0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.07 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.jq4pGUpBOF true 0.19/0.45 % Computer : n015.cluster.edu 0.19/0.45 % Model : x86_64 x86_64 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.19/0.45 % Memory : 8046.5625MB 0.19/0.45 % OS : Linux 6.8.0-71-generic 0.19/0.45 % CPULimit : 1440 0.19/0.45 % WCLimit : 180 0.19/0.45 % DateTime : Mon Jul 27 12:21:04 UTC 2026 0.19/0.45 % CPUTime : 0.19/0.45 % Running portfolio for 1440 s 0.19/0.45 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.19/0.45 % Number of cores: 8 0.19/0.46 % Python version: Python 3.12.3 0.19/0.46 % Running in HO mode 0.40/0.92 % Total configuration time : 828 0.40/0.92 % Estimated wc time : 1656 0.40/0.92 % Estimated cpu time (8 cpus) : 207.0 0.40/1.00 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 2.11/1.12 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 2.11/1.12 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 2.11/1.12 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 2.11/1.12 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 2.11/1.13 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 2.11/1.13 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 2.11/1.15 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 50.27/7.23 % Solved by lams/20_acsne_simpl.sh. 50.27/7.23 % done 1215 iterations in 5.990s 50.27/7.23 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 50.27/7.23 % SZS output start Refutation 50.27/7.23 thf(a_type, type, a: $tType). 50.27/7.23 thf('#sk1_type', type, '#sk1': a > a > $o). 50.27/7.23 thf('#sk2_type', type, '#sk2': a). 50.27/7.23 thf('#sk24_type', type, '#sk24': (a > $o) > a > $o). 50.27/7.23 thf('#sk28_type', type, '#sk28': (a > $o) > a). 50.27/7.23 thf('#_fresh_sk90_type', type, '#_fresh_sk90': (a > $o) > a). 50.27/7.23 thf('#_fresh_sk52_type', type, '#_fresh_sk52': (a > $o) > a). 50.27/7.23 thf('#sk17_type', type, '#sk17': (a > $o) > a). 50.27/7.23 thf(cTHM260_pme, conjecture, 50.27/7.23 (![R:( a > a > $o )]: 50.27/7.23 ( ( ( ![Xx:a,Xy:a]: ( ( R @ Xx @ Xy ) => ( R @ Xy @ Xx ) ) ) & 50.27/7.23 ( ![Xx:a,Xy:a,Xz:a]: 50.27/7.23 ( ( ( R @ Xy @ Xz ) & ( R @ Xx @ Xy ) ) => ( R @ Xx @ Xz ) ) ) & 50.27/7.23 ( ![Xx:a]: ( R @ Xx @ Xx ) ) ) => 50.27/7.23 ( ( ![Xp:( a > $o )]: 50.27/7.23 ( ( ( ![Xx:a]: 50.27/7.23 ( ( Xp @ Xx ) => 50.27/7.23 ( ![Xy:a]: ( ( R @ Xx @ Xy ) <=> ( Xp @ Xy ) ) ) ) ) & 50.27/7.23 ( ?[Xz:a]: ( Xp @ Xz ) ) ) => 50.27/7.23 ( ?[Xz:a]: ( Xp @ Xz ) ) ) ) & 50.27/7.23 ( ![Xx:a]: 50.27/7.23 ( ?[Xp:( a > $o )]: 50.27/7.23 ( ( ?[Xz:a]: ( Xp @ Xz ) ) & 50.27/7.23 ( ![Xx0:a]: 50.27/7.23 ( ( Xp @ Xx0 ) => 50.27/7.23 ( ![Xy:a]: ( ( R @ Xx0 @ Xy ) <=> ( Xp @ Xy ) ) ) ) ) & 50.27/7.23 ( Xp @ Xx ) & 50.27/7.23 ( ![Xq:( a > $o )]: 50.27/7.23 ( ( ( ?[Xz:a]: ( Xq @ Xz ) ) & ( Xq @ Xx ) & 50.27/7.23 ( ![Xx0:a]: 50.27/7.23 ( ( Xq @ Xx0 ) => 50.27/7.23 ( ![Xy:a]: ( ( R @ Xx0 @ Xy ) <=> ( Xq @ Xy ) ) ) ) ) ) => 50.27/7.23 ( ( Xq ) = ( Xp ) ) ) ) ) ) ) ) ))). 50.27/7.23 thf(zf_stmt_0, negated_conjecture, 50.27/7.23 (~( ![R:( a > a > $o )]: 50.27/7.23 ( ( ( ![Xx:a,Xy:a]: ( ( R @ Xx @ Xy ) => ( R @ Xy @ Xx ) ) ) & 50.27/7.23 ( ![Xx:a,Xy:a,Xz:a]: 50.27/7.23 ( ( ( R @ Xy @ Xz ) & ( R @ Xx @ Xy ) ) => ( R @ Xx @ Xz ) ) ) & 50.27/7.23 ( ![Xx:a]: ( R @ Xx @ Xx ) ) ) => 50.27/7.23 ( ( ![Xp:( a > $o )]: 50.27/7.23 ( ( ( ![Xx:a]: 50.27/7.23 ( ( Xp @ Xx ) => 50.27/7.23 ( ![Xy:a]: ( ( R @ Xx @ Xy ) <=> ( Xp @ Xy ) ) ) ) ) & 50.27/7.23 ( ?[Xz:a]: ( Xp @ Xz ) ) ) => 50.27/7.23 ( ?[Xz:a]: ( Xp @ Xz ) ) ) ) & 50.27/7.23 ( ![Xx:a]: 50.27/7.23 ( ?[Xp:( a > $o )]: 50.27/7.23 ( ( ?[Xz:a]: ( Xp @ Xz ) ) & 50.27/7.23 ( ![Xx0:a]: 50.27/7.23 ( ( Xp @ Xx0 ) => 50.27/7.23 ( ![Xy:a]: ( ( R @ Xx0 @ Xy ) <=> ( Xp @ Xy ) ) ) ) ) & 50.27/7.23 ( Xp @ Xx ) & 50.27/7.23 ( ![Xq:( a > $o )]: 50.27/7.23 ( ( ( ?[Xz:a]: ( Xq @ Xz ) ) & ( Xq @ Xx ) & 50.27/7.23 ( ![Xx0:a]: 50.27/7.23 ( ( Xq @ Xx0 ) => 50.27/7.23 ( ![Xy:a]: ( ( R @ Xx0 @ Xy ) <=> ( Xq @ Xy ) ) ) ) ) ) => 50.27/7.23 ( ( Xq ) = ( Xp ) ) ) ) ) ) ) ) ) )), 50.27/7.23 inference('cnf.neg', [status(esa)], [cTHM260_pme])). 50.27/7.23 thf(zip_derived_cl0, plain, 50.27/7.23 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.27/7.23 (((((((!!) @ (^[Y1 : a]: 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 (((Y0 @ Y1 @ Y2) => (Y0 @ 50.27/7.23 Y2 @ Y1))))))))) & 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 (((!!) @ (^[Y3 : a]: 50.27/7.23 (((((Y0 @ Y2 @ 50.27/7.23 Y3) & (Y0 @ 50.27/7.23 Y1 @ Y2))) => 50.27/7.23 (Y0 @ Y1 @ Y3)))))))))))) & 50.27/7.23 (((!!) @ (^[Y1 : a]: (Y0 @ Y1 @ Y1)))))) => 50.27/7.23 (((((!!) @ (^[Y1 : a > $o]: 50.27/7.23 (((((((!!) @ (^[Y2 : a]: 50.27/7.23 (((Y1 @ Y2) => 50.27/7.23 (((!!) @ (^[Y3 : a]: 50.27/7.23 (((Y0 @ 50.27/7.23 Y2 @ 50.27/7.23 Y3) <=> 50.27/7.23 (Y1 @ Y3))))))))))) & 50.27/7.23 (((??) @ (^[Y2 : a]: (Y1 @ Y2)))))) => 50.27/7.23 (((??) @ (^[Y2 : a]: (Y1 @ Y2))))))))) & 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 (((??) @ (^[Y2 : a > $o]: 50.27/7.23 (((((??) @ (^[Y3 : a]: 50.27/7.23 (Y2 @ Y3)))) & 50.27/7.23 (((!!) @ (^[Y3 : a]: 50.27/7.23 (((Y2 @ Y3) => 50.27/7.23 (((!!) @ ( 50.27/7.23 ^[Y4 : a]: 50.27/7.23 (( 50.27/7.23 (Y0 @ 50.27/7.23 Y3 @ 50.27/7.23 Y4) <=> 50.27/7.23 (Y2 @ Y4))))))))))) & 50.27/7.23 (Y2 @ Y1) & 50.27/7.23 (((!!) @ (^[Y3 : a > $o]: 50.27/7.23 (((((((??) @ ( 50.27/7.23 ^[Y4 : a]: 50.27/7.23 (Y3 @ Y4)))) & 50.27/7.23 (Y3 @ Y1) & 50.27/7.23 (((!!) @ ( 50.27/7.23 ^[Y4 : a]: 50.27/7.23 (( 50.27/7.23 (Y3 @ 50.27/7.23 Y4) => 50.27/7.23 (( 50.27/7.23 (!!) @ ( 50.27/7.23 ^[Y5 : a]: 50.27/7.23 (( 50.27/7.23 (Y0 @ 50.27/7.23 Y4 @ 50.27/7.23 Y5) <=> 50.27/7.23 (Y3 @ Y5))))))))))))) => 50.27/7.23 (((Y3) = (Y2)))))))))))))))))))))))), 50.27/7.23 inference('cnf', [status(esa)], [zf_stmt_0])). 50.27/7.23 thf(zip_derived_cl1, plain, 50.27/7.23 (~ (((!!) @ (^[Y0 : a > a > $o]: 50.27/7.23 (((((((!!) @ (^[Y1 : a]: 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 (((Y0 @ Y1 @ Y2) => (Y0 @ 50.27/7.23 Y2 @ Y1))))))))) & 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 (((!!) @ (^[Y3 : a]: 50.27/7.23 (((((Y0 @ Y2 @ 50.27/7.23 Y3) & (Y0 @ 50.27/7.23 Y1 @ Y2))) => 50.27/7.23 (Y0 @ Y1 @ Y3)))))))))))) & 50.27/7.23 (((!!) @ (^[Y1 : a]: (Y0 @ Y1 @ Y1)))))) => 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 (((??) @ (^[Y2 : a > $o]: 50.27/7.23 (((((??) @ (^[Y3 : a]: (Y2 @ Y3)))) & 50.27/7.23 (((!!) @ (^[Y3 : a]: 50.27/7.23 (((Y2 @ Y3) => 50.27/7.23 (((!!) @ ( 50.27/7.23 ^[Y4 : a]: 50.27/7.23 (((Y0 @ 50.27/7.23 Y3 @ 50.27/7.23 Y4) <=> 50.27/7.23 (Y2 @ Y4))))))))))) & 50.27/7.23 (Y2 @ Y1) & 50.27/7.23 (((!!) @ (^[Y3 : a > $o]: 50.27/7.23 (((((((??) @ ( 50.27/7.23 ^[Y4 : a]: 50.27/7.23 (Y3 @ Y4)))) & 50.27/7.23 (Y3 @ Y1) & 50.27/7.23 (((!!) @ ( 50.27/7.23 ^[Y4 : a]: 50.27/7.23 (( 50.27/7.23 (Y3 @ 50.27/7.23 Y4) => 50.27/7.23 (( 50.27/7.23 (!!) @ ( 50.27/7.23 ^[Y5 : a]: 50.27/7.23 (( 50.27/7.23 (Y0 @ 50.27/7.23 Y4 @ 50.27/7.23 Y5) <=> 50.27/7.23 (Y3 @ Y5))))))))))))) => 50.27/7.23 (((Y3) = (Y2)))))))))))))))))))))), 50.27/7.23 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl0])). 50.27/7.23 thf(zip_derived_cl2, plain, 50.27/7.23 (~ (((((((!!) @ (^[Y0 : a]: 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 ((('#sk1' @ Y0 @ Y1) => ('#sk1' @ Y1 @ Y0))))))))) & 50.27/7.23 (((!!) @ (^[Y0 : a]: 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 ((((('#sk1' @ Y1 @ Y2) & 50.27/7.23 ('#sk1' @ Y0 @ Y1))) => 50.27/7.23 ('#sk1' @ Y0 @ Y2)))))))))))) & 50.27/7.23 (((!!) @ (^[Y0 : a]: ('#sk1' @ Y0 @ Y0)))))) => 50.27/7.23 (((!!) @ (^[Y0 : a]: 50.27/7.23 (((??) @ (^[Y1 : a > $o]: 50.27/7.23 (((((??) @ (^[Y2 : a]: (Y1 @ Y2)))) & 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 (((Y1 @ Y2) => 50.27/7.23 (((!!) @ (^[Y3 : a]: 50.27/7.23 ((('#sk1' @ 50.27/7.23 Y2 @ Y3) <=> 50.27/7.23 (Y1 @ Y3))))))))))) & 50.27/7.23 (Y1 @ Y0) & 50.27/7.23 (((!!) @ (^[Y2 : a > $o]: 50.27/7.23 (((((((??) @ (^[Y3 : a]: 50.27/7.23 (Y2 @ Y3)))) & 50.27/7.23 (Y2 @ Y0) & 50.27/7.23 (((!!) @ (^[Y3 : a]: 50.27/7.23 (((Y2 @ Y3) => 50.27/7.23 (((!!) @ ( 50.27/7.23 ^[Y4 : a]: 50.27/7.23 (( 50.27/7.23 ('#sk1' @ 50.27/7.23 Y3 @ 50.27/7.23 Y4) <=> 50.27/7.23 (Y2 @ Y4))))))))))))) => 50.27/7.23 (((Y2) = (Y1))))))))))))))))))), 50.27/7.23 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 50.27/7.23 thf(zip_derived_cl3, plain, 50.27/7.23 ( (((((!!) @ (^[Y0 : a]: 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 ((('#sk1' @ Y0 @ Y1) => ('#sk1' @ Y1 @ Y0))))))))) & 50.27/7.23 (((!!) @ (^[Y0 : a]: 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 ((((('#sk1' @ Y1 @ Y2) & 50.27/7.23 ('#sk1' @ Y0 @ Y1))) => 50.27/7.23 ('#sk1' @ Y0 @ Y2)))))))))))) & 50.27/7.23 (((!!) @ (^[Y0 : a]: ('#sk1' @ Y0 @ Y0))))))), 50.27/7.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 50.27/7.23 thf(zip_derived_cl7, plain, ( (((!!) @ (^[Y0 : a]: ('#sk1' @ Y0 @ Y0))))), 50.27/7.23 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])). 50.27/7.23 thf(zip_derived_cl11, plain, (![X2 : a]: ('#sk1' @ X2 @ X2)), 50.27/7.23 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 50.27/7.23 thf(zip_derived_cl4, plain, 50.27/7.23 (~ (((!!) @ (^[Y0 : a]: 50.27/7.23 (((??) @ (^[Y1 : a > $o]: 50.27/7.23 (((((??) @ (^[Y2 : a]: (Y1 @ Y2)))) & 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 (((Y1 @ Y2) => 50.27/7.23 (((!!) @ (^[Y3 : a]: 50.27/7.23 ((('#sk1' @ Y2 @ 50.27/7.23 Y3) <=> (Y1 @ 50.27/7.23 Y3))))))))))) & 50.27/7.23 (Y1 @ Y0) & 50.27/7.23 (((!!) @ (^[Y2 : a > $o]: 50.27/7.23 (((((((??) @ (^[Y3 : a]: 50.27/7.23 (Y2 @ Y3)))) & 50.27/7.23 (Y2 @ Y0) & 50.27/7.23 (((!!) @ (^[Y3 : a]: 50.27/7.23 (((Y2 @ Y3) => 50.27/7.23 (((!!) @ ( 50.27/7.23 ^[Y4 : a]: 50.27/7.23 (( 50.27/7.23 ('#sk1' @ 50.27/7.23 Y3 @ 50.27/7.23 Y4) <=> 50.27/7.23 (Y2 @ Y4))))))))))))) => 50.27/7.23 (((Y2) = (Y1))))))))))))))))), 50.27/7.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 50.27/7.23 thf(zip_derived_cl8, plain, 50.27/7.23 (~ (((??) @ (^[Y0 : a > $o]: 50.27/7.23 (((((??) @ (^[Y1 : a]: (Y0 @ Y1)))) & 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 (((Y0 @ Y1) => 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 ((('#sk1' @ Y1 @ Y2) <=> 50.27/7.23 (Y0 @ Y2))))))))))) & 50.27/7.23 (Y0 @ '#sk2') & 50.27/7.23 (((!!) @ (^[Y1 : a > $o]: 50.27/7.23 (((((((??) @ (^[Y2 : a]: (Y1 @ Y2)))) & 50.27/7.23 (Y1 @ '#sk2') & 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 (((Y1 @ Y2) => 50.27/7.23 (((!!) @ (^[Y3 : a]: 50.27/7.23 ((('#sk1' @ 50.27/7.23 Y2 @ Y3) <=> 50.27/7.23 (Y1 @ Y3))))))))))))) => 50.27/7.23 (((Y1) = (Y0)))))))))))))), 50.27/7.23 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl4])). 50.27/7.23 thf(zip_derived_cl12, plain, 50.27/7.23 (![X2 : a > $o]: 50.27/7.23 ~ (((((??) @ (^[Y0 : a]: (X2 @ Y0)))) & 50.27/7.23 (((!!) @ (^[Y0 : a]: 50.27/7.23 (((X2 @ Y0) => 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 ((('#sk1' @ Y0 @ Y1) <=> (X2 @ Y1))))))))))) & 50.27/7.23 (X2 @ '#sk2') & 50.27/7.23 (((!!) @ (^[Y0 : a > $o]: 50.27/7.23 (((((((??) @ (^[Y1 : a]: (Y0 @ Y1)))) & 50.27/7.23 (Y0 @ '#sk2') & 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 (((Y0 @ Y1) => 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 ((('#sk1' @ Y1 @ Y2) <=> 50.27/7.23 (Y0 @ Y2))))))))))))) => 50.27/7.23 (((Y0) = (X2))))))))))), 50.27/7.23 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 50.27/7.23 thf(zip_derived_cl15, plain, 50.27/7.23 (![X2 : a > $o]: 50.27/7.23 (~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))) 50.27/7.23 | ~ (((!!) @ (^[Y0 : a]: 50.27/7.23 (((X2 @ Y0) => 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 ((('#sk1' @ Y0 @ Y1) <=> (X2 @ Y1))))))))))) 50.27/7.23 | ~ (X2 @ '#sk2') 50.27/7.23 | ~ (((!!) @ (^[Y0 : a > $o]: 50.27/7.23 (((((((??) @ (^[Y1 : a]: (Y0 @ Y1)))) & 50.27/7.23 (Y0 @ '#sk2') & 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 (((Y0 @ Y1) => 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 ((('#sk1' @ Y1 @ 50.27/7.23 Y2) <=> (Y0 @ Y2))))))))))))) => 50.27/7.23 (((Y0) = (X2)))))))))), 50.27/7.23 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl12])). 50.27/7.23 thf(zip_derived_cl18, plain, 50.27/7.23 (![X2 : a > $o, X4 : a]: 50.27/7.23 (~ (X2 @ X4) 50.27/7.23 | ~ (((!!) @ (^[Y0 : a > $o]: 50.27/7.23 (((((((??) @ (^[Y1 : a]: (Y0 @ Y1)))) & 50.27/7.23 (Y0 @ '#sk2') & 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 (((Y0 @ Y1) => 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 ((('#sk1' @ Y1 @ 50.27/7.23 Y2) <=> (Y0 @ Y2))))))))))))) => 50.27/7.23 (((Y0) = (X2)))))))) 50.27/7.23 | ~ (X2 @ '#sk2') 50.27/7.23 | ~ (((!!) @ (^[Y0 : a]: 50.27/7.23 (((X2 @ Y0) => 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 ((('#sk1' @ Y0 @ Y1) <=> (X2 @ Y1))))))))))))), 50.27/7.23 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 50.27/7.23 thf(zip_derived_cl20, plain, 50.27/7.23 (![X0 : a > $o]: 50.27/7.23 (~ (((!!) @ (^[Y0 : a]: 50.27/7.23 (((X0 @ Y0) => 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 ((('#sk1' @ Y0 @ Y1) <=> (X0 @ Y1))))))))))) 50.27/7.23 | ~ (((!!) @ (^[Y0 : a > $o]: 50.27/7.23 (((((((??) @ (^[Y1 : a]: (Y0 @ Y1)))) & 50.27/7.23 (Y0 @ '#sk2') & 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 (((Y0 @ Y1) => 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 ((('#sk1' @ Y1 @ 50.27/7.23 Y2) <=> (Y0 @ Y2))))))))))))) => 50.27/7.23 (((Y0) = (X0)))))))) 50.27/7.23 | ~ (X0 @ '#sk2'))), 50.27/7.23 inference('condensation', [status(thm)], [zip_derived_cl18])). 50.27/7.23 thf(zip_derived_cl21, plain, 50.27/7.23 (![X0 : a > $o]: 50.27/7.23 (~ (((X0 @ ('#sk17' @ X0)) => 50.27/7.23 (((!!) @ (^[Y0 : a]: 50.27/7.23 ((('#sk1' @ ('#sk17' @ X0) @ Y0) <=> (X0 @ Y0)))))))) 50.27/7.23 | ~ (X0 @ '#sk2') 50.27/7.23 | ~ (((!!) @ (^[Y0 : a > $o]: 50.27/7.23 (((((((??) @ (^[Y1 : a]: (Y0 @ Y1)))) & 50.27/7.23 (Y0 @ '#sk2') & 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 (((Y0 @ Y1) => 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 ((('#sk1' @ Y1 @ 50.27/7.23 Y2) <=> (Y0 @ Y2))))))))))))) => 50.27/7.23 (((Y0) = (X0)))))))))), 50.27/7.23 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl20])). 50.27/7.23 thf(zip_derived_cl24, plain, 50.27/7.23 (![X0 : a > $o]: 50.27/7.23 (~ (((!!) @ (^[Y0 : a]: 50.27/7.23 ((('#sk1' @ ('#sk17' @ X0) @ Y0) <=> (X0 @ Y0)))))) 50.27/7.23 | ~ (((!!) @ (^[Y0 : a > $o]: 50.27/7.23 (((((((??) @ (^[Y1 : a]: (Y0 @ Y1)))) & 50.27/7.23 (Y0 @ '#sk2') & 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 (((Y0 @ Y1) => 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 ((('#sk1' @ Y1 @ 50.27/7.23 Y2) <=> (Y0 @ Y2))))))))))))) => 50.27/7.23 (((Y0) = (X0)))))))) 50.27/7.23 | ~ (X0 @ '#sk2'))), 50.27/7.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 50.27/7.23 thf(zip_derived_cl27, plain, 50.27/7.23 (![X0 : a > $o]: 50.27/7.23 (~ ((('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) <=> (X0 @ 50.27/7.23 ('#sk28' @ X0)))) 50.27/7.23 | ~ (X0 @ '#sk2') 50.27/7.23 | ~ (((!!) @ (^[Y0 : a > $o]: 50.27/7.23 (((((((??) @ (^[Y1 : a]: (Y0 @ Y1)))) & 50.27/7.23 (Y0 @ '#sk2') & 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 (((Y0 @ Y1) => 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 ((('#sk1' @ Y1 @ 50.27/7.23 Y2) <=> (Y0 @ Y2))))))))))))) => 50.27/7.23 (((Y0) = (X0)))))))))), 50.27/7.23 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl24])). 50.27/7.23 thf(zip_derived_cl30, plain, 50.27/7.23 (![X0 : a > $o]: 50.27/7.23 ((('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) != (X0 @ ('#sk28' @ X0))) 50.27/7.23 | ~ (X0 @ '#sk2') 50.27/7.23 | ~ (((!!) @ (^[Y0 : a > $o]: 50.27/7.23 (((((((??) @ (^[Y1 : a]: (Y0 @ Y1)))) & 50.27/7.23 (Y0 @ '#sk2') & 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 (((Y0 @ Y1) => 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 ((('#sk1' @ Y1 @ 50.27/7.23 Y2) <=> (Y0 @ Y2))))))))))))) => 50.27/7.23 (((Y0) = (X0)))))))))), 50.27/7.23 inference('simplify nested equalities', [status(thm)], [zip_derived_cl27])). 50.27/7.23 thf(zip_derived_cl31, plain, 50.27/7.23 (![X0 : a > $o]: 50.27/7.23 (~ (((((((??) @ (^[Y0 : a]: ('#sk24' @ X0 @ Y0)))) & 50.27/7.23 ('#sk24' @ X0 @ '#sk2') & 50.27/7.23 (((!!) @ (^[Y0 : a]: 50.27/7.23 ((('#sk24' @ X0 @ Y0) => 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 ((('#sk1' @ Y0 @ Y1) <=> ('#sk24' @ 50.27/7.23 X0 @ Y1))))))))))))) => 50.27/7.23 ((('#sk24' @ X0) = (X0))))) 50.27/7.23 | ~ (X0 @ '#sk2') 50.27/7.23 | (('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) 50.27/7.23 != (X0 @ ('#sk28' @ X0))))), 50.27/7.23 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])). 50.27/7.23 thf(zip_derived_cl38, plain, 50.27/7.23 (![X0 : a > $o]: 50.27/7.23 (~ ((('#sk24' @ X0) = (X0))) 50.27/7.23 | (('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) 50.27/7.23 != (X0 @ ('#sk28' @ X0))) 50.27/7.23 | ~ (X0 @ '#sk2'))), 50.27/7.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl31])). 50.27/7.23 thf(zip_derived_cl44, plain, 50.27/7.23 (![X0 : a > $o]: 50.27/7.23 ((('#sk24' @ X0) != (X0)) 50.27/7.23 | (('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) 50.27/7.23 != (X0 @ ('#sk28' @ X0))) 50.27/7.23 | ~ (X0 @ '#sk2'))), 50.27/7.23 inference('simplify nested equalities', [status(thm)], [zip_derived_cl38])). 50.27/7.23 thf(zip_derived_cl45, plain, 50.27/7.23 (![X0 : a > $o]: 50.27/7.23 ((('#sk24' @ X0 @ ('#_fresh_sk90' @ X0)) 50.27/7.23 != (X0 @ ('#_fresh_sk90' @ X0))) 50.27/7.23 | (('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) 50.27/7.23 != (X0 @ ('#sk28' @ X0))) 50.27/7.23 | ~ (X0 @ '#sk2'))), 50.27/7.23 inference('neg_ext_simpl', [status(thm)], [zip_derived_cl44])). 50.27/7.23 thf(zip_derived_cl148, plain, 50.27/7.23 (((('#sk1' @ 50.27/7.23 ('#sk17' @ 50.27/7.23 (^[Y0 : a]: 50.27/7.23 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.23 ((^[Y1 : a]: (Y1)) @ Y0)))) @ 50.27/7.23 ('#sk28' @ 50.27/7.23 (^[Y0 : a]: 50.27/7.23 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.23 ((^[Y1 : a]: (Y1)) @ Y0))))) 50.27/7.23 != ((^[Y0 : a]: 50.27/7.23 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.23 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.23 ('#sk28' @ 50.27/7.23 (^[Y0 : a]: 50.27/7.23 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.23 ((^[Y1 : a]: (Y1)) @ Y0)))))) 50.27/7.23 | (('#sk24' @ 50.27/7.23 (^[Y0 : a]: 50.27/7.23 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.23 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.23 ('#_fresh_sk90' @ 50.27/7.23 (^[Y0 : a]: 50.27/7.23 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.23 ((^[Y1 : a]: (Y1)) @ Y0))))) 50.27/7.23 != ((^[Y0 : a]: 50.27/7.23 ('#sk1' @ 50.27/7.23 ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.23 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.23 ('#_fresh_sk90' @ 50.27/7.23 (^[Y0 : a]: 50.27/7.23 ('#sk1' @ 50.27/7.23 ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.23 ((^[Y1 : a]: (Y1)) @ Y0)))))))), 50.27/7.23 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl45])). 50.27/7.23 thf(zip_derived_cl153, plain, 50.27/7.23 (((('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.23 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.23 != ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2')))) 50.27/7.23 | (('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.23 != ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2')))))), 50.27/7.23 inference('ho_norm', [status(thm)], [zip_derived_cl148])). 50.27/7.23 thf(zip_derived_cl11, plain, (![X2 : a]: ('#sk1' @ X2 @ X2)), 50.27/7.23 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 50.27/7.23 thf(zip_derived_cl23, plain, 50.27/7.23 (![X0 : a > $o]: 50.27/7.23 ( (X0 @ ('#sk17' @ X0)) 50.27/7.23 | ~ (((!!) @ (^[Y0 : a > $o]: 50.27/7.23 (((((((??) @ (^[Y1 : a]: (Y0 @ Y1)))) & 50.27/7.23 (Y0 @ '#sk2') & 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 (((Y0 @ Y1) => 50.27/7.23 (((!!) @ (^[Y2 : a]: 50.27/7.23 ((('#sk1' @ Y1 @ 50.27/7.23 Y2) <=> (Y0 @ Y2))))))))))))) => 50.27/7.23 (((Y0) = (X0)))))))) 50.27/7.23 | ~ (X0 @ '#sk2'))), 50.27/7.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 50.27/7.23 thf(zip_derived_cl26, plain, 50.27/7.23 (![X0 : a > $o]: 50.27/7.23 (~ (((((((??) @ (^[Y0 : a]: ('#sk24' @ X0 @ Y0)))) & 50.27/7.23 ('#sk24' @ X0 @ '#sk2') & 50.27/7.23 (((!!) @ (^[Y0 : a]: 50.27/7.23 ((('#sk24' @ X0 @ Y0) => 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 ((('#sk1' @ Y0 @ Y1) <=> ('#sk24' @ 50.27/7.23 X0 @ Y1))))))))))))) => 50.27/7.23 ((('#sk24' @ X0) = (X0))))) 50.27/7.23 | ~ (X0 @ '#sk2') 50.27/7.23 | (X0 @ ('#sk17' @ X0)))), 50.27/7.23 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl23])). 50.27/7.23 thf(zip_derived_cl28, plain, 50.27/7.23 (![X0 : a > $o]: 50.27/7.23 ( (((((??) @ (^[Y0 : a]: ('#sk24' @ X0 @ Y0)))) & 50.27/7.23 ('#sk24' @ X0 @ '#sk2') & 50.27/7.23 (((!!) @ (^[Y0 : a]: 50.27/7.23 ((('#sk24' @ X0 @ Y0) => 50.27/7.23 (((!!) @ (^[Y1 : a]: 50.27/7.23 ((('#sk1' @ Y0 @ Y1) <=> ('#sk24' @ 50.27/7.23 X0 @ Y1))))))))))))) 50.27/7.23 | (X0 @ ('#sk17' @ X0)) 50.27/7.23 | ~ (X0 @ '#sk2'))), 50.27/7.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 50.27/7.23 thf(zip_derived_cl33, plain, 50.27/7.23 (![X0 : a > $o]: 50.27/7.23 ( ('#sk24' @ X0 @ '#sk2') | ~ (X0 @ '#sk2') | (X0 @ ('#sk17' @ X0)))), 50.27/7.23 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl28])). 50.27/7.24 thf(zip_derived_cl85, plain, 50.27/7.24 (( ((^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.24 ('#sk17' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))))) 50.27/7.24 | ('#sk24' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.24 '#sk2'))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl33])). 50.27/7.24 thf(zip_derived_cl89, plain, 50.27/7.24 (( ('#sk1' @ '#sk2' @ ('#sk17' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | ('#sk24' @ ('#sk1' @ '#sk2') @ '#sk2'))), 50.27/7.24 inference('ho_norm', [status(thm)], [zip_derived_cl85])). 50.27/7.24 thf(zip_derived_cl11, plain, (![X2 : a]: ('#sk1' @ X2 @ X2)), 50.27/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 50.27/7.24 thf(zip_derived_cl34, plain, 50.27/7.24 (![X0 : a > $o]: 50.27/7.24 ( (((!!) @ (^[Y0 : a]: 50.27/7.24 ((('#sk24' @ X0 @ Y0) => 50.27/7.24 (((!!) @ (^[Y1 : a]: 50.27/7.24 ((('#sk1' @ Y0 @ Y1) <=> ('#sk24' @ X0 @ 50.27/7.24 Y1))))))))))) 50.27/7.24 | ~ (X0 @ '#sk2') 50.27/7.24 | (X0 @ ('#sk17' @ X0)))), 50.27/7.24 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl28])). 50.27/7.24 thf(zip_derived_cl40, plain, 50.27/7.24 (![X0 : a > $o, X2 : a]: 50.27/7.24 ( ((('#sk24' @ X0 @ X2) => 50.27/7.24 (((!!) @ (^[Y0 : a]: 50.27/7.24 ((('#sk1' @ X2 @ Y0) <=> ('#sk24' @ X0 @ Y0)))))))) 50.27/7.24 | (X0 @ ('#sk17' @ X0)) 50.27/7.24 | ~ (X0 @ '#sk2'))), 50.27/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 50.27/7.24 thf(zip_derived_cl46, plain, 50.27/7.24 (![X0 : a > $o, X2 : a]: 50.27/7.24 (~ ('#sk24' @ X0 @ X2) 50.27/7.24 | (((!!) @ (^[Y0 : a]: 50.27/7.24 ((('#sk1' @ X2 @ Y0) <=> ('#sk24' @ X0 @ Y0)))))) 50.27/7.24 | ~ (X0 @ '#sk2') 50.27/7.24 | (X0 @ ('#sk17' @ X0)))), 50.27/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])). 50.27/7.24 thf(zip_derived_cl49, plain, 50.27/7.24 (![X0 : a > $o, X2 : a, X4 : a]: 50.27/7.24 ( ((('#sk1' @ X2 @ X4) <=> ('#sk24' @ X0 @ X4))) 50.27/7.24 | (X0 @ ('#sk17' @ X0)) 50.27/7.24 | ~ (X0 @ '#sk2') 50.27/7.24 | ~ ('#sk24' @ X0 @ X2))), 50.27/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl46])). 50.27/7.24 thf(zip_derived_cl51, plain, 50.27/7.24 (![X0 : a > $o, X2 : a, X4 : a]: 50.27/7.24 ((('#sk1' @ X2 @ X4) = ('#sk24' @ X0 @ X4)) 50.27/7.24 | (X0 @ ('#sk17' @ X0)) 50.27/7.24 | ~ (X0 @ '#sk2') 50.27/7.24 | ~ ('#sk24' @ X0 @ X2))), 50.27/7.24 inference('simplify nested equalities', [status(thm)], [zip_derived_cl49])). 50.27/7.24 thf(zip_derived_cl244, plain, 50.27/7.24 (![X0 : a, X1 : a]: 50.27/7.24 (~ ('#sk24' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.24 X0) 50.27/7.24 | ((^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.24 ('#sk17' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))))) 50.27/7.24 | (('#sk1' @ X0 @ X1) 50.27/7.24 = ('#sk24' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ 50.27/7.24 ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.24 X1)))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl51])). 50.27/7.24 thf(zip_derived_cl248, plain, 50.27/7.24 (![X0 : a, X1 : a]: 50.27/7.24 (~ ('#sk24' @ ('#sk1' @ '#sk2') @ X0) 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk17' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | (('#sk1' @ X0 @ X1) = ('#sk24' @ ('#sk1' @ '#sk2') @ X1)))), 50.27/7.24 inference('ho_norm', [status(thm)], [zip_derived_cl244])). 50.27/7.24 thf(zip_derived_cl1309, plain, 50.27/7.24 (![X0 : a]: 50.27/7.24 ( ('#sk1' @ '#sk2' @ ('#sk17' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | (('#sk1' @ '#sk2' @ X0) = ('#sk24' @ ('#sk1' @ '#sk2') @ X0)) 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl89, zip_derived_cl248])). 50.27/7.24 thf(zip_derived_cl1326, plain, 50.27/7.24 (![X0 : a]: 50.27/7.24 ((('#sk1' @ '#sk2' @ X0) = ('#sk24' @ ('#sk1' @ '#sk2') @ X0)) 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.24 inference('simplify', [status(thm)], [zip_derived_cl1309])). 50.27/7.24 thf(zip_derived_cl11, plain, (![X2 : a]: ('#sk1' @ X2 @ X2)), 50.27/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 50.27/7.24 thf(zip_derived_cl29, plain, 50.27/7.24 (![X0 : a > $o]: 50.27/7.24 (~ ((('#sk24' @ X0) = (X0))) 50.27/7.24 | (X0 @ ('#sk17' @ X0)) 50.27/7.24 | ~ (X0 @ '#sk2'))), 50.27/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 50.27/7.24 thf(zip_derived_cl35, plain, 50.27/7.24 (![X0 : a > $o]: 50.27/7.24 ((('#sk24' @ X0) != (X0)) | (X0 @ ('#sk17' @ X0)) | ~ (X0 @ '#sk2'))), 50.27/7.24 inference('simplify nested equalities', [status(thm)], [zip_derived_cl29])). 50.27/7.24 thf(zip_derived_cl36, plain, 50.27/7.24 (![X0 : a > $o]: 50.27/7.24 ((('#sk24' @ X0 @ ('#_fresh_sk52' @ X0)) 50.27/7.24 != (X0 @ ('#_fresh_sk52' @ X0))) 50.27/7.24 | (X0 @ ('#sk17' @ X0)) 50.27/7.24 | ~ (X0 @ '#sk2'))), 50.27/7.24 inference('neg_ext_simpl', [status(thm)], [zip_derived_cl35])). 50.27/7.24 thf(zip_derived_cl136, plain, 50.27/7.24 (( ((^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.24 ('#sk17' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))))) 50.27/7.24 | (('#sk24' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.24 ('#_fresh_sk52' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))))) 50.27/7.24 != ((^[Y0 : a]: 50.27/7.24 ('#sk1' @ 50.27/7.24 ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.24 ('#_fresh_sk52' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ 50.27/7.24 ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0)))))))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl36])). 50.27/7.24 thf(zip_derived_cl141, plain, 50.27/7.24 (( ('#sk1' @ '#sk2' @ ('#sk17' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | (('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk52' @ ('#sk1' @ '#sk2'))) 50.27/7.24 != ('#sk1' @ '#sk2' @ ('#_fresh_sk52' @ ('#sk1' @ '#sk2')))))), 50.27/7.24 inference('ho_norm', [status(thm)], [zip_derived_cl136])). 50.27/7.24 thf(zip_derived_cl1338, plain, 50.27/7.24 (((('#sk1' @ '#sk2' @ ('#_fresh_sk52' @ ('#sk1' @ '#sk2'))) 50.27/7.24 != ('#sk1' @ '#sk2' @ ('#_fresh_sk52' @ ('#sk1' @ '#sk2')))) 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk17' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl1326, zip_derived_cl141])). 50.27/7.24 thf(zip_derived_cl1371, plain, 50.27/7.24 ( ('#sk1' @ '#sk2' @ ('#sk17' @ ('#sk1' @ '#sk2')))), 50.27/7.24 inference('simplify', [status(thm)], [zip_derived_cl1338])). 50.27/7.24 thf(zip_derived_cl5, plain, 50.27/7.24 ( (((!!) @ (^[Y0 : a]: 50.27/7.24 (((!!) @ (^[Y1 : a]: 50.27/7.24 ((('#sk1' @ Y0 @ Y1) => ('#sk1' @ Y1 @ Y0)))))))))), 50.27/7.24 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])). 50.27/7.24 thf(zip_derived_cl9, plain, 50.27/7.24 (![X2 : a]: 50.27/7.24 (((!!) @ (^[Y0 : a]: ((('#sk1' @ X2 @ Y0) => ('#sk1' @ Y0 @ X2))))))), 50.27/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 50.27/7.24 thf(zip_derived_cl13, plain, 50.27/7.24 (![X2 : a, X4 : a]: ((('#sk1' @ X2 @ X4) => ('#sk1' @ X4 @ X2)))), 50.27/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])). 50.27/7.24 thf(zip_derived_cl16, plain, 50.27/7.24 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.24 thf(zip_derived_cl1401, plain, 50.27/7.24 ( ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ '#sk2')), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl1371, zip_derived_cl16])). 50.27/7.24 thf(zip_derived_cl6, plain, 50.27/7.24 ( (((!!) @ (^[Y0 : a]: 50.27/7.24 (((!!) @ (^[Y1 : a]: 50.27/7.24 (((!!) @ (^[Y2 : a]: 50.27/7.24 ((((('#sk1' @ Y1 @ Y2) & ('#sk1' @ 50.27/7.24 Y0 @ Y1))) => 50.27/7.24 ('#sk1' @ Y0 @ Y2))))))))))))), 50.27/7.24 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])). 50.27/7.24 thf(zip_derived_cl10, plain, 50.27/7.24 (![X2 : a]: 50.27/7.24 (((!!) @ (^[Y0 : a]: 50.27/7.24 (((!!) @ (^[Y1 : a]: 50.27/7.24 ((((('#sk1' @ Y0 @ Y1) & ('#sk1' @ X2 @ Y0))) => 50.27/7.24 ('#sk1' @ X2 @ Y1)))))))))), 50.27/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 50.27/7.24 thf(zip_derived_cl14, plain, 50.27/7.24 (![X2 : a, X4 : a]: 50.27/7.24 (((!!) @ (^[Y0 : a]: 50.27/7.24 ((((('#sk1' @ X4 @ Y0) & ('#sk1' @ X2 @ X4))) => 50.27/7.24 ('#sk1' @ X2 @ Y0))))))), 50.27/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 50.27/7.24 thf(zip_derived_cl17, plain, 50.27/7.24 (![X2 : a, X4 : a, X6 : a]: 50.27/7.24 ((((('#sk1' @ X4 @ X6) & ('#sk1' @ X2 @ X4))) => ('#sk1' @ X2 @ X6)))), 50.27/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 50.27/7.24 thf(zip_derived_cl19, plain, 50.27/7.24 (![X2 : a, X4 : a, X6 : a]: 50.27/7.24 (~ ((('#sk1' @ X4 @ X6) & ('#sk1' @ X2 @ X4))) | ('#sk1' @ X2 @ X6))), 50.27/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 50.27/7.24 thf(zip_derived_cl22, plain, 50.27/7.24 (![X2 : a, X4 : a, X6 : a]: 50.27/7.24 (~ ('#sk1' @ X4 @ X6) | ~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X2 @ X6))), 50.27/7.24 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl19])). 50.27/7.24 thf(zip_derived_cl1452, plain, 50.27/7.24 (![X0 : a]: 50.27/7.24 ( ('#sk1' @ X0 @ '#sk2') 50.27/7.24 | ~ ('#sk1' @ X0 @ ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl1401, zip_derived_cl22])). 50.27/7.24 thf(zip_derived_cl11, plain, (![X2 : a]: ('#sk1' @ X2 @ X2)), 50.27/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 50.27/7.24 thf(zip_derived_cl37, plain, 50.27/7.24 (![X0 : a > $o]: 50.27/7.24 ( (((((??) @ (^[Y0 : a]: ('#sk24' @ X0 @ Y0)))) & 50.27/7.24 ('#sk24' @ X0 @ '#sk2') & 50.27/7.24 (((!!) @ (^[Y0 : a]: 50.27/7.24 ((('#sk24' @ X0 @ Y0) => 50.27/7.24 (((!!) @ (^[Y1 : a]: 50.27/7.24 ((('#sk1' @ Y0 @ Y1) <=> ('#sk24' @ 50.27/7.24 X0 @ Y1))))))))))))) 50.27/7.24 | (('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) 50.27/7.24 != (X0 @ ('#sk28' @ X0))) 50.27/7.24 | ~ (X0 @ '#sk2'))), 50.27/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl31])). 50.27/7.24 thf(zip_derived_cl42, plain, 50.27/7.24 (![X0 : a > $o]: 50.27/7.24 ( ('#sk24' @ X0 @ '#sk2') 50.27/7.24 | ~ (X0 @ '#sk2') 50.27/7.24 | (('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) 50.27/7.24 != (X0 @ ('#sk28' @ X0))))), 50.27/7.24 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl37])). 50.27/7.24 thf(zip_derived_cl147, plain, 50.27/7.24 (((('#sk1' @ 50.27/7.24 ('#sk17' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0)))) @ 50.27/7.24 ('#sk28' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))))) 50.27/7.24 != ((^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.24 ('#sk28' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0)))))) 50.27/7.24 | ('#sk24' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.24 '#sk2'))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl42])). 50.27/7.24 thf(zip_derived_cl152, plain, 50.27/7.24 (((('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.24 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 != ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2')))) 50.27/7.24 | ('#sk24' @ ('#sk1' @ '#sk2') @ '#sk2'))), 50.27/7.24 inference('ho_norm', [status(thm)], [zip_derived_cl147])). 50.27/7.24 thf(zip_derived_cl223, plain, 50.27/7.24 (( ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.24 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | ('#sk24' @ ('#sk1' @ '#sk2') @ '#sk2'))), 50.27/7.24 inference('eq_elim', [status(thm)], [zip_derived_cl152])). 50.27/7.24 thf(zip_derived_cl16, plain, 50.27/7.24 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.24 thf(zip_derived_cl251, plain, 50.27/7.24 (( ('#sk24' @ ('#sk1' @ '#sk2') @ '#sk2') 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ 50.27/7.24 ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl223, zip_derived_cl16])). 50.27/7.24 thf(zip_derived_cl1562, plain, 50.27/7.24 (( ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ '#sk2') 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | ('#sk24' @ ('#sk1' @ '#sk2') @ '#sk2'))), 50.27/7.24 inference('sup+', [status(thm)], [zip_derived_cl1452, zip_derived_cl251])). 50.27/7.24 thf(zip_derived_cl16, plain, 50.27/7.24 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.24 thf(zip_derived_cl2548, plain, 50.27/7.24 (( ('#sk24' @ ('#sk1' @ '#sk2') @ '#sk2') 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))))), 50.27/7.24 inference('clc', [status(thm)], [zip_derived_cl1562, zip_derived_cl16])). 50.27/7.24 thf(zip_derived_cl11, plain, (![X2 : a]: ('#sk1' @ X2 @ X2)), 50.27/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 50.27/7.24 thf(zip_derived_cl43, plain, 50.27/7.24 (![X0 : a > $o]: 50.27/7.24 ( (((!!) @ (^[Y0 : a]: 50.27/7.24 ((('#sk24' @ X0 @ Y0) => 50.27/7.24 (((!!) @ (^[Y1 : a]: 50.27/7.24 ((('#sk1' @ Y0 @ Y1) <=> ('#sk24' @ X0 @ 50.27/7.24 Y1))))))))))) 50.27/7.24 | ~ (X0 @ '#sk2') 50.27/7.24 | (('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) 50.27/7.24 != (X0 @ ('#sk28' @ X0))))), 50.27/7.24 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl37])). 50.27/7.24 thf(zip_derived_cl48, plain, 50.27/7.24 (![X0 : a > $o, X2 : a]: 50.27/7.24 ( ((('#sk24' @ X0 @ X2) => 50.27/7.24 (((!!) @ (^[Y0 : a]: 50.27/7.24 ((('#sk1' @ X2 @ Y0) <=> ('#sk24' @ X0 @ Y0)))))))) 50.27/7.24 | (('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) 50.27/7.24 != (X0 @ ('#sk28' @ X0))) 50.27/7.24 | ~ (X0 @ '#sk2'))), 50.27/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 50.27/7.24 thf(zip_derived_cl50, plain, 50.27/7.24 (![X0 : a > $o, X2 : a]: 50.27/7.24 (~ ('#sk24' @ X0 @ X2) 50.27/7.24 | (((!!) @ (^[Y0 : a]: 50.27/7.24 ((('#sk1' @ X2 @ Y0) <=> ('#sk24' @ X0 @ Y0)))))) 50.27/7.24 | ~ (X0 @ '#sk2') 50.27/7.24 | (('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) 50.27/7.24 != (X0 @ ('#sk28' @ X0))))), 50.27/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 50.27/7.24 thf(zip_derived_cl52, plain, 50.27/7.24 (![X0 : a > $o, X2 : a, X4 : a]: 50.27/7.24 ( ((('#sk1' @ X2 @ X4) <=> ('#sk24' @ X0 @ X4))) 50.27/7.24 | (('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) 50.27/7.24 != (X0 @ ('#sk28' @ X0))) 50.27/7.24 | ~ (X0 @ '#sk2') 50.27/7.24 | ~ ('#sk24' @ X0 @ X2))), 50.27/7.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl50])). 50.27/7.24 thf(zip_derived_cl53, plain, 50.27/7.24 (![X0 : a > $o, X2 : a, X4 : a]: 50.27/7.24 ((('#sk1' @ X2 @ X4) = ('#sk24' @ X0 @ X4)) 50.27/7.24 | (('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) 50.27/7.24 != (X0 @ ('#sk28' @ X0))) 50.27/7.24 | ~ (X0 @ '#sk2') 50.27/7.24 | ~ ('#sk24' @ X0 @ X2))), 50.27/7.24 inference('simplify nested equalities', [status(thm)], [zip_derived_cl52])). 50.27/7.24 thf(zip_derived_cl322, plain, 50.27/7.24 (![X0 : a, X1 : a]: 50.27/7.24 (~ ('#sk24' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.24 X0) 50.27/7.24 | (('#sk1' @ 50.27/7.24 ('#sk17' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0)))) @ 50.27/7.24 ('#sk28' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))))) 50.27/7.24 != ((^[Y0 : a]: 50.27/7.24 ('#sk1' @ 50.27/7.24 ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.24 ('#sk28' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ 50.27/7.24 ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0)))))) 50.27/7.24 | (('#sk1' @ X0 @ X1) 50.27/7.24 = ('#sk24' @ 50.27/7.24 (^[Y0 : a]: 50.27/7.24 ('#sk1' @ 50.27/7.24 ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.24 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.24 X1)))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl53])). 50.27/7.24 thf(zip_derived_cl327, plain, 50.27/7.24 (![X0 : a, X1 : a]: 50.27/7.24 (~ ('#sk24' @ ('#sk1' @ '#sk2') @ X0) 50.27/7.24 | (('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.24 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 != ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2')))) 50.27/7.24 | (('#sk1' @ X0 @ X1) = ('#sk24' @ ('#sk1' @ '#sk2') @ X1)))), 50.27/7.24 inference('ho_norm', [status(thm)], [zip_derived_cl322])). 50.27/7.24 thf(zip_derived_cl2506, plain, 50.27/7.24 (![X0 : a, X1 : a]: 50.27/7.24 ( ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.24 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | (('#sk1' @ X0 @ X1) = ('#sk24' @ ('#sk1' @ '#sk2') @ X1)) 50.27/7.24 | ~ ('#sk24' @ ('#sk1' @ '#sk2') @ X0))), 50.27/7.24 inference('eq_elim', [status(thm)], [zip_derived_cl327])). 50.27/7.24 thf(zip_derived_cl3520, plain, 50.27/7.24 (![X0 : a]: 50.27/7.24 ( ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | (('#sk1' @ '#sk2' @ X0) = ('#sk24' @ ('#sk1' @ '#sk2') @ X0)) 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.24 ('#sk28' @ ('#sk1' @ '#sk2'))))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl2548, zip_derived_cl2506])). 50.27/7.24 thf(zip_derived_cl3535, plain, 50.27/7.24 (![X0 : a]: 50.27/7.24 ( ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.24 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | (('#sk1' @ '#sk2' @ X0) = ('#sk24' @ ('#sk1' @ '#sk2') @ X0)) 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))))), 50.27/7.24 inference('simplify', [status(thm)], [zip_derived_cl3520])). 50.27/7.24 thf(zip_derived_cl16, plain, 50.27/7.24 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.24 thf(zip_derived_cl3560, plain, 50.27/7.24 (![X0 : a]: 50.27/7.24 ( ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | (('#sk1' @ '#sk2' @ X0) = ('#sk24' @ ('#sk1' @ '#sk2') @ X0)) 50.27/7.24 | ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ 50.27/7.24 ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl3535, zip_derived_cl16])). 50.27/7.24 thf(zip_derived_cl1452, plain, 50.27/7.24 (![X0 : a]: 50.27/7.24 ( ('#sk1' @ X0 @ '#sk2') 50.27/7.24 | ~ ('#sk1' @ X0 @ ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl1401, zip_derived_cl22])). 50.27/7.24 thf(zip_derived_cl3587, plain, 50.27/7.24 (![X0 : a]: 50.27/7.24 ((('#sk1' @ '#sk2' @ X0) = ('#sk24' @ ('#sk1' @ '#sk2') @ X0)) 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ '#sk2'))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl3560, zip_derived_cl1452])). 50.27/7.24 thf(zip_derived_cl16, plain, 50.27/7.24 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.24 thf(zip_derived_cl3609, plain, 50.27/7.24 (![X0 : a]: 50.27/7.24 ( ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ '#sk2') 50.27/7.24 | (('#sk1' @ '#sk2' @ X0) = ('#sk24' @ ('#sk1' @ '#sk2') @ X0)))), 50.27/7.24 inference('clc', [status(thm)], [zip_derived_cl3587, zip_derived_cl16])). 50.27/7.24 thf(zip_derived_cl16, plain, 50.27/7.24 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.24 thf(zip_derived_cl3617, plain, 50.27/7.24 (![X0 : a]: 50.27/7.24 ((('#sk1' @ '#sk2' @ X0) = ('#sk24' @ ('#sk1' @ '#sk2') @ X0)) 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl3609, zip_derived_cl16])). 50.27/7.24 thf(zip_derived_cl153, plain, 50.27/7.24 (((('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.24 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 != ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2')))) 50.27/7.24 | (('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.24 != ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2')))))), 50.27/7.24 inference('ho_norm', [status(thm)], [zip_derived_cl148])). 50.27/7.24 thf(zip_derived_cl378, plain, 50.27/7.24 (( ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.24 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | (('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.24 != ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2')))))), 50.27/7.24 inference('eq_elim', [status(thm)], [zip_derived_cl153])). 50.27/7.24 thf(zip_derived_cl3671, plain, 50.27/7.24 (((('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.24 != ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2')))) 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.24 ('#sk28' @ ('#sk1' @ '#sk2'))))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl3617, zip_derived_cl378])). 50.27/7.24 thf(zip_derived_cl3695, plain, 50.27/7.24 (( ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.24 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))))), 50.27/7.24 inference('simplify', [status(thm)], [zip_derived_cl3671])). 50.27/7.24 thf(zip_derived_cl16, plain, 50.27/7.24 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.24 thf(zip_derived_cl3747, plain, 50.27/7.24 (( ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ 50.27/7.24 ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl3695, zip_derived_cl16])). 50.27/7.24 thf(zip_derived_cl1452, plain, 50.27/7.24 (![X0 : a]: 50.27/7.24 ( ('#sk1' @ X0 @ '#sk2') 50.27/7.24 | ~ ('#sk1' @ X0 @ ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl1401, zip_derived_cl22])). 50.27/7.24 thf(zip_derived_cl3917, plain, 50.27/7.24 (( ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ '#sk2'))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl3747, zip_derived_cl1452])). 50.27/7.24 thf(zip_derived_cl16, plain, 50.27/7.24 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.24 thf(zip_derived_cl3931, plain, 50.27/7.24 ( ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ '#sk2')), 50.27/7.24 inference('clc', [status(thm)], [zip_derived_cl3917, zip_derived_cl16])). 50.27/7.24 thf(zip_derived_cl16, plain, 50.27/7.24 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.24 thf(zip_derived_cl3938, plain, 50.27/7.24 ( ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2')))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl3931, zip_derived_cl16])). 50.27/7.24 thf(zip_derived_cl3946, plain, 50.27/7.24 ((~ ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.24 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | (('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.24 != ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2')))))), 50.27/7.24 inference('demod', [status(thm)], [zip_derived_cl153, zip_derived_cl3938])). 50.27/7.24 thf(zip_derived_cl3931, plain, 50.27/7.24 ( ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ '#sk2')), 50.27/7.24 inference('clc', [status(thm)], [zip_derived_cl3917, zip_derived_cl16])). 50.27/7.24 thf(zip_derived_cl1371, plain, 50.27/7.24 ( ('#sk1' @ '#sk2' @ ('#sk17' @ ('#sk1' @ '#sk2')))), 50.27/7.24 inference('simplify', [status(thm)], [zip_derived_cl1338])). 50.27/7.24 thf(zip_derived_cl22, plain, 50.27/7.24 (![X2 : a, X4 : a, X6 : a]: 50.27/7.24 (~ ('#sk1' @ X4 @ X6) | ~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X2 @ X6))), 50.27/7.24 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl19])). 50.27/7.24 thf(zip_derived_cl1400, plain, 50.27/7.24 (![X0 : a]: 50.27/7.24 ( ('#sk1' @ X0 @ ('#sk17' @ ('#sk1' @ '#sk2'))) 50.27/7.24 | ~ ('#sk1' @ X0 @ '#sk2'))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl1371, zip_derived_cl22])). 50.27/7.24 thf(zip_derived_cl16, plain, 50.27/7.24 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.24 thf(zip_derived_cl1627, plain, 50.27/7.24 (![X0 : a]: 50.27/7.24 (~ ('#sk1' @ X0 @ '#sk2') 50.27/7.24 | ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ X0))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl1400, zip_derived_cl16])). 50.27/7.24 thf(zip_derived_cl3932, plain, 50.27/7.24 ( ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ ('#sk28' @ ('#sk1' @ '#sk2')))), 50.27/7.24 inference('sup-', [status(thm)], [zip_derived_cl3931, zip_derived_cl1627])). 50.27/7.24 thf(zip_derived_cl4001, plain, 50.27/7.24 ((('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.24 != ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))))), 50.27/7.24 inference('demod', [status(thm)], 50.27/7.24 [zip_derived_cl3946, zip_derived_cl3932])). 50.27/7.24 thf(zip_derived_cl153, plain, 50.27/7.24 (((('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.24 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.24 != ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2')))) 50.27/7.25 | (('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 != ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2')))))), 50.27/7.25 inference('ho_norm', [status(thm)], [zip_derived_cl148])). 50.27/7.25 thf(zip_derived_cl380, plain, 50.27/7.25 (( ('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | (('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 != ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2')))))), 50.27/7.25 inference('eq_elim', [status(thm)], [zip_derived_cl153])). 50.27/7.25 thf(zip_derived_cl3185, plain, 50.27/7.25 (( ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('eq_elim', [status(thm)], [zip_derived_cl380])). 50.27/7.25 thf(zip_derived_cl16, plain, 50.27/7.25 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.25 thf(zip_derived_cl3251, plain, 50.27/7.25 (( ('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl3185, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl1452, plain, 50.27/7.25 (![X0 : a]: 50.27/7.25 ( ('#sk1' @ X0 @ '#sk2') 50.27/7.25 | ~ ('#sk1' @ X0 @ ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl1401, zip_derived_cl22])). 50.27/7.25 thf(zip_derived_cl3305, plain, 50.27/7.25 (( ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ '#sk2'))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl3251, zip_derived_cl1452])). 50.27/7.25 thf(zip_derived_cl16, plain, 50.27/7.25 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.25 thf(zip_derived_cl3319, plain, 50.27/7.25 (( ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ '#sk2') 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('clc', [status(thm)], [zip_derived_cl3305, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl1627, plain, 50.27/7.25 (![X0 : a]: 50.27/7.25 (~ ('#sk1' @ X0 @ '#sk2') 50.27/7.25 | ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ X0))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl1400, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl3320, plain, 50.27/7.25 (( ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl3319, zip_derived_cl1627])). 50.27/7.25 thf(zip_derived_cl380, plain, 50.27/7.25 (( ('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | (('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 != ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2')))))), 50.27/7.25 inference('eq_elim', [status(thm)], [zip_derived_cl153])). 50.27/7.25 thf(zip_derived_cl3346, plain, 50.27/7.25 ((~ ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl3320, zip_derived_cl380])). 50.27/7.25 thf(zip_derived_cl3376, plain, 50.27/7.25 (( ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ~ ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('simplify', [status(thm)], [zip_derived_cl3346])). 50.27/7.25 thf(zip_derived_cl3319, plain, 50.27/7.25 (( ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ '#sk2') 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('clc', [status(thm)], [zip_derived_cl3305, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl16, plain, 50.27/7.25 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.25 thf(zip_derived_cl3326, plain, 50.27/7.25 (( ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl3319, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl3387, plain, 50.27/7.25 (( ('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('clc', [status(thm)], [zip_derived_cl3376, zip_derived_cl3326])). 50.27/7.25 thf(zip_derived_cl152, plain, 50.27/7.25 (((('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 != ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2')))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ '#sk2'))), 50.27/7.25 inference('ho_norm', [status(thm)], [zip_derived_cl147])). 50.27/7.25 thf(zip_derived_cl224, plain, 50.27/7.25 ((~ ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ~ ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ '#sk2'))), 50.27/7.25 inference('eq_elim', [status(thm)], [zip_derived_cl152])). 50.27/7.25 thf(zip_derived_cl11, plain, (![X2 : a]: ('#sk1' @ X2 @ X2)), 50.27/7.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 50.27/7.25 thf(zip_derived_cl3609, plain, 50.27/7.25 (![X0 : a]: 50.27/7.25 ( ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ '#sk2') 50.27/7.25 | (('#sk1' @ '#sk2' @ X0) = ('#sk24' @ ('#sk1' @ '#sk2') @ X0)))), 50.27/7.25 inference('clc', [status(thm)], [zip_derived_cl3587, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl3619, plain, 50.27/7.25 (![X0 : a]: 50.27/7.25 (~ ('#sk1' @ '#sk2' @ X0) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ X0) 50.27/7.25 | ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ '#sk2'))), 50.27/7.25 inference('eq_elim', [status(thm)], [zip_derived_cl3609])). 50.27/7.25 thf(zip_derived_cl3834, plain, 50.27/7.25 (( ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ '#sk2') 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ '#sk2'))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl3619])). 50.27/7.25 thf(zip_derived_cl1627, plain, 50.27/7.25 (![X0 : a]: 50.27/7.25 (~ ('#sk1' @ X0 @ '#sk2') 50.27/7.25 | ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ X0))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl1400, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl3842, plain, 50.27/7.25 (( ('#sk24' @ ('#sk1' @ '#sk2') @ '#sk2') 50.27/7.25 | ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl3834, zip_derived_cl1627])). 50.27/7.25 thf(zip_derived_cl3874, plain, 50.27/7.25 (( ('#sk24' @ ('#sk1' @ '#sk2') @ '#sk2') 50.27/7.25 | ~ ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ '#sk2'))), 50.27/7.25 inference('sup+', [status(thm)], [zip_derived_cl224, zip_derived_cl3842])). 50.27/7.25 thf(zip_derived_cl3894, plain, 50.27/7.25 ((~ ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ '#sk2'))), 50.27/7.25 inference('simplify', [status(thm)], [zip_derived_cl3874])). 50.27/7.25 thf(zip_derived_cl2548, plain, 50.27/7.25 (( ('#sk24' @ ('#sk1' @ '#sk2') @ '#sk2') 50.27/7.25 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('clc', [status(thm)], [zip_derived_cl1562, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl3900, plain, ( ('#sk24' @ ('#sk1' @ '#sk2') @ '#sk2')), 50.27/7.25 inference('clc', [status(thm)], [zip_derived_cl3894, zip_derived_cl2548])). 50.27/7.25 thf(zip_derived_cl327, plain, 50.27/7.25 (![X0 : a, X1 : a]: 50.27/7.25 (~ ('#sk24' @ ('#sk1' @ '#sk2') @ X0) 50.27/7.25 | (('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 != ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2')))) 50.27/7.25 | (('#sk1' @ X0 @ X1) = ('#sk24' @ ('#sk1' @ '#sk2') @ X1)))), 50.27/7.25 inference('ho_norm', [status(thm)], [zip_derived_cl322])). 50.27/7.25 thf(zip_derived_cl2508, plain, 50.27/7.25 (![X0 : a, X1 : a]: 50.27/7.25 ( ('#sk1' @ X0 @ X1) 50.27/7.25 | ~ ('#sk24' @ ('#sk1' @ '#sk2') @ X1) 50.27/7.25 | (('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 != ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2')))) 50.27/7.25 | ~ ('#sk24' @ ('#sk1' @ '#sk2') @ X0))), 50.27/7.25 inference('eq_elim', [status(thm)], [zip_derived_cl327])). 50.27/7.25 thf(zip_derived_cl3938, plain, 50.27/7.25 ( ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2')))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl3931, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl3954, plain, 50.27/7.25 (![X0 : a, X1 : a]: 50.27/7.25 ( ('#sk1' @ X0 @ X1) 50.27/7.25 | ~ ('#sk24' @ ('#sk1' @ '#sk2') @ X1) 50.27/7.25 | ~ ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ~ ('#sk24' @ ('#sk1' @ '#sk2') @ X0))), 50.27/7.25 inference('demod', [status(thm)], 50.27/7.25 [zip_derived_cl2508, zip_derived_cl3938])). 50.27/7.25 thf(zip_derived_cl3932, plain, 50.27/7.25 ( ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ ('#sk28' @ ('#sk1' @ '#sk2')))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl3931, zip_derived_cl1627])). 50.27/7.25 thf(zip_derived_cl4062, plain, 50.27/7.25 (![X0 : a, X1 : a]: 50.27/7.25 ( ('#sk1' @ X0 @ X1) 50.27/7.25 | ~ ('#sk24' @ ('#sk1' @ '#sk2') @ X1) 50.27/7.25 | ~ ('#sk24' @ ('#sk1' @ '#sk2') @ X0))), 50.27/7.25 inference('demod', [status(thm)], 50.27/7.25 [zip_derived_cl3954, zip_derived_cl3932])). 50.27/7.25 thf(zip_derived_cl4065, plain, 50.27/7.25 (![X0 : a]: 50.27/7.25 (~ ('#sk24' @ ('#sk1' @ '#sk2') @ X0) | ('#sk1' @ X0 @ '#sk2'))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl3900, zip_derived_cl4062])). 50.27/7.25 thf(zip_derived_cl4077, plain, 50.27/7.25 (( ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2')) @ '#sk2'))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl3387, zip_derived_cl4065])). 50.27/7.25 thf(zip_derived_cl16, plain, 50.27/7.25 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.25 thf(zip_derived_cl4123, plain, 50.27/7.25 ( ('#sk1' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2')) @ '#sk2')), 50.27/7.25 inference('clc', [status(thm)], [zip_derived_cl4077, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl16, plain, 50.27/7.25 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.25 thf(zip_derived_cl4130, plain, 50.27/7.25 ( ('#sk1' @ '#sk2' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2')))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl4123, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl4138, plain, 50.27/7.25 (~ ('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2')))), 50.27/7.25 inference('demod', [status(thm)], 50.27/7.25 [zip_derived_cl4001, zip_derived_cl4130])). 50.27/7.25 thf(zip_derived_cl11, plain, (![X2 : a]: ('#sk1' @ X2 @ X2)), 50.27/7.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 50.27/7.25 thf(zip_derived_cl1371, plain, 50.27/7.25 ( ('#sk1' @ '#sk2' @ ('#sk17' @ ('#sk1' @ '#sk2')))), 50.27/7.25 inference('simplify', [status(thm)], [zip_derived_cl1338])). 50.27/7.25 thf(zip_derived_cl53, plain, 50.27/7.25 (![X0 : a > $o, X2 : a, X4 : a]: 50.27/7.25 ((('#sk1' @ X2 @ X4) = ('#sk24' @ X0 @ X4)) 50.27/7.25 | (('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) 50.27/7.25 != (X0 @ ('#sk28' @ X0))) 50.27/7.25 | ~ (X0 @ '#sk2') 50.27/7.25 | ~ ('#sk24' @ X0 @ X2))), 50.27/7.25 inference('simplify nested equalities', [status(thm)], [zip_derived_cl52])). 50.27/7.25 thf(zip_derived_cl313, plain, 50.27/7.25 (![X0 : a > $o, X2 : a, X4 : a]: 50.27/7.25 (~ ('#sk1' @ X2 @ X4) 50.27/7.25 | ('#sk24' @ X0 @ X4) 50.27/7.25 | ~ ('#sk24' @ X0 @ X2) 50.27/7.25 | ~ (X0 @ '#sk2') 50.27/7.25 | (('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) 50.27/7.25 != (X0 @ ('#sk28' @ X0))))), 50.27/7.25 inference('eq_elim', [status(thm)], [zip_derived_cl53])). 50.27/7.25 thf(zip_derived_cl2643, plain, 50.27/7.25 (![X0 : a > $o]: 50.27/7.25 ((('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) != (X0 @ ('#sk28' @ X0))) 50.27/7.25 | ~ (X0 @ '#sk2') 50.27/7.25 | ~ ('#sk24' @ X0 @ '#sk2') 50.27/7.25 | ('#sk24' @ X0 @ ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl1371, zip_derived_cl313])). 50.27/7.25 thf(zip_derived_cl42, plain, 50.27/7.25 (![X0 : a > $o]: 50.27/7.25 ( ('#sk24' @ X0 @ '#sk2') 50.27/7.25 | ~ (X0 @ '#sk2') 50.27/7.25 | (('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) 50.27/7.25 != (X0 @ ('#sk28' @ X0))))), 50.27/7.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl37])). 50.27/7.25 thf(zip_derived_cl2671, plain, 50.27/7.25 (![X0 : a > $o]: 50.27/7.25 ( ('#sk24' @ X0 @ ('#sk17' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ~ (X0 @ '#sk2') 50.27/7.25 | (('#sk1' @ ('#sk17' @ X0) @ ('#sk28' @ X0)) 50.27/7.25 != (X0 @ ('#sk28' @ X0))))), 50.27/7.25 inference('clc', [status(thm)], [zip_derived_cl2643, zip_derived_cl42])). 50.27/7.25 thf(zip_derived_cl2677, plain, 50.27/7.25 (((('#sk1' @ 50.27/7.25 ('#sk17' @ 50.27/7.25 (^[Y0 : a]: 50.27/7.25 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.25 ((^[Y1 : a]: (Y1)) @ Y0)))) @ 50.27/7.25 ('#sk28' @ 50.27/7.25 (^[Y0 : a]: 50.27/7.25 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.25 ((^[Y1 : a]: (Y1)) @ Y0))))) 50.27/7.25 != ((^[Y0 : a]: 50.27/7.25 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.25 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.25 ('#sk28' @ 50.27/7.25 (^[Y0 : a]: 50.27/7.25 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.25 ((^[Y1 : a]: (Y1)) @ Y0)))))) 50.27/7.25 | ('#sk24' @ 50.27/7.25 (^[Y0 : a]: 50.27/7.25 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 50.27/7.25 ((^[Y1 : a]: (Y1)) @ Y0))) @ 50.27/7.25 ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl2671])). 50.27/7.25 thf(zip_derived_cl2681, plain, 50.27/7.25 (((('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 != ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2')))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('ho_norm', [status(thm)], [zip_derived_cl2677])). 50.27/7.25 thf(zip_derived_cl2684, plain, 50.27/7.25 ((~ ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ~ ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('eq_elim', [status(thm)], [zip_derived_cl2681])). 50.27/7.25 thf(zip_derived_cl2681, plain, 50.27/7.25 (((('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 != ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2')))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('ho_norm', [status(thm)], [zip_derived_cl2677])). 50.27/7.25 thf(zip_derived_cl2683, plain, 50.27/7.25 (( ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('eq_elim', [status(thm)], [zip_derived_cl2681])). 50.27/7.25 thf(zip_derived_cl16, plain, 50.27/7.25 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.25 thf(zip_derived_cl3043, plain, 50.27/7.25 (( ('#sk24' @ ('#sk1' @ '#sk2') @ ('#sk17' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl2683, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl1452, plain, 50.27/7.25 (![X0 : a]: 50.27/7.25 ( ('#sk1' @ X0 @ '#sk2') 50.27/7.25 | ~ ('#sk1' @ X0 @ ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl1401, zip_derived_cl22])). 50.27/7.25 thf(zip_derived_cl3070, plain, 50.27/7.25 (( ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#sk17' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ '#sk2'))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl3043, zip_derived_cl1452])). 50.27/7.25 thf(zip_derived_cl16, plain, 50.27/7.25 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.25 thf(zip_derived_cl3084, plain, 50.27/7.25 (( ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ '#sk2') 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('clc', [status(thm)], [zip_derived_cl3070, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl1627, plain, 50.27/7.25 (![X0 : a]: 50.27/7.25 (~ ('#sk1' @ X0 @ '#sk2') 50.27/7.25 | ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ X0))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl1400, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl3085, plain, 50.27/7.25 (( ('#sk24' @ ('#sk1' @ '#sk2') @ ('#sk17' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl3084, zip_derived_cl1627])). 50.27/7.25 thf(zip_derived_cl3130, plain, 50.27/7.25 (( ('#sk24' @ ('#sk1' @ '#sk2') @ ('#sk17' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ~ ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('sup+', [status(thm)], [zip_derived_cl2684, zip_derived_cl3085])). 50.27/7.25 thf(zip_derived_cl3150, plain, 50.27/7.25 ((~ ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('simplify', [status(thm)], [zip_derived_cl3130])). 50.27/7.25 thf(zip_derived_cl3084, plain, 50.27/7.25 (( ('#sk1' @ ('#sk28' @ ('#sk1' @ '#sk2')) @ '#sk2') 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ ('#sk17' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('clc', [status(thm)], [zip_derived_cl3070, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl16, plain, 50.27/7.25 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 50.27/7.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 50.27/7.25 thf(zip_derived_cl3091, plain, 50.27/7.25 (( ('#sk24' @ ('#sk1' @ '#sk2') @ ('#sk17' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2'))))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl3084, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl3156, plain, 50.27/7.25 ( ('#sk24' @ ('#sk1' @ '#sk2') @ ('#sk17' @ ('#sk1' @ '#sk2')))), 50.27/7.25 inference('clc', [status(thm)], [zip_derived_cl3150, zip_derived_cl3091])). 50.27/7.25 thf(zip_derived_cl327, plain, 50.27/7.25 (![X0 : a, X1 : a]: 50.27/7.25 (~ ('#sk24' @ ('#sk1' @ '#sk2') @ X0) 50.27/7.25 | (('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 != ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2')))) 50.27/7.25 | (('#sk1' @ X0 @ X1) = ('#sk24' @ ('#sk1' @ '#sk2') @ X1)))), 50.27/7.25 inference('ho_norm', [status(thm)], [zip_derived_cl322])). 50.27/7.25 thf(zip_derived_cl2509, plain, 50.27/7.25 (![X0 : a, X1 : a]: 50.27/7.25 (~ ('#sk1' @ X0 @ X1) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ X1) 50.27/7.25 | (('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 != ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2')))) 50.27/7.25 | ~ ('#sk24' @ ('#sk1' @ '#sk2') @ X0))), 50.27/7.25 inference('eq_elim', [status(thm)], [zip_derived_cl327])). 50.27/7.25 thf(zip_derived_cl3938, plain, 50.27/7.25 ( ('#sk1' @ '#sk2' @ ('#sk28' @ ('#sk1' @ '#sk2')))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl3931, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl3955, plain, 50.27/7.25 (![X0 : a, X1 : a]: 50.27/7.25 (~ ('#sk1' @ X0 @ X1) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ X1) 50.27/7.25 | ~ ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#sk28' @ ('#sk1' @ '#sk2'))) 50.27/7.25 | ~ ('#sk24' @ ('#sk1' @ '#sk2') @ X0))), 50.27/7.25 inference('demod', [status(thm)], 50.27/7.25 [zip_derived_cl2509, zip_derived_cl3938])). 50.27/7.25 thf(zip_derived_cl3932, plain, 50.27/7.25 ( ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ ('#sk28' @ ('#sk1' @ '#sk2')))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl3931, zip_derived_cl1627])). 50.27/7.25 thf(zip_derived_cl4355, plain, 50.27/7.25 (![X0 : a, X1 : a]: 50.27/7.25 (~ ('#sk1' @ X0 @ X1) 50.27/7.25 | ('#sk24' @ ('#sk1' @ '#sk2') @ X1) 50.27/7.25 | ~ ('#sk24' @ ('#sk1' @ '#sk2') @ X0))), 50.27/7.25 inference('demod', [status(thm)], 50.27/7.25 [zip_derived_cl3955, zip_derived_cl3932])). 50.27/7.25 thf(zip_derived_cl4356, plain, 50.27/7.25 (![X0 : a]: 50.27/7.25 ( ('#sk24' @ ('#sk1' @ '#sk2') @ X0) 50.27/7.25 | ~ ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ X0))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl3156, zip_derived_cl4355])). 50.27/7.25 thf(zip_derived_cl4123, plain, 50.27/7.25 ( ('#sk1' @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2')) @ '#sk2')), 50.27/7.25 inference('clc', [status(thm)], [zip_derived_cl4077, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl1627, plain, 50.27/7.25 (![X0 : a]: 50.27/7.25 (~ ('#sk1' @ X0 @ '#sk2') 50.27/7.25 | ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ X0))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl1400, zip_derived_cl16])). 50.27/7.25 thf(zip_derived_cl4124, plain, 50.27/7.25 ( ('#sk1' @ ('#sk17' @ ('#sk1' @ '#sk2')) @ 50.27/7.25 ('#_fresh_sk90' @ ('#sk1' @ '#sk2')))), 50.27/7.25 inference('sup-', [status(thm)], [zip_derived_cl4123, zip_derived_cl1627])). 50.27/7.25 thf(zip_derived_cl4367, plain, 50.27/7.25 ( ('#sk24' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk90' @ ('#sk1' @ '#sk2')))), 50.27/7.25 inference('sup+', [status(thm)], [zip_derived_cl4356, zip_derived_cl4124])). 50.27/7.25 thf(zip_derived_cl4395, plain, ($false), 50.27/7.25 inference('demod', [status(thm)], 50.27/7.25 [zip_derived_cl4138, zip_derived_cl4367])). 50.27/7.25 50.27/7.25 % SZS output end Refutation 50.27/7.25 50.27/7.25 50.27/7.25 % Terminating... 50.27/7.29 % Runner terminated. 0.25/7.31 % Zipperpin 1.5 exiting 0.25/7.32 EOF