0.00/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.D2Zf60niC8 true 0.13/0.34 % Computer : n011.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 02:20:06 EDT 2022 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 960 s 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.34 % Python version: Python 3.6.8 0.13/0.34 % 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 0.55/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.55/0.72 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.55/0.72 % /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 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.56/0.79 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.56/0.81 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 52.14/7.21 % Solved by lams/20_acsne_simpl.sh. 52.14/7.21 % done 451 iterations in 6.245s 52.14/7.21 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 52.14/7.21 % SZS output start Refutation 52.14/7.21 thf(a_type, type, a: $tType). 52.14/7.21 thf('#sk101_type', type, '#sk101': (a > $o) > a). 52.14/7.21 thf('#sk12_type', type, '#sk12': a). 52.14/7.21 thf('#sk20_type', type, '#sk20': a > $o). 52.14/7.21 thf('#sk284_type', type, '#sk284': (a > $o) > a). 52.14/7.21 thf('#sk16_type', type, '#sk16': a > $o). 52.14/7.21 thf('#sk227_type', type, '#sk227': (a > $o) > a). 52.14/7.21 thf('#sk6_type', type, '#sk6': a). 52.14/7.21 thf('#sk82_type', type, '#sk82': (a > $o) > a). 52.14/7.21 thf('#sk5_type', type, '#sk5': a > $o). 52.14/7.21 thf('#sk4_type', type, '#sk4': a). 52.14/7.21 thf('#sk57_type', type, '#sk57': (a > $o) > a). 52.14/7.21 thf('#sk140_type', type, '#sk140': (a > $o) > a). 52.14/7.21 thf('#sk61_type', type, '#sk61': (a > $o) > a). 52.14/7.21 thf('#form9_type', type, '#form9': $o). 52.14/7.21 thf('#form11_type', type, '#form11': $o). 52.14/7.21 thf('#sk8_type', type, '#sk8': a). 52.14/7.21 thf('#form45_type', type, '#form45': $o). 52.14/7.21 thf('#sk166_type', type, '#sk166': (a > $o) > a). 52.14/7.21 thf('#sk49_type', type, '#sk49': (a > $o) > a). 52.14/7.21 thf('#sk171_type', type, '#sk171': (a > $o) > a). 52.14/7.21 thf('#sk3_type', type, '#sk3': a). 52.14/7.21 thf('#sk7_type', type, '#sk7': a). 52.14/7.21 thf('#sk27_type', type, '#sk27': (a > $o) > a). 52.14/7.21 thf('#sk1_type', type, '#sk1': a > a > $o). 52.14/7.21 thf('#sk122_type', type, '#sk122': (a > $o) > a). 52.14/7.21 thf('#sk2_type', type, '#sk2': a > a > $o). 52.14/7.21 thf('#sk126_type', type, '#sk126': (a > $o) > a). 52.14/7.21 thf('#sk289_type', type, '#sk289': (a > $o) > a). 52.14/7.21 thf('#sk130_type', type, '#sk130': (a > $o) > a). 52.14/7.21 thf('#form283_type', type, '#form283': (a > $o) > $o). 52.14/7.21 thf('#sk10_type', type, '#sk10': a). 52.14/7.21 thf(cTHM251D_pme, conjecture, 52.14/7.21 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 52.14/7.21 ( ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 52.14/7.21 ( ( ( ![Xq:( a > $o )]: 52.14/7.21 ( ( ( ![Xw:a]: 52.14/7.21 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 52.14/7.21 ( Xq @ Xw ) ) ) & 52.14/7.21 ( ![Xu:a,Xv:a]: 52.14/7.21 ( ( ( Xq @ Xu ) & 52.14/7.21 ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 52.14/7.21 ( Xq @ Xv ) ) ) ) => 52.14/7.21 ( Xq @ Xy0 ) ) ) & 52.14/7.21 ( ![Xq:( a > $o )]: 52.14/7.21 ( ( ( ![Xw:a]: 52.14/7.21 ( ( ( S @ Xy0 @ Xw ) | ( R @ Xy0 @ Xw ) ) => 52.14/7.21 ( Xq @ Xw ) ) ) & 52.14/7.21 ( ![Xu:a,Xv:a]: 52.14/7.21 ( ( ( Xq @ Xu ) & 52.14/7.21 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 52.14/7.21 ( Xq @ Xv ) ) ) ) => 52.14/7.21 ( Xq @ Xz ) ) ) ) => 52.14/7.21 ( ![Xq:( a > $o )]: 52.14/7.21 ( ( ( ![Xu:a,Xv:a]: 52.14/7.21 ( ( ( Xq @ Xu ) & ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 52.14/7.21 ( Xq @ Xv ) ) ) & 52.14/7.21 ( ![Xw:a]: 52.14/7.21 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 52.14/7.21 ( Xq @ Xz ) ) ) ) ) & 52.14/7.21 ( ![Xx0:a,Xy0:a]: 52.14/7.21 ( ( ( ![Xq:( a > $o )]: 52.14/7.21 ( ( ( ![Xu:a,Xv:a]: 52.14/7.21 ( ( ( Xq @ Xu ) & ( R @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) & 52.14/7.21 ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 52.14/7.21 ( Xq @ Xy0 ) ) ) | 52.14/7.21 ( ![Xq:( a > $o )]: 52.14/7.21 ( ( ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 52.14/7.21 ( ![Xu:a,Xv:a]: 52.14/7.21 ( ( ( Xq @ Xu ) & ( S @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) ) => 52.14/7.21 ( Xq @ Xy0 ) ) ) ) => 52.14/7.21 ( ![Xq:( a > $o )]: 52.14/7.21 ( ( ( ![Xw:a]: 52.14/7.21 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => ( Xq @ Xw ) ) ) & 52.14/7.21 ( ![Xu:a,Xv:a]: 52.14/7.21 ( ( ( Xq @ Xu ) & ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 52.14/7.21 ( Xq @ Xv ) ) ) ) => 52.14/7.21 ( Xq @ Xy0 ) ) ) ) ) ) => 52.14/7.21 ( ![Xq:( a > $o )]: 52.14/7.21 ( ( ( ![Xw:a]: 52.14/7.21 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 52.14/7.21 ( ![Xu:a,Xv:a]: 52.14/7.21 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 52.14/7.21 ( Xq @ Xv ) ) ) ) => 52.14/7.21 ( Xq @ Xy ) ) ) ) => 52.14/7.21 ( ![Xq:( a > $o )]: 52.14/7.21 ( ( ( ![Xu:a,Xv:a]: 52.14/7.21 ( ( ( Xq @ Xu ) & ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 52.14/7.21 ( Xq @ Xv ) ) ) & 52.14/7.21 ( ![Xw:a]: 52.14/7.21 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 52.14/7.21 ( Xq @ Xy ) ) ) ))). 52.14/7.21 thf(zf_stmt_0, negated_conjecture, 52.14/7.21 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 52.14/7.21 ( ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 52.14/7.21 ( ( ( ![Xq:( a > $o )]: 52.14/7.21 ( ( ( ![Xw:a]: 52.14/7.21 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 52.14/7.21 ( Xq @ Xw ) ) ) & 52.14/7.21 ( ![Xu:a,Xv:a]: 52.14/7.21 ( ( ( Xq @ Xu ) & 52.14/7.21 ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 52.14/7.21 ( Xq @ Xv ) ) ) ) => 52.14/7.21 ( Xq @ Xy0 ) ) ) & 52.14/7.21 ( ![Xq:( a > $o )]: 52.14/7.21 ( ( ( ![Xw:a]: 52.14/7.21 ( ( ( S @ Xy0 @ Xw ) | ( R @ Xy0 @ Xw ) ) => 52.14/7.21 ( Xq @ Xw ) ) ) & 52.14/7.21 ( ![Xu:a,Xv:a]: 52.14/7.21 ( ( ( Xq @ Xu ) & 52.14/7.21 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 52.14/7.21 ( Xq @ Xv ) ) ) ) => 52.14/7.21 ( Xq @ Xz ) ) ) ) => 52.14/7.21 ( ![Xq:( a > $o )]: 52.14/7.21 ( ( ( ![Xu:a,Xv:a]: 52.14/7.21 ( ( ( Xq @ Xu ) & 52.14/7.21 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 52.14/7.21 ( Xq @ Xv ) ) ) & 52.14/7.21 ( ![Xw:a]: 52.14/7.21 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 52.14/7.21 ( Xq @ Xw ) ) ) ) => 52.14/7.21 ( Xq @ Xz ) ) ) ) ) & 52.14/7.21 ( ![Xx0:a,Xy0:a]: 52.14/7.21 ( ( ( ![Xq:( a > $o )]: 52.14/7.21 ( ( ( ![Xu:a,Xv:a]: 52.14/7.21 ( ( ( Xq @ Xu ) & ( R @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) & 52.14/7.21 ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 52.14/7.21 ( Xq @ Xy0 ) ) ) | 52.14/7.21 ( ![Xq:( a > $o )]: 52.14/7.21 ( ( ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 52.14/7.21 ( ![Xu:a,Xv:a]: 52.14/7.21 ( ( ( Xq @ Xu ) & ( S @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) ) => 52.14/7.21 ( Xq @ Xy0 ) ) ) ) => 52.14/7.21 ( ![Xq:( a > $o )]: 52.14/7.21 ( ( ( ![Xw:a]: 52.14/7.21 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 52.14/7.21 ( Xq @ Xw ) ) ) & 52.14/7.21 ( ![Xu:a,Xv:a]: 52.14/7.21 ( ( ( Xq @ Xu ) & 52.14/7.21 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 52.14/7.21 ( Xq @ Xv ) ) ) ) => 52.14/7.21 ( Xq @ Xy0 ) ) ) ) ) ) => 52.14/7.21 ( ![Xq:( a > $o )]: 52.14/7.21 ( ( ( ![Xw:a]: 52.14/7.21 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 52.14/7.21 ( ![Xu:a,Xv:a]: 52.14/7.21 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 52.14/7.21 ( Xq @ Xv ) ) ) ) => 52.14/7.21 ( Xq @ Xy ) ) ) ) => 52.14/7.21 ( ![Xq:( a > $o )]: 52.14/7.21 ( ( ( ![Xu:a,Xv:a]: 52.14/7.21 ( ( ( Xq @ Xu ) & ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 52.14/7.21 ( Xq @ Xv ) ) ) & 52.14/7.21 ( ![Xw:a]: 52.14/7.21 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 52.14/7.21 ( Xq @ Xy ) ) ) ) )), 52.14/7.21 inference('cnf.neg', [status(esa)], [cTHM251D_pme])). 52.14/7.21 thf(zip_derived_cl0, plain, 52.14/7.21 (~ (((!!) @ (^[Y0 : a > a > $o]: 52.14/7.21 (((!!) @ (^[Y1 : a > a > $o]: 52.14/7.21 (((!!) @ (^[Y2 : a]: 52.14/7.21 (((!!) @ (^[Y3 : a]: 52.14/7.21 (((((((((!!) @ ( 52.14/7.21 ^[Y4 : a]: 52.14/7.21 (((!!) @ ( 52.14/7.21 ^[Y5 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y8 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y1 @ 52.14/7.21 Y4 @ 52.14/7.21 Y8) | 52.14/7.21 (Y0 @ 52.14/7.21 Y4 @ Y8))) => 52.14/7.21 (Y7 @ Y8)))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y8 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y9 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y7 @ 52.14/7.21 Y8) & 52.14/7.21 (( 52.14/7.21 (Y1 @ 52.14/7.21 Y8 @ 52.14/7.21 Y9) | 52.14/7.21 (Y0 @ 52.14/7.21 Y8 @ Y9))))) => 52.14/7.21 (Y7 @ Y9))))))))))) => 52.14/7.21 (Y7 @ Y5)))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y8 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y1 @ 52.14/7.21 Y5 @ 52.14/7.21 Y8) | 52.14/7.21 (Y0 @ 52.14/7.21 Y5 @ Y8))) => 52.14/7.21 (Y7 @ Y8)))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y8 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y9 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y7 @ 52.14/7.21 Y8) & 52.14/7.21 (( 52.14/7.21 (Y0 @ 52.14/7.21 Y8 @ 52.14/7.21 Y9) | 52.14/7.21 (Y1 @ 52.14/7.21 Y8 @ Y9))))) => 52.14/7.21 (Y7 @ Y9))))))))))) => 52.14/7.21 (Y7 @ Y6)))))))) => 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y8 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y9 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y7 @ 52.14/7.21 Y8) & 52.14/7.21 (( 52.14/7.21 (Y0 @ 52.14/7.21 Y8 @ 52.14/7.21 Y9) | 52.14/7.21 (Y1 @ 52.14/7.21 Y8 @ Y9))))) => 52.14/7.21 (Y7 @ Y9))))))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y8 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y0 @ 52.14/7.21 Y4 @ 52.14/7.21 Y8) | 52.14/7.21 (Y1 @ 52.14/7.21 Y4 @ Y8))) => 52.14/7.21 (Y7 @ Y8)))))))) => 52.14/7.21 (Y7 @ Y6))))))))))))))))) & 52.14/7.21 (((!!) @ ( 52.14/7.21 ^[Y4 : a]: 52.14/7.21 (((!!) @ ( 52.14/7.21 ^[Y5 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y8 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y6 @ 52.14/7.21 Y7) & 52.14/7.21 (Y0 @ 52.14/7.21 Y7 @ Y8))) => 52.14/7.21 (Y6 @ Y8))))))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (Y0 @ 52.14/7.21 Y4 @ 52.14/7.21 Y7) => 52.14/7.21 (Y6 @ Y7)))))))) => 52.14/7.21 (Y6 @ Y5)))))) | 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (Y1 @ 52.14/7.21 Y4 @ 52.14/7.21 Y7) => 52.14/7.21 (Y6 @ Y7)))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y8 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y6 @ 52.14/7.21 Y7) & 52.14/7.21 (Y1 @ 52.14/7.21 Y7 @ Y8))) => 52.14/7.21 (Y6 @ Y8))))))))))) => 52.14/7.21 (Y6 @ Y5)))))))) => 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y1 @ 52.14/7.21 Y4 @ 52.14/7.21 Y7) | 52.14/7.21 (Y0 @ 52.14/7.21 Y4 @ Y7))) => 52.14/7.21 (Y6 @ Y7)))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y8 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y6 @ 52.14/7.21 Y7) & 52.14/7.21 (( 52.14/7.21 (Y0 @ 52.14/7.21 Y7 @ 52.14/7.21 Y8) | 52.14/7.21 (Y1 @ 52.14/7.21 Y7 @ Y8))))) => 52.14/7.21 (Y6 @ Y8))))))))))) => 52.14/7.21 (Y6 @ Y5)))))))))))))))) => 52.14/7.21 (((!!) @ ( 52.14/7.21 ^[Y4 : a > $o]: 52.14/7.21 (((((( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y5 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y1 @ 52.14/7.21 Y2 @ 52.14/7.21 Y5) | 52.14/7.21 (Y0 @ 52.14/7.21 Y2 @ Y5))) => 52.14/7.21 (Y4 @ Y5)))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y5 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y1 @ 52.14/7.21 Y5 @ 52.14/7.21 Y6) | 52.14/7.21 (Y0 @ 52.14/7.21 Y5 @ Y6))) & 52.14/7.21 (Y4 @ Y5))) => 52.14/7.21 (Y4 @ Y6))))))))))) => 52.14/7.21 (Y4 @ Y3)))))))) => 52.14/7.21 (((!!) @ (^[Y4 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y5 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y4 @ 52.14/7.21 Y5) & 52.14/7.21 (( 52.14/7.21 (Y0 @ 52.14/7.21 Y5 @ 52.14/7.21 Y6) | 52.14/7.21 (Y1 @ 52.14/7.21 Y5 @ Y6))))) => 52.14/7.21 (Y4 @ Y6))))))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y5 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y1 @ 52.14/7.21 Y2 @ 52.14/7.21 Y5) | 52.14/7.21 (Y0 @ 52.14/7.21 Y2 @ Y5))) => 52.14/7.21 (Y4 @ Y5)))))))) => 52.14/7.21 (Y4 @ Y3))))))))))))))))))))), 52.14/7.21 inference('cnf', [status(esa)], [zf_stmt_0])). 52.14/7.21 thf(zip_derived_cl1, plain, 52.14/7.21 (~ (((!!) @ (^[Y0 : a > a > $o]: 52.14/7.21 (((!!) @ (^[Y1 : a]: 52.14/7.21 (((!!) @ (^[Y2 : a]: 52.14/7.21 (((((((((!!) @ (^[Y3 : a]: 52.14/7.21 (((!!) @ ( 52.14/7.21 ^[Y4 : a]: 52.14/7.21 (((!!) @ ( 52.14/7.21 ^[Y5 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y0 @ 52.14/7.21 Y3 @ 52.14/7.21 Y7) | 52.14/7.21 ('#sk1' @ 52.14/7.21 Y3 @ Y7))) => 52.14/7.21 (Y6 @ Y7)))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y8 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y6 @ 52.14/7.21 Y7) & 52.14/7.21 (( 52.14/7.21 (Y0 @ 52.14/7.21 Y7 @ 52.14/7.21 Y8) | 52.14/7.21 ('#sk1' @ 52.14/7.21 Y7 @ Y8))))) => 52.14/7.21 (Y6 @ Y8))))))))))) => 52.14/7.21 (Y6 @ Y4)))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y0 @ 52.14/7.21 Y4 @ 52.14/7.21 Y7) | 52.14/7.21 ('#sk1' @ 52.14/7.21 Y4 @ Y7))) => 52.14/7.21 (Y6 @ Y7)))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y8 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y6 @ 52.14/7.21 Y7) & 52.14/7.21 (( 52.14/7.21 ('#sk1' @ 52.14/7.21 Y7 @ 52.14/7.21 Y8) | 52.14/7.21 (Y0 @ 52.14/7.21 Y7 @ Y8))))) => 52.14/7.21 (Y6 @ Y8))))))))))) => 52.14/7.21 (Y6 @ Y5)))))))) => 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y8 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y6 @ 52.14/7.21 Y7) & 52.14/7.21 (( 52.14/7.21 ('#sk1' @ 52.14/7.21 Y7 @ 52.14/7.21 Y8) | 52.14/7.21 (Y0 @ 52.14/7.21 Y7 @ Y8))))) => 52.14/7.21 (Y6 @ Y8))))))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 ('#sk1' @ 52.14/7.21 Y3 @ 52.14/7.21 Y7) | 52.14/7.21 (Y0 @ 52.14/7.21 Y3 @ Y7))) => 52.14/7.21 (Y6 @ Y7)))))))) => 52.14/7.21 (Y6 @ Y5))))))))))))))))) & 52.14/7.21 (((!!) @ (^[Y3 : a]: 52.14/7.21 (((!!) @ ( 52.14/7.21 ^[Y4 : a]: 52.14/7.21 (((( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y5 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y5 @ 52.14/7.21 Y6) & 52.14/7.21 ('#sk1' @ 52.14/7.21 Y6 @ Y7))) => 52.14/7.21 (Y5 @ Y7))))))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 ('#sk1' @ 52.14/7.21 Y3 @ 52.14/7.21 Y6) => 52.14/7.21 (Y5 @ Y6)))))))) => 52.14/7.21 (Y5 @ Y4)))))) | 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y5 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 (Y0 @ 52.14/7.21 Y3 @ 52.14/7.21 Y6) => 52.14/7.21 (Y5 @ Y6)))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y5 @ 52.14/7.21 Y6) & 52.14/7.21 (Y0 @ 52.14/7.21 Y6 @ Y7))) => 52.14/7.21 (Y5 @ Y7))))))))))) => 52.14/7.21 (Y5 @ Y4)))))))) => 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y5 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y0 @ 52.14/7.21 Y3 @ 52.14/7.21 Y6) | 52.14/7.21 ('#sk1' @ 52.14/7.21 Y3 @ Y6))) => 52.14/7.21 (Y5 @ Y6)))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y5 @ 52.14/7.21 Y6) & 52.14/7.21 (( 52.14/7.21 ('#sk1' @ 52.14/7.21 Y6 @ 52.14/7.21 Y7) | 52.14/7.21 (Y0 @ 52.14/7.21 Y6 @ Y7))))) => 52.14/7.21 (Y5 @ Y7))))))))))) => 52.14/7.21 (Y5 @ Y4)))))))))))))))) => 52.14/7.21 (((!!) @ (^[Y3 : a > $o]: 52.14/7.21 (((((((!!) @ ( 52.14/7.21 ^[Y4 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y0 @ 52.14/7.21 Y1 @ 52.14/7.21 Y4) | 52.14/7.21 ('#sk1' @ 52.14/7.21 Y1 @ Y4))) => 52.14/7.21 (Y3 @ Y4)))))) & 52.14/7.21 (((!!) @ ( 52.14/7.21 ^[Y4 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y5 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y0 @ 52.14/7.21 Y4 @ 52.14/7.21 Y5) | 52.14/7.21 ('#sk1' @ 52.14/7.21 Y4 @ Y5))) & 52.14/7.21 (Y3 @ Y4))) => 52.14/7.21 (Y3 @ Y5))))))))))) => 52.14/7.21 (Y3 @ Y2)))))))) => 52.14/7.21 (((!!) @ (^[Y3 : a > $o]: 52.14/7.21 (((((((!!) @ ( 52.14/7.21 ^[Y4 : a]: 52.14/7.21 (((!!) @ ( 52.14/7.21 ^[Y5 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y3 @ 52.14/7.21 Y4) & 52.14/7.21 (( 52.14/7.21 ('#sk1' @ 52.14/7.21 Y4 @ 52.14/7.21 Y5) | 52.14/7.21 (Y0 @ 52.14/7.21 Y4 @ Y5))))) => 52.14/7.21 (Y3 @ Y5))))))))) & 52.14/7.21 (((!!) @ ( 52.14/7.21 ^[Y4 : a]: 52.14/7.21 (((( 52.14/7.21 (Y0 @ 52.14/7.21 Y1 @ Y4) | 52.14/7.21 ('#sk1' @ 52.14/7.21 Y1 @ Y4))) => 52.14/7.21 (Y3 @ Y4)))))))) => 52.14/7.21 (Y3 @ Y2)))))))))))))))))), 52.14/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 52.14/7.21 thf(zip_derived_cl2, plain, 52.14/7.21 (~ (((!!) @ (^[Y0 : a]: 52.14/7.21 (((!!) @ (^[Y1 : a]: 52.14/7.21 (((((((((!!) @ (^[Y2 : a]: 52.14/7.21 (((!!) @ (^[Y3 : a]: 52.14/7.21 (((!!) @ ( 52.14/7.21 ^[Y4 : a]: 52.14/7.21 (((( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y5 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 ('#sk2' @ 52.14/7.21 Y2 @ 52.14/7.21 Y6) | 52.14/7.21 ('#sk1' @ 52.14/7.21 Y2 @ Y6))) => 52.14/7.21 (Y5 @ Y6)))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y5 @ 52.14/7.21 Y6) & 52.14/7.21 (( 52.14/7.21 ('#sk2' @ 52.14/7.21 Y6 @ 52.14/7.21 Y7) | 52.14/7.21 ('#sk1' @ 52.14/7.21 Y6 @ Y7))))) => 52.14/7.21 (Y5 @ Y7))))))))))) => 52.14/7.21 (Y5 @ Y3)))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y5 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 ('#sk2' @ 52.14/7.21 Y3 @ 52.14/7.21 Y6) | 52.14/7.21 ('#sk1' @ 52.14/7.21 Y3 @ Y6))) => 52.14/7.21 (Y5 @ Y6)))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y5 @ 52.14/7.21 Y6) & 52.14/7.21 (( 52.14/7.21 ('#sk1' @ 52.14/7.21 Y6 @ 52.14/7.21 Y7) | 52.14/7.21 ('#sk2' @ 52.14/7.21 Y6 @ Y7))))) => 52.14/7.21 (Y5 @ Y7))))))))))) => 52.14/7.21 (Y5 @ Y4)))))))) => 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y5 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y7 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y5 @ 52.14/7.21 Y6) & 52.14/7.21 (( 52.14/7.21 ('#sk1' @ 52.14/7.21 Y6 @ 52.14/7.21 Y7) | 52.14/7.21 ('#sk2' @ 52.14/7.21 Y6 @ Y7))))) => 52.14/7.21 (Y5 @ Y7))))))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 ('#sk1' @ 52.14/7.21 Y2 @ 52.14/7.21 Y6) | 52.14/7.21 ('#sk2' @ 52.14/7.21 Y2 @ Y6))) => 52.14/7.21 (Y5 @ Y6)))))))) => 52.14/7.21 (Y5 @ Y4))))))))))))))))) & 52.14/7.21 (((!!) @ (^[Y2 : a]: 52.14/7.21 (((!!) @ (^[Y3 : a]: 52.14/7.21 (((((((!!) @ ( 52.14/7.21 ^[Y4 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y5 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y4 @ 52.14/7.21 Y5) & 52.14/7.21 ('#sk1' @ 52.14/7.21 Y5 @ Y6))) => 52.14/7.21 (Y4 @ Y6))))))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y5 : a]: 52.14/7.21 (( 52.14/7.21 ('#sk1' @ 52.14/7.21 Y2 @ 52.14/7.21 Y5) => 52.14/7.21 (Y4 @ Y5)))))))) => 52.14/7.21 (Y4 @ Y3)))))) | 52.14/7.21 (((!!) @ ( 52.14/7.21 ^[Y4 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y5 : a]: 52.14/7.21 (( 52.14/7.21 ('#sk2' @ 52.14/7.21 Y2 @ 52.14/7.21 Y5) => 52.14/7.21 (Y4 @ Y5)))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y5 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y4 @ 52.14/7.21 Y5) & 52.14/7.21 ('#sk2' @ 52.14/7.21 Y5 @ Y6))) => 52.14/7.21 (Y4 @ Y6))))))))))) => 52.14/7.21 (Y4 @ Y3)))))))) => 52.14/7.21 (((!!) @ ( 52.14/7.21 ^[Y4 : a > $o]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y5 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 ('#sk2' @ 52.14/7.21 Y2 @ 52.14/7.21 Y5) | 52.14/7.21 ('#sk1' @ 52.14/7.21 Y2 @ Y5))) => 52.14/7.21 (Y4 @ Y5)))))) & 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y5 : a]: 52.14/7.21 (( 52.14/7.21 (!!) @ ( 52.14/7.21 ^[Y6 : a]: 52.14/7.21 (( 52.14/7.21 (( 52.14/7.21 (Y4 @ 52.14/7.21 Y5) & 52.14/7.21 (( 52.14/7.21 ('#sk1' @ 52.14/7.21 Y5 @ 52.14/7.21 Y6) | 52.14/7.21 ('#sk2' @ 52.14/7.21 Y5 @ 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(Y1 @ '#sk7')))))) & 52.14/7.22 (((!!) @ (^[Y1 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y2 : a]: 52.14/7.22 ((((('#sk2' @ '#sk7' @ 52.14/7.22 Y2) | ('#sk1' @ 52.14/7.22 '#sk7' @ Y2))) => 52.14/7.22 (Y1 @ Y2)))))) & 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((((Y1 @ 52.14/7.22 Y2) & 52.14/7.22 (( 52.14/7.22 ('#sk1' @ 52.14/7.22 Y2 @ 52.14/7.22 Y3) | 52.14/7.22 ('#sk2' @ 52.14/7.22 Y2 @ Y3))))) => 52.14/7.22 (Y1 @ Y3))))))))))) => 52.14/7.22 (Y1 @ Y0)))))))) => 52.14/7.22 (((!!) @ (^[Y1 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y2 : a]: 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((((Y1 @ Y2) & 52.14/7.22 ((('#sk1' @ 52.14/7.22 Y2 @ 52.14/7.22 Y3) | 52.14/7.22 ('#sk2' @ 52.14/7.22 Y2 @ Y3))))) => 52.14/7.22 (Y1 @ Y3))))))))) & 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 ((((('#sk1' @ '#sk6' @ 52.14/7.22 Y2) | ('#sk2' @ 52.14/7.22 '#sk6' @ Y2))) => 52.14/7.22 (Y1 @ Y2)))))))) => 52.14/7.22 (Y1 @ Y0))))))))))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk1' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))))) => 52.14/7.22 (Y2 @ Y1)))))) | 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))) => 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) | 52.14/7.22 ('#sk1' @ 52.14/7.22 Y0 @ Y3))) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 ( 52.14/7.22 ( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 (( 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ 52.14/7.22 Y4) | 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))))))))) 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk3' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 ((((((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))) & 52.14/7.22 (Y0 @ Y1))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk4')))))))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 52.14/7.22 thf(zip_derived_cl18, plain, 52.14/7.22 ((~ (((((((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk6' @ Y1) | 52.14/7.22 ('#sk1' @ '#sk6' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk2' @ Y1 @ 52.14/7.22 Y2) | ('#sk1' @ 52.14/7.22 Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk7')))))) & 52.14/7.22 (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk7' @ Y1) | 52.14/7.22 ('#sk1' @ '#sk7' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk1' @ Y1 @ 52.14/7.22 Y2) | ('#sk2' @ 52.14/7.22 Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk8')))))))) => 52.14/7.22 (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk1' @ Y1 @ Y2) | 52.14/7.22 ('#sk2' @ Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk1' @ '#sk6' @ Y1) | ('#sk2' @ 52.14/7.22 '#sk6' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))))) => 52.14/7.22 (Y0 @ '#sk8')))))))) 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk3' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 ((((((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))) & 52.14/7.22 (Y0 @ Y1))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk4')))))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk1' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))))) => 52.14/7.22 (Y2 @ Y1)))))) | 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))) => 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) | 52.14/7.22 ('#sk1' @ 52.14/7.22 Y0 @ Y3))) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 ( 52.14/7.22 ( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 (( 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ 52.14/7.22 Y4) | 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))))))))))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])). 52.14/7.22 thf(zip_derived_cl22, plain, 52.14/7.22 ((~ (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk1' @ Y1 @ Y2) | 52.14/7.22 ('#sk2' @ Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk1' @ '#sk6' @ Y1) | ('#sk2' @ 52.14/7.22 '#sk6' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))))) => 52.14/7.22 (Y0 @ '#sk8')))))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk1' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))))) => 52.14/7.22 (Y2 @ Y1)))))) | 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))) => 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) | 52.14/7.22 ('#sk1' @ 52.14/7.22 Y0 @ Y3))) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 ( 52.14/7.22 ( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 (( 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ 52.14/7.22 Y4) | 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))))))))) 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk3' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 ((((((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))) & 52.14/7.22 (Y0 @ Y1))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk4')))))))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 52.14/7.22 thf(zip_derived_cl22, plain, 52.14/7.22 ((~ (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk1' @ Y1 @ Y2) | 52.14/7.22 ('#sk2' @ Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk1' @ '#sk6' @ Y1) | ('#sk2' @ 52.14/7.22 '#sk6' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))))) => 52.14/7.22 (Y0 @ '#sk8')))))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk1' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))))) => 52.14/7.22 (Y2 @ Y1)))))) | 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))) => 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) | 52.14/7.22 ('#sk1' @ 52.14/7.22 Y0 @ Y3))) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 ( 52.14/7.22 ( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 (( 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ 52.14/7.22 Y4) | 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))))))))) 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk3' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 ((((((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))) & 52.14/7.22 (Y0 @ Y1))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk4')))))))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 52.14/7.22 thf(zip_derived_cl28, plain, 52.14/7.22 (( ('#form9') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk1' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))))) => 52.14/7.22 (Y2 @ Y1)))))) | 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))) => 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) | 52.14/7.22 ('#sk1' @ 52.14/7.22 Y0 @ Y3))) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 ( 52.14/7.22 ( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 (( 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ 52.14/7.22 Y4) | 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))))))))))), 52.14/7.22 define([status(thm)])). 52.14/7.22 thf(zip_derived_cl30, plain, 52.14/7.22 ((~ ('#form9') 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk3' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 ((((((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))) & 52.14/7.22 (Y0 @ Y1))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk4')))))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk1' @ Y1 @ Y2) | 52.14/7.22 ('#sk2' @ Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk1' @ '#sk6' @ Y1) | ('#sk2' @ 52.14/7.22 '#sk6' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))))) => 52.14/7.22 (Y0 @ '#sk8')))))))), 52.14/7.22 inference('renaming', [status(thm)], [zip_derived_cl22, zip_derived_cl28])). 52.14/7.22 thf(zip_derived_cl21, plain, 52.14/7.22 (( (((((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk6' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk7')))))) & 52.14/7.22 (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk7' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk7' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk1' @ Y1 @ Y2) | 52.14/7.22 ('#sk2' @ Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk8')))))))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk1' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))))) => 52.14/7.22 (Y2 @ Y1)))))) | 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))) => 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) | 52.14/7.22 ('#sk1' @ 52.14/7.22 Y0 @ Y3))) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 ( 52.14/7.22 ( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 (( 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ 52.14/7.22 Y4) | 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))))))))) 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk3' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 ((((((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))) & 52.14/7.22 (Y0 @ Y1))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk4')))))))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 52.14/7.22 thf(zip_derived_cl26, plain, 52.14/7.22 (( (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk6' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk7')))))) 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk3' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 ((((((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))) & 52.14/7.22 (Y0 @ Y1))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk4')))))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk1' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))))) => 52.14/7.22 (Y2 @ Y1)))))) | 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))) => 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) | 52.14/7.22 ('#sk1' @ 52.14/7.22 Y0 @ Y3))) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 ( 52.14/7.22 ( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 (( 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ 52.14/7.22 Y4) | 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))))))))))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 52.14/7.22 thf(zip_derived_cl32, plain, 52.14/7.22 ((~ ('#form11') 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk3' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 ((((((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))) & 52.14/7.22 (Y0 @ Y1))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk4')))))))), 52.14/7.22 define([status(thm)])). 52.14/7.22 thf(zip_derived_cl37, plain, 52.14/7.22 (( ('#form11') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk1' @ Y1 @ Y2) | 52.14/7.22 ('#sk2' @ Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk1' @ '#sk6' @ Y1) | ('#sk2' @ 52.14/7.22 '#sk6' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))))) => 52.14/7.22 (Y0 @ '#sk8')))))) 52.14/7.22 | ~ ('#form9'))), 52.14/7.22 inference('renaming', [status(thm)], [zip_derived_cl30, zip_derived_cl32])). 52.14/7.22 thf(zip_derived_cl45, plain, 52.14/7.22 ((~ (((((((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk16' @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 52.14/7.22 Y0 @ Y1))))) => 52.14/7.22 ('#sk16' @ Y1))))))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 52.14/7.22 ('#sk16' @ Y0)))))))) => 52.14/7.22 ('#sk16' @ '#sk8'))) 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl37])). 52.14/7.22 thf(zip_derived_cl55, plain, 52.14/7.22 (( (((((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk16' @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.14/7.22 Y1))))) => 52.14/7.22 ('#sk16' @ Y1))))))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 52.14/7.22 ('#sk16' @ Y0)))))))) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 52.14/7.22 thf(zip_derived_cl66, plain, 52.14/7.22 (( (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk1' @ '#sk6' @ Y0) | ('#sk2' @ '#sk6' @ Y0))) => 52.14/7.22 ('#sk16' @ Y0)))))) 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 52.14/7.22 thf(zip_derived_cl78, plain, 52.14/7.22 (![X2 : a]: 52.14/7.22 ( ((((('#sk1' @ '#sk6' @ X2) | ('#sk2' @ '#sk6' @ X2))) => ('#sk16' @ 52.14/7.22 X2))) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9'))), 52.14/7.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl66])). 52.14/7.22 thf(zip_derived_cl92, plain, 52.14/7.22 (![X2 : a]: 52.14/7.22 (~ ((('#sk1' @ '#sk6' @ X2) | ('#sk2' @ '#sk6' @ X2))) 52.14/7.22 | ('#sk16' @ X2) 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 52.14/7.22 thf(zip_derived_cl104, plain, 52.14/7.22 (![X2 : a]: 52.14/7.22 (~ ('#sk1' @ '#sk6' @ X2) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#sk16' @ X2))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl92])). 52.14/7.22 thf(zip_derived_cl26, plain, 52.14/7.22 (( (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk6' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk7')))))) 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk3' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 ((((((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))) & 52.14/7.22 (Y0 @ Y1))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk4')))))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk1' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))))) => 52.14/7.22 (Y2 @ Y1)))))) | 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))) => 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) | 52.14/7.22 ('#sk1' @ 52.14/7.22 Y0 @ Y3))) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 ( 52.14/7.22 ( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 (( 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ 52.14/7.22 Y4) | 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))))))))))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 52.14/7.22 thf(zip_derived_cl32, plain, 52.14/7.22 ((~ ('#form11') 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk3' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 ((((((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))) & 52.14/7.22 (Y0 @ Y1))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk4')))))))), 52.14/7.22 define([status(thm)])). 52.14/7.22 thf(zip_derived_cl35, plain, 52.14/7.22 (( ('#form11') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk1' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))))) => 52.14/7.22 (Y2 @ Y1)))))) | 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))) => 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) | 52.14/7.22 ('#sk1' @ 52.14/7.22 Y0 @ Y3))) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 ( 52.14/7.22 ( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 (( 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ 52.14/7.22 Y4) | 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))))))))) 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk6' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk7')))))))), 52.14/7.22 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl32])). 52.14/7.22 thf(zip_derived_cl28, plain, 52.14/7.22 (( ('#form9') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk1' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))))) => 52.14/7.22 (Y2 @ Y1)))))) | 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))) => 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) | 52.14/7.22 ('#sk1' @ 52.14/7.22 Y0 @ Y3))) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 ( 52.14/7.22 ( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 (( 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ 52.14/7.22 Y4) | 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))))))))))), 52.14/7.22 define([status(thm)])). 52.14/7.22 thf(zip_derived_cl41, plain, 52.14/7.22 ((~ ('#form9') 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk6' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk7')))))) 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('renaming', [status(thm)], [zip_derived_cl35, zip_derived_cl28])). 52.14/7.22 thf(zip_derived_cl48, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( (((((((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 52.14/7.22 (X2 @ Y0)))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & 52.14/7.22 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.14/7.22 Y0 @ Y1))))) => 52.14/7.22 (X2 @ Y1))))))))))) => 52.14/7.22 (X2 @ '#sk7'))) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9'))), 52.14/7.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 52.14/7.22 thf(zip_derived_cl62, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 52.14/7.22 (X2 @ Y0)))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & 52.14/7.22 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.14/7.22 Y0 @ Y1))))) => 52.14/7.22 (X2 @ Y1))))))))))) 52.14/7.22 | (X2 @ '#sk7') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 52.14/7.22 thf(zip_derived_cl73, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 52.14/7.22 (X2 @ Y0)))))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & 52.14/7.22 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.14/7.22 Y0 @ Y1))))) => 52.14/7.22 (X2 @ Y1))))))))) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | (X2 @ '#sk7'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl62])). 52.14/7.22 thf(zip_derived_cl87, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ ((((('#sk2' @ '#sk6' @ ('#sk49' @ X2)) | ('#sk1' @ '#sk6' @ 52.14/7.22 ('#sk49' @ X2)))) => 52.14/7.22 (X2 @ ('#sk49' @ X2)))) 52.14/7.22 | (X2 @ '#sk7') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & 52.14/7.22 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.14/7.22 Y0 @ Y1))))) => 52.14/7.22 (X2 @ Y1))))))))))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl73])). 52.14/7.22 thf(zip_derived_cl97, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ((('#sk2' @ '#sk6' @ ('#sk49' @ X2)) | ('#sk1' @ '#sk6' @ 52.14/7.22 ('#sk49' @ X2)))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & 52.14/7.22 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.14/7.22 Y0 @ Y1))))) => 52.14/7.22 (X2 @ Y1))))))))) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | (X2 @ '#sk7'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl87])). 52.14/7.22 thf(zip_derived_cl110, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ('#sk2' @ '#sk6' @ ('#sk49' @ X2)) 52.14/7.22 | ('#sk1' @ '#sk6' @ ('#sk49' @ X2)) 52.14/7.22 | (X2 @ '#sk7') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & 52.14/7.22 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.14/7.22 Y0 @ Y1))))) => 52.14/7.22 (X2 @ Y1))))))))))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl97])). 52.14/7.22 thf(zip_derived_cl123, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((((X2 @ ('#sk101' @ X2)) & 52.14/7.22 ((('#sk2' @ ('#sk101' @ X2) @ Y0) | ('#sk1' @ 52.14/7.22 ('#sk101' @ X2) @ Y0))))) => 52.14/7.22 (X2 @ Y0)))))) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | (X2 @ '#sk7') 52.14/7.22 | ('#sk1' @ '#sk6' @ ('#sk49' @ X2)) 52.14/7.22 | ('#sk2' @ '#sk6' @ ('#sk49' @ X2)))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl110])). 52.14/7.22 thf(zip_derived_cl137, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((((X2 @ ('#sk101' @ X2)) & 52.14/7.22 ((('#sk2' @ ('#sk101' @ X2) @ ('#sk140' @ X2)) | ('#sk1' @ 52.14/7.22 ('#sk101' @ X2) @ ('#sk140' @ X2)))))) => 52.14/7.22 (X2 @ ('#sk140' @ X2)))) 52.14/7.22 | ('#sk2' @ '#sk6' @ ('#sk49' @ X2)) 52.14/7.22 | ('#sk1' @ '#sk6' @ ('#sk49' @ X2)) 52.14/7.22 | (X2 @ '#sk7') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl123])). 52.14/7.22 thf(zip_derived_cl153, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (X2 @ ('#sk140' @ X2)) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | (X2 @ '#sk7') 52.14/7.22 | ('#sk1' @ '#sk6' @ ('#sk49' @ X2)) 52.14/7.22 | ('#sk2' @ '#sk6' @ ('#sk49' @ X2)))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])). 52.14/7.22 thf(zip_derived_cl152, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( (((X2 @ ('#sk101' @ X2)) & 52.14/7.22 ((('#sk2' @ ('#sk101' @ X2) @ ('#sk140' @ X2)) | ('#sk1' @ 52.14/7.22 ('#sk101' @ X2) @ ('#sk140' @ X2)))))) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | (X2 @ '#sk7') 52.14/7.22 | ('#sk1' @ '#sk6' @ ('#sk49' @ X2)) 52.14/7.22 | ('#sk2' @ '#sk6' @ ('#sk49' @ X2)))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])). 52.14/7.22 thf(zip_derived_cl168, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( (X2 @ ('#sk101' @ X2)) 52.14/7.22 | ('#sk2' @ '#sk6' @ ('#sk49' @ X2)) 52.14/7.22 | ('#sk1' @ '#sk6' @ ('#sk49' @ X2)) 52.14/7.22 | (X2 @ '#sk7') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl152])). 52.14/7.22 thf(zip_derived_cl169, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ((('#sk2' @ ('#sk101' @ X2) @ ('#sk140' @ X2)) | ('#sk1' @ 52.14/7.22 ('#sk101' @ X2) @ ('#sk140' @ X2)))) 52.14/7.22 | ('#sk2' @ '#sk6' @ ('#sk49' @ X2)) 52.14/7.22 | ('#sk1' @ '#sk6' @ ('#sk49' @ X2)) 52.14/7.22 | (X2 @ '#sk7') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl152])). 52.14/7.22 thf(zip_derived_cl182, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ('#sk2' @ ('#sk101' @ X2) @ ('#sk140' @ X2)) 52.14/7.22 | ('#sk1' @ ('#sk101' @ X2) @ ('#sk140' @ X2)) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | (X2 @ '#sk7') 52.14/7.22 | ('#sk1' @ '#sk6' @ ('#sk49' @ X2)) 52.14/7.22 | ('#sk2' @ '#sk6' @ ('#sk49' @ X2)))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl169])). 52.14/7.22 thf(zip_derived_cl98, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (X2 @ ('#sk49' @ X2)) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & 52.14/7.22 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.14/7.22 Y0 @ Y1))))) => 52.14/7.22 (X2 @ Y1))))))))) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | (X2 @ '#sk7'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl87])). 52.14/7.22 thf(zip_derived_cl111, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((((X2 @ ('#sk101' @ X2)) & 52.14/7.22 ((('#sk2' @ ('#sk101' @ X2) @ Y0) | ('#sk1' @ 52.14/7.22 ('#sk101' @ X2) @ Y0))))) => 52.14/7.22 (X2 @ Y0)))))) 52.14/7.22 | (X2 @ '#sk7') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11') 52.14/7.22 | ~ (X2 @ ('#sk49' @ X2)))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl98])). 52.14/7.22 thf(zip_derived_cl124, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((((X2 @ ('#sk101' @ X2)) & 52.14/7.22 ((('#sk2' @ ('#sk101' @ X2) @ ('#sk140' @ X2)) | ('#sk1' @ 52.14/7.22 ('#sk101' @ X2) @ ('#sk140' @ X2)))))) => 52.14/7.22 (X2 @ ('#sk140' @ X2)))) 52.14/7.22 | ~ (X2 @ ('#sk49' @ X2)) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | (X2 @ '#sk7'))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl111])). 52.14/7.22 thf(zip_derived_cl139, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (X2 @ ('#sk140' @ X2)) 52.14/7.22 | (X2 @ '#sk7') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11') 52.14/7.22 | ~ (X2 @ ('#sk49' @ X2)))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl124])). 52.14/7.22 thf(zip_derived_cl138, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( (((X2 @ ('#sk101' @ X2)) & 52.14/7.22 ((('#sk2' @ ('#sk101' @ X2) @ ('#sk140' @ X2)) | ('#sk1' @ 52.14/7.22 ('#sk101' @ X2) @ ('#sk140' @ X2)))))) 52.14/7.22 | (X2 @ '#sk7') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11') 52.14/7.22 | ~ (X2 @ ('#sk49' @ X2)))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl124])). 52.14/7.22 thf(zip_derived_cl154, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( (X2 @ ('#sk101' @ X2)) 52.14/7.22 | ~ (X2 @ ('#sk49' @ X2)) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | (X2 @ '#sk7'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl138])). 52.14/7.22 thf(zip_derived_cl105, plain, 52.14/7.22 (![X2 : a]: 52.14/7.22 (~ ('#sk2' @ '#sk6' @ X2) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#sk16' @ X2))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl92])). 52.14/7.22 thf(zip_derived_cl155, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ((('#sk2' @ ('#sk101' @ X2) @ ('#sk140' @ X2)) | ('#sk1' @ 52.14/7.22 ('#sk101' @ X2) @ ('#sk140' @ X2)))) 52.14/7.22 | ~ (X2 @ ('#sk49' @ X2)) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | (X2 @ '#sk7'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl138])). 52.14/7.22 thf(zip_derived_cl170, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ('#sk2' @ ('#sk101' @ X2) @ ('#sk140' @ X2)) 52.14/7.22 | ('#sk1' @ ('#sk101' @ X2) @ ('#sk140' @ X2)) 52.14/7.22 | (X2 @ '#sk7') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11') 52.14/7.22 | ~ (X2 @ ('#sk49' @ X2)))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl155])). 52.14/7.22 thf(zip_derived_cl28, plain, 52.14/7.22 (( ('#form9') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk1' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))))) => 52.14/7.22 (Y2 @ Y1)))))) | 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))) => 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) | 52.14/7.22 ('#sk1' @ 52.14/7.22 Y0 @ Y3))) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 ( 52.14/7.22 ( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 (( 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ 52.14/7.22 Y4) | 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))))))))))), 52.14/7.22 define([status(thm)])). 52.14/7.22 thf(zip_derived_cl29, plain, 52.14/7.22 ((~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((((((!!) @ (^[Y1 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y2 : a]: 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((((Y1 @ 52.14/7.22 Y2) & 52.14/7.22 ('#sk1' @ 52.14/7.22 Y2 @ Y3))) => 52.14/7.22 (Y1 @ Y3))))))))) & 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 ((('#sk1' @ '#sk10' @ 52.14/7.22 Y2) => (Y1 @ Y2)))))))) => 52.14/7.22 (Y1 @ Y0)))))) | 52.14/7.22 (((!!) @ (^[Y1 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y2 : a]: 52.14/7.22 ((('#sk2' @ '#sk10' @ 52.14/7.22 Y2) => (Y1 @ Y2)))))) & 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((((Y1 @ 52.14/7.22 Y2) & 52.14/7.22 ('#sk2' @ 52.14/7.22 Y2 @ Y3))) => 52.14/7.22 (Y1 @ Y3))))))))))) => 52.14/7.22 (Y1 @ Y0)))))))) => 52.14/7.22 (((!!) @ (^[Y1 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y2 : a]: 52.14/7.22 ((((('#sk2' @ '#sk10' @ 52.14/7.22 Y2) | ('#sk1' @ 52.14/7.22 '#sk10' @ Y2))) => 52.14/7.22 (Y1 @ Y2)))))) & 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((((Y1 @ Y2) & 52.14/7.22 ((('#sk1' @ 52.14/7.22 Y2 @ 52.14/7.22 Y3) | 52.14/7.22 ('#sk2' @ 52.14/7.22 Y2 @ Y3))))) => 52.14/7.22 (Y1 @ Y3))))))))))) => 52.14/7.22 (Y1 @ Y0))))))))))) 52.14/7.22 | ('#form9'))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl28])). 52.14/7.22 thf(zip_derived_cl38, plain, 52.14/7.22 ((~ (((((((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ('#sk1' @ Y1 @ Y2))) => 52.14/7.22 (Y0 @ Y2))))))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ 52.14/7.22 Y1)))))))) => 52.14/7.22 (Y0 @ '#sk12')))))) | 52.14/7.22 (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ 52.14/7.22 Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ('#sk2' @ Y1 @ Y2))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk12')))))))) => 52.14/7.22 (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk10' @ Y1) | 52.14/7.22 ('#sk1' @ '#sk10' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk1' @ Y1 @ Y2) | 52.14/7.22 ('#sk2' @ Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk12')))))))) 52.14/7.22 | ('#form9'))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl29])). 52.14/7.22 thf(zip_derived_cl46, plain, 52.14/7.22 (( (((((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & ('#sk1' @ 52.14/7.22 Y1 @ Y2))) => 52.14/7.22 (Y0 @ Y2))))))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))))) => 52.14/7.22 (Y0 @ '#sk12')))))) | 52.14/7.22 (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & ('#sk2' @ 52.14/7.22 Y1 @ Y2))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk12')))))))) 52.14/7.22 | ('#form9'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 52.14/7.22 thf(zip_derived_cl57, plain, 52.14/7.22 (( (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & ('#sk1' @ 52.14/7.22 Y1 @ Y2))) => 52.14/7.22 (Y0 @ Y2))))))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))))) => 52.14/7.22 (Y0 @ '#sk12')))))) 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & ('#sk2' @ 52.14/7.22 Y1 @ Y2))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk12')))))) 52.14/7.22 | ('#form9'))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl46])). 52.14/7.22 thf(zip_derived_cl67, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( (((((((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.14/7.22 (X2 @ Y1))))))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 52.14/7.22 (X2 @ '#sk12'))) 52.14/7.22 | ('#form9') 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & ('#sk2' @ 52.14/7.22 Y1 @ Y2))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk12')))))))), 52.14/7.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 52.14/7.22 thf(zip_derived_cl79, plain, 52.14/7.22 ((~ ('#form45') 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & ('#sk2' @ 52.14/7.22 Y1 @ Y2))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk12')))))))), 52.14/7.22 define([status(thm)])). 52.14/7.22 thf(zip_derived_cl80, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( (((((((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.14/7.22 (X2 @ Y1))))))))))) => 52.14/7.22 (X2 @ '#sk12'))) 52.14/7.22 | ~ ('#form45'))), 52.14/7.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl79])). 52.14/7.22 thf(zip_derived_cl94, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.14/7.22 (X2 @ Y1))))))))))) 52.14/7.22 | (X2 @ '#sk12') 52.14/7.22 | ~ ('#form45'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])). 52.14/7.22 thf(zip_derived_cl107, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.14/7.22 (X2 @ Y1))))))))) 52.14/7.22 | ~ ('#form45') 52.14/7.22 | (X2 @ '#sk12'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl94])). 52.14/7.22 thf(zip_derived_cl119, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ ((('#sk2' @ '#sk10' @ ('#sk130' @ X2)) => (X2 @ ('#sk130' @ X2)))) 52.14/7.22 | (X2 @ '#sk12') 52.14/7.22 | ~ ('#form45') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.14/7.22 (X2 @ Y1))))))))))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl107])). 52.14/7.22 thf(zip_derived_cl134, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ('#sk2' @ '#sk10' @ ('#sk130' @ X2)) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.14/7.22 (X2 @ Y1))))))))) 52.14/7.22 | ~ ('#form45') 52.14/7.22 | (X2 @ '#sk12'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl119])). 52.14/7.22 thf(zip_derived_cl148, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((((X2 @ ('#sk227' @ X2)) & ('#sk2' @ 52.14/7.22 ('#sk227' @ X2) @ Y0))) => 52.14/7.22 (X2 @ Y0)))))) 52.14/7.22 | (X2 @ '#sk12') 52.14/7.22 | ~ ('#form45') 52.14/7.22 | ('#sk2' @ '#sk10' @ ('#sk130' @ X2)))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl134])). 52.14/7.22 thf(zip_derived_cl166, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((((X2 @ ('#sk227' @ X2)) & ('#sk2' @ ('#sk227' @ X2) @ 52.14/7.22 ('#sk289' @ X2)))) => 52.14/7.22 (X2 @ ('#sk289' @ X2)))) 52.14/7.22 | ('#sk2' @ '#sk10' @ ('#sk130' @ X2)) 52.14/7.22 | ~ ('#form45') 52.14/7.22 | (X2 @ '#sk12'))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl148])). 52.14/7.22 thf(zip_derived_cl178, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( (((X2 @ ('#sk227' @ X2)) & ('#sk2' @ ('#sk227' @ X2) @ 52.14/7.22 ('#sk289' @ X2)))) 52.14/7.22 | (X2 @ '#sk12') 52.14/7.22 | ~ ('#form45') 52.14/7.22 | ('#sk2' @ '#sk10' @ ('#sk130' @ X2)))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl166])). 52.14/7.22 thf(zip_derived_cl186, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( (X2 @ ('#sk227' @ X2)) 52.14/7.22 | ('#sk2' @ '#sk10' @ ('#sk130' @ X2)) 52.14/7.22 | ~ ('#form45') 52.14/7.22 | (X2 @ '#sk12'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl178])). 52.14/7.22 thf(zip_derived_cl187, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ('#sk2' @ ('#sk227' @ X2) @ ('#sk289' @ X2)) 52.14/7.22 | ('#sk2' @ '#sk10' @ ('#sk130' @ X2)) 52.14/7.22 | ~ ('#form45') 52.14/7.22 | (X2 @ '#sk12'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl178])). 52.14/7.22 thf(zip_derived_cl27, plain, 52.14/7.22 (( (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk7' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk7' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk1' @ Y1 @ Y2) | 52.14/7.22 ('#sk2' @ Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk8')))))) 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk3' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 ((((((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))) & 52.14/7.22 (Y0 @ Y1))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk4')))))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk1' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))))) => 52.14/7.22 (Y2 @ Y1)))))) | 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))) => 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) | 52.14/7.22 ('#sk1' @ 52.14/7.22 Y0 @ Y3))) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 ( 52.14/7.22 ( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 (( 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ 52.14/7.22 Y4) | 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))))))))))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 52.14/7.22 thf(zip_derived_cl32, plain, 52.14/7.22 ((~ ('#form11') 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk3' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 ((((((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))) & 52.14/7.22 (Y0 @ Y1))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk4')))))))), 52.14/7.22 define([status(thm)])). 52.14/7.22 thf(zip_derived_cl36, plain, 52.14/7.22 (( ('#form11') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk1' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))))) => 52.14/7.22 (Y2 @ Y1)))))) | 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))) => 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) | 52.14/7.22 ('#sk1' @ 52.14/7.22 Y0 @ Y3))) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 ( 52.14/7.22 ( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 (( 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ 52.14/7.22 Y4) | 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))))))))) 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk7' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk7' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk1' @ Y1 @ Y2) | 52.14/7.22 ('#sk2' @ Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk8')))))))), 52.14/7.22 inference('renaming', [status(thm)], [zip_derived_cl27, zip_derived_cl32])). 52.14/7.22 thf(zip_derived_cl28, plain, 52.14/7.22 (( ('#form9') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk1' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))))) => 52.14/7.22 (Y2 @ Y1)))))) | 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 (( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))) => 52.14/7.22 (((!!) @ (^[Y2 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y3 : a]: 52.14/7.22 ((((('#sk2' @ 52.14/7.22 Y0 @ 52.14/7.22 Y3) | 52.14/7.22 ('#sk1' @ 52.14/7.22 Y0 @ Y3))) => 52.14/7.22 (Y2 @ Y3)))))) & 52.14/7.22 (((!!) @ (^[Y3 : a]: 52.14/7.22 (((!!) @ ( 52.14/7.22 ^[Y4 : a]: 52.14/7.22 ( 52.14/7.22 ( 52.14/7.22 (( 52.14/7.22 (Y2 @ 52.14/7.22 Y3) & 52.14/7.22 (( 52.14/7.22 ('#sk1' @ 52.14/7.22 Y3 @ 52.14/7.22 Y4) | 52.14/7.22 ('#sk2' @ 52.14/7.22 Y3 @ Y4))))) => 52.14/7.22 (Y2 @ Y4))))))))))) => 52.14/7.22 (Y2 @ Y1)))))))))))))))), 52.14/7.22 define([status(thm)])). 52.14/7.22 thf(zip_derived_cl43, plain, 52.14/7.22 ((~ ('#form9') 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk7' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk7' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk1' @ Y1 @ Y2) | 52.14/7.22 ('#sk2' @ Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk8')))))) 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('renaming', [status(thm)], [zip_derived_cl36, zip_derived_cl28])). 52.14/7.22 thf(zip_derived_cl52, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( (((((((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 52.14/7.22 (X2 @ Y0)))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 52.14/7.22 Y0 @ Y1))))) => 52.14/7.22 (X2 @ Y1))))))))))) => 52.14/7.22 (X2 @ '#sk8'))) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9'))), 52.14/7.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 52.14/7.22 thf(zip_derived_cl53, plain, 52.14/7.22 (( (((((((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 52.14/7.22 ('#sk16' @ Y0)))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk16' @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.14/7.22 Y1))))) => 52.14/7.22 ('#sk16' @ Y1))))))))))) => 52.14/7.22 ('#sk16' @ '#sk8'))) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9'))), 52.14/7.22 inference('triggered_bool_instantiation', [status(thm)], 52.14/7.22 [zip_derived_cl52])). 52.14/7.22 thf(zip_derived_cl374, plain, 52.14/7.22 ((~ (((((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 52.14/7.22 ('#sk16' @ Y0)))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk16' @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.14/7.22 Y1))))) => 52.14/7.22 ('#sk16' @ Y1))))))))))) 52.14/7.22 | ('#sk16' @ '#sk8') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 52.14/7.22 thf(zip_derived_cl56, plain, 52.14/7.22 ((~ ('#sk16' @ '#sk8') | ('#form11') | ~ ('#form9'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 52.14/7.22 thf(zip_derived_cl375, plain, 52.14/7.22 (( ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ~ (((((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 52.14/7.22 ('#sk16' @ Y0)))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk16' @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 52.14/7.22 Y0 @ Y1))))) => 52.14/7.22 ('#sk16' @ Y1))))))))))))), 52.14/7.22 inference('clc', [status(thm)], [zip_derived_cl374, zip_derived_cl56])). 52.14/7.22 thf(zip_derived_cl376, plain, 52.14/7.22 ((~ (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 52.14/7.22 ('#sk16' @ Y0)))))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk16' @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.14/7.22 Y1))))) => 52.14/7.22 ('#sk16' @ Y1))))))))) 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl375])). 52.14/7.22 thf(zip_derived_cl377, plain, 52.14/7.22 ((~ ((((('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) | ('#sk1' @ '#sk7' @ 52.14/7.22 ('#sk61' @ '#sk16')))) => 52.14/7.22 ('#sk16' @ ('#sk61' @ '#sk16')))) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk16' @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.14/7.22 Y1))))) => 52.14/7.22 ('#sk16' @ Y1))))))))))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl376])). 52.14/7.22 thf(zip_derived_cl378, plain, 52.14/7.22 (( ((('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) | ('#sk1' @ '#sk7' @ 52.14/7.22 ('#sk61' @ '#sk16')))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk16' @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.14/7.22 Y1))))) => 52.14/7.22 ('#sk16' @ Y1))))))))) 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl377])). 52.14/7.22 thf(zip_derived_cl380, plain, 52.14/7.22 (( ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 52.14/7.22 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk16' @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.14/7.22 Y1))))) => 52.14/7.22 ('#sk16' @ Y1))))))))))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl378])). 52.14/7.22 thf(zip_derived_cl382, plain, 52.14/7.22 ((~ (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk16' @ ('#sk122' @ '#sk16')) & 52.14/7.22 ((('#sk1' @ ('#sk122' @ '#sk16') @ Y0) | ('#sk2' @ 52.14/7.22 ('#sk122' @ '#sk16') @ Y0))))) => 52.14/7.22 ('#sk16' @ Y0)))))) 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11') 52.14/7.22 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) 52.14/7.22 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl380])). 52.14/7.22 thf(zip_derived_cl384, plain, 52.14/7.22 ((~ ((((('#sk16' @ ('#sk122' @ '#sk16')) & 52.14/7.22 ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk166' @ '#sk16')) | 52.14/7.22 ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk166' @ '#sk16')))))) => 52.14/7.22 ('#sk16' @ ('#sk166' @ '#sk16')))) 52.14/7.22 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 52.14/7.22 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9'))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl382])). 52.14/7.22 thf(zip_derived_cl387, plain, 52.14/7.22 (( ((('#sk16' @ ('#sk122' @ '#sk16')) & 52.14/7.22 ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk166' @ '#sk16')) | 52.14/7.22 ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk166' @ '#sk16')))))) 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11') 52.14/7.22 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) 52.14/7.22 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl384])). 52.14/7.22 thf(zip_derived_cl391, plain, 52.14/7.22 (( ('#sk16' @ ('#sk122' @ '#sk16')) 52.14/7.22 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 52.14/7.22 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl387])). 52.14/7.22 thf(zip_derived_cl379, plain, 52.14/7.22 ((~ ('#sk16' @ ('#sk61' @ '#sk16')) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk16' @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.14/7.22 Y1))))) => 52.14/7.22 ('#sk16' @ Y1))))))))) 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl377])). 52.14/7.22 thf(zip_derived_cl381, plain, 52.14/7.22 ((~ (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk16' @ ('#sk122' @ '#sk16')) & 52.14/7.22 ((('#sk1' @ ('#sk122' @ '#sk16') @ Y0) | ('#sk2' @ 52.14/7.22 ('#sk122' @ '#sk16') @ Y0))))) => 52.14/7.22 ('#sk16' @ Y0)))))) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ~ ('#sk16' @ ('#sk61' @ '#sk16')))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl379])). 52.14/7.22 thf(zip_derived_cl383, plain, 52.14/7.22 ((~ ((((('#sk16' @ ('#sk122' @ '#sk16')) & 52.14/7.22 ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk166' @ '#sk16')) | 52.14/7.22 ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk166' @ '#sk16')))))) => 52.14/7.22 ('#sk16' @ ('#sk166' @ '#sk16')))) 52.14/7.22 | ~ ('#sk16' @ ('#sk61' @ '#sk16')) 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl381])). 52.14/7.22 thf(zip_derived_cl386, plain, 52.14/7.22 ((~ ('#sk16' @ ('#sk166' @ '#sk16')) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ~ ('#sk16' @ ('#sk61' @ '#sk16')))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl383])). 52.14/7.22 thf(zip_derived_cl385, plain, 52.14/7.22 (( ((('#sk16' @ ('#sk122' @ '#sk16')) & 52.14/7.22 ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk166' @ '#sk16')) | 52.14/7.22 ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk166' @ '#sk16')))))) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ~ ('#sk16' @ ('#sk61' @ '#sk16')))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl383])). 52.14/7.22 thf(zip_derived_cl389, plain, 52.14/7.22 (( ('#sk16' @ ('#sk122' @ '#sk16')) 52.14/7.22 | ~ ('#sk16' @ ('#sk61' @ '#sk16')) 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl385])). 52.14/7.22 thf(zip_derived_cl390, plain, 52.14/7.22 (( ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk166' @ '#sk16')) | ('#sk2' @ 52.14/7.22 ('#sk122' @ '#sk16') @ ('#sk166' @ '#sk16')))) 52.14/7.22 | ~ ('#sk16' @ ('#sk61' @ '#sk16')) 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl385])). 52.14/7.22 thf(zip_derived_cl393, plain, 52.14/7.22 (( ('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk166' @ '#sk16')) 52.14/7.22 | ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk166' @ '#sk16')) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ~ ('#sk16' @ ('#sk61' @ '#sk16')))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl390])). 52.14/7.22 thf(zip_derived_cl47, plain, 52.14/7.22 ((~ (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk10' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk10' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk1' @ Y1 @ Y2) | 52.14/7.22 ('#sk2' @ Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk12')))))) 52.14/7.22 | ('#form9'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 52.14/7.22 thf(zip_derived_cl61, plain, 52.14/7.22 ((~ (((((((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 52.14/7.22 ('#sk20' @ Y0)))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk20' @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 52.14/7.22 Y0 @ Y1))))) => 52.14/7.22 ('#sk20' @ Y1))))))))))) => 52.14/7.22 ('#sk20' @ '#sk12'))) 52.14/7.22 | ('#form9'))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 52.14/7.22 thf(zip_derived_cl72, plain, ((~ ('#sk20' @ '#sk12') | ('#form9'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 52.14/7.22 thf(zip_derived_cl71, plain, 52.14/7.22 (( (((((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 52.14/7.22 ('#sk20' @ Y0)))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk20' @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.14/7.22 Y1))))) => 52.14/7.22 ('#sk20' @ Y1))))))))))) 52.14/7.22 | ('#form9'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 52.14/7.22 thf(zip_derived_cl86, plain, 52.14/7.22 (( (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk20' @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 52.14/7.22 ('#sk20' @ Y1))))))))) 52.14/7.22 | ('#form9'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl71])). 52.14/7.22 thf(zip_derived_cl96, plain, 52.14/7.22 (![X2 : a]: 52.14/7.22 ( (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk20' @ X2) & 52.14/7.22 ((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))))) => 52.14/7.22 ('#sk20' @ Y0)))))) 52.14/7.22 | ('#form9'))), 52.14/7.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl86])). 52.14/7.22 thf(zip_derived_cl109, plain, 52.14/7.22 (![X2 : a, X4 : a]: 52.14/7.22 ( ((((('#sk20' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) => 52.14/7.22 ('#sk20' @ X4))) 52.14/7.22 | ('#form9'))), 52.14/7.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl96])). 52.14/7.22 thf(zip_derived_cl122, plain, 52.14/7.22 (![X2 : a, X4 : a]: 52.14/7.22 (~ ((('#sk20' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) 52.14/7.22 | ('#sk20' @ X4) 52.14/7.22 | ('#form9'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl109])). 52.14/7.22 thf(zip_derived_cl136, plain, 52.14/7.22 (![X2 : a, X4 : a]: 52.14/7.22 (~ ('#sk20' @ X2) 52.14/7.22 | ~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 52.14/7.22 | ('#form9') 52.14/7.22 | ('#sk20' @ X4))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl122])). 52.14/7.22 thf(zip_derived_cl151, plain, 52.14/7.22 (![X2 : a, X4 : a]: 52.14/7.22 (~ ('#sk2' @ X2 @ X4) 52.14/7.22 | ('#sk20' @ X4) 52.14/7.22 | ('#form9') 52.14/7.22 | ~ ('#sk20' @ X2))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl136])). 52.14/7.22 thf(zip_derived_cl179, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (X2 @ ('#sk289' @ X2)) 52.14/7.22 | (X2 @ '#sk12') 52.14/7.22 | ~ ('#form45') 52.14/7.22 | ('#sk2' @ '#sk10' @ ('#sk130' @ X2)))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl166])). 52.14/7.22 thf(zip_derived_cl135, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (X2 @ ('#sk130' @ X2)) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 52.14/7.22 (X2 @ Y1))))))))) 52.14/7.22 | ~ ('#form45') 52.14/7.22 | (X2 @ '#sk12'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl119])). 52.14/7.22 thf(zip_derived_cl149, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((((X2 @ ('#sk227' @ X2)) & ('#sk2' @ 52.14/7.22 ('#sk227' @ X2) @ Y0))) => 52.14/7.22 (X2 @ Y0)))))) 52.14/7.22 | (X2 @ '#sk12') 52.14/7.22 | ~ ('#form45') 52.14/7.22 | ~ (X2 @ ('#sk130' @ X2)))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl135])). 52.14/7.22 thf(zip_derived_cl167, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((((X2 @ ('#sk227' @ X2)) & ('#sk2' @ ('#sk227' @ X2) @ 52.14/7.22 ('#sk289' @ X2)))) => 52.14/7.22 (X2 @ ('#sk289' @ X2)))) 52.14/7.22 | ~ (X2 @ ('#sk130' @ X2)) 52.14/7.22 | ~ ('#form45') 52.14/7.22 | (X2 @ '#sk12'))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl149])). 52.14/7.22 thf(zip_derived_cl181, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (X2 @ ('#sk289' @ X2)) 52.14/7.22 | (X2 @ '#sk12') 52.14/7.22 | ~ ('#form45') 52.14/7.22 | ~ (X2 @ ('#sk130' @ X2)))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl167])). 52.14/7.22 thf(zip_derived_cl388, plain, 52.14/7.22 ((~ ('#sk16' @ ('#sk166' @ '#sk16')) 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11') 52.14/7.22 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) 52.14/7.22 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl384])). 52.14/7.22 thf(zip_derived_cl180, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( (((X2 @ ('#sk227' @ X2)) & ('#sk2' @ ('#sk227' @ X2) @ 52.14/7.22 ('#sk289' @ X2)))) 52.14/7.22 | (X2 @ '#sk12') 52.14/7.22 | ~ ('#form45') 52.14/7.22 | ~ (X2 @ ('#sk130' @ X2)))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl167])). 52.14/7.22 thf(zip_derived_cl188, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( (X2 @ ('#sk227' @ X2)) 52.14/7.22 | ~ (X2 @ ('#sk130' @ X2)) 52.14/7.22 | ~ ('#form45') 52.14/7.22 | (X2 @ '#sk12'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl180])). 52.14/7.22 thf(zip_derived_cl67, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( (((((((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.14/7.22 (X2 @ Y1))))))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 52.14/7.22 (X2 @ '#sk12'))) 52.14/7.22 | ('#form9') 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & ('#sk2' @ 52.14/7.22 Y1 @ Y2))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk12')))))))), 52.14/7.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 52.14/7.22 thf(zip_derived_cl68, plain, 52.14/7.22 (( (((((((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk20' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.14/7.22 ('#sk20' @ Y1))))))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))) => 52.14/7.22 ('#sk20' @ '#sk12'))) 52.14/7.22 | ('#form9') 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & ('#sk2' @ 52.14/7.22 Y1 @ Y2))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk12')))))))), 52.14/7.22 inference('triggered_bool_instantiation', [status(thm)], 52.14/7.22 [zip_derived_cl67])). 52.14/7.22 thf(zip_derived_cl79, plain, 52.14/7.22 ((~ ('#form45') 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & ('#sk2' @ 52.14/7.22 Y1 @ Y2))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk12')))))))), 52.14/7.22 define([status(thm)])). 52.14/7.22 thf(zip_derived_cl323, plain, 52.14/7.22 (( ('#form45') 52.14/7.22 | ('#form9') 52.14/7.22 | (((((((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk20' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.14/7.22 ('#sk20' @ Y1))))))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 ((('#sk1' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))) => 52.14/7.22 ('#sk20' @ '#sk12'))))), 52.14/7.22 inference('renaming', [status(thm)], [zip_derived_cl68, zip_derived_cl79])). 52.14/7.22 thf(zip_derived_cl324, plain, 52.14/7.22 ((~ (((((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk20' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.14/7.22 ('#sk20' @ Y1))))))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))) 52.14/7.22 | ('#sk20' @ '#sk12') 52.14/7.22 | ('#form9') 52.14/7.22 | ('#form45'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl323])). 52.14/7.22 thf(zip_derived_cl72, plain, ((~ ('#sk20' @ '#sk12') | ('#form9'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 52.14/7.22 thf(zip_derived_cl325, plain, 52.14/7.22 (( ('#form45') 52.14/7.22 | ('#form9') 52.14/7.22 | ~ (((((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk20' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.14/7.22 ('#sk20' @ Y1))))))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 ((('#sk1' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))))))), 52.14/7.22 inference('clc', [status(thm)], [zip_derived_cl324, zip_derived_cl72])). 52.14/7.22 thf(zip_derived_cl326, plain, 52.14/7.22 ((~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk20' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.14/7.22 ('#sk20' @ Y1))))))))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))) 52.14/7.22 | ('#form9') 52.14/7.22 | ('#form45'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl325])). 52.14/7.22 thf(zip_derived_cl67, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( (((((((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.14/7.22 (X2 @ Y1))))))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 52.14/7.22 (X2 @ '#sk12'))) 52.14/7.22 | ('#form9') 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & ('#sk2' @ 52.14/7.22 Y1 @ Y2))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk12')))))))), 52.14/7.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 52.14/7.22 thf(zip_derived_cl79, plain, 52.14/7.22 ((~ ('#form45') 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & ('#sk2' @ 52.14/7.22 Y1 @ Y2))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk12')))))))), 52.14/7.22 define([status(thm)])). 52.14/7.22 thf(zip_derived_cl84, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ('#form45') 52.14/7.22 | ('#form9') 52.14/7.22 | (((((((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.14/7.22 (X2 @ Y1))))))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 52.14/7.22 (X2 @ '#sk12'))))), 52.14/7.22 inference('renaming', [status(thm)], [zip_derived_cl67, zip_derived_cl79])). 52.14/7.22 thf(zip_derived_cl93, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.14/7.22 (X2 @ Y1))))))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) 52.14/7.22 | (X2 @ '#sk12') 52.14/7.22 | ('#form9') 52.14/7.22 | ('#form45'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl84])). 52.14/7.22 thf(zip_derived_cl106, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.14/7.22 (X2 @ Y1))))))))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 52.14/7.22 | ('#form45') 52.14/7.22 | ('#form9') 52.14/7.22 | (X2 @ '#sk12'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl93])). 52.14/7.22 thf(zip_derived_cl118, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((((X2 @ ('#sk126' @ X2)) & ('#sk1' @ 52.14/7.22 ('#sk126' @ X2) @ Y0))) => 52.14/7.22 (X2 @ Y0)))))) 52.14/7.22 | (X2 @ '#sk12') 52.14/7.22 | ('#form9') 52.14/7.22 | ('#form45') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl106])). 52.14/7.22 thf(zip_derived_cl133, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((((X2 @ ('#sk126' @ X2)) & ('#sk1' @ ('#sk126' @ X2) @ 52.14/7.22 ('#sk171' @ X2)))) => 52.14/7.22 (X2 @ ('#sk171' @ X2)))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 52.14/7.22 | ('#form45') 52.14/7.22 | ('#form9') 52.14/7.22 | (X2 @ '#sk12'))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl118])). 52.14/7.22 thf(zip_derived_cl147, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (X2 @ ('#sk171' @ X2)) 52.14/7.22 | (X2 @ '#sk12') 52.14/7.22 | ('#form9') 52.14/7.22 | ('#form45') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl133])). 52.14/7.22 thf(zip_derived_cl163, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ('#form283' @ X2) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 52.14/7.22 define([status(thm)])). 52.14/7.22 thf(zip_derived_cl327, plain, 52.14/7.22 ((~ ('#form283' @ '#sk20') 52.14/7.22 | ('#form45') 52.14/7.22 | ('#form9') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk20' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 52.14/7.22 ('#sk20' @ Y1))))))))))), 52.14/7.22 inference('renaming', [status(thm)], 52.14/7.22 [zip_derived_cl326, zip_derived_cl163])). 52.14/7.22 thf(zip_derived_cl328, plain, 52.14/7.22 ((~ (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk20' @ ('#sk126' @ '#sk20')) & ('#sk1' @ 52.14/7.22 ('#sk126' @ '#sk20') @ Y0))) => 52.14/7.22 ('#sk20' @ Y0)))))) 52.14/7.22 | ('#form9') 52.14/7.22 | ('#form45') 52.14/7.22 | ~ ('#form283' @ '#sk20'))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl327])). 52.14/7.22 thf(zip_derived_cl329, plain, 52.14/7.22 ((~ ((((('#sk20' @ ('#sk126' @ '#sk20')) & ('#sk1' @ 52.14/7.22 ('#sk126' @ '#sk20') @ ('#sk171' @ '#sk20')))) => 52.14/7.22 ('#sk20' @ ('#sk171' @ '#sk20')))) 52.14/7.22 | ~ ('#form283' @ '#sk20') 52.14/7.22 | ('#form45') 52.14/7.22 | ('#form9'))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl328])). 52.14/7.22 thf(zip_derived_cl330, plain, 52.14/7.22 (( ((('#sk20' @ ('#sk126' @ '#sk20')) & ('#sk1' @ ('#sk126' @ '#sk20') @ 52.14/7.22 ('#sk171' @ '#sk20')))) 52.14/7.22 | ('#form9') 52.14/7.22 | ('#form45') 52.14/7.22 | ~ ('#form283' @ '#sk20'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl329])). 52.14/7.22 thf(zip_derived_cl332, plain, 52.14/7.22 (( ('#sk20' @ ('#sk126' @ '#sk20')) 52.14/7.22 | ~ ('#form283' @ '#sk20') 52.14/7.22 | ('#form45') 52.14/7.22 | ('#form9'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl330])). 52.14/7.22 thf(zip_derived_cl85, plain, 52.14/7.22 (( (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk10' @ Y0) | ('#sk1' @ '#sk10' @ Y0))) => 52.14/7.22 ('#sk20' @ Y0)))))) 52.14/7.22 | ('#form9'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl71])). 52.14/7.22 thf(zip_derived_cl95, plain, 52.14/7.22 (![X2 : a]: 52.14/7.22 ( ((((('#sk2' @ '#sk10' @ X2) | ('#sk1' @ '#sk10' @ X2))) => 52.14/7.22 ('#sk20' @ X2))) 52.14/7.22 | ('#form9'))), 52.14/7.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 52.14/7.22 thf(zip_derived_cl108, plain, 52.14/7.22 (![X2 : a]: 52.14/7.22 (~ ((('#sk2' @ '#sk10' @ X2) | ('#sk1' @ '#sk10' @ X2))) 52.14/7.22 | ('#sk20' @ X2) 52.14/7.22 | ('#form9'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])). 52.14/7.22 thf(zip_derived_cl120, plain, 52.14/7.22 (![X2 : a]: (~ ('#sk2' @ '#sk10' @ X2) | ('#form9') | ('#sk20' @ X2))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl108])). 52.14/7.22 thf(zip_derived_cl189, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ('#sk2' @ ('#sk227' @ X2) @ ('#sk289' @ X2)) 52.14/7.22 | ~ (X2 @ ('#sk130' @ X2)) 52.14/7.22 | ~ ('#form45') 52.14/7.22 | (X2 @ '#sk12'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl180])). 52.14/7.22 thf(zip_derived_cl331, plain, 52.14/7.22 ((~ ('#sk20' @ ('#sk171' @ '#sk20')) 52.14/7.22 | ('#form9') 52.14/7.22 | ('#form45') 52.14/7.22 | ~ ('#form283' @ '#sk20'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl329])). 52.14/7.22 thf(zip_derived_cl65, plain, 52.14/7.22 (( (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk16' @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 52.14/7.22 ('#sk16' @ Y1))))))))) 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 52.14/7.22 thf(zip_derived_cl77, plain, 52.14/7.22 (![X2 : a]: 52.14/7.22 ( (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk16' @ X2) & 52.14/7.22 ((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))))) => 52.14/7.22 ('#sk16' @ Y0)))))) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9'))), 52.14/7.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl65])). 52.14/7.22 thf(zip_derived_cl91, plain, 52.14/7.22 (![X2 : a, X4 : a]: 52.14/7.22 ( ((((('#sk16' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) => 52.14/7.22 ('#sk16' @ X4))) 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11'))), 52.14/7.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl77])). 52.14/7.22 thf(zip_derived_cl103, plain, 52.14/7.22 (![X2 : a, X4 : a]: 52.14/7.22 (~ ((('#sk16' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) 52.14/7.22 | ('#sk16' @ X4) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl91])). 52.14/7.22 thf(zip_derived_cl117, plain, 52.14/7.22 (![X2 : a, X4 : a]: 52.14/7.22 (~ ('#sk16' @ X2) 52.14/7.22 | ~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11') 52.14/7.22 | ('#sk16' @ X4))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl103])). 52.14/7.22 thf(zip_derived_cl132, plain, 52.14/7.22 (![X2 : a, X4 : a]: 52.14/7.22 (~ ('#sk2' @ X2 @ X4) 52.14/7.22 | ('#sk16' @ X4) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ~ ('#sk16' @ X2))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl117])). 52.14/7.22 thf(zip_derived_cl333, plain, 52.14/7.22 (( ('#sk1' @ ('#sk126' @ '#sk20') @ ('#sk171' @ '#sk20')) 52.14/7.22 | ~ ('#form283' @ '#sk20') 52.14/7.22 | ('#form45') 52.14/7.22 | ('#form9'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl330])). 52.14/7.22 thf(zip_derived_cl131, plain, 52.14/7.22 (![X2 : a, X4 : a]: 52.14/7.22 (~ ('#sk1' @ X2 @ X4) 52.14/7.22 | ('#sk16' @ X4) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ~ ('#sk16' @ X2))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl117])). 52.14/7.22 thf(zip_derived_cl163, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ('#form283' @ X2) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 52.14/7.22 define([status(thm)])). 52.14/7.22 thf(zip_derived_cl164, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ ((('#sk1' @ '#sk10' @ ('#sk284' @ X2)) => (X2 @ ('#sk284' @ X2)))) 52.14/7.22 | ('#form283' @ X2))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl163])). 52.14/7.22 thf(zip_derived_cl176, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ('#sk1' @ '#sk10' @ ('#sk284' @ X2)) | ('#form283' @ X2))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])). 52.14/7.22 thf(zip_derived_cl150, plain, 52.14/7.22 (![X2 : a, X4 : a]: 52.14/7.22 (~ ('#sk1' @ X2 @ X4) 52.14/7.22 | ('#sk20' @ X4) 52.14/7.22 | ('#form9') 52.14/7.22 | ~ ('#sk20' @ X2))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl136])). 52.14/7.22 thf(zip_derived_cl392, plain, 52.14/7.22 (( ((('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk166' @ '#sk16')) | ('#sk2' @ 52.14/7.22 ('#sk122' @ '#sk16') @ ('#sk166' @ '#sk16')))) 52.14/7.22 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')) 52.14/7.22 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) 52.14/7.22 | ('#form11') 52.14/7.22 | ~ ('#form9'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl387])). 52.14/7.22 thf(zip_derived_cl394, plain, 52.14/7.22 (( ('#sk1' @ ('#sk122' @ '#sk16') @ ('#sk166' @ '#sk16')) 52.14/7.22 | ('#sk2' @ ('#sk122' @ '#sk16') @ ('#sk166' @ '#sk16')) 52.14/7.22 | ~ ('#form9') 52.14/7.22 | ('#form11') 52.14/7.22 | ('#sk1' @ '#sk7' @ ('#sk61' @ '#sk16')) 52.14/7.22 | ('#sk2' @ '#sk7' @ ('#sk61' @ '#sk16')))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl392])). 52.14/7.22 thf(zip_derived_cl121, plain, 52.14/7.22 (![X2 : a]: (~ ('#sk1' @ '#sk10' @ X2) | ('#form9') | ('#sk20' @ X2))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl108])). 52.14/7.22 thf(zip_derived_cl177, plain, 52.14/7.22 (![X2 : a > $o]: (~ (X2 @ ('#sk284' @ X2)) | ('#form283' @ X2))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])). 52.14/7.22 thf(zip_derived_cl32, plain, 52.14/7.22 ((~ ('#form11') 52.14/7.22 | (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk3' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 ((((((('#sk2' @ Y1 @ Y2) | 52.14/7.22 ('#sk1' @ Y1 @ Y2))) & 52.14/7.22 (Y0 @ Y1))) => 52.14/7.22 (Y0 @ Y2))))))))))) => 52.14/7.22 (Y0 @ '#sk4')))))))), 52.14/7.22 define([status(thm)])). 52.14/7.22 thf(zip_derived_cl33, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( (((((((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 52.14/7.22 (X2 @ Y0)))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.14/7.22 Y0 @ Y1))) & 52.14/7.22 (X2 @ Y0))) => 52.14/7.22 (X2 @ Y1))))))))))) => 52.14/7.22 (X2 @ '#sk4'))) 52.14/7.22 | ~ ('#form11'))), 52.14/7.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 52.14/7.22 thf(zip_derived_cl34, plain, 52.14/7.22 (( (((((((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 52.14/7.22 ('#sk5' @ Y0)))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.14/7.22 Y1))) & 52.14/7.22 ('#sk5' @ Y0))) => 52.14/7.22 ('#sk5' @ Y1))))))))))) => 52.14/7.22 ('#sk5' @ '#sk4'))) 52.14/7.22 | ~ ('#form11'))), 52.14/7.22 inference('triggered_bool_instantiation', [status(thm)], 52.14/7.22 [zip_derived_cl33])). 52.14/7.22 thf(zip_derived_cl6, plain, 52.14/7.22 (~ (((!!) @ (^[Y0 : a > $o]: 52.14/7.22 (((((((!!) @ (^[Y1 : a]: 52.14/7.22 (((!!) @ (^[Y2 : a]: 52.14/7.22 (((((Y0 @ Y1) & 52.14/7.22 ((('#sk1' @ Y1 @ Y2) | 52.14/7.22 ('#sk2' @ Y1 @ Y2))))) => 52.14/7.22 (Y0 @ Y2))))))))) & 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 52.14/7.22 '#sk3' @ Y1))) => 52.14/7.22 (Y0 @ Y1)))))))) => 52.14/7.22 (Y0 @ '#sk4'))))))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 52.14/7.22 thf(zip_derived_cl8, plain, 52.14/7.22 (~ (((((((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk5' @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 52.14/7.22 Y1))))) => 52.14/7.22 ('#sk5' @ Y1))))))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 52.14/7.22 ('#sk5' @ Y0)))))))) => 52.14/7.22 ('#sk5' @ '#sk4')))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 52.14/7.22 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk4')), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 52.14/7.22 thf(zip_derived_cl207, plain, 52.14/7.22 (( (((((((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 52.14/7.22 ('#sk5' @ Y0)))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.14/7.22 Y1))) & 52.14/7.22 ('#sk5' @ Y0))) => 52.14/7.22 ('#sk5' @ Y1))))))))))) => 52.14/7.22 ($false))) 52.14/7.22 | ~ ('#form11'))), 52.14/7.22 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl11])). 52.14/7.22 thf(zip_derived_cl208, plain, 52.14/7.22 (( (((~) @ (((((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ 52.14/7.22 Y0))) => 52.14/7.22 ('#sk5' @ Y0)))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((((('#sk2' @ Y0 @ Y1) | 52.14/7.22 ('#sk1' @ Y0 @ Y1))) & 52.14/7.22 ('#sk5' @ Y0))) => 52.14/7.22 ('#sk5' @ Y1))))))))))))) 52.14/7.22 | ~ ('#form11'))), 52.14/7.22 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl207])). 52.14/7.22 thf(zip_derived_cl209, plain, 52.14/7.22 ((~ (((((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 52.14/7.22 ('#sk5' @ Y0)))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.14/7.22 Y1))) & 52.14/7.22 ('#sk5' @ Y0))) => 52.14/7.22 ('#sk5' @ Y1))))))))))) 52.14/7.22 | ~ ('#form11'))), 52.14/7.22 inference('simplify nested equalities', [status(thm)], 52.14/7.22 [zip_derived_cl208])). 52.14/7.22 thf(zip_derived_cl210, plain, 52.14/7.22 ((~ (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 52.14/7.22 ('#sk5' @ Y0)))))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.14/7.22 Y1))) & 52.14/7.22 ('#sk5' @ Y0))) => 52.14/7.22 ('#sk5' @ Y1))))))))) 52.14/7.22 | ~ ('#form11'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl209])). 52.14/7.22 thf(zip_derived_cl211, plain, 52.14/7.22 ((~ ((((('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')) | ('#sk1' @ '#sk3' @ 52.14/7.22 ('#sk27' @ '#sk5')))) => 52.14/7.22 ('#sk5' @ ('#sk27' @ '#sk5')))) 52.14/7.22 | ~ ('#form11') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.14/7.22 Y1))) & 52.14/7.22 ('#sk5' @ Y0))) => 52.14/7.22 ('#sk5' @ Y1))))))))))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl210])). 52.14/7.22 thf(zip_derived_cl212, plain, 52.14/7.22 (( ((('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')) | ('#sk1' @ '#sk3' @ 52.14/7.22 ('#sk27' @ '#sk5')))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.14/7.22 Y1))) & 52.14/7.22 ('#sk5' @ Y0))) => 52.14/7.22 ('#sk5' @ Y1))))))))) 52.14/7.22 | ~ ('#form11'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl211])). 52.14/7.22 thf(zip_derived_cl214, plain, 52.14/7.22 (( ('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')) 52.14/7.22 | ('#sk1' @ '#sk3' @ ('#sk27' @ '#sk5')) 52.14/7.22 | ~ ('#form11') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.14/7.22 Y1))) & 52.14/7.22 ('#sk5' @ Y0))) => 52.14/7.22 ('#sk5' @ Y1))))))))))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl212])). 52.14/7.22 thf(zip_derived_cl216, plain, 52.14/7.22 ((~ (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((((('#sk2' @ ('#sk57' @ '#sk5') @ Y0) | ('#sk1' @ 52.14/7.22 ('#sk57' @ '#sk5') @ Y0))) & 52.14/7.22 ('#sk5' @ ('#sk57' @ '#sk5')))) => 52.14/7.22 ('#sk5' @ Y0)))))) 52.14/7.22 | ~ ('#form11') 52.14/7.22 | ('#sk1' @ '#sk3' @ ('#sk27' @ '#sk5')) 52.14/7.22 | ('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl214])). 52.14/7.22 thf(zip_derived_cl218, plain, 52.14/7.22 ((~ ((((((('#sk2' @ ('#sk57' @ '#sk5') @ ('#sk82' @ '#sk5')) | ('#sk1' @ 52.14/7.22 ('#sk57' @ '#sk5') @ ('#sk82' @ '#sk5')))) & 52.14/7.22 ('#sk5' @ ('#sk57' @ '#sk5')))) => 52.14/7.22 ('#sk5' @ ('#sk82' @ '#sk5')))) 52.14/7.22 | ('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')) 52.14/7.22 | ('#sk1' @ '#sk3' @ ('#sk27' @ '#sk5')) 52.14/7.22 | ~ ('#form11'))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl216])). 52.14/7.22 thf(zip_derived_cl221, plain, 52.14/7.22 (( ((((('#sk2' @ ('#sk57' @ '#sk5') @ ('#sk82' @ '#sk5')) | ('#sk1' @ 52.14/7.22 ('#sk57' @ '#sk5') @ ('#sk82' @ '#sk5')))) & 52.14/7.22 ('#sk5' @ ('#sk57' @ '#sk5')))) 52.14/7.22 | ~ ('#form11') 52.14/7.22 | ('#sk1' @ '#sk3' @ ('#sk27' @ '#sk5')) 52.14/7.22 | ('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl218])). 52.14/7.22 thf(zip_derived_cl226, plain, 52.14/7.22 (( ('#sk5' @ ('#sk57' @ '#sk5')) 52.14/7.22 | ('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')) 52.14/7.22 | ('#sk1' @ '#sk3' @ ('#sk27' @ '#sk5')) 52.14/7.22 | ~ ('#form11'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl221])). 52.14/7.22 thf(zip_derived_cl10, plain, 52.14/7.22 ( (((((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk5' @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 52.14/7.22 ('#sk5' @ Y1))))))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 52.14/7.22 ('#sk5' @ Y0))))))))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 52.14/7.22 thf(zip_derived_cl14, plain, 52.14/7.22 ( (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 52.14/7.22 ('#sk5' @ Y0))))))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 52.14/7.22 thf(zip_derived_cl17, plain, 52.14/7.22 (![X2 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ X2) | ('#sk1' @ '#sk3' @ X2))) => ('#sk5' @ 52.14/7.22 X2)))), 52.14/7.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 52.14/7.22 thf(zip_derived_cl20, plain, 52.14/7.22 (![X2 : a]: 52.14/7.22 (~ ((('#sk2' @ '#sk3' @ X2) | ('#sk1' @ '#sk3' @ X2))) 52.14/7.22 | ('#sk5' @ X2))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 52.14/7.22 thf(zip_derived_cl25, plain, 52.14/7.22 (![X2 : a]: (~ ('#sk1' @ '#sk3' @ X2) | ('#sk5' @ X2))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 52.14/7.22 thf(zip_derived_cl213, plain, 52.14/7.22 ((~ ('#sk5' @ ('#sk27' @ '#sk5')) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 52.14/7.22 Y1))) & 52.14/7.22 ('#sk5' @ Y0))) => 52.14/7.22 ('#sk5' @ Y1))))))))) 52.14/7.22 | ~ ('#form11'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl211])). 52.14/7.22 thf(zip_derived_cl215, plain, 52.14/7.22 ((~ (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((((('#sk2' @ ('#sk57' @ '#sk5') @ Y0) | ('#sk1' @ 52.14/7.22 ('#sk57' @ '#sk5') @ Y0))) & 52.14/7.22 ('#sk5' @ ('#sk57' @ '#sk5')))) => 52.14/7.22 ('#sk5' @ Y0)))))) 52.14/7.22 | ~ ('#form11') 52.14/7.22 | ~ ('#sk5' @ ('#sk27' @ '#sk5')))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl213])). 52.14/7.22 thf(zip_derived_cl217, plain, 52.14/7.22 ((~ ((((((('#sk2' @ ('#sk57' @ '#sk5') @ ('#sk82' @ '#sk5')) | ('#sk1' @ 52.14/7.22 ('#sk57' @ '#sk5') @ ('#sk82' @ '#sk5')))) & 52.14/7.22 ('#sk5' @ ('#sk57' @ '#sk5')))) => 52.14/7.22 ('#sk5' @ ('#sk82' @ '#sk5')))) 52.14/7.22 | ~ ('#sk5' @ ('#sk27' @ '#sk5')) 52.14/7.22 | ~ ('#form11'))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl215])). 52.14/7.22 thf(zip_derived_cl220, plain, 52.14/7.22 ((~ ('#sk5' @ ('#sk82' @ '#sk5')) 52.14/7.22 | ~ ('#form11') 52.14/7.22 | ~ ('#sk5' @ ('#sk27' @ '#sk5')))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl217])). 52.14/7.22 thf(zip_derived_cl219, plain, 52.14/7.22 (( ((((('#sk2' @ ('#sk57' @ '#sk5') @ ('#sk82' @ '#sk5')) | ('#sk1' @ 52.14/7.22 ('#sk57' @ '#sk5') @ ('#sk82' @ '#sk5')))) & 52.14/7.22 ('#sk5' @ ('#sk57' @ '#sk5')))) 52.14/7.22 | ~ ('#form11') 52.14/7.22 | ~ ('#sk5' @ ('#sk27' @ '#sk5')))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl217])). 52.14/7.22 thf(zip_derived_cl224, plain, 52.14/7.22 (( ('#sk5' @ ('#sk57' @ '#sk5')) 52.14/7.22 | ~ ('#sk5' @ ('#sk27' @ '#sk5')) 52.14/7.22 | ~ ('#form11'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl219])). 52.14/7.22 thf(zip_derived_cl223, plain, 52.14/7.22 (( ((('#sk2' @ ('#sk57' @ '#sk5') @ ('#sk82' @ '#sk5')) | ('#sk1' @ 52.14/7.22 ('#sk57' @ '#sk5') @ ('#sk82' @ '#sk5')))) 52.14/7.22 | ~ ('#sk5' @ ('#sk27' @ '#sk5')) 52.14/7.22 | ~ ('#form11'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl219])). 52.14/7.22 thf(zip_derived_cl227, plain, 52.14/7.22 (( ('#sk2' @ ('#sk57' @ '#sk5') @ ('#sk82' @ '#sk5')) 52.14/7.22 | ('#sk1' @ ('#sk57' @ '#sk5') @ ('#sk82' @ '#sk5')) 52.14/7.22 | ~ ('#form11') 52.14/7.22 | ~ ('#sk5' @ ('#sk27' @ '#sk5')))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl223])). 52.14/7.22 thf(zip_derived_cl33, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( (((((((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 52.14/7.22 (X2 @ Y0)))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.14/7.22 Y0 @ Y1))) & 52.14/7.22 (X2 @ Y0))) => 52.14/7.22 (X2 @ Y1))))))))))) => 52.14/7.22 (X2 @ '#sk4'))) 52.14/7.22 | ~ ('#form11'))), 52.14/7.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 52.14/7.22 thf(zip_derived_cl42, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 52.14/7.22 (X2 @ Y0)))))) & 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.14/7.22 Y0 @ Y1))) & 52.14/7.22 (X2 @ Y0))) => 52.14/7.22 (X2 @ Y1))))))))))) 52.14/7.22 | (X2 @ '#sk4') 52.14/7.22 | ~ ('#form11'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])). 52.14/7.22 thf(zip_derived_cl51, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 52.14/7.22 (X2 @ Y0)))))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.14/7.22 Y0 @ Y1))) & 52.14/7.22 (X2 @ Y0))) => 52.14/7.22 (X2 @ Y1))))))))) 52.14/7.22 | ~ ('#form11') 52.14/7.22 | (X2 @ '#sk4'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl42])). 52.14/7.22 thf(zip_derived_cl63, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ ((((('#sk2' @ '#sk3' @ ('#sk27' @ X2)) | ('#sk1' @ '#sk3' @ 52.14/7.22 ('#sk27' @ X2)))) => 52.14/7.22 (X2 @ ('#sk27' @ X2)))) 52.14/7.22 | (X2 @ '#sk4') 52.14/7.22 | ~ ('#form11') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.14/7.22 Y0 @ Y1))) & 52.14/7.22 (X2 @ Y0))) => 52.14/7.22 (X2 @ Y1))))))))))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl51])). 52.14/7.22 thf(zip_derived_cl74, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ((('#sk2' @ '#sk3' @ ('#sk27' @ X2)) | ('#sk1' @ '#sk3' @ 52.14/7.22 ('#sk27' @ X2)))) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.14/7.22 Y0 @ Y1))) & 52.14/7.22 (X2 @ Y0))) => 52.14/7.22 (X2 @ Y1))))))))) 52.14/7.22 | ~ ('#form11') 52.14/7.22 | (X2 @ '#sk4'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl63])). 52.14/7.22 thf(zip_derived_cl88, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ('#sk2' @ '#sk3' @ ('#sk27' @ X2)) 52.14/7.22 | ('#sk1' @ '#sk3' @ ('#sk27' @ X2)) 52.14/7.22 | (X2 @ '#sk4') 52.14/7.22 | ~ ('#form11') 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.14/7.22 Y0 @ Y1))) & 52.14/7.22 (X2 @ Y0))) => 52.14/7.22 (X2 @ Y1))))))))))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl74])). 52.14/7.22 thf(zip_derived_cl99, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((((('#sk2' @ ('#sk57' @ X2) @ Y0) | ('#sk1' @ 52.14/7.22 ('#sk57' @ X2) @ Y0))) & 52.14/7.22 (X2 @ ('#sk57' @ X2)))) => 52.14/7.22 (X2 @ Y0)))))) 52.14/7.22 | ~ ('#form11') 52.14/7.22 | (X2 @ '#sk4') 52.14/7.22 | ('#sk1' @ '#sk3' @ ('#sk27' @ X2)) 52.14/7.22 | ('#sk2' @ '#sk3' @ ('#sk27' @ X2)))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl88])). 52.14/7.22 thf(zip_derived_cl112, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ ((((((('#sk2' @ ('#sk57' @ X2) @ ('#sk82' @ X2)) | ('#sk1' @ 52.14/7.22 ('#sk57' @ X2) @ ('#sk82' @ X2)))) & 52.14/7.22 (X2 @ ('#sk57' @ X2)))) => 52.14/7.22 (X2 @ ('#sk82' @ X2)))) 52.14/7.22 | ('#sk2' @ '#sk3' @ ('#sk27' @ X2)) 52.14/7.22 | ('#sk1' @ '#sk3' @ ('#sk27' @ X2)) 52.14/7.22 | (X2 @ '#sk4') 52.14/7.22 | ~ ('#form11'))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl99])). 52.14/7.22 thf(zip_derived_cl126, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (X2 @ ('#sk82' @ X2)) 52.14/7.22 | ~ ('#form11') 52.14/7.22 | (X2 @ '#sk4') 52.14/7.22 | ('#sk1' @ '#sk3' @ ('#sk27' @ X2)) 52.14/7.22 | ('#sk2' @ '#sk3' @ ('#sk27' @ X2)))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl112])). 52.14/7.22 thf(zip_derived_cl225, plain, 52.14/7.22 (( ((('#sk2' @ ('#sk57' @ '#sk5') @ ('#sk82' @ '#sk5')) | ('#sk1' @ 52.14/7.22 ('#sk57' @ '#sk5') @ ('#sk82' @ '#sk5')))) 52.14/7.22 | ('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')) 52.14/7.22 | ('#sk1' @ '#sk3' @ ('#sk27' @ '#sk5')) 52.14/7.22 | ~ ('#form11'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl221])). 52.14/7.22 thf(zip_derived_cl228, plain, 52.14/7.22 (( ('#sk2' @ ('#sk57' @ '#sk5') @ ('#sk82' @ '#sk5')) 52.14/7.22 | ('#sk1' @ ('#sk57' @ '#sk5') @ ('#sk82' @ '#sk5')) 52.14/7.22 | ~ ('#form11') 52.14/7.22 | ('#sk1' @ '#sk3' @ ('#sk27' @ '#sk5')) 52.14/7.22 | ('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl225])). 52.14/7.22 thf(zip_derived_cl13, plain, 52.14/7.22 ( (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((('#sk5' @ Y0) & 52.14/7.22 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))))) => 52.14/7.22 ('#sk5' @ Y1)))))))))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 52.14/7.22 thf(zip_derived_cl16, plain, 52.14/7.22 (![X2 : a]: 52.14/7.22 (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((('#sk5' @ X2) & 52.14/7.22 ((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))))) => 52.14/7.22 ('#sk5' @ Y0))))))), 52.14/7.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 52.14/7.22 thf(zip_derived_cl19, plain, 52.14/7.22 (![X2 : a, X4 : a]: 52.14/7.22 ((((('#sk5' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) => 52.14/7.22 ('#sk5' @ X4)))), 52.14/7.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 52.14/7.22 thf(zip_derived_cl23, plain, 52.14/7.22 (![X2 : a, X4 : a]: 52.14/7.22 (~ ((('#sk5' @ X2) & ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))))) 52.14/7.22 | ('#sk5' @ X4))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 52.14/7.22 thf(zip_derived_cl31, plain, 52.14/7.22 (![X2 : a, X4 : a]: 52.14/7.22 (~ ('#sk5' @ X2) 52.14/7.22 | ~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 52.14/7.22 | ('#sk5' @ X4))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])). 52.14/7.22 thf(zip_derived_cl40, plain, 52.14/7.22 (![X2 : a, X4 : a]: 52.14/7.22 (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 52.14/7.22 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk4')), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 52.14/7.22 thf(zip_derived_cl39, plain, 52.14/7.22 (![X2 : a, X4 : a]: 52.14/7.22 (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 52.14/7.22 thf(zip_derived_cl75, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (X2 @ ('#sk27' @ X2)) 52.14/7.22 | ~ (((!!) @ (^[Y0 : a]: 52.14/7.22 (((!!) @ (^[Y1 : a]: 52.14/7.22 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 52.14/7.22 Y0 @ Y1))) & 52.14/7.22 (X2 @ Y0))) => 52.14/7.22 (X2 @ Y1))))))))) 52.14/7.22 | ~ ('#form11') 52.14/7.22 | (X2 @ '#sk4'))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl63])). 52.14/7.22 thf(zip_derived_cl89, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (((!!) @ (^[Y0 : a]: 52.14/7.22 ((((((('#sk2' @ ('#sk57' @ X2) @ Y0) | ('#sk1' @ 52.14/7.22 ('#sk57' @ X2) @ Y0))) & 52.14/7.22 (X2 @ ('#sk57' @ X2)))) => 52.14/7.22 (X2 @ Y0)))))) 52.14/7.22 | (X2 @ '#sk4') 52.14/7.22 | ~ ('#form11') 52.14/7.22 | ~ (X2 @ ('#sk27' @ X2)))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl75])). 52.14/7.22 thf(zip_derived_cl100, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ ((((((('#sk2' @ ('#sk57' @ X2) @ ('#sk82' @ X2)) | ('#sk1' @ 52.14/7.22 ('#sk57' @ X2) @ ('#sk82' @ X2)))) & 52.14/7.22 (X2 @ ('#sk57' @ X2)))) => 52.14/7.22 (X2 @ ('#sk82' @ X2)))) 52.14/7.22 | ~ (X2 @ ('#sk27' @ X2)) 52.14/7.22 | ~ ('#form11') 52.14/7.22 | (X2 @ '#sk4'))), 52.14/7.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl89])). 52.14/7.22 thf(zip_derived_cl114, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 (~ (X2 @ ('#sk82' @ X2)) 52.14/7.22 | (X2 @ '#sk4') 52.14/7.22 | ~ ('#form11') 52.14/7.22 | ~ (X2 @ ('#sk27' @ X2)))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 52.14/7.22 thf(zip_derived_cl113, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ((((('#sk2' @ ('#sk57' @ X2) @ ('#sk82' @ X2)) | ('#sk1' @ 52.14/7.22 ('#sk57' @ X2) @ ('#sk82' @ X2)))) & 52.14/7.22 (X2 @ ('#sk57' @ X2)))) 52.14/7.22 | (X2 @ '#sk4') 52.14/7.22 | ~ ('#form11') 52.14/7.22 | ~ (X2 @ ('#sk27' @ X2)))), 52.14/7.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 52.14/7.22 thf(zip_derived_cl128, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( (X2 @ ('#sk57' @ X2)) 52.14/7.22 | ~ (X2 @ ('#sk27' @ X2)) 52.14/7.22 | ~ ('#form11') 52.14/7.22 | (X2 @ '#sk4'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl113])). 52.14/7.22 thf(zip_derived_cl24, plain, 52.14/7.22 (![X2 : a]: (~ ('#sk2' @ '#sk3' @ X2) | ('#sk5' @ X2))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 52.14/7.22 thf(zip_derived_cl127, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ((('#sk2' @ ('#sk57' @ X2) @ ('#sk82' @ X2)) | ('#sk1' @ 52.14/7.22 ('#sk57' @ X2) @ ('#sk82' @ X2)))) 52.14/7.22 | ~ (X2 @ ('#sk27' @ X2)) 52.14/7.22 | ~ ('#form11') 52.14/7.22 | (X2 @ '#sk4'))), 52.14/7.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl113])). 52.14/7.22 thf(zip_derived_cl142, plain, 52.14/7.22 (![X2 : a > $o]: 52.14/7.22 ( ('#sk2' @ ('#sk57' @ X2) @ ('#sk82' @ X2)) 52.14/7.22 | ('#sk1' @ ('#sk57' @ X2) @ ('#sk82' @ X2)) 52.14/7.22 | (X2 @ '#sk4') 52.14/7.22 | ~ ('#form11') 52.14/7.22 | ~ (X2 @ ('#sk27' @ X2)))), 52.14/7.22 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl127])). 52.14/7.22 thf(zip_derived_cl13311, plain, ($false), 52.14/7.22 inference('eprover', [status(thm)], 52.14/7.22 [zip_derived_cl104, zip_derived_cl153, zip_derived_cl168, 52.14/7.22 zip_derived_cl182, zip_derived_cl139, zip_derived_cl154, 52.14/7.22 zip_derived_cl105, zip_derived_cl170, zip_derived_cl186, 52.14/7.22 zip_derived_cl187, zip_derived_cl391, zip_derived_cl386, 52.14/7.22 zip_derived_cl389, zip_derived_cl393, zip_derived_cl72, 52.14/7.22 zip_derived_cl151, zip_derived_cl179, zip_derived_cl181, 52.14/7.22 zip_derived_cl388, zip_derived_cl188, zip_derived_cl332, 52.14/7.22 zip_derived_cl120, zip_derived_cl189, zip_derived_cl331, 52.14/7.22 zip_derived_cl132, zip_derived_cl333, zip_derived_cl131, 52.14/7.22 zip_derived_cl176, zip_derived_cl150, zip_derived_cl394, 52.14/7.22 zip_derived_cl121, zip_derived_cl177, zip_derived_cl226, 52.14/7.22 zip_derived_cl25, zip_derived_cl220, zip_derived_cl224, 52.14/7.22 zip_derived_cl227, zip_derived_cl126, zip_derived_cl228, 52.14/7.22 zip_derived_cl40, zip_derived_cl11, zip_derived_cl39, 52.14/7.22 zip_derived_cl114, zip_derived_cl128, zip_derived_cl24, 52.14/7.22 zip_derived_cl142])). 52.14/7.22 52.14/7.22 % SZS output end Refutation 52.14/7.22 52.14/7.22 52.14/7.22 % Terminating... 52.86/7.32 % Runner terminated. 52.86/7.33 % Zipperpin 1.5 exiting 52.86/7.33 EOF