))) => 31.65/4.63 (X2 @ Y1))))))))) & 31.65/4.63 (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.65/4.63 (X2 @ Y0)))))))) => 31.65/4.63 (X2 @ '#sk4'))) 31.65/4.63 | ~ ('#form11'))), 31.65/4.63 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 31.65/4.63 thf(zip_derived_cl34, plain, 31.65/4.63 (( (((((((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.65/4.63 Y1))) & 31.65/4.63 ('#sk5' @ Y0))) => 31.65/4.63 ('#sk5' @ Y1))))))))) & 31.65/4.63 (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.65/4.63 ('#sk5' @ Y0)))))))) => 31.65/4.63 ('#sk5' @ '#sk4'))) 31.65/4.63 | ~ ('#form11'))), 31.65/4.63 inference('triggered_bool_instantiation', [status(thm)], 31.65/4.63 [zip_derived_cl33])). 31.65/4.63 thf(zip_derived_cl6, plain, 31.65/4.63 (~ (((!!) @ (^[Y0 : a > $o]: 31.65/4.63 (((((((!!) @ (^[Y1 : a]: 31.65/4.63 (((!!) @ (^[Y2 : a]: 31.65/4.63 ((((((('#sk2' @ Y1 @ Y2) | 31.65/4.63 ('#sk1' @ Y1 @ Y2))) & 31.65/4.63 (Y0 @ Y1))) => 31.65/4.63 (Y0 @ Y2))))))))) & 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 31.65/4.63 '#sk3' @ Y1))) => 31.65/4.63 (Y0 @ Y1)))))))) => 31.65/4.63 (Y0 @ '#sk4'))))))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 31.65/4.63 thf(zip_derived_cl8, plain, 31.65/4.63 (~ (((((((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.65/4.63 Y1))) & 31.65/4.63 ('#sk5' @ Y0))) => 31.65/4.63 ('#sk5' @ Y1))))))))) & 31.65/4.63 (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.65/4.63 ('#sk5' @ Y0)))))))) => 31.65/4.63 ('#sk5' @ '#sk4')))), 31.65/4.63 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 31.65/4.63 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk4')), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 31.65/4.63 thf(zip_derived_cl191, plain, 31.65/4.63 (( (((((((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.65/4.63 Y1))) & 31.65/4.63 ('#sk5' @ Y0))) => 31.65/4.63 ('#sk5' @ Y1))))))))) & 31.65/4.63 (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.65/4.63 ('#sk5' @ Y0)))))))) => 31.65/4.63 ($false))) 31.65/4.63 | ~ ('#form11'))), 31.65/4.63 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl11])). 31.65/4.63 thf(zip_derived_cl192, plain, 31.65/4.63 (( (((~) @ (((((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk2' @ Y0 @ Y1) | 31.65/4.63 ('#sk1' @ Y0 @ Y1))) & 31.65/4.63 ('#sk5' @ Y0))) => 31.65/4.63 ('#sk5' @ Y1))))))))) & 31.65/4.63 (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ 31.65/4.63 Y0))) => 31.65/4.63 ('#sk5' @ Y0)))))))))) 31.65/4.63 | ~ ('#form11'))), 31.65/4.63 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl191])). 31.65/4.63 thf(zip_derived_cl193, plain, 31.65/4.63 ((~ (((((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.65/4.63 Y1))) & 31.65/4.63 ('#sk5' @ Y0))) => 31.65/4.63 ('#sk5' @ Y1))))))))) & 31.65/4.63 (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.65/4.63 ('#sk5' @ Y0)))))))) 31.65/4.63 | ~ ('#form11'))), 31.65/4.63 inference('simplify nested equalities', [status(thm)], 31.65/4.63 [zip_derived_cl192])). 31.65/4.63 thf(zip_derived_cl194, plain, 31.65/4.63 ((~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 31.65/4.63 ('#sk5' @ Y0))) => 31.65/4.63 ('#sk5' @ Y1))))))))) 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.65/4.63 ('#sk5' @ Y0)))))) 31.65/4.63 | ~ ('#form11'))), 31.65/4.63 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl193])). 31.65/4.63 thf(zip_derived_cl100, plain, 31.65/4.63 (![X2 : a > $o]: 31.65/4.63 ( ('#form81' @ X2) 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.65/4.63 (X2 @ Y0)))))))), 31.65/4.63 define([status(thm)])). 31.65/4.63 thf(zip_derived_cl195, plain, 31.65/4.63 ((~ ('#form81' @ '#sk5') 31.65/4.63 | ~ ('#form11') 31.65/4.63 | ~ (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 31.65/4.63 Y1))) & 31.65/4.63 ('#sk5' @ Y0))) => 31.65/4.63 ('#sk5' @ Y1))))))))))), 31.65/4.63 inference('renaming', [status(thm)], 31.65/4.63 [zip_derived_cl194, zip_derived_cl100])). 31.65/4.63 thf(zip_derived_cl196, plain, 31.65/4.63 ((~ (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((((('#sk2' @ ('#sk27' @ '#sk5') @ Y0) | ('#sk1' @ 31.65/4.63 ('#sk27' @ '#sk5') @ Y0))) & 31.65/4.63 ('#sk5' @ ('#sk27' @ '#sk5')))) => 31.65/4.63 ('#sk5' @ Y0)))))) 31.65/4.63 | ~ ('#form11') 31.65/4.63 | ~ ('#form81' @ '#sk5'))), 31.65/4.63 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl195])). 31.65/4.63 thf(zip_derived_cl197, plain, 31.65/4.63 ((~ ((((((('#sk2' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) | ('#sk1' @ 31.65/4.63 ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')))) & 31.65/4.63 ('#sk5' @ ('#sk27' @ '#sk5')))) => 31.65/4.63 ('#sk5' @ ('#sk39' @ '#sk5')))) 31.65/4.63 | ~ ('#form81' @ '#sk5') 31.65/4.63 | ~ ('#form11'))), 31.65/4.63 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl196])). 31.65/4.63 thf(zip_derived_cl199, plain, 31.65/4.63 ((~ ('#sk5' @ ('#sk39' @ '#sk5')) 31.65/4.63 | ~ ('#form11') 31.65/4.63 | ~ ('#form81' @ '#sk5'))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl197])). 31.65/4.63 thf(zip_derived_cl198, plain, 31.65/4.63 (( ((((('#sk2' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) | ('#sk1' @ 31.65/4.63 ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')))) & 31.65/4.63 ('#sk5' @ ('#sk27' @ '#sk5')))) 31.65/4.63 | ~ ('#form11') 31.65/4.63 | ~ ('#form81' @ '#sk5'))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl197])). 31.65/4.63 thf(zip_derived_cl201, plain, 31.65/4.63 (( ('#sk5' @ ('#sk27' @ '#sk5')) | ~ ('#form81' @ '#sk5') | ~ ('#form11'))), 31.65/4.63 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl198])). 31.65/4.63 thf(zip_derived_cl200, plain, 31.65/4.63 (( ((('#sk2' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) | ('#sk1' @ 31.65/4.63 ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')))) 31.65/4.63 | ~ ('#form81' @ '#sk5') 31.65/4.63 | ~ ('#form11'))), 31.65/4.63 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl198])). 31.65/4.63 thf(zip_derived_cl202, plain, 31.65/4.63 (( ('#sk2' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) 31.65/4.63 | ('#sk1' @ ('#sk27' @ '#sk5') @ ('#sk39' @ '#sk5')) 31.65/4.63 | ~ ('#form11') 31.65/4.63 | ~ ('#form81' @ '#sk5'))), 31.65/4.63 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl200])). 31.65/4.63 thf(zip_derived_cl10, plain, 31.65/4.63 ( (((((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 31.65/4.63 ('#sk5' @ Y0))) => 31.65/4.63 ('#sk5' @ Y1))))))))) & 31.65/4.63 (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.65/4.63 ('#sk5' @ Y0))))))))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 31.65/4.63 thf(zip_derived_cl13, plain, 31.65/4.63 ( (((!!) @ (^[Y0 : a]: 31.65/4.63 (((!!) @ (^[Y1 : a]: 31.65/4.63 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 31.65/4.63 ('#sk5' @ Y0))) => 31.65/4.63 ('#sk5' @ Y1)))))))))), 31.65/4.63 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 31.65/4.63 thf(zip_derived_cl16, plain, 31.65/4.63 (![X2 : a]: 31.65/4.63 (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) & 31.65/4.63 ('#sk5' @ X2))) => 31.65/4.63 ('#sk5' @ Y0))))))), 31.65/4.63 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 31.65/4.63 thf(zip_derived_cl19, plain, 31.65/4.63 (![X2 : a, X4 : a]: 31.65/4.63 ((((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk5' @ X2))) => 31.65/4.63 ('#sk5' @ X4)))), 31.65/4.63 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 31.65/4.63 thf(zip_derived_cl23, plain, 31.65/4.63 (![X2 : a, X4 : a]: 31.65/4.63 (~ ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk5' @ X2))) 31.65/4.63 | ('#sk5' @ X4))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 31.65/4.63 thf(zip_derived_cl31, plain, 31.65/4.63 (![X2 : a, X4 : a]: 31.65/4.63 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 31.65/4.63 | ~ ('#sk5' @ X2) 31.65/4.63 | ('#sk5' @ X4))), 31.65/4.63 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])). 31.65/4.63 thf(zip_derived_cl39, plain, 31.65/4.63 (![X2 : a, X4 : a]: 31.65/4.63 (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 31.65/4.63 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 31.65/4.63 thf(zip_derived_cl14, plain, 31.65/4.63 ( (((!!) @ (^[Y0 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 31.65/4.63 ('#sk5' @ Y0))))))), 31.65/4.63 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 31.65/4.63 thf(zip_derived_cl17, plain, 31.65/4.63 (![X2 : a]: 31.65/4.63 ((((('#sk1' @ '#sk3' @ X2) | ('#sk2' @ '#sk3' @ X2))) => ('#sk5' @ 31.65/4.63 X2)))), 31.65/4.63 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 31.65/4.63 thf(zip_derived_cl20, plain, 31.65/4.63 (![X2 : a]: 31.65/4.63 (~ ((('#sk1' @ '#sk3' @ X2) | ('#sk2' @ '#sk3' @ X2))) 31.65/4.63 | ('#sk5' @ X2))), 31.65/4.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 31.65/4.63 thf(zip_derived_cl25, plain, 31.65/4.63 (![X2 : a]: (~ ('#sk2' @ '#sk3' @ X2) | ('#sk5' @ X2))), 31.65/4.63 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 31.65/4.63 thf(zip_derived_cl24, plain, 31.65/4.63 (![X2 : a]: (~ ('#sk1' @ '#sk3' @ X2) | ('#sk5' @ X2))), 31.65/4.63 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 31.65/4.63 thf(zip_derived_cl40, plain, 31.65/4.63 (![X2 : a, X4 : a]: 31.65/4.63 (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 31.65/4.63 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 31.65/4.63 thf(zip_derived_cl5666, plain, ($false), 31.65/4.63 inference('eprover', [status(thm)], 31.65/4.63 [zip_derived_cl167, zip_derived_cl173, zip_derived_cl72, 31.65/4.63 zip_derived_cl165, zip_derived_cl172, zip_derived_cl171, 31.65/4.63 zip_derived_cl151, zip_derived_cl56, zip_derived_cl127, 31.65/4.63 zip_derived_cl266, zip_derived_cl170, zip_derived_cl145, 31.65/4.63 zip_derived_cl265, zip_derived_cl137, zip_derived_cl130, 31.65/4.63 zip_derived_cl152, zip_derived_cl120, zip_derived_cl139, 31.65/4.63 zip_derived_cl267, zip_derived_cl150, zip_derived_cl106, 31.65/4.63 zip_derived_cl129, zip_derived_cl138, zip_derived_cl135, 31.65/4.63 zip_derived_cl107, zip_derived_cl162, zip_derived_cl163, 31.65/4.63 zip_derived_cl126, zip_derived_cl134, zip_derived_cl118, 31.65/4.63 zip_derived_cl199, zip_derived_cl201, zip_derived_cl202, 31.65/4.63 zip_derived_cl39, zip_derived_cl25, zip_derived_cl24, 31.65/4.63 zip_derived_cl40])). 31.65/4.63 31.65/4.63 % SZS output end Refutation 31.65/4.63 31.65/4.63 31.65/4.63 % Terminating... 32.69/4.83 % Runner terminated. 32.69/4.84 % Zipperpin 1.5 exiting 32.69/4.85 EOF