0.03/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.13/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.hT81cMIoql true 0.14/0.36 % Computer : n005.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 1200 0.14/0.36 % WCLimit : 120 0.14/0.36 % DateTime : Tue Jul 13 12:11:48 EDT 2021 0.14/0.36 % CPUTime : 0.14/0.36 % Running portfolio for 120 s 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.14/0.36 % Number of cores: 8 0.14/0.36 % Python version: Python 3.6.8 0.14/0.36 % Running in HO mode 0.55/0.64 % Total configuration time : 828 0.55/0.64 % Estimated wc time : 983 0.55/0.64 % Estimated cpu time (8 cpus) : 122.875 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 47s 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 47s 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 47s 0.57/0.80 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 41s 0.57/0.80 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 18s 0.58/0.80 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 53s 0.58/0.83 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.58/0.85 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 35s 138.07/18.83 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 53s 187.98/25.18 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 33s 205.95/27.55 % Solved by lams/30_b.l.sh. 205.95/27.55 % running E: timeout 14 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.hT81cMIoql/e_inputf65fcb --cpu-limit=12 --auto -s -p 205.95/27.55 % done 191 iterations in 8.619s 205.95/27.55 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 205.95/27.55 % SZS output start Refutation 205.95/27.55 thf(a_type, type, a: $tType). 205.95/27.55 thf('#sk2_type', type, '#sk2': a > a > $o). 205.95/27.55 thf('#sk126_type', type, '#sk126': (a > $o) > a). 205.95/27.55 thf('#sk109_type', type, '#sk109': (a > $o) > a). 205.95/27.55 thf('#form180_type', type, '#form180': (a > $o) > $o). 205.95/27.55 thf('#sk327_type', type, '#sk327': (a > $o) > (a > $o) > a). 205.95/27.55 thf('#sk311_type', type, '#sk311': (a > $o) > a). 205.95/27.55 thf('#sk3_type', type, '#sk3': a). 205.95/27.55 thf('#sk151_type', type, '#sk151': (a > $o) > a). 205.95/27.55 thf('#sk341_type', type, '#sk341': (a > $o) > a). 205.95/27.55 thf('#form167_type', type, '#form167': (a > $o) > $o). 205.95/27.55 thf('#form204_type', type, '#form204': (a > $o) > (a > $o) > $o). 205.95/27.55 thf('#sk21_type', type, '#sk21': (a > $o) > a). 205.95/27.55 thf('#form150_type', type, '#form150': (a > $o) > $o). 205.95/27.55 thf('#sk36_type', type, '#sk36': (a > $o) > a). 205.95/27.55 thf('#sk116_type', type, '#sk116': (a > $o) > a). 205.95/27.55 thf('#form35_type', type, '#form35': (a > $o) > $o). 205.95/27.55 thf('#sk185_type', type, '#sk185': (a > $o) > a). 205.95/27.55 thf('#sk332_type', type, '#sk332': (a > $o) > a). 205.95/27.55 thf('#sk205_type', type, '#sk205': (a > $o) > (a > $o) > a). 205.95/27.55 thf('#form310_type', type, '#form310': (a > $o) > $o). 205.95/27.55 thf('#sk15_type', type, '#sk15': (a > $o) > a). 205.95/27.55 thf('#sk4_type', type, '#sk4': a). 205.95/27.55 thf('#sk5_type', type, '#sk5': a > $o). 205.95/27.55 thf('#sk1_type', type, '#sk1': a > a > $o). 205.95/27.55 thf(cTHM251C_pme, conjecture, 205.95/27.55 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 205.95/27.55 ( ( ![Xq:( a > $o )]: 205.95/27.55 ( ( ( ![Xu:a,Xv:a]: 205.95/27.55 ( ( ( Xq @ Xu ) & 205.95/27.55 ( ( ![Xq0:( a > $o )]: 205.95/27.55 ( ( ( ![Xu0:a,Xv0:a]: 205.95/27.55 ( ( ( R @ Xu0 @ Xv0 ) & ( Xq0 @ Xu0 ) ) => 205.95/27.55 ( Xq0 @ Xv0 ) ) ) & 205.95/27.55 ( ![Xw:a]: ( ( R @ Xu @ Xw ) => ( Xq0 @ Xw ) ) ) ) => 205.95/27.55 ( Xq0 @ Xv ) ) ) | 205.95/27.55 ( ![Xq0:( a > $o )]: 205.95/27.55 ( ( ( ![Xw:a]: ( ( S @ Xu @ Xw ) => ( Xq0 @ Xw ) ) ) & 205.95/27.55 ( ![Xu0:a,Xv0:a]: 205.95/27.55 ( ( ( S @ Xu0 @ Xv0 ) & ( Xq0 @ Xu0 ) ) => 205.95/27.55 ( Xq0 @ Xv0 ) ) ) ) => 205.95/27.55 ( Xq0 @ Xv ) ) ) ) ) => 205.95/27.55 ( Xq @ Xv ) ) ) & 205.95/27.55 ( ![Xw:a]: 205.95/27.55 ( ( ( ![Xq0:( a > $o )]: 205.95/27.55 ( ( ( ![Xw0:a]: ( ( R @ Xx @ Xw0 ) => ( Xq0 @ Xw0 ) ) ) & 205.95/27.55 ( ![Xu:a,Xv:a]: 205.95/27.55 ( ( ( Xq0 @ Xu ) & ( R @ Xu @ Xv ) ) => ( Xq0 @ Xv ) ) ) ) => 205.95/27.55 ( Xq0 @ Xw ) ) ) | 205.95/27.55 ( ![Xq0:( a > $o )]: 205.95/27.55 ( ( ( ![Xu:a,Xv:a]: 205.95/27.55 ( ( ( S @ Xu @ Xv ) & ( Xq0 @ Xu ) ) => ( Xq0 @ Xv ) ) ) & 205.95/27.55 ( ![Xw0:a]: ( ( S @ Xx @ Xw0 ) => ( Xq0 @ Xw0 ) ) ) ) => 205.95/27.55 ( Xq0 @ Xw ) ) ) ) => 205.95/27.55 ( Xq @ Xw ) ) ) ) => 205.95/27.55 ( Xq @ Xy ) ) ) => 205.95/27.55 ( ![Xq:( a > $o )]: 205.95/27.55 ( ( ( ![Xw:a]: 205.95/27.55 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 205.95/27.55 ( ![Xu:a,Xv:a]: 205.95/27.55 ( ( ( Xq @ Xu ) & ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 205.95/27.55 ( Xq @ Xv ) ) ) ) => 205.95/27.55 ( Xq @ Xy ) ) ) ))). 205.95/27.55 thf(zf_stmt_0, negated_conjecture, 205.95/27.55 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 205.95/27.55 ( ( ![Xq:( a > $o )]: 205.95/27.55 ( ( ( ![Xu:a,Xv:a]: 205.95/27.55 ( ( ( Xq @ Xu ) & 205.95/27.55 ( ( ![Xq0:( a > $o )]: 205.95/27.55 ( ( ( ![Xu0:a,Xv0:a]: 205.95/27.55 ( ( ( R @ Xu0 @ Xv0 ) & ( Xq0 @ Xu0 ) ) => 205.95/27.55 ( Xq0 @ Xv0 ) ) ) & 205.95/27.55 ( ![Xw:a]: ( ( R @ Xu @ Xw ) => ( Xq0 @ Xw ) ) ) ) => 205.95/27.55 ( Xq0 @ Xv ) ) ) | 205.95/27.55 ( ![Xq0:( a > $o )]: 205.95/27.55 ( ( ( ![Xw:a]: ( ( S @ Xu @ Xw ) => ( Xq0 @ Xw ) ) ) & 205.95/27.55 ( ![Xu0:a,Xv0:a]: 205.95/27.55 ( ( ( S @ Xu0 @ Xv0 ) & ( Xq0 @ Xu0 ) ) => 205.95/27.55 ( Xq0 @ Xv0 ) ) ) ) => 205.95/27.55 ( Xq0 @ Xv ) ) ) ) ) => 205.95/27.55 ( Xq @ Xv ) ) ) & 205.95/27.55 ( ![Xw:a]: 205.95/27.55 ( ( ( ![Xq0:( a > $o )]: 205.95/27.55 ( ( ( ![Xw0:a]: ( ( R @ Xx @ Xw0 ) => ( Xq0 @ Xw0 ) ) ) & 205.95/27.55 ( ![Xu:a,Xv:a]: 205.95/27.55 ( ( ( Xq0 @ Xu ) & ( R @ Xu @ Xv ) ) => 205.95/27.55 ( Xq0 @ Xv ) ) ) ) => 205.95/27.55 ( Xq0 @ Xw ) ) ) | 205.95/27.55 ( ![Xq0:( a > $o )]: 205.95/27.55 ( ( ( ![Xu:a,Xv:a]: 205.95/27.55 ( ( ( S @ Xu @ Xv ) & ( Xq0 @ Xu ) ) => 205.95/27.55 ( Xq0 @ Xv ) ) ) & 205.95/27.55 ( ![Xw0:a]: ( ( S @ Xx @ Xw0 ) => ( Xq0 @ Xw0 ) ) ) ) => 205.95/27.55 ( Xq0 @ Xw ) ) ) ) => 205.95/27.55 ( Xq @ Xw ) ) ) ) => 205.95/27.55 ( Xq @ Xy ) ) ) => 205.95/27.55 ( ![Xq:( a > $o )]: 205.95/27.55 ( ( ( ![Xw:a]: 205.95/27.55 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 205.95/27.55 ( ![Xu:a,Xv:a]: 205.95/27.55 ( ( ( Xq @ Xu ) & ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 205.95/27.55 ( Xq @ Xv ) ) ) ) => 205.95/27.55 ( Xq @ Xy ) ) ) ) )), 205.95/27.55 inference('cnf.neg', [status(esa)], [cTHM251C_pme])). 205.95/27.55 thf(zip_derived_cl0, plain, 205.95/27.55 (~ (((!!) @ (^[Y0 : a > a > $o]: 205.95/27.55 (((!!) @ (^[Y1 : a > a > $o]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 (((((!!) @ (^[Y4 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (Y4 @ 205.95/27.55 Y5) & 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y7 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y8 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y9 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (Y0 @ 205.95/27.55 Y8 @ 205.95/27.55 Y9) & 205.95/27.55 (Y7 @ Y8))) => 205.95/27.55 (Y7 @ Y9))))))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y8 : a]: 205.95/27.55 (( 205.95/27.55 (Y0 @ 205.95/27.55 Y5 @ 205.95/27.55 Y8) => 205.95/27.55 (Y7 @ Y8)))))))) => 205.95/27.55 (Y7 @ Y6)))))) | 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y7 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y8 : a]: 205.95/27.55 (( 205.95/27.55 (Y1 @ 205.95/27.55 Y5 @ 205.95/27.55 Y8) => 205.95/27.55 (Y7 @ Y8)))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y8 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y9 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (Y1 @ 205.95/27.55 Y8 @ 205.95/27.55 Y9) & 205.95/27.55 (Y7 @ Y8))) => 205.95/27.55 (Y7 @ Y9))))))))))) => 205.95/27.55 (Y7 @ Y6)))))))))) => 205.95/27.55 (Y4 @ Y6))))))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y7 : a]: 205.95/27.55 (( 205.95/27.55 (Y0 @ 205.95/27.55 Y2 @ 205.95/27.55 Y7) => 205.95/27.55 (Y6 @ Y7)))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y7 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y8 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (Y6 @ 205.95/27.55 Y7) & 205.95/27.55 (Y0 @ 205.95/27.55 Y7 @ Y8))) => 205.95/27.55 (Y6 @ Y8))))))))))) => 205.95/27.55 (Y6 @ Y5)))))) | 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y7 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y8 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (Y1 @ 205.95/27.55 Y7 @ 205.95/27.55 Y8) & 205.95/27.55 (Y6 @ Y7))) => 205.95/27.55 (Y6 @ Y8))))))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y7 : a]: 205.95/27.55 (( 205.95/27.55 (Y1 @ 205.95/27.55 Y2 @ 205.95/27.55 Y7) => 205.95/27.55 (Y6 @ Y7)))))))) => 205.95/27.55 (Y6 @ Y5)))))))) => 205.95/27.55 (Y4 @ Y5)))))))) => 205.95/27.55 (Y4 @ Y3)))))) => 205.95/27.55 (((!!) @ (^[Y4 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (Y0 @ 205.95/27.55 Y2 @ 205.95/27.55 Y5) | 205.95/27.55 (Y1 @ 205.95/27.55 Y2 @ Y5))) => 205.95/27.55 (Y4 @ Y5)))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (Y4 @ 205.95/27.55 Y5) & 205.95/27.55 (( 205.95/27.55 (Y1 @ 205.95/27.55 Y5 @ 205.95/27.55 Y6) | 205.95/27.55 (Y0 @ 205.95/27.55 Y5 @ Y6))))) => 205.95/27.55 (Y4 @ Y6))))))))))) => 205.95/27.55 (Y4 @ Y3))))))))))))))))))))), 205.95/27.55 inference('cnf', [status(esa)], [zf_stmt_0])). 205.95/27.55 thf(zip_derived_cl1, plain, 205.95/27.55 (~ (((!!) @ (^[Y0 : a > a > $o]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((((!!) @ (^[Y3 : a > $o]: 205.95/27.55 (((((((!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (((!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (Y3 @ 205.95/27.55 Y4) & 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y7 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y8 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y7 @ 205.95/27.55 Y8) & 205.95/27.55 (Y6 @ Y7))) => 205.95/27.55 (Y6 @ Y8))))))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y7 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y4 @ 205.95/27.55 Y7) => 205.95/27.55 (Y6 @ Y7)))))))) => 205.95/27.55 (Y6 @ Y5)))))) | 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y7 : a]: 205.95/27.55 (( 205.95/27.55 (Y0 @ 205.95/27.55 Y4 @ 205.95/27.55 Y7) => 205.95/27.55 (Y6 @ Y7)))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y7 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y8 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (Y0 @ 205.95/27.55 Y7 @ 205.95/27.55 Y8) & 205.95/27.55 (Y6 @ Y7))) => 205.95/27.55 (Y6 @ Y8))))))))))) => 205.95/27.55 (Y6 @ Y5)))))))))) => 205.95/27.55 (Y3 @ Y5))))))))) & 205.95/27.55 (((!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (((( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y1 @ 205.95/27.55 Y6) => 205.95/27.55 (Y5 @ Y6)))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y7 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (Y5 @ 205.95/27.55 Y6) & 205.95/27.55 ('#sk1' @ 205.95/27.55 Y6 @ Y7))) => 205.95/27.55 (Y5 @ Y7))))))))))) => 205.95/27.55 (Y5 @ Y4)))))) | 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y7 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (Y0 @ 205.95/27.55 Y6 @ 205.95/27.55 Y7) & 205.95/27.55 (Y5 @ Y6))) => 205.95/27.55 (Y5 @ Y7))))))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a]: 205.95/27.55 (( 205.95/27.55 (Y0 @ 205.95/27.55 Y1 @ 205.95/27.55 Y6) => 205.95/27.55 (Y5 @ Y6)))))))) => 205.95/27.55 (Y5 @ Y4)))))))) => 205.95/27.55 (Y3 @ Y4)))))))) => 205.95/27.55 (Y3 @ Y2)))))) => 205.95/27.55 (((!!) @ (^[Y3 : a > $o]: 205.95/27.55 (((((((!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (((( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y1 @ Y4) | 205.95/27.55 (Y0 @ 205.95/27.55 Y1 @ Y4))) => 205.95/27.55 (Y3 @ Y4)))))) & 205.95/27.55 (((!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (((!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (Y3 @ 205.95/27.55 Y4) & 205.95/27.55 (( 205.95/27.55 (Y0 @ 205.95/27.55 Y4 @ 205.95/27.55 Y5) | 205.95/27.55 ('#sk1' @ 205.95/27.55 Y4 @ Y5))))) => 205.95/27.55 (Y3 @ Y5))))))))))) => 205.95/27.55 (Y3 @ Y2)))))))))))))))))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 205.95/27.55 thf(zip_derived_cl2, plain, 205.95/27.55 (~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((((!!) @ (^[Y2 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y3 : a]: 205.95/27.55 (((!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (((( 205.95/27.55 (Y2 @ 205.95/27.55 Y3) & 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y7 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y6 @ 205.95/27.55 Y7) & 205.95/27.55 (Y5 @ Y6))) => 205.95/27.55 (Y5 @ Y7))))))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y3 @ 205.95/27.55 Y6) => 205.95/27.55 (Y5 @ Y6)))))))) => 205.95/27.55 (Y5 @ Y4)))))) | 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y3 @ 205.95/27.55 Y6) => 205.95/27.55 (Y5 @ Y6)))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y7 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y6 @ 205.95/27.55 Y7) & 205.95/27.55 (Y5 @ Y6))) => 205.95/27.55 (Y5 @ Y7))))))))))) => 205.95/27.55 (Y5 @ Y4)))))))))) => 205.95/27.55 (Y2 @ Y4))))))))) & 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 (((((((!!) @ ( 205.95/27.55 ^[Y4 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y0 @ 205.95/27.55 Y5) => 205.95/27.55 (Y4 @ Y5)))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (Y4 @ 205.95/27.55 Y5) & 205.95/27.55 ('#sk1' @ 205.95/27.55 Y5 @ Y6))) => 205.95/27.55 (Y4 @ Y6))))))))))) => 205.95/27.55 (Y4 @ Y3)))))) | 205.95/27.55 (((!!) @ ( 205.95/27.55 ^[Y4 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y5 @ 205.95/27.55 Y6) & 205.95/27.55 (Y4 @ Y5))) => 205.95/27.55 (Y4 @ Y6))))))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y0 @ 205.95/27.55 Y5) => 205.95/27.55 (Y4 @ Y5)))))))) => 205.95/27.55 (Y4 @ Y3)))))))) => 205.95/27.55 (Y2 @ Y3)))))))) => 205.95/27.55 (Y2 @ Y1)))))) => 205.95/27.55 (((!!) @ (^[Y2 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y3 : a]: 205.95/27.55 ((((('#sk1' @ 205.95/27.55 Y0 @ Y3) | 205.95/27.55 ('#sk2' @ 205.95/27.55 Y0 @ Y3))) => 205.95/27.55 (Y2 @ Y3)))))) & 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 (((!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (((( 205.95/27.55 (Y2 @ 205.95/27.55 Y3) & 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y3 @ Y4) | 205.95/27.55 ('#sk1' @ 205.95/27.55 Y3 @ Y4))))) => 205.95/27.55 (Y2 @ Y4))))))))))) => 205.95/27.55 (Y2 @ Y1))))))))))))))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 205.95/27.55 thf(zip_derived_cl3, plain, 205.95/27.55 (~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 (((((Y1 @ Y2) & 205.95/27.55 (((( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y5 @ 205.95/27.55 Y6) & 205.95/27.55 (Y4 @ Y5))) => 205.95/27.55 (Y4 @ Y6))))))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y2 @ 205.95/27.55 Y5) => 205.95/27.55 (Y4 @ Y5)))))))) => 205.95/27.55 (Y4 @ Y3)))))) | 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y2 @ 205.95/27.55 Y5) => 205.95/27.55 (Y4 @ Y5)))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y6 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y5 @ 205.95/27.55 Y6) & 205.95/27.55 (Y4 @ Y5))) => 205.95/27.55 (Y4 @ Y6))))))))))) => 205.95/27.55 (Y4 @ Y3)))))))))) => 205.95/27.55 (Y1 @ Y3))))))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((((((!!) @ (^[Y3 : a > $o]: 205.95/27.55 (((( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 '#sk3' @ 205.95/27.55 Y4) => 205.95/27.55 (Y3 @ Y4)))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (Y3 @ 205.95/27.55 Y4) & 205.95/27.55 ('#sk1' @ 205.95/27.55 Y4 @ Y5))) => 205.95/27.55 (Y3 @ Y5))))))))))) => 205.95/27.55 (Y3 @ Y2)))))) | 205.95/27.55 (((!!) @ (^[Y3 : a > $o]: 205.95/27.55 (((( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y4 @ 205.95/27.55 Y5) & 205.95/27.55 (Y3 @ Y4))) => 205.95/27.55 (Y3 @ Y5))))))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 '#sk3' @ 205.95/27.55 Y4) => 205.95/27.55 (Y3 @ Y4)))))))) => 205.95/27.55 (Y3 @ Y2)))))))) => 205.95/27.55 (Y1 @ Y2)))))))) => 205.95/27.55 (Y1 @ Y0)))))) => 205.95/27.55 (((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk1' @ '#sk3' @ Y2) | 205.95/27.55 ('#sk2' @ '#sk3' @ Y2))) => 205.95/27.55 (Y1 @ Y2)))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 (((((Y1 @ Y2) & 205.95/27.55 ((('#sk2' @ 205.95/27.55 Y2 @ Y3) | 205.95/27.55 ('#sk1' @ 205.95/27.55 Y2 @ Y3))))) => 205.95/27.55 (Y1 @ Y3))))))))))) => 205.95/27.55 (Y1 @ Y0)))))))))))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 205.95/27.55 thf(zip_derived_cl4, plain, 205.95/27.55 (~ (((((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((((Y0 @ Y1) & 205.95/27.55 (((((!!) @ (^[Y3 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y4 @ 205.95/27.55 Y5) & 205.95/27.55 (Y3 @ Y4))) => 205.95/27.55 (Y3 @ Y5))))))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y1 @ 205.95/27.55 Y4) => 205.95/27.55 (Y3 @ Y4)))))))) => 205.95/27.55 (Y3 @ Y2)))))) | 205.95/27.55 (((!!) @ (^[Y3 : a > $o]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y1 @ 205.95/27.55 Y4) => 205.95/27.55 (Y3 @ Y4)))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y4 @ 205.95/27.55 Y5) & 205.95/27.55 (Y3 @ Y4))) => 205.95/27.55 (Y3 @ Y5))))))))))) => 205.95/27.55 (Y3 @ Y2)))))))))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((((((!!) @ (^[Y2 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y3 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 '#sk3' @ 205.95/27.55 Y3) => 205.95/27.55 (Y2 @ Y3)))))) & 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (Y2 @ 205.95/27.55 Y3) & 205.95/27.55 ('#sk1' @ 205.95/27.55 Y3 @ Y4))) => 205.95/27.55 (Y2 @ Y4))))))))))) => 205.95/27.55 (Y2 @ Y1)))))) | 205.95/27.55 (((!!) @ (^[Y2 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y3 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y3 @ 205.95/27.55 Y4) & 205.95/27.55 (Y2 @ Y3))) => 205.95/27.55 (Y2 @ Y4))))))))) & 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 '#sk3' @ 205.95/27.55 Y3) => 205.95/27.55 (Y2 @ Y3)))))))) => 205.95/27.55 (Y2 @ Y1)))))))) => 205.95/27.55 (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ '#sk4')))))) => 205.95/27.55 (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 205.95/27.55 '#sk3' @ Y1))) => 205.95/27.55 (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((((Y0 @ Y1) & 205.95/27.55 ((('#sk2' @ Y1 @ Y2) | 205.95/27.55 ('#sk1' @ Y1 @ Y2))))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ '#sk4'))))))))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 205.95/27.55 thf(zip_derived_cl5, plain, 205.95/27.55 ( (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((((Y0 @ Y1) & 205.95/27.55 (((((!!) @ (^[Y3 : a > $o]: 205.95/27.55 (((((( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y4 @ 205.95/27.55 Y5) & 205.95/27.55 (Y3 @ Y4))) => 205.95/27.55 (Y3 @ Y5))))))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y1 @ 205.95/27.55 Y4) => 205.95/27.55 (Y3 @ Y4)))))))) => 205.95/27.55 (Y3 @ Y2)))))) | 205.95/27.55 (((!!) @ (^[Y3 : a > $o]: 205.95/27.55 (((((( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y1 @ 205.95/27.55 Y4) => 205.95/27.55 (Y3 @ Y4)))))) & 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y5 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y4 @ 205.95/27.55 Y5) & 205.95/27.55 (Y3 @ Y4))) => 205.95/27.55 (Y3 @ Y5))))))))))) => 205.95/27.55 (Y3 @ Y2)))))))))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((((((!!) @ (^[Y2 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y3 : a]: 205.95/27.55 ((('#sk1' @ 205.95/27.55 '#sk3' @ 205.95/27.55 Y3) => 205.95/27.55 (Y2 @ Y3)))))) & 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 (((!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 (Y2 @ 205.95/27.55 Y3) & 205.95/27.55 ('#sk1' @ 205.95/27.55 Y3 @ Y4))) => 205.95/27.55 (Y2 @ Y4))))))))))) => 205.95/27.55 (Y2 @ Y1)))))) | 205.95/27.55 (((!!) @ (^[Y2 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y3 : a]: 205.95/27.55 (((!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y3 @ 205.95/27.55 Y4) & 205.95/27.55 (Y2 @ Y3))) => 205.95/27.55 (Y2 @ Y4))))))))) & 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ((('#sk2' @ 205.95/27.55 '#sk3' @ 205.95/27.55 Y3) => 205.95/27.55 (Y2 @ Y3)))))))) => 205.95/27.55 (Y2 @ Y1)))))))) => 205.95/27.55 (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ '#sk4'))))))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 205.95/27.55 thf(zip_derived_cl7, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((((X2 @ Y0) & 205.95/27.55 (((((!!) @ (^[Y2 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y3 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y3 @ 205.95/27.55 Y4) & 205.95/27.55 (Y2 @ Y3))) => 205.95/27.55 (Y2 @ Y4))))))))) & 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y0 @ 205.95/27.55 Y3) => 205.95/27.55 (Y2 @ Y3)))))))) => 205.95/27.55 (Y2 @ Y1)))))) | 205.95/27.55 (((!!) @ (^[Y2 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y3 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y0 @ 205.95/27.55 Y3) => 205.95/27.55 (Y2 @ Y3)))))) & 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y3 @ 205.95/27.55 Y4) & 205.95/27.55 (Y2 @ Y3))) => 205.95/27.55 (Y2 @ Y4))))))))))) => 205.95/27.55 (Y2 @ Y1)))))))))) => 205.95/27.55 (X2 @ Y1))))))))) & 205.95/27.55 (((!!) @ (^[Y0 : a]: 205.95/27.55 (((((((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk1' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 (Y1 @ 205.95/27.55 Y2) & 205.95/27.55 ('#sk1' @ 205.95/27.55 Y2 @ Y3))) => 205.95/27.55 (Y1 @ Y3))))))))))) => 205.95/27.55 (Y1 @ Y0)))))) | 205.95/27.55 (((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y2 @ 205.95/27.55 Y3) & 205.95/27.55 (Y1 @ Y2))) => 205.95/27.55 (Y1 @ Y3))))))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))))) => 205.95/27.55 (Y1 @ Y0)))))))) => 205.95/27.55 (X2 @ Y0)))))))) => 205.95/27.55 (X2 @ '#sk4')))), 205.95/27.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 205.95/27.55 thf(zip_derived_cl9, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 (~ (((((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((((X2 @ Y0) & 205.95/27.55 (((((!!) @ (^[Y2 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y3 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y3 @ 205.95/27.55 Y4) & 205.95/27.55 (Y2 @ Y3))) => 205.95/27.55 (Y2 @ Y4))))))))) & 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y0 @ 205.95/27.55 Y3) => 205.95/27.55 (Y2 @ Y3)))))))) => 205.95/27.55 (Y2 @ Y1)))))) | 205.95/27.55 (((!!) @ (^[Y2 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y3 : a]: 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y0 @ 205.95/27.55 Y3) => 205.95/27.55 (Y2 @ Y3)))))) & 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 (( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y3 @ 205.95/27.55 Y4) & 205.95/27.55 (Y2 @ Y3))) => 205.95/27.55 (Y2 @ Y4))))))))))) => 205.95/27.55 (Y2 @ Y1)))))))))) => 205.95/27.55 (X2 @ Y1))))))))) & 205.95/27.55 (((!!) @ (^[Y0 : a]: 205.95/27.55 (((((((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk1' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 (Y1 @ 205.95/27.55 Y2) & 205.95/27.55 ('#sk1' @ 205.95/27.55 Y2 @ Y3))) => 205.95/27.55 (Y1 @ Y3))))))))))) => 205.95/27.55 (Y1 @ Y0)))))) | 205.95/27.55 (((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y2 @ 205.95/27.55 Y3) & 205.95/27.55 (Y1 @ Y2))) => 205.95/27.55 (Y1 @ Y3))))))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))))) => 205.95/27.55 (Y1 @ Y0)))))))) => 205.95/27.55 (X2 @ Y0)))))))) 205.95/27.55 | (X2 @ '#sk4'))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 205.95/27.55 thf(zip_derived_cl12, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 (~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((((X2 @ Y0) & 205.95/27.55 (((((!!) @ (^[Y2 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y3 @ 205.95/27.55 Y4) & 205.95/27.55 (Y2 @ Y3))) => 205.95/27.55 (Y2 @ Y4))))))))) & 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y0 @ 205.95/27.55 Y3) => 205.95/27.55 (Y2 @ Y3)))))))) => 205.95/27.55 (Y2 @ Y1)))))) | 205.95/27.55 (((!!) @ (^[Y2 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y0 @ 205.95/27.55 Y3) => 205.95/27.55 (Y2 @ Y3)))))) & 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (!!) @ ( 205.95/27.55 ^[Y4 : a]: 205.95/27.55 (( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y3 @ 205.95/27.55 Y4) & 205.95/27.55 (Y2 @ Y3))) => 205.95/27.55 (Y2 @ Y4))))))))))) => 205.95/27.55 (Y2 @ Y1)))))))))) => 205.95/27.55 (X2 @ Y1))))))))) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((((((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk1' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 (Y1 @ 205.95/27.55 Y2) & 205.95/27.55 ('#sk1' @ 205.95/27.55 Y2 @ Y3))) => 205.95/27.55 (Y1 @ Y3))))))))))) => 205.95/27.55 (Y1 @ Y0)))))) | 205.95/27.55 (((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y2 @ 205.95/27.55 Y3) & 205.95/27.55 (Y1 @ Y2))) => 205.95/27.55 (Y1 @ Y3))))))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))))) => 205.95/27.55 (Y1 @ Y0)))))))) => 205.95/27.55 (X2 @ Y0)))))) 205.95/27.55 | (X2 @ '#sk4'))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl9])). 205.95/27.55 thf(zip_derived_cl15, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 (~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((((X2 @ ('#sk15' @ X2)) & 205.95/27.55 (((((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 ('#sk1' @ 205.95/27.55 Y2 @ 205.95/27.55 Y3) & 205.95/27.55 (Y1 @ Y2))) => 205.95/27.55 (Y1 @ Y3))))))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk1' @ 205.95/27.55 ('#sk15' @ X2) @ 205.95/27.55 Y2) => (Y1 @ Y2)))))))) => 205.95/27.55 (Y1 @ Y0)))))) | 205.95/27.55 (((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk2' @ 205.95/27.55 ('#sk15' @ X2) @ 205.95/27.55 Y2) => (Y1 @ Y2)))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y2 @ 205.95/27.55 Y3) & 205.95/27.55 (Y1 @ Y2))) => 205.95/27.55 (Y1 @ Y3))))))))))) => 205.95/27.55 (Y1 @ Y0)))))))))) => 205.95/27.55 (X2 @ Y0)))))) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((((((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk1' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 (Y1 @ 205.95/27.55 Y2) & 205.95/27.55 ('#sk1' @ 205.95/27.55 Y2 @ Y3))) => 205.95/27.55 (Y1 @ Y3))))))))))) => 205.95/27.55 (Y1 @ Y0)))))) | 205.95/27.55 (((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y2 @ 205.95/27.55 Y3) & 205.95/27.55 (Y1 @ Y2))) => 205.95/27.55 (Y1 @ Y3))))))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))))) => 205.95/27.55 (Y1 @ Y0)))))))) => 205.95/27.55 (X2 @ Y0)))))))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 205.95/27.55 thf(zip_derived_cl18, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 (~ (((((X2 @ ('#sk15' @ X2)) & 205.95/27.55 (((((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk1' @ Y1 @ 205.95/27.55 Y2) & (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ 205.95/27.55 Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))) | 205.95/27.55 (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ 205.95/27.55 Y1) => (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ 205.95/27.55 Y2) & (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))))))) => 205.95/27.55 (X2 @ ('#sk21' @ X2)))) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((((((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk1' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 (Y1 @ 205.95/27.55 Y2) & 205.95/27.55 ('#sk1' @ 205.95/27.55 Y2 @ Y3))) => 205.95/27.55 (Y1 @ Y3))))))))))) => 205.95/27.55 (Y1 @ Y0)))))) | 205.95/27.55 (((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y2 @ 205.95/27.55 Y3) & 205.95/27.55 (Y1 @ Y2))) => 205.95/27.55 (Y1 @ Y3))))))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))))) => 205.95/27.55 (Y1 @ Y0)))))))) => 205.95/27.55 (X2 @ Y0)))))) 205.95/27.55 | (X2 @ '#sk4'))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])). 205.95/27.55 thf(zip_derived_cl21, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 ( (((X2 @ ('#sk15' @ X2)) & 205.95/27.55 (((((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk1' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))) | 205.95/27.55 (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))))))) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((((((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk1' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 (Y1 @ 205.95/27.55 Y2) & 205.95/27.55 ('#sk1' @ 205.95/27.55 Y2 @ Y3))) => 205.95/27.55 (Y1 @ Y3))))))))))) => 205.95/27.55 (Y1 @ Y0)))))) | 205.95/27.55 (((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y2 @ 205.95/27.55 Y3) & 205.95/27.55 (Y1 @ Y2))) => 205.95/27.55 (Y1 @ Y3))))))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))))) => 205.95/27.55 (Y1 @ Y0)))))))) => 205.95/27.55 (X2 @ Y0)))))))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 205.95/27.55 thf(zip_derived_cl21, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 ( (((X2 @ ('#sk15' @ X2)) & 205.95/27.55 (((((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk1' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))) | 205.95/27.55 (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))))))) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((((((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk1' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 (Y1 @ 205.95/27.55 Y2) & 205.95/27.55 ('#sk1' @ 205.95/27.55 Y2 @ Y3))) => 205.95/27.55 (Y1 @ Y3))))))))))) => 205.95/27.55 (Y1 @ Y0)))))) | 205.95/27.55 (((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y2 @ 205.95/27.55 Y3) & 205.95/27.55 (Y1 @ Y2))) => 205.95/27.55 (Y1 @ Y3))))))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))))) => 205.95/27.55 (Y1 @ Y0)))))))) => 205.95/27.55 (X2 @ Y0)))))))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 205.95/27.55 thf(zip_derived_cl26, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 ( ('#form35' @ X2) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((((((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk1' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 (Y1 @ 205.95/27.55 Y2) & 205.95/27.55 ('#sk1' @ 205.95/27.55 Y2 @ Y3))) => 205.95/27.55 (Y1 @ Y3))))))))))) => 205.95/27.55 (Y1 @ Y0)))))) | 205.95/27.55 (((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y2 @ 205.95/27.55 Y3) & 205.95/27.55 (Y1 @ Y2))) => 205.95/27.55 (Y1 @ Y3))))))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))))) => 205.95/27.55 (Y1 @ Y0)))))))) => 205.95/27.55 (X2 @ Y0)))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl28, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 (~ ('#form35' @ X2) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | (((X2 @ ('#sk15' @ X2)) & 205.95/27.55 (((((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk1' @ Y1 @ 205.95/27.55 Y2) & (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ 205.95/27.55 Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))) | 205.95/27.55 (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ 205.95/27.55 Y1) => (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ 205.95/27.55 Y2) & (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))))))))), 205.95/27.55 inference('renaming', [status(thm)], [zip_derived_cl21, zip_derived_cl26])). 205.95/27.55 thf(zip_derived_cl32, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 ( (((((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk1' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))) | 205.95/27.55 (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))))) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ ('#form35' @ X2))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl28])). 205.95/27.55 thf(zip_derived_cl38, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 ( (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk1' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))) 205.95/27.55 | ~ ('#form35' @ X2) 205.95/27.55 | (X2 @ '#sk4'))), 205.95/27.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl32])). 205.95/27.55 thf(zip_derived_cl40, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( (((((((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk1' @ Y0 @ Y1) & (X4 @ Y0))) => 205.95/27.55 (X4 @ Y1))))))))) & 205.95/27.55 (((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))) => 205.95/27.55 (X4 @ ('#sk21' @ X2)))) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ ('#form35' @ X2) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))))), 205.95/27.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl38])). 205.95/27.55 thf(zip_derived_cl42, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ (((((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk1' @ Y0 @ Y1) & (X4 @ Y0))) => 205.95/27.55 (X4 @ Y1))))))))) & 205.95/27.55 (((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))) 205.95/27.55 | ~ ('#form35' @ X2) 205.95/27.55 | (X2 @ '#sk4'))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])). 205.95/27.55 thf(zip_derived_cl44, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk1' @ Y0 @ Y1) & (X4 @ Y0))) => 205.95/27.55 (X4 @ Y1))))))))) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ ('#form35' @ X2) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))) 205.95/27.55 | (X4 @ ('#sk21' @ X2)))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl42])). 205.95/27.55 thf(zip_derived_cl46, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ (((!!) @ (^[Y0 : a]: 205.95/27.55 ((((('#sk1' @ ('#sk109' @ X4) @ Y0) & (X4 @ 205.95/27.55 ('#sk109' @ X4)))) => 205.95/27.55 (X4 @ Y0)))))) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))) 205.95/27.55 | ~ ('#form35' @ X2) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl44])). 205.95/27.55 thf(zip_derived_cl48, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ ((((('#sk1' @ ('#sk109' @ X4) @ ('#sk126' @ X4)) & (X4 @ 205.95/27.55 ('#sk109' @ X4)))) => 205.95/27.55 (X4 @ ('#sk126' @ X4)))) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ ('#form35' @ X2) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))) 205.95/27.55 | (X4 @ ('#sk21' @ X2)))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl46])). 205.95/27.55 thf(zip_derived_cl51, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( ((('#sk1' @ ('#sk109' @ X4) @ ('#sk126' @ X4)) & (X4 @ 205.95/27.55 ('#sk109' @ X4)))) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))) 205.95/27.55 | ~ ('#form35' @ X2) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 205.95/27.55 thf(zip_derived_cl57, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 (~ ('#form167' @ X2) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl58, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( (((((((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) & 205.95/27.55 (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk2' @ Y0 @ Y1) & (X4 @ Y0))) => 205.95/27.55 (X4 @ Y1))))))))))) => 205.95/27.55 (X4 @ ('#sk21' @ X2)))) 205.95/27.55 | ~ ('#form167' @ X2))), 205.95/27.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 205.95/27.55 thf(zip_derived_cl70, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ (((((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) & 205.95/27.55 (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk2' @ Y0 @ Y1) & (X4 @ Y0))) => 205.95/27.55 (X4 @ Y1))))))))))) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | ~ ('#form167' @ X2))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 205.95/27.55 thf(zip_derived_cl79, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ (((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk2' @ Y0 @ Y1) & (X4 @ Y0))) => 205.95/27.55 (X4 @ Y1))))))))) 205.95/27.55 | ~ ('#form167' @ X2) 205.95/27.55 | (X4 @ ('#sk21' @ X2)))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl70])). 205.95/27.55 thf(zip_derived_cl79, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ (((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk2' @ Y0 @ Y1) & (X4 @ Y0))) => 205.95/27.55 (X4 @ Y1))))))))) 205.95/27.55 | ~ ('#form167' @ X2) 205.95/27.55 | (X4 @ ('#sk21' @ X2)))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl70])). 205.95/27.55 thf(zip_derived_cl84, plain, 205.95/27.55 (![X4 : a > $o]: 205.95/27.55 ( ('#form310' @ X4) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk2' @ Y0 @ Y1) & (X4 @ Y0))) => 205.95/27.55 (X4 @ Y1))))))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl86, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ ('#form310' @ X4) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | ~ ('#form167' @ X2) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))), 205.95/27.55 inference('renaming', [status(thm)], [zip_derived_cl79, zip_derived_cl84])). 205.95/27.55 thf(zip_derived_cl88, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ ((('#sk2' @ ('#sk15' @ X2) @ ('#sk327' @ X2 @ X4)) => (X4 @ 205.95/27.55 ('#sk327' @ X2 @ X4)))) 205.95/27.55 | ~ ('#form167' @ X2) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | ~ ('#form310' @ X4))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl86])). 205.95/27.55 thf(zip_derived_cl93, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ (X4 @ ('#sk327' @ X2 @ X4)) 205.95/27.55 | ~ ('#form310' @ X4) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | ~ ('#form167' @ X2))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl88])). 205.95/27.55 thf(zip_derived_cl22, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 (~ (X2 @ ('#sk21' @ X2)) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((((((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk1' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 (Y1 @ 205.95/27.55 Y2) & 205.95/27.55 ('#sk1' @ 205.95/27.55 Y2 @ Y3))) => 205.95/27.55 (Y1 @ Y3))))))))))) => 205.95/27.55 (Y1 @ Y0)))))) | 205.95/27.55 (((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y2 @ 205.95/27.55 Y3) & 205.95/27.55 (Y1 @ Y2))) => 205.95/27.55 (Y1 @ Y3))))))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))))) => 205.95/27.55 (Y1 @ Y0)))))))) => 205.95/27.55 (X2 @ Y0)))))))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 205.95/27.55 thf(zip_derived_cl26, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 ( ('#form35' @ X2) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((((((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk1' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 (Y1 @ 205.95/27.55 Y2) & 205.95/27.55 ('#sk1' @ 205.95/27.55 Y2 @ Y3))) => 205.95/27.55 (Y1 @ Y3))))))))))) => 205.95/27.55 (Y1 @ Y0)))))) | 205.95/27.55 (((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y2 @ 205.95/27.55 Y3) & 205.95/27.55 (Y1 @ Y2))) => 205.95/27.55 (Y1 @ Y3))))))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))))) => 205.95/27.55 (Y1 @ Y0)))))))) => 205.95/27.55 (X2 @ Y0)))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl29, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 (~ ('#form35' @ (^[Y0 : a]: (X2 @ Y0))) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ (X2 @ ('#sk21' @ X2)))), 205.95/27.55 inference('renaming', [status(thm)], [zip_derived_cl22, zip_derived_cl26])). 205.95/27.55 thf(zip_derived_cl35, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 (~ ('#form35' @ X2) | (X2 @ '#sk4') | ~ (X2 @ ('#sk21' @ X2)))), 205.95/27.55 inference('ho_norm', [status(thm)], [zip_derived_cl29])). 205.95/27.55 thf(zip_derived_cl92, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( ('#sk2' @ ('#sk15' @ X2) @ ('#sk327' @ X2 @ X4)) 205.95/27.55 | ~ ('#form310' @ X4) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | ~ ('#form167' @ X2))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl88])). 205.95/27.55 thf(zip_derived_cl52, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ (X4 @ ('#sk126' @ X4)) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))) 205.95/27.55 | ~ ('#form35' @ X2) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 205.95/27.55 thf(zip_derived_cl57, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 (~ ('#form167' @ X2) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl60, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( ('#form167' @ X2) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ ('#form35' @ X2) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | ~ (X4 @ ('#sk126' @ X4)))), 205.95/27.55 inference('renaming', [status(thm)], [zip_derived_cl52, zip_derived_cl57])). 205.95/27.55 thf(zip_derived_cl51, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( ((('#sk1' @ ('#sk109' @ X4) @ ('#sk126' @ X4)) & (X4 @ 205.95/27.55 ('#sk109' @ X4)))) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))) 205.95/27.55 | ~ ('#form35' @ X2) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 205.95/27.55 thf(zip_derived_cl57, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 (~ ('#form167' @ X2) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 205.95/27.55 (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk21' @ X2))))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl59, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( ('#form167' @ X2) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ ('#form35' @ X2) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | ((('#sk1' @ ('#sk109' @ X4) @ ('#sk126' @ X4)) & (X4 @ 205.95/27.55 ('#sk109' @ X4)))))), 205.95/27.55 inference('renaming', [status(thm)], [zip_derived_cl51, zip_derived_cl57])). 205.95/27.55 thf(zip_derived_cl67, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( ('#form204' @ X2 @ X4) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl71, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ ('#form204' @ X2 @ (^[Y0 : a]: (X4 @ Y0))) 205.95/27.55 | ~ (X4 @ ('#sk126' @ X4)) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | ~ ('#form35' @ X2) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ('#form167' @ X2))), 205.95/27.55 inference('renaming', [status(thm)], [zip_derived_cl60, zip_derived_cl67])). 205.95/27.55 thf(zip_derived_cl80, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ ('#form204' @ X2 @ X4) 205.95/27.55 | ~ (X4 @ ('#sk126' @ X4)) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | ~ ('#form35' @ X2) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ('#form167' @ X2))), 205.95/27.55 inference('ho_norm', [status(thm)], [zip_derived_cl71])). 205.95/27.55 thf(zip_derived_cl59, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( ('#form167' @ X2) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ ('#form35' @ X2) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | ((('#sk1' @ ('#sk109' @ X4) @ ('#sk126' @ X4)) & (X4 @ 205.95/27.55 ('#sk109' @ X4)))))), 205.95/27.55 inference('renaming', [status(thm)], [zip_derived_cl51, zip_derived_cl57])). 205.95/27.55 thf(zip_derived_cl67, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( ('#form204' @ X2 @ X4) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl69, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ ('#form204' @ X2 @ X4) 205.95/27.55 | ((('#sk1' @ ('#sk109' @ X4) @ ('#sk126' @ X4)) & (X4 @ 205.95/27.55 ('#sk109' @ X4)))) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | ~ ('#form35' @ X2) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ('#form167' @ X2))), 205.95/27.55 inference('renaming', [status(thm)], [zip_derived_cl59, zip_derived_cl67])). 205.95/27.55 thf(zip_derived_cl76, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( (X4 @ ('#sk109' @ X4)) 205.95/27.55 | ('#form167' @ X2) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ ('#form35' @ X2) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | ~ ('#form204' @ X2 @ X4))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 205.95/27.55 thf(zip_derived_cl75, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( ('#sk1' @ ('#sk109' @ X4) @ ('#sk126' @ X4)) 205.95/27.55 | ('#form167' @ X2) 205.95/27.55 | (X2 @ '#sk4') 205.95/27.55 | ~ ('#form35' @ X2) 205.95/27.55 | (X4 @ ('#sk21' @ X2)) 205.95/27.55 | ~ ('#form204' @ X2 @ X4))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 205.95/27.55 thf(zip_derived_cl67, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( ('#form204' @ X2 @ X4) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl68, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ ((('#sk1' @ ('#sk15' @ X2) @ ('#sk205' @ X2 @ X4)) => (X4 @ 205.95/27.55 ('#sk205' @ X2 @ X4)))) 205.95/27.55 | ('#form204' @ X2 @ X4))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl67])). 205.95/27.55 thf(zip_derived_cl78, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ (X4 @ ('#sk205' @ X2 @ X4)) | ('#form204' @ X2 @ X4))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 205.95/27.55 thf(zip_derived_cl6, plain, 205.95/27.55 (~ (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 205.95/27.55 '#sk3' @ Y1))) => 205.95/27.55 (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((((Y0 @ Y1) & 205.95/27.55 ((('#sk2' @ Y1 @ Y2) | 205.95/27.55 ('#sk1' @ Y1 @ Y2))))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ '#sk4'))))))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 205.95/27.55 thf(zip_derived_cl8, plain, 205.95/27.55 (~ (((((((!!) @ (^[Y0 : a]: 205.95/27.55 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 205.95/27.55 ('#sk5' @ Y0)))))) & 205.95/27.55 (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk5' @ Y0) & 205.95/27.55 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 205.95/27.55 Y1))))) => 205.95/27.55 ('#sk5' @ Y1))))))))))) => 205.95/27.55 ('#sk5' @ '#sk4')))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 205.95/27.55 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk4')), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 205.95/27.55 thf(zip_derived_cl31, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 ( (X2 @ ('#sk15' @ X2)) | (X2 @ '#sk4') | ~ ('#form35' @ X2))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl28])). 205.95/27.55 thf(zip_derived_cl77, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( ('#sk1' @ ('#sk15' @ X2) @ ('#sk205' @ X2 @ X4)) 205.95/27.55 | ('#form204' @ X2 @ X4))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 205.95/27.55 thf(zip_derived_cl31, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 ( (X2 @ ('#sk15' @ X2)) | (X2 @ '#sk4') | ~ ('#form35' @ X2))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl28])). 205.95/27.55 thf(zip_derived_cl26, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 ( ('#form35' @ X2) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((((((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk1' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 (Y1 @ 205.95/27.55 Y2) & 205.95/27.55 ('#sk1' @ 205.95/27.55 Y2 @ Y3))) => 205.95/27.55 (Y1 @ Y3))))))))))) => 205.95/27.55 (Y1 @ Y0)))))) | 205.95/27.55 (((!!) @ (^[Y1 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y2 : a]: 205.95/27.55 (((!!) @ (^[Y3 : a]: 205.95/27.55 ( 205.95/27.55 ( 205.95/27.55 (( 205.95/27.55 ('#sk2' @ 205.95/27.55 Y2 @ 205.95/27.55 Y3) & 205.95/27.55 (Y1 @ Y2))) => 205.95/27.55 (Y1 @ Y3))))))))) & 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ 205.95/27.55 Y2) => (Y1 @ Y2)))))))) => 205.95/27.55 (Y1 @ Y0)))))))) => 205.95/27.55 (X2 @ Y0)))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl27, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 (~ (((((((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk1' @ '#sk3' @ Y1) => (Y0 @ 205.95/27.55 Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((((Y0 @ Y1) & 205.95/27.55 ('#sk1' @ Y1 @ Y2))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))) | 205.95/27.55 (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ 205.95/27.55 Y2) & (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ 205.95/27.55 Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))))) => 205.95/27.55 (X2 @ ('#sk36' @ X2)))) 205.95/27.55 | ('#form35' @ X2))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl26])). 205.95/27.55 thf(zip_derived_cl34, plain, 205.95/27.55 (![X2 : a > $o]: (~ (X2 @ ('#sk36' @ X2)) | ('#form35' @ X2))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])). 205.95/27.55 thf(zip_derived_cl391, plain, 205.95/27.55 (![X0 : a > $o]: 205.95/27.55 ( (X0 @ '#sk4') | (X0 @ ('#sk15' @ X0)) | ~ (X0 @ ('#sk36' @ X0)))), 205.95/27.55 inference('sup+', [status(thm)], [zip_derived_cl31, zip_derived_cl34])). 205.95/27.55 thf(zip_derived_cl84, plain, 205.95/27.55 (![X4 : a > $o]: 205.95/27.55 ( ('#form310' @ X4) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk2' @ Y0 @ Y1) & (X4 @ Y0))) => 205.95/27.55 (X4 @ Y1))))))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl85, plain, 205.95/27.55 (![X4 : a > $o]: 205.95/27.55 (~ (((!!) @ (^[Y0 : a]: 205.95/27.55 ((((('#sk2' @ ('#sk311' @ X4) @ Y0) & (X4 @ 205.95/27.55 ('#sk311' @ X4)))) => 205.95/27.55 (X4 @ Y0)))))) 205.95/27.55 | ('#form310' @ X4))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl84])). 205.95/27.55 thf(zip_derived_cl89, plain, 205.95/27.55 (![X4 : a > $o]: 205.95/27.55 (~ ((((('#sk2' @ ('#sk311' @ X4) @ ('#sk332' @ X4)) & (X4 @ 205.95/27.55 ('#sk311' @ X4)))) => 205.95/27.55 (X4 @ ('#sk332' @ X4)))) 205.95/27.55 | ('#form310' @ X4))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl85])). 205.95/27.55 thf(zip_derived_cl94, plain, 205.95/27.55 (![X4 : a > $o]: 205.95/27.55 ( ((('#sk2' @ ('#sk311' @ X4) @ ('#sk332' @ X4)) & (X4 @ 205.95/27.55 ('#sk311' @ X4)))) 205.95/27.55 | ('#form310' @ X4))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl89])). 205.95/27.55 thf(zip_derived_cl99, plain, 205.95/27.55 (![X4 : a > $o]: ( (X4 @ ('#sk311' @ X4)) | ('#form310' @ X4))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl94])). 205.95/27.55 thf(zip_derived_cl33, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 ( (((((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk1' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((((Y0 @ Y1) & ('#sk1' @ 205.95/27.55 Y1 @ Y2))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))) | 205.95/27.55 (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))))) 205.95/27.55 | ('#form35' @ X2))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])). 205.95/27.55 thf(zip_derived_cl39, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 ( (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk1' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 (((((Y0 @ Y1) & ('#sk1' @ 205.95/27.55 Y1 @ Y2))) => 205.95/27.55 (Y0 @ Y2))))))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))) 205.95/27.55 | ('#form35' @ X2))), 205.95/27.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl33])). 205.95/27.55 thf(zip_derived_cl41, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))) & 205.95/27.55 (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((((X4 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 205.95/27.55 (X4 @ Y1))))))))))) => 205.95/27.55 (X4 @ ('#sk36' @ X2)))) 205.95/27.55 | ('#form35' @ X2) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))))), 205.95/27.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl39])). 205.95/27.55 thf(zip_derived_cl43, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ (((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))) & 205.95/27.55 (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((((X4 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 205.95/27.55 (X4 @ Y1))))))))))) 205.95/27.55 | (X4 @ ('#sk36' @ X2)) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))) 205.95/27.55 | ('#form35' @ X2))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])). 205.95/27.55 thf(zip_derived_cl45, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((((X4 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 205.95/27.55 (X4 @ Y1))))))))) 205.95/27.55 | ('#form35' @ X2) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))) 205.95/27.55 | (X4 @ ('#sk36' @ X2)))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl43])). 205.95/27.55 thf(zip_derived_cl47, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ ((('#sk1' @ '#sk3' @ ('#sk116' @ X4)) => (X4 @ ('#sk116' @ X4)))) 205.95/27.55 | (X4 @ ('#sk36' @ X2)) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))) 205.95/27.55 | ('#form35' @ X2) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((((X4 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 205.95/27.55 (X4 @ Y1))))))))))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl45])). 205.95/27.55 thf(zip_derived_cl49, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( ('#sk1' @ '#sk3' @ ('#sk116' @ X4)) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((((X4 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 205.95/27.55 (X4 @ Y1))))))))) 205.95/27.55 | ('#form35' @ X2) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))) 205.95/27.55 | (X4 @ ('#sk36' @ X2)))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 205.95/27.55 thf(zip_derived_cl49, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( ('#sk1' @ '#sk3' @ ('#sk116' @ X4)) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((((X4 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 205.95/27.55 (X4 @ Y1))))))))) 205.95/27.55 | ('#form35' @ X2) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))) 205.95/27.55 | (X4 @ ('#sk36' @ X2)))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 205.95/27.55 thf(zip_derived_cl53, plain, 205.95/27.55 (![X4 : a > $o]: 205.95/27.55 ( ('#form150' @ X4) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((((X4 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 205.95/27.55 (X4 @ Y1))))))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl55, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ ('#form150' @ X4) 205.95/27.55 | (X4 @ ('#sk36' @ X2)) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))) 205.95/27.55 | ('#form35' @ X2) 205.95/27.55 | ('#sk1' @ '#sk3' @ ('#sk116' @ X4)))), 205.95/27.55 inference('renaming', [status(thm)], [zip_derived_cl49, zip_derived_cl53])). 205.95/27.55 thf(zip_derived_cl61, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 (~ ('#form180' @ X2) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl62, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( (((((((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk2' @ Y0 @ Y1) & (X4 @ Y0))) => 205.95/27.55 (X4 @ Y1))))))))) & 205.95/27.55 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))))) => 205.95/27.55 (X4 @ ('#sk36' @ X2)))) 205.95/27.55 | ~ ('#form180' @ X2))), 205.95/27.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl61])). 205.95/27.55 thf(zip_derived_cl72, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ (((((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk2' @ Y0 @ Y1) & (X4 @ Y0))) => 205.95/27.55 (X4 @ Y1))))))))) & 205.95/27.55 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))))) 205.95/27.55 | (X4 @ ('#sk36' @ X2)) 205.95/27.55 | ~ ('#form180' @ X2))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 205.95/27.55 thf(zip_derived_cl81, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk2' @ Y0 @ Y1) & (X4 @ Y0))) => 205.95/27.55 (X4 @ Y1))))))))) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))) 205.95/27.55 | ~ ('#form180' @ X2) 205.95/27.55 | (X4 @ ('#sk36' @ X2)))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl72])). 205.95/27.55 thf(zip_derived_cl84, plain, 205.95/27.55 (![X4 : a > $o]: 205.95/27.55 ( ('#form310' @ X4) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk2' @ Y0 @ Y1) & (X4 @ Y0))) => 205.95/27.55 (X4 @ Y1))))))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl87, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ ('#form310' @ (^[Y0 : a]: (X4 @ Y0))) 205.95/27.55 | (X4 @ ('#sk36' @ X2)) 205.95/27.55 | ~ ('#form180' @ X2) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 205.95/27.55 inference('renaming', [status(thm)], [zip_derived_cl81, zip_derived_cl84])). 205.95/27.55 thf(zip_derived_cl90, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ ('#form310' @ X4) 205.95/27.55 | (X4 @ ('#sk36' @ X2)) 205.95/27.55 | ~ ('#form180' @ X2) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 205.95/27.55 inference('ho_norm', [status(thm)], [zip_derived_cl87])). 205.95/27.55 thf(zip_derived_cl91, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ ((('#sk2' @ '#sk3' @ ('#sk341' @ X4)) => (X4 @ ('#sk341' @ X4)))) 205.95/27.55 | ~ ('#form180' @ X2) 205.95/27.55 | (X4 @ ('#sk36' @ X2)) 205.95/27.55 | ~ ('#form310' @ X4))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl90])). 205.95/27.55 thf(zip_derived_cl97, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ (X4 @ ('#sk341' @ X4)) 205.95/27.55 | ~ ('#form310' @ X4) 205.95/27.55 | (X4 @ ('#sk36' @ X2)) 205.95/27.55 | ~ ('#form180' @ X2))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl91])). 205.95/27.55 thf(zip_derived_cl53, plain, 205.95/27.55 (![X4 : a > $o]: 205.95/27.55 ( ('#form150' @ X4) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((((X4 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 205.95/27.55 (X4 @ Y1))))))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl54, plain, 205.95/27.55 (![X4 : a > $o]: 205.95/27.55 (~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((((X4 @ ('#sk151' @ X4)) & ('#sk1' @ 205.95/27.55 ('#sk151' @ X4) @ Y0))) => 205.95/27.55 (X4 @ Y0)))))) 205.95/27.55 | ('#form150' @ X4))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl53])). 205.95/27.55 thf(zip_derived_cl64, plain, 205.95/27.55 (![X4 : a > $o]: 205.95/27.55 (~ (((((X4 @ ('#sk151' @ X4)) & ('#sk1' @ ('#sk151' @ X4) @ 205.95/27.55 ('#sk185' @ X4)))) => 205.95/27.55 (X4 @ ('#sk185' @ X4)))) 205.95/27.55 | ('#form150' @ X4))), 205.95/27.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl54])). 205.95/27.55 thf(zip_derived_cl73, plain, 205.95/27.55 (![X4 : a > $o]: 205.95/27.55 ( (((X4 @ ('#sk151' @ X4)) & ('#sk1' @ ('#sk151' @ X4) @ 205.95/27.55 ('#sk185' @ X4)))) 205.95/27.55 | ('#form150' @ X4))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])). 205.95/27.55 thf(zip_derived_cl82, plain, 205.95/27.55 (![X4 : a > $o]: ( (X4 @ ('#sk151' @ X4)) | ('#form150' @ X4))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl73])). 205.95/27.55 thf(zip_derived_cl50, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ (X4 @ ('#sk116' @ X4)) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((((X4 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 205.95/27.55 (X4 @ Y1))))))))) 205.95/27.55 | ('#form35' @ X2) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))) 205.95/27.55 | (X4 @ ('#sk36' @ X2)))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 205.95/27.55 thf(zip_derived_cl53, plain, 205.95/27.55 (![X4 : a > $o]: 205.95/27.55 ( ('#form150' @ X4) 205.95/27.55 | ~ (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 (((((X4 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 205.95/27.55 (X4 @ Y1))))))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl56, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ ('#form150' @ (^[Y0 : a]: (X4 @ Y0))) 205.95/27.55 | (X4 @ ('#sk36' @ X2)) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))) 205.95/27.55 | ('#form35' @ X2) 205.95/27.55 | ~ (X4 @ ('#sk116' @ X4)))), 205.95/27.55 inference('renaming', [status(thm)], [zip_derived_cl50, zip_derived_cl53])). 205.95/27.55 thf(zip_derived_cl65, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ ('#form150' @ X4) 205.95/27.55 | (X4 @ ('#sk36' @ X2)) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))) 205.95/27.55 | ('#form35' @ X2) 205.95/27.55 | ~ (X4 @ ('#sk116' @ X4)))), 205.95/27.55 inference('ho_norm', [status(thm)], [zip_derived_cl56])). 205.95/27.55 thf(zip_derived_cl61, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 (~ ('#form180' @ X2) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl66, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( ('#form180' @ X2) 205.95/27.55 | ~ (X4 @ ('#sk116' @ X4)) 205.95/27.55 | ('#form35' @ X2) 205.95/27.55 | (X4 @ ('#sk36' @ X2)) 205.95/27.55 | ~ ('#form150' @ X4))), 205.95/27.55 inference('renaming', [status(thm)], [zip_derived_cl65, zip_derived_cl61])). 205.95/27.55 thf(zip_derived_cl95, plain, 205.95/27.55 (![X4 : a > $o]: (~ (X4 @ ('#sk332' @ X4)) | ('#form310' @ X4))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl89])). 205.95/27.55 thf(zip_derived_cl98, plain, 205.95/27.55 (![X4 : a > $o]: 205.95/27.55 ( ('#sk2' @ ('#sk311' @ X4) @ ('#sk332' @ X4)) | ('#form310' @ X4))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl94])). 205.95/27.55 thf(zip_derived_cl10, plain, 205.95/27.55 ( (((((!!) @ (^[Y0 : a]: 205.95/27.55 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 205.95/27.55 ('#sk5' @ Y0)))))) & 205.95/27.55 (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk5' @ Y0) & 205.95/27.55 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))))) => 205.95/27.55 ('#sk5' @ Y1)))))))))))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 205.95/27.55 thf(zip_derived_cl13, plain, 205.95/27.55 ( (((!!) @ (^[Y0 : a]: 205.95/27.55 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 205.95/27.55 ('#sk5' @ Y0))))))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 205.95/27.55 thf(zip_derived_cl16, plain, 205.95/27.55 (![X2 : a]: 205.95/27.55 ((((('#sk1' @ '#sk3' @ X2) | ('#sk2' @ '#sk3' @ X2))) => ('#sk5' @ 205.95/27.55 X2)))), 205.95/27.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 205.95/27.55 thf(zip_derived_cl19, plain, 205.95/27.55 (![X2 : a]: 205.95/27.55 (~ ((('#sk1' @ '#sk3' @ X2) | ('#sk2' @ '#sk3' @ X2))) 205.95/27.55 | ('#sk5' @ X2))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 205.95/27.55 thf(zip_derived_cl24, plain, 205.95/27.55 (![X2 : a]: (~ ('#sk2' @ '#sk3' @ X2) | ('#sk5' @ X2))), 205.95/27.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 205.95/27.55 thf(zip_derived_cl74, plain, 205.95/27.55 (![X4 : a > $o]: (~ (X4 @ ('#sk185' @ X4)) | ('#form150' @ X4))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])). 205.95/27.55 thf(zip_derived_cl83, plain, 205.95/27.55 (![X4 : a > $o]: 205.95/27.55 ( ('#sk1' @ ('#sk151' @ X4) @ ('#sk185' @ X4)) | ('#form150' @ X4))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl73])). 205.95/27.55 thf(zip_derived_cl23, plain, 205.95/27.55 (![X2 : a]: (~ ('#sk1' @ '#sk3' @ X2) | ('#sk5' @ X2))), 205.95/27.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 205.95/27.55 thf(zip_derived_cl14, plain, 205.95/27.55 ( (((!!) @ (^[Y0 : a]: 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((((('#sk5' @ Y0) & 205.95/27.55 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))))) => 205.95/27.55 ('#sk5' @ Y1)))))))))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 205.95/27.55 thf(zip_derived_cl17, plain, 205.95/27.55 (![X2 : a]: 205.95/27.55 (((!!) @ (^[Y0 : a]: 205.95/27.55 ((((('#sk5' @ X2) & 205.95/27.55 ((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))))) => 205.95/27.55 ('#sk5' @ Y0))))))), 205.95/27.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 205.95/27.55 thf(zip_derived_cl20, plain, 205.95/27.55 (![X2 : a, X4 : a]: 205.95/27.55 ((((('#sk5' @ X2) & ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))))) => 205.95/27.55 ('#sk5' @ X4)))), 205.95/27.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 205.95/27.55 thf(zip_derived_cl25, plain, 205.95/27.55 (![X2 : a, X4 : a]: 205.95/27.55 (~ ((('#sk5' @ X2) & ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))))) 205.95/27.55 | ('#sk5' @ X4))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 205.95/27.55 thf(zip_derived_cl30, plain, 205.95/27.55 (![X2 : a, X4 : a]: 205.95/27.55 (~ ('#sk5' @ X2) 205.95/27.55 | ~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 205.95/27.55 | ('#sk5' @ X4))), 205.95/27.55 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl25])). 205.95/27.55 thf(zip_derived_cl36, plain, 205.95/27.55 (![X2 : a, X4 : a]: 205.95/27.55 (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 205.95/27.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 205.95/27.55 thf(zip_derived_cl96, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( ('#sk2' @ '#sk3' @ ('#sk341' @ X4)) 205.95/27.55 | ~ ('#form310' @ X4) 205.95/27.55 | (X4 @ ('#sk36' @ X2)) 205.95/27.55 | ~ ('#form180' @ X2))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl91])). 205.95/27.55 thf(zip_derived_cl37, plain, 205.95/27.55 (![X2 : a, X4 : a]: 205.95/27.55 (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 205.95/27.55 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 205.95/27.55 thf(zip_derived_cl55, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 (~ ('#form150' @ X4) 205.95/27.55 | (X4 @ ('#sk36' @ X2)) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))) 205.95/27.55 | ('#form35' @ X2) 205.95/27.55 | ('#sk1' @ '#sk3' @ ('#sk116' @ X4)))), 205.95/27.55 inference('renaming', [status(thm)], [zip_derived_cl49, zip_derived_cl53])). 205.95/27.55 thf(zip_derived_cl61, plain, 205.95/27.55 (![X2 : a > $o]: 205.95/27.55 (~ ('#form180' @ X2) 205.95/27.55 | (((!!) @ (^[Y0 : a > $o]: 205.95/27.55 (((((((!!) @ (^[Y1 : a]: 205.95/27.55 (((!!) @ (^[Y2 : a]: 205.95/27.55 ((((('#sk2' @ Y1 @ Y2) & 205.95/27.55 (Y0 @ Y1))) => 205.95/27.55 (Y0 @ Y2))))))))) & 205.95/27.55 (((!!) @ (^[Y1 : a]: 205.95/27.55 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 205.95/27.55 (Y0 @ ('#sk36' @ X2))))))))), 205.95/27.55 define([status(thm)])). 205.95/27.55 thf(zip_derived_cl63, plain, 205.95/27.55 (![X2 : a > $o, X4 : a > $o]: 205.95/27.55 ( ('#form180' @ X2) 205.95/27.55 | ('#sk1' @ '#sk3' @ ('#sk116' @ X4)) 205.95/27.55 | ('#form35' @ X2) 205.95/27.55 | (X4 @ ('#sk36' @ X2)) 205.95/27.55 | ~ ('#form150' @ X4))), 205.95/27.55 inference('renaming', [status(thm)], [zip_derived_cl55, zip_derived_cl61])). 205.95/27.55 thf(zip_derived_cl34, plain, 205.95/27.55 (![X2 : a > $o]: (~ (X2 @ ('#sk36' @ X2)) | ('#form35' @ X2))), 205.95/27.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])). 205.95/27.55 thf(zip_derived_cl6259, plain, ($false), 205.95/27.55 inference('eprover', [status(thm)], 205.95/27.55 [zip_derived_cl93, zip_derived_cl35, zip_derived_cl92, 205.95/27.55 zip_derived_cl80, zip_derived_cl76, zip_derived_cl75, 205.95/27.55 zip_derived_cl78, zip_derived_cl11, zip_derived_cl31, 205.95/27.55 zip_derived_cl77, zip_derived_cl391, zip_derived_cl99, 205.95/27.55 zip_derived_cl97, zip_derived_cl82, zip_derived_cl66, 205.95/27.55 zip_derived_cl95, zip_derived_cl98, zip_derived_cl24, 205.95/27.55 zip_derived_cl74, zip_derived_cl83, zip_derived_cl23, 205.95/27.55 zip_derived_cl36, zip_derived_cl96, zip_derived_cl37, 205.95/27.55 zip_derived_cl63, zip_derived_cl34])). 205.95/27.55 205.95/27.55 % SZS output end Refutation 205.95/27.55 205.95/27.55 205.95/27.55 % Terminating... 206.49/27.62 % Runner terminated. 206.49/27.62 % Zipperpin 1.5 exiting 206.49/27.64 EOF