0.04/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.x1LZr415Zq true 0.13/0.35 % Computer : n008.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 1920 0.13/0.35 % WCLimit : 240 0.13/0.35 % DateTime : Wed Jul 30 02:01:34 EDT 2025 0.13/0.35 % CPUTime : 0.13/0.35 % Running portfolio for 1920 s 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.35 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.36 % Running in HO mode 0.55/0.66 % Total configuration time : 828 0.55/0.66 % Estimated wc time : 1656 0.55/0.66 % Estimated cpu time (8 cpus) : 207.0 0.55/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.55/0.71 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.55/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 52.29/7.21 % Solved by lams/20_acsne_simpl.sh. 52.29/7.21 % done 363 iterations in 6.316s 52.29/7.21 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 52.29/7.21 % SZS output start Refutation 52.29/7.21 thf(a_type, type, a: $tType). 52.29/7.21 thf('#sk403_type', type, '#sk403': (a > $o) > a). 52.29/7.21 thf('#sk473_type', type, '#sk473': (a > $o) > (a > $o) > a). 52.29/7.21 thf('#sk3_type', type, '#sk3': a). 52.29/7.21 thf('#form472_type', type, '#form472': (a > $o) > (a > $o) > $o). 52.29/7.21 thf('#sk115_type', type, '#sk115': (a > $o) > (a > $o) > a). 52.29/7.21 thf('#sk438_type', type, '#sk438': (a > $o) > a). 52.29/7.21 thf('#sk4_type', type, '#sk4': a). 52.29/7.21 thf('#sk485_type', type, '#sk485': (a > $o) > a). 52.29/7.21 thf('#form245_type', type, '#form245': (a > $o) > $o). 52.29/7.21 thf('#sk150_type', type, '#sk150': (a > $o) > a). 52.29/7.21 thf('#sk182_type', type, '#sk182': (a > $o) > a). 52.29/7.21 thf('#form484_type', type, '#form484': (a > $o) > $o). 52.29/7.21 thf('#sk1_type', type, '#sk1': a > a > $o). 52.29/7.21 thf('#form37_type', type, '#form37': (a > $o) > $o). 52.29/7.21 thf('#sk21_type', type, '#sk21': (a > $o) > a). 52.29/7.21 thf('#sk165_type', type, '#sk165': (a > $o) > a). 52.29/7.21 thf('#sk38_type', type, '#sk38': (a > $o) > a). 52.29/7.21 thf('#sk122_type', type, '#sk122': (a > $o) > a). 52.29/7.21 thf('#form861_type', type, '#form861': $o). 52.29/7.21 thf('#sk199_type', type, '#sk199': (a > $o) > a). 52.29/7.21 thf('#sk15_type', type, '#sk15': (a > $o) > a). 52.29/7.21 thf('#sk5_type', type, '#sk5': a > $o). 52.29/7.21 thf('#form228_type', type, '#form228': (a > $o) > $o). 52.29/7.21 thf('#sk2_type', type, '#sk2': a > a > $o). 52.29/7.21 thf(cTHM251C_pme, conjecture, 52.29/7.21 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 52.29/7.21 ( ( ![Xq:( a > $o )]: 52.29/7.21 ( ( ( ![Xu:a,Xv:a]: 52.29/7.21 ( ( ( Xq @ Xu ) & 52.29/7.21 ( ( ![Xq0:( a > $o )]: 52.29/7.21 ( ( ( ![Xw:a]: ( ( S @ Xu @ Xw ) => ( Xq0 @ Xw ) ) ) & 52.29/7.21 ( ![Xu0:a,Xv0:a]: 52.29/7.21 ( ( ( Xq0 @ Xu0 ) & ( S @ Xu0 @ Xv0 ) ) => 52.29/7.21 ( Xq0 @ Xv0 ) ) ) ) => 52.29/7.21 ( Xq0 @ Xv ) ) ) | 52.29/7.21 ( ![Xq0:( a > $o )]: 52.29/7.21 ( ( ( ![Xu0:a,Xv0:a]: 52.29/7.21 ( ( ( R @ Xu0 @ Xv0 ) & ( Xq0 @ Xu0 ) ) => 52.29/7.21 ( Xq0 @ Xv0 ) ) ) & 52.29/7.21 ( ![Xw:a]: ( ( R @ Xu @ Xw ) => ( Xq0 @ Xw ) ) ) ) => 52.29/7.21 ( Xq0 @ Xv ) ) ) ) ) => 52.29/7.21 ( Xq @ Xv ) ) ) & 52.29/7.21 ( ![Xw:a]: 52.29/7.21 ( ( ( ![Xq0:( a > $o )]: 52.29/7.21 ( ( ( ![Xw0:a]: ( ( R @ Xx @ Xw0 ) => ( Xq0 @ Xw0 ) ) ) & 52.29/7.21 ( ![Xu:a,Xv:a]: 52.29/7.21 ( ( ( Xq0 @ Xu ) & ( R @ Xu @ Xv ) ) => ( Xq0 @ Xv ) ) ) ) => 52.29/7.21 ( Xq0 @ Xw ) ) ) | 52.29/7.21 ( ![Xq0:( a > $o )]: 52.29/7.21 ( ( ( ![Xu:a,Xv:a]: 52.29/7.21 ( ( ( Xq0 @ Xu ) & ( S @ Xu @ Xv ) ) => ( Xq0 @ Xv ) ) ) & 52.29/7.21 ( ![Xw0:a]: ( ( S @ Xx @ Xw0 ) => ( Xq0 @ Xw0 ) ) ) ) => 52.29/7.21 ( Xq0 @ Xw ) ) ) ) => 52.29/7.21 ( Xq @ Xw ) ) ) ) => 52.29/7.21 ( Xq @ Xy ) ) ) => 52.29/7.21 ( ![Xq:( a > $o )]: 52.29/7.21 ( ( ( ![Xw:a]: 52.29/7.21 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 52.29/7.21 ( ![Xu:a,Xv:a]: 52.29/7.21 ( ( ( Xq @ Xu ) & ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 52.29/7.21 ( Xq @ Xv ) ) ) ) => 52.29/7.21 ( Xq @ Xy ) ) ) ))). 52.29/7.21 thf(zf_stmt_0, negated_conjecture, 52.29/7.21 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 52.29/7.21 ( ( ![Xq:( a > $o )]: 52.29/7.21 ( ( ( ![Xu:a,Xv:a]: 52.29/7.21 ( ( ( Xq @ Xu ) & 52.29/7.21 ( ( ![Xq0:( a > $o )]: 52.29/7.21 ( ( ( ![Xw:a]: ( ( S @ Xu @ Xw ) => ( Xq0 @ Xw ) ) ) & 52.29/7.21 ( ![Xu0:a,Xv0:a]: 52.29/7.21 ( ( ( Xq0 @ Xu0 ) & ( S @ Xu0 @ Xv0 ) ) => 52.29/7.21 ( Xq0 @ Xv0 ) ) ) ) => 52.29/7.21 ( Xq0 @ Xv ) ) ) | 52.29/7.21 ( ![Xq0:( a > $o )]: 52.29/7.21 ( ( ( ![Xu0:a,Xv0:a]: 52.29/7.21 ( ( ( R @ Xu0 @ Xv0 ) & ( Xq0 @ Xu0 ) ) => 52.29/7.21 ( Xq0 @ Xv0 ) ) ) & 52.29/7.21 ( ![Xw:a]: ( ( R @ Xu @ Xw ) => ( Xq0 @ Xw ) ) ) ) => 52.29/7.21 ( Xq0 @ Xv ) ) ) ) ) => 52.29/7.21 ( Xq @ Xv ) ) ) & 52.29/7.21 ( ![Xw:a]: 52.29/7.21 ( ( ( ![Xq0:( a > $o )]: 52.29/7.21 ( ( ( ![Xw0:a]: ( ( R @ Xx @ Xw0 ) => ( Xq0 @ Xw0 ) ) ) & 52.29/7.21 ( ![Xu:a,Xv:a]: 52.29/7.21 ( ( ( Xq0 @ Xu ) & ( R @ Xu @ Xv ) ) => 52.29/7.21 ( Xq0 @ Xv ) ) ) ) => 52.29/7.21 ( Xq0 @ Xw ) ) ) | 52.29/7.21 ( ![Xq0:( a > $o )]: 52.29/7.21 ( ( ( ![Xu:a,Xv:a]: 52.29/7.21 ( ( ( Xq0 @ Xu ) & ( S @ Xu @ Xv ) ) => 52.29/7.21 ( Xq0 @ Xv ) ) ) & 52.29/7.21 ( ![Xw0:a]: ( ( S @ Xx @ Xw0 ) => ( Xq0 @ Xw0 ) ) ) ) => 52.29/7.21 ( Xq0 @ Xw ) ) ) ) => 52.29/7.21 ( Xq @ Xw ) ) ) ) => 52.29/7.21 ( Xq @ Xy ) ) ) => 52.29/7.21 ( ![Xq:( a > $o )]: 52.29/7.21 ( ( ( ![Xw:a]: 52.29/7.21 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 52.29/7.21 ( ![Xu:a,Xv:a]: 52.29/7.21 ( ( ( Xq @ Xu ) & ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 52.29/7.21 ( Xq @ Xv ) ) ) ) => 52.29/7.21 ( Xq @ Xy ) ) ) ) )), 52.29/7.21 inference('cnf.neg', [status(esa)], [cTHM251C_pme])). 52.29/7.21 thf(zip_derived_cl0, plain, 52.29/7.21 (~ (((!!) @ (^[Y0 : a > a > $o]: 52.29/7.21 (((!!) @ (^[Y1 : a > a > $o]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (((((!!) @ (^[Y4 : a > $o]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y5 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y6 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y4 @ 52.29/7.21 Y5) & 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y7 : a > $o]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y8 : a]: 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y5 @ 52.29/7.21 Y8) => 52.29/7.21 (Y7 @ Y8)))))) & 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y8 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y9 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y7 @ 52.29/7.21 Y8) & 52.29/7.21 (Y1 @ 52.29/7.21 Y8 @ Y9))) => 52.29/7.21 (Y7 @ Y9))))))))))) => 52.29/7.21 (Y7 @ Y6)))))) | 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y7 : a > $o]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y8 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y9 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y0 @ 52.29/7.21 Y8 @ 52.29/7.21 Y9) & 52.29/7.21 (Y7 @ Y8))) => 52.29/7.21 (Y7 @ Y9))))))))) & 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y8 : a]: 52.29/7.21 (( 52.29/7.21 (Y0 @ 52.29/7.21 Y5 @ 52.29/7.21 Y8) => 52.29/7.21 (Y7 @ Y8)))))))) => 52.29/7.21 (Y7 @ Y6)))))))))) => 52.29/7.21 (Y4 @ Y6))))))))) & 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y5 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y6 : a > $o]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y7 : a]: 52.29/7.21 (( 52.29/7.21 (Y0 @ 52.29/7.21 Y2 @ 52.29/7.21 Y7) => 52.29/7.21 (Y6 @ Y7)))))) & 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y7 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y8 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y6 @ 52.29/7.21 Y7) & 52.29/7.21 (Y0 @ 52.29/7.21 Y7 @ Y8))) => 52.29/7.21 (Y6 @ Y8))))))))))) => 52.29/7.21 (Y6 @ Y5)))))) | 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y6 : a > $o]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y7 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y8 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y6 @ 52.29/7.21 Y7) & 52.29/7.21 (Y1 @ 52.29/7.21 Y7 @ Y8))) => 52.29/7.21 (Y6 @ Y8))))))))) & 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y7 : a]: 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2 @ 52.29/7.21 Y7) => 52.29/7.21 (Y6 @ Y7)))))))) => 52.29/7.21 (Y6 @ Y5)))))))) => 52.29/7.21 (Y4 @ Y5)))))))) => 52.29/7.21 (Y4 @ Y3)))))) => 52.29/7.21 (((!!) @ (^[Y4 : a > $o]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y5 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2 @ 52.29/7.21 Y5) | 52.29/7.21 (Y0 @ 52.29/7.21 Y2 @ Y5))) => 52.29/7.21 (Y4 @ Y5)))))) & 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y5 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y6 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y4 @ 52.29/7.21 Y5) & 52.29/7.21 (( 52.29/7.21 (Y0 @ 52.29/7.21 Y5 @ 52.29/7.21 Y6) | 52.29/7.21 (Y1 @ 52.29/7.21 Y5 @ Y6))))) => 52.29/7.21 (Y4 @ Y6))))))))))) => 52.29/7.21 (Y4 @ Y3))))))))))))))))))))), 52.29/7.21 inference('cnf', [status(esa)], [zf_stmt_0])). 52.29/7.21 thf(zip_derived_cl1, plain, 52.29/7.21 (~ (((!!) @ (^[Y0 : a > a > $o]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((!!) @ (^[Y3 : a > $o]: 52.29/7.21 (((((((!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (((!!) @ ( 52.29/7.21 ^[Y5 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y3 @ 52.29/7.21 Y4) & 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y6 : a > $o]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y7 : a]: 52.29/7.21 (( 52.29/7.21 (Y0 @ 52.29/7.21 Y4 @ 52.29/7.21 Y7) => 52.29/7.21 (Y6 @ Y7)))))) & 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y7 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y8 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y6 @ 52.29/7.21 Y7) & 52.29/7.21 (Y0 @ 52.29/7.21 Y7 @ Y8))) => 52.29/7.21 (Y6 @ Y8))))))))))) => 52.29/7.21 (Y6 @ Y5)))))) | 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y6 : a > $o]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y7 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y8 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y7 @ 52.29/7.21 Y8) & 52.29/7.21 (Y6 @ Y7))) => 52.29/7.21 (Y6 @ Y8))))))))) & 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y7 : a]: 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y4 @ 52.29/7.21 Y7) => 52.29/7.21 (Y6 @ Y7)))))))) => 52.29/7.21 (Y6 @ Y5)))))))))) => 52.29/7.21 (Y3 @ Y5))))))))) & 52.29/7.21 (((!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (((( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y5 : a > $o]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y6 : a]: 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y1 @ 52.29/7.21 Y6) => 52.29/7.21 (Y5 @ Y6)))))) & 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y6 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y7 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y5 @ 52.29/7.21 Y6) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y6 @ Y7))) => 52.29/7.21 (Y5 @ Y7))))))))))) => 52.29/7.21 (Y5 @ Y4)))))) | 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y5 : a > $o]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y6 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y7 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y5 @ 52.29/7.21 Y6) & 52.29/7.21 (Y0 @ 52.29/7.21 Y6 @ Y7))) => 52.29/7.21 (Y5 @ Y7))))))))) & 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y6 : a]: 52.29/7.21 (( 52.29/7.21 (Y0 @ 52.29/7.21 Y1 @ 52.29/7.21 Y6) => 52.29/7.21 (Y5 @ Y6)))))))) => 52.29/7.21 (Y5 @ Y4)))))))) => 52.29/7.21 (Y3 @ Y4)))))))) => 52.29/7.21 (Y3 @ Y2)))))) => 52.29/7.21 (((!!) @ (^[Y3 : a > $o]: 52.29/7.21 (((((((!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (((( 52.29/7.21 (Y0 @ 52.29/7.21 Y1 @ Y4) | 52.29/7.21 ('#sk1' @ 52.29/7.21 Y1 @ Y4))) => 52.29/7.21 (Y3 @ Y4)))))) & 52.29/7.21 (((!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (((!!) @ ( 52.29/7.21 ^[Y5 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y3 @ 52.29/7.21 Y4) & 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y4 @ 52.29/7.21 Y5) | 52.29/7.21 (Y0 @ 52.29/7.21 Y4 @ Y5))))) => 52.29/7.21 (Y3 @ Y5))))))))))) => 52.29/7.21 (Y3 @ Y2)))))))))))))))))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 52.29/7.21 thf(zip_derived_cl2, plain, 52.29/7.21 (~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 (((!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (((( 52.29/7.21 (Y2 @ 52.29/7.21 Y3) & 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y5 : a > $o]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y6 : a]: 52.29/7.21 (( 52.29/7.21 ('#sk2' @ 52.29/7.21 Y3 @ 52.29/7.21 Y6) => 52.29/7.21 (Y5 @ Y6)))))) & 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y6 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y7 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y5 @ 52.29/7.21 Y6) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y6 @ Y7))) => 52.29/7.21 (Y5 @ Y7))))))))))) => 52.29/7.21 (Y5 @ Y4)))))) | 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y5 : a > $o]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 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(((!!) @ ( 52.29/7.21 ^[Y4 : a > $o]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y5 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y6 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y4 @ 52.29/7.21 Y5) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y5 @ Y6))) => 52.29/7.21 (Y4 @ Y6))))))))) & 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y5 : a]: 52.29/7.21 (( 52.29/7.21 ('#sk2' @ 52.29/7.21 Y0 @ 52.29/7.21 Y5) => 52.29/7.21 (Y4 @ Y5)))))))) => 52.29/7.21 (Y4 @ Y3)))))))) => 52.29/7.21 (Y2 @ Y3)))))))) => 52.29/7.21 (Y2 @ Y1)))))) => 52.29/7.21 (((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 ((((('#sk2' @ 52.29/7.21 Y0 @ Y3) | 52.29/7.21 ('#sk1' @ 52.29/7.21 Y0 @ Y3))) => 52.29/7.21 (Y2 @ Y3)))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (((!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (((( 52.29/7.21 (Y2 @ 52.29/7.21 Y3) & 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y3 @ Y4) | 52.29/7.21 ('#sk2' @ 52.29/7.21 Y3 @ Y4))))) => 52.29/7.21 (Y2 @ Y4))))))))))) => 52.29/7.21 (Y2 @ Y1))))))))))))))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 52.29/7.21 thf(zip_derived_cl3, plain, 52.29/7.21 (~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (((((Y1 @ Y2) & 52.29/7.21 (((( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a > $o]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y5 : a]: 52.29/7.21 (( 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ 52.29/7.21 Y5) => 52.29/7.21 (Y4 @ Y5)))))) & 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y5 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y6 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y4 @ 52.29/7.21 Y5) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y5 @ Y6))) => 52.29/7.21 (Y4 @ Y6))))))))))) => 52.29/7.21 (Y4 @ Y3)))))) | 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a > $o]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y5 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y6 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y5 @ 52.29/7.21 Y6) & 52.29/7.21 (Y4 @ Y5))) => 52.29/7.21 (Y4 @ Y6))))))))) & 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y5 : a]: 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ 52.29/7.21 Y5) => 52.29/7.21 (Y4 @ Y5)))))))) => 52.29/7.21 (Y4 @ Y3)))))))))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((((!!) @ (^[Y3 : a > $o]: 52.29/7.21 (((( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 '#sk3' @ 52.29/7.21 Y4) => 52.29/7.21 (Y3 @ Y4)))))) & 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y5 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y3 @ 52.29/7.21 Y4) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y4 @ Y5))) => 52.29/7.21 (Y3 @ Y5))))))))))) => 52.29/7.21 (Y3 @ Y2)))))) | 52.29/7.21 (((!!) @ (^[Y3 : a > 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[status(thm)], [zip_derived_cl2])). 52.29/7.21 thf(zip_derived_cl4, plain, 52.29/7.21 (~ (((((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & 52.29/7.21 (((((!!) @ (^[Y3 : a > $o]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 ('#sk2' @ 52.29/7.21 Y1 @ 52.29/7.21 Y4) => 52.29/7.21 (Y3 @ Y4)))))) & 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y5 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y3 @ 52.29/7.21 Y4) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y4 @ Y5))) => 52.29/7.21 (Y3 @ Y5))))))))))) => 52.29/7.21 (Y3 @ Y2)))))) | 52.29/7.21 (((!!) @ (^[Y3 : a > $o]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y5 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y4 @ 52.29/7.21 Y5) & 52.29/7.21 (Y3 @ Y4))) => 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(((!!) @ (^[Y3 : a]: 52.29/7.21 (( 52.29/7.21 ('#sk2' @ 52.29/7.21 '#sk3' @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))))) => 52.29/7.21 (Y2 @ Y1)))))))) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ '#sk4')))))) => 52.29/7.21 (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 52.29/7.21 '#sk3' @ Y1))) => 52.29/7.21 (Y0 @ Y1)))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & 52.29/7.21 ((('#sk1' @ Y1 @ Y2) | 52.29/7.21 ('#sk2' @ Y1 @ Y2))))) => 52.29/7.21 (Y0 @ Y2))))))))))) => 52.29/7.21 (Y0 @ '#sk4'))))))))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 52.29/7.21 thf(zip_derived_cl5, plain, 52.29/7.21 ( (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & 52.29/7.21 (((((!!) @ (^[Y3 : a > $o]: 52.29/7.21 (((((( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 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(^[Y1 : a]: 52.29/7.21 (((((X2 @ Y0) & 52.29/7.21 (((((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 (( 52.29/7.21 ('#sk2' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y2 @ 52.29/7.21 Y3) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y3 @ Y4))) => 52.29/7.21 (Y2 @ Y4))))))))))) => 52.29/7.21 (Y2 @ Y1)))))) | 52.29/7.21 (((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y3 @ 52.29/7.21 Y4) & 52.29/7.21 (Y2 @ Y3))) => 52.29/7.21 (Y2 @ Y4))))))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))))) => 52.29/7.21 (Y2 @ Y1)))))))))) => 52.29/7.21 (X2 @ Y1))))))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 (X2 @ Y0)))))))) => 52.29/7.21 (X2 @ '#sk4')))), 52.29/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 52.29/7.21 thf(zip_derived_cl10, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 (~ (((((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X2 @ Y0) & 52.29/7.21 (((((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 (( 52.29/7.21 ('#sk2' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y2 @ 52.29/7.21 Y3) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y3 @ Y4))) => 52.29/7.21 (Y2 @ Y4))))))))))) => 52.29/7.21 (Y2 @ Y1)))))) | 52.29/7.21 (((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y3 @ 52.29/7.21 Y4) & 52.29/7.21 (Y2 @ Y3))) => 52.29/7.21 (Y2 @ Y4))))))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))))) => 52.29/7.21 (Y2 @ Y1)))))))))) => 52.29/7.21 (X2 @ Y1))))))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 (X2 @ Y0)))))))) 52.29/7.21 | (X2 @ '#sk4'))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 52.29/7.21 thf(zip_derived_cl13, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 (~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X2 @ Y0) & 52.29/7.21 (((((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 ('#sk2' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y2 @ 52.29/7.21 Y3) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y3 @ Y4))) => 52.29/7.21 (Y2 @ Y4))))))))))) => 52.29/7.21 (Y2 @ Y1)))))) | 52.29/7.21 (((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y3 @ 52.29/7.21 Y4) & 52.29/7.21 (Y2 @ Y3))) => 52.29/7.21 (Y2 @ Y4))))))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))))) => 52.29/7.21 (Y2 @ Y1)))))))))) => 52.29/7.21 (X2 @ Y1))))))))) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 (X2 @ Y0)))))) 52.29/7.21 | (X2 @ '#sk4'))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 52.29/7.21 thf(zip_derived_cl16, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 (~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((X2 @ ('#sk15' @ X2)) & 52.29/7.21 (((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ 52.29/7.21 ('#sk15' @ X2) @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ 52.29/7.21 Y3) & 52.29/7.21 (Y1 @ Y2))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ 52.29/7.21 ('#sk15' @ X2) @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))))) => 52.29/7.21 (X2 @ Y0)))))) 52.29/7.21 | (X2 @ '#sk4') 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 (X2 @ Y0)))))))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl13])). 52.29/7.21 thf(zip_derived_cl19, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 (~ (((((X2 @ ('#sk15' @ X2)) & 52.29/7.21 (((((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ X2) @ 52.29/7.21 Y1) => (Y0 @ Y1)))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & 52.29/7.21 ('#sk2' @ Y1 @ 52.29/7.21 Y2))) => 52.29/7.21 (Y0 @ Y2))))))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))) | 52.29/7.21 (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ 52.29/7.21 Y2) & (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ 52.29/7.21 Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))))))) => 52.29/7.21 (X2 @ ('#sk21' @ X2)))) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 (X2 @ Y0)))))) 52.29/7.21 | (X2 @ '#sk4'))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl16])). 52.29/7.21 thf(zip_derived_cl23, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 (~ (X2 @ ('#sk21' @ X2)) 52.29/7.21 | (X2 @ '#sk4') 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 (X2 @ Y0)))))))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 52.29/7.21 thf(zip_derived_cl29, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 ( ('#form37' @ X2) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 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(^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & 52.29/7.21 ('#sk1' @ Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))) | 52.29/7.21 (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & 52.29/7.21 ('#sk2' @ Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ 52.29/7.21 Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))))) => 52.29/7.21 (X2 @ ('#sk38' @ X2)))) 52.29/7.21 | ('#form37' @ X2))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl29])). 52.29/7.21 thf(zip_derived_cl35, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 ( (((((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk1' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))) | 52.29/7.21 (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))))) 52.29/7.21 | ('#form37' @ X2))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl30])). 52.29/7.21 thf(zip_derived_cl42, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 ( (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ Y1) => (Y0 @ Y1)))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk1' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))) 52.29/7.21 | ('#form37' @ X2))), 52.29/7.21 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl35])). 52.29/7.21 thf(zip_derived_cl45, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X4 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.29/7.21 (X4 @ Y1))))))))))) => 52.29/7.21 (X4 @ ('#sk38' @ X2)))) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))))), 52.29/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl42])). 52.29/7.21 thf(zip_derived_cl48, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X4 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.29/7.21 (X4 @ Y1))))))))))) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))) 52.29/7.21 | ('#form37' @ X2))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 52.29/7.21 thf(zip_derived_cl50, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk3' @ Y0) => (X4 @ Y0)))))) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X4 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.29/7.21 (X4 @ Y1))))))))) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))) 52.29/7.21 | (X4 @ ('#sk38' @ X2)))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl48])). 52.29/7.21 thf(zip_derived_cl52, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ ((('#sk1' @ '#sk3' @ ('#sk122' @ X4)) => (X4 @ ('#sk122' @ X4)))) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X4 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.29/7.21 (X4 @ Y1))))))))))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl50])). 52.29/7.21 thf(zip_derived_cl56, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (X4 @ ('#sk122' @ X4)) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X4 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.29/7.21 (X4 @ Y1))))))))) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))) 52.29/7.21 | (X4 @ ('#sk38' @ X2)))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 52.29/7.21 thf(zip_derived_cl60, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((X4 @ ('#sk165' @ X4)) & ('#sk1' @ 52.29/7.21 ('#sk165' @ X4) @ Y0))) => 52.29/7.21 (X4 @ Y0)))))) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | ~ (X4 @ ('#sk122' @ X4)))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl56])). 52.29/7.21 thf(zip_derived_cl64, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((((X4 @ ('#sk165' @ X4)) & ('#sk1' @ ('#sk165' @ X4) @ 52.29/7.21 ('#sk199' @ X4)))) => 52.29/7.21 (X4 @ ('#sk199' @ X4)))) 52.29/7.21 | ~ (X4 @ ('#sk122' @ X4)) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))) 52.29/7.21 | (X4 @ ('#sk38' @ X2)))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl60])). 52.29/7.21 thf(zip_derived_cl73, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 (~ ('#form245' @ X2) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl74, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( (((((((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 (X4 @ Y1))))))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))))) => 52.29/7.21 (X4 @ ('#sk38' @ X2)))) 52.29/7.21 | ~ ('#form245' @ X2))), 52.29/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl73])). 52.29/7.21 thf(zip_derived_cl86, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 (X4 @ Y1))))))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))))) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ~ ('#form245' @ X2))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])). 52.29/7.21 thf(zip_derived_cl96, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 (X4 @ Y1))))))))) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))) 52.29/7.21 | ~ ('#form245' @ X2) 52.29/7.21 | (X4 @ ('#sk38' @ X2)))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl86])). 52.29/7.21 thf(zip_derived_cl98, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((X4 @ ('#sk150' @ X4)) & ('#sk2' @ 52.29/7.21 ('#sk150' @ X4) @ Y0))) => 52.29/7.21 (X4 @ Y0)))))) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ~ ('#form245' @ X2) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 52.29/7.21 thf(zip_derived_cl100, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((((X4 @ ('#sk150' @ X4)) & ('#sk2' @ ('#sk150' @ X4) @ 52.29/7.21 ('#sk182' @ X4)))) => 52.29/7.21 (X4 @ ('#sk182' @ X4)))) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))) 52.29/7.21 | ~ ('#form245' @ X2) 52.29/7.21 | (X4 @ ('#sk38' @ X2)))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl98])). 52.29/7.21 thf(zip_derived_cl104, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (X4 @ ('#sk182' @ X4)) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ~ ('#form245' @ X2) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 52.29/7.21 thf(zip_derived_cl104, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (X4 @ ('#sk182' @ X4)) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ~ ('#form245' @ X2) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 52.29/7.21 thf(zip_derived_cl112, plain, 52.29/7.21 (![X4 : a > $o]: 52.29/7.21 ( ('#form484' @ X4) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl114, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ ('#form484' @ X4) 52.29/7.21 | ~ ('#form245' @ X2) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ~ (X4 @ ('#sk182' @ X4)))), 52.29/7.21 inference('renaming', [status(thm)], 52.29/7.21 [zip_derived_cl104, zip_derived_cl112])). 52.29/7.21 thf(zip_derived_cl103, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( (((X4 @ ('#sk150' @ X4)) & ('#sk2' @ ('#sk150' @ X4) @ 52.29/7.21 ('#sk182' @ X4)))) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ~ ('#form245' @ X2) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 52.29/7.21 thf(zip_derived_cl111, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( ('#sk2' @ ('#sk150' @ X4) @ ('#sk182' @ X4)) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))) 52.29/7.21 | ~ ('#form245' @ X2) 52.29/7.21 | (X4 @ ('#sk38' @ X2)))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl103])). 52.29/7.21 thf(zip_derived_cl112, plain, 52.29/7.21 (![X4 : a > $o]: 52.29/7.21 ( ('#form484' @ X4) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl120, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ ('#form484' @ (^[Y0 : a]: (X4 @ Y0))) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ~ ('#form245' @ X2) 52.29/7.21 | ('#sk2' @ ('#sk150' @ X4) @ ('#sk182' @ X4)))), 52.29/7.21 inference('renaming', [status(thm)], 52.29/7.21 [zip_derived_cl111, zip_derived_cl112])). 52.29/7.21 thf(zip_derived_cl126, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ ('#form484' @ X4) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ~ ('#form245' @ X2) 52.29/7.21 | ('#sk2' @ ('#sk150' @ X4) @ ('#sk182' @ X4)))), 52.29/7.21 inference('ho_norm', [status(thm)], [zip_derived_cl120])). 52.29/7.21 thf(zip_derived_cl112, plain, 52.29/7.21 (![X4 : a > $o]: 52.29/7.21 ( ('#form484' @ X4) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl113, plain, 52.29/7.21 (![X4 : a > $o]: 52.29/7.21 (~ ((('#sk2' @ '#sk3' @ ('#sk485' @ X4)) => (X4 @ ('#sk485' @ X4)))) 52.29/7.21 | ('#form484' @ X4))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl112])). 52.29/7.21 thf(zip_derived_cl121, plain, 52.29/7.21 (![X4 : a > $o]: 52.29/7.21 ( ('#sk2' @ '#sk3' @ ('#sk485' @ X4)) | ('#form484' @ X4))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl113])). 52.29/7.21 thf(zip_derived_cl122, plain, 52.29/7.21 (![X4 : a > $o]: (~ (X4 @ ('#sk485' @ X4)) | ('#form484' @ X4))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl113])). 52.29/7.21 thf(zip_derived_cl110, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( (X4 @ ('#sk150' @ X4)) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))) 52.29/7.21 | ~ ('#form245' @ X2) 52.29/7.21 | (X4 @ ('#sk38' @ X2)))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl103])). 52.29/7.21 thf(zip_derived_cl112, plain, 52.29/7.21 (![X4 : a > $o]: 52.29/7.21 ( ('#form484' @ X4) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk3' @ Y0) => (X4 @ Y0)))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl119, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ ('#form484' @ (^[Y0 : a]: (X4 @ Y0))) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ~ ('#form245' @ X2) 52.29/7.21 | (X4 @ ('#sk150' @ X4)))), 52.29/7.21 inference('renaming', [status(thm)], 52.29/7.21 [zip_derived_cl110, zip_derived_cl112])). 52.29/7.21 thf(zip_derived_cl125, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ ('#form484' @ X4) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ~ ('#form245' @ X2) 52.29/7.21 | (X4 @ ('#sk150' @ X4)))), 52.29/7.21 inference('ho_norm', [status(thm)], [zip_derived_cl119])). 52.29/7.21 thf(zip_derived_cl6, plain, 52.29/7.21 (~ (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 52.29/7.21 '#sk3' @ Y1))) => 52.29/7.21 (Y0 @ Y1)))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & 52.29/7.21 ((('#sk1' @ Y1 @ Y2) | 52.29/7.21 ('#sk2' @ Y1 @ Y2))))) => 52.29/7.21 (Y0 @ Y2))))))))))) => 52.29/7.21 (Y0 @ '#sk4'))))))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 52.29/7.21 thf(zip_derived_cl9, plain, 52.29/7.21 (~ (((((((!!) @ (^[Y0 : a]: 52.29/7.21 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 52.29/7.21 ('#sk5' @ Y0)))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & 52.29/7.21 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.29/7.21 Y1))))) => 52.29/7.21 ('#sk5' @ Y1))))))))))) => 52.29/7.21 ('#sk5' @ '#sk4')))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 52.29/7.21 thf(zip_derived_cl11, plain, 52.29/7.21 ( (((((!!) @ (^[Y0 : a]: 52.29/7.21 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 52.29/7.21 ('#sk5' @ Y0)))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & 52.29/7.21 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 52.29/7.21 ('#sk5' @ Y1)))))))))))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl9])). 52.29/7.21 thf(zip_derived_cl14, plain, 52.29/7.21 ( (((!!) @ (^[Y0 : a]: 52.29/7.21 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 52.29/7.21 ('#sk5' @ Y0))))))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl11])). 52.29/7.21 thf(zip_derived_cl17, plain, 52.29/7.21 (![X2 : a]: 52.29/7.21 ((((('#sk2' @ '#sk3' @ X2) | ('#sk1' @ '#sk3' @ X2))) => ('#sk5' @ 52.29/7.21 X2)))), 52.29/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 52.29/7.21 thf(zip_derived_cl20, plain, 52.29/7.21 (![X2 : a]: 52.29/7.21 (~ ((('#sk2' @ '#sk3' @ X2) | ('#sk1' @ '#sk3' @ X2))) 52.29/7.21 | ('#sk5' @ X2))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 52.29/7.21 thf(zip_derived_cl24, plain, 52.29/7.21 (![X2 : a]: (~ ('#sk2' @ '#sk3' @ X2) | ('#sk5' @ X2))), 52.29/7.21 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 52.29/7.21 thf(zip_derived_cl36, plain, 52.29/7.21 (![X2 : a > $o]: (~ (X2 @ ('#sk38' @ X2)) | ('#form37' @ X2))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl30])). 52.29/7.21 thf(zip_derived_cl64, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((((X4 @ ('#sk165' @ X4)) & ('#sk1' @ ('#sk165' @ X4) @ 52.29/7.21 ('#sk199' @ X4)))) => 52.29/7.21 (X4 @ ('#sk199' @ X4)))) 52.29/7.21 | ~ (X4 @ ('#sk122' @ X4)) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))) 52.29/7.21 | (X4 @ ('#sk38' @ X2)))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl60])). 52.29/7.21 thf(zip_derived_cl73, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 (~ ('#form245' @ X2) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl76, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( ('#form245' @ X2) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | ~ (X4 @ ('#sk122' @ X4)) 52.29/7.21 | ~ (((((X4 @ ('#sk165' @ X4)) & ('#sk1' @ ('#sk165' @ X4) @ 52.29/7.21 ('#sk199' @ X4)))) => 52.29/7.21 (X4 @ ('#sk199' @ X4)))))), 52.29/7.21 inference('renaming', [status(thm)], [zip_derived_cl64, zip_derived_cl73])). 52.29/7.21 thf(zip_derived_cl85, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (X4 @ ('#sk199' @ X4)) 52.29/7.21 | ~ (X4 @ ('#sk122' @ X4)) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ('#form245' @ X2))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl76])). 52.29/7.21 thf(zip_derived_cl7, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X2 @ Y0) & 52.29/7.21 (((((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 (( 52.29/7.21 ('#sk2' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y2 @ 52.29/7.21 Y3) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y3 @ Y4))) => 52.29/7.21 (Y2 @ Y4))))))))))) => 52.29/7.21 (Y2 @ Y1)))))) | 52.29/7.21 (((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y3 @ 52.29/7.21 Y4) & 52.29/7.21 (Y2 @ Y3))) => 52.29/7.21 (Y2 @ Y4))))))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))))) => 52.29/7.21 (Y2 @ Y1)))))))))) => 52.29/7.21 (X2 @ Y1))))))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 (X2 @ Y0)))))))) => 52.29/7.21 (X2 @ '#sk4')))), 52.29/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 52.29/7.21 thf(zip_derived_cl8, plain, 52.29/7.21 ( (((((((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & 52.29/7.21 (((((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 ('#sk2' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y2 @ 52.29/7.21 Y3) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y3 @ Y4))) => 52.29/7.21 (Y2 @ Y4))))))))))) => 52.29/7.21 (Y2 @ Y1)))))) | 52.29/7.21 (((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y3 @ 52.29/7.21 Y4) & 52.29/7.21 (Y2 @ Y3))) => 52.29/7.21 (Y2 @ Y4))))))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))))) => 52.29/7.21 (Y2 @ Y1)))))))))) => 52.29/7.21 ('#sk5' @ Y1))))))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (((( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (((( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 ('#sk5' @ Y0)))))))) => 52.29/7.21 ('#sk5' @ '#sk4')))), 52.29/7.21 inference('triggered_bool_instantiation', [status(thm)], 52.29/7.21 [zip_derived_cl7])). 52.29/7.21 thf(zip_derived_cl12, plain, (~ ('#sk5' @ '#sk4')), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl9])). 52.29/7.21 thf(zip_derived_cl145, plain, 52.29/7.21 ( (((((((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & 52.29/7.21 (((((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 ('#sk2' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y2 @ 52.29/7.21 Y3) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y3 @ Y4))) => 52.29/7.21 (Y2 @ Y4))))))))))) => 52.29/7.21 (Y2 @ Y1)))))) | 52.29/7.21 (((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y3 @ 52.29/7.21 Y4) & 52.29/7.21 (Y2 @ Y3))) => 52.29/7.21 (Y2 @ Y4))))))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))))) => 52.29/7.21 (Y2 @ Y1)))))))))) => 52.29/7.21 ('#sk5' @ Y1))))))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (((( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (((( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 ('#sk5' @ Y0)))))))) => 52.29/7.21 ($false)))), 52.29/7.21 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl12])). 52.29/7.21 thf(zip_derived_cl146, plain, 52.29/7.21 ( (((~) @ (((((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & 52.29/7.21 (((((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ ( 52.29/7.21 ^[Y3 : a]: 52.29/7.21 ((('#sk2' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))) & 52.29/7.21 (((!!) @ ( 52.29/7.21 ^[Y3 : a]: 52.29/7.21 (((!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y2 @ 52.29/7.21 Y3) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y3 @ Y4))) => 52.29/7.21 (Y2 @ Y4))))))))))) => 52.29/7.21 (Y2 @ Y1)))))) | 52.29/7.21 (((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ ( 52.29/7.21 ^[Y3 : a]: 52.29/7.21 (((!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y3 @ 52.29/7.21 Y4) & 52.29/7.21 (Y2 @ Y3))) => 52.29/7.21 (Y2 @ Y4))))))))) & 52.29/7.21 (((!!) @ ( 52.29/7.21 ^[Y3 : a]: 52.29/7.21 ((('#sk1' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))))) => 52.29/7.21 (Y2 @ Y1)))))))))) => 52.29/7.21 ('#sk5' @ Y1))))))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ 52.29/7.21 '#sk3' @ Y2) => 52.29/7.21 (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ ( 52.29/7.21 ^[Y3 : a]: 52.29/7.21 (((((Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ ( 52.29/7.21 ^[Y3 : a]: 52.29/7.21 (((((Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ 52.29/7.21 '#sk3' @ Y2) => 52.29/7.21 (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 ('#sk5' @ Y0))))))))))), 52.29/7.21 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl145])). 52.29/7.21 thf(zip_derived_cl147, plain, 52.29/7.21 (~ (((((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & 52.29/7.21 (((((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 (( 52.29/7.21 ('#sk2' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y2 @ 52.29/7.21 Y3) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y3 @ Y4))) => 52.29/7.21 (Y2 @ Y4))))))))))) => 52.29/7.21 (Y2 @ Y1)))))) | 52.29/7.21 (((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 (( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y3 @ 52.29/7.21 Y4) & 52.29/7.21 (Y2 @ Y3))) => 52.29/7.21 (Y2 @ Y4))))))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))))) => 52.29/7.21 (Y2 @ Y1)))))))))) => 52.29/7.21 ('#sk5' @ Y1))))))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (((( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (((( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 ('#sk5' @ Y0))))))))), 52.29/7.21 inference('simplify nested equalities', [status(thm)], 52.29/7.21 [zip_derived_cl146])). 52.29/7.21 thf(zip_derived_cl148, plain, 52.29/7.21 ((~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & 52.29/7.21 (((((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 ((('#sk2' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (((!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y2 @ 52.29/7.21 Y3) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y3 @ Y4))) => 52.29/7.21 (Y2 @ Y4))))))))))) => 52.29/7.21 (Y2 @ Y1)))))) | 52.29/7.21 (((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 (((!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y3 @ 52.29/7.21 Y4) & 52.29/7.21 (Y2 @ Y3))) => 52.29/7.21 (Y2 @ Y4))))))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ((('#sk1' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))))) => 52.29/7.21 (Y2 @ Y1)))))))))) => 52.29/7.21 ('#sk5' @ Y1))))))))) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (((( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (((( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 ('#sk5' @ Y0)))))))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl147])). 52.29/7.21 thf(zip_derived_cl29, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 ( ('#form37' @ X2) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 (X2 @ Y0)))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl149, plain, 52.29/7.21 ((~ ('#form37' @ '#sk5') 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & 52.29/7.21 (((((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 ('#sk2' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 (Y2 @ 52.29/7.21 Y3) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y3 @ Y4))) => 52.29/7.21 (Y2 @ Y4))))))))))) => 52.29/7.21 (Y2 @ Y1)))))) | 52.29/7.21 (((!!) @ (^[Y2 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (!!) @ ( 52.29/7.21 ^[Y4 : a]: 52.29/7.21 (( 52.29/7.21 (( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y3 @ 52.29/7.21 Y4) & 52.29/7.21 (Y2 @ Y3))) => 52.29/7.21 (Y2 @ Y4))))))))) & 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y0 @ 52.29/7.21 Y3) => 52.29/7.21 (Y2 @ Y3)))))))) => 52.29/7.21 (Y2 @ Y1)))))))))) => 52.29/7.21 ('#sk5' @ Y1))))))))))), 52.29/7.21 inference('renaming', [status(thm)], 52.29/7.21 [zip_derived_cl148, zip_derived_cl29])). 52.29/7.21 thf(zip_derived_cl150, plain, 52.29/7.21 ((~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((((('#sk5' @ ('#sk15' @ '#sk5')) & 52.29/7.21 (((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ 52.29/7.21 ('#sk15' @ '#sk5') @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (((( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 (((( 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ 52.29/7.21 Y3) & 52.29/7.21 (Y1 @ Y2))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ 52.29/7.21 ('#sk15' @ '#sk5') @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))))) => 52.29/7.21 ('#sk5' @ Y0)))))) 52.29/7.21 | ~ ('#form37' @ '#sk5'))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl149])). 52.29/7.21 thf(zip_derived_cl151, plain, 52.29/7.21 ((~ ((((('#sk5' @ ('#sk15' @ '#sk5')) & 52.29/7.21 (((((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ '#sk5') @ 52.29/7.21 Y1) => (Y0 @ Y1)))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & 52.29/7.21 ('#sk2' @ Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ '#sk5'))))))) | 52.29/7.21 (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ 52.29/7.21 Y2) & (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ '#sk5') @ 52.29/7.21 Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ '#sk5'))))))))))) => 52.29/7.21 ('#sk5' @ ('#sk21' @ '#sk5')))) 52.29/7.21 | ~ ('#form37' @ '#sk5'))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl150])). 52.29/7.21 thf(zip_derived_cl153, plain, 52.29/7.21 ((~ ('#sk5' @ ('#sk21' @ '#sk5')) | ~ ('#form37' @ '#sk5'))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl151])). 52.29/7.21 thf(zip_derived_cl12, plain, (~ ('#sk5' @ '#sk4')), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl9])). 52.29/7.21 thf(zip_derived_cl22, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 ( (((X2 @ ('#sk15' @ X2)) & 52.29/7.21 (((((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & 52.29/7.21 ('#sk2' @ Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))) | 52.29/7.21 (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))))))) 52.29/7.21 | (X2 @ '#sk4') 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 (X2 @ Y0)))))))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 52.29/7.21 thf(zip_derived_cl28, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 ( (((((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))) | 52.29/7.21 (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))))) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 (X2 @ Y0)))))) 52.29/7.21 | (X2 @ '#sk4'))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl22])). 52.29/7.21 thf(zip_derived_cl29, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 ( ('#form37' @ X2) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 (X2 @ Y0)))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl34, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 (~ ('#form37' @ (^[Y0 : a]: (X2 @ Y0))) 52.29/7.21 | (X2 @ '#sk4') 52.29/7.21 | (((((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & 52.29/7.21 ('#sk2' @ Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))) | 52.29/7.21 (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))))))), 52.29/7.21 inference('renaming', [status(thm)], [zip_derived_cl28, zip_derived_cl29])). 52.29/7.21 thf(zip_derived_cl40, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 (~ ('#form37' @ X2) 52.29/7.21 | (X2 @ '#sk4') 52.29/7.21 | (((((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & 52.29/7.21 ('#sk2' @ Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))) | 52.29/7.21 (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))))))), 52.29/7.21 inference('ho_norm', [status(thm)], [zip_derived_cl34])). 52.29/7.21 thf(zip_derived_cl41, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 ( (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))) 52.29/7.21 | (X2 @ '#sk4') 52.29/7.21 | ~ ('#form37' @ X2))), 52.29/7.21 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])). 52.29/7.21 thf(zip_derived_cl43, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( (((((((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 (X4 @ Y1))))))))))) => 52.29/7.21 (X4 @ ('#sk21' @ X2)))) 52.29/7.21 | ~ ('#form37' @ X2) 52.29/7.21 | (X2 @ '#sk4') 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))))), 52.29/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 52.29/7.21 thf(zip_derived_cl47, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 (X4 @ Y1))))))))))) 52.29/7.21 | (X4 @ ('#sk21' @ X2)) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))) 52.29/7.21 | (X2 @ '#sk4') 52.29/7.21 | ~ ('#form37' @ X2))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl43])). 52.29/7.21 thf(zip_derived_cl49, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 (X4 @ Y1))))))))) 52.29/7.21 | ~ ('#form37' @ X2) 52.29/7.21 | (X2 @ '#sk4') 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))) 52.29/7.21 | (X4 @ ('#sk21' @ X2)))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl47])). 52.29/7.21 thf(zip_derived_cl51, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ ((('#sk2' @ ('#sk15' @ X2) @ ('#sk115' @ X2 @ X4)) => (X4 @ 52.29/7.21 ('#sk115' @ X2 @ X4)))) 52.29/7.21 | (X4 @ ('#sk21' @ X2)) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))) 52.29/7.21 | (X2 @ '#sk4') 52.29/7.21 | ~ ('#form37' @ X2) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 (X4 @ Y1))))))))))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl49])). 52.29/7.21 thf(zip_derived_cl54, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (X4 @ ('#sk115' @ X2 @ X4)) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 (X4 @ Y1))))))))) 52.29/7.21 | ~ ('#form37' @ X2) 52.29/7.21 | (X2 @ '#sk4') 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))) 52.29/7.21 | (X4 @ ('#sk21' @ X2)))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 52.29/7.21 thf(zip_derived_cl58, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((X4 @ ('#sk150' @ X4)) & ('#sk2' @ 52.29/7.21 ('#sk150' @ X4) @ Y0))) => 52.29/7.21 (X4 @ Y0)))))) 52.29/7.21 | (X4 @ ('#sk21' @ X2)) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))) 52.29/7.21 | (X2 @ '#sk4') 52.29/7.21 | ~ ('#form37' @ X2) 52.29/7.21 | ~ (X4 @ ('#sk115' @ X2 @ X4)))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl54])). 52.29/7.21 thf(zip_derived_cl62, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((((X4 @ ('#sk150' @ X4)) & ('#sk2' @ ('#sk150' @ X4) @ 52.29/7.21 ('#sk182' @ X4)))) => 52.29/7.21 (X4 @ ('#sk182' @ X4)))) 52.29/7.21 | ~ (X4 @ ('#sk115' @ X2 @ X4)) 52.29/7.21 | ~ ('#form37' @ X2) 52.29/7.21 | (X2 @ '#sk4') 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))) 52.29/7.21 | (X4 @ ('#sk21' @ X2)))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl58])). 52.29/7.21 thf(zip_derived_cl67, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 (~ ('#form228' @ X2) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl68, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( (((((((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk1' @ Y0 @ Y1) & (X4 @ Y0))) => 52.29/7.21 (X4 @ Y1))))))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))) => 52.29/7.21 (X4 @ ('#sk21' @ X2)))) 52.29/7.21 | ~ ('#form228' @ X2))), 52.29/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl67])). 52.29/7.21 thf(zip_derived_cl81, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk1' @ Y0 @ Y1) & (X4 @ Y0))) => 52.29/7.21 (X4 @ Y1))))))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))) 52.29/7.21 | (X4 @ ('#sk21' @ X2)) 52.29/7.21 | ~ ('#form228' @ X2))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 52.29/7.21 thf(zip_derived_cl91, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk1' @ Y0 @ Y1) & (X4 @ Y0))) => 52.29/7.21 (X4 @ Y1))))))))) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) 52.29/7.21 | ~ ('#form228' @ X2) 52.29/7.21 | (X4 @ ('#sk21' @ X2)))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl81])). 52.29/7.21 thf(zip_derived_cl97, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((((('#sk1' @ ('#sk403' @ X4) @ Y0) & (X4 @ 52.29/7.21 ('#sk403' @ X4)))) => 52.29/7.21 (X4 @ Y0)))))) 52.29/7.21 | (X4 @ ('#sk21' @ X2)) 52.29/7.21 | ~ ('#form228' @ X2) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl91])). 52.29/7.21 thf(zip_derived_cl99, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ ((((('#sk1' @ ('#sk403' @ X4) @ ('#sk438' @ X4)) & (X4 @ 52.29/7.21 ('#sk403' @ X4)))) => 52.29/7.21 (X4 @ ('#sk438' @ X4)))) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) 52.29/7.21 | ~ ('#form228' @ X2) 52.29/7.21 | (X4 @ ('#sk21' @ X2)))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl97])). 52.29/7.21 thf(zip_derived_cl102, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (X4 @ ('#sk438' @ X4)) 52.29/7.21 | (X4 @ ('#sk21' @ X2)) 52.29/7.21 | ~ ('#form228' @ X2) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl99])). 52.29/7.21 thf(zip_derived_cl102, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (X4 @ ('#sk438' @ X4)) 52.29/7.21 | (X4 @ ('#sk21' @ X2)) 52.29/7.21 | ~ ('#form228' @ X2) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl99])). 52.29/7.21 thf(zip_derived_cl107, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( ('#form472' @ X2 @ X4) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl109, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ ('#form472' @ X2 @ X4) 52.29/7.21 | ~ ('#form228' @ X2) 52.29/7.21 | (X4 @ ('#sk21' @ X2)) 52.29/7.21 | ~ (X4 @ ('#sk438' @ X4)))), 52.29/7.21 inference('renaming', [status(thm)], 52.29/7.21 [zip_derived_cl102, zip_derived_cl107])). 52.29/7.21 thf(zip_derived_cl84, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( (((X4 @ ('#sk165' @ X4)) & ('#sk1' @ ('#sk165' @ X4) @ 52.29/7.21 ('#sk199' @ X4)))) 52.29/7.21 | ~ (X4 @ ('#sk122' @ X4)) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ('#form245' @ X2))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl76])). 52.29/7.21 thf(zip_derived_cl94, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( (X4 @ ('#sk165' @ X4)) 52.29/7.21 | ('#form245' @ X2) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | ~ (X4 @ ('#sk122' @ X4)))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl84])). 52.29/7.21 thf(zip_derived_cl95, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( ('#sk1' @ ('#sk165' @ X4) @ ('#sk199' @ X4)) 52.29/7.21 | ('#form245' @ X2) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | ~ (X4 @ ('#sk122' @ X4)))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl84])). 52.29/7.21 thf(zip_derived_cl152, plain, 52.29/7.21 (( ((('#sk5' @ ('#sk15' @ '#sk5')) & 52.29/7.21 (((((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ '#sk5') @ 52.29/7.21 Y1) => (Y0 @ Y1)))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ '#sk5'))))))) | 52.29/7.21 (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ '#sk5') @ 52.29/7.21 Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ '#sk5'))))))))))) 52.29/7.21 | ~ ('#form37' @ '#sk5'))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl151])). 52.29/7.21 thf(zip_derived_cl154, plain, 52.29/7.21 (( ('#sk5' @ ('#sk15' @ '#sk5')) | ~ ('#form37' @ '#sk5'))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl152])). 52.29/7.21 thf(zip_derived_cl27, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 ( (X2 @ ('#sk15' @ X2)) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 (X2 @ Y0)))))) 52.29/7.21 | (X2 @ '#sk4'))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl22])). 52.29/7.21 thf(zip_derived_cl29, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 ( ('#form37' @ X2) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk1' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk1' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))))) => 52.29/7.21 (Y1 @ Y0)))))) | 52.29/7.21 (((!!) @ (^[Y1 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y2 : a]: 52.29/7.21 (((!!) @ (^[Y3 : a]: 52.29/7.21 ( 52.29/7.21 ( 52.29/7.21 (( 52.29/7.21 (Y1 @ 52.29/7.21 Y2) & 52.29/7.21 ('#sk2' @ 52.29/7.21 Y2 @ Y3))) => 52.29/7.21 (Y1 @ Y3))))))))) & 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ 52.29/7.21 Y2) => (Y1 @ Y2)))))))) => 52.29/7.21 (Y1 @ Y0)))))))) => 52.29/7.21 (X2 @ Y0)))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl33, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 (~ ('#form37' @ (^[Y0 : a]: (X2 @ Y0))) 52.29/7.21 | (X2 @ '#sk4') 52.29/7.21 | (X2 @ ('#sk15' @ X2)))), 52.29/7.21 inference('renaming', [status(thm)], [zip_derived_cl27, zip_derived_cl29])). 52.29/7.21 thf(zip_derived_cl39, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 (~ ('#form37' @ X2) | (X2 @ '#sk4') | (X2 @ ('#sk15' @ X2)))), 52.29/7.21 inference('ho_norm', [status(thm)], [zip_derived_cl33])). 52.29/7.21 thf(zip_derived_cl55, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( ('#sk1' @ '#sk3' @ ('#sk122' @ X4)) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X4 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.29/7.21 (X4 @ Y1))))))))) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))) 52.29/7.21 | (X4 @ ('#sk38' @ X2)))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 52.29/7.21 thf(zip_derived_cl59, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((((X4 @ ('#sk165' @ X4)) & ('#sk1' @ 52.29/7.21 ('#sk165' @ X4) @ Y0))) => 52.29/7.21 (X4 @ Y0)))))) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | ('#sk1' @ '#sk3' @ ('#sk122' @ X4)))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl55])). 52.29/7.21 thf(zip_derived_cl63, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (((((X4 @ ('#sk165' @ X4)) & ('#sk1' @ ('#sk165' @ X4) @ 52.29/7.21 ('#sk199' @ X4)))) => 52.29/7.21 (X4 @ ('#sk199' @ X4)))) 52.29/7.21 | ('#sk1' @ '#sk3' @ ('#sk122' @ X4)) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))) 52.29/7.21 | (X4 @ ('#sk38' @ X2)))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl59])). 52.29/7.21 thf(zip_derived_cl72, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (X4 @ ('#sk199' @ X4)) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | ('#sk1' @ '#sk3' @ ('#sk122' @ X4)))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl63])). 52.29/7.21 thf(zip_derived_cl73, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 (~ ('#form245' @ X2) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl83, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( ('#form245' @ X2) 52.29/7.21 | ('#sk1' @ '#sk3' @ ('#sk122' @ X4)) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ~ (X4 @ ('#sk199' @ X4)))), 52.29/7.21 inference('renaming', [status(thm)], [zip_derived_cl72, zip_derived_cl73])). 52.29/7.21 thf(zip_derived_cl71, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( (((X4 @ ('#sk165' @ X4)) & ('#sk1' @ ('#sk165' @ X4) @ 52.29/7.21 ('#sk199' @ X4)))) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | ('#sk1' @ '#sk3' @ ('#sk122' @ X4)))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl63])). 52.29/7.21 thf(zip_derived_cl73, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 (~ ('#form245' @ X2) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ '#sk3' @ Y1) => (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk38' @ X2))))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl82, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( ('#form245' @ X2) 52.29/7.21 | ('#sk1' @ '#sk3' @ ('#sk122' @ X4)) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | (((X4 @ ('#sk165' @ X4)) & ('#sk1' @ ('#sk165' @ X4) @ 52.29/7.21 ('#sk199' @ X4)))))), 52.29/7.21 inference('renaming', [status(thm)], [zip_derived_cl71, zip_derived_cl73])). 52.29/7.21 thf(zip_derived_cl92, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( (X4 @ ('#sk165' @ X4)) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | ('#sk1' @ '#sk3' @ ('#sk122' @ X4)) 52.29/7.21 | ('#form245' @ X2))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl82])). 52.29/7.21 thf(zip_derived_cl93, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( ('#sk1' @ ('#sk165' @ X4) @ ('#sk199' @ X4)) 52.29/7.21 | (X4 @ ('#sk38' @ X2)) 52.29/7.21 | ('#form37' @ X2) 52.29/7.21 | ('#sk1' @ '#sk3' @ ('#sk122' @ X4)) 52.29/7.21 | ('#form245' @ X2))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl82])). 52.29/7.21 thf(zip_derived_cl101, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( ((('#sk1' @ ('#sk403' @ X4) @ ('#sk438' @ X4)) & (X4 @ 52.29/7.21 ('#sk403' @ X4)))) 52.29/7.21 | (X4 @ ('#sk21' @ X2)) 52.29/7.21 | ~ ('#form228' @ X2) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl99])). 52.29/7.21 thf(zip_derived_cl106, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( (X4 @ ('#sk403' @ X4)) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) 52.29/7.21 | ~ ('#form228' @ X2) 52.29/7.21 | (X4 @ ('#sk21' @ X2)))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl101])). 52.29/7.21 thf(zip_derived_cl107, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( ('#form472' @ X2 @ X4) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl116, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ ('#form472' @ X2 @ (^[Y0 : a]: (X4 @ Y0))) 52.29/7.21 | (X4 @ ('#sk21' @ X2)) 52.29/7.21 | ~ ('#form228' @ X2) 52.29/7.21 | (X4 @ ('#sk403' @ X4)))), 52.29/7.21 inference('renaming', [status(thm)], 52.29/7.21 [zip_derived_cl106, zip_derived_cl107])). 52.29/7.21 thf(zip_derived_cl124, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ ('#form472' @ X2 @ X4) 52.29/7.21 | (X4 @ ('#sk21' @ X2)) 52.29/7.21 | ~ ('#form228' @ X2) 52.29/7.21 | (X4 @ ('#sk403' @ X4)))), 52.29/7.21 inference('ho_norm', [status(thm)], [zip_derived_cl116])). 52.29/7.21 thf(zip_derived_cl155, plain, 52.29/7.21 (( (((((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ '#sk5') @ Y1) => 52.29/7.21 (Y0 @ Y1)))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ '#sk5'))))))) | 52.29/7.21 (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ '#sk5') @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ '#sk5'))))))))) 52.29/7.21 | ~ ('#form37' @ '#sk5'))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl152])). 52.29/7.21 thf(zip_derived_cl156, plain, 52.29/7.21 (( (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ '#sk5') @ Y1) => 52.29/7.21 (Y0 @ Y1)))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ '#sk5'))))))) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ '#sk5') @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ '#sk5'))))))) 52.29/7.21 | ~ ('#form37' @ '#sk5'))), 52.29/7.21 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl155])). 52.29/7.21 thf(zip_derived_cl67, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 (~ ('#form228' @ X2) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl157, plain, 52.29/7.21 (( ('#form228' @ '#sk5') 52.29/7.21 | ~ ('#form37' @ '#sk5') 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ '#sk5') @ Y1) => 52.29/7.21 (Y0 @ Y1)))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 (((((Y0 @ Y1) & ('#sk2' @ 52.29/7.21 Y1 @ Y2))) => 52.29/7.21 (Y0 @ Y2))))))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ '#sk5'))))))))), 52.29/7.21 inference('renaming', [status(thm)], 52.29/7.21 [zip_derived_cl156, zip_derived_cl67])). 52.29/7.21 thf(zip_derived_cl158, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 ( (((((((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ '#sk5') @ Y0) => (X2 @ Y0)))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 (X2 @ Y1))))))))))) => 52.29/7.21 (X2 @ ('#sk21' @ '#sk5')))) 52.29/7.21 | ~ ('#form37' @ '#sk5') 52.29/7.21 | ('#form228' @ '#sk5'))), 52.29/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl157])). 52.29/7.21 thf(zip_derived_cl159, plain, 52.29/7.21 (( (((((((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ '#sk5') @ Y0) => ('#sk5' @ Y0)))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 ('#sk5' @ Y1))))))))))) => 52.29/7.21 ('#sk5' @ ('#sk21' @ '#sk5')))) 52.29/7.21 | ~ ('#form37' @ '#sk5') 52.29/7.21 | ('#form228' @ '#sk5'))), 52.29/7.21 inference('triggered_bool_instantiation', [status(thm)], 52.29/7.21 [zip_derived_cl158])). 52.29/7.21 thf(zip_derived_cl210, plain, 52.29/7.21 ((~ (((((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ '#sk5') @ Y0) => ('#sk5' @ Y0)))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 ('#sk5' @ Y1))))))))))) 52.29/7.21 | ('#sk5' @ ('#sk21' @ '#sk5')) 52.29/7.21 | ('#form228' @ '#sk5') 52.29/7.21 | ~ ('#form37' @ '#sk5'))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])). 52.29/7.21 thf(zip_derived_cl153, plain, 52.29/7.21 ((~ ('#sk5' @ ('#sk21' @ '#sk5')) | ~ ('#form37' @ '#sk5'))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl151])). 52.29/7.21 thf(zip_derived_cl211, plain, 52.29/7.21 ((~ ('#form37' @ '#sk5') 52.29/7.21 | ('#form228' @ '#sk5') 52.29/7.21 | ~ (((((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ '#sk5') @ Y0) => ('#sk5' @ Y0)))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 ('#sk5' @ Y1))))))))))))), 52.29/7.21 inference('clc', [status(thm)], [zip_derived_cl210, zip_derived_cl153])). 52.29/7.21 thf(zip_derived_cl212, plain, 52.29/7.21 ((~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ '#sk5') @ Y0) => ('#sk5' @ Y0)))))) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 ('#sk5' @ Y1))))))))) 52.29/7.21 | ('#form228' @ '#sk5') 52.29/7.21 | ~ ('#form37' @ '#sk5'))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl211])). 52.29/7.21 thf(zip_derived_cl43, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( (((((((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 (((((X4 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 (X4 @ Y1))))))))))) => 52.29/7.21 (X4 @ ('#sk21' @ X2)))) 52.29/7.21 | ~ ('#form37' @ X2) 52.29/7.21 | (X2 @ '#sk4') 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))))), 52.29/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 52.29/7.21 thf(zip_derived_cl44, plain, 52.29/7.21 (![X0 : a > $o]: 52.29/7.21 ( (((((((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ X0) @ Y0) => ('#sk5' @ Y0)))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 ('#sk5' @ Y1))))))))))) => 52.29/7.21 ('#sk5' @ ('#sk21' @ X0)))) 52.29/7.21 | ~ ('#form37' @ X0) 52.29/7.21 | (X0 @ '#sk4') 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X0) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X0))))))))), 52.29/7.21 inference('triggered_bool_instantiation', [status(thm)], 52.29/7.21 [zip_derived_cl43])). 52.29/7.21 thf(zip_derived_cl67, plain, 52.29/7.21 (![X2 : a > $o]: 52.29/7.21 (~ ('#form228' @ X2) 52.29/7.21 | (((!!) @ (^[Y0 : a > $o]: 52.29/7.21 (((((((!!) @ (^[Y1 : a]: 52.29/7.21 (((!!) @ (^[Y2 : a]: 52.29/7.21 ((((('#sk1' @ Y1 @ Y2) & 52.29/7.21 (Y0 @ Y1))) => 52.29/7.21 (Y0 @ Y2))))))))) & 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y1) => 52.29/7.21 (Y0 @ Y1)))))))) => 52.29/7.21 (Y0 @ ('#sk21' @ X2))))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl195, plain, 52.29/7.21 (![X0 : a > $o]: 52.29/7.21 ( ('#form228' @ X0) 52.29/7.21 | (X0 @ '#sk4') 52.29/7.21 | ~ ('#form37' @ X0) 52.29/7.21 | (((((((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ X0) @ Y0) => ('#sk5' @ Y0)))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 ('#sk5' @ Y1))))))))))) => 52.29/7.21 ('#sk5' @ ('#sk21' @ X0)))))), 52.29/7.21 inference('renaming', [status(thm)], [zip_derived_cl44, zip_derived_cl67])). 52.29/7.21 thf(zip_derived_cl196, plain, 52.29/7.21 (![X0 : a > $o]: 52.29/7.21 (~ (((((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ X0) @ Y0) => ('#sk5' @ Y0)))))) & 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 ('#sk5' @ Y1))))))))))) 52.29/7.21 | ('#sk5' @ ('#sk21' @ X0)) 52.29/7.21 | ~ ('#form37' @ X0) 52.29/7.21 | (X0 @ '#sk4') 52.29/7.21 | ('#form228' @ X0))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl195])). 52.29/7.21 thf(zip_derived_cl197, plain, 52.29/7.21 (![X0 : a > $o]: 52.29/7.21 (~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ X0) @ Y0) => ('#sk5' @ Y0)))))) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 ('#sk5' @ Y1))))))))) 52.29/7.21 | ('#form228' @ X0) 52.29/7.21 | (X0 @ '#sk4') 52.29/7.21 | ~ ('#form37' @ X0) 52.29/7.21 | ('#sk5' @ ('#sk21' @ X0)))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl196])). 52.29/7.21 thf(zip_derived_cl198, plain, 52.29/7.21 (![X0 : a > $o]: 52.29/7.21 (~ ((('#sk2' @ ('#sk15' @ X0) @ ('#sk115' @ X0 @ '#sk5')) => 52.29/7.21 ('#sk5' @ ('#sk115' @ X0 @ '#sk5')))) 52.29/7.21 | ('#sk5' @ ('#sk21' @ X0)) 52.29/7.21 | ~ ('#form37' @ X0) 52.29/7.21 | (X0 @ '#sk4') 52.29/7.21 | ('#form228' @ X0) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 ('#sk5' @ Y1))))))))))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl197])). 52.29/7.21 thf(zip_derived_cl199, plain, 52.29/7.21 (![X0 : a > $o]: 52.29/7.21 ( ('#sk2' @ ('#sk15' @ X0) @ ('#sk115' @ X0 @ '#sk5')) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 ('#sk5' @ Y1))))))))) 52.29/7.21 | ('#form228' @ X0) 52.29/7.21 | (X0 @ '#sk4') 52.29/7.21 | ~ ('#form37' @ X0) 52.29/7.21 | ('#sk5' @ ('#sk21' @ X0)))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl198])). 52.29/7.21 thf(zip_derived_cl201, plain, 52.29/7.21 (( ('#form861') 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 ('#sk5' @ Y1))))))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl213, plain, 52.29/7.21 ((~ ('#form861') 52.29/7.21 | ~ ('#form37' @ '#sk5') 52.29/7.21 | ('#form228' @ '#sk5') 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk2' @ ('#sk15' @ '#sk5') @ Y0) => ('#sk5' @ Y0)))))))), 52.29/7.21 inference('renaming', [status(thm)], 52.29/7.21 [zip_derived_cl212, zip_derived_cl201])). 52.29/7.21 thf(zip_derived_cl214, plain, 52.29/7.21 ((~ ((('#sk2' @ ('#sk15' @ '#sk5') @ ('#sk115' @ '#sk5' @ '#sk5')) => 52.29/7.21 ('#sk5' @ ('#sk115' @ '#sk5' @ '#sk5')))) 52.29/7.21 | ('#form228' @ '#sk5') 52.29/7.21 | ~ ('#form37' @ '#sk5') 52.29/7.21 | ~ ('#form861'))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl213])). 52.29/7.21 thf(zip_derived_cl216, plain, 52.29/7.21 ((~ ('#sk5' @ ('#sk115' @ '#sk5' @ '#sk5')) 52.29/7.21 | ~ ('#form861') 52.29/7.21 | ~ ('#form37' @ '#sk5') 52.29/7.21 | ('#form228' @ '#sk5'))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl214])). 52.29/7.21 thf(zip_derived_cl201, plain, 52.29/7.21 (( ('#form861') 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.29/7.21 ('#sk5' @ Y1))))))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl202, plain, 52.29/7.21 ((~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((((('#sk5' @ ('#sk150' @ '#sk5')) & ('#sk2' @ 52.29/7.21 ('#sk150' @ '#sk5') @ Y0))) => 52.29/7.21 ('#sk5' @ Y0)))))) 52.29/7.21 | ('#form861'))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl201])). 52.29/7.21 thf(zip_derived_cl205, plain, 52.29/7.21 ((~ ((((('#sk5' @ ('#sk150' @ '#sk5')) & ('#sk2' @ ('#sk150' @ '#sk5') @ 52.29/7.21 ('#sk182' @ '#sk5')))) => 52.29/7.21 ('#sk5' @ ('#sk182' @ '#sk5')))) 52.29/7.21 | ('#form861'))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl202])). 52.29/7.21 thf(zip_derived_cl206, plain, 52.29/7.21 (( ((('#sk5' @ ('#sk150' @ '#sk5')) & ('#sk2' @ ('#sk150' @ '#sk5') @ 52.29/7.21 ('#sk182' @ '#sk5')))) 52.29/7.21 | ('#form861'))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl205])). 52.29/7.21 thf(zip_derived_cl208, plain, 52.29/7.21 (( ('#sk5' @ ('#sk150' @ '#sk5')) | ('#form861'))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl206])). 52.29/7.21 thf(zip_derived_cl209, plain, 52.29/7.21 (( ('#sk2' @ ('#sk150' @ '#sk5') @ ('#sk182' @ '#sk5')) | ('#form861'))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl206])). 52.29/7.21 thf(zip_derived_cl215, plain, 52.29/7.21 (( ('#sk2' @ ('#sk15' @ '#sk5') @ ('#sk115' @ '#sk5' @ '#sk5')) 52.29/7.21 | ~ ('#form861') 52.29/7.21 | ~ ('#form37' @ '#sk5') 52.29/7.21 | ('#form228' @ '#sk5'))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl214])). 52.29/7.21 thf(zip_derived_cl105, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( ('#sk1' @ ('#sk403' @ X4) @ ('#sk438' @ X4)) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))) 52.29/7.21 | ~ ('#form228' @ X2) 52.29/7.21 | (X4 @ ('#sk21' @ X2)))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl101])). 52.29/7.21 thf(zip_derived_cl107, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( ('#form472' @ X2 @ X4) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl115, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ ('#form472' @ X2 @ (^[Y0 : a]: (X4 @ Y0))) 52.29/7.21 | (X4 @ ('#sk21' @ X2)) 52.29/7.21 | ~ ('#form228' @ X2) 52.29/7.21 | ('#sk1' @ ('#sk403' @ X4) @ ('#sk438' @ X4)))), 52.29/7.21 inference('renaming', [status(thm)], 52.29/7.21 [zip_derived_cl105, zip_derived_cl107])). 52.29/7.21 thf(zip_derived_cl123, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ ('#form472' @ X2 @ X4) 52.29/7.21 | (X4 @ ('#sk21' @ X2)) 52.29/7.21 | ~ ('#form228' @ X2) 52.29/7.21 | ('#sk1' @ ('#sk403' @ X4) @ ('#sk438' @ X4)))), 52.29/7.21 inference('ho_norm', [status(thm)], [zip_derived_cl115])). 52.29/7.21 thf(zip_derived_cl25, plain, 52.29/7.21 (![X2 : a]: (~ ('#sk1' @ '#sk3' @ X2) | ('#sk5' @ X2))), 52.29/7.21 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 52.29/7.21 thf(zip_derived_cl207, plain, 52.29/7.21 ((~ ('#sk5' @ ('#sk182' @ '#sk5')) | ('#form861'))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl205])). 52.29/7.21 thf(zip_derived_cl107, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( ('#form472' @ X2 @ X4) 52.29/7.21 | ~ (((!!) @ (^[Y0 : a]: 52.29/7.21 ((('#sk1' @ ('#sk15' @ X2) @ Y0) => (X4 @ Y0)))))))), 52.29/7.21 define([status(thm)])). 52.29/7.21 thf(zip_derived_cl108, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ ((('#sk1' @ ('#sk15' @ X2) @ ('#sk473' @ X2 @ X4)) => (X4 @ 52.29/7.21 ('#sk473' @ X2 @ X4)))) 52.29/7.21 | ('#form472' @ X2 @ X4))), 52.29/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl107])). 52.29/7.21 thf(zip_derived_cl117, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 ( ('#sk1' @ ('#sk15' @ X2) @ ('#sk473' @ X2 @ X4)) 52.29/7.21 | ('#form472' @ X2 @ X4))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 52.29/7.21 thf(zip_derived_cl118, plain, 52.29/7.21 (![X2 : a > $o, X4 : a > $o]: 52.29/7.21 (~ (X4 @ ('#sk473' @ X2 @ X4)) | ('#form472' @ X2 @ X4))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 52.29/7.21 thf(zip_derived_cl15, plain, 52.29/7.21 ( (((!!) @ (^[Y0 : a]: 52.29/7.21 (((!!) @ (^[Y1 : a]: 52.29/7.21 ((((('#sk5' @ Y0) & 52.29/7.21 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 52.29/7.21 ('#sk5' @ Y1)))))))))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl11])). 52.29/7.21 thf(zip_derived_cl18, plain, 52.29/7.21 (![X2 : a]: 52.29/7.21 (((!!) @ (^[Y0 : a]: 52.29/7.21 ((((('#sk5' @ X2) & 52.29/7.21 ((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))))) => 52.29/7.21 ('#sk5' @ Y0))))))), 52.29/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 52.29/7.21 thf(zip_derived_cl21, plain, 52.29/7.21 (![X2 : a, X4 : a]: 52.29/7.21 ((((('#sk5' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) => 52.29/7.21 ('#sk5' @ X4)))), 52.29/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])). 52.29/7.21 thf(zip_derived_cl26, plain, 52.29/7.21 (![X2 : a, X4 : a]: 52.29/7.21 (~ ((('#sk5' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) 52.29/7.21 | ('#sk5' @ X4))), 52.29/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 52.29/7.21 thf(zip_derived_cl32, plain, 52.29/7.21 (![X2 : a, X4 : a]: 52.29/7.21 (~ ('#sk5' @ X2) 52.29/7.21 | ~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 52.29/7.21 | ('#sk5' @ X4))), 52.29/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 52.29/7.21 thf(zip_derived_cl38, plain, 52.29/7.21 (![X2 : a, X4 : a]: 52.29/7.21 (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 52.29/7.21 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl32])). 52.29/7.21 thf(zip_derived_cl37, plain, 52.29/7.21 (![X2 : a, X4 : a]: 52.29/7.21 (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 52.29/7.21 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl32])). 52.29/7.21 thf(zip_derived_cl10030, plain, ($false), 52.29/7.21 inference('eprover', [status(thm)], 52.29/7.21 [zip_derived_cl114, zip_derived_cl126, zip_derived_cl121, 52.29/7.21 zip_derived_cl122, zip_derived_cl125, zip_derived_cl24, 52.29/7.21 zip_derived_cl36, zip_derived_cl85, zip_derived_cl153, 52.29/7.21 zip_derived_cl12, zip_derived_cl109, zip_derived_cl94, 52.29/7.21 zip_derived_cl95, zip_derived_cl154, zip_derived_cl39, 52.29/7.21 zip_derived_cl83, zip_derived_cl92, zip_derived_cl93, 52.29/7.21 zip_derived_cl124, zip_derived_cl216, zip_derived_cl208, 52.29/7.21 zip_derived_cl209, zip_derived_cl215, zip_derived_cl123, 52.29/7.21 zip_derived_cl25, zip_derived_cl207, zip_derived_cl117, 52.29/7.21 zip_derived_cl118, zip_derived_cl38, zip_derived_cl37])). 52.29/7.21 52.29/7.21 % SZS output end Refutation 52.29/7.21 52.29/7.21 52.29/7.21 % Terminating... 52.93/7.32 % Runner terminated. 52.93/7.32 % Zipperpin 1.5 exiting 52.93/7.32 EOF