0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.D6u6xCoNw2 true 0.14/0.36 % Computer : n021.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 1200 0.14/0.36 % WCLimit : 120 0.14/0.36 % DateTime : Tue Jul 13 12:24:55 EDT 2021 0.14/0.36 % CPUTime : 0.14/0.36 % Running portfolio for 120 s 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.14/0.36 % Number of cores: 8 0.14/0.37 % Python version: Python 3.6.8 0.14/0.37 % Running in HO mode 0.59/0.70 % Total configuration time : 828 0.59/0.70 % Estimated wc time : 983 0.59/0.70 % Estimated cpu time (8 cpus) : 122.875 0.59/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 47s 0.59/0.76 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 47s 0.59/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 18s 0.59/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 47s 0.59/0.78 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 53s 0.59/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 41s 0.59/0.79 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 35s 0.59/0.79 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 24s 32.70/4.76 % Solved by lams/20_acsne_simpl.sh. 32.70/4.76 % running E: timeout 13 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.D6u6xCoNw2/e_inputb41652 --cpu-limit=11 --auto -s -p 32.70/4.76 % done 382 iterations in 3.870s 32.70/4.76 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 32.70/4.76 % SZS output start Refutation 32.70/4.76 thf(a_type, type, a: $tType). 32.70/4.76 thf('#sk175_type', type, '#sk175': (a > $o) > a). 32.70/4.76 thf('#form11_type', type, '#form11': $o). 32.70/4.76 thf('#form45_type', type, '#form45': $o). 32.70/4.76 thf('#sk12_type', type, '#sk12': a). 32.70/4.76 thf('#sk5_type', type, '#sk5': a > $o). 32.70/4.76 thf('#sk83_type', type, '#sk83': (a > $o) > a). 32.70/4.76 thf('#form295_type', type, '#form295': (a > $o) > $o). 32.70/4.76 thf('#sk57_type', type, '#sk57': (a > $o) > a). 32.70/4.76 thf('#sk122_type', type, '#sk122': (a > $o) > a). 32.70/4.76 thf('#sk73_type', type, '#sk73': (a > $o) > a). 32.70/4.76 thf('#sk27_type', type, '#sk27': (a > $o) > a). 32.70/4.76 thf('#sk4_type', type, '#sk4': a). 32.70/4.76 thf('#sk130_type', type, '#sk130': (a > $o) > a). 32.70/4.76 thf('#sk3_type', type, '#sk3': a). 32.70/4.76 thf('#sk166_type', type, '#sk166': (a > $o) > a). 32.70/4.76 thf('#sk140_type', type, '#sk140': (a > $o) > a). 32.70/4.76 thf('#form139_type', type, '#form139': (a > $o) > $o). 32.70/4.76 thf('#sk8_type', type, '#sk8': a). 32.70/4.76 thf('#sk284_type', type, '#sk284': (a > $o) > a). 32.70/4.76 thf('#sk222_type', type, '#sk222': (a > $o) > a). 32.70/4.76 thf('#sk10_type', type, '#sk10': a). 32.70/4.76 thf('#sk7_type', type, '#sk7': a). 32.70/4.76 thf('#sk2_type', type, '#sk2': a > a > $o). 32.70/4.76 thf('#sk6_type', type, '#sk6': a). 32.70/4.76 thf('#sk20_type', type, '#sk20': a > $o). 32.70/4.76 thf('#sk16_type', type, '#sk16': a > $o). 32.70/4.76 thf('#sk49_type', type, '#sk49': (a > $o) > a). 32.70/4.76 thf('#sk1_type', type, '#sk1': a > a > $o). 32.70/4.76 thf('#sk296_type', type, '#sk296': (a > $o) > a). 32.70/4.76 thf('#form9_type', type, '#form9': $o). 32.70/4.76 thf('#sk126_type', type, '#sk126': (a > $o) > a). 32.70/4.76 thf('#sk61_type', type, '#sk61': (a > $o) > a). 32.70/4.76 thf(cTHM251G_pme, conjecture, 32.70/4.76 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 32.70/4.76 ( ( ~( ( ( ![Xx0:a,Xy0:a,Xz:a]: 32.70/4.76 ( ( ( ![Xq:( a > $o )]: 32.70/4.76 ( ( ( ![Xu:a,Xv:a]: 32.70/4.76 ( ( ( Xq @ Xu ) & 32.70/4.76 ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 32.70/4.76 ( Xq @ Xv ) ) ) & 32.70/4.76 ( ![Xw:a]: 32.70/4.76 ( ( ( S @ Xy0 @ Xw ) | ( R @ Xy0 @ Xw ) ) => 32.70/4.76 ( Xq @ Xw ) ) ) ) => 32.70/4.76 ( Xq @ Xz ) ) ) & 32.70/4.76 ( ![Xq:( a > $o )]: 32.70/4.76 ( ( ( ![Xw:a]: 32.70/4.76 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 32.70/4.76 ( Xq @ Xw ) ) ) & 32.70/4.76 ( ![Xu:a,Xv:a]: 32.70/4.76 ( ( ( Xq @ Xu ) & 32.70/4.76 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 32.70/4.76 ( Xq @ Xv ) ) ) ) => 32.70/4.76 ( Xq @ Xy0 ) ) ) ) => 32.70/4.76 ( ![Xq:( a > $o )]: 32.70/4.76 ( ( ( ![Xw:a]: 32.70/4.76 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 32.70/4.76 ( Xq @ Xw ) ) ) & 32.70/4.76 ( ![Xu:a,Xv:a]: 32.70/4.76 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & 32.70/4.76 ( Xq @ Xu ) ) => 32.70/4.76 ( Xq @ Xv ) ) ) ) => 32.70/4.76 ( Xq @ Xz ) ) ) ) ) & 32.70/4.76 ( ![Xx0:a,Xy0:a]: 32.70/4.76 ( ( ( ![Xq:( a > $o )]: 32.70/4.76 ( ( ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 32.70/4.76 ( ![Xu:a,Xv:a]: 32.70/4.76 ( ( ( S @ Xu @ Xv ) & ( Xq @ Xu ) ) => ( Xq @ Xv ) ) ) ) => 32.70/4.76 ( Xq @ Xy0 ) ) ) | 32.70/4.76 ( ![Xq:( a > $o )]: 32.70/4.76 ( ( ( ![Xu:a,Xv:a]: 32.70/4.76 ( ( ( Xq @ Xu ) & ( R @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) & 32.70/4.76 ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 32.70/4.76 ( Xq @ Xy0 ) ) ) ) => 32.70/4.76 ( ![Xq:( a > $o )]: 32.70/4.76 ( ( ( ![Xu:a,Xv:a]: 32.70/4.76 ( ( ( Xq @ Xu ) & 32.70/4.76 ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 32.70/4.76 ( Xq @ Xv ) ) ) & 32.70/4.76 ( ![Xw:a]: 32.70/4.76 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 32.70/4.76 ( Xq @ Xw ) ) ) ) => 32.70/4.76 ( Xq @ Xy0 ) ) ) ) ) ) => 32.70/4.76 ( ![Xq:( a > $o )]: 32.70/4.76 ( ( ( ![Xw:a]: 32.70/4.76 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 32.70/4.76 ( ![Xu:a,Xv:a]: 32.70/4.76 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 32.70/4.76 ( Xq @ Xv ) ) ) ) => 32.70/4.76 ( Xq @ Xy ) ) ) ) ) | 32.70/4.76 ( ![Xq:( a > $o )]: 32.70/4.76 ( ( ( ![Xw:a]: 32.70/4.76 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 32.70/4.76 ( ![Xu:a,Xv:a]: 32.70/4.76 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 32.70/4.76 ( Xq @ Xv ) ) ) ) => 32.70/4.76 ( Xq @ Xy ) ) ) ))). 32.70/4.76 thf(zf_stmt_0, negated_conjecture, 32.70/4.76 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 32.70/4.76 ( ( ~( ( ( ![Xx0:a,Xy0:a,Xz:a]: 32.70/4.76 ( ( ( ![Xq:( a > $o )]: 32.70/4.76 ( ( ( ![Xu:a,Xv:a]: 32.70/4.76 ( ( ( Xq @ Xu ) & 32.70/4.76 ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 32.70/4.76 ( Xq @ Xv ) ) ) & 32.70/4.76 ( ![Xw:a]: 32.70/4.76 ( ( ( S @ Xy0 @ Xw ) | ( R @ Xy0 @ Xw ) ) => 32.70/4.76 ( Xq @ Xw ) ) ) ) => 32.70/4.76 ( Xq @ Xz ) ) ) & 32.70/4.76 ( ![Xq:( a > $o )]: 32.70/4.76 ( ( ( ![Xw:a]: 32.70/4.76 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 32.70/4.76 ( Xq @ Xw ) ) ) & 32.70/4.76 ( ![Xu:a,Xv:a]: 32.70/4.76 ( ( ( Xq @ Xu ) & 32.70/4.76 ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) ) => 32.70/4.76 ( Xq @ Xv ) ) ) ) => 32.70/4.76 ( Xq @ Xy0 ) ) ) ) => 32.70/4.76 ( ![Xq:( a > $o )]: 32.70/4.76 ( ( ( ![Xw:a]: 32.70/4.76 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 32.70/4.76 ( Xq @ Xw ) ) ) & 32.70/4.76 ( ![Xu:a,Xv:a]: 32.70/4.76 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & 32.70/4.76 ( Xq @ Xu ) ) => 32.70/4.76 ( Xq @ Xv ) ) ) ) => 32.70/4.76 ( Xq @ Xz ) ) ) ) ) & 32.70/4.76 ( ![Xx0:a,Xy0:a]: 32.70/4.76 ( ( ( ![Xq:( a > $o )]: 32.70/4.76 ( ( ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 32.70/4.76 ( ![Xu:a,Xv:a]: 32.70/4.76 ( ( ( S @ Xu @ Xv ) & ( Xq @ Xu ) ) => 32.70/4.76 ( Xq @ Xv ) ) ) ) => 32.70/4.76 ( Xq @ Xy0 ) ) ) | 32.70/4.76 ( ![Xq:( a > $o )]: 32.70/4.76 ( ( ( ![Xu:a,Xv:a]: 32.70/4.76 ( ( ( Xq @ Xu ) & ( R @ Xu @ Xv ) ) => 32.70/4.76 ( Xq @ Xv ) ) ) & 32.70/4.76 ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 32.70/4.76 ( Xq @ Xy0 ) ) ) ) => 32.70/4.76 ( ![Xq:( a > $o )]: 32.70/4.76 ( ( ( ![Xu:a,Xv:a]: 32.70/4.76 ( ( ( Xq @ Xu ) & 32.70/4.76 ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 32.70/4.76 ( Xq @ Xv ) ) ) & 32.70/4.76 ( ![Xw:a]: 32.70/4.76 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 32.70/4.76 ( Xq @ Xw ) ) ) ) => 32.70/4.76 ( Xq @ Xy0 ) ) ) ) ) ) => 32.70/4.76 ( ![Xq:( a > $o )]: 32.70/4.76 ( ( ( ![Xw:a]: 32.70/4.76 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 32.70/4.76 ( ![Xu:a,Xv:a]: 32.70/4.76 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 32.70/4.76 ( Xq @ Xv ) ) ) ) => 32.70/4.76 ( Xq @ Xy ) ) ) ) ) | 32.70/4.76 ( ![Xq:( a > $o )]: 32.70/4.76 ( ( ( ![Xw:a]: 32.70/4.76 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) & 32.70/4.76 ( ![Xu:a,Xv:a]: 32.70/4.76 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 32.70/4.76 ( Xq @ Xv ) ) ) ) => 32.70/4.76 ( Xq @ Xy ) ) ) ) )), 32.70/4.76 inference('cnf.neg', [status(esa)], [cTHM251G_pme])). 32.70/4.76 thf(zip_derived_cl0, plain, 32.70/4.76 (~ (((!!) @ (^[Y0 : a > a > $o]: 32.70/4.76 (((!!) @ (^[Y1 : a > a > $o]: 32.70/4.76 (((!!) @ (^[Y2 : a]: 32.70/4.76 (((!!) @ (^[Y3 : a]: 32.70/4.76 (((((~) @ (((( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y4 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y8 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y9 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y7 @ 32.70/4.76 Y8) & 32.70/4.76 (( 32.70/4.76 (Y1 @ 32.70/4.76 Y8 @ 32.70/4.76 Y9) | 32.70/4.76 (Y0 @ 32.70/4.76 Y8 @ Y9))))) => 32.70/4.76 (Y7 @ Y9))))))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y8 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y1 @ 32.70/4.76 Y5 @ 32.70/4.76 Y8) | 32.70/4.76 (Y0 @ 32.70/4.76 Y5 @ Y8))) => 32.70/4.76 (Y7 @ Y8)))))))) => 32.70/4.76 (Y7 @ Y6)))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y8 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y1 @ 32.70/4.76 Y4 @ 32.70/4.76 Y8) | 32.70/4.76 (Y0 @ 32.70/4.76 Y4 @ Y8))) => 32.70/4.76 (Y7 @ Y8)))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y8 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y9 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y7 @ 32.70/4.76 Y8) & 32.70/4.76 (( 32.70/4.76 (Y0 @ 32.70/4.76 Y8 @ 32.70/4.76 Y9) | 32.70/4.76 (Y1 @ 32.70/4.76 Y8 @ Y9))))) => 32.70/4.76 (Y7 @ Y9))))))))))) => 32.70/4.76 (Y7 @ Y5)))))))) => 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y8 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y1 @ 32.70/4.76 Y4 @ 32.70/4.76 Y8) | 32.70/4.76 (Y0 @ 32.70/4.76 Y4 @ Y8))) => 32.70/4.76 (Y7 @ Y8)))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y8 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y9 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y1 @ 32.70/4.76 Y8 @ 32.70/4.76 Y9) | 32.70/4.76 (Y0 @ 32.70/4.76 Y8 @ Y9))) & 32.70/4.76 (Y7 @ Y8))) => 32.70/4.76 (Y7 @ Y9))))))))))) => 32.70/4.76 (Y7 @ Y6))))))))))))))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y4 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (Y1 @ 32.70/4.76 Y4 @ 32.70/4.76 Y7) => 32.70/4.76 (Y6 @ Y7)))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y8 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y1 @ 32.70/4.76 Y7 @ 32.70/4.76 Y8) & 32.70/4.76 (Y6 @ Y7))) => 32.70/4.76 (Y6 @ Y8))))))))))) => 32.70/4.76 (Y6 @ Y5)))))) | 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y8 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y6 @ 32.70/4.76 Y7) & 32.70/4.76 (Y0 @ 32.70/4.76 Y7 @ Y8))) => 32.70/4.76 (Y6 @ Y8))))))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (Y0 @ 32.70/4.76 Y4 @ 32.70/4.76 Y7) => 32.70/4.76 (Y6 @ Y7)))))))) => 32.70/4.76 (Y6 @ Y5)))))))) => 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y8 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y6 @ 32.70/4.76 Y7) & 32.70/4.76 (( 32.70/4.76 (Y1 @ 32.70/4.76 Y7 @ 32.70/4.76 Y8) | 32.70/4.76 (Y0 @ 32.70/4.76 Y7 @ Y8))))) => 32.70/4.76 (Y6 @ Y8))))))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y0 @ 32.70/4.76 Y4 @ 32.70/4.76 Y7) | 32.70/4.76 (Y1 @ 32.70/4.76 Y4 @ Y7))) => 32.70/4.76 (Y6 @ Y7)))))))) => 32.70/4.76 (Y6 @ Y5)))))))))))))))) => 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y4 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y1 @ 32.70/4.76 Y2 @ 32.70/4.76 Y5) | 32.70/4.76 (Y0 @ 32.70/4.76 Y2 @ Y5))) => 32.70/4.76 (Y4 @ Y5)))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y1 @ 32.70/4.76 Y5 @ 32.70/4.76 Y6) | 32.70/4.76 (Y0 @ 32.70/4.76 Y5 @ Y6))) & 32.70/4.76 (Y4 @ Y5))) => 32.70/4.76 (Y4 @ Y6))))))))))) => 32.70/4.76 (Y4 @ Y3)))))))))) | 32.70/4.76 (((!!) @ (^[Y4 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y1 @ 32.70/4.76 Y2 @ 32.70/4.76 Y5) | 32.70/4.76 (Y0 @ 32.70/4.76 Y2 @ Y5))) => 32.70/4.76 (Y4 @ Y5)))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y0 @ 32.70/4.76 Y5 @ 32.70/4.76 Y6) | 32.70/4.76 (Y1 @ 32.70/4.76 Y5 @ Y6))) & 32.70/4.76 (Y4 @ Y5))) => 32.70/4.76 (Y4 @ Y6))))))))))) => 32.70/4.76 (Y4 @ Y3))))))))))))))))))))), 32.70/4.76 inference('cnf', [status(esa)], [zf_stmt_0])). 32.70/4.76 thf(zip_derived_cl1, plain, 32.70/4.76 (~ (((!!) @ (^[Y0 : a > a > $o]: 32.70/4.76 (((!!) @ (^[Y1 : a]: 32.70/4.76 (((!!) @ (^[Y2 : a]: 32.70/4.76 (((((~) @ (((((((!!) @ (^[Y3 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y4 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y8 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y6 @ 32.70/4.76 Y7) & 32.70/4.76 (( 32.70/4.76 (Y0 @ 32.70/4.76 Y7 @ 32.70/4.76 Y8) | 32.70/4.76 ('#sk1' @ 32.70/4.76 Y7 @ Y8))))) => 32.70/4.76 (Y6 @ Y8))))))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y0 @ 32.70/4.76 Y4 @ 32.70/4.76 Y7) | 32.70/4.76 ('#sk1' @ 32.70/4.76 Y4 @ Y7))) => 32.70/4.76 (Y6 @ Y7)))))))) => 32.70/4.76 (Y6 @ Y5)))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y0 @ 32.70/4.76 Y3 @ 32.70/4.76 Y7) | 32.70/4.76 ('#sk1' @ 32.70/4.76 Y3 @ Y7))) => 32.70/4.76 (Y6 @ Y7)))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y8 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y6 @ 32.70/4.76 Y7) & 32.70/4.76 (( 32.70/4.76 ('#sk1' @ 32.70/4.76 Y7 @ 32.70/4.76 Y8) | 32.70/4.76 (Y0 @ 32.70/4.76 Y7 @ Y8))))) => 32.70/4.76 (Y6 @ Y8))))))))))) => 32.70/4.76 (Y6 @ Y4)))))))) => 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y0 @ 32.70/4.76 Y3 @ 32.70/4.76 Y7) | 32.70/4.76 ('#sk1' @ 32.70/4.76 Y3 @ Y7))) => 32.70/4.76 (Y6 @ Y7)))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y8 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y0 @ 32.70/4.76 Y7 @ 32.70/4.76 Y8) | 32.70/4.76 ('#sk1' @ 32.70/4.76 Y7 @ Y8))) & 32.70/4.76 (Y6 @ Y7))) => 32.70/4.76 (Y6 @ Y8))))))))))) => 32.70/4.76 (Y6 @ Y5))))))))))))))))) & 32.70/4.76 (((!!) @ (^[Y3 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y4 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a]: 32.70/4.76 (( 32.70/4.76 (Y0 @ 32.70/4.76 Y3 @ 32.70/4.76 Y6) => 32.70/4.76 (Y5 @ Y6)))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y0 @ 32.70/4.76 Y6 @ 32.70/4.76 Y7) & 32.70/4.76 (Y5 @ Y6))) => 32.70/4.76 (Y5 @ Y7))))))))))) => 32.70/4.76 (Y5 @ Y4)))))) | 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y5 @ 32.70/4.76 Y6) & 32.70/4.76 ('#sk1' @ 32.70/4.76 Y6 @ Y7))) => 32.70/4.76 (Y5 @ Y7))))))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a]: 32.70/4.76 (( 32.70/4.76 ('#sk1' @ 32.70/4.76 Y3 @ 32.70/4.76 Y6) => 32.70/4.76 (Y5 @ Y6)))))))) => 32.70/4.76 (Y5 @ Y4)))))))) => 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y5 @ 32.70/4.76 Y6) & 32.70/4.76 (( 32.70/4.76 (Y0 @ 32.70/4.76 Y6 @ 32.70/4.76 Y7) | 32.70/4.76 ('#sk1' @ 32.70/4.76 Y6 @ Y7))))) => 32.70/4.76 (Y5 @ Y7))))))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 ('#sk1' @ 32.70/4.76 Y3 @ 32.70/4.76 Y6) | 32.70/4.76 (Y0 @ 32.70/4.76 Y3 @ Y6))) => 32.70/4.76 (Y5 @ Y6)))))))) => 32.70/4.76 (Y5 @ Y4)))))))))))))))) => 32.70/4.76 (((!!) @ (^[Y3 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y4 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y0 @ 32.70/4.76 Y1 @ 32.70/4.76 Y4) | 32.70/4.76 ('#sk1' @ 32.70/4.76 Y1 @ Y4))) => 32.70/4.76 (Y3 @ Y4)))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y4 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y0 @ 32.70/4.76 Y4 @ 32.70/4.76 Y5) | 32.70/4.76 ('#sk1' @ 32.70/4.76 Y4 @ Y5))) & 32.70/4.76 (Y3 @ Y4))) => 32.70/4.76 (Y3 @ Y5))))))))))) => 32.70/4.76 (Y3 @ Y2)))))))))) | 32.70/4.76 (((!!) @ (^[Y3 : a > $o]: 32.70/4.76 (((((((!!) @ ( 32.70/4.76 ^[Y4 : a]: 32.70/4.76 (((( 32.70/4.76 (Y0 @ 32.70/4.76 Y1 @ Y4) | 32.70/4.76 ('#sk1' @ 32.70/4.76 Y1 @ Y4))) => 32.70/4.76 (Y3 @ Y4)))))) & 32.70/4.76 (((!!) @ ( 32.70/4.76 ^[Y4 : a]: 32.70/4.76 (((!!) @ ( 32.70/4.76 ^[Y5 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 ('#sk1' @ 32.70/4.76 Y4 @ 32.70/4.76 Y5) | 32.70/4.76 (Y0 @ 32.70/4.76 Y4 @ Y5))) & 32.70/4.76 (Y3 @ Y4))) => 32.70/4.76 (Y3 @ Y5))))))))))) => 32.70/4.76 (Y3 @ Y2)))))))))))))))))), 32.70/4.76 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 32.70/4.76 thf(zip_derived_cl2, plain, 32.70/4.76 (~ (((!!) @ (^[Y0 : a]: 32.70/4.76 (((!!) @ (^[Y1 : a]: 32.70/4.76 (((((~) @ (((((((!!) @ (^[Y2 : a]: 32.70/4.76 (((!!) @ (^[Y3 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y4 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y5 @ 32.70/4.76 Y6) & 32.70/4.76 (( 32.70/4.76 ('#sk2' @ 32.70/4.76 Y6 @ 32.70/4.76 Y7) | 32.70/4.76 ('#sk1' @ 32.70/4.76 Y6 @ Y7))))) => 32.70/4.76 (Y5 @ Y7))))))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 ('#sk2' @ 32.70/4.76 Y3 @ 32.70/4.76 Y6) | 32.70/4.76 ('#sk1' @ 32.70/4.76 Y3 @ Y6))) => 32.70/4.76 (Y5 @ Y6)))))))) => 32.70/4.76 (Y5 @ Y4)))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 ('#sk2' @ 32.70/4.76 Y2 @ 32.70/4.76 Y6) | 32.70/4.76 ('#sk1' @ 32.70/4.76 Y2 @ Y6))) => 32.70/4.76 (Y5 @ Y6)))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y5 @ 32.70/4.76 Y6) & 32.70/4.76 (( 32.70/4.76 ('#sk1' @ 32.70/4.76 Y6 @ 32.70/4.76 Y7) | 32.70/4.76 ('#sk2' @ 32.70/4.76 Y6 @ Y7))))) => 32.70/4.76 (Y5 @ Y7))))))))))) => 32.70/4.76 (Y5 @ Y3)))))))) => 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 ('#sk2' @ 32.70/4.76 Y2 @ 32.70/4.76 Y6) | 32.70/4.76 ('#sk1' @ 32.70/4.76 Y2 @ Y6))) => 32.70/4.76 (Y5 @ Y6)))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y7 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 ('#sk2' @ 32.70/4.76 Y6 @ 32.70/4.76 Y7) | 32.70/4.76 ('#sk1' @ 32.70/4.76 Y6 @ Y7))) & 32.70/4.76 (Y5 @ Y6))) => 32.70/4.76 (Y5 @ Y7))))))))))) => 32.70/4.76 (Y5 @ Y4))))))))))))))))) & 32.70/4.76 (((!!) @ (^[Y2 : a]: 32.70/4.76 (((!!) @ (^[Y3 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y4 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a]: 32.70/4.76 (( 32.70/4.76 ('#sk2' @ 32.70/4.76 Y2 @ 32.70/4.76 Y5) => 32.70/4.76 (Y4 @ Y5)))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 ('#sk2' @ 32.70/4.76 Y5 @ 32.70/4.76 Y6) & 32.70/4.76 (Y4 @ Y5))) => 32.70/4.76 (Y4 @ Y6))))))))))) => 32.70/4.76 (Y4 @ Y3)))))) | 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y4 : a > $o]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a]: 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y6 : a]: 32.70/4.76 (( 32.70/4.76 (( 32.70/4.76 (Y4 @ 32.70/4.76 Y5) & 32.70/4.76 ('#sk1' @ 32.70/4.76 Y5 @ Y6))) => 32.70/4.76 (Y4 @ Y6))))))))) & 32.70/4.76 (( 32.70/4.76 (!!) @ ( 32.70/4.76 ^[Y5 : a]: 32.70/4.76 (( 32.70/4.76 ('#sk1' @ 32.70/4.76 Y2 @ 32.70/4.76 Y5) => 32.70/4.76 (Y4 @ Y5)))))))) => 32.70/4.76 (Y4 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Y4))))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk2' @ 32.70/4.77 Y0 @ Y3))) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))))))))))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl9])). 32.70/4.77 thf(zip_derived_cl15, plain, 32.70/4.77 ((~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((((((!!) @ (^[Y1 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y2 : a]: 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((((Y1 @ 32.70/4.77 Y2) & 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y2 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk1' @ 32.70/4.77 Y2 @ Y3))))) => 32.70/4.77 (Y1 @ Y3))))))))) & 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ 32.70/4.77 Y2) | ('#sk1' @ 32.70/4.77 '#sk7' @ Y2))) => 32.70/4.77 (Y1 @ Y2)))))))) => 32.70/4.77 (Y1 @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y2 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ 32.70/4.77 Y2) | ('#sk1' @ 32.70/4.77 '#sk6' @ Y2))) => 32.70/4.77 (Y1 @ Y2)))))) & 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((((Y1 @ 32.70/4.77 Y2) & 32.70/4.77 (( 32.70/4.77 ('#sk1' @ 32.70/4.77 Y2 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk2' @ 32.70/4.77 Y2 @ Y3))))) => 32.70/4.77 (Y1 @ Y3))))))))))) => 32.70/4.77 (Y1 @ '#sk7')))))))) => 32.70/4.77 (((!!) @ (^[Y1 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y2 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ 32.70/4.77 Y2) | ('#sk1' @ 32.70/4.77 '#sk6' @ Y2))) => 32.70/4.77 (Y1 @ Y2)))))) & 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((((((('#sk2' @ 32.70/4.77 Y2 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk1' @ 32.70/4.77 Y2 @ Y3))) & 32.70/4.77 (Y1 @ Y2))) => 32.70/4.77 (Y1 @ Y3))))))))))) => 32.70/4.77 (Y1 @ Y0))))))))))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk2' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) & 32.70/4.77 (Y2 @ Y3))) => 32.70/4.77 (Y2 @ Y4))))))))))) => 32.70/4.77 (Y2 @ Y1)))))) | 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))) => 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 ( 32.70/4.77 ( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) | 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk2' @ 32.70/4.77 Y0 @ Y3))) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))))))))) 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk3' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk4')))))))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 32.70/4.77 thf(zip_derived_cl18, plain, 32.70/4.77 ((~ (((((((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & 32.70/4.77 ((('#sk2' @ Y1 @ 32.70/4.77 Y2) | ('#sk1' @ 32.70/4.77 Y1 @ Y2))))) => 32.70/4.77 (Y0 @ Y2))))))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y1) | 32.70/4.77 ('#sk1' @ '#sk7' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))))) => 32.70/4.77 (Y0 @ '#sk8')))))) & 32.70/4.77 (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ Y1) | 32.70/4.77 ('#sk1' @ '#sk6' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & 32.70/4.77 ((('#sk1' @ Y1 @ 32.70/4.77 Y2) | ('#sk2' @ 32.70/4.77 Y1 @ Y2))))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk7')))))))) => 32.70/4.77 (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk6' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk8')))))))) 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk3' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk4')))))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk2' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) & 32.70/4.77 (Y2 @ Y3))) => 32.70/4.77 (Y2 @ Y4))))))))))) => 32.70/4.77 (Y2 @ Y1)))))) | 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))) => 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 ( 32.70/4.77 ( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) | 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk2' @ 32.70/4.77 Y0 @ Y3))) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))))))))))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])). 32.70/4.77 thf(zip_derived_cl21, plain, 32.70/4.77 (( (((((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & 32.70/4.77 ((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))))) => 32.70/4.77 (Y0 @ Y2))))))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk7' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))))) => 32.70/4.77 (Y0 @ '#sk8')))))) & 32.70/4.77 (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk6' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & 32.70/4.77 ((('#sk1' @ Y1 @ Y2) | 32.70/4.77 ('#sk2' @ Y1 @ Y2))))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk7')))))))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk2' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) & 32.70/4.77 (Y2 @ Y3))) => 32.70/4.77 (Y2 @ Y4))))))))))) => 32.70/4.77 (Y2 @ Y1)))))) | 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))) => 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 ( 32.70/4.77 ( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) | 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk2' @ 32.70/4.77 Y0 @ Y3))) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))))))))) 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk3' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk4')))))))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 32.70/4.77 thf(zip_derived_cl26, plain, 32.70/4.77 (( (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & 32.70/4.77 ((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))))) => 32.70/4.77 (Y0 @ Y2))))))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk7' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))))) => 32.70/4.77 (Y0 @ '#sk8')))))) 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk3' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk4')))))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk2' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) & 32.70/4.77 (Y2 @ Y3))) => 32.70/4.77 (Y2 @ Y4))))))))))) => 32.70/4.77 (Y2 @ Y1)))))) | 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))) => 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 ( 32.70/4.77 ( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) | 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk2' @ 32.70/4.77 Y0 @ Y3))) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))))))))))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 32.70/4.77 thf(zip_derived_cl32, plain, 32.70/4.77 ((~ ('#form11') 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk3' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk4')))))))), 32.70/4.77 define([status(thm)])). 32.70/4.77 thf(zip_derived_cl33, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( (((((((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 32.70/4.77 (X2 @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 32.70/4.77 Y0 @ Y1))) & 32.70/4.77 (X2 @ Y0))) => 32.70/4.77 (X2 @ Y1))))))))))) => 32.70/4.77 (X2 @ '#sk4'))) 32.70/4.77 | ~ ('#form11'))), 32.70/4.77 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 32.70/4.77 thf(zip_derived_cl34, plain, 32.70/4.77 (( (((((((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 32.70/4.77 ('#sk5' @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 32.70/4.77 Y1))) & 32.70/4.77 ('#sk5' @ Y0))) => 32.70/4.77 ('#sk5' @ Y1))))))))))) => 32.70/4.77 ('#sk5' @ '#sk4'))) 32.70/4.77 | ~ ('#form11'))), 32.70/4.77 inference('triggered_bool_instantiation', [status(thm)], 32.70/4.77 [zip_derived_cl33])). 32.70/4.77 thf(zip_derived_cl6, plain, 32.70/4.77 (~ (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk3' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk1' @ Y1 @ Y2) | 32.70/4.77 ('#sk2' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk4'))))))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 32.70/4.77 thf(zip_derived_cl8, plain, 32.70/4.77 (~ (((((((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 32.70/4.77 ('#sk5' @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 32.70/4.77 Y1))) & 32.70/4.77 ('#sk5' @ Y0))) => 32.70/4.77 ('#sk5' @ Y1))))))))))) => 32.70/4.77 ('#sk5' @ '#sk4')))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 32.70/4.77 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk4')), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 32.70/4.77 thf(zip_derived_cl207, plain, 32.70/4.77 (( (((((((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 32.70/4.77 ('#sk5' @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 32.70/4.77 Y1))) & 32.70/4.77 ('#sk5' @ Y0))) => 32.70/4.77 ('#sk5' @ Y1))))))))))) => 32.70/4.77 ($false))) 32.70/4.77 | ~ ('#form11'))), 32.70/4.77 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl11])). 32.70/4.77 thf(zip_derived_cl208, plain, 32.70/4.77 (( (((~) @ (((((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ 32.70/4.77 Y0))) => 32.70/4.77 ('#sk5' @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((((('#sk2' @ Y0 @ Y1) | 32.70/4.77 ('#sk1' @ Y0 @ Y1))) & 32.70/4.77 ('#sk5' @ Y0))) => 32.70/4.77 ('#sk5' @ Y1))))))))))))) 32.70/4.77 | ~ ('#form11'))), 32.70/4.77 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl207])). 32.70/4.77 thf(zip_derived_cl209, plain, 32.70/4.77 ((~ (((((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 32.70/4.77 ('#sk5' @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 32.70/4.77 Y1))) & 32.70/4.77 ('#sk5' @ Y0))) => 32.70/4.77 ('#sk5' @ Y1))))))))))) 32.70/4.77 | ~ ('#form11'))), 32.70/4.77 inference('simplify nested equalities', [status(thm)], 32.70/4.77 [zip_derived_cl208])). 32.70/4.77 thf(zip_derived_cl210, plain, 32.70/4.77 ((~ (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 32.70/4.77 ('#sk5' @ Y0)))))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 32.70/4.77 Y1))) & 32.70/4.77 ('#sk5' @ Y0))) => 32.70/4.77 ('#sk5' @ Y1))))))))) 32.70/4.77 | ~ ('#form11'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl209])). 32.70/4.77 thf(zip_derived_cl211, plain, 32.70/4.77 ((~ ((((('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')) | ('#sk1' @ '#sk3' @ 32.70/4.77 ('#sk27' @ '#sk5')))) => 32.70/4.77 ('#sk5' @ ('#sk27' @ '#sk5')))) 32.70/4.77 | ~ ('#form11') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 32.70/4.77 Y1))) & 32.70/4.77 ('#sk5' @ Y0))) => 32.70/4.77 ('#sk5' @ Y1))))))))))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl210])). 32.70/4.77 thf(zip_derived_cl213, plain, 32.70/4.77 ((~ ('#sk5' @ ('#sk27' @ '#sk5')) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 32.70/4.77 Y1))) & 32.70/4.77 ('#sk5' @ Y0))) => 32.70/4.77 ('#sk5' @ Y1))))))))) 32.70/4.77 | ~ ('#form11'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl211])). 32.70/4.77 thf(zip_derived_cl215, plain, 32.70/4.77 ((~ (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((((('#sk2' @ ('#sk57' @ '#sk5') @ Y0) | ('#sk1' @ 32.70/4.77 ('#sk57' @ '#sk5') @ Y0))) & 32.70/4.77 ('#sk5' @ ('#sk57' @ '#sk5')))) => 32.70/4.77 ('#sk5' @ Y0)))))) 32.70/4.77 | ~ ('#form11') 32.70/4.77 | ~ ('#sk5' @ ('#sk27' @ '#sk5')))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl213])). 32.70/4.77 thf(zip_derived_cl217, plain, 32.70/4.77 ((~ ((((((('#sk2' @ ('#sk57' @ '#sk5') @ ('#sk83' @ '#sk5')) | ('#sk1' @ 32.70/4.77 ('#sk57' @ '#sk5') @ ('#sk83' @ '#sk5')))) & 32.70/4.77 ('#sk5' @ ('#sk57' @ '#sk5')))) => 32.70/4.77 ('#sk5' @ ('#sk83' @ '#sk5')))) 32.70/4.77 | ~ ('#sk5' @ ('#sk27' @ '#sk5')) 32.70/4.77 | ~ ('#form11'))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl215])). 32.70/4.77 thf(zip_derived_cl220, plain, 32.70/4.77 ((~ ('#sk5' @ ('#sk83' @ '#sk5')) 32.70/4.77 | ~ ('#form11') 32.70/4.77 | ~ ('#sk5' @ ('#sk27' @ '#sk5')))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl217])). 32.70/4.77 thf(zip_derived_cl219, plain, 32.70/4.77 (( ((((('#sk2' @ ('#sk57' @ '#sk5') @ ('#sk83' @ '#sk5')) | ('#sk1' @ 32.70/4.77 ('#sk57' @ '#sk5') @ ('#sk83' @ '#sk5')))) & 32.70/4.77 ('#sk5' @ ('#sk57' @ '#sk5')))) 32.70/4.77 | ~ ('#form11') 32.70/4.77 | ~ ('#sk5' @ ('#sk27' @ '#sk5')))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl217])). 32.70/4.77 thf(zip_derived_cl223, plain, 32.70/4.77 (( ((('#sk2' @ ('#sk57' @ '#sk5') @ ('#sk83' @ '#sk5')) | ('#sk1' @ 32.70/4.77 ('#sk57' @ '#sk5') @ ('#sk83' @ '#sk5')))) 32.70/4.77 | ~ ('#sk5' @ ('#sk27' @ '#sk5')) 32.70/4.77 | ~ ('#form11'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl219])). 32.70/4.77 thf(zip_derived_cl227, plain, 32.70/4.77 (( ('#sk2' @ ('#sk57' @ '#sk5') @ ('#sk83' @ '#sk5')) 32.70/4.77 | ('#sk1' @ ('#sk57' @ '#sk5') @ ('#sk83' @ '#sk5')) 32.70/4.77 | ~ ('#form11') 32.70/4.77 | ~ ('#sk5' @ ('#sk27' @ '#sk5')))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl223])). 32.70/4.77 thf(zip_derived_cl10, plain, 32.70/4.77 ( (((((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 32.70/4.77 ('#sk5' @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 32.70/4.77 ('#sk5' @ Y0))) => 32.70/4.77 ('#sk5' @ Y1)))))))))))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 32.70/4.77 thf(zip_derived_cl13, plain, 32.70/4.77 ( (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 32.70/4.77 ('#sk5' @ Y0))))))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 32.70/4.77 thf(zip_derived_cl16, plain, 32.70/4.77 (![X2 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ X2) | ('#sk1' @ '#sk3' @ X2))) => ('#sk5' @ 32.70/4.77 X2)))), 32.70/4.77 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 32.70/4.77 thf(zip_derived_cl19, plain, 32.70/4.77 (![X2 : a]: 32.70/4.77 (~ ((('#sk2' @ '#sk3' @ X2) | ('#sk1' @ '#sk3' @ X2))) 32.70/4.77 | ('#sk5' @ X2))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 32.70/4.77 thf(zip_derived_cl23, plain, 32.70/4.77 (![X2 : a]: (~ ('#sk2' @ '#sk3' @ X2) | ('#sk5' @ X2))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 32.70/4.77 thf(zip_derived_cl14, plain, 32.70/4.77 ( (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 32.70/4.77 ('#sk5' @ Y0))) => 32.70/4.77 ('#sk5' @ Y1)))))))))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 32.70/4.77 thf(zip_derived_cl17, plain, 32.70/4.77 (![X2 : a]: 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) & 32.70/4.77 ('#sk5' @ X2))) => 32.70/4.77 ('#sk5' @ Y0))))))), 32.70/4.77 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 32.70/4.77 thf(zip_derived_cl20, plain, 32.70/4.77 (![X2 : a, X4 : a]: 32.70/4.77 ((((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk5' @ X2))) => 32.70/4.77 ('#sk5' @ X4)))), 32.70/4.77 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 32.70/4.77 thf(zip_derived_cl25, plain, 32.70/4.77 (![X2 : a, X4 : a]: 32.70/4.77 (~ ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk5' @ X2))) 32.70/4.77 | ('#sk5' @ X4))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 32.70/4.77 thf(zip_derived_cl31, plain, 32.70/4.77 (![X2 : a, X4 : a]: 32.70/4.77 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 32.70/4.77 | ~ ('#sk5' @ X2) 32.70/4.77 | ('#sk5' @ X4))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl25])). 32.70/4.77 thf(zip_derived_cl40, plain, 32.70/4.77 (![X2 : a, X4 : a]: 32.70/4.77 (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 32.70/4.77 thf(zip_derived_cl212, plain, 32.70/4.77 (( ((('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')) | ('#sk1' @ '#sk3' @ 32.70/4.77 ('#sk27' @ '#sk5')))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 32.70/4.77 Y1))) & 32.70/4.77 ('#sk5' @ Y0))) => 32.70/4.77 ('#sk5' @ Y1))))))))) 32.70/4.77 | ~ ('#form11'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl211])). 32.70/4.77 thf(zip_derived_cl214, plain, 32.70/4.77 (( ('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')) 32.70/4.77 | ('#sk1' @ '#sk3' @ ('#sk27' @ '#sk5')) 32.70/4.77 | ~ ('#form11') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 32.70/4.77 Y1))) & 32.70/4.77 ('#sk5' @ Y0))) => 32.70/4.77 ('#sk5' @ Y1))))))))))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl212])). 32.70/4.77 thf(zip_derived_cl216, plain, 32.70/4.77 ((~ (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((((('#sk2' @ ('#sk57' @ '#sk5') @ Y0) | ('#sk1' @ 32.70/4.77 ('#sk57' @ '#sk5') @ Y0))) & 32.70/4.77 ('#sk5' @ ('#sk57' @ '#sk5')))) => 32.70/4.77 ('#sk5' @ Y0)))))) 32.70/4.77 | ~ ('#form11') 32.70/4.77 | ('#sk1' @ '#sk3' @ ('#sk27' @ '#sk5')) 32.70/4.77 | ('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl214])). 32.70/4.77 thf(zip_derived_cl218, plain, 32.70/4.77 ((~ ((((((('#sk2' @ ('#sk57' @ '#sk5') @ ('#sk83' @ '#sk5')) | ('#sk1' @ 32.70/4.77 ('#sk57' @ '#sk5') @ ('#sk83' @ '#sk5')))) & 32.70/4.77 ('#sk5' @ ('#sk57' @ '#sk5')))) => 32.70/4.77 ('#sk5' @ ('#sk83' @ '#sk5')))) 32.70/4.77 | ('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')) 32.70/4.77 | ('#sk1' @ '#sk3' @ ('#sk27' @ '#sk5')) 32.70/4.77 | ~ ('#form11'))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl216])). 32.70/4.77 thf(zip_derived_cl222, plain, 32.70/4.77 ((~ ('#sk5' @ ('#sk83' @ '#sk5')) 32.70/4.77 | ~ ('#form11') 32.70/4.77 | ('#sk1' @ '#sk3' @ ('#sk27' @ '#sk5')) 32.70/4.77 | ('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl218])). 32.70/4.77 thf(zip_derived_cl221, plain, 32.70/4.77 (( ((((('#sk2' @ ('#sk57' @ '#sk5') @ ('#sk83' @ '#sk5')) | ('#sk1' @ 32.70/4.77 ('#sk57' @ '#sk5') @ ('#sk83' @ '#sk5')))) & 32.70/4.77 ('#sk5' @ ('#sk57' @ '#sk5')))) 32.70/4.77 | ~ ('#form11') 32.70/4.77 | ('#sk1' @ '#sk3' @ ('#sk27' @ '#sk5')) 32.70/4.77 | ('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl218])). 32.70/4.77 thf(zip_derived_cl225, plain, 32.70/4.77 (( ((('#sk2' @ ('#sk57' @ '#sk5') @ ('#sk83' @ '#sk5')) | ('#sk1' @ 32.70/4.77 ('#sk57' @ '#sk5') @ ('#sk83' @ '#sk5')))) 32.70/4.77 | ('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')) 32.70/4.77 | ('#sk1' @ '#sk3' @ ('#sk27' @ '#sk5')) 32.70/4.77 | ~ ('#form11'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl221])). 32.70/4.77 thf(zip_derived_cl228, plain, 32.70/4.77 (( ('#sk2' @ ('#sk57' @ '#sk5') @ ('#sk83' @ '#sk5')) 32.70/4.77 | ('#sk1' @ ('#sk57' @ '#sk5') @ ('#sk83' @ '#sk5')) 32.70/4.77 | ~ ('#form11') 32.70/4.77 | ('#sk1' @ '#sk3' @ ('#sk27' @ '#sk5')) 32.70/4.77 | ('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl225])). 32.70/4.77 thf(zip_derived_cl39, plain, 32.70/4.77 (![X2 : a, X4 : a]: 32.70/4.77 (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 32.70/4.77 thf(zip_derived_cl224, plain, 32.70/4.77 (( ('#sk5' @ ('#sk57' @ '#sk5')) 32.70/4.77 | ~ ('#sk5' @ ('#sk27' @ '#sk5')) 32.70/4.77 | ~ ('#form11'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl219])). 32.70/4.77 thf(zip_derived_cl226, plain, 32.70/4.77 (( ('#sk5' @ ('#sk57' @ '#sk5')) 32.70/4.77 | ('#sk2' @ '#sk3' @ ('#sk27' @ '#sk5')) 32.70/4.77 | ('#sk1' @ '#sk3' @ ('#sk27' @ '#sk5')) 32.70/4.77 | ~ ('#form11'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl221])). 32.70/4.77 thf(zip_derived_cl24, plain, 32.70/4.77 (![X2 : a]: (~ ('#sk1' @ '#sk3' @ X2) | ('#sk5' @ X2))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 32.70/4.77 thf(zip_derived_cl26, plain, 32.70/4.77 (( (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & 32.70/4.77 ((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))))) => 32.70/4.77 (Y0 @ Y2))))))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk7' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))))) => 32.70/4.77 (Y0 @ '#sk8')))))) 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk3' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk4')))))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk2' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) & 32.70/4.77 (Y2 @ Y3))) => 32.70/4.77 (Y2 @ Y4))))))))))) => 32.70/4.77 (Y2 @ Y1)))))) | 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))) => 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 ( 32.70/4.77 ( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) | 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk2' @ 32.70/4.77 Y0 @ Y3))) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))))))))))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 32.70/4.77 thf(zip_derived_cl32, plain, 32.70/4.77 ((~ ('#form11') 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk3' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk4')))))))), 32.70/4.77 define([status(thm)])). 32.70/4.77 thf(zip_derived_cl35, plain, 32.70/4.77 (( ('#form11') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk2' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) & 32.70/4.77 (Y2 @ Y3))) => 32.70/4.77 (Y2 @ Y4))))))))))) => 32.70/4.77 (Y2 @ Y1)))))) | 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))) => 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 ( 32.70/4.77 ( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) | 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk2' @ 32.70/4.77 Y0 @ Y3))) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))))))))) 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & 32.70/4.77 ((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))))) => 32.70/4.77 (Y0 @ Y2))))))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk7' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))))) => 32.70/4.77 (Y0 @ '#sk8')))))))), 32.70/4.77 inference('renaming', [status(thm)], [zip_derived_cl26, zip_derived_cl32])). 32.70/4.77 thf(zip_derived_cl22, plain, 32.70/4.77 ((~ (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk6' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk8')))))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk2' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) & 32.70/4.77 (Y2 @ Y3))) => 32.70/4.77 (Y2 @ Y4))))))))))) => 32.70/4.77 (Y2 @ Y1)))))) | 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))) => 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 ( 32.70/4.77 ( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) | 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk2' @ 32.70/4.77 Y0 @ Y3))) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))))))))) 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk3' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk4')))))))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 32.70/4.77 thf(zip_derived_cl28, plain, 32.70/4.77 (( ('#form9') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk2' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) & 32.70/4.77 (Y2 @ Y3))) => 32.70/4.77 (Y2 @ Y4))))))))))) => 32.70/4.77 (Y2 @ Y1)))))) | 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))) => 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 ( 32.70/4.77 ( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) | 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk2' @ 32.70/4.77 Y0 @ Y3))) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))))))))))), 32.70/4.77 define([status(thm)])). 32.70/4.77 thf(zip_derived_cl41, plain, 32.70/4.77 ((~ ('#form9') 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & 32.70/4.77 ((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))))) => 32.70/4.77 (Y0 @ Y2))))))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk7' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))))) => 32.70/4.77 (Y0 @ '#sk8')))))) 32.70/4.77 | ('#form11'))), 32.70/4.77 inference('renaming', [status(thm)], [zip_derived_cl35, zip_derived_cl28])). 32.70/4.77 thf(zip_derived_cl48, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( (((((((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((X2 @ Y0) & 32.70/4.77 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 32.70/4.77 Y0 @ Y1))))) => 32.70/4.77 (X2 @ Y1))))))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 32.70/4.77 (X2 @ Y0)))))))) => 32.70/4.77 (X2 @ '#sk8'))) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9'))), 32.70/4.77 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 32.70/4.77 thf(zip_derived_cl49, plain, 32.70/4.77 (( (((((((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk16' @ Y0) & 32.70/4.77 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 32.70/4.77 Y1))))) => 32.70/4.77 ('#sk16' @ Y1))))))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 32.70/4.77 ('#sk16' @ Y0)))))))) => 32.70/4.77 ('#sk16' @ '#sk8'))) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9'))), 32.70/4.77 inference('triggered_bool_instantiation', [status(thm)], 32.70/4.77 [zip_derived_cl48])). 32.70/4.77 thf(zip_derived_cl258, plain, 32.70/4.77 ((~ (((((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk16' @ Y0) & 32.70/4.77 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 32.70/4.77 Y1))))) => 32.70/4.77 ('#sk16' @ Y1))))))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 32.70/4.77 ('#sk16' @ Y0)))))))) 32.70/4.77 | ('#sk16' @ '#sk8') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 32.70/4.77 thf(zip_derived_cl22, plain, 32.70/4.77 ((~ (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk6' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk8')))))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk2' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) & 32.70/4.77 (Y2 @ Y3))) => 32.70/4.77 (Y2 @ Y4))))))))))) => 32.70/4.77 (Y2 @ Y1)))))) | 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))) => 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 ( 32.70/4.77 ( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) | 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk2' @ 32.70/4.77 Y0 @ Y3))) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))))))))) 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk3' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk4')))))))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 32.70/4.77 thf(zip_derived_cl28, plain, 32.70/4.77 (( ('#form9') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk2' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) & 32.70/4.77 (Y2 @ Y3))) => 32.70/4.77 (Y2 @ Y4))))))))))) => 32.70/4.77 (Y2 @ Y1)))))) | 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))) => 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 ( 32.70/4.77 ( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) | 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk2' @ 32.70/4.77 Y0 @ Y3))) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))))))))))), 32.70/4.77 define([status(thm)])). 32.70/4.77 thf(zip_derived_cl30, plain, 32.70/4.77 ((~ ('#form9') 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk3' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk4')))))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk6' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk8')))))))), 32.70/4.77 inference('renaming', [status(thm)], [zip_derived_cl22, zip_derived_cl28])). 32.70/4.77 thf(zip_derived_cl32, plain, 32.70/4.77 ((~ ('#form11') 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk3' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk4')))))))), 32.70/4.77 define([status(thm)])). 32.70/4.77 thf(zip_derived_cl37, plain, 32.70/4.77 (( ('#form11') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk6' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk8')))))) 32.70/4.77 | ~ ('#form9'))), 32.70/4.77 inference('renaming', [status(thm)], [zip_derived_cl30, zip_derived_cl32])). 32.70/4.77 thf(zip_derived_cl45, plain, 32.70/4.77 ((~ (((((((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 32.70/4.77 ('#sk16' @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 32.70/4.77 Y0 @ Y1))) & 32.70/4.77 ('#sk16' @ Y0))) => 32.70/4.77 ('#sk16' @ Y1))))))))))) => 32.70/4.77 ('#sk16' @ '#sk8'))) 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11'))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl37])). 32.70/4.77 thf(zip_derived_cl56, plain, 32.70/4.77 ((~ ('#sk16' @ '#sk8') | ('#form11') | ~ ('#form9'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 32.70/4.77 thf(zip_derived_cl259, plain, 32.70/4.77 (( ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ~ (((((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk16' @ Y0) & 32.70/4.77 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 32.70/4.77 Y0 @ Y1))))) => 32.70/4.77 ('#sk16' @ Y1))))))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 32.70/4.77 ('#sk16' @ Y0)))))))))), 32.70/4.77 inference('clc', [status(thm)], [zip_derived_cl258, zip_derived_cl56])). 32.70/4.77 thf(zip_derived_cl260, plain, 32.70/4.77 ((~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk16' @ Y0) & 32.70/4.77 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))))) => 32.70/4.77 ('#sk16' @ Y1))))))))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 32.70/4.77 ('#sk16' @ Y0)))))) 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl259])). 32.70/4.77 thf(zip_derived_cl48, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( (((((((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((X2 @ Y0) & 32.70/4.77 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 32.70/4.77 Y0 @ Y1))))) => 32.70/4.77 (X2 @ Y1))))))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 32.70/4.77 (X2 @ Y0)))))))) => 32.70/4.77 (X2 @ '#sk8'))) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9'))), 32.70/4.77 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 32.70/4.77 thf(zip_derived_cl62, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (((((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((X2 @ Y0) & 32.70/4.77 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 32.70/4.77 Y0 @ Y1))))) => 32.70/4.77 (X2 @ Y1))))))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 32.70/4.77 (X2 @ Y0)))))))) 32.70/4.77 | (X2 @ '#sk8') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 32.70/4.77 thf(zip_derived_cl73, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((X2 @ Y0) & 32.70/4.77 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 32.70/4.77 Y1))))) => 32.70/4.77 (X2 @ Y1))))))))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 32.70/4.77 (X2 @ Y0)))))) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | (X2 @ '#sk8'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl62])). 32.70/4.77 thf(zip_derived_cl87, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((((X2 @ ('#sk49' @ X2)) & 32.70/4.77 ((('#sk2' @ ('#sk49' @ X2) @ Y0) | ('#sk1' @ 32.70/4.77 ('#sk49' @ X2) @ Y0))))) => 32.70/4.77 (X2 @ Y0)))))) 32.70/4.77 | (X2 @ '#sk8') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 32.70/4.77 (X2 @ Y0)))))))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl73])). 32.70/4.77 thf(zip_derived_cl97, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (((((X2 @ ('#sk49' @ X2)) & 32.70/4.77 ((('#sk2' @ ('#sk49' @ X2) @ ('#sk73' @ X2)) | ('#sk1' @ 32.70/4.77 ('#sk49' @ X2) @ ('#sk73' @ X2)))))) => 32.70/4.77 (X2 @ ('#sk73' @ X2)))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 32.70/4.77 (X2 @ Y0)))))) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | (X2 @ '#sk8'))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl87])). 32.70/4.77 thf(zip_derived_cl110, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (X2 @ ('#sk73' @ X2)) 32.70/4.77 | (X2 @ '#sk8') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 32.70/4.77 (X2 @ Y0)))))))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])). 32.70/4.77 thf(zip_derived_cl124, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( ('#form139' @ X2) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 32.70/4.77 (X2 @ Y0)))))))), 32.70/4.77 define([status(thm)])). 32.70/4.77 thf(zip_derived_cl261, plain, 32.70/4.77 ((~ ('#form139' @ '#sk16') 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk16' @ Y0) & 32.70/4.77 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 32.70/4.77 Y1))))) => 32.70/4.77 ('#sk16' @ Y1))))))))))), 32.70/4.77 inference('renaming', [status(thm)], 32.70/4.77 [zip_derived_cl260, zip_derived_cl124])). 32.70/4.77 thf(zip_derived_cl262, plain, 32.70/4.77 ((~ (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk16' @ ('#sk49' @ '#sk16')) & 32.70/4.77 ((('#sk2' @ ('#sk49' @ '#sk16') @ Y0) | ('#sk1' @ 32.70/4.77 ('#sk49' @ '#sk16') @ Y0))))) => 32.70/4.77 ('#sk16' @ Y0)))))) 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form139' @ '#sk16'))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl261])). 32.70/4.77 thf(zip_derived_cl263, plain, 32.70/4.77 ((~ ((((('#sk16' @ ('#sk49' @ '#sk16')) & 32.70/4.77 ((('#sk2' @ ('#sk49' @ '#sk16') @ ('#sk73' @ '#sk16')) | 32.70/4.77 ('#sk1' @ ('#sk49' @ '#sk16') @ ('#sk73' @ '#sk16')))))) => 32.70/4.77 ('#sk16' @ ('#sk73' @ '#sk16')))) 32.70/4.77 | ~ ('#form139' @ '#sk16') 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9'))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl262])). 32.70/4.77 thf(zip_derived_cl265, plain, 32.70/4.77 ((~ ('#sk16' @ ('#sk73' @ '#sk16')) 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form139' @ '#sk16'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl263])). 32.70/4.77 thf(zip_derived_cl264, plain, 32.70/4.77 (( ((('#sk16' @ ('#sk49' @ '#sk16')) & 32.70/4.77 ((('#sk2' @ ('#sk49' @ '#sk16') @ ('#sk73' @ '#sk16')) | ('#sk1' @ 32.70/4.77 ('#sk49' @ '#sk16') @ ('#sk73' @ '#sk16')))))) 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form139' @ '#sk16'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl263])). 32.70/4.77 thf(zip_derived_cl266, plain, 32.70/4.77 (( ('#sk16' @ ('#sk49' @ '#sk16')) 32.70/4.77 | ~ ('#form139' @ '#sk16') 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl264])). 32.70/4.77 thf(zip_derived_cl267, plain, 32.70/4.77 (( ((('#sk2' @ ('#sk49' @ '#sk16') @ ('#sk73' @ '#sk16')) | ('#sk1' @ 32.70/4.77 ('#sk49' @ '#sk16') @ ('#sk73' @ '#sk16')))) 32.70/4.77 | ~ ('#form139' @ '#sk16') 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl264])). 32.70/4.77 thf(zip_derived_cl268, plain, 32.70/4.77 (( ('#sk2' @ ('#sk49' @ '#sk16') @ ('#sk73' @ '#sk16')) 32.70/4.77 | ('#sk1' @ ('#sk49' @ '#sk16') @ ('#sk73' @ '#sk16')) 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form139' @ '#sk16'))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl267])). 32.70/4.77 thf(zip_derived_cl124, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( ('#form139' @ X2) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk7' @ Y0) | ('#sk1' @ '#sk7' @ Y0))) => 32.70/4.77 (X2 @ Y0)))))))), 32.70/4.77 define([status(thm)])). 32.70/4.77 thf(zip_derived_cl125, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ ((((('#sk2' @ '#sk7' @ ('#sk140' @ X2)) | ('#sk1' @ '#sk7' @ 32.70/4.77 ('#sk140' @ X2)))) => 32.70/4.77 (X2 @ ('#sk140' @ X2)))) 32.70/4.77 | ('#form139' @ X2))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl124])). 32.70/4.77 thf(zip_derived_cl142, plain, 32.70/4.77 (![X2 : a > $o]: (~ (X2 @ ('#sk140' @ X2)) | ('#form139' @ X2))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])). 32.70/4.77 thf(zip_derived_cl141, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( ((('#sk2' @ '#sk7' @ ('#sk140' @ X2)) | ('#sk1' @ '#sk7' @ 32.70/4.77 ('#sk140' @ X2)))) 32.70/4.77 | ('#form139' @ X2))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])). 32.70/4.77 thf(zip_derived_cl158, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( ('#sk2' @ '#sk7' @ ('#sk140' @ X2)) 32.70/4.77 | ('#sk1' @ '#sk7' @ ('#sk140' @ X2)) 32.70/4.77 | ('#form139' @ X2))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl141])). 32.70/4.77 thf(zip_derived_cl27, plain, 32.70/4.77 (( (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk6' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & 32.70/4.77 ((('#sk1' @ Y1 @ Y2) | 32.70/4.77 ('#sk2' @ Y1 @ Y2))))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk7')))))) 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk3' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk4')))))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk2' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) & 32.70/4.77 (Y2 @ Y3))) => 32.70/4.77 (Y2 @ Y4))))))))))) => 32.70/4.77 (Y2 @ Y1)))))) | 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))) => 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 ( 32.70/4.77 ( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) | 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk2' @ 32.70/4.77 Y0 @ Y3))) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))))))))))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 32.70/4.77 thf(zip_derived_cl32, plain, 32.70/4.77 ((~ ('#form11') 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk3' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk4')))))))), 32.70/4.77 define([status(thm)])). 32.70/4.77 thf(zip_derived_cl36, plain, 32.70/4.77 (( ('#form11') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk2' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) & 32.70/4.77 (Y2 @ Y3))) => 32.70/4.77 (Y2 @ Y4))))))))))) => 32.70/4.77 (Y2 @ Y1)))))) | 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))) => 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 ( 32.70/4.77 ( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) | 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk2' @ 32.70/4.77 Y0 @ Y3))) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))))))))) 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk6' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & 32.70/4.77 ((('#sk1' @ Y1 @ Y2) | 32.70/4.77 ('#sk2' @ Y1 @ Y2))))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk7')))))))), 32.70/4.77 inference('renaming', [status(thm)], [zip_derived_cl27, zip_derived_cl32])). 32.70/4.77 thf(zip_derived_cl28, plain, 32.70/4.77 (( ('#form9') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk2' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) & 32.70/4.77 (Y2 @ Y3))) => 32.70/4.77 (Y2 @ Y4))))))))))) => 32.70/4.77 (Y2 @ Y1)))))) | 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))) => 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 ( 32.70/4.77 ( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) | 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk2' @ 32.70/4.77 Y0 @ Y3))) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))))))))))), 32.70/4.77 define([status(thm)])). 32.70/4.77 thf(zip_derived_cl43, plain, 32.70/4.77 ((~ ('#form9') 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 32.70/4.77 '#sk6' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & 32.70/4.77 ((('#sk1' @ Y1 @ Y2) | 32.70/4.77 ('#sk2' @ Y1 @ Y2))))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk7')))))) 32.70/4.77 | ('#form11'))), 32.70/4.77 inference('renaming', [status(thm)], [zip_derived_cl36, zip_derived_cl28])). 32.70/4.77 thf(zip_derived_cl52, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( (((((((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 32.70/4.77 (X2 @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((X2 @ Y0) & 32.70/4.77 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 32.70/4.77 Y0 @ Y1))))) => 32.70/4.77 (X2 @ Y1))))))))))) => 32.70/4.77 (X2 @ '#sk7'))) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9'))), 32.70/4.77 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 32.70/4.77 thf(zip_derived_cl64, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (((((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 32.70/4.77 (X2 @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((X2 @ Y0) & 32.70/4.77 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 32.70/4.77 Y0 @ Y1))))) => 32.70/4.77 (X2 @ Y1))))))))))) 32.70/4.77 | (X2 @ '#sk7') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 32.70/4.77 thf(zip_derived_cl76, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 32.70/4.77 (X2 @ Y0)))))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((X2 @ Y0) & 32.70/4.77 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 32.70/4.77 Y0 @ Y1))))) => 32.70/4.77 (X2 @ Y1))))))))) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | (X2 @ '#sk7'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl64])). 32.70/4.77 thf(zip_derived_cl90, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ ((((('#sk2' @ '#sk6' @ ('#sk61' @ X2)) | ('#sk1' @ '#sk6' @ 32.70/4.77 ('#sk61' @ X2)))) => 32.70/4.77 (X2 @ ('#sk61' @ X2)))) 32.70/4.77 | (X2 @ '#sk7') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((X2 @ Y0) & 32.70/4.77 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 32.70/4.77 Y0 @ Y1))))) => 32.70/4.77 (X2 @ Y1))))))))))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl76])). 32.70/4.77 thf(zip_derived_cl101, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (X2 @ ('#sk61' @ X2)) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((X2 @ Y0) & 32.70/4.77 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 32.70/4.77 Y0 @ Y1))))) => 32.70/4.77 (X2 @ Y1))))))))) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | (X2 @ '#sk7'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl90])). 32.70/4.77 thf(zip_derived_cl115, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((((X2 @ ('#sk122' @ X2)) & 32.70/4.77 ((('#sk1' @ ('#sk122' @ X2) @ Y0) | ('#sk2' @ 32.70/4.77 ('#sk122' @ X2) @ Y0))))) => 32.70/4.77 (X2 @ Y0)))))) 32.70/4.77 | (X2 @ '#sk7') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11') 32.70/4.77 | ~ (X2 @ ('#sk61' @ X2)))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl101])). 32.70/4.77 thf(zip_derived_cl132, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (((((X2 @ ('#sk122' @ X2)) & 32.70/4.77 ((('#sk1' @ ('#sk122' @ X2) @ ('#sk166' @ X2)) | ('#sk2' @ 32.70/4.77 ('#sk122' @ X2) @ ('#sk166' @ X2)))))) => 32.70/4.77 (X2 @ ('#sk166' @ X2)))) 32.70/4.77 | ~ (X2 @ ('#sk61' @ X2)) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | (X2 @ '#sk7'))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl115])). 32.70/4.77 thf(zip_derived_cl148, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (X2 @ ('#sk166' @ X2)) 32.70/4.77 | (X2 @ '#sk7') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11') 32.70/4.77 | ~ (X2 @ ('#sk61' @ X2)))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl132])). 32.70/4.77 thf(zip_derived_cl147, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( (((X2 @ ('#sk122' @ X2)) & 32.70/4.77 ((('#sk1' @ ('#sk122' @ X2) @ ('#sk166' @ X2)) | ('#sk2' @ 32.70/4.77 ('#sk122' @ X2) @ ('#sk166' @ X2)))))) 32.70/4.77 | (X2 @ '#sk7') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11') 32.70/4.77 | ~ (X2 @ ('#sk61' @ X2)))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl132])). 32.70/4.77 thf(zip_derived_cl162, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( (X2 @ ('#sk122' @ X2)) 32.70/4.77 | ~ (X2 @ ('#sk61' @ X2)) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | (X2 @ '#sk7'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl147])). 32.70/4.77 thf(zip_derived_cl163, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( ((('#sk1' @ ('#sk122' @ X2) @ ('#sk166' @ X2)) | ('#sk2' @ 32.70/4.77 ('#sk122' @ X2) @ ('#sk166' @ X2)))) 32.70/4.77 | ~ (X2 @ ('#sk61' @ X2)) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | (X2 @ '#sk7'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl147])). 32.70/4.77 thf(zip_derived_cl173, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( ('#sk1' @ ('#sk122' @ X2) @ ('#sk166' @ X2)) 32.70/4.77 | ('#sk2' @ ('#sk122' @ X2) @ ('#sk166' @ X2)) 32.70/4.77 | (X2 @ '#sk7') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11') 32.70/4.77 | ~ (X2 @ ('#sk61' @ X2)))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl163])). 32.70/4.77 thf(zip_derived_cl55, plain, 32.70/4.77 (( (((((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 32.70/4.77 ('#sk16' @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 32.70/4.77 Y1))) & 32.70/4.77 ('#sk16' @ Y0))) => 32.70/4.77 ('#sk16' @ Y1))))))))))) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 32.70/4.77 thf(zip_derived_cl65, plain, 32.70/4.77 (( (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 32.70/4.77 ('#sk16' @ Y0)))))) 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 32.70/4.77 thf(zip_derived_cl77, plain, 32.70/4.77 (![X2 : a]: 32.70/4.77 ( ((((('#sk2' @ '#sk6' @ X2) | ('#sk1' @ '#sk6' @ X2))) => ('#sk16' @ 32.70/4.77 X2))) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9'))), 32.70/4.77 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl65])). 32.70/4.77 thf(zip_derived_cl91, plain, 32.70/4.77 (![X2 : a]: 32.70/4.77 (~ ((('#sk2' @ '#sk6' @ X2) | ('#sk1' @ '#sk6' @ X2))) 32.70/4.77 | ('#sk16' @ X2) 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl77])). 32.70/4.77 thf(zip_derived_cl102, plain, 32.70/4.77 (![X2 : a]: 32.70/4.77 (~ ('#sk2' @ '#sk6' @ X2) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#sk16' @ X2))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl91])). 32.70/4.77 thf(zip_derived_cl103, plain, 32.70/4.77 (![X2 : a]: 32.70/4.77 (~ ('#sk1' @ '#sk6' @ X2) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#sk16' @ X2))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl91])). 32.70/4.77 thf(zip_derived_cl100, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( ((('#sk2' @ '#sk6' @ ('#sk61' @ X2)) | ('#sk1' @ '#sk6' @ 32.70/4.77 ('#sk61' @ X2)))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((X2 @ Y0) & 32.70/4.77 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 32.70/4.77 Y0 @ Y1))))) => 32.70/4.77 (X2 @ Y1))))))))) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | (X2 @ '#sk7'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl90])). 32.70/4.77 thf(zip_derived_cl114, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( ('#sk2' @ '#sk6' @ ('#sk61' @ X2)) 32.70/4.77 | ('#sk1' @ '#sk6' @ ('#sk61' @ X2)) 32.70/4.77 | (X2 @ '#sk7') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((X2 @ Y0) & 32.70/4.77 ((('#sk1' @ Y0 @ Y1) | ('#sk2' @ 32.70/4.77 Y0 @ Y1))))) => 32.70/4.77 (X2 @ Y1))))))))))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl100])). 32.70/4.77 thf(zip_derived_cl131, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((((X2 @ ('#sk122' @ X2)) & 32.70/4.77 ((('#sk1' @ ('#sk122' @ X2) @ Y0) | ('#sk2' @ 32.70/4.77 ('#sk122' @ X2) @ Y0))))) => 32.70/4.77 (X2 @ Y0)))))) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | (X2 @ '#sk7') 32.70/4.77 | ('#sk1' @ '#sk6' @ ('#sk61' @ X2)) 32.70/4.77 | ('#sk2' @ '#sk6' @ ('#sk61' @ X2)))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl114])). 32.70/4.77 thf(zip_derived_cl146, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (((((X2 @ ('#sk122' @ X2)) & 32.70/4.77 ((('#sk1' @ ('#sk122' @ X2) @ ('#sk166' @ X2)) | ('#sk2' @ 32.70/4.77 ('#sk122' @ X2) @ ('#sk166' @ X2)))))) => 32.70/4.77 (X2 @ ('#sk166' @ X2)))) 32.70/4.77 | ('#sk2' @ '#sk6' @ ('#sk61' @ X2)) 32.70/4.77 | ('#sk1' @ '#sk6' @ ('#sk61' @ X2)) 32.70/4.77 | (X2 @ '#sk7') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11'))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl131])). 32.70/4.77 thf(zip_derived_cl161, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (X2 @ ('#sk166' @ X2)) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | (X2 @ '#sk7') 32.70/4.77 | ('#sk1' @ '#sk6' @ ('#sk61' @ X2)) 32.70/4.77 | ('#sk2' @ '#sk6' @ ('#sk61' @ X2)))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl146])). 32.70/4.77 thf(zip_derived_cl160, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( (((X2 @ ('#sk122' @ X2)) & 32.70/4.77 ((('#sk1' @ ('#sk122' @ X2) @ ('#sk166' @ X2)) | ('#sk2' @ 32.70/4.77 ('#sk122' @ X2) @ ('#sk166' @ X2)))))) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | (X2 @ '#sk7') 32.70/4.77 | ('#sk1' @ '#sk6' @ ('#sk61' @ X2)) 32.70/4.77 | ('#sk2' @ '#sk6' @ ('#sk61' @ X2)))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl146])). 32.70/4.77 thf(zip_derived_cl171, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( (X2 @ ('#sk122' @ X2)) 32.70/4.77 | ('#sk2' @ '#sk6' @ ('#sk61' @ X2)) 32.70/4.77 | ('#sk1' @ '#sk6' @ ('#sk61' @ X2)) 32.70/4.77 | (X2 @ '#sk7') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl160])). 32.70/4.77 thf(zip_derived_cl66, plain, 32.70/4.77 (( (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 32.70/4.77 ('#sk16' @ Y0))) => 32.70/4.77 ('#sk16' @ Y1))))))))) 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 32.70/4.77 thf(zip_derived_cl78, plain, 32.70/4.77 (![X2 : a]: 32.70/4.77 ( (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) & 32.70/4.77 ('#sk16' @ X2))) => 32.70/4.77 ('#sk16' @ Y0)))))) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9'))), 32.70/4.77 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl66])). 32.70/4.77 thf(zip_derived_cl92, plain, 32.70/4.77 (![X2 : a, X4 : a]: 32.70/4.77 ( ((((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk16' @ X2))) => 32.70/4.77 ('#sk16' @ X4))) 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11'))), 32.70/4.77 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl78])). 32.70/4.77 thf(zip_derived_cl104, plain, 32.70/4.77 (![X2 : a, X4 : a]: 32.70/4.77 (~ ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk16' @ X2))) 32.70/4.77 | ('#sk16' @ X4) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])). 32.70/4.77 thf(zip_derived_cl116, plain, 32.70/4.77 (![X2 : a, X4 : a]: 32.70/4.77 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 32.70/4.77 | ~ ('#sk16' @ X2) 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11') 32.70/4.77 | ('#sk16' @ X4))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl104])). 32.70/4.77 thf(zip_derived_cl133, plain, 32.70/4.77 (![X2 : a, X4 : a]: 32.70/4.77 (~ ('#sk2' @ X2 @ X4) 32.70/4.77 | ('#sk16' @ X4) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ~ ('#sk16' @ X2))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl116])). 32.70/4.77 thf(zip_derived_cl172, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( ((('#sk1' @ ('#sk122' @ X2) @ ('#sk166' @ X2)) | ('#sk2' @ 32.70/4.77 ('#sk122' @ X2) @ ('#sk166' @ X2)))) 32.70/4.77 | ('#sk2' @ '#sk6' @ ('#sk61' @ X2)) 32.70/4.77 | ('#sk1' @ '#sk6' @ ('#sk61' @ X2)) 32.70/4.77 | (X2 @ '#sk7') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ('#form11'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl160])). 32.70/4.77 thf(zip_derived_cl182, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( ('#sk1' @ ('#sk122' @ X2) @ ('#sk166' @ X2)) 32.70/4.77 | ('#sk2' @ ('#sk122' @ X2) @ ('#sk166' @ X2)) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | (X2 @ '#sk7') 32.70/4.77 | ('#sk1' @ '#sk6' @ ('#sk61' @ X2)) 32.70/4.77 | ('#sk2' @ '#sk6' @ ('#sk61' @ X2)))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl172])). 32.70/4.77 thf(zip_derived_cl134, plain, 32.70/4.77 (![X2 : a, X4 : a]: 32.70/4.77 (~ ('#sk1' @ X2 @ X4) 32.70/4.77 | ('#sk16' @ X4) 32.70/4.77 | ('#form11') 32.70/4.77 | ~ ('#form9') 32.70/4.77 | ~ ('#sk16' @ X2))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl116])). 32.70/4.77 thf(zip_derived_cl28, plain, 32.70/4.77 (( ('#form9') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk2' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) & 32.70/4.77 (Y2 @ Y3))) => 32.70/4.77 (Y2 @ Y4))))))))))) => 32.70/4.77 (Y2 @ Y1)))))) | 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 (( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))) => 32.70/4.77 (((!!) @ (^[Y2 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y3 : a]: 32.70/4.77 (((!!) @ ( 32.70/4.77 ^[Y4 : a]: 32.70/4.77 ( 32.70/4.77 ( 32.70/4.77 (( 32.70/4.77 (Y2 @ 32.70/4.77 Y3) & 32.70/4.77 (( 32.70/4.77 ('#sk2' @ 32.70/4.77 Y3 @ 32.70/4.77 Y4) | 32.70/4.77 ('#sk1' @ 32.70/4.77 Y3 @ Y4))))) => 32.70/4.77 (Y2 @ Y4))))))))) & 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((((('#sk1' @ 32.70/4.77 Y0 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk2' @ 32.70/4.77 Y0 @ Y3))) => 32.70/4.77 (Y2 @ Y3)))))))) => 32.70/4.77 (Y2 @ Y1)))))))))))))))), 32.70/4.77 define([status(thm)])). 32.70/4.77 thf(zip_derived_cl29, plain, 32.70/4.77 ((~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((((((!!) @ (^[Y1 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y2 : a]: 32.70/4.77 ((('#sk2' @ '#sk10' @ 32.70/4.77 Y2) => (Y1 @ Y2)))))) & 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 ((((('#sk2' @ 32.70/4.77 Y2 @ 32.70/4.77 Y3) & 32.70/4.77 (Y1 @ Y2))) => 32.70/4.77 (Y1 @ Y3))))))))))) => 32.70/4.77 (Y1 @ Y0)))))) | 32.70/4.77 (((!!) @ (^[Y1 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y2 : a]: 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((((Y1 @ 32.70/4.77 Y2) & 32.70/4.77 ('#sk1' @ 32.70/4.77 Y2 @ Y3))) => 32.70/4.77 (Y1 @ Y3))))))))) & 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((('#sk1' @ '#sk10' @ 32.70/4.77 Y2) => (Y1 @ Y2)))))))) => 32.70/4.77 (Y1 @ Y0)))))))) => 32.70/4.77 (((!!) @ (^[Y1 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y2 : a]: 32.70/4.77 (((!!) @ (^[Y3 : a]: 32.70/4.77 (((((Y1 @ Y2) & 32.70/4.77 ((('#sk2' @ 32.70/4.77 Y2 @ 32.70/4.77 Y3) | 32.70/4.77 ('#sk1' @ 32.70/4.77 Y2 @ Y3))))) => 32.70/4.77 (Y1 @ Y3))))))))) & 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((('#sk1' @ '#sk10' @ 32.70/4.77 Y2) | ('#sk2' @ 32.70/4.77 '#sk10' @ Y2))) => 32.70/4.77 (Y1 @ Y2)))))))) => 32.70/4.77 (Y1 @ Y0))))))))))) 32.70/4.77 | ('#form9'))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl28])). 32.70/4.77 thf(zip_derived_cl38, plain, 32.70/4.77 ((~ (((((((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ 32.70/4.77 Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((('#sk2' @ Y1 @ Y2) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk12')))))) | 32.70/4.77 (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & 32.70/4.77 ('#sk1' @ Y1 @ Y2))) => 32.70/4.77 (Y0 @ Y2))))))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ 32.70/4.77 Y1)))))))) => 32.70/4.77 (Y0 @ '#sk12')))))))) => 32.70/4.77 (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & 32.70/4.77 ((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))))) => 32.70/4.77 (Y0 @ Y2))))))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk1' @ '#sk10' @ Y1) | 32.70/4.77 ('#sk2' @ '#sk10' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))))) => 32.70/4.77 (Y0 @ '#sk12')))))))) 32.70/4.77 | ('#form9'))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl29])). 32.70/4.77 thf(zip_derived_cl46, plain, 32.70/4.77 (( (((((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((('#sk2' @ Y1 @ Y2) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk12')))))) | 32.70/4.77 (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & ('#sk1' @ 32.70/4.77 Y1 @ Y2))) => 32.70/4.77 (Y0 @ Y2))))))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))))) => 32.70/4.77 (Y0 @ '#sk12')))))))) 32.70/4.77 | ('#form9'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 32.70/4.77 thf(zip_derived_cl57, plain, 32.70/4.77 (( (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 ((('#sk2' @ '#sk10' @ Y1) => (Y0 @ Y1)))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 ((((('#sk2' @ Y1 @ Y2) & 32.70/4.77 (Y0 @ Y1))) => 32.70/4.77 (Y0 @ Y2))))))))))) => 32.70/4.77 (Y0 @ '#sk12')))))) 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & ('#sk1' @ 32.70/4.77 Y1 @ Y2))) => 32.70/4.77 (Y0 @ Y2))))))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))))) => 32.70/4.77 (Y0 @ '#sk12')))))) 32.70/4.77 | ('#form9'))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl46])). 32.70/4.77 thf(zip_derived_cl67, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( (((((((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 32.70/4.77 (X2 @ Y1))))))))))) => 32.70/4.77 (X2 @ '#sk12'))) 32.70/4.77 | ('#form9') 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & ('#sk1' @ 32.70/4.77 Y1 @ Y2))) => 32.70/4.77 (Y0 @ Y2))))))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))))) => 32.70/4.77 (Y0 @ '#sk12')))))))), 32.70/4.77 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 32.70/4.77 thf(zip_derived_cl79, plain, 32.70/4.77 ((~ ('#form45') 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & ('#sk1' @ 32.70/4.77 Y1 @ Y2))) => 32.70/4.77 (Y0 @ Y2))))))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))))) => 32.70/4.77 (Y0 @ '#sk12')))))))), 32.70/4.77 define([status(thm)])). 32.70/4.77 thf(zip_derived_cl80, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( (((((((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 32.70/4.77 (X2 @ Y1))))))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) => 32.70/4.77 (X2 @ '#sk12'))) 32.70/4.77 | ~ ('#form45'))), 32.70/4.77 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl79])). 32.70/4.77 thf(zip_derived_cl94, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (((((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 32.70/4.77 (X2 @ Y1))))))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))) 32.70/4.77 | (X2 @ '#sk12') 32.70/4.77 | ~ ('#form45'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])). 32.70/4.77 thf(zip_derived_cl106, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 32.70/4.77 (X2 @ Y1))))))))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 32.70/4.77 | ~ ('#form45') 32.70/4.77 | (X2 @ '#sk12'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl94])). 32.70/4.77 thf(zip_derived_cl118, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((((X2 @ ('#sk130' @ X2)) & ('#sk1' @ 32.70/4.77 ('#sk130' @ X2) @ Y0))) => 32.70/4.77 (X2 @ Y0)))))) 32.70/4.77 | (X2 @ '#sk12') 32.70/4.77 | ~ ('#form45') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl106])). 32.70/4.77 thf(zip_derived_cl137, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (((((X2 @ ('#sk130' @ X2)) & ('#sk1' @ ('#sk130' @ X2) @ 32.70/4.77 ('#sk175' @ X2)))) => 32.70/4.77 (X2 @ ('#sk175' @ X2)))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 32.70/4.77 | ~ ('#form45') 32.70/4.77 | (X2 @ '#sk12'))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl118])). 32.70/4.77 thf(zip_derived_cl152, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (X2 @ ('#sk175' @ X2)) 32.70/4.77 | (X2 @ '#sk12') 32.70/4.77 | ~ ('#form45') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])). 32.70/4.77 thf(zip_derived_cl152, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ (X2 @ ('#sk175' @ X2)) 32.70/4.77 | (X2 @ '#sk12') 32.70/4.77 | ~ ('#form45') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])). 32.70/4.77 thf(zip_derived_cl168, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( ('#form295' @ X2) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 32.70/4.77 define([status(thm)])). 32.70/4.77 thf(zip_derived_cl170, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ ('#form295' @ X2) 32.70/4.77 | ~ ('#form45') 32.70/4.77 | (X2 @ '#sk12') 32.70/4.77 | ~ (X2 @ ('#sk175' @ X2)))), 32.70/4.77 inference('renaming', [status(thm)], 32.70/4.77 [zip_derived_cl152, zip_derived_cl168])). 32.70/4.77 thf(zip_derived_cl47, plain, 32.70/4.77 ((~ (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & 32.70/4.77 ((('#sk2' @ Y1 @ Y2) | 32.70/4.77 ('#sk1' @ Y1 @ Y2))))) => 32.70/4.77 (Y0 @ Y2))))))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk1' @ '#sk10' @ Y1) | ('#sk2' @ 32.70/4.77 '#sk10' @ Y1))) => 32.70/4.77 (Y0 @ Y1)))))))) => 32.70/4.77 (Y0 @ '#sk12')))))) 32.70/4.77 | ('#form9'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 32.70/4.77 thf(zip_derived_cl61, plain, 32.70/4.77 ((~ (((((((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk20' @ Y0) & 32.70/4.77 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 32.70/4.77 Y0 @ Y1))))) => 32.70/4.77 ('#sk20' @ Y1))))))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 32.70/4.77 ('#sk20' @ Y0)))))))) => 32.70/4.77 ('#sk20' @ '#sk12'))) 32.70/4.77 | ('#form9'))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 32.70/4.77 thf(zip_derived_cl72, plain, ((~ ('#sk20' @ '#sk12') | ('#form9'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 32.70/4.77 thf(zip_derived_cl71, plain, 32.70/4.77 (( (((((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk20' @ Y0) & 32.70/4.77 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 32.70/4.77 Y1))))) => 32.70/4.77 ('#sk20' @ Y1))))))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 32.70/4.77 ('#sk20' @ Y0)))))))) 32.70/4.77 | ('#form9'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 32.70/4.77 thf(zip_derived_cl85, plain, 32.70/4.77 (( (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk20' @ Y0) & 32.70/4.77 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))))) => 32.70/4.77 ('#sk20' @ Y1))))))))) 32.70/4.77 | ('#form9'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl71])). 32.70/4.77 thf(zip_derived_cl95, plain, 32.70/4.77 (![X2 : a]: 32.70/4.77 ( (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk20' @ X2) & 32.70/4.77 ((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))))) => 32.70/4.77 ('#sk20' @ Y0)))))) 32.70/4.77 | ('#form9'))), 32.70/4.77 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 32.70/4.77 thf(zip_derived_cl107, plain, 32.70/4.77 (![X2 : a, X4 : a]: 32.70/4.77 ( ((((('#sk20' @ X2) & ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))))) => 32.70/4.77 ('#sk20' @ X4))) 32.70/4.77 | ('#form9'))), 32.70/4.77 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl95])). 32.70/4.77 thf(zip_derived_cl119, plain, 32.70/4.77 (![X2 : a, X4 : a]: 32.70/4.77 (~ ((('#sk20' @ X2) & ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))))) 32.70/4.77 | ('#sk20' @ X4) 32.70/4.77 | ('#form9'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])). 32.70/4.77 thf(zip_derived_cl138, plain, 32.70/4.77 (![X2 : a, X4 : a]: 32.70/4.77 (~ ('#sk20' @ X2) 32.70/4.77 | ~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 32.70/4.77 | ('#form9') 32.70/4.77 | ('#sk20' @ X4))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl119])). 32.70/4.77 thf(zip_derived_cl154, plain, 32.70/4.77 (![X2 : a, X4 : a]: 32.70/4.77 (~ ('#sk1' @ X2 @ X4) 32.70/4.77 | ('#sk20' @ X4) 32.70/4.77 | ('#form9') 32.70/4.77 | ~ ('#sk20' @ X2))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl138])). 32.70/4.77 thf(zip_derived_cl151, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( (((X2 @ ('#sk130' @ X2)) & ('#sk1' @ ('#sk130' @ X2) @ 32.70/4.77 ('#sk175' @ X2)))) 32.70/4.77 | (X2 @ '#sk12') 32.70/4.77 | ~ ('#form45') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])). 32.70/4.77 thf(zip_derived_cl166, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( (X2 @ ('#sk130' @ X2)) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 32.70/4.77 | ~ ('#form45') 32.70/4.77 | (X2 @ '#sk12'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl151])). 32.70/4.77 thf(zip_derived_cl168, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( ('#form295' @ X2) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 32.70/4.77 define([status(thm)])). 32.70/4.77 thf(zip_derived_cl178, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ ('#form295' @ (^[Y0 : a]: (X2 @ Y0))) 32.70/4.77 | (X2 @ '#sk12') 32.70/4.77 | ~ ('#form45') 32.70/4.77 | (X2 @ ('#sk130' @ X2)))), 32.70/4.77 inference('renaming', [status(thm)], 32.70/4.77 [zip_derived_cl166, zip_derived_cl168])). 32.70/4.77 thf(zip_derived_cl187, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ ('#form295' @ X2) 32.70/4.77 | (X2 @ '#sk12') 32.70/4.77 | ~ ('#form45') 32.70/4.77 | (X2 @ ('#sk130' @ X2)))), 32.70/4.77 inference('ho_norm', [status(thm)], [zip_derived_cl178])). 32.70/4.77 thf(zip_derived_cl168, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( ('#form295' @ X2) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 32.70/4.77 define([status(thm)])). 32.70/4.77 thf(zip_derived_cl169, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ ((('#sk1' @ '#sk10' @ ('#sk296' @ X2)) => (X2 @ ('#sk296' @ X2)))) 32.70/4.77 | ('#form295' @ X2))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl168])). 32.70/4.77 thf(zip_derived_cl180, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( ('#sk1' @ '#sk10' @ ('#sk296' @ X2)) | ('#form295' @ X2))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl169])). 32.70/4.77 thf(zip_derived_cl181, plain, 32.70/4.77 (![X2 : a > $o]: (~ (X2 @ ('#sk296' @ X2)) | ('#form295' @ X2))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl169])). 32.70/4.77 thf(zip_derived_cl167, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( ('#sk1' @ ('#sk130' @ X2) @ ('#sk175' @ X2)) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))) 32.70/4.77 | ~ ('#form45') 32.70/4.77 | (X2 @ '#sk12'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl151])). 32.70/4.77 thf(zip_derived_cl168, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( ('#form295' @ X2) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk10' @ Y0) => (X2 @ Y0)))))))), 32.70/4.77 define([status(thm)])). 32.70/4.77 thf(zip_derived_cl179, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ ('#form295' @ (^[Y0 : a]: (X2 @ Y0))) 32.70/4.77 | (X2 @ '#sk12') 32.70/4.77 | ~ ('#form45') 32.70/4.77 | ('#sk1' @ ('#sk130' @ X2) @ ('#sk175' @ X2)))), 32.70/4.77 inference('renaming', [status(thm)], 32.70/4.77 [zip_derived_cl167, zip_derived_cl168])). 32.70/4.77 thf(zip_derived_cl188, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 (~ ('#form295' @ X2) 32.70/4.77 | (X2 @ '#sk12') 32.70/4.77 | ~ ('#form45') 32.70/4.77 | ('#sk1' @ ('#sk130' @ X2) @ ('#sk175' @ X2)))), 32.70/4.77 inference('ho_norm', [status(thm)], [zip_derived_cl179])). 32.70/4.77 thf(zip_derived_cl86, plain, 32.70/4.77 (( (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 32.70/4.77 ('#sk20' @ Y0)))))) 32.70/4.77 | ('#form9'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl71])). 32.70/4.77 thf(zip_derived_cl96, plain, 32.70/4.77 (![X2 : a]: 32.70/4.77 ( ((((('#sk1' @ '#sk10' @ X2) | ('#sk2' @ '#sk10' @ X2))) => 32.70/4.77 ('#sk20' @ X2))) 32.70/4.77 | ('#form9'))), 32.70/4.77 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl86])). 32.70/4.77 thf(zip_derived_cl108, plain, 32.70/4.77 (![X2 : a]: 32.70/4.77 (~ ((('#sk1' @ '#sk10' @ X2) | ('#sk2' @ '#sk10' @ X2))) 32.70/4.77 | ('#sk20' @ X2) 32.70/4.77 | ('#form9'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 32.70/4.77 thf(zip_derived_cl120, plain, 32.70/4.77 (![X2 : a]: (~ ('#sk1' @ '#sk10' @ X2) | ('#form9') | ('#sk20' @ X2))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl108])). 32.70/4.77 thf(zip_derived_cl67, plain, 32.70/4.77 (![X2 : a > $o]: 32.70/4.77 ( (((((((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => (X2 @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ Y0 @ Y1) & (X2 @ Y0))) => 32.70/4.77 (X2 @ Y1))))))))))) => 32.70/4.77 (X2 @ '#sk12'))) 32.70/4.77 | ('#form9') 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & ('#sk1' @ 32.70/4.77 Y1 @ Y2))) => 32.70/4.77 (Y0 @ Y2))))))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))))) => 32.70/4.77 (Y0 @ '#sk12')))))))), 32.70/4.77 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 32.70/4.77 thf(zip_derived_cl68, plain, 32.70/4.77 (( (((((((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 32.70/4.77 ('#sk20' @ Y1))))))))))) => 32.70/4.77 ('#sk20' @ '#sk12'))) 32.70/4.77 | ('#form9') 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & ('#sk1' @ 32.70/4.77 Y1 @ Y2))) => 32.70/4.77 (Y0 @ Y2))))))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))))) => 32.70/4.77 (Y0 @ '#sk12')))))))), 32.70/4.77 inference('triggered_bool_instantiation', [status(thm)], 32.70/4.77 [zip_derived_cl67])). 32.70/4.77 thf(zip_derived_cl79, plain, 32.70/4.77 ((~ ('#form45') 32.70/4.77 | (((!!) @ (^[Y0 : a > $o]: 32.70/4.77 (((((((!!) @ (^[Y1 : a]: 32.70/4.77 (((!!) @ (^[Y2 : a]: 32.70/4.77 (((((Y0 @ Y1) & ('#sk1' @ 32.70/4.77 Y1 @ Y2))) => 32.70/4.77 (Y0 @ Y2))))))))) & 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((('#sk1' @ '#sk10' @ Y1) => (Y0 @ Y1)))))))) => 32.70/4.77 (Y0 @ '#sk12')))))))), 32.70/4.77 define([status(thm)])). 32.70/4.77 thf(zip_derived_cl299, plain, 32.70/4.77 (( ('#form45') 32.70/4.77 | ('#form9') 32.70/4.77 | (((((((!!) @ (^[Y0 : a]: 32.70/4.77 ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 32.70/4.77 ('#sk20' @ Y1))))))))))) => 32.70/4.77 ('#sk20' @ '#sk12'))))), 32.70/4.77 inference('renaming', [status(thm)], [zip_derived_cl68, zip_derived_cl79])). 32.70/4.77 thf(zip_derived_cl300, plain, 32.70/4.77 ((~ (((((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 32.70/4.77 ('#sk20' @ Y1))))))))))) 32.70/4.77 | ('#sk20' @ '#sk12') 32.70/4.77 | ('#form9') 32.70/4.77 | ('#form45'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl299])). 32.70/4.77 thf(zip_derived_cl72, plain, ((~ ('#sk20' @ '#sk12') | ('#form9'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 32.70/4.77 thf(zip_derived_cl301, plain, 32.70/4.77 (( ('#form45') 32.70/4.77 | ('#form9') 32.70/4.77 | ~ (((((!!) @ (^[Y0 : a]: 32.70/4.77 ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))) & 32.70/4.77 (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 32.70/4.77 ('#sk20' @ Y1))))))))))))), 32.70/4.77 inference('clc', [status(thm)], [zip_derived_cl300, zip_derived_cl72])). 32.70/4.77 thf(zip_derived_cl302, plain, 32.70/4.77 ((~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk10' @ Y0) => ('#sk20' @ Y0)))))) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 32.70/4.77 ('#sk20' @ Y1))))))))) 32.70/4.77 | ('#form9') 32.70/4.77 | ('#form45'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl301])). 32.70/4.77 thf(zip_derived_cl303, plain, 32.70/4.77 ((~ ((('#sk2' @ '#sk10' @ ('#sk126' @ '#sk20')) => ('#sk20' @ 32.70/4.77 ('#sk126' @ '#sk20')))) 32.70/4.77 | ('#form45') 32.70/4.77 | ('#form9') 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 32.70/4.77 ('#sk20' @ Y1))))))))))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl302])). 32.70/4.77 thf(zip_derived_cl305, plain, 32.70/4.77 ((~ ('#sk20' @ ('#sk126' @ '#sk20')) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 32.70/4.77 ('#sk20' @ Y1))))))))) 32.70/4.77 | ('#form9') 32.70/4.77 | ('#form45'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl303])). 32.70/4.77 thf(zip_derived_cl307, plain, 32.70/4.77 ((~ (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ ('#sk222' @ '#sk20') @ Y0) & ('#sk20' @ 32.70/4.77 ('#sk222' @ '#sk20')))) => 32.70/4.77 ('#sk20' @ Y0)))))) 32.70/4.77 | ('#form45') 32.70/4.77 | ('#form9') 32.70/4.77 | ~ ('#sk20' @ ('#sk126' @ '#sk20')))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl305])). 32.70/4.77 thf(zip_derived_cl309, plain, 32.70/4.77 ((~ ((((('#sk2' @ ('#sk222' @ '#sk20') @ ('#sk284' @ '#sk20')) & 32.70/4.77 ('#sk20' @ ('#sk222' @ '#sk20')))) => 32.70/4.77 ('#sk20' @ ('#sk284' @ '#sk20')))) 32.70/4.77 | ~ ('#sk20' @ ('#sk126' @ '#sk20')) 32.70/4.77 | ('#form9') 32.70/4.77 | ('#form45'))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl307])). 32.70/4.77 thf(zip_derived_cl313, plain, 32.70/4.77 ((~ ('#sk20' @ ('#sk284' @ '#sk20')) 32.70/4.77 | ('#form45') 32.70/4.77 | ('#form9') 32.70/4.77 | ~ ('#sk20' @ ('#sk126' @ '#sk20')))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl309])). 32.70/4.77 thf(zip_derived_cl312, plain, 32.70/4.77 (( ((('#sk2' @ ('#sk222' @ '#sk20') @ ('#sk284' @ '#sk20')) & ('#sk20' @ 32.70/4.77 ('#sk222' @ '#sk20')))) 32.70/4.77 | ('#form45') 32.70/4.77 | ('#form9') 32.70/4.77 | ~ ('#sk20' @ ('#sk126' @ '#sk20')))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl309])). 32.70/4.77 thf(zip_derived_cl317, plain, 32.70/4.77 (( ('#sk20' @ ('#sk222' @ '#sk20')) 32.70/4.77 | ~ ('#sk20' @ ('#sk126' @ '#sk20')) 32.70/4.77 | ('#form9') 32.70/4.77 | ('#form45'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl312])). 32.70/4.77 thf(zip_derived_cl316, plain, 32.70/4.77 (( ('#sk2' @ ('#sk222' @ '#sk20') @ ('#sk284' @ '#sk20')) 32.70/4.77 | ~ ('#sk20' @ ('#sk126' @ '#sk20')) 32.70/4.77 | ('#form9') 32.70/4.77 | ('#form45'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl312])). 32.70/4.77 thf(zip_derived_cl304, plain, 32.70/4.77 (( ('#sk2' @ '#sk10' @ ('#sk126' @ '#sk20')) 32.70/4.77 | ~ (((!!) @ (^[Y0 : a]: 32.70/4.77 (((!!) @ (^[Y1 : a]: 32.70/4.77 ((((('#sk2' @ Y0 @ Y1) & ('#sk20' @ Y0))) => 32.70/4.77 ('#sk20' @ Y1))))))))) 32.70/4.77 | ('#form9') 32.70/4.77 | ('#form45'))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl303])). 32.70/4.77 thf(zip_derived_cl306, plain, 32.70/4.77 ((~ (((!!) @ (^[Y0 : a]: 32.70/4.77 ((((('#sk2' @ ('#sk222' @ '#sk20') @ Y0) & ('#sk20' @ 32.70/4.77 ('#sk222' @ '#sk20')))) => 32.70/4.77 ('#sk20' @ Y0)))))) 32.70/4.77 | ('#form45') 32.70/4.77 | ('#form9') 32.70/4.77 | ('#sk2' @ '#sk10' @ ('#sk126' @ '#sk20')))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl304])). 32.70/4.77 thf(zip_derived_cl308, plain, 32.70/4.77 ((~ ((((('#sk2' @ ('#sk222' @ '#sk20') @ ('#sk284' @ '#sk20')) & 32.70/4.77 ('#sk20' @ ('#sk222' @ '#sk20')))) => 32.70/4.77 ('#sk20' @ ('#sk284' @ '#sk20')))) 32.70/4.77 | ('#sk2' @ '#sk10' @ ('#sk126' @ '#sk20')) 32.70/4.77 | ('#form9') 32.70/4.77 | ('#form45'))), 32.70/4.77 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl306])). 32.70/4.77 thf(zip_derived_cl310, plain, 32.70/4.77 (( ((('#sk2' @ ('#sk222' @ '#sk20') @ ('#sk284' @ '#sk20')) & ('#sk20' @ 32.70/4.77 ('#sk222' @ '#sk20')))) 32.70/4.77 | ('#form45') 32.70/4.77 | ('#form9') 32.70/4.77 | ('#sk2' @ '#sk10' @ ('#sk126' @ '#sk20')))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl308])). 32.70/4.77 thf(zip_derived_cl315, plain, 32.70/4.77 (( ('#sk20' @ ('#sk222' @ '#sk20')) 32.70/4.77 | ('#sk2' @ '#sk10' @ ('#sk126' @ '#sk20')) 32.70/4.77 | ('#form9') 32.70/4.77 | ('#form45'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl310])). 32.70/4.77 thf(zip_derived_cl314, plain, 32.70/4.77 (( ('#sk2' @ ('#sk222' @ '#sk20') @ ('#sk284' @ '#sk20')) 32.70/4.77 | ('#sk2' @ '#sk10' @ ('#sk126' @ '#sk20')) 32.70/4.77 | ('#form9') 32.70/4.77 | ('#form45'))), 32.70/4.77 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl310])). 32.70/4.77 thf(zip_derived_cl311, plain, 32.70/4.77 ((~ ('#sk20' @ ('#sk284' @ '#sk20')) 32.70/4.77 | ('#form45') 32.70/4.77 | ('#form9') 32.70/4.77 | ('#sk2' @ '#sk10' @ ('#sk126' @ '#sk20')))), 32.70/4.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl308])). 32.70/4.77 thf(zip_derived_cl121, plain, 32.70/4.77 (![X2 : a]: (~ ('#sk2' @ '#sk10' @ X2) | ('#form9') | ('#sk20' @ X2))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl108])). 32.70/4.77 thf(zip_derived_cl153, plain, 32.70/4.77 (![X2 : a, X4 : a]: 32.70/4.77 (~ ('#sk2' @ X2 @ X4) 32.70/4.77 | ('#sk20' @ X4) 32.70/4.77 | ('#form9') 32.70/4.77 | ~ ('#sk20' @ X2))), 32.70/4.77 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl138])). 32.70/4.77 thf(zip_derived_cl6193, plain, ($false), 32.70/4.77 inference('eprover', [status(thm)], 32.70/4.77 [zip_derived_cl220, zip_derived_cl227, zip_derived_cl23, 32.70/4.77 zip_derived_cl40, zip_derived_cl222, zip_derived_cl228, 32.70/4.77 zip_derived_cl39, zip_derived_cl224, zip_derived_cl226, 32.70/4.77 zip_derived_cl24, zip_derived_cl265, zip_derived_cl266, 32.70/4.77 zip_derived_cl268, zip_derived_cl142, zip_derived_cl158, 32.70/4.77 zip_derived_cl148, zip_derived_cl162, zip_derived_cl173, 32.70/4.77 zip_derived_cl102, zip_derived_cl103, zip_derived_cl161, 32.70/4.77 zip_derived_cl171, zip_derived_cl133, zip_derived_cl182, 32.70/4.77 zip_derived_cl134, zip_derived_cl170, zip_derived_cl72, 32.70/4.77 zip_derived_cl154, zip_derived_cl187, zip_derived_cl180, 32.70/4.77 zip_derived_cl181, zip_derived_cl188, zip_derived_cl120, 32.70/4.77 zip_derived_cl313, zip_derived_cl317, zip_derived_cl316, 32.70/4.77 zip_derived_cl315, zip_derived_cl314, zip_derived_cl311, 32.70/4.77 zip_derived_cl121, zip_derived_cl153])). 32.70/4.77 32.70/4.77 % SZS output end Refutation 32.70/4.77 32.70/4.77 32.70/4.77 % Terminating... 32.70/4.82 % Runner terminated. 32.70/4.83 % Zipperpin 1.5 exiting 32.70/4.85 EOF