0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.u8318SndNb true 0.14/0.33 % Computer : n014.cluster.edu 0.14/0.33 % Model : x86_64 x86_64 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.33 % Memory : 8042.1875MB 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.33 % CPULimit : 1440 0.14/0.33 % WCLimit : 180 0.14/0.33 % DateTime : Mon Jul 3 04:30:54 EDT 2023 0.14/0.34 % CPUTime : 0.14/0.34 % Running portfolio for 1440 s 0.14/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.14/0.34 % Number of cores: 8 0.14/0.34 % Python version: Python 3.6.8 0.14/0.34 % Running in HO mode 0.54/0.63 % Total configuration time : 828 0.54/0.63 % Estimated wc time : 1656 0.54/0.63 % Estimated cpu time (8 cpus) : 207.0 0.54/0.68 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.54/0.70 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.54/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.54/0.73 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.54/0.73 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 54.17/7.40 % Solved by lams/20_acsne_simpl.sh. 54.17/7.40 % done 843 iterations in 6.490s 54.17/7.40 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 54.17/7.40 % SZS output start Refutation 54.17/7.40 thf(a_type, type, a: $tType). 54.17/7.40 thf('#sk60_type', type, '#sk60': (a > $o) > a). 54.17/7.40 thf('#sk6_type', type, '#sk6': a). 54.17/7.40 thf('#form19_type', type, '#form19': $o). 54.17/7.40 thf('#sk82_type', type, '#sk82': (a > $o) > a). 54.17/7.40 thf('#sk115_type', type, '#sk115': (a > $o) > a). 54.17/7.40 thf('#sk5_type', type, '#sk5': a > $o). 54.17/7.40 thf('#form14_type', type, '#form14': $o). 54.17/7.40 thf('#form276_type', type, '#form276': (a > $o) > $o). 54.17/7.40 thf('#sk4_type', type, '#sk4': a). 54.17/7.40 thf('#sk56_type', type, '#sk56': (a > $o) > a). 54.17/7.40 thf('#sk140_type', type, '#sk140': (a > $o) > a). 54.17/7.40 thf('#sk15_type', type, '#sk15': a). 54.17/7.40 thf('#form9_type', type, '#form9': $o). 54.17/7.40 thf('#sk188_type', type, '#sk188': (a > $o) > a). 54.17/7.40 thf('#sk99_type', type, '#sk99': (a > $o) > a). 54.17/7.40 thf('#form98_type', type, '#form98': (a > $o) > $o). 54.17/7.40 thf('#sk23_type', type, '#sk23': a). 54.17/7.40 thf('#sk8_type', type, '#sk8': a > $o). 54.17/7.40 thf('#sk136_type', type, '#sk136': (a > $o) > a). 54.17/7.40 thf('#sk43_type', type, '#sk43': a > $o). 54.17/7.40 thf('#sk86_type', type, '#sk86': (a > $o) > a). 54.17/7.40 thf('#sk277_type', type, '#sk277': (a > $o) > a). 54.17/7.40 thf('#sk267_type', type, '#sk267': (a > $o) > a). 54.17/7.40 thf('#sk3_type', type, '#sk3': a). 54.17/7.40 thf('#sk7_type', type, '#sk7': a). 54.17/7.40 thf('#sk1_type', type, '#sk1': a > a > $o). 54.17/7.40 thf('#sk42_type', type, '#sk42': (a > $o) > a). 54.17/7.40 thf('#sk50_type', type, '#sk50': (a > $o) > a). 54.17/7.40 thf('#sk2_type', type, '#sk2': a > a > $o). 54.17/7.40 thf('#form147_type', type, '#form147': (a > $o) > $o). 54.17/7.40 thf('#sk148_type', type, '#sk148': (a > $o) > a). 54.17/7.40 thf('#sk10_type', type, '#sk10': a). 54.17/7.40 thf('#sk226_type', type, '#sk226': (a > $o) > a). 54.17/7.40 thf(cTHM251G_pme, conjecture, 54.17/7.40 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 54.17/7.40 ( ( ~( ( ( ![Xx0:a,Xy0:a]: 54.17/7.40 ( ( ( ![Xq:( a > $o )]: 54.17/7.40 ( ( ( ![Xu:a,Xv:a]: 54.17/7.40 ( ( ( S @ Xu @ Xv ) & ( Xq @ Xu ) ) => ( Xq @ Xv ) ) ) & 54.17/7.40 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 54.17/7.40 ( Xq @ Xy0 ) ) ) | 54.17/7.40 ( ![Xq:( a > $o )]: 54.17/7.40 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 54.17/7.40 ( ![Xu:a,Xv:a]: 54.17/7.40 ( ( ( R @ Xu @ Xv ) & ( Xq @ Xu ) ) => ( Xq @ Xv ) ) ) ) => 54.17/7.40 ( Xq @ Xy0 ) ) ) ) => 54.17/7.40 ( ![Xq:( a > $o )]: 54.17/7.40 ( ( ( ![Xu:a,Xv:a]: 54.17/7.40 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & 54.17/7.40 ( Xq @ Xu ) ) => 54.17/7.40 ( Xq @ Xv ) ) ) & 54.17/7.40 ( ![Xw:a]: 54.17/7.40 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 54.17/7.40 ( Xq @ Xw ) ) ) ) => 54.17/7.40 ( Xq @ Xy0 ) ) ) ) ) & 54.17/7.40 ( ![Xx0:a,Xy0:a,Xz:a]: 54.17/7.40 ( ( ( ![Xq:( a > $o )]: 54.17/7.40 ( ( ( ![Xw:a]: 54.17/7.40 ( ( ( S @ Xy0 @ Xw ) | ( R @ Xy0 @ Xw ) ) => 54.17/7.40 ( Xq @ Xw ) ) ) & 54.17/7.40 ( ![Xu:a,Xv:a]: 54.17/7.40 ( ( ( Xq @ Xu ) & 54.17/7.40 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 54.17/7.40 ( Xq @ Xv ) ) ) ) => 54.17/7.40 ( Xq @ Xz ) ) ) & 54.17/7.40 ( ![Xq:( a > $o )]: 54.17/7.40 ( ( ( ![Xu:a,Xv:a]: 54.17/7.40 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & 54.17/7.40 ( Xq @ Xu ) ) => 54.17/7.40 ( Xq @ Xv ) ) ) & 54.17/7.40 ( ![Xw:a]: 54.17/7.40 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 54.17/7.40 ( Xq @ Xw ) ) ) ) => 54.17/7.40 ( Xq @ Xy0 ) ) ) ) => 54.17/7.40 ( ![Xq:( a > $o )]: 54.17/7.40 ( ( ( ![Xw:a]: 54.17/7.40 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 54.17/7.40 ( Xq @ Xw ) ) ) & 54.17/7.40 ( ![Xu:a,Xv:a]: 54.17/7.40 ( ( ( Xq @ Xu ) & 54.17/7.40 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 54.17/7.40 ( Xq @ Xv ) ) ) ) => 54.17/7.40 ( Xq @ Xz ) ) ) ) ) ) => 54.17/7.40 ( ![Xq:( a > $o )]: 54.17/7.40 ( ( ( ![Xu:a,Xv:a]: 54.17/7.40 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 54.17/7.40 ( Xq @ Xv ) ) ) & 54.17/7.40 ( ![Xw:a]: 54.17/7.40 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 54.17/7.40 ( Xq @ Xy ) ) ) ) ) | 54.17/7.40 ( ![Xq:( a > $o )]: 54.17/7.40 ( ( ( ![Xw:a]: 54.17/7.40 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 54.17/7.40 ( ![Xu:a,Xv:a]: 54.17/7.40 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 54.17/7.40 ( Xq @ Xv ) ) ) ) => 54.17/7.40 ( Xq @ Xy ) ) ) ))). 54.17/7.40 thf(zf_stmt_0, negated_conjecture, 54.17/7.40 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 54.17/7.40 ( ( ~( ( ( ![Xx0:a,Xy0:a]: 54.17/7.40 ( ( ( ![Xq:( a > $o )]: 54.17/7.40 ( ( ( ![Xu:a,Xv:a]: 54.17/7.40 ( ( ( S @ Xu @ Xv ) & ( Xq @ Xu ) ) => 54.17/7.40 ( Xq @ Xv ) ) ) & 54.17/7.40 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 54.17/7.40 ( Xq @ Xy0 ) ) ) | 54.17/7.40 ( ![Xq:( a > $o )]: 54.17/7.40 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 54.17/7.40 ( ![Xu:a,Xv:a]: 54.17/7.40 ( ( ( R @ Xu @ Xv ) & ( Xq @ Xu ) ) => 54.17/7.40 ( Xq @ Xv ) ) ) ) => 54.17/7.40 ( Xq @ Xy0 ) ) ) ) => 54.17/7.40 ( ![Xq:( a > $o )]: 54.17/7.40 ( ( ( ![Xu:a,Xv:a]: 54.17/7.40 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & 54.17/7.40 ( Xq @ Xu ) ) => 54.17/7.40 ( Xq @ Xv ) ) ) & 54.17/7.40 ( ![Xw:a]: 54.17/7.40 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 54.17/7.40 ( Xq @ Xw ) ) ) ) => 54.17/7.40 ( Xq @ Xy0 ) ) ) ) ) & 54.17/7.40 ( ![Xx0:a,Xy0:a,Xz:a]: 54.17/7.40 ( ( ( ![Xq:( a > $o )]: 54.17/7.40 ( ( ( ![Xw:a]: 54.17/7.40 ( ( ( S @ Xy0 @ Xw ) | ( R @ Xy0 @ Xw ) ) => 54.17/7.40 ( Xq @ Xw ) ) ) & 54.17/7.40 ( ![Xu:a,Xv:a]: 54.17/7.40 ( ( ( Xq @ Xu ) & 54.17/7.40 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 54.17/7.40 ( Xq @ Xv ) ) ) ) => 54.17/7.40 ( Xq @ Xz ) ) ) & 54.17/7.40 ( ![Xq:( a > $o )]: 54.17/7.40 ( ( ( ![Xu:a,Xv:a]: 54.17/7.40 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & 54.17/7.40 ( Xq @ Xu ) ) => 54.17/7.40 ( Xq @ Xv ) ) ) & 54.17/7.40 ( ![Xw:a]: 54.17/7.40 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 54.17/7.40 ( Xq @ Xw ) ) ) ) => 54.17/7.40 ( Xq @ Xy0 ) ) ) ) => 54.17/7.40 ( ![Xq:( a > $o )]: 54.17/7.40 ( ( ( ![Xw:a]: 54.17/7.40 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 54.17/7.40 ( Xq @ Xw ) ) ) & 54.17/7.40 ( ![Xu:a,Xv:a]: 54.17/7.40 ( ( ( Xq @ Xu ) & 54.17/7.40 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 54.17/7.40 ( Xq @ Xv ) ) ) ) => 54.17/7.40 ( Xq @ Xz ) ) ) ) ) ) => 54.17/7.40 ( ![Xq:( a > $o )]: 54.17/7.40 ( ( ( ![Xu:a,Xv:a]: 54.17/7.40 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 54.17/7.40 ( Xq @ Xv ) ) ) & 54.17/7.40 ( ![Xw:a]: 54.17/7.40 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 54.17/7.40 ( Xq @ Xy ) ) ) ) ) | 54.17/7.40 ( ![Xq:( a > $o )]: 54.17/7.40 ( ( ( ![Xw:a]: 54.17/7.40 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 54.17/7.40 ( ![Xu:a,Xv:a]: 54.17/7.40 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 54.17/7.40 ( Xq @ Xv ) ) ) ) => 54.17/7.40 ( Xq @ Xy ) ) ) ) )), 54.17/7.40 inference('cnf.neg', [status(esa)], [cTHM251G_pme])). 54.17/7.40 thf(zip_derived_cl0, plain, 54.17/7.40 (~ (((!!) @ (^[Y0 : a > a > $o]: 54.17/7.40 (((!!) @ (^[Y1 : a > a > $o]: 54.17/7.40 (((!!) @ (^[Y2 : a]: 54.17/7.40 (((!!) @ (^[Y3 : a]: 54.17/7.40 (((((~) @ (((( 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y4 : a]: 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y5 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y6 : a > $o]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y7 : a]: 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y8 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (Y1 @ 54.17/7.40 Y7 @ 54.17/7.40 Y8) & 54.17/7.40 (Y6 @ Y7))) => 54.17/7.40 (Y6 @ Y8))))))))) & 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y7 : a]: 54.17/7.40 (( 54.17/7.40 (Y1 @ 54.17/7.40 Y4 @ 54.17/7.40 Y7) => 54.17/7.40 (Y6 @ Y7)))))))) => 54.17/7.40 (Y6 @ Y5)))))) | 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y6 : a > $o]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y7 : a]: 54.17/7.40 (( 54.17/7.40 (Y0 @ 54.17/7.40 Y4 @ 54.17/7.40 Y7) => 54.17/7.40 (Y6 @ Y7)))))) & 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y7 : a]: 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y8 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (Y0 @ 54.17/7.40 Y7 @ 54.17/7.40 Y8) & 54.17/7.40 (Y6 @ Y7))) => 54.17/7.40 (Y6 @ Y8))))))))))) => 54.17/7.40 (Y6 @ Y5)))))))) => 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y6 : a > $o]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y7 : a]: 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y8 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (Y0 @ 54.17/7.40 Y7 @ 54.17/7.40 Y8) | 54.17/7.40 (Y1 @ 54.17/7.40 Y7 @ Y8))) & 54.17/7.40 (Y6 @ Y7))) => 54.17/7.40 (Y6 @ Y8))))))))) & 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y7 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (Y0 @ 54.17/7.40 Y4 @ 54.17/7.40 Y7) | 54.17/7.40 (Y1 @ 54.17/7.40 Y4 @ Y7))) => 54.17/7.40 (Y6 @ Y7)))))))) => 54.17/7.40 (Y6 @ Y5)))))))))))))) & 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y4 : a]: 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y5 : a]: 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y6 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y7 : a > $o]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y8 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (Y1 @ 54.17/7.40 Y5 @ 54.17/7.40 Y8) | 54.17/7.40 (Y0 @ 54.17/7.40 Y5 @ Y8))) => 54.17/7.40 (Y7 @ Y8)))))) & 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y8 : a]: 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y9 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (Y7 @ 54.17/7.40 Y8) & 54.17/7.40 (( 54.17/7.40 (Y0 @ 54.17/7.40 Y8 @ 54.17/7.40 Y9) | 54.17/7.40 (Y1 @ 54.17/7.40 Y8 @ Y9))))) => 54.17/7.40 (Y7 @ Y9))))))))))) => 54.17/7.40 (Y7 @ Y6)))))) & 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y7 : a > $o]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y8 : a]: 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y9 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (Y1 @ 54.17/7.40 Y8 @ 54.17/7.40 Y9) | 54.17/7.40 (Y0 @ 54.17/7.40 Y8 @ Y9))) & 54.17/7.40 (Y7 @ Y8))) => 54.17/7.40 (Y7 @ Y9))))))))) & 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y8 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (Y1 @ 54.17/7.40 Y4 @ 54.17/7.40 Y8) | 54.17/7.40 (Y0 @ 54.17/7.40 Y4 @ Y8))) => 54.17/7.40 (Y7 @ Y8)))))))) => 54.17/7.40 (Y7 @ Y5)))))))) => 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y7 : a > $o]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y8 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (Y1 @ 54.17/7.40 Y4 @ 54.17/7.40 Y8) | 54.17/7.40 (Y0 @ 54.17/7.40 Y4 @ Y8))) => 54.17/7.40 (Y7 @ Y8)))))) & 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y8 : a]: 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y9 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (Y7 @ 54.17/7.40 Y8) & 54.17/7.40 (( 54.17/7.40 (Y0 @ 54.17/7.40 Y8 @ 54.17/7.40 Y9) | 54.17/7.40 (Y1 @ 54.17/7.40 Y8 @ Y9))))) => 54.17/7.40 (Y7 @ Y9))))))))))) => 54.17/7.40 (Y7 @ Y6))))))))))))))))))) => 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y4 : a > $o]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y5 : a]: 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y6 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (Y0 @ 54.17/7.40 Y5 @ 54.17/7.40 Y6) | 54.17/7.40 (Y1 @ 54.17/7.40 Y5 @ Y6))) & 54.17/7.40 (Y4 @ Y5))) => 54.17/7.40 (Y4 @ Y6))))))))) & 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y5 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (Y0 @ 54.17/7.40 Y2 @ 54.17/7.40 Y5) | 54.17/7.40 (Y1 @ 54.17/7.40 Y2 @ Y5))) => 54.17/7.40 (Y4 @ Y5)))))))) => 54.17/7.40 (Y4 @ Y3)))))))))) | 54.17/7.40 (((!!) @ (^[Y4 : a > $o]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y5 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (Y1 @ 54.17/7.40 Y2 @ 54.17/7.40 Y5) | 54.17/7.40 (Y0 @ 54.17/7.40 Y2 @ Y5))) => 54.17/7.40 (Y4 @ Y5)))))) & 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y5 : a]: 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y6 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (Y0 @ 54.17/7.40 Y5 @ 54.17/7.40 Y6) | 54.17/7.40 (Y1 @ 54.17/7.40 Y5 @ Y6))) & 54.17/7.40 (Y4 @ Y5))) => 54.17/7.40 (Y4 @ Y6))))))))))) => 54.17/7.40 (Y4 @ Y3))))))))))))))))))))), 54.17/7.40 inference('cnf', [status(esa)], [zf_stmt_0])). 54.17/7.40 thf(zip_derived_cl1, plain, 54.17/7.40 (~ (((!!) @ (^[Y0 : a > a > $o]: 54.17/7.40 (((!!) @ (^[Y1 : a]: 54.17/7.40 (((!!) @ (^[Y2 : a]: 54.17/7.40 (((((~) @ (((((((!!) @ (^[Y3 : a]: 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y4 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y5 : a > $o]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y6 : a]: 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y7 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (Y0 @ 54.17/7.40 Y6 @ 54.17/7.40 Y7) & 54.17/7.40 (Y5 @ Y6))) => 54.17/7.40 (Y5 @ Y7))))))))) & 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y6 : a]: 54.17/7.40 (( 54.17/7.40 (Y0 @ 54.17/7.40 Y3 @ 54.17/7.40 Y6) => 54.17/7.40 (Y5 @ Y6)))))))) => 54.17/7.40 (Y5 @ Y4)))))) | 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y5 : a > $o]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y6 : a]: 54.17/7.40 (( 54.17/7.40 ('#sk1' @ 54.17/7.40 Y3 @ 54.17/7.40 Y6) => 54.17/7.40 (Y5 @ Y6)))))) & 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y6 : a]: 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y7 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 ('#sk1' @ 54.17/7.40 Y6 @ 54.17/7.40 Y7) & 54.17/7.40 (Y5 @ Y6))) => 54.17/7.40 (Y5 @ Y7))))))))))) => 54.17/7.40 (Y5 @ Y4)))))))) => 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y5 : a > $o]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y6 : a]: 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y7 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 ('#sk1' @ 54.17/7.40 Y6 @ 54.17/7.40 Y7) | 54.17/7.40 (Y0 @ 54.17/7.40 Y6 @ Y7))) & 54.17/7.40 (Y5 @ Y6))) => 54.17/7.40 (Y5 @ Y7))))))))) & 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y6 : a]: 54.17/7.40 (( 54.17/7.40 (( 54.17/7.40 ('#sk1' @ 54.17/7.40 Y3 @ 54.17/7.40 Y6) | 54.17/7.40 (Y0 @ 54.17/7.40 Y3 @ Y6))) => 54.17/7.40 (Y5 @ Y6)))))))) => 54.17/7.40 (Y5 @ Y4)))))))))))))) & 54.17/7.40 (((!!) @ (^[Y3 : a]: 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y4 : a]: 54.17/7.40 (( 54.17/7.40 (!!) @ ( 54.17/7.40 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y6 : a > $o]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y7 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y0 @ 54.17/7.41 Y4 @ 54.17/7.41 Y7) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y7))) => 54.17/7.41 (Y6 @ Y7)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y7 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y8 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y6 @ 54.17/7.41 Y7) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y7 @ 54.17/7.41 Y8) | 54.17/7.41 (Y0 @ 54.17/7.41 Y7 @ Y8))))) => 54.17/7.41 (Y6 @ Y8))))))))))) => 54.17/7.41 (Y6 @ Y5)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y6 : a > $o]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y7 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y8 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y0 @ 54.17/7.41 Y7 @ 54.17/7.41 Y8) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y7 @ Y8))) & 54.17/7.41 (Y6 @ Y7))) => 54.17/7.41 (Y6 @ Y8))))))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y7 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y0 @ 54.17/7.41 Y3 @ 54.17/7.41 Y7) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y3 @ Y7))) => 54.17/7.41 (Y6 @ Y7)))))))) => 54.17/7.41 (Y6 @ Y4)))))))) => 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y6 : a > $o]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y7 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y0 @ 54.17/7.41 Y3 @ 54.17/7.41 Y7) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y3 @ Y7))) => 54.17/7.41 (Y6 @ Y7)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y7 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y8 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y6 @ 54.17/7.41 Y7) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y7 @ 54.17/7.41 Y8) | 54.17/7.41 (Y0 @ 54.17/7.41 Y7 @ Y8))))) => 54.17/7.41 (Y6 @ Y8))))))))))) => 54.17/7.41 (Y6 @ Y5))))))))))))))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 (Y0 @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 (Y0 @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y2)))))))))) | 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (((( 54.17/7.41 (Y0 @ 54.17/7.41 Y1 @ Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 (Y0 @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))))))))))))))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 54.17/7.41 thf(zip_derived_cl2, plain, 54.17/7.41 (~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((((~) @ (((((((!!) @ (^[Y2 : a]: 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a > $o]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y6 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y5 @ 54.17/7.41 Y6) & 54.17/7.41 (Y4 @ Y5))) => 54.17/7.41 (Y4 @ Y6))))))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y2 @ 54.17/7.41 Y5) => 54.17/7.41 (Y4 @ Y5)))))))) => 54.17/7.41 (Y4 @ Y3)))))) | 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a > $o]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y2 @ 54.17/7.41 Y5) => 54.17/7.41 (Y4 @ Y5)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y6 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y5 @ 54.17/7.41 Y6) & 54.17/7.41 (Y4 @ Y5))) => 54.17/7.41 (Y4 @ Y6))))))))))) => 54.17/7.41 (Y4 @ Y3)))))))) => 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a > $o]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y6 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y5 @ 54.17/7.41 Y6) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y5 @ Y6))) & 54.17/7.41 (Y4 @ Y5))) => 54.17/7.41 (Y4 @ Y6))))))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y2 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y2 @ Y5))) => 54.17/7.41 (Y4 @ Y5)))))))) => 54.17/7.41 (Y4 @ Y3)))))))))))))) & 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a > $o]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y6 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y3 @ 54.17/7.41 Y6) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y3 @ Y6))) => 54.17/7.41 (Y5 @ Y6)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y6 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y7 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y5 @ 54.17/7.41 Y6) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y6 @ 54.17/7.41 Y7) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y6 @ Y7))))) => 54.17/7.41 (Y5 @ Y7))))))))))) => 54.17/7.41 (Y5 @ Y4)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a > $o]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y6 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y7 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y6 @ 54.17/7.41 Y7) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y6 @ Y7))) & 54.17/7.41 (Y5 @ Y6))) => 54.17/7.41 (Y5 @ Y7))))))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y6 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y2 @ 54.17/7.41 Y6) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y2 @ Y6))) => 54.17/7.41 (Y5 @ Y6)))))))) => 54.17/7.41 (Y5 @ Y3)))))))) => 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a > $o]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y6 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y2 @ 54.17/7.41 Y6) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y2 @ Y6))) => 54.17/7.41 (Y5 @ Y6)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y6 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y7 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y5 @ 54.17/7.41 Y6) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y6 @ 54.17/7.41 Y7) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y6 @ Y7))))) => 54.17/7.41 (Y5 @ Y7))))))))))) => 54.17/7.41 (Y5 @ Y4))))))))))))))))))) => 54.17/7.41 (((!!) @ (^[Y2 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y3 : a]: 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y3 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y3 @ Y4))) & 54.17/7.41 (Y2 @ Y3))) => 54.17/7.41 (Y2 @ Y4))))))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y3 : a]: 54.17/7.41 ((((('#sk1' @ 54.17/7.41 Y0 @ Y3) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ Y3))) => 54.17/7.41 (Y2 @ Y3)))))))) => 54.17/7.41 (Y2 @ Y1)))))))))) | 54.17/7.41 (((!!) @ (^[Y2 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y3 : a]: 54.17/7.41 ((((('#sk2' @ 54.17/7.41 Y0 @ Y3) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y3))) => 54.17/7.41 (Y2 @ Y3)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (((( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y3 @ Y4) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y3 @ Y4))) & 54.17/7.41 (Y2 @ Y3))) => 54.17/7.41 (Y2 @ Y4))))))))))) => 54.17/7.41 (Y2 @ Y1))))))))))))))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 54.17/7.41 thf(zip_derived_cl3, plain, 54.17/7.41 (~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((((~) @ (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y3 : a > $o]: 54.17/7.41 (((( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y2)))))) | 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y3 : a > $o]: 54.17/7.41 (((( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))))) => 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y3 : a > $o]: 54.17/7.41 (((((( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y2)))))))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a > $o]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y2 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y2 @ Y5))) => 54.17/7.41 (Y4 @ Y5)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y6 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y4 @ 54.17/7.41 Y5) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y5 @ 54.17/7.41 Y6) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y5 @ Y6))))) => 54.17/7.41 (Y4 @ Y6))))))))))) => 54.17/7.41 (Y4 @ Y3)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a > $o]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y6 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y5 @ 54.17/7.41 Y6) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y5 @ Y6))) & 54.17/7.41 (Y4 @ Y5))) => 54.17/7.41 (Y4 @ Y6))))))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y5))) => 54.17/7.41 (Y4 @ Y5)))))))) => 54.17/7.41 (Y4 @ Y2)))))))) => 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a > $o]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y5))) => 54.17/7.41 (Y4 @ Y5)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y6 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y4 @ 54.17/7.41 Y5) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y5 @ 54.17/7.41 Y6) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y5 @ Y6))))) => 54.17/7.41 (Y4 @ Y6))))))))))) => 54.17/7.41 (Y4 @ Y3))))))))))))))))))) => 54.17/7.41 (((!!) @ (^[Y1 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y2 : a]: 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y3 : a]: 54.17/7.41 (((((( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y2 @ Y3) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y2 @ Y3))) & 54.17/7.41 (Y1 @ Y2))) => 54.17/7.41 (Y1 @ Y3))))))))) & 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((('#sk1' @ 54.17/7.41 '#sk3' @ Y2) | 54.17/7.41 ('#sk2' @ 54.17/7.41 '#sk3' @ Y2))) => 54.17/7.41 (Y1 @ Y2)))))))) => 54.17/7.41 (Y1 @ Y0)))))))))) | 54.17/7.41 (((!!) @ (^[Y1 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y2 : a]: 54.17/7.41 ((((('#sk2' @ '#sk3' @ Y2) | 54.17/7.41 ('#sk1' @ '#sk3' @ Y2))) => 54.17/7.41 (Y1 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 ((((((('#sk1' @ 54.17/7.41 Y2 @ Y3) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y2 @ Y3))) & 54.17/7.41 (Y1 @ Y2))) => 54.17/7.41 (Y1 @ Y3))))))))))) => 54.17/7.41 (Y1 @ Y0)))))))))))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 54.17/7.41 thf(zip_derived_cl4, plain, 54.17/7.41 (~ (((((~) @ (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((((((!!) @ (^[Y2 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y3 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (Y2 @ Y3))) => 54.17/7.41 (Y2 @ Y4))))))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y3 : a]: 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y3) => 54.17/7.41 (Y2 @ Y3)))))))) => 54.17/7.41 (Y2 @ Y1)))))) | 54.17/7.41 (((!!) @ (^[Y2 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y3 : a]: 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ 54.17/7.41 Y3) => 54.17/7.41 (Y2 @ Y3)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y3 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (Y2 @ Y3))) => 54.17/7.41 (Y2 @ Y4))))))))))) => 54.17/7.41 (Y2 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y2 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y3 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y3 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y3 @ Y4))) & 54.17/7.41 (Y2 @ Y3))) => 54.17/7.41 (Y2 @ Y4))))))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y3 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ 54.17/7.41 Y3) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ Y3))) => 54.17/7.41 (Y2 @ Y3)))))))) => 54.17/7.41 (Y2 @ Y1)))))))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y3 : a > $o]: 54.17/7.41 (((( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y3 : a > $o]: 54.17/7.41 (((( 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y3 : a > $o]: 54.17/7.41 (((((( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))))) => 54.17/7.41 (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ 54.17/7.41 Y1 @ Y2) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y1) | 54.17/7.41 ('#sk2' @ '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk4')))))))))) | 54.17/7.41 (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 54.17/7.41 '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk4'))))))))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 54.17/7.41 thf(zip_derived_cl6, plain, 54.17/7.41 (~ (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 54.17/7.41 '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk4'))))))), 54.17/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 54.17/7.41 thf(zip_derived_cl8, plain, 54.17/7.41 (~ (((((((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 54.17/7.41 ('#sk5' @ Y0)))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.17/7.41 Y1))) & 54.17/7.41 ('#sk5' @ Y0))) => 54.17/7.41 ('#sk5' @ Y1))))))))))) => 54.17/7.41 ('#sk5' @ '#sk4')))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 54.17/7.41 thf(zip_derived_cl10, plain, 54.17/7.41 ( (((((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 54.17/7.41 ('#sk5' @ Y0)))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 54.17/7.41 ('#sk5' @ Y0))) => 54.17/7.41 ('#sk5' @ Y1)))))))))))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 54.17/7.41 thf(zip_derived_cl14, plain, 54.17/7.41 ( (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 54.17/7.41 ('#sk5' @ Y0))) => 54.17/7.41 ('#sk5' @ Y1)))))))))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 54.17/7.41 thf(zip_derived_cl17, plain, 54.17/7.41 (![X2 : a]: 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) & 54.17/7.41 ('#sk5' @ X2))) => 54.17/7.41 ('#sk5' @ Y0))))))), 54.17/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 54.17/7.41 thf(zip_derived_cl21, plain, 54.17/7.41 (![X2 : a, X4 : a]: 54.17/7.41 ((((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk5' @ X2))) => 54.17/7.41 ('#sk5' @ X4)))), 54.17/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 54.17/7.41 thf(zip_derived_cl26, plain, 54.17/7.41 (![X2 : a, X4 : a]: 54.17/7.41 (~ ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk5' @ X2))) 54.17/7.41 | ('#sk5' @ X4))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 54.17/7.41 thf(zip_derived_cl33, plain, 54.17/7.41 (![X2 : a, X4 : a]: 54.17/7.41 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 54.17/7.41 | ~ ('#sk5' @ X2) 54.17/7.41 | ('#sk5' @ X4))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 54.17/7.41 thf(zip_derived_cl41, plain, 54.17/7.41 (![X2 : a, X4 : a]: 54.17/7.41 (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 54.17/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl33])). 54.17/7.41 thf(zip_derived_cl42, plain, 54.17/7.41 (![X2 : a, X4 : a]: 54.17/7.41 (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 54.17/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl33])). 54.17/7.41 thf(zip_derived_cl5, plain, 54.17/7.41 ( (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((((((!!) @ (^[Y2 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y3 : a]: 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (Y2 @ Y3))) => 54.17/7.41 (Y2 @ Y4))))))))) & 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 ((('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y3) => 54.17/7.41 (Y2 @ Y3)))))))) => 54.17/7.41 (Y2 @ Y1)))))) | 54.17/7.41 (((!!) @ (^[Y2 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y3 : a]: 54.17/7.41 ((('#sk1' @ 54.17/7.41 Y0 @ 54.17/7.41 Y3) => 54.17/7.41 (Y2 @ Y3)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (Y2 @ Y3))) => 54.17/7.41 (Y2 @ Y4))))))))))) => 54.17/7.41 (Y2 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y2 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y3 : a]: 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y3 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y3 @ Y4))) & 54.17/7.41 (Y2 @ Y3))) => 54.17/7.41 (Y2 @ Y4))))))))) & 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 ((((('#sk1' @ 54.17/7.41 Y0 @ 54.17/7.41 Y3) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ Y3))) => 54.17/7.41 (Y2 @ Y3)))))))) => 54.17/7.41 (Y2 @ Y1)))))))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))))) => 54.17/7.41 (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 54.17/7.41 '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk4'))))))))), 54.17/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 54.17/7.41 thf(zip_derived_cl7, plain, 54.17/7.41 ((~ (((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((((((!!) @ (^[Y2 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y3 : a]: 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (Y2 @ Y3))) => 54.17/7.41 (Y2 @ Y4))))))))) & 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 ((('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y3) => 54.17/7.41 (Y2 @ Y3)))))))) => 54.17/7.41 (Y2 @ Y1)))))) | 54.17/7.41 (((!!) @ (^[Y2 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y3 : a]: 54.17/7.41 ((('#sk1' @ 54.17/7.41 Y0 @ 54.17/7.41 Y3) => 54.17/7.41 (Y2 @ Y3)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (Y2 @ Y3))) => 54.17/7.41 (Y2 @ Y4))))))))))) => 54.17/7.41 (Y2 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y2 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y3 : a]: 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y3 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y3 @ Y4))) & 54.17/7.41 (Y2 @ Y3))) => 54.17/7.41 (Y2 @ Y4))))))))) & 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 ((((('#sk1' @ 54.17/7.41 Y0 @ 54.17/7.41 Y3) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ Y3))) => 54.17/7.41 (Y2 @ Y3)))))))) => 54.17/7.41 (Y2 @ Y1)))))))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))))) 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 54.17/7.41 '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk4')))))))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 54.17/7.41 thf(zip_derived_cl9, plain, 54.17/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((((((!!) @ (^[Y2 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y3 : a]: 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (Y2 @ Y3))) => 54.17/7.41 (Y2 @ Y4))))))))) & 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 ((('#sk2' @ 54.17/7.41 Y0 @ Y3) => 54.17/7.41 (Y2 @ Y3)))))))) => 54.17/7.41 (Y2 @ Y1)))))) | 54.17/7.41 (((!!) @ (^[Y2 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y3 : a]: 54.17/7.41 ((('#sk1' @ 54.17/7.41 Y0 @ Y3) => 54.17/7.41 (Y2 @ Y3)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (Y2 @ Y3))) => 54.17/7.41 (Y2 @ Y4))))))))))) => 54.17/7.41 (Y2 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y2 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y3 : a]: 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (((( 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y3 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y3 @ Y4))) & 54.17/7.41 (Y2 @ Y3))) => 54.17/7.41 (Y2 @ Y4))))))))) & 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 ((((('#sk1' @ 54.17/7.41 Y0 @ Y3) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ Y3))) => 54.17/7.41 (Y2 @ Y3)))))))) => 54.17/7.41 (Y2 @ Y1)))))))))))))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))) 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 54.17/7.41 '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk4')))))))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl7])). 54.17/7.41 thf(zip_derived_cl12, plain, 54.17/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((((((!!) @ (^[Y1 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y2 : a]: 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 ((((('#sk2' @ 54.17/7.41 Y2 @ 54.17/7.41 Y3) & 54.17/7.41 (Y1 @ Y2))) => 54.17/7.41 (Y1 @ Y3))))))))) & 54.17/7.41 (((!!) @ (^[Y2 : 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54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk7')))))) 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((('#sk1' @ Y1 @ Y2) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk7')))))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))) 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 54.17/7.41 '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk4')))))))), 54.17/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl18])). 54.17/7.41 thf(zip_derived_cl27, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) => 54.17/7.41 (X2 @ '#sk7'))) 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y1) | 54.17/7.41 ('#sk2' @ '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk4')))))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))) 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((('#sk1' @ Y1 @ Y2) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk7')))))))), 54.17/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 54.17/7.41 thf(zip_derived_cl34, plain, 54.17/7.41 ((~ ('#form14') 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 54.17/7.41 '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk4')))))))), 54.17/7.41 define([status(thm)])). 54.17/7.41 thf(zip_derived_cl35, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 54.17/7.41 Y0 @ Y1))) & 54.17/7.41 (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 54.17/7.41 (X2 @ Y0)))))))) => 54.17/7.41 (X2 @ '#sk4'))) 54.17/7.41 | ~ ('#form14'))), 54.17/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 54.17/7.41 thf(zip_derived_cl37, plain, 54.17/7.41 (( (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.17/7.41 Y1))) & 54.17/7.41 ('#sk5' @ Y0))) => 54.17/7.41 ('#sk5' @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 54.17/7.41 ('#sk5' @ Y0)))))))) => 54.17/7.41 ('#sk5' @ '#sk4'))) 54.17/7.41 | ~ ('#form14'))), 54.17/7.41 inference('triggered_bool_instantiation', [status(thm)], 54.17/7.41 [zip_derived_cl35])). 54.17/7.41 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk4')), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 54.17/7.41 thf(zip_derived_cl272, plain, 54.17/7.41 (( (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.17/7.41 Y1))) & 54.17/7.41 ('#sk5' @ Y0))) => 54.17/7.41 ('#sk5' @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 54.17/7.41 ('#sk5' @ Y0)))))))) => 54.17/7.41 ($false))) 54.17/7.41 | ~ ('#form14'))), 54.17/7.41 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl11])). 54.17/7.41 thf(zip_derived_cl273, plain, 54.17/7.41 (( (((~) @ (((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | 54.17/7.41 ('#sk2' @ Y0 @ Y1))) & 54.17/7.41 ('#sk5' @ Y0))) => 54.17/7.41 ('#sk5' @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ 54.17/7.41 Y0))) => 54.17/7.41 ('#sk5' @ Y0)))))))))) 54.17/7.41 | ~ ('#form14'))), 54.17/7.41 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl272])). 54.17/7.41 thf(zip_derived_cl274, plain, 54.17/7.41 ((~ (((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.17/7.41 Y1))) & 54.17/7.41 ('#sk5' @ Y0))) => 54.17/7.41 ('#sk5' @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 54.17/7.41 ('#sk5' @ Y0)))))))) 54.17/7.41 | ~ ('#form14'))), 54.17/7.41 inference('simplify nested equalities', [status(thm)], 54.17/7.41 [zip_derived_cl273])). 54.17/7.41 thf(zip_derived_cl275, plain, 54.17/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 54.17/7.41 ('#sk5' @ Y0))) => 54.17/7.41 ('#sk5' @ Y1))))))))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 54.17/7.41 ('#sk5' @ Y0)))))) 54.17/7.41 | ~ ('#form14'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl274])). 54.17/7.41 thf(zip_derived_cl35, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 54.17/7.41 Y0 @ Y1))) & 54.17/7.41 (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 54.17/7.41 (X2 @ Y0)))))))) => 54.17/7.41 (X2 @ '#sk4'))) 54.17/7.41 | ~ ('#form14'))), 54.17/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 54.17/7.41 thf(zip_derived_cl48, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 54.17/7.41 Y0 @ Y1))) & 54.17/7.41 (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 54.17/7.41 (X2 @ Y0)))))))) 54.17/7.41 | (X2 @ '#sk4') 54.17/7.41 | ~ ('#form14'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 54.17/7.41 thf(zip_derived_cl54, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.17/7.41 Y1))) & 54.17/7.41 (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 54.17/7.41 (X2 @ Y0)))))) 54.17/7.41 | ~ ('#form14') 54.17/7.41 | (X2 @ '#sk4'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl48])). 54.17/7.41 thf(zip_derived_cl61, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((((('#sk1' @ ('#sk42' @ X2) @ Y0) | ('#sk2' @ 54.17/7.41 ('#sk42' @ X2) @ Y0))) & 54.17/7.41 (X2 @ ('#sk42' @ X2)))) => 54.17/7.41 (X2 @ Y0)))))) 54.17/7.41 | (X2 @ '#sk4') 54.17/7.41 | ~ ('#form14') 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 54.17/7.41 (X2 @ Y0)))))))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl54])). 54.17/7.41 thf(zip_derived_cl72, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ ((((((('#sk1' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) | ('#sk2' @ 54.17/7.41 ('#sk42' @ X2) @ ('#sk56' @ X2)))) & 54.17/7.41 (X2 @ ('#sk42' @ X2)))) => 54.17/7.41 (X2 @ ('#sk56' @ X2)))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 54.17/7.41 (X2 @ Y0)))))) 54.17/7.41 | ~ ('#form14') 54.17/7.41 | (X2 @ '#sk4'))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl61])). 54.17/7.41 thf(zip_derived_cl89, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (X2 @ ('#sk56' @ X2)) 54.17/7.41 | (X2 @ '#sk4') 54.17/7.41 | ~ ('#form14') 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 54.17/7.41 (X2 @ Y0)))))))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl72])). 54.17/7.41 thf(zip_derived_cl102, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ('#form98' @ X2) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 54.17/7.41 (X2 @ Y0)))))))), 54.17/7.41 define([status(thm)])). 54.17/7.41 thf(zip_derived_cl276, plain, 54.17/7.41 ((~ ('#form98' @ '#sk5') 54.17/7.41 | ~ ('#form14') 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.17/7.41 Y1))) & 54.17/7.41 ('#sk5' @ Y0))) => 54.17/7.41 ('#sk5' @ Y1))))))))))), 54.17/7.41 inference('renaming', [status(thm)], 54.17/7.41 [zip_derived_cl275, zip_derived_cl102])). 54.17/7.41 thf(zip_derived_cl277, plain, 54.17/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((((('#sk1' @ ('#sk42' @ '#sk5') @ Y0) | ('#sk2' @ 54.17/7.41 ('#sk42' @ '#sk5') @ Y0))) & 54.17/7.41 ('#sk5' @ ('#sk42' @ '#sk5')))) => 54.17/7.41 ('#sk5' @ Y0)))))) 54.17/7.41 | ~ ('#form14') 54.17/7.41 | ~ ('#form98' @ '#sk5'))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl276])). 54.17/7.41 thf(zip_derived_cl278, plain, 54.17/7.41 ((~ ((((((('#sk1' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) | ('#sk2' @ 54.17/7.41 ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')))) & 54.17/7.41 ('#sk5' @ ('#sk42' @ '#sk5')))) => 54.17/7.41 ('#sk5' @ ('#sk56' @ '#sk5')))) 54.17/7.41 | ~ ('#form98' @ '#sk5') 54.17/7.41 | ~ ('#form14'))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl277])). 54.17/7.41 thf(zip_derived_cl280, plain, 54.17/7.41 ((~ ('#sk5' @ ('#sk56' @ '#sk5')) 54.17/7.41 | ~ ('#form14') 54.17/7.41 | ~ ('#form98' @ '#sk5'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl278])). 54.17/7.41 thf(zip_derived_cl279, plain, 54.17/7.41 (( ((((('#sk1' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) | ('#sk2' @ 54.17/7.41 ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')))) & 54.17/7.41 ('#sk5' @ ('#sk42' @ '#sk5')))) 54.17/7.41 | ~ ('#form14') 54.17/7.41 | ~ ('#form98' @ '#sk5'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl278])). 54.17/7.41 thf(zip_derived_cl282, plain, 54.17/7.41 (( ('#sk5' @ ('#sk42' @ '#sk5')) | ~ ('#form98' @ '#sk5') | ~ ('#form14'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl279])). 54.17/7.41 thf(zip_derived_cl281, plain, 54.17/7.41 (( ((('#sk1' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) | ('#sk2' @ 54.17/7.41 ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')))) 54.17/7.41 | ~ ('#form98' @ '#sk5') 54.17/7.41 | ~ ('#form14'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl279])). 54.17/7.41 thf(zip_derived_cl283, plain, 54.17/7.41 (( ('#sk1' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) 54.17/7.41 | ('#sk2' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) 54.17/7.41 | ~ ('#form14') 54.17/7.41 | ~ ('#form98' @ '#sk5'))), 54.17/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl281])). 54.17/7.41 thf(zip_derived_cl102, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ('#form98' @ X2) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 54.17/7.41 (X2 @ Y0)))))))), 54.17/7.41 define([status(thm)])). 54.17/7.41 thf(zip_derived_cl103, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ ((((('#sk1' @ '#sk3' @ ('#sk99' @ X2)) | ('#sk2' @ '#sk3' @ 54.17/7.41 ('#sk99' @ X2)))) => 54.17/7.41 (X2 @ ('#sk99' @ X2)))) 54.17/7.41 | ('#form98' @ X2))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl102])). 54.17/7.41 thf(zip_derived_cl116, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ((('#sk1' @ '#sk3' @ ('#sk99' @ X2)) | ('#sk2' @ '#sk3' @ 54.17/7.41 ('#sk99' @ X2)))) 54.17/7.41 | ('#form98' @ X2))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])). 54.17/7.41 thf(zip_derived_cl136, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ('#sk1' @ '#sk3' @ ('#sk99' @ X2)) 54.17/7.41 | ('#sk2' @ '#sk3' @ ('#sk99' @ X2)) 54.17/7.41 | ('#form98' @ X2))), 54.17/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl116])). 54.17/7.41 thf(zip_derived_cl27, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) => 54.17/7.41 (X2 @ '#sk7'))) 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y1) | 54.17/7.41 ('#sk2' @ '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk4')))))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))) 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((('#sk1' @ Y1 @ Y2) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk7')))))))), 54.17/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 54.17/7.41 thf(zip_derived_cl34, plain, 54.17/7.41 ((~ ('#form14') 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 54.17/7.41 '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk4')))))))), 54.17/7.41 define([status(thm)])). 54.17/7.41 thf(zip_derived_cl38, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ('#form14') 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((('#sk1' @ Y1 @ Y2) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk7')))))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))) 54.17/7.41 | (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) => 54.17/7.41 (X2 @ '#sk7'))))), 54.17/7.41 inference('renaming', [status(thm)], [zip_derived_cl27, zip_derived_cl34])). 54.17/7.41 thf(zip_derived_cl43, plain, 54.17/7.41 ((~ ('#form19') 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((('#sk1' @ Y1 @ Y2) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk7')))))))), 54.17/7.41 define([status(thm)])). 54.17/7.41 thf(zip_derived_cl44, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))))) => 54.17/7.41 (X2 @ '#sk7'))) 54.17/7.41 | ~ ('#form19'))), 54.17/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 54.17/7.41 thf(zip_derived_cl53, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))))) 54.17/7.41 | (X2 @ '#sk7') 54.17/7.41 | ~ ('#form19'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 54.17/7.41 thf(zip_derived_cl60, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))) 54.17/7.41 | ~ ('#form19') 54.17/7.41 | (X2 @ '#sk7'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl53])). 54.17/7.41 thf(zip_derived_cl71, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ ((('#sk1' @ '#sk6' @ ('#sk50' @ X2)) => (X2 @ ('#sk50' @ X2)))) 54.17/7.41 | (X2 @ '#sk7') 54.17/7.41 | ~ ('#form19') 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl60])). 54.17/7.41 thf(zip_derived_cl87, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (X2 @ ('#sk50' @ X2)) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))) 54.17/7.41 | ~ ('#form19') 54.17/7.41 | (X2 @ '#sk7'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 54.17/7.41 thf(zip_derived_cl99, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ ('#sk86' @ X2) @ Y0) & (X2 @ 54.17/7.41 ('#sk86' @ X2)))) => 54.17/7.41 (X2 @ Y0)))))) 54.17/7.41 | (X2 @ '#sk7') 54.17/7.41 | ~ ('#form19') 54.17/7.41 | ~ (X2 @ ('#sk50' @ X2)))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl87])). 54.17/7.41 thf(zip_derived_cl113, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ ((((('#sk1' @ ('#sk86' @ X2) @ ('#sk115' @ X2)) & (X2 @ 54.17/7.41 ('#sk86' @ X2)))) => 54.17/7.41 (X2 @ ('#sk115' @ X2)))) 54.17/7.41 | ~ (X2 @ ('#sk50' @ X2)) 54.17/7.41 | ~ ('#form19') 54.17/7.41 | (X2 @ '#sk7'))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl99])). 54.17/7.41 thf(zip_derived_cl132, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (X2 @ ('#sk115' @ X2)) 54.17/7.41 | (X2 @ '#sk7') 54.17/7.41 | ~ ('#form19') 54.17/7.41 | ~ (X2 @ ('#sk50' @ X2)))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl113])). 54.17/7.41 thf(zip_derived_cl131, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ((('#sk1' @ ('#sk86' @ X2) @ ('#sk115' @ X2)) & (X2 @ 54.17/7.41 ('#sk86' @ X2)))) 54.17/7.41 | (X2 @ '#sk7') 54.17/7.41 | ~ ('#form19') 54.17/7.41 | ~ (X2 @ ('#sk50' @ X2)))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl113])). 54.17/7.41 thf(zip_derived_cl150, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( (X2 @ ('#sk86' @ X2)) 54.17/7.41 | ~ (X2 @ ('#sk50' @ X2)) 54.17/7.41 | ~ ('#form19') 54.17/7.41 | (X2 @ '#sk7'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl131])). 54.17/7.41 thf(zip_derived_cl149, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ('#sk1' @ ('#sk86' @ X2) @ ('#sk115' @ X2)) 54.17/7.41 | ~ (X2 @ ('#sk50' @ X2)) 54.17/7.41 | ~ ('#form19') 54.17/7.41 | (X2 @ '#sk7'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl131])). 54.17/7.41 thf(zip_derived_cl13, plain, 54.17/7.41 ( (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 54.17/7.41 ('#sk5' @ Y0))))))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 54.17/7.41 thf(zip_derived_cl16, plain, 54.17/7.41 (![X2 : a]: 54.17/7.41 ((((('#sk2' @ '#sk3' @ X2) | ('#sk1' @ '#sk3' @ X2))) => ('#sk5' @ 54.17/7.41 X2)))), 54.17/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 54.17/7.41 thf(zip_derived_cl20, plain, 54.17/7.41 (![X2 : a]: 54.17/7.41 (~ ((('#sk2' @ '#sk3' @ X2) | ('#sk1' @ '#sk3' @ X2))) 54.17/7.41 | ('#sk5' @ X2))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 54.17/7.41 thf(zip_derived_cl25, plain, 54.17/7.41 (![X2 : a]: (~ ('#sk1' @ '#sk3' @ X2) | ('#sk5' @ X2))), 54.17/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 54.17/7.41 thf(zip_derived_cl24, plain, 54.17/7.41 (![X2 : a]: (~ ('#sk2' @ '#sk3' @ X2) | ('#sk5' @ X2))), 54.17/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 54.17/7.41 thf(zip_derived_cl117, plain, 54.17/7.41 (![X2 : a > $o]: (~ (X2 @ ('#sk99' @ X2)) | ('#form98' @ X2))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])). 54.17/7.41 thf(zip_derived_cl19, plain, 54.17/7.41 ((~ (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk6' @ Y1) | ('#sk2' @ 54.17/7.41 '#sk6' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk7')))))) 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 54.17/7.41 '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk4')))))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 54.17/7.41 thf(zip_derived_cl23, plain, 54.17/7.41 ((~ (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 54.17/7.41 Y0 @ Y1))) & 54.17/7.41 ('#sk8' @ Y0))) => 54.17/7.41 ('#sk8' @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 54.17/7.41 ('#sk8' @ Y0)))))))) => 54.17/7.41 ('#sk8' @ '#sk7'))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))) 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 54.17/7.41 '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk4')))))))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 54.17/7.41 thf(zip_derived_cl23, plain, 54.17/7.41 ((~ (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 54.17/7.41 Y0 @ Y1))) & 54.17/7.41 ('#sk8' @ Y0))) => 54.17/7.41 ('#sk8' @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 54.17/7.41 ('#sk8' @ Y0)))))))) => 54.17/7.41 ('#sk8' @ '#sk7'))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))) 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 54.17/7.41 '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk4')))))))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 54.17/7.41 thf(zip_derived_cl30, plain, 54.17/7.41 (( ('#form9') 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))))), 54.17/7.41 define([status(thm)])). 54.17/7.41 thf(zip_derived_cl32, plain, 54.17/7.41 ((~ ('#form9') 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 54.17/7.41 '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk4')))))) 54.17/7.41 | ~ (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 54.17/7.41 Y0 @ Y1))) & 54.17/7.41 ('#sk8' @ Y0))) => 54.17/7.41 ('#sk8' @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 54.17/7.41 ('#sk8' @ Y0)))))))) => 54.17/7.41 ('#sk8' @ '#sk7'))))), 54.17/7.41 inference('renaming', [status(thm)], [zip_derived_cl23, zip_derived_cl30])). 54.17/7.41 thf(zip_derived_cl34, plain, 54.17/7.41 ((~ ('#form14') 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 54.17/7.41 '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk4')))))))), 54.17/7.41 define([status(thm)])). 54.17/7.41 thf(zip_derived_cl39, plain, 54.17/7.41 (( ('#form14') 54.17/7.41 | ~ (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 54.17/7.41 Y0 @ Y1))) & 54.17/7.41 ('#sk8' @ Y0))) => 54.17/7.41 ('#sk8' @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 54.17/7.41 ('#sk8' @ Y0)))))))) => 54.17/7.41 ('#sk8' @ '#sk7'))) 54.17/7.41 | ~ ('#form9'))), 54.17/7.41 inference('renaming', [status(thm)], [zip_derived_cl32, zip_derived_cl34])). 54.17/7.41 thf(zip_derived_cl49, plain, 54.17/7.41 (( (((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.17/7.41 Y1))) & 54.17/7.41 ('#sk8' @ Y0))) => 54.17/7.41 ('#sk8' @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 54.17/7.41 ('#sk8' @ Y0)))))))) 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ('#form14'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 54.17/7.41 thf(zip_derived_cl56, plain, 54.17/7.41 (( (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 54.17/7.41 ('#sk8' @ Y0)))))) 54.17/7.41 | ('#form14') 54.17/7.41 | ~ ('#form9'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl49])). 54.17/7.41 thf(zip_derived_cl63, plain, 54.17/7.41 (![X2 : a]: 54.17/7.41 ( ((((('#sk1' @ '#sk6' @ X2) | ('#sk2' @ '#sk6' @ X2))) => ('#sk8' @ 54.17/7.41 X2))) 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ('#form14'))), 54.17/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl56])). 54.17/7.41 thf(zip_derived_cl74, plain, 54.17/7.41 (![X2 : a]: 54.17/7.41 (~ ((('#sk1' @ '#sk6' @ X2) | ('#sk2' @ '#sk6' @ X2))) 54.17/7.41 | ('#sk8' @ X2) 54.17/7.41 | ('#form14') 54.17/7.41 | ~ ('#form9'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl63])). 54.17/7.41 thf(zip_derived_cl91, plain, 54.17/7.41 (![X2 : a]: 54.17/7.41 (~ ('#sk1' @ '#sk6' @ X2) 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ('#form14') 54.17/7.41 | ('#sk8' @ X2))), 54.17/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl74])). 54.17/7.41 thf(zip_derived_cl50, plain, 54.17/7.41 ((~ ('#sk8' @ '#sk7') | ~ ('#form9') | ('#form14'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 54.17/7.41 thf(zip_derived_cl86, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ('#sk1' @ '#sk6' @ ('#sk50' @ X2)) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))) 54.17/7.41 | ~ ('#form19') 54.17/7.41 | (X2 @ '#sk7'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 54.17/7.41 thf(zip_derived_cl98, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk1' @ ('#sk86' @ X2) @ Y0) & (X2 @ 54.17/7.41 ('#sk86' @ X2)))) => 54.17/7.41 (X2 @ Y0)))))) 54.17/7.41 | (X2 @ '#sk7') 54.17/7.41 | ~ ('#form19') 54.17/7.41 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl86])). 54.17/7.41 thf(zip_derived_cl112, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ ((((('#sk1' @ ('#sk86' @ X2) @ ('#sk115' @ X2)) & (X2 @ 54.17/7.41 ('#sk86' @ X2)))) => 54.17/7.41 (X2 @ ('#sk115' @ X2)))) 54.17/7.41 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)) 54.17/7.41 | ~ ('#form19') 54.17/7.41 | (X2 @ '#sk7'))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl98])). 54.17/7.41 thf(zip_derived_cl130, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (X2 @ ('#sk115' @ X2)) 54.17/7.41 | (X2 @ '#sk7') 54.17/7.41 | ~ ('#form19') 54.17/7.41 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl112])). 54.17/7.41 thf(zip_derived_cl129, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ((('#sk1' @ ('#sk86' @ X2) @ ('#sk115' @ X2)) & (X2 @ 54.17/7.41 ('#sk86' @ X2)))) 54.17/7.41 | (X2 @ '#sk7') 54.17/7.41 | ~ ('#form19') 54.17/7.41 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl112])). 54.17/7.41 thf(zip_derived_cl148, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( (X2 @ ('#sk86' @ X2)) 54.17/7.41 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)) 54.17/7.41 | ~ ('#form19') 54.17/7.41 | (X2 @ '#sk7'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl129])). 54.17/7.41 thf(zip_derived_cl147, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ('#sk1' @ ('#sk86' @ X2) @ ('#sk115' @ X2)) 54.17/7.41 | ('#sk1' @ '#sk6' @ ('#sk50' @ X2)) 54.17/7.41 | ~ ('#form19') 54.17/7.41 | (X2 @ '#sk7'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl129])). 54.17/7.41 thf(zip_derived_cl55, plain, 54.17/7.41 (( (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 54.17/7.41 ('#sk8' @ Y0))) => 54.17/7.41 ('#sk8' @ Y1))))))))) 54.17/7.41 | ('#form14') 54.17/7.41 | ~ ('#form9'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl49])). 54.17/7.41 thf(zip_derived_cl62, plain, 54.17/7.41 (![X2 : a]: 54.17/7.41 ( (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) & 54.17/7.41 ('#sk8' @ X2))) => 54.17/7.41 ('#sk8' @ Y0)))))) 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ('#form14'))), 54.17/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl55])). 54.17/7.41 thf(zip_derived_cl73, plain, 54.17/7.41 (![X2 : a, X4 : a]: 54.17/7.41 ( ((((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk8' @ X2))) => 54.17/7.41 ('#sk8' @ X4))) 54.17/7.41 | ('#form14') 54.17/7.41 | ~ ('#form9'))), 54.17/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl62])). 54.17/7.41 thf(zip_derived_cl90, plain, 54.17/7.41 (![X2 : a, X4 : a]: 54.17/7.41 (~ ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk8' @ X2))) 54.17/7.41 | ('#sk8' @ X4) 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ('#form14'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 54.17/7.41 thf(zip_derived_cl105, plain, 54.17/7.41 (![X2 : a, X4 : a]: 54.17/7.41 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 54.17/7.41 | ~ ('#sk8' @ X2) 54.17/7.41 | ('#form14') 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ('#sk8' @ X4))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl90])). 54.17/7.41 thf(zip_derived_cl118, plain, 54.17/7.41 (![X2 : a, X4 : a]: 54.17/7.41 (~ ('#sk1' @ X2 @ X4) 54.17/7.41 | ('#sk8' @ X4) 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ('#form14') 54.17/7.41 | ~ ('#sk8' @ X2))), 54.17/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl105])). 54.17/7.41 thf(zip_derived_cl27, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) => 54.17/7.41 (X2 @ '#sk7'))) 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y1) | 54.17/7.41 ('#sk2' @ '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk4')))))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))) 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((('#sk1' @ Y1 @ Y2) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk7')))))))), 54.17/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 54.17/7.41 thf(zip_derived_cl28, plain, 54.17/7.41 (( (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 54.17/7.41 ('#sk8' @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))))) => 54.17/7.41 ('#sk8' @ '#sk7'))) 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 54.17/7.41 '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk4')))))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))) 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((('#sk1' @ Y1 @ Y2) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk7')))))))), 54.17/7.41 inference('triggered_bool_instantiation', [status(thm)], 54.17/7.41 [zip_derived_cl27])). 54.17/7.41 thf(zip_derived_cl34, plain, 54.17/7.41 ((~ ('#form14') 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 54.17/7.41 '#sk3' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk4')))))))), 54.17/7.41 define([status(thm)])). 54.17/7.41 thf(zip_derived_cl203, plain, 54.17/7.41 (( ('#form14') 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((('#sk1' @ Y1 @ Y2) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk7')))))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))) 54.17/7.41 | (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 54.17/7.41 ('#sk8' @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))))) => 54.17/7.41 ('#sk8' @ '#sk7'))))), 54.17/7.41 inference('renaming', [status(thm)], [zip_derived_cl28, zip_derived_cl34])). 54.17/7.41 thf(zip_derived_cl43, plain, 54.17/7.41 ((~ ('#form19') 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((('#sk1' @ Y1 @ Y2) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk7')))))))), 54.17/7.41 define([status(thm)])). 54.17/7.41 thf(zip_derived_cl204, plain, 54.17/7.41 (( ('#form19') 54.17/7.41 | (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 54.17/7.41 ('#sk8' @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))))) => 54.17/7.41 ('#sk8' @ '#sk7'))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))) 54.17/7.41 | ('#form14'))), 54.17/7.41 inference('renaming', [status(thm)], 54.17/7.41 [zip_derived_cl203, zip_derived_cl43])). 54.17/7.41 thf(zip_derived_cl30, plain, 54.17/7.41 (( ('#form9') 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))))), 54.17/7.41 define([status(thm)])). 54.17/7.41 thf(zip_derived_cl205, plain, 54.17/7.41 ((~ ('#form9') 54.17/7.41 | ('#form14') 54.17/7.41 | (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 54.17/7.41 ('#sk8' @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))))) => 54.17/7.41 ('#sk8' @ '#sk7'))) 54.17/7.41 | ('#form19'))), 54.17/7.41 inference('renaming', [status(thm)], 54.17/7.41 [zip_derived_cl204, zip_derived_cl30])). 54.17/7.41 thf(zip_derived_cl206, plain, 54.17/7.41 ((~ (((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 54.17/7.41 ('#sk8' @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))))) 54.17/7.41 | ('#sk8' @ '#sk7') 54.17/7.41 | ('#form19') 54.17/7.41 | ('#form14') 54.17/7.41 | ~ ('#form9'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl205])). 54.17/7.41 thf(zip_derived_cl50, plain, 54.17/7.41 ((~ ('#sk8' @ '#sk7') | ~ ('#form9') | ('#form14'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 54.17/7.41 thf(zip_derived_cl207, plain, 54.17/7.41 ((~ ('#form9') 54.17/7.41 | ('#form14') 54.17/7.41 | ('#form19') 54.17/7.41 | ~ (((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 54.17/7.41 ('#sk8' @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))))))), 54.17/7.41 inference('clc', [status(thm)], [zip_derived_cl206, zip_derived_cl50])). 54.17/7.41 thf(zip_derived_cl208, plain, 54.17/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 54.17/7.41 ('#sk8' @ Y1))))))))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) 54.17/7.41 | ('#form19') 54.17/7.41 | ('#form14') 54.17/7.41 | ~ ('#form9'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl207])). 54.17/7.41 thf(zip_derived_cl38, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ('#form14') 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((('#sk1' @ Y1 @ Y2) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk7')))))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))) 54.17/7.41 | (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) => 54.17/7.41 (X2 @ '#sk7'))))), 54.17/7.41 inference('renaming', [status(thm)], [zip_derived_cl27, zip_derived_cl34])). 54.17/7.41 thf(zip_derived_cl43, plain, 54.17/7.41 ((~ ('#form19') 54.17/7.41 | (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((('#sk1' @ Y1 @ Y2) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk7')))))))), 54.17/7.41 define([status(thm)])). 54.17/7.41 thf(zip_derived_cl47, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ('#form19') 54.17/7.41 | (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) => 54.17/7.41 (X2 @ '#sk7'))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))) 54.17/7.41 | ('#form14'))), 54.17/7.41 inference('renaming', [status(thm)], [zip_derived_cl38, zip_derived_cl43])). 54.17/7.41 thf(zip_derived_cl30, plain, 54.17/7.41 (( ('#form9') 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))))), 54.17/7.41 define([status(thm)])). 54.17/7.41 thf(zip_derived_cl52, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ ('#form9') 54.17/7.41 | ('#form14') 54.17/7.41 | (((((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) => 54.17/7.41 (X2 @ '#sk7'))) 54.17/7.41 | ('#form19'))), 54.17/7.41 inference('renaming', [status(thm)], [zip_derived_cl47, zip_derived_cl30])). 54.17/7.41 thf(zip_derived_cl59, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (((((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) 54.17/7.41 | (X2 @ '#sk7') 54.17/7.41 | ('#form19') 54.17/7.41 | ('#form14') 54.17/7.41 | ~ ('#form9'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 54.17/7.41 thf(zip_derived_cl70, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 54.17/7.41 (X2 @ Y1))))))))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ('#form14') 54.17/7.41 | ('#form19') 54.17/7.41 | (X2 @ '#sk7'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl59])). 54.17/7.41 thf(zip_derived_cl85, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk2' @ ('#sk60' @ X2) @ Y0) & (X2 @ 54.17/7.41 ('#sk60' @ X2)))) => 54.17/7.41 (X2 @ Y0)))))) 54.17/7.41 | (X2 @ '#sk7') 54.17/7.41 | ('#form19') 54.17/7.41 | ('#form14') 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl70])). 54.17/7.41 thf(zip_derived_cl97, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ ((((('#sk2' @ ('#sk60' @ X2) @ ('#sk82' @ X2)) & (X2 @ 54.17/7.41 ('#sk60' @ X2)))) => 54.17/7.41 (X2 @ ('#sk82' @ X2)))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ('#form14') 54.17/7.41 | ('#form19') 54.17/7.41 | (X2 @ '#sk7'))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl85])). 54.17/7.41 thf(zip_derived_cl111, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (X2 @ ('#sk82' @ X2)) 54.17/7.41 | (X2 @ '#sk7') 54.17/7.41 | ('#form19') 54.17/7.41 | ('#form14') 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])). 54.17/7.41 thf(zip_derived_cl126, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ('#form147' @ X2) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 54.17/7.41 define([status(thm)])). 54.17/7.41 thf(zip_derived_cl209, plain, 54.17/7.41 ((~ ('#form147' @ '#sk8') 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ('#form14') 54.17/7.41 | ('#form19') 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ Y0 @ Y1) & ('#sk8' @ Y0))) => 54.17/7.41 ('#sk8' @ Y1))))))))))), 54.17/7.41 inference('renaming', [status(thm)], 54.17/7.41 [zip_derived_cl208, zip_derived_cl126])). 54.17/7.41 thf(zip_derived_cl210, plain, 54.17/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk2' @ ('#sk60' @ '#sk8') @ Y0) & ('#sk8' @ 54.17/7.41 ('#sk60' @ '#sk8')))) => 54.17/7.41 ('#sk8' @ Y0)))))) 54.17/7.41 | ('#form19') 54.17/7.41 | ('#form14') 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ~ ('#form147' @ '#sk8'))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl209])). 54.17/7.41 thf(zip_derived_cl211, plain, 54.17/7.41 ((~ ((((('#sk2' @ ('#sk60' @ '#sk8') @ ('#sk82' @ '#sk8')) & ('#sk8' @ 54.17/7.41 ('#sk60' @ '#sk8')))) => 54.17/7.41 ('#sk8' @ ('#sk82' @ '#sk8')))) 54.17/7.41 | ~ ('#form147' @ '#sk8') 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ('#form14') 54.17/7.41 | ('#form19'))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl210])). 54.17/7.41 thf(zip_derived_cl213, plain, 54.17/7.41 ((~ ('#sk8' @ ('#sk82' @ '#sk8')) 54.17/7.41 | ('#form19') 54.17/7.41 | ('#form14') 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ~ ('#form147' @ '#sk8'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl211])). 54.17/7.41 thf(zip_derived_cl212, plain, 54.17/7.41 (( ((('#sk2' @ ('#sk60' @ '#sk8') @ ('#sk82' @ '#sk8')) & ('#sk8' @ 54.17/7.41 ('#sk60' @ '#sk8')))) 54.17/7.41 | ('#form19') 54.17/7.41 | ('#form14') 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ~ ('#form147' @ '#sk8'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl211])). 54.17/7.41 thf(zip_derived_cl215, plain, 54.17/7.41 (( ('#sk8' @ ('#sk60' @ '#sk8')) 54.17/7.41 | ~ ('#form147' @ '#sk8') 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ('#form14') 54.17/7.41 | ('#form19'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl212])). 54.17/7.41 thf(zip_derived_cl214, plain, 54.17/7.41 (( ('#sk2' @ ('#sk60' @ '#sk8') @ ('#sk82' @ '#sk8')) 54.17/7.41 | ~ ('#form147' @ '#sk8') 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ('#form14') 54.17/7.41 | ('#form19'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl212])). 54.17/7.41 thf(zip_derived_cl119, plain, 54.17/7.41 (![X2 : a, X4 : a]: 54.17/7.41 (~ ('#sk2' @ X2 @ X4) 54.17/7.41 | ('#sk8' @ X4) 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ('#form14') 54.17/7.41 | ~ ('#sk8' @ X2))), 54.17/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl105])). 54.17/7.41 thf(zip_derived_cl126, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ('#form147' @ X2) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 54.17/7.41 define([status(thm)])). 54.17/7.41 thf(zip_derived_cl127, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ ((('#sk2' @ '#sk6' @ ('#sk148' @ X2)) => (X2 @ ('#sk148' @ X2)))) 54.17/7.41 | ('#form147' @ X2))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl126])). 54.17/7.41 thf(zip_derived_cl145, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ('#sk2' @ '#sk6' @ ('#sk148' @ X2)) | ('#form147' @ X2))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 54.17/7.41 thf(zip_derived_cl146, plain, 54.17/7.41 (![X2 : a > $o]: (~ (X2 @ ('#sk148' @ X2)) | ('#form147' @ X2))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 54.17/7.41 thf(zip_derived_cl92, plain, 54.17/7.41 (![X2 : a]: 54.17/7.41 (~ ('#sk2' @ '#sk6' @ X2) 54.17/7.41 | ~ ('#form9') 54.17/7.41 | ('#form14') 54.17/7.41 | ('#sk8' @ X2))), 54.17/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl74])). 54.17/7.41 thf(zip_derived_cl30, plain, 54.17/7.41 (( ('#form9') 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y1 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y1 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ Y5))) & 54.17/7.41 (Y3 @ Y4))) => 54.17/7.41 (Y3 @ Y5))))))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))))) => 54.17/7.41 (Y3 @ Y1)))))))) => 54.17/7.41 (((!!) @ (^[Y3 : a > $o]: 54.17/7.41 (((((((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y4))) => 54.17/7.41 (Y3 @ Y4)))))) & 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (!!) @ ( 54.17/7.41 ^[Y5 : a]: 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 (Y3 @ 54.17/7.41 Y4) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y4 @ 54.17/7.41 Y5) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y4 @ Y5))))) => 54.17/7.41 (Y3 @ Y5))))))))))) => 54.17/7.41 (Y3 @ Y2))))))))))))))))))), 54.17/7.41 define([status(thm)])). 54.17/7.41 thf(zip_derived_cl31, plain, 54.17/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((((((!!) @ (^[Y2 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y3 : a]: 54.17/7.41 ((((('#sk2' @ 54.17/7.41 Y0 @ 54.17/7.41 Y3) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y0 @ Y3))) => 54.17/7.41 (Y2 @ Y3)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 (Y2 @ 54.17/7.41 Y3) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y3 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y3 @ Y4))))) => 54.17/7.41 (Y2 @ Y4))))))))))) => 54.17/7.41 (Y2 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y2 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y3 : a]: 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 ( 54.17/7.41 ( 54.17/7.41 (( 54.17/7.41 (( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y3 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y3 @ Y4))) & 54.17/7.41 (Y2 @ Y3))) => 54.17/7.41 (Y2 @ Y4))))))))) & 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 ((((('#sk2' @ 54.17/7.41 '#sk10' @ 54.17/7.41 Y3) | 54.17/7.41 ('#sk1' @ 54.17/7.41 '#sk10' @ 54.17/7.41 Y3))) => 54.17/7.41 (Y2 @ Y3)))))))) => 54.17/7.41 (Y2 @ Y0)))))))) => 54.17/7.41 (((!!) @ (^[Y2 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y3 : a]: 54.17/7.41 ((((('#sk2' @ 54.17/7.41 '#sk10' @ 54.17/7.41 Y3) | 54.17/7.41 ('#sk1' @ 54.17/7.41 '#sk10' @ 54.17/7.41 Y3))) => 54.17/7.41 (Y2 @ Y3)))))) & 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 (((!!) @ ( 54.17/7.41 ^[Y4 : a]: 54.17/7.41 (((( 54.17/7.41 (Y2 @ 54.17/7.41 Y3) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y3 @ 54.17/7.41 Y4) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y3 @ Y4))))) => 54.17/7.41 (Y2 @ Y4))))))))))) => 54.17/7.41 (Y2 @ Y1)))))))))))))) 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])). 54.17/7.41 thf(zip_derived_cl40, plain, 54.17/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((((((!!) @ (^[Y1 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y2 : a]: 54.17/7.41 ((((('#sk2' @ '#sk15' @ 54.17/7.41 Y2) | ('#sk1' @ 54.17/7.41 '#sk15' @ Y2))) => 54.17/7.41 (Y1 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 (((((Y1 @ 54.17/7.41 Y2) & 54.17/7.41 (( 54.17/7.41 ('#sk1' @ 54.17/7.41 Y2 @ 54.17/7.41 Y3) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y2 @ Y3))))) => 54.17/7.41 (Y1 @ Y3))))))))))) => 54.17/7.41 (Y1 @ Y0)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y2 : a]: 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 (((((( 54.17/7.41 ('#sk2' @ 54.17/7.41 Y2 @ 54.17/7.41 Y3) | 54.17/7.41 ('#sk1' @ 54.17/7.41 Y2 @ Y3))) & 54.17/7.41 (Y1 @ Y2))) => 54.17/7.41 (Y1 @ Y3))))))))) & 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((('#sk2' @ '#sk10' @ 54.17/7.41 Y2) | ('#sk1' @ 54.17/7.41 '#sk10' @ Y2))) => 54.17/7.41 (Y1 @ Y2)))))))) => 54.17/7.41 (Y1 @ '#sk15')))))))) => 54.17/7.41 (((!!) @ (^[Y1 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y2 : a]: 54.17/7.41 ((((('#sk2' @ '#sk10' @ 54.17/7.41 Y2) | ('#sk1' @ 54.17/7.41 '#sk10' @ Y2))) => 54.17/7.41 (Y1 @ Y2)))))) & 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((!!) @ (^[Y3 : a]: 54.17/7.41 (((((Y1 @ Y2) & 54.17/7.41 ((('#sk1' @ 54.17/7.41 Y2 @ 54.17/7.41 Y3) | 54.17/7.41 ('#sk2' @ 54.17/7.41 Y2 @ Y3))))) => 54.17/7.41 (Y1 @ Y3))))))))))) => 54.17/7.41 (Y1 @ Y0))))))))))) 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl31])). 54.17/7.41 thf(zip_derived_cl51, plain, 54.17/7.41 ((~ (((((((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ '#sk15' @ Y1) | 54.17/7.41 ('#sk1' @ '#sk15' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((Y0 @ Y1) & 54.17/7.41 ((('#sk1' @ Y1 @ 54.17/7.41 Y2) | ('#sk2' @ 54.17/7.41 Y1 @ Y2))))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk23')))))) & 54.17/7.41 (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk2' @ Y1 @ 54.17/7.41 Y2) | ('#sk1' @ 54.17/7.41 Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ '#sk10' @ Y1) | 54.17/7.41 ('#sk1' @ '#sk10' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk15')))))))) => 54.17/7.41 (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ '#sk10' @ Y1) | 54.17/7.41 ('#sk1' @ '#sk10' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((Y0 @ Y1) & 54.17/7.41 ((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk23')))))))) 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl40])). 54.17/7.41 thf(zip_derived_cl57, plain, 54.17/7.41 (( (((((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ '#sk15' @ Y1) | ('#sk1' @ 54.17/7.41 '#sk15' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((Y0 @ Y1) & 54.17/7.41 ((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk23')))))) & 54.17/7.41 (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 ((((((('#sk2' @ Y1 @ Y2) | 54.17/7.41 ('#sk1' @ Y1 @ Y2))) & 54.17/7.41 (Y0 @ Y1))) => 54.17/7.41 (Y0 @ Y2))))))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ '#sk10' @ Y1) | ('#sk1' @ 54.17/7.41 '#sk10' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))))) => 54.17/7.41 (Y0 @ '#sk15')))))))) 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 54.17/7.41 thf(zip_derived_cl64, plain, 54.17/7.41 (( (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ '#sk15' @ Y1) | ('#sk1' @ 54.17/7.41 '#sk15' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((Y0 @ Y1) & 54.17/7.41 ((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk23')))))) 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl57])). 54.17/7.41 thf(zip_derived_cl75, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( (((((((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ 54.17/7.41 Y0))) => 54.17/7.41 (X2 @ Y0)))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((((X2 @ Y0) & 54.17/7.41 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 54.17/7.41 Y0 @ Y1))))) => 54.17/7.41 (X2 @ Y1))))))))))) => 54.17/7.41 (X2 @ '#sk23'))) 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl64])). 54.17/7.41 thf(zip_derived_cl76, plain, 54.17/7.41 (( (((((((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 54.17/7.41 ('#sk43' @ Y0)))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk43' @ Y0) & 54.17/7.41 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.17/7.41 Y1))))) => 54.17/7.41 ('#sk43' @ Y1))))))))))) => 54.17/7.41 ('#sk43' @ '#sk23'))) 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('triggered_bool_instantiation', [status(thm)], 54.17/7.41 [zip_derived_cl75])). 54.17/7.41 thf(zip_derived_cl294, plain, 54.17/7.41 ((~ (((((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 54.17/7.41 ('#sk43' @ Y0)))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk43' @ Y0) & 54.17/7.41 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.17/7.41 Y1))))) => 54.17/7.41 ('#sk43' @ Y1))))))))))) 54.17/7.41 | ('#sk43' @ '#sk23') 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl76])). 54.17/7.41 thf(zip_derived_cl58, plain, 54.17/7.41 ((~ (((!!) @ (^[Y0 : a > $o]: 54.17/7.41 (((((((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk2' @ '#sk10' @ Y1) | ('#sk1' @ 54.17/7.41 '#sk10' @ Y1))) => 54.17/7.41 (Y0 @ Y1)))))) & 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((!!) @ (^[Y2 : a]: 54.17/7.41 (((((Y0 @ Y1) & 54.17/7.41 ((('#sk1' @ Y1 @ Y2) | 54.17/7.41 ('#sk2' @ Y1 @ Y2))))) => 54.17/7.41 (Y0 @ Y2))))))))))) => 54.17/7.41 (Y0 @ '#sk23')))))) 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 54.17/7.41 thf(zip_derived_cl69, plain, 54.17/7.41 ((~ (((((((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 54.17/7.41 ('#sk43' @ Y0)))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk43' @ Y0) & 54.17/7.41 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 54.17/7.41 Y0 @ Y1))))) => 54.17/7.41 ('#sk43' @ Y1))))))))))) => 54.17/7.41 ('#sk43' @ '#sk23'))) 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl58])). 54.17/7.41 thf(zip_derived_cl84, plain, ((~ ('#sk43' @ '#sk23') | ('#form9'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl69])). 54.17/7.41 thf(zip_derived_cl295, plain, 54.17/7.41 (( ('#form9') 54.17/7.41 | ~ (((((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 54.17/7.41 ('#sk43' @ Y0)))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk43' @ Y0) & 54.17/7.41 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 54.17/7.41 Y0 @ Y1))))) => 54.17/7.41 ('#sk43' @ Y1))))))))))))), 54.17/7.41 inference('clc', [status(thm)], [zip_derived_cl294, zip_derived_cl84])). 54.17/7.41 thf(zip_derived_cl296, plain, 54.17/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 54.17/7.41 ('#sk43' @ Y0)))))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk43' @ Y0) & 54.17/7.41 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.17/7.41 Y1))))) => 54.17/7.41 ('#sk43' @ Y1))))))))) 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl295])). 54.17/7.41 thf(zip_derived_cl297, plain, 54.17/7.41 ((~ ((((('#sk2' @ '#sk15' @ ('#sk136' @ '#sk43')) | ('#sk1' @ '#sk15' @ 54.17/7.41 ('#sk136' @ '#sk43')))) => 54.17/7.41 ('#sk43' @ ('#sk136' @ '#sk43')))) 54.17/7.41 | ('#form9') 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk43' @ Y0) & 54.17/7.41 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.17/7.41 Y1))))) => 54.17/7.41 ('#sk43' @ Y1))))))))))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl296])). 54.17/7.41 thf(zip_derived_cl299, plain, 54.17/7.41 ((~ ('#sk43' @ ('#sk136' @ '#sk43')) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk43' @ Y0) & 54.17/7.41 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.17/7.41 Y1))))) => 54.17/7.41 ('#sk43' @ Y1))))))))) 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl297])). 54.17/7.41 thf(zip_derived_cl301, plain, 54.17/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk43' @ ('#sk226' @ '#sk43')) & 54.17/7.41 ((('#sk1' @ ('#sk226' @ '#sk43') @ Y0) | ('#sk2' @ 54.17/7.41 ('#sk226' @ '#sk43') @ Y0))))) => 54.17/7.41 ('#sk43' @ Y0)))))) 54.17/7.41 | ('#form9') 54.17/7.41 | ~ ('#sk43' @ ('#sk136' @ '#sk43')))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl299])). 54.17/7.41 thf(zip_derived_cl303, plain, 54.17/7.41 ((~ ((((('#sk43' @ ('#sk226' @ '#sk43')) & 54.17/7.41 ((('#sk1' @ ('#sk226' @ '#sk43') @ ('#sk267' @ '#sk43')) | 54.17/7.41 ('#sk2' @ ('#sk226' @ '#sk43') @ ('#sk267' @ '#sk43')))))) => 54.17/7.41 ('#sk43' @ ('#sk267' @ '#sk43')))) 54.17/7.41 | ~ ('#sk43' @ ('#sk136' @ '#sk43')) 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl301])). 54.17/7.41 thf(zip_derived_cl305, plain, 54.17/7.41 (( ((('#sk43' @ ('#sk226' @ '#sk43')) & 54.17/7.41 ((('#sk1' @ ('#sk226' @ '#sk43') @ ('#sk267' @ '#sk43')) | 54.17/7.41 ('#sk2' @ ('#sk226' @ '#sk43') @ ('#sk267' @ '#sk43')))))) 54.17/7.41 | ('#form9') 54.17/7.41 | ~ ('#sk43' @ ('#sk136' @ '#sk43')))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl303])). 54.17/7.41 thf(zip_derived_cl310, plain, 54.17/7.41 (( ((('#sk1' @ ('#sk226' @ '#sk43') @ ('#sk267' @ '#sk43')) | ('#sk2' @ 54.17/7.41 ('#sk226' @ '#sk43') @ ('#sk267' @ '#sk43')))) 54.17/7.41 | ~ ('#sk43' @ ('#sk136' @ '#sk43')) 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl305])). 54.17/7.41 thf(zip_derived_cl313, plain, 54.17/7.41 (( ('#sk1' @ ('#sk226' @ '#sk43') @ ('#sk267' @ '#sk43')) 54.17/7.41 | ('#sk2' @ ('#sk226' @ '#sk43') @ ('#sk267' @ '#sk43')) 54.17/7.41 | ('#form9') 54.17/7.41 | ~ ('#sk43' @ ('#sk136' @ '#sk43')))), 54.17/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl310])). 54.17/7.41 thf(zip_derived_cl75, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( (((((((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ 54.17/7.41 Y0))) => 54.17/7.41 (X2 @ Y0)))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((((X2 @ Y0) & 54.17/7.41 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 54.17/7.41 Y0 @ Y1))))) => 54.17/7.41 (X2 @ Y1))))))))))) => 54.17/7.41 (X2 @ '#sk23'))) 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl64])). 54.17/7.41 thf(zip_derived_cl93, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (((((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 54.17/7.41 (X2 @ Y0)))))) & 54.17/7.41 (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((((X2 @ Y0) & 54.17/7.41 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 54.17/7.41 Y0 @ Y1))))) => 54.17/7.41 (X2 @ Y1))))))))))) 54.17/7.41 | (X2 @ '#sk23') 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 54.17/7.41 thf(zip_derived_cl106, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 54.17/7.41 (X2 @ Y0)))))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((((X2 @ Y0) & 54.17/7.41 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 54.17/7.41 Y0 @ Y1))))) => 54.17/7.41 (X2 @ Y1))))))))) 54.17/7.41 | ('#form9') 54.17/7.41 | (X2 @ '#sk23'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl93])). 54.17/7.41 thf(zip_derived_cl120, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ ((((('#sk2' @ '#sk15' @ ('#sk136' @ X2)) | ('#sk1' @ '#sk15' @ 54.17/7.41 ('#sk136' @ X2)))) => 54.17/7.41 (X2 @ ('#sk136' @ X2)))) 54.17/7.41 | (X2 @ '#sk23') 54.17/7.41 | ('#form9') 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((((X2 @ Y0) & 54.17/7.41 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 54.17/7.41 Y0 @ Y1))))) => 54.17/7.41 (X2 @ Y1))))))))))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl106])). 54.17/7.41 thf(zip_derived_cl138, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (X2 @ ('#sk136' @ X2)) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((((X2 @ Y0) & 54.17/7.41 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 54.17/7.41 Y0 @ Y1))))) => 54.17/7.41 (X2 @ Y1))))))))) 54.17/7.41 | ('#form9') 54.17/7.41 | (X2 @ '#sk23'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl120])). 54.17/7.41 thf(zip_derived_cl152, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((((X2 @ ('#sk226' @ X2)) & 54.17/7.41 ((('#sk1' @ ('#sk226' @ X2) @ Y0) | ('#sk2' @ 54.17/7.41 ('#sk226' @ X2) @ Y0))))) => 54.17/7.41 (X2 @ Y0)))))) 54.17/7.41 | (X2 @ '#sk23') 54.17/7.41 | ('#form9') 54.17/7.41 | ~ (X2 @ ('#sk136' @ X2)))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl138])). 54.17/7.41 thf(zip_derived_cl159, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (((((X2 @ ('#sk226' @ X2)) & 54.17/7.41 ((('#sk1' @ ('#sk226' @ X2) @ ('#sk267' @ X2)) | ('#sk2' @ 54.17/7.41 ('#sk226' @ X2) @ ('#sk267' @ X2)))))) => 54.17/7.41 (X2 @ ('#sk267' @ X2)))) 54.17/7.41 | ~ (X2 @ ('#sk136' @ X2)) 54.17/7.41 | ('#form9') 54.17/7.41 | (X2 @ '#sk23'))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl152])). 54.17/7.41 thf(zip_derived_cl169, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (X2 @ ('#sk267' @ X2)) 54.17/7.41 | (X2 @ '#sk23') 54.17/7.41 | ('#form9') 54.17/7.41 | ~ (X2 @ ('#sk136' @ X2)))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])). 54.17/7.41 thf(zip_derived_cl298, plain, 54.17/7.41 (( ((('#sk2' @ '#sk15' @ ('#sk136' @ '#sk43')) | ('#sk1' @ '#sk15' @ 54.17/7.41 ('#sk136' @ '#sk43')))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk43' @ Y0) & 54.17/7.41 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.17/7.41 Y1))))) => 54.17/7.41 ('#sk43' @ Y1))))))))) 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl297])). 54.17/7.41 thf(zip_derived_cl300, plain, 54.17/7.41 (( ('#sk2' @ '#sk15' @ ('#sk136' @ '#sk43')) 54.17/7.41 | ('#sk1' @ '#sk15' @ ('#sk136' @ '#sk43')) 54.17/7.41 | ('#form9') 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 ((((('#sk43' @ Y0) & 54.17/7.41 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.17/7.41 Y1))))) => 54.17/7.41 ('#sk43' @ Y1))))))))))), 54.17/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl298])). 54.17/7.41 thf(zip_derived_cl302, plain, 54.17/7.41 ((~ (((!!) @ (^[Y0 : a]: 54.17/7.41 ((((('#sk43' @ ('#sk226' @ '#sk43')) & 54.17/7.41 ((('#sk1' @ ('#sk226' @ '#sk43') @ Y0) | ('#sk2' @ 54.17/7.41 ('#sk226' @ '#sk43') @ Y0))))) => 54.17/7.41 ('#sk43' @ Y0)))))) 54.17/7.41 | ('#form9') 54.17/7.41 | ('#sk1' @ '#sk15' @ ('#sk136' @ '#sk43')) 54.17/7.41 | ('#sk2' @ '#sk15' @ ('#sk136' @ '#sk43')))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl300])). 54.17/7.41 thf(zip_derived_cl304, plain, 54.17/7.41 ((~ ((((('#sk43' @ ('#sk226' @ '#sk43')) & 54.17/7.41 ((('#sk1' @ ('#sk226' @ '#sk43') @ ('#sk267' @ '#sk43')) | 54.17/7.41 ('#sk2' @ ('#sk226' @ '#sk43') @ ('#sk267' @ '#sk43')))))) => 54.17/7.41 ('#sk43' @ ('#sk267' @ '#sk43')))) 54.17/7.41 | ('#sk2' @ '#sk15' @ ('#sk136' @ '#sk43')) 54.17/7.41 | ('#sk1' @ '#sk15' @ ('#sk136' @ '#sk43')) 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl302])). 54.17/7.41 thf(zip_derived_cl308, plain, 54.17/7.41 ((~ ('#sk43' @ ('#sk267' @ '#sk43')) 54.17/7.41 | ('#form9') 54.17/7.41 | ('#sk1' @ '#sk15' @ ('#sk136' @ '#sk43')) 54.17/7.41 | ('#sk2' @ '#sk15' @ ('#sk136' @ '#sk43')))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl304])). 54.17/7.41 thf(zip_derived_cl84, plain, ((~ ('#sk43' @ '#sk23') | ('#form9'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl69])). 54.17/7.41 thf(zip_derived_cl137, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ((('#sk2' @ '#sk15' @ ('#sk136' @ X2)) | ('#sk1' @ '#sk15' @ 54.17/7.41 ('#sk136' @ X2)))) 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((((X2 @ Y0) & 54.17/7.41 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 54.17/7.41 Y0 @ Y1))))) => 54.17/7.41 (X2 @ Y1))))))))) 54.17/7.41 | ('#form9') 54.17/7.41 | (X2 @ '#sk23'))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl120])). 54.17/7.41 thf(zip_derived_cl151, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ('#sk2' @ '#sk15' @ ('#sk136' @ X2)) 54.17/7.41 | ('#sk1' @ '#sk15' @ ('#sk136' @ X2)) 54.17/7.41 | (X2 @ '#sk23') 54.17/7.41 | ('#form9') 54.17/7.41 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((!!) @ (^[Y1 : a]: 54.17/7.41 (((((X2 @ Y0) & 54.17/7.41 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 54.17/7.41 Y0 @ Y1))))) => 54.17/7.41 (X2 @ Y1))))))))))), 54.17/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl137])). 54.17/7.41 thf(zip_derived_cl158, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (((!!) @ (^[Y0 : a]: 54.17/7.41 (((((X2 @ ('#sk226' @ X2)) & 54.17/7.41 ((('#sk1' @ ('#sk226' @ X2) @ Y0) | ('#sk2' @ 54.17/7.41 ('#sk226' @ X2) @ Y0))))) => 54.17/7.41 (X2 @ Y0)))))) 54.17/7.41 | ('#form9') 54.17/7.41 | (X2 @ '#sk23') 54.17/7.41 | ('#sk1' @ '#sk15' @ ('#sk136' @ X2)) 54.17/7.41 | ('#sk2' @ '#sk15' @ ('#sk136' @ X2)))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl151])). 54.17/7.41 thf(zip_derived_cl167, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 (~ (((((X2 @ ('#sk226' @ X2)) & 54.17/7.41 ((('#sk1' @ ('#sk226' @ X2) @ ('#sk267' @ X2)) | ('#sk2' @ 54.17/7.41 ('#sk226' @ X2) @ ('#sk267' @ X2)))))) => 54.17/7.41 (X2 @ ('#sk267' @ X2)))) 54.17/7.41 | ('#sk2' @ '#sk15' @ ('#sk136' @ X2)) 54.17/7.41 | ('#sk1' @ '#sk15' @ ('#sk136' @ X2)) 54.17/7.41 | (X2 @ '#sk23') 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl158])). 54.17/7.41 thf(zip_derived_cl174, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( (((X2 @ ('#sk226' @ X2)) & 54.17/7.41 ((('#sk1' @ ('#sk226' @ X2) @ ('#sk267' @ X2)) | ('#sk2' @ 54.17/7.41 ('#sk226' @ X2) @ ('#sk267' @ X2)))))) 54.17/7.41 | ('#form9') 54.17/7.41 | (X2 @ '#sk23') 54.17/7.41 | ('#sk1' @ '#sk15' @ ('#sk136' @ X2)) 54.17/7.41 | ('#sk2' @ '#sk15' @ ('#sk136' @ X2)))), 54.17/7.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl167])). 54.17/7.41 thf(zip_derived_cl183, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ((('#sk1' @ ('#sk226' @ X2) @ ('#sk267' @ X2)) | ('#sk2' @ 54.17/7.41 ('#sk226' @ X2) @ ('#sk267' @ X2)))) 54.17/7.41 | ('#sk2' @ '#sk15' @ ('#sk136' @ X2)) 54.17/7.41 | ('#sk1' @ '#sk15' @ ('#sk136' @ X2)) 54.17/7.41 | (X2 @ '#sk23') 54.17/7.41 | ('#form9'))), 54.17/7.41 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl174])). 54.17/7.41 thf(zip_derived_cl185, plain, 54.17/7.41 (![X2 : a > $o]: 54.17/7.41 ( ('#sk1' @ ('#sk226' @ X2) @ ('#sk267' @ X2)) 54.17/7.41 | ('#sk2' @ ('#sk226' @ X2) @ ('#sk267' @ X2)) 54.17/7.41 | ('#form9') 54.17/7.41 | (X2 @ '#sk23') 54.17/7.41 | ('#sk1' @ '#sk15' @ ('#sk136' @ X2)) 54.17/7.41 | ('#sk2' @ '#sk15' @ ('#sk136' @ X2)))), 54.17/7.41 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl183])). 54.17/7.41 thf(zip_derived_cl307, plain, 54.17/7.41 (( ((('#sk43' @ ('#sk226' @ '#sk43')) & 54.17/7.41 ((('#sk1' @ ('#sk226' @ '#sk43') @ ('#sk267' @ '#sk43')) | 54.17/7.41 ('#sk2' @ ('#sk226' @ '#sk43') @ ('#sk267' @ '#sk43')))))) 54.17/7.42 | ('#form9') 54.17/7.42 | ('#sk1' @ '#sk15' @ ('#sk136' @ '#sk43')) 54.17/7.42 | ('#sk2' @ '#sk15' @ ('#sk136' @ '#sk43')))), 54.17/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl304])). 54.17/7.42 thf(zip_derived_cl311, plain, 54.17/7.42 (( ('#sk43' @ ('#sk226' @ '#sk43')) 54.17/7.42 | ('#sk2' @ '#sk15' @ ('#sk136' @ '#sk43')) 54.17/7.42 | ('#sk1' @ '#sk15' @ ('#sk136' @ '#sk43')) 54.17/7.42 | ('#form9'))), 54.17/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl307])). 54.17/7.42 thf(zip_derived_cl309, plain, 54.17/7.42 (( ('#sk43' @ ('#sk226' @ '#sk43')) 54.17/7.42 | ~ ('#sk43' @ ('#sk136' @ '#sk43')) 54.17/7.42 | ('#form9'))), 54.17/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl305])). 54.17/7.42 thf(zip_derived_cl65, plain, 54.17/7.42 (( (((!!) @ (^[Y0 : a > $o]: 54.17/7.42 (((((((!!) @ (^[Y1 : a]: 54.17/7.42 (((!!) @ (^[Y2 : a]: 54.17/7.42 ((((((('#sk2' @ Y1 @ Y2) | 54.17/7.42 ('#sk1' @ Y1 @ Y2))) & 54.17/7.42 (Y0 @ Y1))) => 54.17/7.42 (Y0 @ Y2))))))))) & 54.17/7.42 (((!!) @ (^[Y1 : a]: 54.17/7.42 ((((('#sk2' @ '#sk10' @ Y1) | ('#sk1' @ 54.17/7.42 '#sk10' @ Y1))) => 54.17/7.42 (Y0 @ Y1)))))))) => 54.17/7.42 (Y0 @ '#sk15')))))) 54.17/7.42 | ('#form9'))), 54.17/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl57])). 54.17/7.42 thf(zip_derived_cl79, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 ( (((((((!!) @ (^[Y0 : a]: 54.17/7.42 (((!!) @ (^[Y1 : a]: 54.17/7.42 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 54.17/7.42 Y0 @ Y1))) & 54.17/7.42 (X2 @ Y0))) => 54.17/7.42 (X2 @ Y1))))))))) & 54.17/7.42 (((!!) @ (^[Y0 : a]: 54.17/7.42 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ 54.17/7.42 Y0))) => 54.17/7.42 (X2 @ Y0)))))))) => 54.17/7.42 (X2 @ '#sk15'))) 54.17/7.42 | ('#form9'))), 54.17/7.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl65])). 54.17/7.42 thf(zip_derived_cl94, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 (~ (((((!!) @ (^[Y0 : a]: 54.17/7.42 (((!!) @ (^[Y1 : a]: 54.17/7.42 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 54.17/7.42 Y0 @ Y1))) & 54.17/7.42 (X2 @ Y0))) => 54.17/7.42 (X2 @ Y1))))))))) & 54.17/7.42 (((!!) @ (^[Y0 : a]: 54.17/7.42 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 54.17/7.42 (X2 @ Y0)))))))) 54.17/7.42 | (X2 @ '#sk15') 54.17/7.42 | ('#form9'))), 54.17/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])). 54.17/7.42 thf(zip_derived_cl107, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 (~ (((!!) @ (^[Y0 : a]: 54.17/7.42 (((!!) @ (^[Y1 : a]: 54.17/7.42 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 54.17/7.42 Y1))) & 54.17/7.42 (X2 @ Y0))) => 54.17/7.42 (X2 @ Y1))))))))) 54.17/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.42 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 54.17/7.42 (X2 @ Y0)))))) 54.17/7.42 | ('#form9') 54.17/7.42 | (X2 @ '#sk15'))), 54.17/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl94])). 54.17/7.42 thf(zip_derived_cl121, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 (~ (((!!) @ (^[Y0 : a]: 54.17/7.42 ((((((('#sk2' @ ('#sk140' @ X2) @ Y0) | ('#sk1' @ 54.17/7.42 ('#sk140' @ X2) @ Y0))) & 54.17/7.42 (X2 @ ('#sk140' @ X2)))) => 54.17/7.42 (X2 @ Y0)))))) 54.17/7.42 | (X2 @ '#sk15') 54.17/7.42 | ('#form9') 54.17/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.42 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 54.17/7.42 (X2 @ Y0)))))))), 54.17/7.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl107])). 54.17/7.42 thf(zip_derived_cl139, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 (~ ((((((('#sk2' @ ('#sk140' @ X2) @ ('#sk188' @ X2)) | ('#sk1' @ 54.17/7.42 ('#sk140' @ X2) @ ('#sk188' @ X2)))) & 54.17/7.42 (X2 @ ('#sk140' @ X2)))) => 54.17/7.42 (X2 @ ('#sk188' @ X2)))) 54.17/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.42 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 54.17/7.42 (X2 @ Y0)))))) 54.17/7.42 | ('#form9') 54.17/7.42 | (X2 @ '#sk15'))), 54.17/7.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl121])). 54.17/7.42 thf(zip_derived_cl154, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 (~ (X2 @ ('#sk188' @ X2)) 54.17/7.42 | (X2 @ '#sk15') 54.17/7.42 | ('#form9') 54.17/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.42 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 54.17/7.42 (X2 @ Y0)))))))), 54.17/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl139])). 54.17/7.42 thf(zip_derived_cl154, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 (~ (X2 @ ('#sk188' @ X2)) 54.17/7.42 | (X2 @ '#sk15') 54.17/7.42 | ('#form9') 54.17/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.42 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 54.17/7.42 (X2 @ Y0)))))))), 54.17/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl139])). 54.17/7.42 thf(zip_derived_cl162, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 ( ('#form276' @ X2) 54.17/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.42 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 54.17/7.42 (X2 @ Y0)))))))), 54.17/7.42 define([status(thm)])). 54.17/7.42 thf(zip_derived_cl164, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 (~ ('#form276' @ X2) 54.17/7.42 | ('#form9') 54.17/7.42 | (X2 @ '#sk15') 54.17/7.42 | ~ (X2 @ ('#sk188' @ X2)))), 54.17/7.42 inference('renaming', [status(thm)], 54.17/7.42 [zip_derived_cl154, zip_derived_cl162])). 54.17/7.42 thf(zip_derived_cl83, plain, 54.17/7.42 (( (((((!!) @ (^[Y0 : a]: 54.17/7.42 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 54.17/7.42 ('#sk43' @ Y0)))))) & 54.17/7.42 (((!!) @ (^[Y0 : a]: 54.17/7.42 (((!!) @ (^[Y1 : a]: 54.17/7.42 ((((('#sk43' @ Y0) & 54.17/7.42 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 54.17/7.42 Y1))))) => 54.17/7.42 ('#sk43' @ Y1))))))))))) 54.17/7.42 | ('#form9'))), 54.17/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl69])). 54.17/7.42 thf(zip_derived_cl96, plain, 54.17/7.42 (( (((!!) @ (^[Y0 : a]: 54.17/7.42 (((!!) @ (^[Y1 : a]: 54.17/7.42 ((((('#sk43' @ Y0) & 54.17/7.42 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 54.17/7.42 ('#sk43' @ Y1))))))))) 54.17/7.42 | ('#form9'))), 54.17/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl83])). 54.17/7.42 thf(zip_derived_cl109, plain, 54.17/7.42 (![X2 : a]: 54.17/7.42 ( (((!!) @ (^[Y0 : a]: 54.17/7.42 ((((('#sk43' @ X2) & 54.17/7.42 ((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))))) => 54.17/7.42 ('#sk43' @ Y0)))))) 54.17/7.42 | ('#form9'))), 54.17/7.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl96])). 54.17/7.42 thf(zip_derived_cl123, plain, 54.17/7.42 (![X2 : a, X4 : a]: 54.17/7.42 ( ((((('#sk43' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) => 54.17/7.42 ('#sk43' @ X4))) 54.17/7.42 | ('#form9'))), 54.17/7.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl109])). 54.17/7.42 thf(zip_derived_cl142, plain, 54.17/7.42 (![X2 : a, X4 : a]: 54.17/7.42 (~ ((('#sk43' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) 54.17/7.42 | ('#sk43' @ X4) 54.17/7.42 | ('#form9'))), 54.17/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])). 54.17/7.42 thf(zip_derived_cl155, plain, 54.17/7.42 (![X2 : a, X4 : a]: 54.17/7.42 (~ ('#sk43' @ X2) 54.17/7.42 | ~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 54.17/7.42 | ('#form9') 54.17/7.42 | ('#sk43' @ X4))), 54.17/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl142])). 54.17/7.42 thf(zip_derived_cl165, plain, 54.17/7.42 (![X2 : a, X4 : a]: 54.17/7.42 (~ ('#sk1' @ X2 @ X4) 54.17/7.42 | ('#sk43' @ X4) 54.17/7.42 | ('#form9') 54.17/7.42 | ~ ('#sk43' @ X2))), 54.17/7.42 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl155])). 54.17/7.42 thf(zip_derived_cl166, plain, 54.17/7.42 (![X2 : a, X4 : a]: 54.17/7.42 (~ ('#sk2' @ X2 @ X4) 54.17/7.42 | ('#sk43' @ X4) 54.17/7.42 | ('#form9') 54.17/7.42 | ~ ('#sk43' @ X2))), 54.17/7.42 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl155])). 54.17/7.42 thf(zip_derived_cl153, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 ( ((((('#sk2' @ ('#sk140' @ X2) @ ('#sk188' @ X2)) | ('#sk1' @ 54.17/7.42 ('#sk140' @ X2) @ ('#sk188' @ X2)))) & 54.17/7.42 (X2 @ ('#sk140' @ X2)))) 54.17/7.42 | (X2 @ '#sk15') 54.17/7.42 | ('#form9') 54.17/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.42 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 54.17/7.42 (X2 @ Y0)))))))), 54.17/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl139])). 54.17/7.42 thf(zip_derived_cl161, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 ( (X2 @ ('#sk140' @ X2)) 54.17/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.42 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 54.17/7.42 (X2 @ Y0)))))) 54.17/7.42 | ('#form9') 54.17/7.42 | (X2 @ '#sk15'))), 54.17/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl153])). 54.17/7.42 thf(zip_derived_cl162, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 ( ('#form276' @ X2) 54.17/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.42 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 54.17/7.42 (X2 @ Y0)))))))), 54.17/7.42 define([status(thm)])). 54.17/7.42 thf(zip_derived_cl171, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 (~ ('#form276' @ (^[Y0 : a]: (X2 @ Y0))) 54.17/7.42 | (X2 @ '#sk15') 54.17/7.42 | ('#form9') 54.17/7.42 | (X2 @ ('#sk140' @ X2)))), 54.17/7.42 inference('renaming', [status(thm)], 54.17/7.42 [zip_derived_cl161, zip_derived_cl162])). 54.17/7.42 thf(zip_derived_cl180, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 (~ ('#form276' @ X2) 54.17/7.42 | (X2 @ '#sk15') 54.17/7.42 | ('#form9') 54.17/7.42 | (X2 @ ('#sk140' @ X2)))), 54.17/7.42 inference('ho_norm', [status(thm)], [zip_derived_cl171])). 54.17/7.42 thf(zip_derived_cl160, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 ( ((('#sk2' @ ('#sk140' @ X2) @ ('#sk188' @ X2)) | ('#sk1' @ 54.17/7.42 ('#sk140' @ X2) @ ('#sk188' @ X2)))) 54.17/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.42 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 54.17/7.42 (X2 @ Y0)))))) 54.17/7.42 | ('#form9') 54.17/7.42 | (X2 @ '#sk15'))), 54.17/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl153])). 54.17/7.42 thf(zip_derived_cl162, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 ( ('#form276' @ X2) 54.17/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.42 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 54.17/7.42 (X2 @ Y0)))))))), 54.17/7.42 define([status(thm)])). 54.17/7.42 thf(zip_derived_cl170, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 (~ ('#form276' @ (^[Y0 : a]: (X2 @ Y0))) 54.17/7.42 | (X2 @ '#sk15') 54.17/7.42 | ('#form9') 54.17/7.42 | ((('#sk2' @ ('#sk140' @ X2) @ ('#sk188' @ X2)) | ('#sk1' @ 54.17/7.42 ('#sk140' @ X2) @ ('#sk188' @ X2)))))), 54.17/7.42 inference('renaming', [status(thm)], 54.17/7.42 [zip_derived_cl160, zip_derived_cl162])). 54.17/7.42 thf(zip_derived_cl178, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 (~ ('#form276' @ X2) 54.17/7.42 | (X2 @ '#sk15') 54.17/7.42 | ('#form9') 54.17/7.42 | ((('#sk2' @ ('#sk140' @ X2) @ ('#sk188' @ X2)) | ('#sk1' @ 54.17/7.42 ('#sk140' @ X2) @ ('#sk188' @ X2)))))), 54.17/7.42 inference('ho_norm', [status(thm)], [zip_derived_cl170])). 54.17/7.42 thf(zip_derived_cl179, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 ( ('#sk2' @ ('#sk140' @ X2) @ ('#sk188' @ X2)) 54.17/7.42 | ('#sk1' @ ('#sk140' @ X2) @ ('#sk188' @ X2)) 54.17/7.42 | ('#form9') 54.17/7.42 | (X2 @ '#sk15') 54.17/7.42 | ~ ('#form276' @ X2))), 54.17/7.42 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl178])). 54.17/7.42 thf(zip_derived_cl162, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 ( ('#form276' @ X2) 54.17/7.42 | ~ (((!!) @ (^[Y0 : a]: 54.17/7.42 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 54.17/7.42 (X2 @ Y0)))))))), 54.17/7.42 define([status(thm)])). 54.17/7.42 thf(zip_derived_cl163, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 (~ ((((('#sk2' @ '#sk10' @ ('#sk277' @ X2)) | ('#sk1' @ '#sk10' @ 54.17/7.42 ('#sk277' @ X2)))) => 54.17/7.42 (X2 @ ('#sk277' @ X2)))) 54.17/7.42 | ('#form276' @ X2))), 54.17/7.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl162])). 54.17/7.42 thf(zip_derived_cl172, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 ( ((('#sk2' @ '#sk10' @ ('#sk277' @ X2)) | ('#sk1' @ '#sk10' @ 54.17/7.42 ('#sk277' @ X2)))) 54.17/7.42 | ('#form276' @ X2))), 54.17/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl163])). 54.17/7.42 thf(zip_derived_cl181, plain, 54.17/7.42 (![X2 : a > $o]: 54.17/7.42 ( ('#sk2' @ '#sk10' @ ('#sk277' @ X2)) 54.17/7.42 | ('#sk1' @ '#sk10' @ ('#sk277' @ X2)) 54.17/7.42 | ('#form276' @ X2))), 54.17/7.42 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl172])). 54.17/7.42 thf(zip_derived_cl173, plain, 54.17/7.42 (![X2 : a > $o]: (~ (X2 @ ('#sk277' @ X2)) | ('#form276' @ X2))), 54.17/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl163])). 54.17/7.42 thf(zip_derived_cl95, plain, 54.17/7.42 (( (((!!) @ (^[Y0 : a]: 54.17/7.42 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 54.17/7.42 ('#sk43' @ Y0)))))) 54.17/7.42 | ('#form9'))), 54.17/7.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl83])). 54.17/7.42 thf(zip_derived_cl108, plain, 54.17/7.42 (![X2 : a]: 54.17/7.42 ( ((((('#sk2' @ '#sk10' @ X2) | ('#sk1' @ '#sk10' @ X2))) => 54.17/7.42 ('#sk43' @ X2))) 54.17/7.42 | ('#form9'))), 54.17/7.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl95])). 54.17/7.42 thf(zip_derived_cl122, plain, 54.17/7.42 (![X2 : a]: 54.17/7.42 (~ ((('#sk2' @ '#sk10' @ X2) | ('#sk1' @ '#sk10' @ X2))) 54.17/7.42 | ('#sk43' @ X2) 54.17/7.42 | ('#form9'))), 54.17/7.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 54.17/7.42 thf(zip_derived_cl141, plain, 54.17/7.42 (![X2 : a]: (~ ('#sk1' @ '#sk10' @ X2) | ('#form9') | ('#sk43' @ X2))), 54.17/7.42 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl122])). 54.17/7.42 thf(zip_derived_cl140, plain, 54.17/7.42 (![X2 : a]: (~ ('#sk2' @ '#sk10' @ X2) | ('#form9') | ('#sk43' @ X2))), 54.17/7.42 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl122])). 54.17/7.42 thf(zip_derived_cl12680, plain, ($false), 54.17/7.42 inference('eprover', [status(thm)], 54.17/7.42 [zip_derived_cl41, zip_derived_cl42, zip_derived_cl280, 54.17/7.42 zip_derived_cl282, zip_derived_cl283, zip_derived_cl136, 54.17/7.42 zip_derived_cl132, zip_derived_cl150, zip_derived_cl149, 54.17/7.42 zip_derived_cl25, zip_derived_cl24, zip_derived_cl117, 54.17/7.42 zip_derived_cl91, zip_derived_cl50, zip_derived_cl130, 54.17/7.42 zip_derived_cl148, zip_derived_cl147, zip_derived_cl118, 54.17/7.42 zip_derived_cl213, zip_derived_cl215, zip_derived_cl214, 54.17/7.42 zip_derived_cl119, zip_derived_cl145, zip_derived_cl146, 54.17/7.42 zip_derived_cl92, zip_derived_cl313, zip_derived_cl169, 54.17/7.42 zip_derived_cl308, zip_derived_cl84, zip_derived_cl185, 54.17/7.42 zip_derived_cl311, zip_derived_cl309, zip_derived_cl164, 54.17/7.42 zip_derived_cl165, zip_derived_cl166, zip_derived_cl180, 54.17/7.42 zip_derived_cl179, zip_derived_cl181, zip_derived_cl173, 54.17/7.42 zip_derived_cl141, zip_derived_cl140])). 54.17/7.42 54.17/7.42 % SZS output end Refutation 54.17/7.42 54.17/7.42 54.17/7.42 % Terminating... 54.37/7.47 % Runner terminated. 54.37/7.48 % Zipperpin 1.5 exiting 54.37/7.49 EOF