0.00/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.srrnb3D2DE true 0.10/0.31 % Computer : n012.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 1200 0.10/0.31 % WCLimit : 120 0.10/0.31 % DateTime : Tue Jul 13 12:57:31 EDT 2021 0.10/0.31 % CPUTime : 0.10/0.31 % Running portfolio for 120 s 0.10/0.31 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.10/0.31 % Number of cores: 8 0.10/0.31 % Python version: Python 3.6.8 0.10/0.31 % Running in HO mode 0.15/0.58 % Total configuration time : 828 0.15/0.58 % Estimated wc time : 983 0.15/0.58 % Estimated cpu time (8 cpus) : 122.875 1.10/0.67 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 47s 1.10/0.67 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 47s 1.10/0.67 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 47s 1.10/0.67 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 18s 1.10/0.67 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 53s 1.10/0.67 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 41s 1.10/0.68 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 24s 1.29/0.70 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 35s 34.82/5.02 % Solved by lams/35_full_unif4.sh. 34.82/5.02 % done 205 iterations in 4.276s 34.82/5.02 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 34.82/5.02 % SZS output start Refutation 34.82/5.02 thf(a_type, type, a: $tType). 34.82/5.02 thf('#sk224_type', type, '#sk224': (a > a > $o) > a). 34.82/5.02 thf('#sk2_type', type, '#sk2': a > a > $o). 34.82/5.02 thf('#sk41_type', type, '#sk41': (a > a > $o) > a). 34.82/5.02 thf('#sk51_type', type, '#sk51': (a > a > $o) > a). 34.82/5.02 thf('#sk240_type', type, '#sk240': (a > a > $o) > a). 34.82/5.02 thf('#sk627_type', type, '#sk627': a > a > $o). 34.82/5.02 thf('#sk3_type', type, '#sk3': a > a > $o). 34.82/5.02 thf('#sk629_type', type, '#sk629': a > a > a > a > $o). 34.82/5.02 thf('#sk213_type', type, '#sk213': (a > a > $o) > a). 34.82/5.02 thf('#sk36_type', type, '#sk36': (a > a > $o) > a). 34.82/5.02 thf('#form15_type', type, '#form15': $o). 34.82/5.02 thf('#sk628_type', type, '#sk628': a > a > a > a > $o). 34.82/5.02 thf('#sk1_type', type, '#sk1': (a > a > $o) > $o). 34.82/5.02 thf('#sk5_type', type, '#sk5': a). 34.82/5.02 thf('#sk61_type', type, '#sk61': (a > a > $o) > a). 34.82/5.02 thf('#sk6_type', type, '#sk6': a > a > $o). 34.82/5.02 thf('#form156_type', type, '#form156': (a > a > $o) > $o). 34.82/5.02 thf('#sk4_type', type, '#sk4': a). 34.82/5.02 thf('#sk254_type', type, '#sk254': (a > a > $o) > a). 34.82/5.02 thf(cTHM252_pme, conjecture, 34.82/5.02 (![PROP:( ( a > a > $o ) > $o ),R:( a > a > $o ),S:( a > a > $o )]: 34.82/5.02 ( ( ^[Xx:a,Xy:a]: 34.82/5.02 ( ![Xp:( a > a > $o )]: 34.82/5.02 ( ( ( PROP @ Xp ) & 34.82/5.02 ( ![Xx0:a,Xy0:a]: 34.82/5.02 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 34.82/5.02 ( Xp @ Xx0 @ Xy0 ) ) ) ) => 34.82/5.02 ( Xp @ Xx @ Xy ) ) ) ) = 34.82/5.02 ( ^[Xx:a,Xy:a]: 34.82/5.02 ( ![Xp:( a > a > $o )]: 34.82/5.02 ( ( ( ![Xx0:a,Xy0:a]: 34.82/5.02 ( ( ( ![Xp0:( a > a > $o )]: 34.82/5.02 ( ( ( PROP @ Xp0 ) & 34.82/5.02 ( ![Xx1:a,Xy1:a]: 34.82/5.02 ( ( R @ Xx1 @ Xy1 ) => ( Xp0 @ Xx1 @ Xy1 ) ) ) ) => 34.82/5.02 ( Xp0 @ Xx0 @ Xy0 ) ) ) | 34.82/5.02 ( ![Xp0:( a > a > $o )]: 34.82/5.02 ( ( ( ![Xx1:a,Xy1:a]: 34.82/5.02 ( ( S @ Xx1 @ Xy1 ) => ( Xp0 @ Xx1 @ Xy1 ) ) ) & 34.82/5.02 ( PROP @ Xp0 ) ) => 34.82/5.02 ( Xp0 @ Xx0 @ Xy0 ) ) ) ) => 34.82/5.02 ( Xp @ Xx0 @ Xy0 ) ) ) & 34.82/5.02 ( PROP @ Xp ) ) => 34.82/5.02 ( Xp @ Xx @ Xy ) ) ) ) ))). 34.82/5.02 thf(zf_stmt_0, negated_conjecture, 34.82/5.02 (~( ![PROP:( ( a > a > $o ) > $o ),R:( a > a > $o ),S:( a > a > $o )]: 34.82/5.02 ( ( ^[Xx:a,Xy:a]: 34.82/5.02 ( ![Xp:( a > a > $o )]: 34.82/5.02 ( ( ( PROP @ Xp ) & 34.82/5.02 ( ![Xx0:a,Xy0:a]: 34.82/5.02 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 34.82/5.02 ( Xp @ Xx0 @ Xy0 ) ) ) ) => 34.82/5.02 ( Xp @ Xx @ Xy ) ) ) ) = 34.82/5.02 ( ^[Xx:a,Xy:a]: 34.82/5.02 ( ![Xp:( a > a > $o )]: 34.82/5.02 ( ( ( ![Xx0:a,Xy0:a]: 34.82/5.02 ( ( ( ![Xp0:( a > a > $o )]: 34.82/5.02 ( ( ( PROP @ Xp0 ) & 34.82/5.02 ( ![Xx1:a,Xy1:a]: 34.82/5.02 ( ( R @ Xx1 @ Xy1 ) => ( Xp0 @ Xx1 @ Xy1 ) ) ) ) => 34.82/5.02 ( Xp0 @ Xx0 @ Xy0 ) ) ) | 34.82/5.02 ( ![Xp0:( a > a > $o )]: 34.82/5.02 ( ( ( ![Xx1:a,Xy1:a]: 34.82/5.02 ( ( S @ Xx1 @ Xy1 ) => ( Xp0 @ Xx1 @ Xy1 ) ) ) & 34.82/5.02 ( PROP @ Xp0 ) ) => 34.82/5.02 ( Xp0 @ Xx0 @ Xy0 ) ) ) ) => 34.82/5.02 ( Xp @ Xx0 @ Xy0 ) ) ) & 34.82/5.02 ( PROP @ Xp ) ) => 34.82/5.02 ( Xp @ Xx @ Xy ) ) ) ) ) )), 34.82/5.02 inference('cnf.neg', [status(esa)], [cTHM252_pme])). 34.82/5.02 thf(zip_derived_cl0, plain, 34.82/5.02 (~ (((!!) @ (^[Y0 : (a > a > $o) > $o]: 34.82/5.02 (((!!) @ (^[Y1 : a > a > $o]: 34.82/5.02 (((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 ((((^[Y3 : a,Y4 : a]: 34.82/5.02 (((!!) @ (^[Y5 : a > a > $o]: 34.82/5.02 (((((Y0 @ Y5) & 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y6 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y7 : a]: 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 (Y2 @ 34.82/5.02 Y6 @ 34.82/5.02 Y7) | 34.82/5.02 (Y1 @ 34.82/5.02 Y6 @ Y7))) => 34.82/5.02 (Y5 @ 34.82/5.02 Y6 @ Y7))))))))))) => 34.82/5.02 (Y5 @ Y3 @ Y4)))))))) = 34.82/5.02 ((^[Y3 : a,Y4 : a]: 34.82/5.02 (((!!) @ (^[Y5 : a > a > $o]: 34.82/5.02 (((((((!!) @ ( 34.82/5.02 ^[Y6 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y7 : a]: 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y8 : 34.82/5.02 a > a > $o]: 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 (Y0 @ 34.82/5.02 Y8) & 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y9 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y10 : a]: 34.82/5.02 (( 34.82/5.02 (Y1 @ 34.82/5.02 Y9 @ 34.82/5.02 Y10) => 34.82/5.02 (Y8 @ 34.82/5.02 Y9 @ Y10))))))))))) => 34.82/5.02 (Y8 @ 34.82/5.02 Y6 @ Y7)))))) | 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y8 : 34.82/5.02 a > a > $o]: 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y9 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y10 : a]: 34.82/5.02 (( 34.82/5.02 (Y2 @ 34.82/5.02 Y9 @ 34.82/5.02 Y10) => 34.82/5.02 (Y8 @ 34.82/5.02 Y9 @ Y10))))))))) & 34.82/5.02 (Y0 @ Y8))) => 34.82/5.02 (Y8 @ 34.82/5.02 Y6 @ Y7)))))))) => 34.82/5.02 (Y5 @ 34.82/5.02 Y6 @ Y7))))))))) & 34.82/5.02 (Y0 @ Y5))) => 34.82/5.02 (Y5 @ Y3 @ Y4)))))))))))))))))))), 34.82/5.02 inference('cnf', [status(esa)], [zf_stmt_0])). 34.82/5.02 thf(zip_derived_cl1, plain, 34.82/5.02 (~ (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 (((!!) @ (^[Y1 : a > a > $o]: 34.82/5.02 ((((^[Y2 : a,Y3 : a]: 34.82/5.02 (((!!) @ (^[Y4 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y4) & 34.82/5.02 (((!!) @ (^[Y5 : a]: 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y6 : a]: 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 (Y1 @ 34.82/5.02 Y5 @ 34.82/5.02 Y6) | 34.82/5.02 (Y0 @ 34.82/5.02 Y5 @ Y6))) => 34.82/5.02 (Y4 @ 34.82/5.02 Y5 @ Y6))))))))))) => 34.82/5.02 (Y4 @ Y2 @ Y3)))))))) = 34.82/5.02 ((^[Y2 : a,Y3 : a]: 34.82/5.02 (((!!) @ (^[Y4 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y5 : a]: 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y6 : a]: 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y7 : 34.82/5.02 a > a > $o]: 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 ('#sk1' @ 34.82/5.02 Y7) & 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y8 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y9 : a]: 34.82/5.02 (( 34.82/5.02 (Y0 @ 34.82/5.02 Y8 @ 34.82/5.02 Y9) => 34.82/5.02 (Y7 @ 34.82/5.02 Y8 @ Y9))))))))))) => 34.82/5.02 (Y7 @ 34.82/5.02 Y5 @ Y6)))))) | 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y7 : 34.82/5.02 a > a > $o]: 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y8 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y9 : a]: 34.82/5.02 (( 34.82/5.02 (Y1 @ 34.82/5.02 Y8 @ 34.82/5.02 Y9) => 34.82/5.02 (Y7 @ 34.82/5.02 Y8 @ Y9))))))))) & 34.82/5.02 ('#sk1' @ 34.82/5.02 Y7))) => 34.82/5.02 (Y7 @ 34.82/5.02 Y5 @ Y6)))))))) => 34.82/5.02 (Y4 @ 34.82/5.02 Y5 @ Y6))))))))) & 34.82/5.02 ('#sk1' @ Y4))) => 34.82/5.02 (Y4 @ Y2 @ Y3))))))))))))))))), 34.82/5.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 34.82/5.02 thf(zip_derived_cl2, plain, 34.82/5.02 (~ (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((^[Y1 : a,Y2 : a]: 34.82/5.02 (((!!) @ (^[Y3 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y3) & 34.82/5.02 (((!!) @ (^[Y4 : a]: 34.82/5.02 (((!!) @ (^[Y5 : a]: 34.82/5.02 (((( 34.82/5.02 (Y0 @ 34.82/5.02 Y4 @ Y5) | 34.82/5.02 ('#sk2' @ 34.82/5.02 Y4 @ Y5))) => 34.82/5.02 (Y3 @ 34.82/5.02 Y4 @ Y5))))))))))) => 34.82/5.02 (Y3 @ Y1 @ Y2)))))))) = 34.82/5.02 ((^[Y1 : a,Y2 : a]: 34.82/5.02 (((!!) @ (^[Y3 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y4 : a]: 34.82/5.02 (((!!) @ (^[Y5 : a]: 34.82/5.02 (((( 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y6 : 34.82/5.02 a > a > $o]: 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 ('#sk1' @ 34.82/5.02 Y6) & 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y7 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y8 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y7 @ 34.82/5.02 Y8) => 34.82/5.02 (Y6 @ 34.82/5.02 Y7 @ Y8))))))))))) => 34.82/5.02 (Y6 @ 34.82/5.02 Y4 @ Y5)))))) | 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y6 : 34.82/5.02 a > a > $o]: 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y7 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y8 : a]: 34.82/5.02 (( 34.82/5.02 (Y0 @ 34.82/5.02 Y7 @ 34.82/5.02 Y8) => 34.82/5.02 (Y6 @ 34.82/5.02 Y7 @ Y8))))))))) & 34.82/5.02 ('#sk1' @ 34.82/5.02 Y6))) => 34.82/5.02 (Y6 @ 34.82/5.02 Y4 @ Y5)))))))) => 34.82/5.02 (Y3 @ 34.82/5.02 Y4 @ Y5))))))))) & 34.82/5.02 ('#sk1' @ Y3))) => 34.82/5.02 (Y3 @ Y1 @ Y2)))))))))))))), 34.82/5.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 34.82/5.02 thf(zip_derived_cl3, plain, 34.82/5.02 (~ ((((^[Y0 : a,Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y2) & 34.82/5.02 (((!!) @ (^[Y3 : a]: 34.82/5.02 (((!!) @ (^[Y4 : a]: 34.82/5.02 ((((('#sk3' @ Y3 @ Y4) | 34.82/5.02 ('#sk2' @ Y3 @ Y4))) => 34.82/5.02 (Y2 @ Y3 @ Y4))))))))))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))))) = 34.82/5.02 ((^[Y0 : a,Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y3 : a]: 34.82/5.02 (((!!) @ (^[Y4 : a]: 34.82/5.02 (((((((!!) @ (^[Y5 : 34.82/5.02 a > a > $o]: 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 ('#sk1' @ 34.82/5.02 Y5) & 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y6 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y7 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y6 @ 34.82/5.02 Y7) => 34.82/5.02 (Y5 @ 34.82/5.02 Y6 @ Y7))))))))))) => 34.82/5.02 (Y5 @ 34.82/5.02 Y3 @ Y4)))))) | 34.82/5.02 (((!!) @ (^[Y5 : 34.82/5.02 a > a > $o]: 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y6 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y7 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y6 @ 34.82/5.02 Y7) => 34.82/5.02 (Y5 @ 34.82/5.02 Y6 @ Y7))))))))) & 34.82/5.02 ('#sk1' @ 34.82/5.02 Y5))) => 34.82/5.02 (Y5 @ 34.82/5.02 Y3 @ Y4)))))))) => 34.82/5.02 (Y2 @ Y3 @ Y4))))))))) & 34.82/5.02 ('#sk1' @ Y2))) => 34.82/5.02 (Y2 @ Y0 @ Y1))))))))))), 34.82/5.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 34.82/5.02 thf(zip_derived_cl4, plain, 34.82/5.02 ((((^[Y0 : a,Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y2) & 34.82/5.02 (((!!) @ (^[Y3 : a]: 34.82/5.02 (((!!) @ (^[Y4 : a]: 34.82/5.02 ((((('#sk3' @ Y3 @ Y4) | 34.82/5.02 ('#sk2' @ Y3 @ Y4))) => 34.82/5.02 (Y2 @ Y3 @ Y4))))))))))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))))) 34.82/5.02 != ((^[Y0 : a,Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y3 : a]: 34.82/5.02 (((!!) @ (^[Y4 : a]: 34.82/5.02 (((((((!!) @ (^[Y5 : 34.82/5.02 a > a > $o]: 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 ('#sk1' @ 34.82/5.02 Y5) & 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y6 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y7 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y6 @ 34.82/5.02 Y7) => 34.82/5.02 (Y5 @ 34.82/5.02 Y6 @ Y7))))))))))) => 34.82/5.02 (Y5 @ 34.82/5.02 Y3 @ Y4)))))) | 34.82/5.02 (((!!) @ (^[Y5 : 34.82/5.02 a > a > $o]: 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y6 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y7 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y6 @ 34.82/5.02 Y7) => 34.82/5.02 (Y5 @ 34.82/5.02 Y6 @ Y7))))))))) & 34.82/5.02 ('#sk1' @ 34.82/5.02 Y5))) => 34.82/5.02 (Y5 @ 34.82/5.02 Y3 @ Y4)))))))) => 34.82/5.02 (Y2 @ Y3 @ Y4))))))))) & 34.82/5.02 ('#sk1' @ Y2))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))))))), 34.82/5.02 inference('simplify nested equalities', [status(thm)], [zip_derived_cl3])). 34.82/5.02 thf(zip_derived_cl5, plain, 34.82/5.02 (((((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ (^[Y1 : a,Y2 : a]: (Y0 @ Y1 @ Y2))) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((((('#sk3' @ Y1 @ Y2) | 34.82/5.02 ('#sk2' @ Y1 @ Y2))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))) 34.82/5.02 != (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 (((((((!!) @ (^[Y3 : 34.82/5.02 a > a > $o]: 34.82/5.02 (((( 34.82/5.02 ('#sk1' @ 34.82/5.02 ( 34.82/5.02 ^[Y4 : a, 34.82/5.02 Y5 : a]: 34.82/5.02 (Y3 @ 34.82/5.02 Y4 @ Y5))) & 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y5 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y4 @ 34.82/5.02 Y5) => 34.82/5.02 (Y3 @ 34.82/5.02 Y4 @ Y5))))))))))) => 34.82/5.02 (Y3 @ 34.82/5.02 Y1 @ Y2)))))) | 34.82/5.02 (((!!) @ (^[Y3 : 34.82/5.02 a > a > $o]: 34.82/5.02 (((( 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y5 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y4 @ 34.82/5.02 Y5) => 34.82/5.02 (Y3 @ 34.82/5.02 Y4 @ Y5))))))))) & 34.82/5.02 ('#sk1' @ 34.82/5.02 ( 34.82/5.02 ^[Y4 : a, 34.82/5.02 Y5 : a]: 34.82/5.02 (Y3 @ 34.82/5.02 Y4 @ Y5))))) => 34.82/5.02 (Y3 @ 34.82/5.02 Y1 @ Y2)))))))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))) & 34.82/5.02 ('#sk1' @ (^[Y1 : a,Y2 : a]: (Y0 @ Y1 @ Y2))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))))), 34.82/5.02 inference('neg_ext', [status(thm)], [zip_derived_cl4])). 34.82/5.02 thf(zip_derived_cl8, plain, 34.82/5.02 (((((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((((('#sk3' @ Y1 @ Y2) | 34.82/5.02 ('#sk2' @ Y1 @ Y2))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))) 34.82/5.02 != (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 (((((((!!) @ (^[Y3 : 34.82/5.02 a > a > $o]: 34.82/5.02 (((( 34.82/5.02 ('#sk1' @ 34.82/5.02 Y3) & 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y5 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y4 @ 34.82/5.02 Y5) => 34.82/5.02 (Y3 @ 34.82/5.02 Y4 @ Y5))))))))))) => 34.82/5.02 (Y3 @ 34.82/5.02 Y1 @ Y2)))))) | 34.82/5.02 (((!!) @ (^[Y3 : 34.82/5.02 a > a > $o]: 34.82/5.02 (((( 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y5 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y4 @ 34.82/5.02 Y5) => 34.82/5.02 (Y3 @ 34.82/5.02 Y4 @ Y5))))))))) & 34.82/5.02 ('#sk1' @ 34.82/5.02 Y3))) => 34.82/5.02 (Y3 @ 34.82/5.02 Y1 @ Y2)))))))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))) & 34.82/5.02 ('#sk1' @ Y0))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))))), 34.82/5.02 inference('ho_norm', [status(thm)], [zip_derived_cl5])). 34.82/5.02 thf(zip_derived_cl15, plain, 34.82/5.02 (((((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((((('#sk3' @ Y1 @ Y2) | 34.82/5.02 ('#sk2' @ Y1 @ Y2))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))) 34.82/5.02 != ((^[Y0 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 (((((((!!) @ (^[Y3 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ 34.82/5.02 (^[Y4 : a, 34.82/5.02 Y5 : a]: 34.82/5.02 (Y3 @ Y4 @ 34.82/5.02 Y5))) & 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y5 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y4 @ 34.82/5.02 Y5) => 34.82/5.02 (Y3 @ 34.82/5.02 Y4 @ Y5))))))))))) => 34.82/5.02 (Y3 @ Y1 @ Y2)))))) | 34.82/5.02 (((!!) @ (^[Y3 : a > a > $o]: 34.82/5.02 (((((((!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y5 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y4 @ 34.82/5.02 Y5) => 34.82/5.02 (Y3 @ 34.82/5.02 Y4 @ Y5))))))))) & 34.82/5.02 ('#sk1' @ 34.82/5.02 (^[Y4 : a, 34.82/5.02 Y5 : a]: 34.82/5.02 (Y3 @ Y4 @ 34.82/5.02 Y5))))) => 34.82/5.02 (Y3 @ Y1 @ Y2)))))))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))) & 34.82/5.02 ('#sk1' @ (^[Y1 : a,Y2 : a]: (Y0 @ Y1 @ Y2))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))) @ 34.82/5.02 '#sk6'))), 34.82/5.02 inference('quantifier_rw', [status(thm)], [zip_derived_cl8])). 34.82/5.02 thf(zip_derived_cl16, plain, 34.82/5.02 (((((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((((('#sk3' @ Y1 @ Y2) | 34.82/5.02 ('#sk2' @ Y1 @ Y2))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))) 34.82/5.02 != (((((((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((((((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y2) & 34.82/5.02 (((!!) @ (^[Y3 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))) | 34.82/5.02 (((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y3 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))) & 34.82/5.02 ('#sk1' @ Y2))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))))) => 34.82/5.02 ('#sk6' @ Y0 @ Y1))))))))) & 34.82/5.02 ('#sk1' @ '#sk6'))) => 34.82/5.02 ('#sk6' @ '#sk4' @ '#sk5'))))), 34.82/5.02 inference('ho_norm', [status(thm)], [zip_derived_cl15])). 34.82/5.02 thf(zip_derived_cl68, plain, 34.82/5.02 ((~ (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((((('#sk3' @ Y1 @ Y2) | 34.82/5.02 ('#sk2' @ Y1 @ Y2))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))) 34.82/5.02 | ~ (((((((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((((((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y2) & 34.82/5.02 (((!!) @ (^[Y3 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))) | 34.82/5.02 (((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y3 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))) & 34.82/5.02 ('#sk1' @ Y2))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))))) => 34.82/5.02 ('#sk6' @ Y0 @ Y1))))))))) & 34.82/5.02 ('#sk1' @ '#sk6'))) => 34.82/5.02 ('#sk6' @ '#sk4' @ '#sk5'))))), 34.82/5.02 inference('eq_elim', [status(thm)], [zip_derived_cl16])). 34.82/5.02 thf(zip_derived_cl97, plain, 34.82/5.02 (( ('#form15') 34.82/5.02 | ~ (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((((('#sk3' @ Y1 @ Y2) | 34.82/5.02 ('#sk2' @ Y1 @ Y2))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))))), 34.82/5.02 define([status(thm)])). 34.82/5.02 thf(zip_derived_cl102, plain, 34.82/5.02 ((~ ((((('#sk1' @ '#sk627') & 34.82/5.02 (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((((('#sk3' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 34.82/5.02 Y1))) => 34.82/5.02 ('#sk627' @ Y0 @ Y1))))))))))) => 34.82/5.02 ('#sk627' @ '#sk4' @ '#sk5'))) 34.82/5.02 | ('#form15'))), 34.82/5.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl97])). 34.82/5.02 thf(zip_derived_cl106, plain, 34.82/5.02 (( ((('#sk1' @ '#sk627') & 34.82/5.02 (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((((('#sk3' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 34.82/5.02 ('#sk627' @ Y0 @ Y1))))))))))) 34.82/5.02 | ('#form15'))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])). 34.82/5.02 thf(zip_derived_cl110, plain, (( ('#sk1' @ '#sk627') | ('#form15'))), 34.82/5.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])). 34.82/5.02 thf(zip_derived_cl8, plain, 34.82/5.02 (((((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((((('#sk3' @ Y1 @ Y2) | 34.82/5.02 ('#sk2' @ Y1 @ Y2))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))) 34.82/5.02 != (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 (((((((!!) @ (^[Y3 : 34.82/5.02 a > a > $o]: 34.82/5.02 (((( 34.82/5.02 ('#sk1' @ 34.82/5.02 Y3) & 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y5 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y4 @ 34.82/5.02 Y5) => 34.82/5.02 (Y3 @ 34.82/5.02 Y4 @ Y5))))))))))) => 34.82/5.02 (Y3 @ 34.82/5.02 Y1 @ Y2)))))) | 34.82/5.02 (((!!) @ (^[Y3 : 34.82/5.02 a > a > $o]: 34.82/5.02 (((( 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y5 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y4 @ 34.82/5.02 Y5) => 34.82/5.02 (Y3 @ 34.82/5.02 Y4 @ Y5))))))))) & 34.82/5.02 ('#sk1' @ 34.82/5.02 Y3))) => 34.82/5.02 (Y3 @ 34.82/5.02 Y1 @ Y2)))))))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))) & 34.82/5.02 ('#sk1' @ Y0))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))))), 34.82/5.02 inference('ho_norm', [status(thm)], [zip_derived_cl5])). 34.82/5.02 thf(zip_derived_cl9, plain, 34.82/5.02 (![X-81 : a > a > $o]: 34.82/5.02 ( ((^[Y0 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 (((((((!!) @ (^[Y3 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y3) & 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y5 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y4 @ 34.82/5.02 Y5) => 34.82/5.02 (Y3 @ 34.82/5.02 Y4 @ Y5))))))))))) => 34.82/5.02 (Y3 @ Y1 @ Y2)))))) | 34.82/5.02 (((!!) @ (^[Y3 : a > a > $o]: 34.82/5.02 (((((((!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y5 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y4 @ 34.82/5.02 Y5) => 34.82/5.02 (Y3 @ 34.82/5.02 Y4 @ Y5))))))))) & 34.82/5.02 ('#sk1' @ Y3))) => 34.82/5.02 (Y3 @ Y1 @ Y2)))))))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))) & 34.82/5.02 ('#sk1' @ Y0))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))) @ 34.82/5.02 X-81) 34.82/5.02 | (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((((('#sk3' @ Y1 @ Y2) | 34.82/5.02 ('#sk2' @ Y1 @ Y2))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))))), 34.82/5.02 inference('forall_hoist', [status(thm)], [zip_derived_cl8])). 34.82/5.02 thf(zip_derived_cl17, plain, 34.82/5.02 (![X-81 : a > a > $o]: 34.82/5.02 ( (((((((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((((((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y2) & 34.82/5.02 (((!!) @ (^[Y3 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))) | 34.82/5.02 (((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y3 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))) & 34.82/5.02 ('#sk1' @ Y2))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))))) => 34.82/5.02 (X-81 @ Y0 @ Y1))))))))) & 34.82/5.02 ('#sk1' @ X-81))) => 34.82/5.02 (X-81 @ '#sk4' @ '#sk5'))) 34.82/5.02 | (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((((('#sk3' @ Y1 @ Y2) | 34.82/5.02 ('#sk2' @ Y1 @ Y2))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))))), 34.82/5.02 inference('ho_norm', [status(thm)], [zip_derived_cl9])). 34.82/5.02 thf(zip_derived_cl18, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 ( (((((((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((((((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y2) & 34.82/5.02 (((!!) @ (^[Y3 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))) | 34.82/5.02 (((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y3 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))) & 34.82/5.02 ('#sk1' @ Y2))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))))) => 34.82/5.02 (X0 @ Y0 @ Y1))))))))) & 34.82/5.02 ('#sk1' @ X0))) => 34.82/5.02 (X0 @ '#sk4' @ '#sk5'))) 34.82/5.02 | (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((((('#sk3' @ Y1 @ Y2) | 34.82/5.02 ('#sk2' @ Y1 @ Y2))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))))), 34.82/5.02 inference('cannonize vars', [status(thm)], [zip_derived_cl17])). 34.82/5.02 thf(zip_derived_cl18, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 ( (((((((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((((((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y2) & 34.82/5.02 (((!!) @ (^[Y3 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))) | 34.82/5.02 (((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y3 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))) & 34.82/5.02 ('#sk1' @ Y2))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))))) => 34.82/5.02 (X0 @ Y0 @ Y1))))))))) & 34.82/5.02 ('#sk1' @ X0))) => 34.82/5.02 (X0 @ '#sk4' @ '#sk5'))) 34.82/5.02 | (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((((('#sk3' @ Y1 @ Y2) | 34.82/5.02 ('#sk2' @ Y1 @ Y2))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))))), 34.82/5.02 inference('cannonize vars', [status(thm)], [zip_derived_cl17])). 34.82/5.02 thf(zip_derived_cl19, plain, 34.82/5.02 ((~ ('#form15') 34.82/5.02 | (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((((('#sk3' @ Y1 @ Y2) | 34.82/5.02 ('#sk2' @ Y1 @ Y2))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))))), 34.82/5.02 define([status(thm)])). 34.82/5.02 thf(zip_derived_cl26, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 ( ('#form15') 34.82/5.02 | (((((((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((((((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y2) & 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y3 : a]: 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))) | 34.82/5.02 (((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 (((((((!!) @ ( 34.82/5.02 ^[Y3 : a]: 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))) & 34.82/5.02 ('#sk1' @ Y2))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))))) => 34.82/5.02 (X0 @ Y0 @ Y1))))))))) & 34.82/5.02 ('#sk1' @ X0))) => 34.82/5.02 (X0 @ '#sk4' @ '#sk5'))))), 34.82/5.02 inference('renaming', [status(thm)], [zip_derived_cl18, zip_derived_cl19])). 34.82/5.02 thf(zip_derived_cl27, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 (~ (((((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((((((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y2) & 34.82/5.02 (((!!) @ (^[Y3 : a]: 34.82/5.02 ( 34.82/5.02 ( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))) | 34.82/5.02 (((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y3 : a]: 34.82/5.02 ( 34.82/5.02 ( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))) & 34.82/5.02 ('#sk1' @ Y2))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))))) => 34.82/5.02 (X0 @ Y0 @ Y1))))))))) & 34.82/5.02 ('#sk1' @ X0))) 34.82/5.02 | (X0 @ '#sk4' @ '#sk5') 34.82/5.02 | ('#form15'))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 34.82/5.02 thf(zip_derived_cl29, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 (~ (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((((((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y2) & 34.82/5.02 (((!!) @ (^[Y3 : a]: 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))) | 34.82/5.02 (((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y3 : a]: 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))) & 34.82/5.02 ('#sk1' @ Y2))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))))) => 34.82/5.02 (X0 @ Y0 @ Y1))))))))) 34.82/5.02 | ~ ('#sk1' @ X0) 34.82/5.02 | ('#form15') 34.82/5.02 | (X0 @ '#sk4' @ '#sk5'))), 34.82/5.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl27])). 34.82/5.02 thf(zip_derived_cl31, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 (~ (((!!) @ (^[Y0 : a]: 34.82/5.02 (((((((!!) @ (^[Y1 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y1) & 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 (((!!) @ (^[Y3 : a]: 34.82/5.02 ((('#sk2' @ 34.82/5.02 Y2 @ 34.82/5.02 Y3) => 34.82/5.02 (Y1 @ 34.82/5.02 Y2 @ Y3))))))))))) => 34.82/5.02 (Y1 @ ('#sk36' @ X0) @ Y0)))))) | 34.82/5.02 (((!!) @ (^[Y1 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y2 : a]: 34.82/5.02 (((!!) @ (^[Y3 : a]: 34.82/5.02 ((('#sk3' @ 34.82/5.02 Y2 @ 34.82/5.02 Y3) => 34.82/5.02 (Y1 @ 34.82/5.02 Y2 @ Y3))))))))) & 34.82/5.02 ('#sk1' @ Y1))) => 34.82/5.02 (Y1 @ ('#sk36' @ X0) @ Y0)))))))) => 34.82/5.02 (X0 @ ('#sk36' @ X0) @ Y0)))))) 34.82/5.02 | (X0 @ '#sk4' @ '#sk5') 34.82/5.02 | ('#form15') 34.82/5.02 | ~ ('#sk1' @ X0))), 34.82/5.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl29])). 34.82/5.02 thf(zip_derived_cl33, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 (~ (((((((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((('#sk2' @ Y1 @ Y2) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))))) | 34.82/5.02 (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((('#sk3' @ Y1 @ Y2) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))) & 34.82/5.02 ('#sk1' @ Y0))) => 34.82/5.02 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))))))) => 34.82/5.02 (X0 @ ('#sk36' @ X0) @ ('#sk51' @ X0)))) 34.82/5.02 | ~ ('#sk1' @ X0) 34.82/5.02 | ('#form15') 34.82/5.02 | (X0 @ '#sk4' @ '#sk5'))), 34.82/5.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl31])). 34.82/5.02 thf(zip_derived_cl36, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 (~ (X0 @ ('#sk36' @ X0) @ ('#sk51' @ X0)) 34.82/5.02 | (X0 @ '#sk4' @ '#sk5') 34.82/5.02 | ('#form15') 34.82/5.02 | ~ ('#sk1' @ X0))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])). 34.82/5.02 thf(zip_derived_cl245, plain, 34.82/5.02 (( ('#form15') 34.82/5.02 | ('#form15') 34.82/5.02 | ('#sk627' @ '#sk4' @ '#sk5') 34.82/5.02 | ~ ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627')))), 34.82/5.02 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl36])). 34.82/5.02 thf(zip_derived_cl252, plain, 34.82/5.02 ((~ ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627')) 34.82/5.02 | ('#sk627' @ '#sk4' @ '#sk5') 34.82/5.02 | ('#form15'))), 34.82/5.02 inference('simplify', [status(thm)], [zip_derived_cl245])). 34.82/5.02 thf(zip_derived_cl107, plain, 34.82/5.02 ((~ ('#sk627' @ '#sk4' @ '#sk5') | ('#form15'))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])). 34.82/5.02 thf(zip_derived_cl278, plain, 34.82/5.02 (( ('#form15') 34.82/5.02 | ~ ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627')))), 34.82/5.02 inference('clc', [status(thm)], [zip_derived_cl252, zip_derived_cl107])). 34.82/5.02 thf(zip_derived_cl19, plain, 34.82/5.02 ((~ ('#form15') 34.82/5.02 | (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((((('#sk3' @ Y1 @ Y2) | 34.82/5.02 ('#sk2' @ Y1 @ Y2))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))))), 34.82/5.02 define([status(thm)])). 34.82/5.02 thf(zip_derived_cl20, plain, 34.82/5.02 (![X2 : a > a > $o]: 34.82/5.02 ( ((((('#sk1' @ X2) & 34.82/5.02 (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((((('#sk3' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 34.82/5.02 Y1))) => 34.82/5.02 (X2 @ Y0 @ Y1))))))))))) => 34.82/5.02 (X2 @ '#sk4' @ '#sk5'))) 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 34.82/5.02 thf(zip_derived_cl21, plain, 34.82/5.02 (( ((((('#sk1' @ '#sk6') & 34.82/5.02 (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((((('#sk3' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 34.82/5.02 Y1))) => 34.82/5.02 ('#sk6' @ Y0 @ Y1))))))))))) => 34.82/5.02 ('#sk6' @ '#sk4' @ '#sk5'))) 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('triggered_bool_instantiation', [status(thm)], 34.82/5.02 [zip_derived_cl20])). 34.82/5.02 thf(zip_derived_cl75, plain, 34.82/5.02 ((~ ((('#sk1' @ '#sk6') & 34.82/5.02 (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((((('#sk3' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 34.82/5.02 ('#sk6' @ Y0 @ Y1))))))))))) 34.82/5.02 | ('#sk6' @ '#sk4' @ '#sk5') 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 34.82/5.02 thf(zip_derived_cl76, plain, 34.82/5.02 ((~ ('#sk1' @ '#sk6') 34.82/5.02 | ~ (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((((('#sk3' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 34.82/5.02 ('#sk6' @ Y0 @ Y1))))))))) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk6' @ '#sk4' @ '#sk5'))), 34.82/5.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl75])). 34.82/5.02 thf(zip_derived_cl77, plain, 34.82/5.02 ((~ (((!!) @ (^[Y0 : a]: 34.82/5.02 ((((('#sk3' @ ('#sk41' @ '#sk6') @ Y0) | ('#sk2' @ 34.82/5.02 ('#sk41' @ '#sk6') @ Y0))) => 34.82/5.02 ('#sk6' @ ('#sk41' @ '#sk6') @ Y0)))))) 34.82/5.02 | ('#sk6' @ '#sk4' @ '#sk5') 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ~ ('#sk1' @ '#sk6'))), 34.82/5.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl76])). 34.82/5.02 thf(zip_derived_cl78, plain, 34.82/5.02 ((~ ((((('#sk3' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')) | ('#sk2' @ 34.82/5.02 ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')))) => 34.82/5.02 ('#sk6' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')))) 34.82/5.02 | ~ ('#sk1' @ '#sk6') 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk6' @ '#sk4' @ '#sk5'))), 34.82/5.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl77])). 34.82/5.02 thf(zip_derived_cl80, plain, 34.82/5.02 ((~ ('#sk6' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')) 34.82/5.02 | ('#sk6' @ '#sk4' @ '#sk5') 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ~ ('#sk1' @ '#sk6'))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 34.82/5.02 thf(zip_derived_cl80, plain, 34.82/5.02 ((~ ('#sk6' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')) 34.82/5.02 | ('#sk6' @ '#sk4' @ '#sk5') 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ~ ('#sk1' @ '#sk6'))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 34.82/5.02 thf(zip_derived_cl68, plain, 34.82/5.02 ((~ (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((((('#sk3' @ Y1 @ Y2) | 34.82/5.02 ('#sk2' @ Y1 @ Y2))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))) 34.82/5.02 | ~ (((((((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((((((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y2) & 34.82/5.02 (((!!) @ (^[Y3 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))) | 34.82/5.02 (((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y3 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))) & 34.82/5.02 ('#sk1' @ Y2))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))))) => 34.82/5.02 ('#sk6' @ Y0 @ Y1))))))))) & 34.82/5.02 ('#sk1' @ '#sk6'))) => 34.82/5.02 ('#sk6' @ '#sk4' @ '#sk5'))))), 34.82/5.02 inference('eq_elim', [status(thm)], [zip_derived_cl16])). 34.82/5.02 thf(zip_derived_cl97, plain, 34.82/5.02 (( ('#form15') 34.82/5.02 | ~ (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((((('#sk3' @ Y1 @ Y2) | 34.82/5.02 ('#sk2' @ Y1 @ Y2))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))))), 34.82/5.02 define([status(thm)])). 34.82/5.02 thf(zip_derived_cl19, plain, 34.82/5.02 ((~ ('#form15') 34.82/5.02 | (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((((('#sk3' @ Y1 @ Y2) | 34.82/5.02 ('#sk2' @ Y1 @ Y2))) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ '#sk4' @ '#sk5')))))))), 34.82/5.02 define([status(thm)])). 34.82/5.02 thf(zip_derived_cl103, plain, 34.82/5.02 ((~ ('#form15') 34.82/5.02 | ~ (((((((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((((((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y2) & 34.82/5.02 (((!!) @ (^[Y3 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))) | 34.82/5.02 (((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y3 : a]: 34.82/5.02 (( 34.82/5.02 (!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))) & 34.82/5.02 ('#sk1' @ Y2))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))))) => 34.82/5.02 ('#sk6' @ Y0 @ Y1))))))))) & 34.82/5.02 ('#sk1' @ '#sk6'))) => 34.82/5.02 ('#sk6' @ '#sk4' @ '#sk5'))))), 34.82/5.02 inference('renaming', [status(thm)], 34.82/5.02 [zip_derived_cl68, zip_derived_cl97, zip_derived_cl19])). 34.82/5.02 thf(zip_derived_cl104, plain, 34.82/5.02 (( (((((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((((((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y2) & 34.82/5.02 (((!!) @ (^[Y3 : a]: 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))) | 34.82/5.02 (((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y3 : a]: 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))) & 34.82/5.02 ('#sk1' @ Y2))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))))) => 34.82/5.02 ('#sk6' @ Y0 @ Y1))))))))) & 34.82/5.02 ('#sk1' @ '#sk6'))) 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])). 34.82/5.02 thf(zip_derived_cl109, plain, (( ('#sk1' @ '#sk6') | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl104])). 34.82/5.02 thf(zip_derived_cl20, plain, 34.82/5.02 (![X2 : a > a > $o]: 34.82/5.02 ( ((((('#sk1' @ X2) & 34.82/5.02 (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((((('#sk3' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 34.82/5.02 Y1))) => 34.82/5.02 (X2 @ Y0 @ Y1))))))))))) => 34.82/5.02 (X2 @ '#sk4' @ '#sk5'))) 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 34.82/5.02 thf(zip_derived_cl28, plain, 34.82/5.02 (![X2 : a > a > $o]: 34.82/5.02 (~ ((('#sk1' @ X2) & 34.82/5.02 (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((((('#sk3' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 34.82/5.02 Y1))) => 34.82/5.02 (X2 @ Y0 @ Y1))))))))))) 34.82/5.02 | (X2 @ '#sk4' @ '#sk5') 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 34.82/5.02 thf(zip_derived_cl30, plain, 34.82/5.02 (![X2 : a > a > $o]: 34.82/5.02 (~ ('#sk1' @ X2) 34.82/5.02 | ~ (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((((('#sk3' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 34.82/5.02 Y1))) => 34.82/5.02 (X2 @ Y0 @ Y1))))))))) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | (X2 @ '#sk4' @ '#sk5'))), 34.82/5.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl28])). 34.82/5.02 thf(zip_derived_cl32, plain, 34.82/5.02 (![X2 : a > a > $o]: 34.82/5.02 (~ (((!!) @ (^[Y0 : a]: 34.82/5.02 ((((('#sk3' @ ('#sk41' @ X2) @ Y0) | ('#sk2' @ 34.82/5.02 ('#sk41' @ X2) @ Y0))) => 34.82/5.02 (X2 @ ('#sk41' @ X2) @ Y0)))))) 34.82/5.02 | (X2 @ '#sk4' @ '#sk5') 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ~ ('#sk1' @ X2))), 34.82/5.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])). 34.82/5.02 thf(zip_derived_cl34, plain, 34.82/5.02 (![X2 : a > a > $o]: 34.82/5.02 (~ ((((('#sk3' @ ('#sk41' @ X2) @ ('#sk61' @ X2)) | ('#sk2' @ 34.82/5.02 ('#sk41' @ X2) @ ('#sk61' @ X2)))) => 34.82/5.02 (X2 @ ('#sk41' @ X2) @ ('#sk61' @ X2)))) 34.82/5.02 | ~ ('#sk1' @ X2) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | (X2 @ '#sk4' @ '#sk5'))), 34.82/5.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl32])). 34.82/5.02 thf(zip_derived_cl37, plain, 34.82/5.02 (![X2 : a > a > $o]: 34.82/5.02 ( ((('#sk3' @ ('#sk41' @ X2) @ ('#sk61' @ X2)) | ('#sk2' @ 34.82/5.02 ('#sk41' @ X2) @ ('#sk61' @ X2)))) 34.82/5.02 | (X2 @ '#sk4' @ '#sk5') 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ~ ('#sk1' @ X2))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 34.82/5.02 thf(zip_derived_cl40, plain, 34.82/5.02 (![X2 : a > a > $o]: 34.82/5.02 ( ('#sk3' @ ('#sk41' @ X2) @ ('#sk61' @ X2)) 34.82/5.02 | ('#sk2' @ ('#sk41' @ X2) @ ('#sk61' @ X2)) 34.82/5.02 | ~ ('#sk1' @ X2) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | (X2 @ '#sk4' @ '#sk5'))), 34.82/5.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl37])). 34.82/5.02 thf(zip_derived_cl138, plain, 34.82/5.02 ((~ ('#form15') 34.82/5.02 | ('#sk6' @ '#sk4' @ '#sk5') 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk2' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')) 34.82/5.02 | ('#sk3' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')))), 34.82/5.02 inference('sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl40])). 34.82/5.02 thf(zip_derived_cl146, plain, 34.82/5.02 (( ('#sk3' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')) 34.82/5.02 | ('#sk2' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')) 34.82/5.02 | ('#sk6' @ '#sk4' @ '#sk5') 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('simplify', [status(thm)], [zip_derived_cl138])). 34.82/5.02 thf(zip_derived_cl105, plain, 34.82/5.02 ((~ ('#sk6' @ '#sk4' @ '#sk5') | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])). 34.82/5.02 thf(zip_derived_cl364, plain, 34.82/5.02 ((~ ('#form15') 34.82/5.02 | ('#sk2' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')) 34.82/5.02 | ('#sk3' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')))), 34.82/5.02 inference('clc', [status(thm)], [zip_derived_cl146, zip_derived_cl105])). 34.82/5.02 thf(zip_derived_cl108, plain, 34.82/5.02 (( (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((((((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y2) & 34.82/5.02 (((!!) @ (^[Y3 : a]: 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk2' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))) | 34.82/5.02 (((!!) @ (^[Y2 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y3 : a]: 34.82/5.02 (((!!) @ ( 34.82/5.02 ^[Y4 : a]: 34.82/5.02 (( 34.82/5.02 ('#sk3' @ 34.82/5.02 Y3 @ 34.82/5.02 Y4) => 34.82/5.02 (Y2 @ 34.82/5.02 Y3 @ Y4))))))))) & 34.82/5.02 ('#sk1' @ Y2))) => 34.82/5.02 (Y2 @ Y0 @ Y1)))))))) => 34.82/5.02 ('#sk6' @ Y0 @ Y1))))))))) 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl104])). 34.82/5.02 thf(zip_derived_cl112, plain, 34.82/5.02 (![X2 : a]: 34.82/5.02 ( (((!!) @ (^[Y0 : a]: 34.82/5.02 (((((((!!) @ (^[Y1 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y1) & 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 (((!!) @ (^[Y3 : a]: 34.82/5.02 ((('#sk2' @ 34.82/5.02 Y2 @ 34.82/5.02 Y3) => 34.82/5.02 (Y1 @ 34.82/5.02 Y2 @ Y3))))))))))) => 34.82/5.02 (Y1 @ X2 @ Y0)))))) | 34.82/5.02 (((!!) @ (^[Y1 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y2 : a]: 34.82/5.02 (((!!) @ (^[Y3 : a]: 34.82/5.02 ((('#sk3' @ 34.82/5.02 Y2 @ 34.82/5.02 Y3) => 34.82/5.02 (Y1 @ 34.82/5.02 Y2 @ Y3))))))))) & 34.82/5.02 ('#sk1' @ Y1))) => 34.82/5.02 (Y1 @ X2 @ Y0)))))))) => 34.82/5.02 ('#sk6' @ X2 @ Y0)))))) 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl108])). 34.82/5.02 thf(zip_derived_cl114, plain, 34.82/5.02 (![X2 : a, X4 : a]: 34.82/5.02 ( (((((((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((('#sk2' @ Y1 @ Y2) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ X2 @ X4)))))) | 34.82/5.02 (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((('#sk3' @ Y1 @ Y2) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))) & 34.82/5.02 ('#sk1' @ Y0))) => 34.82/5.02 (Y0 @ X2 @ X4)))))))) => 34.82/5.02 ('#sk6' @ X2 @ X4))) 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl112])). 34.82/5.02 thf(zip_derived_cl116, plain, 34.82/5.02 (![X2 : a, X4 : a]: 34.82/5.02 (~ (((((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((('#sk2' @ Y1 @ Y2) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ X2 @ X4)))))) | 34.82/5.02 (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((('#sk3' @ Y1 @ Y2) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))) & 34.82/5.02 ('#sk1' @ Y0))) => 34.82/5.02 (Y0 @ X2 @ X4)))))))) 34.82/5.02 | ('#sk6' @ X2 @ X4) 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl114])). 34.82/5.02 thf(zip_derived_cl118, plain, 34.82/5.02 (![X2 : a, X4 : a]: 34.82/5.02 (~ (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((('#sk2' @ Y1 @ Y2) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ X2 @ X4)))))) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk6' @ X2 @ X4))), 34.82/5.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl116])). 34.82/5.02 thf(zip_derived_cl122, plain, 34.82/5.02 (![X2 : a, X4 : a]: 34.82/5.02 (~ ((((('#sk1' @ ('#sk628' @ X2 @ X4)) & 34.82/5.02 (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((('#sk2' @ Y0 @ Y1) => ('#sk628' @ 34.82/5.02 X2 @ X4 @ Y0 @ Y1))))))))))) => 34.82/5.02 ('#sk628' @ X2 @ X4 @ X2 @ X4))) 34.82/5.02 | ('#sk6' @ X2 @ X4) 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl118])). 34.82/5.02 thf(zip_derived_cl125, plain, 34.82/5.02 (![X2 : a, X4 : a]: 34.82/5.02 (~ ('#sk628' @ X2 @ X4 @ X2 @ X4) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk6' @ X2 @ X4))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl122])). 34.82/5.02 thf(zip_derived_cl124, plain, 34.82/5.02 (![X2 : a, X4 : a]: 34.82/5.02 ( ((('#sk1' @ ('#sk628' @ X2 @ X4)) & 34.82/5.02 (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((('#sk2' @ Y0 @ Y1) => ('#sk628' @ X2 @ 34.82/5.02 X4 @ Y0 @ Y1))))))))))) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk6' @ X2 @ X4))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl122])). 34.82/5.02 thf(zip_derived_cl129, plain, 34.82/5.02 (![X2 : a, X4 : a]: 34.82/5.02 ( (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((('#sk2' @ Y0 @ Y1) => ('#sk628' @ X2 @ 34.82/5.02 X4 @ Y0 @ Y1))))))))) 34.82/5.02 | ('#sk6' @ X2 @ X4) 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl124])). 34.82/5.02 thf(zip_derived_cl132, plain, 34.82/5.02 (![X2 : a, X4 : a, X6 : a]: 34.82/5.02 ( (((!!) @ (^[Y0 : a]: 34.82/5.02 ((('#sk2' @ X6 @ Y0) => ('#sk628' @ X2 @ X4 @ X6 @ Y0)))))) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk6' @ X2 @ X4))), 34.82/5.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl129])). 34.82/5.02 thf(zip_derived_cl134, plain, 34.82/5.02 (![X2 : a, X4 : a, X6 : a, X8 : a]: 34.82/5.02 ( ((('#sk2' @ X6 @ X8) => ('#sk628' @ X2 @ X4 @ X6 @ X8))) 34.82/5.02 | ('#sk6' @ X2 @ X4) 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl132])). 34.82/5.02 thf(zip_derived_cl136, plain, 34.82/5.02 (![X2 : a, X4 : a, X6 : a, X8 : a]: 34.82/5.02 (~ ('#sk2' @ X6 @ X8) 34.82/5.02 | ('#sk628' @ X2 @ X4 @ X6 @ X8) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk6' @ X2 @ X4))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl134])). 34.82/5.02 thf(zip_derived_cl349, plain, 34.82/5.02 (![X0 : a, X1 : a]: 34.82/5.02 ( ('#sk6' @ X1 @ X0) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk6' @ X1 @ X0) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ~ ('#sk2' @ X1 @ X0))), 34.82/5.02 inference('sup+', [status(thm)], [zip_derived_cl125, zip_derived_cl136])). 34.82/5.02 thf(zip_derived_cl352, plain, 34.82/5.02 (![X0 : a, X1 : a]: 34.82/5.02 (~ ('#sk2' @ X1 @ X0) | ~ ('#form15') | ('#sk6' @ X1 @ X0))), 34.82/5.02 inference('simplify', [status(thm)], [zip_derived_cl349])). 34.82/5.02 thf(zip_derived_cl419, plain, 34.82/5.02 (( ('#sk3' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk6' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')) 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('sup-', [status(thm)], [zip_derived_cl364, zip_derived_cl352])). 34.82/5.02 thf(zip_derived_cl421, plain, 34.82/5.02 (( ('#sk6' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk3' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')))), 34.82/5.02 inference('simplify', [status(thm)], [zip_derived_cl419])). 34.82/5.02 thf(zip_derived_cl425, plain, 34.82/5.02 ((~ ('#sk1' @ '#sk6') 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk6' @ '#sk4' @ '#sk5') 34.82/5.02 | ('#sk3' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')) 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('sup+', [status(thm)], [zip_derived_cl80, zip_derived_cl421])). 34.82/5.02 thf(zip_derived_cl429, plain, 34.82/5.02 (( ('#sk3' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')) 34.82/5.02 | ('#sk6' @ '#sk4' @ '#sk5') 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ~ ('#sk1' @ '#sk6'))), 34.82/5.02 inference('simplify', [status(thm)], [zip_derived_cl425])). 34.82/5.02 thf(zip_derived_cl105, plain, 34.82/5.02 ((~ ('#sk6' @ '#sk4' @ '#sk5') | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])). 34.82/5.02 thf(zip_derived_cl433, plain, 34.82/5.02 ((~ ('#sk1' @ '#sk6') 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk3' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')))), 34.82/5.02 inference('clc', [status(thm)], [zip_derived_cl429, zip_derived_cl105])). 34.82/5.02 thf(zip_derived_cl109, plain, (( ('#sk1' @ '#sk6') | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl104])). 34.82/5.02 thf(zip_derived_cl434, plain, 34.82/5.02 (( ('#sk3' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')) | ~ ('#form15'))), 34.82/5.02 inference('clc', [status(thm)], [zip_derived_cl433, zip_derived_cl109])). 34.82/5.02 thf(zip_derived_cl119, plain, 34.82/5.02 (![X2 : a, X4 : a]: 34.82/5.02 (~ (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((('#sk3' @ Y1 @ Y2) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))) & 34.82/5.02 ('#sk1' @ Y0))) => 34.82/5.02 (Y0 @ X2 @ X4)))))) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk6' @ X2 @ X4))), 34.82/5.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl116])). 34.82/5.02 thf(zip_derived_cl123, plain, 34.82/5.02 (![X2 : a, X4 : a]: 34.82/5.02 (~ (((((((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((('#sk3' @ Y0 @ Y1) => ('#sk629' @ 34.82/5.02 X2 @ X4 @ Y0 @ Y1))))))))) & 34.82/5.02 ('#sk1' @ ('#sk629' @ X2 @ X4)))) => 34.82/5.02 ('#sk629' @ X2 @ X4 @ X2 @ X4))) 34.82/5.02 | ('#sk6' @ X2 @ X4) 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl119])). 34.82/5.02 thf(zip_derived_cl127, plain, 34.82/5.02 (![X2 : a, X4 : a]: 34.82/5.02 (~ ('#sk629' @ X2 @ X4 @ X2 @ X4) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk6' @ X2 @ X4))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])). 34.82/5.02 thf(zip_derived_cl126, plain, 34.82/5.02 (![X2 : a, X4 : a]: 34.82/5.02 ( (((((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((('#sk3' @ Y0 @ Y1) => ('#sk629' @ X2 @ 34.82/5.02 X4 @ Y0 @ Y1))))))))) & 34.82/5.02 ('#sk1' @ ('#sk629' @ X2 @ X4)))) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk6' @ X2 @ X4))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])). 34.82/5.02 thf(zip_derived_cl130, plain, 34.82/5.02 (![X2 : a, X4 : a]: 34.82/5.02 ( (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((('#sk3' @ Y0 @ Y1) => ('#sk629' @ X2 @ 34.82/5.02 X4 @ Y0 @ Y1))))))))) 34.82/5.02 | ('#sk6' @ X2 @ X4) 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl126])). 34.82/5.02 thf(zip_derived_cl133, plain, 34.82/5.02 (![X2 : a, X4 : a, X6 : a]: 34.82/5.02 ( (((!!) @ (^[Y0 : a]: 34.82/5.02 ((('#sk3' @ X6 @ Y0) => ('#sk629' @ X2 @ X4 @ X6 @ Y0)))))) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk6' @ X2 @ X4))), 34.82/5.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl130])). 34.82/5.02 thf(zip_derived_cl135, plain, 34.82/5.02 (![X2 : a, X4 : a, X6 : a, X8 : a]: 34.82/5.02 ( ((('#sk3' @ X6 @ X8) => ('#sk629' @ X2 @ X4 @ X6 @ X8))) 34.82/5.02 | ('#sk6' @ X2 @ X4) 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl133])). 34.82/5.02 thf(zip_derived_cl137, plain, 34.82/5.02 (![X2 : a, X4 : a, X6 : a, X8 : a]: 34.82/5.02 (~ ('#sk3' @ X6 @ X8) 34.82/5.02 | ('#sk629' @ X2 @ X4 @ X6 @ X8) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk6' @ X2 @ X4))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl135])). 34.82/5.02 thf(zip_derived_cl357, plain, 34.82/5.02 (![X0 : a, X1 : a]: 34.82/5.02 ( ('#sk6' @ X1 @ X0) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk6' @ X1 @ X0) 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ~ ('#sk3' @ X1 @ X0))), 34.82/5.02 inference('sup+', [status(thm)], [zip_derived_cl127, zip_derived_cl137])). 34.82/5.02 thf(zip_derived_cl360, plain, 34.82/5.02 (![X0 : a, X1 : a]: 34.82/5.02 (~ ('#sk3' @ X1 @ X0) | ~ ('#form15') | ('#sk6' @ X1 @ X0))), 34.82/5.02 inference('simplify', [status(thm)], [zip_derived_cl357])). 34.82/5.02 thf(zip_derived_cl460, plain, 34.82/5.02 ((~ ('#form15') 34.82/5.02 | ('#sk6' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')) 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('sup-', [status(thm)], [zip_derived_cl434, zip_derived_cl360])). 34.82/5.02 thf(zip_derived_cl470, plain, 34.82/5.02 (( ('#sk6' @ ('#sk41' @ '#sk6') @ ('#sk61' @ '#sk6')) | ~ ('#form15'))), 34.82/5.02 inference('simplify', [status(thm)], [zip_derived_cl460])). 34.82/5.02 thf(zip_derived_cl495, plain, 34.82/5.02 ((~ ('#sk1' @ '#sk6') 34.82/5.02 | ~ ('#form15') 34.82/5.02 | ('#sk6' @ '#sk4' @ '#sk5') 34.82/5.02 | ~ ('#form15'))), 34.82/5.02 inference('sup+', [status(thm)], [zip_derived_cl80, zip_derived_cl470])). 34.82/5.02 thf(zip_derived_cl498, plain, 34.82/5.02 (( ('#sk6' @ '#sk4' @ '#sk5') | ~ ('#form15') | ~ ('#sk1' @ '#sk6'))), 34.82/5.02 inference('simplify', [status(thm)], [zip_derived_cl495])). 34.82/5.02 thf(zip_derived_cl105, plain, 34.82/5.02 ((~ ('#sk6' @ '#sk4' @ '#sk5') | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])). 34.82/5.02 thf(zip_derived_cl502, plain, ((~ ('#sk1' @ '#sk6') | ~ ('#form15'))), 34.82/5.02 inference('clc', [status(thm)], [zip_derived_cl498, zip_derived_cl105])). 34.82/5.02 thf(zip_derived_cl109, plain, (( ('#sk1' @ '#sk6') | ~ ('#form15'))), 34.82/5.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl104])). 34.82/5.02 thf(zip_derived_cl503, plain, (~ ('#form15')), 34.82/5.02 inference('clc', [status(thm)], [zip_derived_cl502, zip_derived_cl109])). 34.82/5.02 thf(zip_derived_cl512, plain, 34.82/5.02 (~ ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))), 34.82/5.02 inference('demod', [status(thm)], [zip_derived_cl278, zip_derived_cl503])). 34.82/5.02 thf(zip_derived_cl110, plain, (( ('#sk1' @ '#sk627') | ('#form15'))), 34.82/5.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])). 34.82/5.02 thf(zip_derived_cl503, plain, (~ ('#form15')), 34.82/5.02 inference('clc', [status(thm)], [zip_derived_cl502, zip_derived_cl109])). 34.82/5.02 thf(zip_derived_cl508, plain, ( ('#sk1' @ '#sk627')), 34.82/5.02 inference('demod', [status(thm)], [zip_derived_cl110, zip_derived_cl503])). 34.82/5.02 thf(zip_derived_cl35, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 ( (((((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((('#sk2' @ Y1 @ Y2) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))))) | 34.82/5.02 (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((('#sk3' @ Y1 @ Y2) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))) & 34.82/5.02 ('#sk1' @ Y0))) => 34.82/5.02 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))))))) 34.82/5.02 | (X0 @ '#sk4' @ '#sk5') 34.82/5.02 | ('#form15') 34.82/5.02 | ~ ('#sk1' @ X0))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])). 34.82/5.02 thf(zip_derived_cl39, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 ( (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 ((((('#sk1' @ Y0) & 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((('#sk2' @ Y1 @ Y2) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))))) => 34.82/5.02 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))))) 34.82/5.02 | (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((('#sk3' @ Y1 @ Y2) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))) & 34.82/5.02 ('#sk1' @ Y0))) => 34.82/5.02 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))))) 34.82/5.02 | ~ ('#sk1' @ X0) 34.82/5.02 | ('#form15') 34.82/5.02 | (X0 @ '#sk4' @ '#sk5'))), 34.82/5.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl35])). 34.82/5.02 thf(zip_derived_cl41, plain, 34.82/5.02 (![X0 : a > a > $o, X2 : a > a > $o]: 34.82/5.02 ( ((((('#sk1' @ X2) & 34.82/5.02 (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 34.82/5.02 (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)))) 34.82/5.02 | (X0 @ '#sk4' @ '#sk5') 34.82/5.02 | ('#form15') 34.82/5.02 | ~ ('#sk1' @ X0) 34.82/5.02 | (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((('#sk3' @ Y1 @ Y2) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))) & 34.82/5.02 ('#sk1' @ Y0))) => 34.82/5.02 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))))))), 34.82/5.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl39])). 34.82/5.02 thf(zip_derived_cl47, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 (~ ('#form156' @ X0) 34.82/5.02 | (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((('#sk3' @ Y1 @ Y2) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))) & 34.82/5.02 ('#sk1' @ Y0))) => 34.82/5.02 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))))))), 34.82/5.02 define([status(thm)])). 34.82/5.02 thf(zip_derived_cl48, plain, 34.82/5.02 (![X0 : a > a > $o, X2 : a > a > $o]: 34.82/5.02 ( (((((((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((('#sk3' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 34.82/5.02 ('#sk1' @ X2))) => 34.82/5.02 (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)))) 34.82/5.02 | ~ ('#form156' @ X0))), 34.82/5.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl47])). 34.82/5.02 thf(zip_derived_cl56, plain, 34.82/5.02 (![X0 : a > a > $o, X2 : a > a > $o]: 34.82/5.02 (~ (((((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((('#sk3' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 34.82/5.02 ('#sk1' @ X2))) 34.82/5.02 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)) 34.82/5.02 | ~ ('#form156' @ X0))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 34.82/5.02 thf(zip_derived_cl58, plain, 34.82/5.02 (![X0 : a > a > $o, X2 : a > a > $o]: 34.82/5.02 (~ (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((('#sk3' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 34.82/5.02 | ~ ('#sk1' @ X2) 34.82/5.02 | ~ ('#form156' @ X0) 34.82/5.02 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)))), 34.82/5.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl56])). 34.82/5.02 thf(zip_derived_cl60, plain, 34.82/5.02 (![X0 : a > a > $o, X2 : a > a > $o]: 34.82/5.02 (~ (((!!) @ (^[Y0 : a]: 34.82/5.02 ((('#sk3' @ ('#sk224' @ X2) @ Y0) => (X2 @ 34.82/5.02 ('#sk224' @ X2) @ Y0)))))) 34.82/5.02 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)) 34.82/5.02 | ~ ('#form156' @ X0) 34.82/5.02 | ~ ('#sk1' @ X2))), 34.82/5.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl58])). 34.82/5.02 thf(zip_derived_cl62, plain, 34.82/5.02 (![X0 : a > a > $o, X2 : a > a > $o]: 34.82/5.02 (~ ((('#sk3' @ ('#sk224' @ X2) @ ('#sk254' @ X2)) => (X2 @ 34.82/5.02 ('#sk224' @ X2) @ ('#sk254' @ X2)))) 34.82/5.02 | ~ ('#sk1' @ X2) 34.82/5.02 | ~ ('#form156' @ X0) 34.82/5.02 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)))), 34.82/5.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl60])). 34.82/5.02 thf(zip_derived_cl66, plain, 34.82/5.02 (![X0 : a > a > $o, X2 : a > a > $o]: 34.82/5.02 (~ (X2 @ ('#sk224' @ X2) @ ('#sk254' @ X2)) 34.82/5.02 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)) 34.82/5.02 | ~ ('#form156' @ X0) 34.82/5.02 | ~ ('#sk1' @ X2))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 34.82/5.02 thf(zip_derived_cl908, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 (~ ('#form156' @ X0) 34.82/5.02 | ('#sk627' @ ('#sk36' @ X0) @ ('#sk51' @ X0)) 34.82/5.02 | ~ ('#sk627' @ ('#sk224' @ '#sk627') @ ('#sk254' @ '#sk627')))), 34.82/5.02 inference('sup-', [status(thm)], [zip_derived_cl508, zip_derived_cl66])). 34.82/5.02 thf(zip_derived_cl512, plain, 34.82/5.02 (~ ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))), 34.82/5.02 inference('demod', [status(thm)], [zip_derived_cl278, zip_derived_cl503])). 34.82/5.02 thf(zip_derived_cl508, plain, ( ('#sk1' @ '#sk627')), 34.82/5.02 inference('demod', [status(thm)], [zip_derived_cl110, zip_derived_cl503])). 34.82/5.02 thf(zip_derived_cl65, plain, 34.82/5.02 (![X0 : a > a > $o, X2 : a > a > $o]: 34.82/5.02 ( ('#sk3' @ ('#sk224' @ X2) @ ('#sk254' @ X2)) 34.82/5.02 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)) 34.82/5.02 | ~ ('#form156' @ X0) 34.82/5.02 | ~ ('#sk1' @ X2))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 34.82/5.02 thf(zip_derived_cl1049, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 (~ ('#form156' @ X0) 34.82/5.02 | ('#sk627' @ ('#sk36' @ X0) @ ('#sk51' @ X0)) 34.82/5.02 | ('#sk3' @ ('#sk224' @ '#sk627') @ ('#sk254' @ '#sk627')))), 34.82/5.02 inference('sup-', [status(thm)], [zip_derived_cl508, zip_derived_cl65])). 34.82/5.02 thf(zip_derived_cl1088, plain, 34.82/5.02 (( ('#sk3' @ ('#sk224' @ '#sk627') @ ('#sk254' @ '#sk627')) 34.82/5.02 | ~ ('#form156' @ '#sk627'))), 34.82/5.02 inference('sup+', [status(thm)], [zip_derived_cl512, zip_derived_cl1049])). 34.82/5.02 thf(zip_derived_cl508, plain, ( ('#sk1' @ '#sk627')), 34.82/5.02 inference('demod', [status(thm)], [zip_derived_cl110, zip_derived_cl503])). 34.82/5.02 thf(zip_derived_cl110, plain, (( ('#sk1' @ '#sk627') | ('#form15'))), 34.82/5.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])). 34.82/5.02 thf(zip_derived_cl41, plain, 34.82/5.02 (![X0 : a > a > $o, X2 : a > a > $o]: 34.82/5.02 ( ((((('#sk1' @ X2) & 34.82/5.02 (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 34.82/5.02 (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)))) 34.82/5.02 | (X0 @ '#sk4' @ '#sk5') 34.82/5.02 | ('#form15') 34.82/5.02 | ~ ('#sk1' @ X0) 34.82/5.02 | (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((('#sk3' @ Y1 @ Y2) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))) & 34.82/5.02 ('#sk1' @ Y0))) => 34.82/5.02 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))))))), 34.82/5.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl39])). 34.82/5.02 thf(zip_derived_cl47, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 (~ ('#form156' @ X0) 34.82/5.02 | (((!!) @ (^[Y0 : a > a > $o]: 34.82/5.02 (((((((!!) @ (^[Y1 : a]: 34.82/5.02 (((!!) @ (^[Y2 : a]: 34.82/5.02 ((('#sk3' @ Y1 @ Y2) => 34.82/5.02 (Y0 @ Y1 @ Y2))))))))) & 34.82/5.02 ('#sk1' @ Y0))) => 34.82/5.02 (Y0 @ ('#sk36' @ X0) @ ('#sk51' @ X0))))))))), 34.82/5.02 define([status(thm)])). 34.82/5.02 thf(zip_derived_cl54, plain, 34.82/5.02 (![X0 : a > a > $o, X2 : a > a > $o]: 34.82/5.02 ( ('#form156' @ X0) 34.82/5.02 | ~ ('#sk1' @ X0) 34.82/5.02 | ('#form15') 34.82/5.02 | (X0 @ '#sk4' @ '#sk5') 34.82/5.02 | ((((('#sk1' @ X2) & 34.82/5.02 (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 34.82/5.02 (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)))))), 34.82/5.02 inference('renaming', [status(thm)], [zip_derived_cl41, zip_derived_cl47])). 34.82/5.02 thf(zip_derived_cl55, plain, 34.82/5.02 (![X0 : a > a > $o, X2 : a > a > $o]: 34.82/5.02 (~ ((('#sk1' @ X2) & 34.82/5.02 (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) 34.82/5.02 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)) 34.82/5.02 | (X0 @ '#sk4' @ '#sk5') 34.82/5.02 | ('#form15') 34.82/5.02 | ~ ('#sk1' @ X0) 34.82/5.02 | ('#form156' @ X0))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl54])). 34.82/5.02 thf(zip_derived_cl57, plain, 34.82/5.02 (![X0 : a > a > $o, X2 : a > a > $o]: 34.82/5.02 (~ ('#sk1' @ X2) 34.82/5.02 | ~ (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 34.82/5.02 | ('#form156' @ X0) 34.82/5.02 | ~ ('#sk1' @ X0) 34.82/5.02 | ('#form15') 34.82/5.02 | (X0 @ '#sk4' @ '#sk5') 34.82/5.02 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)))), 34.82/5.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl55])). 34.82/5.02 thf(zip_derived_cl59, plain, 34.82/5.02 (![X0 : a > a > $o, X2 : a > a > $o]: 34.82/5.02 (~ (((!!) @ (^[Y0 : a]: 34.82/5.02 ((('#sk2' @ ('#sk213' @ X2) @ Y0) => (X2 @ 34.82/5.02 ('#sk213' @ X2) @ Y0)))))) 34.82/5.02 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)) 34.82/5.02 | (X0 @ '#sk4' @ '#sk5') 34.82/5.02 | ('#form15') 34.82/5.02 | ~ ('#sk1' @ X0) 34.82/5.02 | ('#form156' @ X0) 34.82/5.02 | ~ ('#sk1' @ X2))), 34.82/5.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl57])). 34.82/5.02 thf(zip_derived_cl61, plain, 34.82/5.02 (![X0 : a > a > $o, X2 : a > a > $o]: 34.82/5.02 (~ ((('#sk2' @ ('#sk213' @ X2) @ ('#sk240' @ X2)) => (X2 @ 34.82/5.02 ('#sk213' @ X2) @ ('#sk240' @ X2)))) 34.82/5.02 | ~ ('#sk1' @ X2) 34.82/5.02 | ('#form156' @ X0) 34.82/5.02 | ~ ('#sk1' @ X0) 34.82/5.02 | ('#form15') 34.82/5.02 | (X0 @ '#sk4' @ '#sk5') 34.82/5.02 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)))), 34.82/5.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl59])). 34.82/5.02 thf(zip_derived_cl64, plain, 34.82/5.02 (![X0 : a > a > $o, X2 : a > a > $o]: 34.82/5.02 (~ (X2 @ ('#sk213' @ X2) @ ('#sk240' @ X2)) 34.82/5.02 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)) 34.82/5.02 | (X0 @ '#sk4' @ '#sk5') 34.82/5.02 | ('#form15') 34.82/5.02 | ~ ('#sk1' @ X0) 34.82/5.02 | ('#form156' @ X0) 34.82/5.02 | ~ ('#sk1' @ X2))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 34.82/5.02 thf(zip_derived_cl243, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 ( ('#form15') 34.82/5.02 | ~ ('#sk1' @ X0) 34.82/5.02 | ('#form156' @ '#sk627') 34.82/5.02 | ('#form15') 34.82/5.02 | ('#sk627' @ '#sk4' @ '#sk5') 34.82/5.02 | (X0 @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627')) 34.82/5.02 | ~ (X0 @ ('#sk213' @ X0) @ ('#sk240' @ X0)))), 34.82/5.02 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl64])). 34.82/5.02 thf(zip_derived_cl250, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 (~ (X0 @ ('#sk213' @ X0) @ ('#sk240' @ X0)) 34.82/5.02 | (X0 @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627')) 34.82/5.02 | ('#sk627' @ '#sk4' @ '#sk5') 34.82/5.02 | ('#form156' @ '#sk627') 34.82/5.02 | ~ ('#sk1' @ X0) 34.82/5.02 | ('#form15'))), 34.82/5.02 inference('simplify', [status(thm)], [zip_derived_cl243])). 34.82/5.02 thf(zip_derived_cl503, plain, (~ ('#form15')), 34.82/5.02 inference('clc', [status(thm)], [zip_derived_cl502, zip_derived_cl109])). 34.82/5.02 thf(zip_derived_cl757, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 (~ (X0 @ ('#sk213' @ X0) @ ('#sk240' @ X0)) 34.82/5.02 | (X0 @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627')) 34.82/5.02 | ('#sk627' @ '#sk4' @ '#sk5') 34.82/5.02 | ('#form156' @ '#sk627') 34.82/5.02 | ~ ('#sk1' @ X0))), 34.82/5.02 inference('demod', [status(thm)], [zip_derived_cl250, zip_derived_cl503])). 34.82/5.02 thf(zip_derived_cl107, plain, 34.82/5.02 ((~ ('#sk627' @ '#sk4' @ '#sk5') | ('#form15'))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])). 34.82/5.02 thf(zip_derived_cl503, plain, (~ ('#form15')), 34.82/5.02 inference('clc', [status(thm)], [zip_derived_cl502, zip_derived_cl109])). 34.82/5.02 thf(zip_derived_cl507, plain, (~ ('#sk627' @ '#sk4' @ '#sk5')), 34.82/5.02 inference('demod', [status(thm)], [zip_derived_cl107, zip_derived_cl503])). 34.82/5.02 thf(zip_derived_cl758, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 (~ ('#sk1' @ X0) 34.82/5.02 | ('#form156' @ '#sk627') 34.82/5.02 | (X0 @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627')) 34.82/5.02 | ~ (X0 @ ('#sk213' @ X0) @ ('#sk240' @ X0)))), 34.82/5.02 inference('clc', [status(thm)], [zip_derived_cl757, zip_derived_cl507])). 34.82/5.02 thf(zip_derived_cl759, plain, 34.82/5.02 ((~ ('#sk627' @ ('#sk213' @ '#sk627') @ ('#sk240' @ '#sk627')) 34.82/5.02 | ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627')) 34.82/5.02 | ('#form156' @ '#sk627'))), 34.82/5.02 inference('sup-', [status(thm)], [zip_derived_cl508, zip_derived_cl758])). 34.82/5.02 thf(zip_derived_cl508, plain, ( ('#sk1' @ '#sk627')), 34.82/5.02 inference('demod', [status(thm)], [zip_derived_cl110, zip_derived_cl503])). 34.82/5.02 thf(zip_derived_cl110, plain, (( ('#sk1' @ '#sk627') | ('#form15'))), 34.82/5.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])). 34.82/5.02 thf(zip_derived_cl63, plain, 34.82/5.02 (![X0 : a > a > $o, X2 : a > a > $o]: 34.82/5.02 ( ('#sk2' @ ('#sk213' @ X2) @ ('#sk240' @ X2)) 34.82/5.02 | (X2 @ ('#sk36' @ X0) @ ('#sk51' @ X0)) 34.82/5.02 | (X0 @ '#sk4' @ '#sk5') 34.82/5.02 | ('#form15') 34.82/5.02 | ~ ('#sk1' @ X0) 34.82/5.02 | ('#form156' @ X0) 34.82/5.02 | ~ ('#sk1' @ X2))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl61])). 34.82/5.02 thf(zip_derived_cl244, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 ( ('#form15') 34.82/5.02 | ~ ('#sk1' @ X0) 34.82/5.02 | ('#form156' @ '#sk627') 34.82/5.02 | ('#form15') 34.82/5.02 | ('#sk627' @ '#sk4' @ '#sk5') 34.82/5.02 | (X0 @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627')) 34.82/5.02 | ('#sk2' @ ('#sk213' @ X0) @ ('#sk240' @ X0)))), 34.82/5.02 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl63])). 34.82/5.02 thf(zip_derived_cl251, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 ( ('#sk2' @ ('#sk213' @ X0) @ ('#sk240' @ X0)) 34.82/5.02 | (X0 @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627')) 34.82/5.02 | ('#sk627' @ '#sk4' @ '#sk5') 34.82/5.02 | ('#form156' @ '#sk627') 34.82/5.02 | ~ ('#sk1' @ X0) 34.82/5.02 | ('#form15'))), 34.82/5.02 inference('simplify', [status(thm)], [zip_derived_cl244])). 34.82/5.02 thf(zip_derived_cl507, plain, (~ ('#sk627' @ '#sk4' @ '#sk5')), 34.82/5.02 inference('demod', [status(thm)], [zip_derived_cl107, zip_derived_cl503])). 34.82/5.02 thf(zip_derived_cl503, plain, (~ ('#form15')), 34.82/5.02 inference('clc', [status(thm)], [zip_derived_cl502, zip_derived_cl109])). 34.82/5.02 thf(zip_derived_cl584, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 ( ('#sk2' @ ('#sk213' @ X0) @ ('#sk240' @ X0)) 34.82/5.02 | (X0 @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627')) 34.82/5.02 | ('#form156' @ '#sk627') 34.82/5.02 | ~ ('#sk1' @ X0))), 34.82/5.02 inference('demod', [status(thm)], 34.82/5.02 [zip_derived_cl251, zip_derived_cl507, zip_derived_cl503])). 34.82/5.02 thf(zip_derived_cl585, plain, 34.82/5.02 (( ('#form156' @ '#sk627') 34.82/5.02 | ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627')) 34.82/5.02 | ('#sk2' @ ('#sk213' @ '#sk627') @ ('#sk240' @ '#sk627')))), 34.82/5.02 inference('sup-', [status(thm)], [zip_derived_cl508, zip_derived_cl584])). 34.82/5.02 thf(zip_derived_cl512, plain, 34.82/5.02 (~ ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))), 34.82/5.02 inference('demod', [status(thm)], [zip_derived_cl278, zip_derived_cl503])). 34.82/5.02 thf(zip_derived_cl587, plain, 34.82/5.02 (( ('#sk2' @ ('#sk213' @ '#sk627') @ ('#sk240' @ '#sk627')) 34.82/5.02 | ('#form156' @ '#sk627'))), 34.82/5.02 inference('clc', [status(thm)], [zip_derived_cl585, zip_derived_cl512])). 34.82/5.02 thf(zip_derived_cl111, plain, 34.82/5.02 (( (((!!) @ (^[Y0 : a]: 34.82/5.02 (((!!) @ (^[Y1 : a]: 34.82/5.02 ((((('#sk3' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 34.82/5.02 ('#sk627' @ Y0 @ Y1))))))))) 34.82/5.02 | ('#form15'))), 34.82/5.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])). 34.82/5.02 thf(zip_derived_cl113, plain, 34.82/5.02 (![X2 : a]: 34.82/5.02 ( (((!!) @ (^[Y0 : a]: 34.82/5.02 ((((('#sk3' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) => 34.82/5.02 ('#sk627' @ X2 @ Y0)))))) 34.82/5.02 | ('#form15'))), 34.82/5.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl111])). 34.82/5.02 thf(zip_derived_cl115, plain, 34.82/5.02 (![X2 : a, X4 : a]: 34.82/5.02 ( ((((('#sk3' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) => ('#sk627' @ X2 @ 34.82/5.02 X4))) 34.82/5.02 | ('#form15'))), 34.82/5.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl113])). 34.82/5.02 thf(zip_derived_cl117, plain, 34.82/5.02 (![X2 : a, X4 : a]: 34.82/5.02 (~ ((('#sk3' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 34.82/5.02 | ('#sk627' @ X2 @ X4) 34.82/5.02 | ('#form15'))), 34.82/5.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl115])). 34.82/5.02 thf(zip_derived_cl121, plain, 34.82/5.02 (![X2 : a, X4 : a]: 34.82/5.02 (~ ('#sk2' @ X2 @ X4) | ('#form15') | ('#sk627' @ X2 @ X4))), 34.82/5.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl117])). 34.82/5.02 thf(zip_derived_cl503, plain, (~ ('#form15')), 34.82/5.02 inference('clc', [status(thm)], [zip_derived_cl502, zip_derived_cl109])). 34.82/5.02 thf(zip_derived_cl510, plain, 34.82/5.02 (![X2 : a, X4 : a]: (~ ('#sk2' @ X2 @ X4) | ('#sk627' @ X2 @ X4))), 34.82/5.02 inference('demod', [status(thm)], [zip_derived_cl121, zip_derived_cl503])). 34.82/5.02 thf(zip_derived_cl588, plain, 34.82/5.02 (( ('#form156' @ '#sk627') 34.82/5.02 | ('#sk627' @ ('#sk213' @ '#sk627') @ ('#sk240' @ '#sk627')))), 34.82/5.02 inference('sup-', [status(thm)], [zip_derived_cl587, zip_derived_cl510])). 34.82/5.02 thf(zip_derived_cl761, plain, 34.82/5.02 (( ('#form156' @ '#sk627') 34.82/5.02 | ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627')))), 34.82/5.02 inference('clc', [status(thm)], [zip_derived_cl759, zip_derived_cl588])). 34.82/5.02 thf(zip_derived_cl512, plain, 34.82/5.02 (~ ('#sk627' @ ('#sk36' @ '#sk627') @ ('#sk51' @ '#sk627'))), 34.82/5.02 inference('demod', [status(thm)], [zip_derived_cl278, zip_derived_cl503])). 34.82/5.02 thf(zip_derived_cl762, plain, ( ('#form156' @ '#sk627')), 34.82/5.02 inference('clc', [status(thm)], [zip_derived_cl761, zip_derived_cl512])). 34.82/5.02 thf(zip_derived_cl1092, plain, 34.82/5.02 ( ('#sk3' @ ('#sk224' @ '#sk627') @ ('#sk254' @ '#sk627'))), 34.82/5.02 inference('demod', [status(thm)], [zip_derived_cl1088, zip_derived_cl762])). 34.82/5.02 thf(zip_derived_cl120, plain, 34.82/5.02 (![X2 : a, X4 : a]: 34.82/5.02 (~ ('#sk3' @ X2 @ X4) | ('#form15') | ('#sk627' @ X2 @ X4))), 34.82/5.02 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl117])). 34.82/5.02 thf(zip_derived_cl503, plain, (~ ('#form15')), 34.82/5.02 inference('clc', [status(thm)], [zip_derived_cl502, zip_derived_cl109])). 34.82/5.02 thf(zip_derived_cl509, plain, 34.82/5.02 (![X2 : a, X4 : a]: (~ ('#sk3' @ X2 @ X4) | ('#sk627' @ X2 @ X4))), 34.82/5.02 inference('demod', [status(thm)], [zip_derived_cl120, zip_derived_cl503])). 34.82/5.02 thf(zip_derived_cl1096, plain, 34.82/5.02 ( ('#sk627' @ ('#sk224' @ '#sk627') @ ('#sk254' @ '#sk627'))), 34.82/5.02 inference('sup-', [status(thm)], [zip_derived_cl1092, zip_derived_cl509])). 34.82/5.02 thf(zip_derived_cl1098, plain, 34.82/5.02 (![X0 : a > a > $o]: 34.82/5.02 (~ ('#form156' @ X0) | ('#sk627' @ ('#sk36' @ X0) @ ('#sk51' @ X0)))), 34.82/5.02 inference('demod', [status(thm)], [zip_derived_cl908, zip_derived_cl1096])). 34.82/5.02 thf(zip_derived_cl1131, plain, (~ ('#form156' @ '#sk627')), 34.82/5.02 inference('sup+', [status(thm)], [zip_derived_cl512, zip_derived_cl1098])). 34.82/5.02 thf(zip_derived_cl762, plain, ( ('#form156' @ '#sk627')), 34.82/5.02 inference('clc', [status(thm)], [zip_derived_cl761, zip_derived_cl512])). 34.82/5.02 thf(zip_derived_cl1134, plain, ($false), 34.82/5.02 inference('demod', [status(thm)], [zip_derived_cl1131, zip_derived_cl762])). 34.82/5.02 34.82/5.02 % SZS output end Refutation 34.82/5.02 34.82/5.02 34.82/5.02 % Terminating... 35.74/5.12 % Runner terminated. 35.74/5.12 % Zipperpin 1.5 exiting 35.74/5.12 EOF