0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.2sZH9ro0ry true 0.13/0.34 % Computer : n028.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 02:32:35 EDT 2022 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 960 s 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.34 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.52/0.62 % Total configuration time : 828 0.52/0.62 % Estimated wc time : 1656 0.52/0.62 % Estimated cpu time (8 cpus) : 207.0 0.52/0.68 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.52/0.69 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.52/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.53/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.53/0.74 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.53/0.74 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.53/0.74 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.53/0.75 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 50.41/7.02 % Solved by lams/20_acsne_simpl.sh. 50.41/7.02 % done 382 iterations in 6.178s 50.41/7.02 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 50.41/7.02 % SZS output start Refutation 50.41/7.02 thf(a_type, type, a: $tType). 50.41/7.02 thf('#sk3_type', type, '#sk3': a). 50.41/7.02 thf('#sk115_type', type, '#sk115': (a > $o) > (a > $o) > a). 50.41/7.02 thf('#form220_type', type, '#form220': (a > $o) > $o). 50.41/7.02 thf('#form733_type', type, '#form733': $o). 50.41/7.02 thf('#sk4_type', type, '#sk4': a). 50.41/7.02 thf('#sk141_type', type, '#sk141': (a > $o) > a). 50.41/7.02 thf('#sk367_type', type, '#sk367': (a > $o) > a). 50.41/7.02 thf('#sk442_type', type, '#sk442': (a > $o) > a). 50.41/7.02 thf('#sk1_type', type, '#sk1': a > a > $o). 50.41/7.02 thf('#form37_type', type, '#form37': (a > $o) > $o). 50.41/7.02 thf('#sk21_type', type, '#sk21': (a > $o) > a). 50.41/7.02 thf('#sk38_type', type, '#sk38': (a > $o) > a). 50.41/7.02 thf('#form418_type', type, '#form418': (a > $o) > $o). 50.41/7.02 thf('#sk419_type', type, '#sk419': (a > $o) > a). 50.41/7.02 thf('#sk122_type', type, '#sk122': (a > $o) > a). 50.41/7.02 thf('#form198_type', type, '#form198': (a > $o) > $o). 50.41/7.02 thf('#sk15_type', type, '#sk15': (a > $o) > a). 50.41/7.02 thf('#sk5_type', type, '#sk5': a > $o). 50.41/7.02 thf('#form227_type', type, '#form227': (a > $o) > $o). 50.41/7.02 thf('#sk228_type', type, '#sk228': (a > $o) > a). 50.41/7.02 thf('#sk2_type', type, '#sk2': a > a > $o). 50.41/7.02 thf('#sk402_type', type, '#sk402': (a > $o) > (a > $o) > a). 50.41/7.02 thf(cTHM251C_pme, conjecture, 50.41/7.02 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 50.41/7.02 ( ( ![Xq:( a > $o )]: 50.41/7.02 ( ( ( ![Xu:a,Xv:a]: 50.41/7.02 ( ( ( Xq @ Xu ) & 50.41/7.02 ( ( ![Xq0:( a > $o )]: 50.41/7.02 ( ( ( ![Xw:a]: ( ( R @ Xu @ Xw ) => ( Xq0 @ Xw ) ) ) & 50.41/7.02 ( ![Xu0:a,Xv0:a]: 50.41/7.02 ( ( ( R @ Xu0 @ Xv0 ) & ( Xq0 @ Xu0 ) ) => 50.41/7.02 ( Xq0 @ Xv0 ) ) ) ) => 50.41/7.02 ( Xq0 @ Xv ) ) ) | 50.41/7.02 ( ![Xq0:( a > $o )]: 50.41/7.02 ( ( ( ![Xw:a]: ( ( S @ Xu @ Xw ) => ( Xq0 @ Xw ) ) ) & 50.41/7.02 ( ![Xu0:a,Xv0:a]: 50.41/7.02 ( ( ( Xq0 @ Xu0 ) & ( S @ Xu0 @ Xv0 ) ) => 50.41/7.02 ( Xq0 @ Xv0 ) ) ) ) => 50.41/7.02 ( Xq0 @ Xv ) ) ) ) ) => 50.41/7.02 ( Xq @ Xv ) ) ) & 50.41/7.02 ( ![Xw:a]: 50.41/7.02 ( ( ( ![Xq0:( a > $o )]: 50.41/7.02 ( ( ( ![Xu:a,Xv:a]: 50.41/7.02 ( ( ( R @ Xu @ Xv ) & ( Xq0 @ Xu ) ) => ( Xq0 @ Xv ) ) ) & 50.41/7.02 ( ![Xw0:a]: ( ( R @ Xx @ Xw0 ) => ( Xq0 @ Xw0 ) ) ) ) => 50.41/7.02 ( Xq0 @ Xw ) ) ) | 50.41/7.02 ( ![Xq0:( a > $o )]: 50.41/7.02 ( ( ( ![Xw0:a]: ( ( S @ Xx @ Xw0 ) => ( Xq0 @ Xw0 ) ) ) & 50.41/7.02 ( ![Xu:a,Xv:a]: 50.41/7.02 ( ( ( Xq0 @ Xu ) & ( S @ Xu @ Xv ) ) => ( Xq0 @ Xv ) ) ) ) => 50.41/7.02 ( Xq0 @ Xw ) ) ) ) => 50.41/7.02 ( Xq @ Xw ) ) ) ) => 50.41/7.02 ( Xq @ Xy ) ) ) => 50.41/7.02 ( ![Xq:( a > $o )]: 50.41/7.02 ( ( ( ![Xw:a]: 50.41/7.02 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 50.41/7.02 ( ![Xu:a,Xv:a]: 50.41/7.02 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 50.41/7.02 ( Xq @ Xv ) ) ) ) => 50.41/7.02 ( Xq @ Xy ) ) ) ))). 50.41/7.02 thf(zf_stmt_0, negated_conjecture, 50.41/7.02 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 50.41/7.02 ( ( ![Xq:( a > $o )]: 50.41/7.02 ( ( ( ![Xu:a,Xv:a]: 50.41/7.02 ( ( ( Xq @ Xu ) & 50.41/7.02 ( ( ![Xq0:( a > $o )]: 50.41/7.02 ( ( ( ![Xw:a]: ( ( R @ Xu @ Xw ) => ( Xq0 @ Xw ) ) ) & 50.41/7.02 ( ![Xu0:a,Xv0:a]: 50.41/7.02 ( ( ( R @ Xu0 @ Xv0 ) & ( Xq0 @ Xu0 ) ) => 50.41/7.02 ( Xq0 @ Xv0 ) ) ) ) => 50.41/7.02 ( Xq0 @ Xv ) ) ) | 50.41/7.02 ( ![Xq0:( a > $o )]: 50.41/7.02 ( ( ( ![Xw:a]: ( ( S @ Xu @ Xw ) => ( Xq0 @ Xw ) ) ) & 50.41/7.02 ( ![Xu0:a,Xv0:a]: 50.41/7.02 ( ( ( Xq0 @ Xu0 ) & ( S @ Xu0 @ Xv0 ) ) => 50.41/7.02 ( Xq0 @ Xv0 ) ) ) ) => 50.41/7.02 ( Xq0 @ Xv ) ) ) ) ) => 50.41/7.02 ( Xq @ Xv ) ) ) & 50.41/7.02 ( ![Xw:a]: 50.41/7.02 ( ( ( ![Xq0:( a > $o )]: 50.41/7.02 ( ( ( ![Xu:a,Xv:a]: 50.41/7.02 ( ( ( R @ Xu @ Xv ) & ( Xq0 @ Xu ) ) => 50.41/7.02 ( Xq0 @ Xv ) ) ) & 50.41/7.02 ( ![Xw0:a]: ( ( R @ Xx @ Xw0 ) => ( Xq0 @ Xw0 ) ) ) ) => 50.41/7.02 ( Xq0 @ Xw ) ) ) | 50.41/7.02 ( ![Xq0:( a > $o )]: 50.41/7.02 ( ( ( ![Xw0:a]: ( ( S @ Xx @ Xw0 ) => ( Xq0 @ Xw0 ) ) ) & 50.41/7.02 ( ![Xu:a,Xv:a]: 50.41/7.02 ( ( ( Xq0 @ Xu ) & ( S @ Xu @ Xv ) ) => 50.41/7.02 ( Xq0 @ Xv ) ) ) ) => 50.41/7.02 ( Xq0 @ Xw ) ) ) ) => 50.41/7.02 ( Xq @ Xw ) ) ) ) => 50.41/7.02 ( Xq @ Xy ) ) ) => 50.41/7.02 ( ![Xq:( a > $o )]: 50.41/7.02 ( ( ( ![Xw:a]: 50.41/7.02 ( ( ( R @ Xx @ Xw ) | ( S @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 50.41/7.02 ( ![Xu:a,Xv:a]: 50.41/7.02 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 50.41/7.02 ( Xq @ Xv ) ) ) ) => 50.41/7.02 ( Xq @ Xy ) ) ) ) )), 50.41/7.02 inference('cnf.neg', [status(esa)], [cTHM251C_pme])). 50.41/7.02 thf(zip_derived_cl0, plain, 50.41/7.02 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.41/7.02 (((!!) @ (^[Y1 : a > a > $o]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((((!!) @ (^[Y4 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y4 @ 50.41/7.02 Y5) & 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y7 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y8 : a]: 50.41/7.02 (( 50.41/7.02 (Y0 @ 50.41/7.02 Y5 @ 50.41/7.02 Y8) => 50.41/7.02 (Y7 @ Y8)))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y8 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y9 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y0 @ 50.41/7.02 Y8 @ 50.41/7.02 Y9) & 50.41/7.02 (Y7 @ Y8))) => 50.41/7.02 (Y7 @ Y9))))))))))) => 50.41/7.02 (Y7 @ Y6)))))) | 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y7 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y8 : a]: 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y5 @ 50.41/7.02 Y8) => 50.41/7.02 (Y7 @ Y8)))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y8 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y9 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y7 @ 50.41/7.02 Y8) & 50.41/7.02 (Y1 @ 50.41/7.02 Y8 @ Y9))) => 50.41/7.02 (Y7 @ Y9))))))))))) => 50.41/7.02 (Y7 @ Y6)))))))))) => 50.41/7.02 (Y4 @ Y6))))))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y7 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y8 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y0 @ 50.41/7.02 Y7 @ 50.41/7.02 Y8) & 50.41/7.02 (Y6 @ Y7))) => 50.41/7.02 (Y6 @ Y8))))))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y7 : a]: 50.41/7.02 (( 50.41/7.02 (Y0 @ 50.41/7.02 Y2 @ 50.41/7.02 Y7) => 50.41/7.02 (Y6 @ Y7)))))))) => 50.41/7.02 (Y6 @ Y5)))))) | 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y7 : a]: 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y2 @ 50.41/7.02 Y7) => 50.41/7.02 (Y6 @ Y7)))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y7 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y8 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y6 @ 50.41/7.02 Y7) & 50.41/7.02 (Y1 @ 50.41/7.02 Y7 @ Y8))) => 50.41/7.02 (Y6 @ Y8))))))))))) => 50.41/7.02 (Y6 @ Y5)))))))) => 50.41/7.02 (Y4 @ Y5)))))))) => 50.41/7.02 (Y4 @ Y3)))))) => 50.41/7.02 (((!!) @ (^[Y4 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y0 @ 50.41/7.02 Y2 @ 50.41/7.02 Y5) | 50.41/7.02 (Y1 @ 50.41/7.02 Y2 @ Y5))) => 50.41/7.02 (Y4 @ Y5)))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y5 @ 50.41/7.02 Y6) | 50.41/7.02 (Y0 @ 50.41/7.02 Y5 @ Y6))) & 50.41/7.02 (Y4 @ Y5))) => 50.41/7.02 (Y4 @ Y6))))))))))) => 50.41/7.02 (Y4 @ Y3))))))))))))))))))))), 50.41/7.02 inference('cnf', [status(esa)], [zf_stmt_0])). 50.41/7.02 thf(zip_derived_cl1, plain, 50.41/7.02 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((!!) @ (^[Y3 : a > $o]: 50.41/7.02 (((((((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y3 @ 50.41/7.02 Y4) & 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y7 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y4 @ 50.41/7.02 Y7) => 50.41/7.02 (Y6 @ Y7)))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y7 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y8 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y7 @ 50.41/7.02 Y8) & 50.41/7.02 (Y6 @ Y7))) => 50.41/7.02 (Y6 @ Y8))))))))))) => 50.41/7.02 (Y6 @ Y5)))))) | 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y7 : a]: 50.41/7.02 (( 50.41/7.02 (Y0 @ 50.41/7.02 Y4 @ 50.41/7.02 Y7) => 50.41/7.02 (Y6 @ Y7)))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y7 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y8 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y6 @ 50.41/7.02 Y7) & 50.41/7.02 (Y0 @ 50.41/7.02 Y7 @ Y8))) => 50.41/7.02 (Y6 @ Y8))))))))))) => 50.41/7.02 (Y6 @ Y5)))))))))) => 50.41/7.02 (Y3 @ Y5))))))))) & 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (((( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y7 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y6 @ 50.41/7.02 Y7) & 50.41/7.02 (Y5 @ Y6))) => 50.41/7.02 (Y5 @ Y7))))))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y1 @ 50.41/7.02 Y6) => 50.41/7.02 (Y5 @ Y6)))))))) => 50.41/7.02 (Y5 @ Y4)))))) | 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a]: 50.41/7.02 (( 50.41/7.02 (Y0 @ 50.41/7.02 Y1 @ 50.41/7.02 Y6) => 50.41/7.02 (Y5 @ Y6)))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y7 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y5 @ 50.41/7.02 Y6) & 50.41/7.02 (Y0 @ 50.41/7.02 Y6 @ Y7))) => 50.41/7.02 (Y5 @ Y7))))))))))) => 50.41/7.02 (Y5 @ Y4)))))))) => 50.41/7.02 (Y3 @ Y4)))))))) => 50.41/7.02 (Y3 @ Y2)))))) => 50.41/7.02 (((!!) @ (^[Y3 : a > $o]: 50.41/7.02 (((((((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (((( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y1 @ Y4) | 50.41/7.02 (Y0 @ 50.41/7.02 Y1 @ Y4))) => 50.41/7.02 (Y3 @ Y4)))))) & 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y0 @ 50.41/7.02 Y4 @ 50.41/7.02 Y5) | 50.41/7.02 ('#sk1' @ 50.41/7.02 Y4 @ Y5))) & 50.41/7.02 (Y3 @ Y4))) => 50.41/7.02 (Y3 @ Y5))))))))))) => 50.41/7.02 (Y3 @ Y2)))))))))))))))))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 50.41/7.02 thf(zip_derived_cl2, plain, 50.41/7.02 (~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (((( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y6) => 50.41/7.02 (Y5 @ Y6)))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y7 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y6 @ 50.41/7.02 Y7) & 50.41/7.02 (Y5 @ Y6))) => 50.41/7.02 (Y5 @ Y7))))))))))) => 50.41/7.02 (Y5 @ Y4)))))) | 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ 50.41/7.02 Y6) => 50.41/7.02 (Y5 @ Y6)))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y7 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y5 @ 50.41/7.02 Y6) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y6 @ Y7))) => 50.41/7.02 (Y5 @ Y7))))))))))) => 50.41/7.02 (Y5 @ Y4)))))))))) => 50.41/7.02 (Y2 @ Y4))))))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((((((!!) @ ( 50.41/7.02 ^[Y4 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y5 @ 50.41/7.02 Y6) & 50.41/7.02 (Y4 @ Y5))) => 50.41/7.02 (Y4 @ Y6))))))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y0 @ 50.41/7.02 Y5) => 50.41/7.02 (Y4 @ Y5)))))))) => 50.41/7.02 (Y4 @ Y3)))))) | 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y5) => 50.41/7.02 (Y4 @ Y5)))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y4 @ 50.41/7.02 Y5) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y5 @ Y6))) => 50.41/7.02 (Y4 @ Y6))))))))))) => 50.41/7.02 (Y4 @ Y3)))))))) => 50.41/7.02 (Y2 @ Y3)))))))) => 50.41/7.02 (Y2 @ Y1)))))) => 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ((((('#sk1' @ 50.41/7.02 Y0 @ Y3) | 50.41/7.02 ('#sk2' @ 50.41/7.02 Y0 @ Y3))) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (((( 50.41/7.02 (( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4) | 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ Y4))) & 50.41/7.02 (Y2 @ Y3))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1))))))))))))))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 50.41/7.02 thf(zip_derived_cl3, plain, 50.41/7.02 (~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((((Y1 @ Y2) & 50.41/7.02 (((( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y5) => 50.41/7.02 (Y4 @ Y5)))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y5 @ 50.41/7.02 Y6) & 50.41/7.02 (Y4 @ Y5))) => 50.41/7.02 (Y4 @ Y6))))))))))) => 50.41/7.02 (Y4 @ Y3)))))) | 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ 50.41/7.02 Y5) => 50.41/7.02 (Y4 @ Y5)))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y6 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y4 @ 50.41/7.02 Y5) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y5 @ Y6))) => 50.41/7.02 (Y4 @ Y6))))))))))) => 50.41/7.02 (Y4 @ Y3)))))))))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((((!!) @ (^[Y3 : a > $o]: 50.41/7.02 (((( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y4 @ 50.41/7.02 Y5) & 50.41/7.02 (Y3 @ Y4))) => 50.41/7.02 (Y3 @ Y5))))))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 '#sk3' @ 50.41/7.02 Y4) => 50.41/7.02 (Y3 @ Y4)))))))) => 50.41/7.02 (Y3 @ Y2)))))) | 50.41/7.02 (((!!) @ (^[Y3 : a > $o]: 50.41/7.02 (((( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk2' @ 50.41/7.02 '#sk3' @ 50.41/7.02 Y4) => 50.41/7.02 (Y3 @ Y4)))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y3 @ 50.41/7.02 Y4) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y4 @ Y5))) => 50.41/7.02 (Y3 @ Y5))))))))))) => 50.41/7.02 (Y3 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) => 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((((('#sk1' @ '#sk3' @ Y2) | 50.41/7.02 ('#sk2' @ '#sk3' @ Y2))) => 50.41/7.02 (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ((((((('#sk2' @ 50.41/7.02 Y2 @ Y3) | 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ Y3))) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))))))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 50.41/7.02 thf(zip_derived_cl4, plain, 50.41/7.02 (~ (((((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & 50.41/7.02 (((((!!) @ (^[Y3 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y1 @ 50.41/7.02 Y4) => 50.41/7.02 (Y3 @ Y4)))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y4 @ 50.41/7.02 Y5) & 50.41/7.02 (Y3 @ Y4))) => 50.41/7.02 (Y3 @ Y5))))))))))) => 50.41/7.02 (Y3 @ Y2)))))) | 50.41/7.02 (((!!) @ (^[Y3 : a > $o]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y1 @ 50.41/7.02 Y4) => 50.41/7.02 (Y3 @ Y4)))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y3 @ 50.41/7.02 Y4) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y4 @ Y5))) => 50.41/7.02 (Y3 @ Y5))))))))))) => 50.41/7.02 (Y3 @ Y2)))))))))) => 50.41/7.02 (Y0 @ Y2))))))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) & 50.41/7.02 (Y2 @ Y3))) => 50.41/7.02 (Y2 @ Y4))))))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 '#sk3' @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))))) => 50.41/7.02 (Y2 @ Y1)))))) | 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk2' @ 50.41/7.02 '#sk3' @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))) => 50.41/7.02 (Y0 @ Y1)))))))) => 50.41/7.02 (Y0 @ '#sk4')))))) => 50.41/7.02 (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 50.41/7.02 '#sk3' @ Y1))) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((((('#sk2' @ Y1 @ Y2) | 50.41/7.02 ('#sk1' @ Y1 @ Y2))) & 50.41/7.02 (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ '#sk4'))))))))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 50.41/7.02 thf(zip_derived_cl5, plain, 50.41/7.02 ( (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & 50.41/7.02 (((((!!) @ (^[Y3 : a > $o]: 50.41/7.02 (((((( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y1 @ 50.41/7.02 Y4) => 50.41/7.02 (Y3 @ Y4)))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y4 @ 50.41/7.02 Y5) & 50.41/7.02 (Y3 @ Y4))) => 50.41/7.02 (Y3 @ Y5))))))))))) => 50.41/7.02 (Y3 @ Y2)))))) | 50.41/7.02 (((!!) @ (^[Y3 : a > $o]: 50.41/7.02 (((((( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y1 @ 50.41/7.02 Y4) => 50.41/7.02 (Y3 @ Y4)))))) & 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y5 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y3 @ 50.41/7.02 Y4) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y4 @ Y5))) => 50.41/7.02 (Y3 @ Y5))))))))))) => 50.41/7.02 (Y3 @ Y2)))))))))) => 50.41/7.02 (Y0 @ Y2))))))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) & 50.41/7.02 (Y2 @ Y3))) => 50.41/7.02 (Y2 @ Y4))))))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ((('#sk1' @ 50.41/7.02 '#sk3' @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))))) => 50.41/7.02 (Y2 @ Y1)))))) | 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ((('#sk2' @ 50.41/7.02 '#sk3' @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))) => 50.41/7.02 (Y0 @ Y1)))))))) => 50.41/7.02 (Y0 @ '#sk4'))))))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 50.41/7.02 thf(zip_derived_cl7, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X2 @ Y0) & 50.41/7.02 (((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) & 50.41/7.02 (Y2 @ Y3))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))) | 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))))) => 50.41/7.02 (X2 @ Y1))))))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 (X2 @ Y0)))))))) => 50.41/7.02 (X2 @ '#sk4')))), 50.41/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 50.41/7.02 thf(zip_derived_cl8, plain, 50.41/7.02 ( (((((((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk5' @ Y0) & 50.41/7.02 (((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) & 50.41/7.02 (Y2 @ Y3))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))) | 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))))) => 50.41/7.02 ('#sk5' @ Y1))))))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 ('#sk5' @ Y0)))))))) => 50.41/7.02 ('#sk5' @ '#sk4')))), 50.41/7.02 inference('triggered_bool_instantiation', [status(thm)], 50.41/7.02 [zip_derived_cl7])). 50.41/7.02 thf(zip_derived_cl6, plain, 50.41/7.02 (~ (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ '#sk3' @ Y1) | ('#sk2' @ 50.41/7.02 '#sk3' @ Y1))) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((((('#sk2' @ Y1 @ Y2) | 50.41/7.02 ('#sk1' @ Y1 @ Y2))) & 50.41/7.02 (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ '#sk4'))))))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 50.41/7.02 thf(zip_derived_cl9, plain, 50.41/7.02 (~ (((((((!!) @ (^[Y0 : a]: 50.41/7.02 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 50.41/7.02 ('#sk5' @ Y0)))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 50.41/7.02 Y1))) & 50.41/7.02 ('#sk5' @ Y0))) => 50.41/7.02 ('#sk5' @ Y1))))))))))) => 50.41/7.02 ('#sk5' @ '#sk4')))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 50.41/7.02 thf(zip_derived_cl12, plain, (~ ('#sk5' @ '#sk4')), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl9])). 50.41/7.02 thf(zip_derived_cl137, plain, 50.41/7.02 ( (((((((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk5' @ Y0) & 50.41/7.02 (((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) & 50.41/7.02 (Y2 @ Y3))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))) | 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))))) => 50.41/7.02 ('#sk5' @ Y1))))))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 ('#sk5' @ Y0)))))))) => 50.41/7.02 ($false)))), 50.41/7.02 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl12])). 50.41/7.02 thf(zip_derived_cl138, plain, 50.41/7.02 ( (((~) @ (((((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk5' @ Y0) & 50.41/7.02 (((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ ( 50.41/7.02 ^[Y3 : a]: 50.41/7.02 ((('#sk1' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) & 50.41/7.02 (Y2 @ Y3))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))) | 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ ( 50.41/7.02 ^[Y3 : a]: 50.41/7.02 ((('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))))) => 50.41/7.02 ('#sk5' @ Y1))))))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y3 : a]: 50.41/7.02 ((((('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ 50.41/7.02 '#sk3' @ Y2) => 50.41/7.02 (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ 50.41/7.02 '#sk3' @ Y2) => 50.41/7.02 (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y3 : a]: 50.41/7.02 (((((Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 ('#sk5' @ Y0))))))))))), 50.41/7.02 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl137])). 50.41/7.02 thf(zip_derived_cl139, plain, 50.41/7.02 (~ (((((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk5' @ Y0) & 50.41/7.02 (((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) & 50.41/7.02 (Y2 @ Y3))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))) | 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))))) => 50.41/7.02 ('#sk5' @ Y1))))))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 ('#sk5' @ Y0))))))))), 50.41/7.02 inference('simplify nested equalities', [status(thm)], 50.41/7.02 [zip_derived_cl138])). 50.41/7.02 thf(zip_derived_cl140, plain, 50.41/7.02 ((~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk5' @ Y0) & 50.41/7.02 (((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ((('#sk1' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) & 50.41/7.02 (Y2 @ Y3))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))) | 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ((('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))))) => 50.41/7.02 ('#sk5' @ Y1))))))))) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 ('#sk5' @ Y0)))))))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl139])). 50.41/7.02 thf(zip_derived_cl7, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X2 @ Y0) & 50.41/7.02 (((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) & 50.41/7.02 (Y2 @ Y3))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))) | 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))))) => 50.41/7.02 (X2 @ Y1))))))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 (X2 @ Y0)))))))) => 50.41/7.02 (X2 @ '#sk4')))), 50.41/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 50.41/7.02 thf(zip_derived_cl10, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (~ (((((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X2 @ Y0) & 50.41/7.02 (((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) & 50.41/7.02 (Y2 @ Y3))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))) | 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))))) => 50.41/7.02 (X2 @ Y1))))))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 (X2 @ Y0)))))))) 50.41/7.02 | (X2 @ '#sk4'))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 50.41/7.02 thf(zip_derived_cl13, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X2 @ Y0) & 50.41/7.02 (((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) & 50.41/7.02 (Y2 @ Y3))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))) | 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))))) => 50.41/7.02 (X2 @ Y1))))))))) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 (X2 @ Y0)))))) 50.41/7.02 | (X2 @ '#sk4'))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 50.41/7.02 thf(zip_derived_cl16, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((X2 @ ('#sk15' @ X2)) & 50.41/7.02 (((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ 50.41/7.02 ('#sk15' @ X2) @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ 50.41/7.02 ('#sk15' @ X2) @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))))) => 50.41/7.02 (X2 @ Y0)))))) 50.41/7.02 | (X2 @ '#sk4') 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 (X2 @ Y0)))))))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl13])). 50.41/7.02 thf(zip_derived_cl19, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (~ (((((X2 @ ('#sk15' @ X2)) & 50.41/7.02 (((((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ X2) @ 50.41/7.02 Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((('#sk1' @ Y1 @ 50.41/7.02 Y2) & (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))) | 50.41/7.02 (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ 50.41/7.02 Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & 50.41/7.02 ('#sk2' @ Y1 @ 50.41/7.02 Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))))))) => 50.41/7.02 (X2 @ ('#sk21' @ X2)))) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 (X2 @ Y0)))))) 50.41/7.02 | (X2 @ '#sk4'))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl16])). 50.41/7.02 thf(zip_derived_cl23, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (~ (X2 @ ('#sk21' @ X2)) 50.41/7.02 | (X2 @ '#sk4') 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 (X2 @ Y0)))))))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 50.41/7.02 thf(zip_derived_cl29, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 ( ('#form37' @ X2) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 (X2 @ Y0)))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl141, plain, 50.41/7.02 ((~ ('#form37' @ '#sk5') 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk5' @ Y0) & 50.41/7.02 (((((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y3 @ 50.41/7.02 Y4) & 50.41/7.02 (Y2 @ Y3))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))) | 50.41/7.02 (((!!) @ (^[Y2 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 ('#sk2' @ 50.41/7.02 Y0 @ 50.41/7.02 Y3) => 50.41/7.02 (Y2 @ Y3)))))) & 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (!!) @ ( 50.41/7.02 ^[Y4 : a]: 50.41/7.02 (( 50.41/7.02 (( 50.41/7.02 (Y2 @ 50.41/7.02 Y3) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y3 @ Y4))) => 50.41/7.02 (Y2 @ Y4))))))))))) => 50.41/7.02 (Y2 @ Y1)))))))))) => 50.41/7.02 ('#sk5' @ Y1))))))))))), 50.41/7.02 inference('renaming', [status(thm)], 50.41/7.02 [zip_derived_cl140, zip_derived_cl29])). 50.41/7.02 thf(zip_derived_cl142, plain, 50.41/7.02 ((~ (((!!) @ (^[Y0 : a]: 50.41/7.02 ((((('#sk5' @ ('#sk15' @ '#sk5')) & 50.41/7.02 (((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ 50.41/7.02 ('#sk15' @ '#sk5') @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ 50.41/7.02 ('#sk15' @ '#sk5') @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 (((( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))))) => 50.41/7.02 ('#sk5' @ Y0)))))) 50.41/7.02 | ~ ('#form37' @ '#sk5'))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl141])). 50.41/7.02 thf(zip_derived_cl143, plain, 50.41/7.02 ((~ ((((('#sk5' @ ('#sk15' @ '#sk5')) & 50.41/7.02 (((((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ '#sk5') @ 50.41/7.02 Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((('#sk1' @ Y1 @ 50.41/7.02 Y2) & (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ '#sk5'))))))) | 50.41/7.02 (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ '#sk5') @ 50.41/7.02 Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & 50.41/7.02 ('#sk2' @ Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ '#sk5'))))))))))) => 50.41/7.02 ('#sk5' @ ('#sk21' @ '#sk5')))) 50.41/7.02 | ~ ('#form37' @ '#sk5'))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl142])). 50.41/7.02 thf(zip_derived_cl145, plain, 50.41/7.02 ((~ ('#sk5' @ ('#sk21' @ '#sk5')) | ~ ('#form37' @ '#sk5'))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl143])). 50.41/7.02 thf(zip_derived_cl22, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 ( (((X2 @ ('#sk15' @ X2)) & 50.41/7.02 (((((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((('#sk1' @ Y1 @ Y2) & 50.41/7.02 (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))) | 50.41/7.02 (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & 50.41/7.02 ('#sk2' @ Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))))))) 50.41/7.02 | (X2 @ '#sk4') 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 (X2 @ Y0)))))))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 50.41/7.02 thf(zip_derived_cl28, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 ( (((((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((('#sk1' @ Y1 @ Y2) & 50.41/7.02 (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))) | 50.41/7.02 (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))))) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 (X2 @ Y0)))))) 50.41/7.02 | (X2 @ '#sk4'))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl22])). 50.41/7.02 thf(zip_derived_cl29, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 ( ('#form37' @ X2) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 (X2 @ Y0)))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl34, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (~ ('#form37' @ (^[Y0 : a]: (X2 @ Y0))) 50.41/7.02 | (X2 @ '#sk4') 50.41/7.02 | (((((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((('#sk1' @ Y1 @ Y2) & 50.41/7.02 (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))) | 50.41/7.02 (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & 50.41/7.02 ('#sk2' @ Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))))))), 50.41/7.02 inference('renaming', [status(thm)], [zip_derived_cl28, zip_derived_cl29])). 50.41/7.02 thf(zip_derived_cl40, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (~ ('#form37' @ X2) 50.41/7.02 | (X2 @ '#sk4') 50.41/7.02 | (((((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((('#sk1' @ Y1 @ Y2) & 50.41/7.02 (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))) | 50.41/7.02 (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & 50.41/7.02 ('#sk2' @ Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))))))), 50.41/7.02 inference('ho_norm', [status(thm)], [zip_derived_cl34])). 50.41/7.02 thf(zip_derived_cl41, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 ( (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((('#sk1' @ Y1 @ Y2) & 50.41/7.02 (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))) 50.41/7.02 | (X2 @ '#sk4') 50.41/7.02 | ~ ('#form37' @ X2))), 50.41/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])). 50.41/7.02 thf(zip_derived_cl43, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 ( (((((((!!) @ (^[Y0 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & (X4 @ Y0))) => 50.41/7.02 (X4 @ Y1))))))))))) => 50.41/7.02 (X4 @ ('#sk21' @ X2)))) 50.41/7.02 | ~ ('#form37' @ X2) 50.41/7.02 | (X2 @ '#sk4') 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))))), 50.41/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 50.41/7.02 thf(zip_derived_cl47, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ (((((!!) @ (^[Y0 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & (X4 @ Y0))) => 50.41/7.02 (X4 @ Y1))))))))))) 50.41/7.02 | (X4 @ ('#sk21' @ X2)) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))) 50.41/7.02 | (X2 @ '#sk4') 50.41/7.02 | ~ ('#form37' @ X2))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl43])). 50.41/7.02 thf(zip_derived_cl49, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ (((!!) @ (^[Y0 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & (X4 @ Y0))) => 50.41/7.02 (X4 @ Y1))))))))) 50.41/7.02 | ~ ('#form37' @ X2) 50.41/7.02 | (X2 @ '#sk4') 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))) 50.41/7.02 | (X4 @ ('#sk21' @ X2)))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl47])). 50.41/7.02 thf(zip_derived_cl51, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ ((('#sk1' @ ('#sk15' @ X2) @ ('#sk115' @ X2 @ X4)) => (X4 @ 50.41/7.02 ('#sk115' @ X2 @ X4)))) 50.41/7.02 | (X4 @ ('#sk21' @ X2)) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))) 50.41/7.02 | (X2 @ '#sk4') 50.41/7.02 | ~ ('#form37' @ X2) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & (X4 @ Y0))) => 50.41/7.02 (X4 @ Y1))))))))))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl49])). 50.41/7.02 thf(zip_derived_cl54, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ (X4 @ ('#sk115' @ X2 @ X4)) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & (X4 @ Y0))) => 50.41/7.02 (X4 @ Y1))))))))) 50.41/7.02 | ~ ('#form37' @ X2) 50.41/7.02 | (X2 @ '#sk4') 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))) 50.41/7.02 | (X4 @ ('#sk21' @ X2)))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 50.41/7.02 thf(zip_derived_cl57, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ (((!!) @ (^[Y0 : a]: 50.41/7.02 ((((('#sk1' @ ('#sk122' @ X4) @ Y0) & (X4 @ 50.41/7.02 ('#sk122' @ X4)))) => 50.41/7.02 (X4 @ Y0)))))) 50.41/7.02 | (X4 @ ('#sk21' @ X2)) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))) 50.41/7.02 | (X2 @ '#sk4') 50.41/7.02 | ~ ('#form37' @ X2) 50.41/7.02 | ~ (X4 @ ('#sk115' @ X2 @ X4)))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl54])). 50.41/7.02 thf(zip_derived_cl61, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ ((((('#sk1' @ ('#sk122' @ X4) @ ('#sk141' @ X4)) & (X4 @ 50.41/7.02 ('#sk122' @ X4)))) => 50.41/7.02 (X4 @ ('#sk141' @ X4)))) 50.41/7.02 | ~ (X4 @ ('#sk115' @ X2 @ X4)) 50.41/7.02 | ~ ('#form37' @ X2) 50.41/7.02 | (X2 @ '#sk4') 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))) 50.41/7.02 | (X4 @ ('#sk21' @ X2)))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl57])). 50.41/7.02 thf(zip_derived_cl70, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (~ ('#form220' @ X2) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl71, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 ( (((((((!!) @ (^[Y0 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.41/7.02 (X4 @ Y1))))))))))) => 50.41/7.02 (X4 @ ('#sk21' @ X2)))) 50.41/7.02 | ~ ('#form220' @ X2))), 50.41/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl70])). 50.41/7.02 thf(zip_derived_cl84, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ (((((!!) @ (^[Y0 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.41/7.02 (X4 @ Y1))))))))))) 50.41/7.02 | (X4 @ ('#sk21' @ X2)) 50.41/7.02 | ~ ('#form220' @ X2))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 50.41/7.02 thf(zip_derived_cl96, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ (((!!) @ (^[Y0 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.41/7.02 (X4 @ Y1))))))))) 50.41/7.02 | ~ ('#form220' @ X2) 50.41/7.02 | (X4 @ ('#sk21' @ X2)))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl84])). 50.41/7.02 thf(zip_derived_cl98, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ ((('#sk2' @ ('#sk15' @ X2) @ ('#sk402' @ X2 @ X4)) => (X4 @ 50.41/7.02 ('#sk402' @ X2 @ X4)))) 50.41/7.02 | (X4 @ ('#sk21' @ X2)) 50.41/7.02 | ~ ('#form220' @ X2) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.41/7.02 (X4 @ Y1))))))))))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 50.41/7.02 thf(zip_derived_cl98, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ ((('#sk2' @ ('#sk15' @ X2) @ ('#sk402' @ X2 @ X4)) => (X4 @ 50.41/7.02 ('#sk402' @ X2 @ X4)))) 50.41/7.02 | (X4 @ ('#sk21' @ X2)) 50.41/7.02 | ~ ('#form220' @ X2) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.41/7.02 (X4 @ Y1))))))))))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 50.41/7.02 thf(zip_derived_cl101, plain, 50.41/7.02 (![X4 : a > $o]: 50.41/7.02 ( ('#form418' @ X4) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.41/7.02 (X4 @ Y1))))))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl103, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ ('#form418' @ X4) 50.41/7.02 | ~ ('#form220' @ X2) 50.41/7.02 | (X4 @ ('#sk21' @ X2)) 50.41/7.02 | ~ ((('#sk2' @ ('#sk15' @ X2) @ ('#sk402' @ X2 @ X4)) => (X4 @ 50.41/7.02 ('#sk402' @ X2 @ X4)))))), 50.41/7.02 inference('renaming', [status(thm)], 50.41/7.02 [zip_derived_cl98, zip_derived_cl101])). 50.41/7.02 thf(zip_derived_cl107, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ (X4 @ ('#sk402' @ X2 @ X4)) 50.41/7.02 | (X4 @ ('#sk21' @ X2)) 50.41/7.02 | ~ ('#form220' @ X2) 50.41/7.02 | ~ ('#form418' @ X4))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])). 50.41/7.02 thf(zip_derived_cl12, plain, (~ ('#sk5' @ '#sk4')), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl9])). 50.41/7.02 thf(zip_derived_cl144, plain, 50.41/7.02 (( ((('#sk5' @ ('#sk15' @ '#sk5')) & 50.41/7.02 (((((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ '#sk5') @ 50.41/7.02 Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((('#sk1' @ Y1 @ Y2) & 50.41/7.02 (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ '#sk5'))))))) | 50.41/7.02 (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ '#sk5') @ 50.41/7.02 Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ '#sk5'))))))))))) 50.41/7.02 | ~ ('#form37' @ '#sk5'))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl143])). 50.41/7.02 thf(zip_derived_cl146, plain, 50.41/7.02 (( ('#sk5' @ ('#sk15' @ '#sk5')) | ~ ('#form37' @ '#sk5'))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl144])). 50.41/7.02 thf(zip_derived_cl27, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 ( (X2 @ ('#sk15' @ X2)) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 (X2 @ Y0)))))) 50.41/7.02 | (X2 @ '#sk4'))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl22])). 50.41/7.02 thf(zip_derived_cl29, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 ( ('#form37' @ X2) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 (X2 @ Y0)))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl33, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (~ ('#form37' @ (^[Y0 : a]: (X2 @ Y0))) 50.41/7.02 | (X2 @ '#sk4') 50.41/7.02 | (X2 @ ('#sk15' @ X2)))), 50.41/7.02 inference('renaming', [status(thm)], [zip_derived_cl27, zip_derived_cl29])). 50.41/7.02 thf(zip_derived_cl39, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (~ ('#form37' @ X2) | (X2 @ '#sk4') | (X2 @ ('#sk15' @ X2)))), 50.41/7.02 inference('ho_norm', [status(thm)], [zip_derived_cl33])). 50.41/7.02 thf(zip_derived_cl29, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 ( ('#form37' @ X2) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 ('#sk1' @ 50.41/7.02 Y2 @ 50.41/7.02 Y3) & 50.41/7.02 (Y1 @ Y2))) => 50.41/7.02 (Y1 @ Y3))))))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))))) => 50.41/7.02 (Y1 @ Y0)))))) | 50.41/7.02 (((!!) @ (^[Y1 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y2 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ 50.41/7.02 Y2) => (Y1 @ Y2)))))) & 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((!!) @ (^[Y3 : a]: 50.41/7.02 ( 50.41/7.02 ( 50.41/7.02 (( 50.41/7.02 (Y1 @ 50.41/7.02 Y2) & 50.41/7.02 ('#sk2' @ 50.41/7.02 Y2 @ Y3))) => 50.41/7.02 (Y1 @ Y3))))))))))) => 50.41/7.02 (Y1 @ Y0)))))))) => 50.41/7.02 (X2 @ Y0)))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl30, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (~ (((((((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((('#sk1' @ Y1 @ 50.41/7.02 Y2) & (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ Y1) => (Y0 @ 50.41/7.02 Y1)))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))) | 50.41/7.02 (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ 50.41/7.02 Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & 50.41/7.02 ('#sk2' @ Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))))) => 50.41/7.02 (X2 @ ('#sk38' @ X2)))) 50.41/7.02 | ('#form37' @ X2))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl29])). 50.41/7.02 thf(zip_derived_cl35, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 ( (((((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((('#sk1' @ Y1 @ Y2) & 50.41/7.02 (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))) | 50.41/7.02 (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))))) 50.41/7.02 | ('#form37' @ X2))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl30])). 50.41/7.02 thf(zip_derived_cl42, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 ( (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((('#sk1' @ Y1 @ Y2) & 50.41/7.02 (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk1' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))) 50.41/7.02 | ('#form37' @ X2))), 50.41/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl35])). 50.41/7.02 thf(zip_derived_cl45, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 ( (((((((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & (X4 @ Y0))) => 50.41/7.02 (X4 @ Y1))))))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))))) => 50.41/7.02 (X4 @ ('#sk38' @ X2)))) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))))), 50.41/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl42])). 50.41/7.02 thf(zip_derived_cl48, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ (((((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & (X4 @ Y0))) => 50.41/7.02 (X4 @ Y1))))))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))))) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))) 50.41/7.02 | ('#form37' @ X2))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 50.41/7.02 thf(zip_derived_cl50, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & (X4 @ Y0))) => 50.41/7.02 (X4 @ Y1))))))))) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))) 50.41/7.02 | (X4 @ ('#sk38' @ X2)))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl48])). 50.41/7.02 thf(zip_derived_cl52, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ (((!!) @ (^[Y0 : a]: 50.41/7.02 ((((('#sk1' @ ('#sk122' @ X4) @ Y0) & (X4 @ 50.41/7.02 ('#sk122' @ X4)))) => 50.41/7.02 (X4 @ Y0)))))) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl50])). 50.41/7.02 thf(zip_derived_cl55, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ ((((('#sk1' @ ('#sk122' @ X4) @ ('#sk141' @ X4)) & (X4 @ 50.41/7.02 ('#sk122' @ X4)))) => 50.41/7.02 (X4 @ ('#sk141' @ X4)))) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))) 50.41/7.02 | (X4 @ ('#sk38' @ X2)))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl52])). 50.41/7.02 thf(zip_derived_cl59, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ (X4 @ ('#sk141' @ X4)) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 50.41/7.02 thf(zip_derived_cl59, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ (X4 @ ('#sk141' @ X4)) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 50.41/7.02 thf(zip_derived_cl64, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (~ ('#form198' @ X2) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl67, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 ( ('#form198' @ X2) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | ~ (X4 @ ('#sk141' @ X4)))), 50.41/7.02 inference('renaming', [status(thm)], [zip_derived_cl59, zip_derived_cl64])). 50.41/7.02 thf(zip_derived_cl58, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 ( ((('#sk1' @ ('#sk122' @ X4) @ ('#sk141' @ X4)) & (X4 @ 50.41/7.02 ('#sk122' @ X4)))) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 50.41/7.02 thf(zip_derived_cl62, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 ( ('#sk1' @ ('#sk122' @ X4) @ ('#sk141' @ X4)) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))) 50.41/7.02 | (X4 @ ('#sk38' @ X2)))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl58])). 50.41/7.02 thf(zip_derived_cl74, plain, 50.41/7.02 (![X4 : a > $o]: 50.41/7.02 ( ('#form227' @ X4) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl78, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ ('#form227' @ (^[Y0 : a]: (X4 @ Y0))) 50.41/7.02 | ~ (X4 @ ('#sk141' @ X4)) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | ('#form198' @ X2))), 50.41/7.02 inference('renaming', [status(thm)], [zip_derived_cl67, zip_derived_cl74])). 50.41/7.02 thf(zip_derived_cl90, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ ('#form227' @ X4) 50.41/7.02 | ~ (X4 @ ('#sk141' @ X4)) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | ('#form198' @ X2))), 50.41/7.02 inference('ho_norm', [status(thm)], [zip_derived_cl78])). 50.41/7.02 thf(zip_derived_cl147, plain, 50.41/7.02 (( (((((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ '#sk5') @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((('#sk1' @ Y1 @ Y2) & 50.41/7.02 (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ '#sk5'))))))) | 50.41/7.02 (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ '#sk5') @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ '#sk5'))))))))) 50.41/7.02 | ~ ('#form37' @ '#sk5'))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl144])). 50.41/7.02 thf(zip_derived_cl148, plain, 50.41/7.02 (( (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ '#sk5') @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((('#sk1' @ Y1 @ Y2) & 50.41/7.02 (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ '#sk5'))))))) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ '#sk5') @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ '#sk5'))))))) 50.41/7.02 | ~ ('#form37' @ '#sk5'))), 50.41/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl147])). 50.41/7.02 thf(zip_derived_cl70, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (~ ('#form220' @ X2) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl149, plain, 50.41/7.02 (( ('#form220' @ '#sk5') 50.41/7.02 | ~ ('#form37' @ '#sk5') 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ '#sk5') @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 ((((('#sk1' @ Y1 @ Y2) & 50.41/7.02 (Y0 @ Y1))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ '#sk5'))))))))), 50.41/7.02 inference('renaming', [status(thm)], 50.41/7.02 [zip_derived_cl148, zip_derived_cl70])). 50.41/7.02 thf(zip_derived_cl150, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 ( (((((((!!) @ (^[Y0 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ '#sk5') @ Y0) => (X2 @ Y0)))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & (X2 @ Y0))) => 50.41/7.02 (X2 @ Y1))))))))))) => 50.41/7.02 (X2 @ ('#sk21' @ '#sk5')))) 50.41/7.02 | ~ ('#form37' @ '#sk5') 50.41/7.02 | ('#form220' @ '#sk5'))), 50.41/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl149])). 50.41/7.02 thf(zip_derived_cl151, plain, 50.41/7.02 (( (((((((!!) @ (^[Y0 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ '#sk5') @ Y0) => ('#sk5' @ Y0)))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & ('#sk5' @ Y0))) => 50.41/7.02 ('#sk5' @ Y1))))))))))) => 50.41/7.02 ('#sk5' @ ('#sk21' @ '#sk5')))) 50.41/7.02 | ~ ('#form37' @ '#sk5') 50.41/7.02 | ('#form220' @ '#sk5'))), 50.41/7.02 inference('triggered_bool_instantiation', [status(thm)], 50.41/7.02 [zip_derived_cl150])). 50.41/7.02 thf(zip_derived_cl184, plain, 50.41/7.02 ((~ (((((!!) @ (^[Y0 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ '#sk5') @ Y0) => ('#sk5' @ Y0)))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & ('#sk5' @ Y0))) => 50.41/7.02 ('#sk5' @ Y1))))))))))) 50.41/7.02 | ('#sk5' @ ('#sk21' @ '#sk5')) 50.41/7.02 | ('#form220' @ '#sk5') 50.41/7.02 | ~ ('#form37' @ '#sk5'))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl151])). 50.41/7.02 thf(zip_derived_cl145, plain, 50.41/7.02 ((~ ('#sk5' @ ('#sk21' @ '#sk5')) | ~ ('#form37' @ '#sk5'))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl143])). 50.41/7.02 thf(zip_derived_cl185, plain, 50.41/7.02 ((~ ('#form37' @ '#sk5') 50.41/7.02 | ('#form220' @ '#sk5') 50.41/7.02 | ~ (((((!!) @ (^[Y0 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ '#sk5') @ Y0) => ('#sk5' @ Y0)))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & ('#sk5' @ Y0))) => 50.41/7.02 ('#sk5' @ Y1))))))))))))), 50.41/7.02 inference('clc', [status(thm)], [zip_derived_cl184, zip_derived_cl145])). 50.41/7.02 thf(zip_derived_cl186, plain, 50.41/7.02 ((~ (((!!) @ (^[Y0 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ '#sk5') @ Y0) => ('#sk5' @ Y0)))))) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & ('#sk5' @ Y0))) => 50.41/7.02 ('#sk5' @ Y1))))))))) 50.41/7.02 | ('#form220' @ '#sk5') 50.41/7.02 | ~ ('#form37' @ '#sk5'))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl185])). 50.41/7.02 thf(zip_derived_cl43, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 ( (((((((!!) @ (^[Y0 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & (X4 @ Y0))) => 50.41/7.02 (X4 @ Y1))))))))))) => 50.41/7.02 (X4 @ ('#sk21' @ X2)))) 50.41/7.02 | ~ ('#form37' @ X2) 50.41/7.02 | (X2 @ '#sk4') 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))))), 50.41/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 50.41/7.02 thf(zip_derived_cl44, plain, 50.41/7.02 (![X0 : a > $o]: 50.41/7.02 ( (((((((!!) @ (^[Y0 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ X0) @ Y0) => ('#sk5' @ Y0)))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & ('#sk5' @ Y0))) => 50.41/7.02 ('#sk5' @ Y1))))))))))) => 50.41/7.02 ('#sk5' @ ('#sk21' @ X0)))) 50.41/7.02 | ~ ('#form37' @ X0) 50.41/7.02 | (X0 @ '#sk4') 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X0) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X0))))))))), 50.41/7.02 inference('triggered_bool_instantiation', [status(thm)], 50.41/7.02 [zip_derived_cl43])). 50.41/7.02 thf(zip_derived_cl70, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (~ ('#form220' @ X2) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 50.41/7.02 (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk21' @ X2))))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl169, plain, 50.41/7.02 (![X0 : a > $o]: 50.41/7.02 ( ('#form220' @ X0) 50.41/7.02 | (X0 @ '#sk4') 50.41/7.02 | ~ ('#form37' @ X0) 50.41/7.02 | (((((((!!) @ (^[Y0 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ X0) @ Y0) => ('#sk5' @ Y0)))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & ('#sk5' @ Y0))) => 50.41/7.02 ('#sk5' @ Y1))))))))))) => 50.41/7.02 ('#sk5' @ ('#sk21' @ X0)))))), 50.41/7.02 inference('renaming', [status(thm)], [zip_derived_cl44, zip_derived_cl70])). 50.41/7.02 thf(zip_derived_cl170, plain, 50.41/7.02 (![X0 : a > $o]: 50.41/7.02 (~ (((((!!) @ (^[Y0 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ X0) @ Y0) => ('#sk5' @ Y0)))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & ('#sk5' @ Y0))) => 50.41/7.02 ('#sk5' @ Y1))))))))))) 50.41/7.02 | ('#sk5' @ ('#sk21' @ X0)) 50.41/7.02 | ~ ('#form37' @ X0) 50.41/7.02 | (X0 @ '#sk4') 50.41/7.02 | ('#form220' @ X0))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl169])). 50.41/7.02 thf(zip_derived_cl171, plain, 50.41/7.02 (![X0 : a > $o]: 50.41/7.02 (~ (((!!) @ (^[Y0 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ X0) @ Y0) => ('#sk5' @ Y0)))))) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & ('#sk5' @ Y0))) => 50.41/7.02 ('#sk5' @ Y1))))))))) 50.41/7.02 | ('#form220' @ X0) 50.41/7.02 | (X0 @ '#sk4') 50.41/7.02 | ~ ('#form37' @ X0) 50.41/7.02 | ('#sk5' @ ('#sk21' @ X0)))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl170])). 50.41/7.02 thf(zip_derived_cl172, plain, 50.41/7.02 (![X0 : a > $o]: 50.41/7.02 (~ ((('#sk1' @ ('#sk15' @ X0) @ ('#sk115' @ X0 @ '#sk5')) => 50.41/7.02 ('#sk5' @ ('#sk115' @ X0 @ '#sk5')))) 50.41/7.02 | ('#sk5' @ ('#sk21' @ X0)) 50.41/7.02 | ~ ('#form37' @ X0) 50.41/7.02 | (X0 @ '#sk4') 50.41/7.02 | ('#form220' @ X0) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & ('#sk5' @ Y0))) => 50.41/7.02 ('#sk5' @ Y1))))))))))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl171])). 50.41/7.02 thf(zip_derived_cl173, plain, 50.41/7.02 (![X0 : a > $o]: 50.41/7.02 ( ('#sk1' @ ('#sk15' @ X0) @ ('#sk115' @ X0 @ '#sk5')) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & ('#sk5' @ Y0))) => 50.41/7.02 ('#sk5' @ Y1))))))))) 50.41/7.02 | ('#form220' @ X0) 50.41/7.02 | (X0 @ '#sk4') 50.41/7.02 | ~ ('#form37' @ X0) 50.41/7.02 | ('#sk5' @ ('#sk21' @ X0)))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl172])). 50.41/7.02 thf(zip_derived_cl175, plain, 50.41/7.02 (( ('#form733') 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & ('#sk5' @ Y0))) => 50.41/7.02 ('#sk5' @ Y1))))))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl187, plain, 50.41/7.02 ((~ ('#form733') 50.41/7.02 | ~ ('#form37' @ '#sk5') 50.41/7.02 | ('#form220' @ '#sk5') 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 ((('#sk1' @ ('#sk15' @ '#sk5') @ Y0) => ('#sk5' @ Y0)))))))), 50.41/7.02 inference('renaming', [status(thm)], 50.41/7.02 [zip_derived_cl186, zip_derived_cl175])). 50.41/7.02 thf(zip_derived_cl188, plain, 50.41/7.02 ((~ ((('#sk1' @ ('#sk15' @ '#sk5') @ ('#sk115' @ '#sk5' @ '#sk5')) => 50.41/7.02 ('#sk5' @ ('#sk115' @ '#sk5' @ '#sk5')))) 50.41/7.02 | ('#form220' @ '#sk5') 50.41/7.02 | ~ ('#form37' @ '#sk5') 50.41/7.02 | ~ ('#form733'))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl187])). 50.41/7.02 thf(zip_derived_cl190, plain, 50.41/7.02 ((~ ('#sk5' @ ('#sk115' @ '#sk5' @ '#sk5')) 50.41/7.02 | ~ ('#form733') 50.41/7.02 | ~ ('#form37' @ '#sk5') 50.41/7.02 | ('#form220' @ '#sk5'))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl188])). 50.41/7.02 thf(zip_derived_cl175, plain, 50.41/7.02 (( ('#form733') 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((('#sk1' @ Y0 @ Y1) & ('#sk5' @ Y0))) => 50.41/7.02 ('#sk5' @ Y1))))))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl176, plain, 50.41/7.02 ((~ (((!!) @ (^[Y0 : a]: 50.41/7.02 ((((('#sk1' @ ('#sk122' @ '#sk5') @ Y0) & ('#sk5' @ 50.41/7.02 ('#sk122' @ '#sk5')))) => 50.41/7.02 ('#sk5' @ Y0)))))) 50.41/7.02 | ('#form733'))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl175])). 50.41/7.02 thf(zip_derived_cl179, plain, 50.41/7.02 ((~ ((((('#sk1' @ ('#sk122' @ '#sk5') @ ('#sk141' @ '#sk5')) & ('#sk5' @ 50.41/7.02 ('#sk122' @ '#sk5')))) => 50.41/7.02 ('#sk5' @ ('#sk141' @ '#sk5')))) 50.41/7.02 | ('#form733'))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl176])). 50.41/7.02 thf(zip_derived_cl180, plain, 50.41/7.02 (( ((('#sk1' @ ('#sk122' @ '#sk5') @ ('#sk141' @ '#sk5')) & ('#sk5' @ 50.41/7.02 ('#sk122' @ '#sk5')))) 50.41/7.02 | ('#form733'))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])). 50.41/7.02 thf(zip_derived_cl183, plain, 50.41/7.02 (( ('#sk5' @ ('#sk122' @ '#sk5')) | ('#form733'))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl180])). 50.41/7.02 thf(zip_derived_cl182, plain, 50.41/7.02 (( ('#sk1' @ ('#sk122' @ '#sk5') @ ('#sk141' @ '#sk5')) | ('#form733'))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl180])). 50.41/7.02 thf(zip_derived_cl189, plain, 50.41/7.02 (( ('#sk1' @ ('#sk15' @ '#sk5') @ ('#sk115' @ '#sk5' @ '#sk5')) 50.41/7.02 | ~ ('#form733') 50.41/7.02 | ~ ('#form37' @ '#sk5') 50.41/7.02 | ('#form220' @ '#sk5'))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl188])). 50.41/7.02 thf(zip_derived_cl106, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 ( ('#sk2' @ ('#sk15' @ X2) @ ('#sk402' @ X2 @ X4)) 50.41/7.02 | (X4 @ ('#sk21' @ X2)) 50.41/7.02 | ~ ('#form220' @ X2) 50.41/7.02 | ~ ('#form418' @ X4))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])). 50.41/7.02 thf(zip_derived_cl181, plain, 50.41/7.02 ((~ ('#sk5' @ ('#sk141' @ '#sk5')) | ('#form733'))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])). 50.41/7.02 thf(zip_derived_cl74, plain, 50.41/7.02 (![X4 : a > $o]: 50.41/7.02 ( ('#form227' @ X4) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl75, plain, 50.41/7.02 (![X4 : a > $o]: 50.41/7.02 (~ ((('#sk1' @ '#sk3' @ ('#sk228' @ X4)) => (X4 @ ('#sk228' @ X4)))) 50.41/7.02 | ('#form227' @ X4))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl74])). 50.41/7.02 thf(zip_derived_cl86, plain, 50.41/7.02 (![X4 : a > $o]: 50.41/7.02 ( ('#sk1' @ '#sk3' @ ('#sk228' @ X4)) | ('#form227' @ X4))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 50.41/7.02 thf(zip_derived_cl87, plain, 50.41/7.02 (![X4 : a > $o]: (~ (X4 @ ('#sk228' @ X4)) | ('#form227' @ X4))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 50.41/7.02 thf(zip_derived_cl11, plain, 50.41/7.02 ( (((((!!) @ (^[Y0 : a]: 50.41/7.02 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 50.41/7.02 ('#sk5' @ Y0)))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 50.41/7.02 ('#sk5' @ Y0))) => 50.41/7.02 ('#sk5' @ Y1)))))))))))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl9])). 50.41/7.02 thf(zip_derived_cl15, plain, 50.41/7.02 ( (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 50.41/7.02 ('#sk5' @ Y0))) => 50.41/7.02 ('#sk5' @ Y1)))))))))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl11])). 50.41/7.02 thf(zip_derived_cl18, plain, 50.41/7.02 (![X2 : a]: 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 ((((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) & 50.41/7.02 ('#sk5' @ X2))) => 50.41/7.02 ('#sk5' @ Y0))))))), 50.41/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 50.41/7.02 thf(zip_derived_cl21, plain, 50.41/7.02 (![X2 : a, X4 : a]: 50.41/7.02 ((((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk5' @ X2))) => 50.41/7.02 ('#sk5' @ X4)))), 50.41/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])). 50.41/7.02 thf(zip_derived_cl26, plain, 50.41/7.02 (![X2 : a, X4 : a]: 50.41/7.02 (~ ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk5' @ X2))) 50.41/7.02 | ('#sk5' @ X4))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 50.41/7.02 thf(zip_derived_cl32, plain, 50.41/7.02 (![X2 : a, X4 : a]: 50.41/7.02 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 50.41/7.02 | ~ ('#sk5' @ X2) 50.41/7.02 | ('#sk5' @ X4))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 50.41/7.02 thf(zip_derived_cl38, plain, 50.41/7.02 (![X2 : a, X4 : a]: 50.41/7.02 (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 50.41/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl32])). 50.41/7.02 thf(zip_derived_cl14, plain, 50.41/7.02 ( (((!!) @ (^[Y0 : a]: 50.41/7.02 ((((('#sk1' @ '#sk3' @ Y0) | ('#sk2' @ '#sk3' @ Y0))) => 50.41/7.02 ('#sk5' @ Y0))))))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl11])). 50.41/7.02 thf(zip_derived_cl17, plain, 50.41/7.02 (![X2 : a]: 50.41/7.02 ((((('#sk1' @ '#sk3' @ X2) | ('#sk2' @ '#sk3' @ X2))) => ('#sk5' @ 50.41/7.02 X2)))), 50.41/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 50.41/7.02 thf(zip_derived_cl20, plain, 50.41/7.02 (![X2 : a]: 50.41/7.02 (~ ((('#sk1' @ '#sk3' @ X2) | ('#sk2' @ '#sk3' @ X2))) 50.41/7.02 | ('#sk5' @ X2))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 50.41/7.02 thf(zip_derived_cl24, plain, 50.41/7.02 (![X2 : a]: (~ ('#sk1' @ '#sk3' @ X2) | ('#sk5' @ X2))), 50.41/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 50.41/7.02 thf(zip_derived_cl63, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 ( (X4 @ ('#sk122' @ X4)) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))) 50.41/7.02 | (X4 @ ('#sk38' @ X2)))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl58])). 50.41/7.02 thf(zip_derived_cl74, plain, 50.41/7.02 (![X4 : a > $o]: 50.41/7.02 ( ('#form227' @ X4) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl77, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ ('#form227' @ (^[Y0 : a]: (X4 @ Y0))) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | (X4 @ ('#sk122' @ X4)))), 50.41/7.02 inference('renaming', [status(thm)], [zip_derived_cl63, zip_derived_cl74])). 50.41/7.02 thf(zip_derived_cl88, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ ('#form227' @ X4) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | (X4 @ ('#sk122' @ X4)))), 50.41/7.02 inference('ho_norm', [status(thm)], [zip_derived_cl77])). 50.41/7.02 thf(zip_derived_cl64, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (~ ('#form198' @ X2) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl89, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 ( ('#form198' @ X2) 50.41/7.02 | (X4 @ ('#sk122' @ X4)) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | ~ ('#form227' @ X4))), 50.41/7.02 inference('renaming', [status(thm)], [zip_derived_cl88, zip_derived_cl64])). 50.41/7.02 thf(zip_derived_cl101, plain, 50.41/7.02 (![X4 : a > $o]: 50.41/7.02 ( ('#form418' @ X4) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.41/7.02 (X4 @ Y1))))))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl102, plain, 50.41/7.02 (![X4 : a > $o]: 50.41/7.02 (~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((((X4 @ ('#sk419' @ X4)) & ('#sk2' @ 50.41/7.02 ('#sk419' @ X4) @ Y0))) => 50.41/7.02 (X4 @ Y0)))))) 50.41/7.02 | ('#form418' @ X4))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl101])). 50.41/7.02 thf(zip_derived_cl108, plain, 50.41/7.02 (![X4 : a > $o]: 50.41/7.02 (~ (((((X4 @ ('#sk419' @ X4)) & ('#sk2' @ ('#sk419' @ X4) @ 50.41/7.02 ('#sk442' @ X4)))) => 50.41/7.02 (X4 @ ('#sk442' @ X4)))) 50.41/7.02 | ('#form418' @ X4))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl102])). 50.41/7.02 thf(zip_derived_cl111, plain, 50.41/7.02 (![X4 : a > $o]: 50.41/7.02 ( (((X4 @ ('#sk419' @ X4)) & ('#sk2' @ ('#sk419' @ X4) @ 50.41/7.02 ('#sk442' @ X4)))) 50.41/7.02 | ('#form418' @ X4))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 50.41/7.02 thf(zip_derived_cl113, plain, 50.41/7.02 (![X4 : a > $o]: ( (X4 @ ('#sk419' @ X4)) | ('#form418' @ X4))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl111])). 50.41/7.02 thf(zip_derived_cl64, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (~ ('#form198' @ X2) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl65, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 ( (((((((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.41/7.02 (X4 @ Y1))))))))))) => 50.41/7.02 (X4 @ ('#sk38' @ X2)))) 50.41/7.02 | ~ ('#form198' @ X2))), 50.41/7.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl64])). 50.41/7.02 thf(zip_derived_cl79, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ (((((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))) & 50.41/7.02 (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.41/7.02 (X4 @ Y1))))))))))) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | ~ ('#form198' @ X2))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl65])). 50.41/7.02 thf(zip_derived_cl91, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.41/7.02 (X4 @ Y1))))))))) 50.41/7.02 | ~ ('#form198' @ X2) 50.41/7.02 | (X4 @ ('#sk38' @ X2)))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl79])). 50.41/7.02 thf(zip_derived_cl97, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ ((('#sk2' @ '#sk3' @ ('#sk367' @ X4)) => (X4 @ ('#sk367' @ X4)))) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | ~ ('#form198' @ X2) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.41/7.02 (X4 @ Y1))))))))))), 50.41/7.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl91])). 50.41/7.02 thf(zip_derived_cl100, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ (X4 @ ('#sk367' @ X4)) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.41/7.02 (X4 @ Y1))))))))) 50.41/7.02 | ~ ('#form198' @ X2) 50.41/7.02 | (X4 @ ('#sk38' @ X2)))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])). 50.41/7.02 thf(zip_derived_cl101, plain, 50.41/7.02 (![X4 : a > $o]: 50.41/7.02 ( ('#form418' @ X4) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.41/7.02 (X4 @ Y1))))))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl105, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ ('#form418' @ (^[Y0 : a]: (X4 @ Y0))) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | ~ ('#form198' @ X2) 50.41/7.02 | ~ (X4 @ ('#sk367' @ X4)))), 50.41/7.02 inference('renaming', [status(thm)], 50.41/7.02 [zip_derived_cl100, zip_derived_cl101])). 50.41/7.02 thf(zip_derived_cl110, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ ('#form418' @ X4) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | ~ ('#form198' @ X2) 50.41/7.02 | ~ (X4 @ ('#sk367' @ X4)))), 50.41/7.02 inference('ho_norm', [status(thm)], [zip_derived_cl105])). 50.41/7.02 thf(zip_derived_cl62, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 ( ('#sk1' @ ('#sk122' @ X4) @ ('#sk141' @ X4)) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))) 50.41/7.02 | (X4 @ ('#sk38' @ X2)))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl58])). 50.41/7.02 thf(zip_derived_cl74, plain, 50.41/7.02 (![X4 : a > $o]: 50.41/7.02 ( ('#form227' @ X4) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl76, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ ('#form227' @ X4) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | ('#sk1' @ ('#sk122' @ X4) @ ('#sk141' @ X4)))), 50.41/7.02 inference('renaming', [status(thm)], [zip_derived_cl62, zip_derived_cl74])). 50.41/7.02 thf(zip_derived_cl64, plain, 50.41/7.02 (![X2 : a > $o]: 50.41/7.02 (~ ('#form198' @ X2) 50.41/7.02 | (((!!) @ (^[Y0 : a > $o]: 50.41/7.02 (((((((!!) @ (^[Y1 : a]: 50.41/7.02 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((!!) @ (^[Y2 : a]: 50.41/7.02 (((((Y0 @ Y1) & ('#sk2' @ 50.41/7.02 Y1 @ Y2))) => 50.41/7.02 (Y0 @ Y2))))))))))) => 50.41/7.02 (Y0 @ ('#sk38' @ X2))))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl85, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 ( ('#form198' @ X2) 50.41/7.02 | ('#sk1' @ ('#sk122' @ X4) @ ('#sk141' @ X4)) 50.41/7.02 | ('#form37' @ X2) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | ~ ('#form227' @ X4))), 50.41/7.02 inference('renaming', [status(thm)], [zip_derived_cl76, zip_derived_cl64])). 50.41/7.02 thf(zip_derived_cl36, plain, 50.41/7.02 (![X2 : a > $o]: (~ (X2 @ ('#sk38' @ X2)) | ('#form37' @ X2))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl30])). 50.41/7.02 thf(zip_derived_cl114, plain, 50.41/7.02 (![X4 : a > $o]: 50.41/7.02 ( ('#sk2' @ ('#sk419' @ X4) @ ('#sk442' @ X4)) | ('#form418' @ X4))), 50.41/7.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl111])). 50.41/7.02 thf(zip_derived_cl112, plain, 50.41/7.02 (![X4 : a > $o]: (~ (X4 @ ('#sk442' @ X4)) | ('#form418' @ X4))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 50.41/7.02 thf(zip_derived_cl99, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 ( ('#sk2' @ '#sk3' @ ('#sk367' @ X4)) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.41/7.02 (X4 @ Y1))))))))) 50.41/7.02 | ~ ('#form198' @ X2) 50.41/7.02 | (X4 @ ('#sk38' @ X2)))), 50.41/7.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])). 50.41/7.02 thf(zip_derived_cl101, plain, 50.41/7.02 (![X4 : a > $o]: 50.41/7.02 ( ('#form418' @ X4) 50.41/7.02 | ~ (((!!) @ (^[Y0 : a]: 50.41/7.02 (((!!) @ (^[Y1 : a]: 50.41/7.02 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 50.41/7.02 (X4 @ Y1))))))))))), 50.41/7.02 define([status(thm)])). 50.41/7.02 thf(zip_derived_cl104, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ ('#form418' @ (^[Y0 : a]: (X4 @ Y0))) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | ~ ('#form198' @ X2) 50.41/7.02 | ('#sk2' @ '#sk3' @ ('#sk367' @ X4)))), 50.41/7.02 inference('renaming', [status(thm)], 50.41/7.02 [zip_derived_cl99, zip_derived_cl101])). 50.41/7.02 thf(zip_derived_cl109, plain, 50.41/7.02 (![X2 : a > $o, X4 : a > $o]: 50.41/7.02 (~ ('#form418' @ X4) 50.41/7.02 | (X4 @ ('#sk38' @ X2)) 50.41/7.02 | ~ ('#form198' @ X2) 50.41/7.02 | ('#sk2' @ '#sk3' @ ('#sk367' @ X4)))), 50.41/7.02 inference('ho_norm', [status(thm)], [zip_derived_cl104])). 50.41/7.02 thf(zip_derived_cl25, plain, 50.41/7.02 (![X2 : a]: (~ ('#sk2' @ '#sk3' @ X2) | ('#sk5' @ X2))), 50.41/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 50.41/7.02 thf(zip_derived_cl37, plain, 50.41/7.02 (![X2 : a, X4 : a]: 50.41/7.02 (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 50.41/7.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl32])). 50.41/7.02 thf(zip_derived_cl8518, plain, ($false), 50.41/7.02 inference('eprover', [status(thm)], 50.41/7.02 [zip_derived_cl145, zip_derived_cl107, zip_derived_cl12, 50.41/7.02 zip_derived_cl146, zip_derived_cl39, zip_derived_cl90, 50.41/7.02 zip_derived_cl190, zip_derived_cl183, zip_derived_cl182, 50.41/7.02 zip_derived_cl189, zip_derived_cl106, zip_derived_cl181, 50.41/7.02 zip_derived_cl86, zip_derived_cl87, zip_derived_cl38, 50.41/7.02 zip_derived_cl24, zip_derived_cl89, zip_derived_cl113, 50.41/7.02 zip_derived_cl110, zip_derived_cl85, zip_derived_cl36, 50.41/7.02 zip_derived_cl114, zip_derived_cl112, zip_derived_cl109, 50.41/7.02 zip_derived_cl25, zip_derived_cl37])). 50.41/7.02 50.41/7.02 % SZS output end Refutation 50.41/7.02 50.41/7.02 50.41/7.02 % Terminating... 51.07/7.08 % Runner terminated. 51.07/7.09 % Zipperpin 1.5 exiting 51.07/7.09 EOF