0.06/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.10 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.F9W5iVX8pE true 0.09/0.30 % Computer : n015.cluster.edu 0.09/0.30 % Model : x86_64 x86_64 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.30 % Memory : 8042.1875MB 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.30 % CPULimit : 1920 0.09/0.30 % WCLimit : 240 0.09/0.30 % DateTime : Wed Jul 30 05:15:49 EDT 2025 0.09/0.30 % CPUTime : 0.09/0.30 % Running portfolio for 1920 s 0.09/0.30 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.09/0.30 % Number of cores: 8 0.09/0.30 % Python version: Python 3.6.8 0.09/0.30 % Running in HO mode 0.48/0.58 % Total configuration time : 828 0.48/0.58 % Estimated wc time : 1656 0.48/0.58 % Estimated cpu time (8 cpus) : 207.0 0.60/0.65 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.66/0.66 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.66/0.66 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.66/0.66 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.66/0.66 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.66/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.66/0.67 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.66/0.67 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 23.42/3.54 % Solved by lams/20_acsne_simpl.sh. 23.42/3.54 % done 697 iterations in 2.813s 23.42/3.54 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 23.42/3.54 % SZS output start Refutation 23.42/3.54 thf(a_type, type, a: $tType). 23.42/3.54 thf('#sk1_type', type, '#sk1': a > a > $o). 23.42/3.54 thf('#sk2_type', type, '#sk2': a). 23.42/3.54 thf('#sk25_type', type, '#sk25': (a > $o) > a). 23.42/3.54 thf('#sk11_type', type, '#sk11': (a > $o) > a). 23.42/3.54 thf('#_fresh_sk125_type', type, '#_fresh_sk125': (a > $o) > a). 23.42/3.54 thf('#_fresh_sk54_type', type, '#_fresh_sk54': (a > $o) > a). 23.42/3.54 thf('#sk20_type', type, '#sk20': (a > $o) > a > $o). 23.42/3.54 thf(cTHM260_pme, conjecture, 23.42/3.54 (![R:( a > a > $o )]: 23.42/3.54 ( ( ( ![Xx:a,Xy:a]: ( ( R @ Xx @ Xy ) => ( R @ Xy @ Xx ) ) ) & 23.42/3.54 ( ![Xx:a,Xy:a,Xz:a]: 23.42/3.54 ( ( ( R @ Xx @ Xy ) & ( R @ Xy @ Xz ) ) => ( R @ Xx @ Xz ) ) ) & 23.42/3.54 ( ![Xx:a]: ( R @ Xx @ Xx ) ) ) => 23.42/3.54 ( ( ![Xx:a]: 23.42/3.54 ( ?[Xp:( a > $o )]: 23.42/3.54 ( ( ![Xx0:a]: 23.42/3.54 ( ( Xp @ Xx0 ) => 23.42/3.54 ( ![Xy:a]: ( ( R @ Xx0 @ Xy ) <=> ( Xp @ Xy ) ) ) ) ) & 23.42/3.54 ( Xp @ Xx ) & 23.42/3.54 ( ![Xq:( a > $o )]: 23.42/3.54 ( ( ( ![Xx0:a]: 23.42/3.54 ( ( Xq @ Xx0 ) => 23.42/3.54 ( ![Xy:a]: ( ( R @ Xx0 @ Xy ) <=> ( Xq @ Xy ) ) ) ) ) & 23.42/3.54 ( Xq @ Xx ) & ( ?[Xz:a]: ( Xq @ Xz ) ) ) => 23.42/3.54 ( ( Xq ) = ( Xp ) ) ) ) & 23.42/3.54 ( ?[Xz:a]: ( Xp @ Xz ) ) ) ) ) & 23.42/3.54 ( ![Xp:( a > $o )]: 23.42/3.54 ( ( ( ?[Xz:a]: ( Xp @ Xz ) ) & 23.42/3.54 ( ![Xx:a]: 23.42/3.54 ( ( Xp @ Xx ) => 23.42/3.54 ( ![Xy:a]: ( ( Xp @ Xy ) <=> ( R @ Xx @ Xy ) ) ) ) ) ) => 23.42/3.54 ( ?[Xz:a]: ( Xp @ Xz ) ) ) ) ) ))). 23.42/3.54 thf(zf_stmt_0, negated_conjecture, 23.42/3.54 (~( ![R:( a > a > $o )]: 23.42/3.54 ( ( ( ![Xx:a,Xy:a]: ( ( R @ Xx @ Xy ) => ( R @ Xy @ Xx ) ) ) & 23.42/3.54 ( ![Xx:a,Xy:a,Xz:a]: 23.42/3.54 ( ( ( R @ Xx @ Xy ) & ( R @ Xy @ Xz ) ) => ( R @ Xx @ Xz ) ) ) & 23.42/3.54 ( ![Xx:a]: ( R @ Xx @ Xx ) ) ) => 23.42/3.54 ( ( ![Xx:a]: 23.42/3.54 ( ?[Xp:( a > $o )]: 23.42/3.54 ( ( ![Xx0:a]: 23.42/3.54 ( ( Xp @ Xx0 ) => 23.42/3.54 ( ![Xy:a]: ( ( R @ Xx0 @ Xy ) <=> ( Xp @ Xy ) ) ) ) ) & 23.42/3.54 ( Xp @ Xx ) & 23.42/3.54 ( ![Xq:( a > $o )]: 23.42/3.54 ( ( ( ![Xx0:a]: 23.42/3.54 ( ( Xq @ Xx0 ) => 23.42/3.54 ( ![Xy:a]: ( ( R @ Xx0 @ Xy ) <=> ( Xq @ Xy ) ) ) ) ) & 23.42/3.54 ( Xq @ Xx ) & ( ?[Xz:a]: ( Xq @ Xz ) ) ) => 23.42/3.54 ( ( Xq ) = ( Xp ) ) ) ) & 23.42/3.54 ( ?[Xz:a]: ( Xp @ Xz ) ) ) ) ) & 23.42/3.54 ( ![Xp:( a > $o )]: 23.42/3.54 ( ( ( ?[Xz:a]: ( Xp @ Xz ) ) & 23.42/3.54 ( ![Xx:a]: 23.42/3.54 ( ( Xp @ Xx ) => 23.42/3.54 ( ![Xy:a]: ( ( Xp @ Xy ) <=> ( R @ Xx @ Xy ) ) ) ) ) ) => 23.42/3.54 ( ?[Xz:a]: ( Xp @ Xz ) ) ) ) ) ) )), 23.42/3.54 inference('cnf.neg', [status(esa)], [cTHM260_pme])). 23.42/3.54 thf(zip_derived_cl0, plain, 23.42/3.54 (~ (((!!) @ (^[Y0 : a > a > $o]: 23.42/3.54 (((((((!!) @ (^[Y1 : a]: 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 (((Y0 @ Y1 @ Y2) => (Y0 @ 23.42/3.54 Y2 @ Y1))))))))) & 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 (((!!) @ (^[Y3 : a]: 23.42/3.54 (((((Y0 @ Y1 @ 23.42/3.54 Y2) & (Y0 @ 23.42/3.54 Y2 @ Y3))) => 23.42/3.54 (Y0 @ Y1 @ Y3)))))))))))) & 23.42/3.54 (((!!) @ (^[Y1 : a]: (Y0 @ Y1 @ Y1)))))) => 23.42/3.54 (((((!!) @ (^[Y1 : a]: 23.42/3.54 (((??) @ (^[Y2 : a > $o]: 23.42/3.54 (((((!!) @ (^[Y3 : a]: 23.42/3.54 (((Y2 @ Y3) => 23.42/3.54 (((!!) @ ( 23.42/3.54 ^[Y4 : a]: 23.42/3.54 (( 23.42/3.54 (Y0 @ 23.42/3.54 Y3 @ 23.42/3.54 Y4) <=> 23.42/3.54 (Y2 @ Y4))))))))))) & 23.42/3.54 (Y2 @ Y1) & 23.42/3.54 (((!!) @ (^[Y3 : a > $o]: 23.42/3.54 (((((((!!) @ ( 23.42/3.54 ^[Y4 : a]: 23.42/3.54 (( 23.42/3.54 (Y3 @ 23.42/3.54 Y4) => 23.42/3.54 (( 23.42/3.54 (!!) @ ( 23.42/3.54 ^[Y5 : a]: 23.42/3.54 (( 23.42/3.54 (Y0 @ 23.42/3.54 Y4 @ 23.42/3.54 Y5) <=> 23.42/3.54 (Y3 @ Y5))))))))))) & 23.42/3.54 (Y3 @ Y1) & 23.42/3.54 (((??) @ ( 23.42/3.54 ^[Y4 : a]: 23.42/3.54 (Y3 @ Y4)))))) => 23.42/3.54 (((Y3) = (Y2)))))))) & 23.42/3.54 (((??) @ (^[Y3 : a]: 23.42/3.54 (Y2 @ Y3)))))))))))) & 23.42/3.54 (((!!) @ (^[Y1 : a > $o]: 23.42/3.54 (((((((??) @ (^[Y2 : a]: (Y1 @ Y2)))) & 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 (((Y1 @ Y2) => 23.42/3.54 (((!!) @ (^[Y3 : a]: 23.42/3.54 (((Y1 @ 23.42/3.54 Y3) <=> 23.42/3.54 (Y0 @ 23.42/3.54 Y2 @ Y3))))))))))))) => 23.42/3.54 (((??) @ (^[Y2 : a]: (Y1 @ Y2))))))))))))))))), 23.42/3.54 inference('cnf', [status(esa)], [zf_stmt_0])). 23.42/3.54 thf(zip_derived_cl1, plain, 23.42/3.54 (~ (((!!) @ (^[Y0 : a > a > $o]: 23.42/3.54 (((((((!!) @ (^[Y1 : a]: 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 (((Y0 @ Y1 @ Y2) => (Y0 @ 23.42/3.54 Y2 @ Y1))))))))) & 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 (((!!) @ (^[Y3 : a]: 23.42/3.54 (((((Y0 @ Y1 @ 23.42/3.54 Y2) & (Y0 @ 23.42/3.54 Y2 @ Y3))) => 23.42/3.54 (Y0 @ Y1 @ Y3)))))))))))) & 23.42/3.54 (((!!) @ (^[Y1 : a]: (Y0 @ Y1 @ Y1)))))) => 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 (((??) @ (^[Y2 : a > $o]: 23.42/3.54 (((((!!) @ (^[Y3 : a]: 23.42/3.54 (((Y2 @ Y3) => 23.42/3.54 (((!!) @ ( 23.42/3.54 ^[Y4 : a]: 23.42/3.54 (((Y0 @ 23.42/3.54 Y3 @ 23.42/3.54 Y4) <=> 23.42/3.54 (Y2 @ Y4))))))))))) & 23.42/3.54 (Y2 @ Y1) & 23.42/3.54 (((!!) @ (^[Y3 : a > $o]: 23.42/3.54 (((((((!!) @ ( 23.42/3.54 ^[Y4 : a]: 23.42/3.54 (( 23.42/3.54 (Y3 @ 23.42/3.54 Y4) => 23.42/3.54 (( 23.42/3.54 (!!) @ ( 23.42/3.54 ^[Y5 : a]: 23.42/3.54 (( 23.42/3.54 (Y0 @ 23.42/3.54 Y4 @ 23.42/3.54 Y5) <=> 23.42/3.54 (Y3 @ Y5))))))))))) & 23.42/3.54 (Y3 @ Y1) & 23.42/3.54 (((??) @ ( 23.42/3.54 ^[Y4 : a]: 23.42/3.54 (Y3 @ Y4)))))) => 23.42/3.54 (((Y3) = (Y2)))))))) & 23.42/3.54 (((??) @ (^[Y3 : a]: (Y2 @ Y3)))))))))))))))))), 23.42/3.54 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl0])). 23.42/3.54 thf(zip_derived_cl2, plain, 23.42/3.54 (~ (((((((!!) @ (^[Y0 : a]: 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 ((('#sk1' @ Y0 @ Y1) => ('#sk1' @ Y1 @ Y0))))))))) & 23.42/3.54 (((!!) @ (^[Y0 : a]: 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 ((((('#sk1' @ Y0 @ Y1) & 23.42/3.54 ('#sk1' @ Y1 @ Y2))) => 23.42/3.54 ('#sk1' @ Y0 @ Y2)))))))))))) & 23.42/3.54 (((!!) @ (^[Y0 : a]: ('#sk1' @ Y0 @ Y0)))))) => 23.42/3.54 (((!!) @ (^[Y0 : a]: 23.42/3.54 (((??) @ (^[Y1 : a > $o]: 23.42/3.54 (((((!!) @ (^[Y2 : a]: 23.42/3.54 (((Y1 @ Y2) => 23.42/3.54 (((!!) @ (^[Y3 : a]: 23.42/3.54 ((('#sk1' @ 23.42/3.54 Y2 @ Y3) <=> 23.42/3.54 (Y1 @ Y3))))))))))) & 23.42/3.54 (Y1 @ Y0) & 23.42/3.54 (((!!) @ (^[Y2 : a > $o]: 23.42/3.54 (((((((!!) @ (^[Y3 : a]: 23.42/3.54 (((Y2 @ Y3) => 23.42/3.54 (((!!) @ ( 23.42/3.54 ^[Y4 : a]: 23.42/3.54 (( 23.42/3.54 ('#sk1' @ 23.42/3.54 Y3 @ 23.42/3.54 Y4) <=> 23.42/3.54 (Y2 @ Y4))))))))))) & 23.42/3.54 (Y2 @ Y0) & 23.42/3.54 (((??) @ (^[Y3 : a]: 23.42/3.54 (Y2 @ Y3)))))) => 23.42/3.54 (((Y2) = (Y1)))))))) & 23.42/3.54 (((??) @ (^[Y2 : a]: (Y1 @ Y2))))))))))))))), 23.42/3.54 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 23.42/3.54 thf(zip_derived_cl3, plain, 23.42/3.54 ( (((((!!) @ (^[Y0 : a]: 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 ((('#sk1' @ Y0 @ Y1) => ('#sk1' @ Y1 @ Y0))))))))) & 23.42/3.54 (((!!) @ (^[Y0 : a]: 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 ((((('#sk1' @ Y0 @ Y1) & 23.42/3.54 ('#sk1' @ Y1 @ Y2))) => 23.42/3.54 ('#sk1' @ Y0 @ Y2)))))))))))) & 23.42/3.54 (((!!) @ (^[Y0 : a]: ('#sk1' @ Y0 @ Y0))))))), 23.42/3.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 23.42/3.54 thf(zip_derived_cl7, plain, ( (((!!) @ (^[Y0 : a]: ('#sk1' @ Y0 @ Y0))))), 23.42/3.54 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])). 23.42/3.54 thf(zip_derived_cl11, plain, (![X2 : a]: ('#sk1' @ X2 @ X2)), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 23.42/3.54 thf(zip_derived_cl4, plain, 23.42/3.54 (~ (((!!) @ (^[Y0 : a]: 23.42/3.54 (((??) @ (^[Y1 : a > $o]: 23.42/3.54 (((((!!) @ (^[Y2 : a]: 23.42/3.54 (((Y1 @ Y2) => 23.42/3.54 (((!!) @ (^[Y3 : a]: 23.42/3.54 ((('#sk1' @ Y2 @ 23.42/3.54 Y3) <=> (Y1 @ 23.42/3.54 Y3))))))))))) & 23.42/3.54 (Y1 @ Y0) & 23.42/3.54 (((!!) @ (^[Y2 : a > $o]: 23.42/3.54 (((((((!!) @ (^[Y3 : a]: 23.42/3.54 (((Y2 @ Y3) => 23.42/3.54 (((!!) @ ( 23.42/3.54 ^[Y4 : a]: 23.42/3.54 (( 23.42/3.54 ('#sk1' @ 23.42/3.54 Y3 @ 23.42/3.54 Y4) <=> 23.42/3.54 (Y2 @ Y4))))))))))) & 23.42/3.54 (Y2 @ Y0) & 23.42/3.54 (((??) @ (^[Y3 : a]: 23.42/3.54 (Y2 @ Y3)))))) => 23.42/3.54 (((Y2) = (Y1)))))))) & 23.42/3.54 (((??) @ (^[Y2 : a]: (Y1 @ Y2))))))))))))), 23.42/3.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 23.42/3.54 thf(zip_derived_cl8, plain, 23.42/3.54 (~ (((??) @ (^[Y0 : a > $o]: 23.42/3.54 (((((!!) @ (^[Y1 : a]: 23.42/3.54 (((Y0 @ Y1) => 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 ((('#sk1' @ Y1 @ Y2) <=> 23.42/3.54 (Y0 @ Y2))))))))))) & 23.42/3.54 (Y0 @ '#sk2') & 23.42/3.54 (((!!) @ (^[Y1 : a > $o]: 23.42/3.54 (((((((!!) @ (^[Y2 : a]: 23.42/3.54 (((Y1 @ Y2) => 23.42/3.54 (((!!) @ (^[Y3 : a]: 23.42/3.54 ((('#sk1' @ 23.42/3.54 Y2 @ Y3) <=> 23.42/3.54 (Y1 @ Y3))))))))))) & 23.42/3.54 (Y1 @ '#sk2') & 23.42/3.54 (((??) @ (^[Y2 : a]: (Y1 @ Y2)))))) => 23.42/3.54 (((Y1) = (Y0)))))))) & 23.42/3.54 (((??) @ (^[Y1 : a]: (Y0 @ Y1)))))))))), 23.42/3.54 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl4])). 23.42/3.54 thf(zip_derived_cl12, plain, 23.42/3.54 (![X2 : a > $o]: 23.42/3.54 ~ (((((!!) @ (^[Y0 : a]: 23.42/3.54 (((X2 @ Y0) => 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 ((('#sk1' @ Y0 @ Y1) <=> (X2 @ Y1))))))))))) & 23.42/3.54 (X2 @ '#sk2') & 23.42/3.54 (((!!) @ (^[Y0 : a > $o]: 23.42/3.54 (((((((!!) @ (^[Y1 : a]: 23.42/3.54 (((Y0 @ Y1) => 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 ((('#sk1' @ Y1 @ Y2) <=> 23.42/3.54 (Y0 @ Y2))))))))))) & 23.42/3.54 (Y0 @ '#sk2') & (((??) @ (^[Y1 : a]: (Y0 @ Y1)))))) => 23.42/3.54 (((Y0) = (X2)))))))) & 23.42/3.54 (((??) @ (^[Y0 : a]: (X2 @ Y0))))))), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 23.42/3.54 thf(zip_derived_cl15, plain, 23.42/3.54 (![X2 : a > $o]: 23.42/3.54 (~ (((!!) @ (^[Y0 : a]: 23.42/3.54 (((X2 @ Y0) => 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 ((('#sk1' @ Y0 @ Y1) <=> (X2 @ Y1))))))))))) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | ~ (((!!) @ (^[Y0 : a > $o]: 23.42/3.54 (((((((!!) @ (^[Y1 : a]: 23.42/3.54 (((Y0 @ Y1) => 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 ((('#sk1' @ Y1 @ 23.42/3.54 Y2) <=> (Y0 @ Y2))))))))))) & 23.42/3.54 (Y0 @ '#sk2') & (((??) @ (^[Y1 : a]: (Y0 @ Y1)))))) => 23.42/3.54 (((Y0) = (X2)))))))) 23.42/3.54 | ~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))))), 23.42/3.54 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl12])). 23.42/3.54 thf(zip_derived_cl18, plain, 23.42/3.54 (![X2 : a > $o]: 23.42/3.54 (~ (((X2 @ ('#sk11' @ X2)) => 23.42/3.54 (((!!) @ (^[Y0 : a]: 23.42/3.54 ((('#sk1' @ ('#sk11' @ X2) @ Y0) <=> (X2 @ Y0)))))))) 23.42/3.54 | ~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))) 23.42/3.54 | ~ (((!!) @ (^[Y0 : a > $o]: 23.42/3.54 (((((((!!) @ (^[Y1 : a]: 23.42/3.54 (((Y0 @ Y1) => 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 ((('#sk1' @ Y1 @ 23.42/3.54 Y2) <=> (Y0 @ Y2))))))))))) & 23.42/3.54 (Y0 @ '#sk2') & (((??) @ (^[Y1 : a]: (Y0 @ Y1)))))) => 23.42/3.54 (((Y0) = (X2)))))))) 23.42/3.54 | ~ (X2 @ '#sk2'))), 23.42/3.54 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])). 23.42/3.54 thf(zip_derived_cl20, plain, 23.42/3.54 (![X2 : a > $o]: 23.42/3.54 ( (X2 @ ('#sk11' @ X2)) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | ~ (((!!) @ (^[Y0 : a > $o]: 23.42/3.54 (((((((!!) @ (^[Y1 : a]: 23.42/3.54 (((Y0 @ Y1) => 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 ((('#sk1' @ Y1 @ 23.42/3.54 Y2) <=> (Y0 @ Y2))))))))))) & 23.42/3.54 (Y0 @ '#sk2') & (((??) @ (^[Y1 : a]: (Y0 @ Y1)))))) => 23.42/3.54 (((Y0) = (X2)))))))) 23.42/3.54 | ~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))))), 23.42/3.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 23.42/3.54 thf(zip_derived_cl24, plain, 23.42/3.54 (![X2 : a > $o]: 23.42/3.54 (~ (((((((!!) @ (^[Y0 : a]: 23.42/3.54 ((('#sk20' @ X2 @ Y0) => 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 ((('#sk1' @ Y0 @ Y1) <=> ('#sk20' @ 23.42/3.54 X2 @ Y1))))))))))) & 23.42/3.54 ('#sk20' @ X2 @ '#sk2') & 23.42/3.54 (((??) @ (^[Y0 : a]: ('#sk20' @ X2 @ Y0)))))) => 23.42/3.54 ((('#sk20' @ X2) = (X2))))) 23.42/3.54 | ~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | (X2 @ ('#sk11' @ X2)))), 23.42/3.54 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl20])). 23.42/3.54 thf(zip_derived_cl26, plain, 23.42/3.54 (![X2 : a > $o]: 23.42/3.54 ( (((((!!) @ (^[Y0 : a]: 23.42/3.54 ((('#sk20' @ X2 @ Y0) => 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 ((('#sk1' @ Y0 @ Y1) <=> ('#sk20' @ 23.42/3.54 X2 @ Y1))))))))))) & 23.42/3.54 ('#sk20' @ X2 @ '#sk2') & 23.42/3.54 (((??) @ (^[Y0 : a]: ('#sk20' @ X2 @ Y0)))))) 23.42/3.54 | (X2 @ ('#sk11' @ X2)) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | ~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))))), 23.42/3.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl24])). 23.42/3.54 thf(zip_derived_cl31, plain, 23.42/3.54 (![X2 : a > $o]: 23.42/3.54 ( ('#sk20' @ X2 @ '#sk2') 23.42/3.54 | ~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | (X2 @ ('#sk11' @ X2)))), 23.42/3.54 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 23.42/3.54 thf(zip_derived_cl39, plain, 23.42/3.54 (![X2 : a > $o, X4 : a]: 23.42/3.54 (~ (X2 @ X4) 23.42/3.54 | (X2 @ ('#sk11' @ X2)) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | ('#sk20' @ X2 @ '#sk2'))), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl31])). 23.42/3.54 thf(zip_derived_cl45, plain, 23.42/3.54 (![X0 : a > $o]: 23.42/3.54 ( ('#sk20' @ X0 @ '#sk2') | (X0 @ ('#sk11' @ X0)) | ~ (X0 @ '#sk2'))), 23.42/3.54 inference('condensation', [status(thm)], [zip_derived_cl39])). 23.42/3.54 thf(zip_derived_cl127, plain, 23.42/3.54 (( ((^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.54 ('#sk11' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))))) 23.42/3.54 | ('#sk20' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.54 '#sk2'))), 23.42/3.54 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl45])). 23.42/3.54 thf(zip_derived_cl131, plain, 23.42/3.54 (( ('#sk1' @ '#sk2' @ ('#sk11' @ ('#sk1' @ '#sk2'))) 23.42/3.54 | ('#sk20' @ ('#sk1' @ '#sk2') @ '#sk2'))), 23.42/3.54 inference('ho_norm', [status(thm)], [zip_derived_cl127])). 23.42/3.54 thf(zip_derived_cl11, plain, (![X2 : a]: ('#sk1' @ X2 @ X2)), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 23.42/3.54 thf(zip_derived_cl30, plain, 23.42/3.54 (![X2 : a > $o]: 23.42/3.54 ( (((!!) @ (^[Y0 : a]: 23.42/3.54 ((('#sk20' @ X2 @ Y0) => 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 ((('#sk1' @ Y0 @ Y1) <=> ('#sk20' @ X2 @ 23.42/3.54 Y1))))))))))) 23.42/3.54 | ~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | (X2 @ ('#sk11' @ X2)))), 23.42/3.54 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 23.42/3.54 thf(zip_derived_cl38, plain, 23.42/3.54 (![X2 : a > $o, X4 : a]: 23.42/3.54 ( ((('#sk20' @ X2 @ X4) => 23.42/3.54 (((!!) @ (^[Y0 : a]: 23.42/3.54 ((('#sk1' @ X4 @ Y0) <=> ('#sk20' @ X2 @ Y0)))))))) 23.42/3.54 | (X2 @ ('#sk11' @ X2)) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | ~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))))), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl30])). 23.42/3.54 thf(zip_derived_cl44, plain, 23.42/3.54 (![X2 : a > $o, X4 : a]: 23.42/3.54 (~ ('#sk20' @ X2 @ X4) 23.42/3.54 | (((!!) @ (^[Y0 : a]: 23.42/3.54 ((('#sk1' @ X4 @ Y0) <=> ('#sk20' @ X2 @ Y0)))))) 23.42/3.54 | ~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | (X2 @ ('#sk11' @ X2)))), 23.42/3.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 23.42/3.54 thf(zip_derived_cl52, plain, 23.42/3.54 (![X2 : a > $o, X4 : a, X6 : a]: 23.42/3.54 ( ((('#sk1' @ X4 @ X6) <=> ('#sk20' @ X2 @ X6))) 23.42/3.54 | (X2 @ ('#sk11' @ X2)) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | ~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))) 23.42/3.54 | ~ ('#sk20' @ X2 @ X4))), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl44])). 23.42/3.54 thf(zip_derived_cl56, plain, 23.42/3.54 (![X2 : a > $o, X4 : a, X6 : a]: 23.42/3.54 ((('#sk1' @ X4 @ X6) = ('#sk20' @ X2 @ X6)) 23.42/3.54 | (X2 @ ('#sk11' @ X2)) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | ~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))) 23.42/3.54 | ~ ('#sk20' @ X2 @ X4))), 23.42/3.54 inference('simplify nested equalities', [status(thm)], [zip_derived_cl52])). 23.42/3.54 thf(zip_derived_cl57, plain, 23.42/3.54 (![X2 : a > $o, X4 : a, X6 : a, X8 : a]: 23.42/3.54 (~ (X2 @ X8) 23.42/3.54 | ~ ('#sk20' @ X2 @ X4) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | (X2 @ ('#sk11' @ X2)) 23.42/3.54 | (('#sk1' @ X4 @ X6) = ('#sk20' @ X2 @ X6)))), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl56])). 23.42/3.54 thf(zip_derived_cl59, plain, 23.42/3.54 (![X0 : a, X1 : a, X2 : a > $o]: 23.42/3.54 ((('#sk1' @ X1 @ X0) = ('#sk20' @ X2 @ X0)) 23.42/3.54 | ~ ('#sk20' @ X2 @ X1) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | (X2 @ ('#sk11' @ X2)))), 23.42/3.54 inference('condensation', [status(thm)], [zip_derived_cl57])). 23.42/3.54 thf(zip_derived_cl246, plain, 23.42/3.54 (![X0 : a, X1 : a]: 23.42/3.54 ( ((^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.54 ('#sk11' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))))) 23.42/3.54 | ~ ('#sk20' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.54 X0) 23.42/3.54 | (('#sk1' @ X0 @ X1) 23.42/3.54 = ('#sk20' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ 23.42/3.54 ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.54 X1)))), 23.42/3.54 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl59])). 23.42/3.54 thf(zip_derived_cl250, plain, 23.42/3.54 (![X0 : a, X1 : a]: 23.42/3.54 ( ('#sk1' @ '#sk2' @ ('#sk11' @ ('#sk1' @ '#sk2'))) 23.42/3.54 | ~ ('#sk20' @ ('#sk1' @ '#sk2') @ X0) 23.42/3.54 | (('#sk1' @ X0 @ X1) = ('#sk20' @ ('#sk1' @ '#sk2') @ X1)))), 23.42/3.54 inference('ho_norm', [status(thm)], [zip_derived_cl246])). 23.42/3.54 thf(zip_derived_cl428, plain, 23.42/3.54 (![X0 : a]: 23.42/3.54 ( ('#sk1' @ '#sk2' @ ('#sk11' @ ('#sk1' @ '#sk2'))) 23.42/3.54 | (('#sk1' @ '#sk2' @ X0) = ('#sk20' @ ('#sk1' @ '#sk2') @ X0)) 23.42/3.54 | ('#sk1' @ '#sk2' @ ('#sk11' @ ('#sk1' @ '#sk2'))))), 23.42/3.54 inference('sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl250])). 23.42/3.54 thf(zip_derived_cl441, plain, 23.42/3.54 (![X0 : a]: 23.42/3.54 ((('#sk1' @ '#sk2' @ X0) = ('#sk20' @ ('#sk1' @ '#sk2') @ X0)) 23.42/3.54 | ('#sk1' @ '#sk2' @ ('#sk11' @ ('#sk1' @ '#sk2'))))), 23.42/3.54 inference('simplify', [status(thm)], [zip_derived_cl428])). 23.42/3.54 thf(zip_derived_cl11, plain, (![X2 : a]: ('#sk1' @ X2 @ X2)), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 23.42/3.54 thf(zip_derived_cl27, plain, 23.42/3.54 (![X2 : a > $o]: 23.42/3.54 (~ ((('#sk20' @ X2) = (X2))) 23.42/3.54 | (X2 @ ('#sk11' @ X2)) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | ~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))))), 23.42/3.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl24])). 23.42/3.54 thf(zip_derived_cl33, plain, 23.42/3.54 (![X2 : a > $o]: 23.42/3.54 ((('#sk20' @ X2) != (X2)) 23.42/3.54 | (X2 @ ('#sk11' @ X2)) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | ~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))))), 23.42/3.54 inference('simplify nested equalities', [status(thm)], [zip_derived_cl27])). 23.42/3.54 thf(zip_derived_cl34, plain, 23.42/3.54 (![X2 : a > $o]: 23.42/3.54 ((('#sk20' @ X2 @ ('#_fresh_sk54' @ X2)) 23.42/3.54 != (X2 @ ('#_fresh_sk54' @ X2))) 23.42/3.54 | (X2 @ ('#sk11' @ X2)) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | ~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))))), 23.42/3.54 inference('neg_ext_simpl', [status(thm)], [zip_derived_cl33])). 23.42/3.54 thf(zip_derived_cl35, plain, 23.42/3.54 (![X2 : a > $o, X4 : a]: 23.42/3.54 (~ (X2 @ X4) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | (X2 @ ('#sk11' @ X2)) 23.42/3.54 | (('#sk20' @ X2 @ ('#_fresh_sk54' @ X2)) 23.42/3.54 != (X2 @ ('#_fresh_sk54' @ X2))))), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 23.42/3.54 thf(zip_derived_cl41, plain, 23.42/3.54 (![X0 : a > $o]: 23.42/3.54 ((('#sk20' @ X0 @ ('#_fresh_sk54' @ X0)) 23.42/3.54 != (X0 @ ('#_fresh_sk54' @ X0))) 23.42/3.54 | ~ (X0 @ '#sk2') 23.42/3.54 | (X0 @ ('#sk11' @ X0)))), 23.42/3.54 inference('condensation', [status(thm)], [zip_derived_cl35])). 23.42/3.54 thf(zip_derived_cl110, plain, 23.42/3.54 (( ((^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.54 ('#sk11' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))))) 23.42/3.54 | (('#sk20' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.54 ('#_fresh_sk54' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))))) 23.42/3.54 != ((^[Y0 : a]: 23.42/3.54 ('#sk1' @ 23.42/3.54 ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.54 ('#_fresh_sk54' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ 23.42/3.54 ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0)))))))), 23.42/3.54 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl41])). 23.42/3.54 thf(zip_derived_cl115, plain, 23.42/3.54 (( ('#sk1' @ '#sk2' @ ('#sk11' @ ('#sk1' @ '#sk2'))) 23.42/3.54 | (('#sk20' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk54' @ ('#sk1' @ '#sk2'))) 23.42/3.54 != ('#sk1' @ '#sk2' @ ('#_fresh_sk54' @ ('#sk1' @ '#sk2')))))), 23.42/3.54 inference('ho_norm', [status(thm)], [zip_derived_cl110])). 23.42/3.54 thf(zip_derived_cl450, plain, 23.42/3.54 (((('#sk1' @ '#sk2' @ ('#_fresh_sk54' @ ('#sk1' @ '#sk2'))) 23.42/3.54 != ('#sk1' @ '#sk2' @ ('#_fresh_sk54' @ ('#sk1' @ '#sk2')))) 23.42/3.54 | ('#sk1' @ '#sk2' @ ('#sk11' @ ('#sk1' @ '#sk2'))) 23.42/3.54 | ('#sk1' @ '#sk2' @ ('#sk11' @ ('#sk1' @ '#sk2'))))), 23.42/3.54 inference('sup-', [status(thm)], [zip_derived_cl441, zip_derived_cl115])). 23.42/3.54 thf(zip_derived_cl471, plain, 23.42/3.54 ( ('#sk1' @ '#sk2' @ ('#sk11' @ ('#sk1' @ '#sk2')))), 23.42/3.54 inference('simplify', [status(thm)], [zip_derived_cl450])). 23.42/3.54 thf(zip_derived_cl5, plain, 23.42/3.54 ( (((!!) @ (^[Y0 : a]: 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 ((('#sk1' @ Y0 @ Y1) => ('#sk1' @ Y1 @ Y0)))))))))), 23.42/3.54 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])). 23.42/3.54 thf(zip_derived_cl9, plain, 23.42/3.54 (![X2 : a]: 23.42/3.54 (((!!) @ (^[Y0 : a]: ((('#sk1' @ X2 @ Y0) => ('#sk1' @ Y0 @ X2))))))), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 23.42/3.54 thf(zip_derived_cl13, plain, 23.42/3.54 (![X2 : a, X4 : a]: ((('#sk1' @ X2 @ X4) => ('#sk1' @ X4 @ X2)))), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])). 23.42/3.54 thf(zip_derived_cl16, plain, 23.42/3.54 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk1' @ X4 @ X2))), 23.42/3.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 23.42/3.54 thf(zip_derived_cl486, plain, 23.42/3.54 ( ('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ '#sk2')), 23.42/3.54 inference('sup-', [status(thm)], [zip_derived_cl471, zip_derived_cl16])). 23.42/3.54 thf(zip_derived_cl6, plain, 23.42/3.54 ( (((!!) @ (^[Y0 : a]: 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 ((((('#sk1' @ Y0 @ Y1) & ('#sk1' @ 23.42/3.54 Y1 @ Y2))) => 23.42/3.54 ('#sk1' @ Y0 @ Y2))))))))))))), 23.42/3.54 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])). 23.42/3.54 thf(zip_derived_cl10, plain, 23.42/3.54 (![X2 : a]: 23.42/3.54 (((!!) @ (^[Y0 : a]: 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 ((((('#sk1' @ X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 23.42/3.54 ('#sk1' @ X2 @ Y1)))))))))), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 23.42/3.54 thf(zip_derived_cl14, plain, 23.42/3.54 (![X2 : a, X4 : a]: 23.42/3.54 (((!!) @ (^[Y0 : a]: 23.42/3.54 ((((('#sk1' @ X2 @ X4) & ('#sk1' @ X4 @ Y0))) => 23.42/3.54 ('#sk1' @ X2 @ Y0))))))), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 23.42/3.54 thf(zip_derived_cl17, plain, 23.42/3.54 (![X2 : a, X4 : a, X6 : a]: 23.42/3.54 ((((('#sk1' @ X2 @ X4) & ('#sk1' @ X4 @ X6))) => ('#sk1' @ X2 @ X6)))), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 23.42/3.54 thf(zip_derived_cl19, plain, 23.42/3.54 (![X2 : a, X4 : a, X6 : a]: 23.42/3.54 (~ ((('#sk1' @ X2 @ X4) & ('#sk1' @ X4 @ X6))) | ('#sk1' @ X2 @ X6))), 23.42/3.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 23.42/3.54 thf(zip_derived_cl22, plain, 23.42/3.54 (![X2 : a, X4 : a, X6 : a]: 23.42/3.54 (~ ('#sk1' @ X2 @ X4) | ~ ('#sk1' @ X4 @ X6) | ('#sk1' @ X2 @ X6))), 23.42/3.54 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl19])). 23.42/3.54 thf(zip_derived_cl489, plain, 23.42/3.54 (![X0 : a]: 23.42/3.54 ( ('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ X0) 23.42/3.54 | ~ ('#sk1' @ '#sk2' @ X0))), 23.42/3.54 inference('sup-', [status(thm)], [zip_derived_cl486, zip_derived_cl22])). 23.42/3.54 thf(zip_derived_cl11, plain, (![X2 : a]: ('#sk1' @ X2 @ X2)), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 23.42/3.54 thf(zip_derived_cl21, plain, 23.42/3.54 (![X2 : a > $o]: 23.42/3.54 (~ (((!!) @ (^[Y0 : a]: 23.42/3.54 ((('#sk1' @ ('#sk11' @ X2) @ Y0) <=> (X2 @ Y0)))))) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | ~ (((!!) @ (^[Y0 : a > $o]: 23.42/3.54 (((((((!!) @ (^[Y1 : a]: 23.42/3.54 (((Y0 @ Y1) => 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 ((('#sk1' @ Y1 @ 23.42/3.54 Y2) <=> (Y0 @ Y2))))))))))) & 23.42/3.54 (Y0 @ '#sk2') & (((??) @ (^[Y1 : a]: (Y0 @ Y1)))))) => 23.42/3.54 (((Y0) = (X2)))))))) 23.42/3.54 | ~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))))), 23.42/3.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 23.42/3.54 thf(zip_derived_cl25, plain, 23.42/3.54 (![X2 : a > $o]: 23.42/3.54 (~ ((('#sk1' @ ('#sk11' @ X2) @ ('#sk25' @ X2)) <=> (X2 @ 23.42/3.54 ('#sk25' @ X2)))) 23.42/3.54 | ~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))) 23.42/3.54 | ~ (((!!) @ (^[Y0 : a > $o]: 23.42/3.54 (((((((!!) @ (^[Y1 : a]: 23.42/3.54 (((Y0 @ Y1) => 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 ((('#sk1' @ Y1 @ 23.42/3.54 Y2) <=> (Y0 @ Y2))))))))))) & 23.42/3.54 (Y0 @ '#sk2') & (((??) @ (^[Y1 : a]: (Y0 @ Y1)))))) => 23.42/3.54 (((Y0) = (X2)))))))) 23.42/3.54 | ~ (X2 @ '#sk2'))), 23.42/3.54 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl21])). 23.42/3.54 thf(zip_derived_cl28, plain, 23.42/3.54 (![X2 : a > $o]: 23.42/3.54 ((('#sk1' @ ('#sk11' @ X2) @ ('#sk25' @ X2)) != (X2 @ ('#sk25' @ X2))) 23.42/3.54 | ~ (((??) @ (^[Y0 : a]: (X2 @ Y0)))) 23.42/3.54 | ~ (((!!) @ (^[Y0 : a > $o]: 23.42/3.54 (((((((!!) @ (^[Y1 : a]: 23.42/3.54 (((Y0 @ Y1) => 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 ((('#sk1' @ Y1 @ 23.42/3.54 Y2) <=> (Y0 @ Y2))))))))))) & 23.42/3.54 (Y0 @ '#sk2') & (((??) @ (^[Y1 : a]: (Y0 @ Y1)))))) => 23.42/3.54 (((Y0) = (X2)))))))) 23.42/3.54 | ~ (X2 @ '#sk2'))), 23.42/3.54 inference('simplify nested equalities', [status(thm)], [zip_derived_cl25])). 23.42/3.54 thf(zip_derived_cl29, plain, 23.42/3.54 (![X2 : a > $o, X4 : a]: 23.42/3.54 (~ (X2 @ X4) 23.42/3.54 | ~ (X2 @ '#sk2') 23.42/3.54 | ~ (((!!) @ (^[Y0 : a > $o]: 23.42/3.54 (((((((!!) @ (^[Y1 : a]: 23.42/3.54 (((Y0 @ Y1) => 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 ((('#sk1' @ Y1 @ 23.42/3.54 Y2) <=> (Y0 @ Y2))))))))))) & 23.42/3.54 (Y0 @ '#sk2') & (((??) @ (^[Y1 : a]: (Y0 @ Y1)))))) => 23.42/3.54 (((Y0) = (X2)))))))) 23.42/3.54 | (('#sk1' @ ('#sk11' @ X2) @ ('#sk25' @ X2)) 23.42/3.54 != (X2 @ ('#sk25' @ X2))))), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 23.42/3.54 thf(zip_derived_cl36, plain, 23.42/3.54 (![X0 : a > $o]: 23.42/3.54 ((('#sk1' @ ('#sk11' @ X0) @ ('#sk25' @ X0)) != (X0 @ ('#sk25' @ X0))) 23.42/3.54 | ~ (X0 @ '#sk2') 23.42/3.54 | ~ (((!!) @ (^[Y0 : a > $o]: 23.42/3.54 (((((((!!) @ (^[Y1 : a]: 23.42/3.54 (((Y0 @ Y1) => 23.42/3.54 (((!!) @ (^[Y2 : a]: 23.42/3.54 ((('#sk1' @ Y1 @ 23.42/3.54 Y2) <=> (Y0 @ Y2))))))))))) & 23.42/3.54 (Y0 @ '#sk2') & (((??) @ (^[Y1 : a]: (Y0 @ Y1)))))) => 23.42/3.54 (((Y0) = (X0)))))))))), 23.42/3.54 inference('condensation', [status(thm)], [zip_derived_cl29])). 23.42/3.54 thf(zip_derived_cl37, plain, 23.42/3.54 (![X0 : a > $o]: 23.42/3.54 (~ (((((((!!) @ (^[Y0 : a]: 23.42/3.54 ((('#sk20' @ X0 @ Y0) => 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 ((('#sk1' @ Y0 @ Y1) <=> ('#sk20' @ 23.42/3.54 X0 @ Y1))))))))))) & 23.42/3.54 ('#sk20' @ X0 @ '#sk2') & 23.42/3.54 (((??) @ (^[Y0 : a]: ('#sk20' @ X0 @ Y0)))))) => 23.42/3.54 ((('#sk20' @ X0) = (X0))))) 23.42/3.54 | ~ (X0 @ '#sk2') 23.42/3.54 | (('#sk1' @ ('#sk11' @ X0) @ ('#sk25' @ X0)) 23.42/3.54 != (X0 @ ('#sk25' @ X0))))), 23.42/3.54 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl36])). 23.42/3.54 thf(zip_derived_cl43, plain, 23.42/3.54 (![X0 : a > $o]: 23.42/3.54 (~ ((('#sk20' @ X0) = (X0))) 23.42/3.54 | (('#sk1' @ ('#sk11' @ X0) @ ('#sk25' @ X0)) 23.42/3.54 != (X0 @ ('#sk25' @ X0))) 23.42/3.54 | ~ (X0 @ '#sk2'))), 23.42/3.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 23.42/3.54 thf(zip_derived_cl50, plain, 23.42/3.54 (![X0 : a > $o]: 23.42/3.54 ((('#sk20' @ X0) != (X0)) 23.42/3.54 | (('#sk1' @ ('#sk11' @ X0) @ ('#sk25' @ X0)) 23.42/3.54 != (X0 @ ('#sk25' @ X0))) 23.42/3.54 | ~ (X0 @ '#sk2'))), 23.42/3.54 inference('simplify nested equalities', [status(thm)], [zip_derived_cl43])). 23.42/3.54 thf(zip_derived_cl51, plain, 23.42/3.54 (![X0 : a > $o]: 23.42/3.54 ((('#sk20' @ X0 @ ('#_fresh_sk125' @ X0)) 23.42/3.54 != (X0 @ ('#_fresh_sk125' @ X0))) 23.42/3.54 | (('#sk1' @ ('#sk11' @ X0) @ ('#sk25' @ X0)) 23.42/3.54 != (X0 @ ('#sk25' @ X0))) 23.42/3.54 | ~ (X0 @ '#sk2'))), 23.42/3.54 inference('neg_ext_simpl', [status(thm)], [zip_derived_cl50])). 23.42/3.54 thf(zip_derived_cl152, plain, 23.42/3.54 (![X0 : a > $o]: 23.42/3.54 (~ ('#sk1' @ ('#sk11' @ X0) @ ('#sk25' @ X0)) 23.42/3.54 | ~ (X0 @ ('#sk25' @ X0)) 23.42/3.54 | ~ (X0 @ '#sk2') 23.42/3.54 | (('#sk20' @ X0 @ ('#_fresh_sk125' @ X0)) 23.42/3.54 != (X0 @ ('#_fresh_sk125' @ X0))))), 23.42/3.54 inference('eq_elim', [status(thm)], [zip_derived_cl51])). 23.42/3.54 thf(zip_derived_cl190, plain, 23.42/3.54 (((('#sk20' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.54 ('#_fresh_sk125' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))))) 23.42/3.54 != ((^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.54 ('#_fresh_sk125' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0)))))) 23.42/3.54 | ~ ((^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.54 ('#sk25' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))))) 23.42/3.54 | ~ ('#sk1' @ 23.42/3.54 ('#sk11' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0)))) @ 23.42/3.54 ('#sk25' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))))))), 23.42/3.54 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl152])). 23.42/3.54 thf(zip_derived_cl195, plain, 23.42/3.54 (((('#sk20' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk125' @ ('#sk1' @ '#sk2'))) 23.42/3.54 != ('#sk1' @ '#sk2' @ ('#_fresh_sk125' @ ('#sk1' @ '#sk2')))) 23.42/3.54 | ~ ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.54 | ~ ('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ 23.42/3.54 ('#sk25' @ ('#sk1' @ '#sk2'))))), 23.42/3.54 inference('ho_norm', [status(thm)], [zip_derived_cl190])). 23.42/3.54 thf(zip_derived_cl11, plain, (![X2 : a]: ('#sk1' @ X2 @ X2)), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 23.42/3.54 thf(zip_derived_cl42, plain, 23.42/3.54 (![X0 : a > $o]: 23.42/3.54 ( (((((!!) @ (^[Y0 : a]: 23.42/3.54 ((('#sk20' @ X0 @ Y0) => 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 ((('#sk1' @ Y0 @ Y1) <=> ('#sk20' @ 23.42/3.54 X0 @ Y1))))))))))) & 23.42/3.54 ('#sk20' @ X0 @ '#sk2') & 23.42/3.54 (((??) @ (^[Y0 : a]: ('#sk20' @ X0 @ Y0)))))) 23.42/3.54 | (('#sk1' @ ('#sk11' @ X0) @ ('#sk25' @ X0)) 23.42/3.54 != (X0 @ ('#sk25' @ X0))) 23.42/3.54 | ~ (X0 @ '#sk2'))), 23.42/3.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 23.42/3.54 thf(zip_derived_cl48, plain, 23.42/3.54 (![X0 : a > $o]: 23.42/3.54 ( ('#sk20' @ X0 @ '#sk2') 23.42/3.54 | ~ (X0 @ '#sk2') 23.42/3.54 | (('#sk1' @ ('#sk11' @ X0) @ ('#sk25' @ X0)) 23.42/3.54 != (X0 @ ('#sk25' @ X0))))), 23.42/3.54 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl42])). 23.42/3.54 thf(zip_derived_cl207, plain, 23.42/3.54 (((('#sk1' @ 23.42/3.54 ('#sk11' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0)))) @ 23.42/3.54 ('#sk25' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))))) 23.42/3.54 != ((^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.54 ('#sk25' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0)))))) 23.42/3.54 | ('#sk20' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.54 '#sk2'))), 23.42/3.54 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl48])). 23.42/3.54 thf(zip_derived_cl211, plain, 23.42/3.54 (((('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ 23.42/3.54 ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.54 != ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2')))) 23.42/3.54 | ('#sk20' @ ('#sk1' @ '#sk2') @ '#sk2'))), 23.42/3.54 inference('ho_norm', [status(thm)], [zip_derived_cl207])). 23.42/3.54 thf(zip_derived_cl213, plain, 23.42/3.54 ((~ ('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ 23.42/3.54 ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.54 | ~ ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.54 | ('#sk20' @ ('#sk1' @ '#sk2') @ '#sk2'))), 23.42/3.54 inference('eq_elim', [status(thm)], [zip_derived_cl211])). 23.42/3.54 thf(zip_derived_cl489, plain, 23.42/3.54 (![X0 : a]: 23.42/3.54 ( ('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ X0) 23.42/3.54 | ~ ('#sk1' @ '#sk2' @ X0))), 23.42/3.54 inference('sup-', [status(thm)], [zip_derived_cl486, zip_derived_cl22])). 23.42/3.54 thf(zip_derived_cl549, plain, 23.42/3.54 (( ('#sk20' @ ('#sk1' @ '#sk2') @ '#sk2') 23.42/3.54 | ~ ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.54 | ~ ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))))), 23.42/3.54 inference('sup+', [status(thm)], [zip_derived_cl213, zip_derived_cl489])). 23.42/3.54 thf(zip_derived_cl561, plain, 23.42/3.54 ((~ ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.54 | ('#sk20' @ ('#sk1' @ '#sk2') @ '#sk2'))), 23.42/3.54 inference('simplify', [status(thm)], [zip_derived_cl549])). 23.42/3.54 thf(zip_derived_cl211, plain, 23.42/3.54 (((('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ 23.42/3.54 ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.54 != ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2')))) 23.42/3.54 | ('#sk20' @ ('#sk1' @ '#sk2') @ '#sk2'))), 23.42/3.54 inference('ho_norm', [status(thm)], [zip_derived_cl207])). 23.42/3.54 thf(zip_derived_cl212, plain, 23.42/3.54 (( ('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ 23.42/3.54 ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.54 | ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.54 | ('#sk20' @ ('#sk1' @ '#sk2') @ '#sk2'))), 23.42/3.54 inference('eq_elim', [status(thm)], [zip_derived_cl211])). 23.42/3.54 thf(zip_derived_cl471, plain, 23.42/3.54 ( ('#sk1' @ '#sk2' @ ('#sk11' @ ('#sk1' @ '#sk2')))), 23.42/3.54 inference('simplify', [status(thm)], [zip_derived_cl450])). 23.42/3.54 thf(zip_derived_cl22, plain, 23.42/3.54 (![X2 : a, X4 : a, X6 : a]: 23.42/3.54 (~ ('#sk1' @ X2 @ X4) | ~ ('#sk1' @ X4 @ X6) | ('#sk1' @ X2 @ X6))), 23.42/3.54 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl19])). 23.42/3.54 thf(zip_derived_cl485, plain, 23.42/3.54 (![X0 : a]: 23.42/3.54 ( ('#sk1' @ '#sk2' @ X0) 23.42/3.54 | ~ ('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ X0))), 23.42/3.54 inference('sup-', [status(thm)], [zip_derived_cl471, zip_derived_cl22])). 23.42/3.54 thf(zip_derived_cl498, plain, 23.42/3.54 (( ('#sk20' @ ('#sk1' @ '#sk2') @ '#sk2') 23.42/3.54 | ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.54 | ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))))), 23.42/3.54 inference('sup-', [status(thm)], [zip_derived_cl212, zip_derived_cl485])). 23.42/3.54 thf(zip_derived_cl509, plain, 23.42/3.54 (( ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.54 | ('#sk20' @ ('#sk1' @ '#sk2') @ '#sk2'))), 23.42/3.54 inference('simplify', [status(thm)], [zip_derived_cl498])). 23.42/3.54 thf(zip_derived_cl571, plain, ( ('#sk20' @ ('#sk1' @ '#sk2') @ '#sk2')), 23.42/3.54 inference('clc', [status(thm)], [zip_derived_cl561, zip_derived_cl509])). 23.42/3.54 thf(zip_derived_cl11, plain, (![X2 : a]: ('#sk1' @ X2 @ X2)), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 23.42/3.54 thf(zip_derived_cl47, plain, 23.42/3.54 (![X0 : a > $o]: 23.42/3.54 ( (((!!) @ (^[Y0 : a]: 23.42/3.54 ((('#sk20' @ X0 @ Y0) => 23.42/3.54 (((!!) @ (^[Y1 : a]: 23.42/3.54 ((('#sk1' @ Y0 @ Y1) <=> ('#sk20' @ X0 @ 23.42/3.54 Y1))))))))))) 23.42/3.54 | ~ (X0 @ '#sk2') 23.42/3.54 | (('#sk1' @ ('#sk11' @ X0) @ ('#sk25' @ X0)) 23.42/3.54 != (X0 @ ('#sk25' @ X0))))), 23.42/3.54 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl42])). 23.42/3.54 thf(zip_derived_cl54, plain, 23.42/3.54 (![X0 : a > $o, X2 : a]: 23.42/3.54 ( ((('#sk20' @ X0 @ X2) => 23.42/3.54 (((!!) @ (^[Y0 : a]: 23.42/3.54 ((('#sk1' @ X2 @ Y0) <=> ('#sk20' @ X0 @ Y0)))))))) 23.42/3.54 | (('#sk1' @ ('#sk11' @ X0) @ ('#sk25' @ X0)) 23.42/3.54 != (X0 @ ('#sk25' @ X0))) 23.42/3.54 | ~ (X0 @ '#sk2'))), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl47])). 23.42/3.54 thf(zip_derived_cl58, plain, 23.42/3.54 (![X0 : a > $o, X2 : a]: 23.42/3.54 (~ ('#sk20' @ X0 @ X2) 23.42/3.54 | (((!!) @ (^[Y0 : a]: 23.42/3.54 ((('#sk1' @ X2 @ Y0) <=> ('#sk20' @ X0 @ Y0)))))) 23.42/3.54 | ~ (X0 @ '#sk2') 23.42/3.54 | (('#sk1' @ ('#sk11' @ X0) @ ('#sk25' @ X0)) 23.42/3.54 != (X0 @ ('#sk25' @ X0))))), 23.42/3.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl54])). 23.42/3.54 thf(zip_derived_cl60, plain, 23.42/3.54 (![X0 : a > $o, X2 : a, X4 : a]: 23.42/3.54 ( ((('#sk1' @ X2 @ X4) <=> ('#sk20' @ X0 @ X4))) 23.42/3.54 | (('#sk1' @ ('#sk11' @ X0) @ ('#sk25' @ X0)) 23.42/3.54 != (X0 @ ('#sk25' @ X0))) 23.42/3.54 | ~ (X0 @ '#sk2') 23.42/3.54 | ~ ('#sk20' @ X0 @ X2))), 23.42/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl58])). 23.42/3.54 thf(zip_derived_cl61, plain, 23.42/3.54 (![X0 : a > $o, X2 : a, X4 : a]: 23.42/3.54 ((('#sk1' @ X2 @ X4) = ('#sk20' @ X0 @ X4)) 23.42/3.54 | (('#sk1' @ ('#sk11' @ X0) @ ('#sk25' @ X0)) 23.42/3.54 != (X0 @ ('#sk25' @ X0))) 23.42/3.54 | ~ (X0 @ '#sk2') 23.42/3.54 | ~ ('#sk20' @ X0 @ X2))), 23.42/3.54 inference('simplify nested equalities', [status(thm)], [zip_derived_cl60])). 23.42/3.54 thf(zip_derived_cl311, plain, 23.42/3.54 (![X0 : a, X1 : a]: 23.42/3.54 (~ ('#sk20' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.54 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.54 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.54 X0) 23.42/3.54 | (('#sk1' @ 23.42/3.54 ('#sk11' @ 23.42/3.54 (^[Y0 : a]: 23.42/3.55 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.55 ((^[Y1 : a]: (Y1)) @ Y0)))) @ 23.42/3.55 ('#sk25' @ 23.42/3.55 (^[Y0 : a]: 23.42/3.55 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.55 ((^[Y1 : a]: (Y1)) @ Y0))))) 23.42/3.55 != ((^[Y0 : a]: 23.42/3.55 ('#sk1' @ 23.42/3.55 ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.55 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.55 ('#sk25' @ 23.42/3.55 (^[Y0 : a]: 23.42/3.55 ('#sk1' @ 23.42/3.55 ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.55 ((^[Y1 : a]: (Y1)) @ Y0)))))) 23.42/3.55 | (('#sk1' @ X0 @ X1) 23.42/3.55 = ('#sk20' @ 23.42/3.55 (^[Y0 : a]: 23.42/3.55 ('#sk1' @ 23.42/3.55 ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.55 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.55 X1)))), 23.42/3.55 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl61])). 23.42/3.55 thf(zip_derived_cl316, plain, 23.42/3.55 (![X0 : a, X1 : a]: 23.42/3.55 (~ ('#sk20' @ ('#sk1' @ '#sk2') @ X0) 23.42/3.55 | (('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ 23.42/3.55 ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.55 != ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2')))) 23.42/3.55 | (('#sk1' @ X0 @ X1) = ('#sk20' @ ('#sk1' @ '#sk2') @ X1)))), 23.42/3.55 inference('ho_norm', [status(thm)], [zip_derived_cl311])). 23.42/3.55 thf(zip_derived_cl418, plain, 23.42/3.55 (![X0 : a, X1 : a]: 23.42/3.55 ( ('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ 23.42/3.55 ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.55 | ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.55 | (('#sk1' @ X0 @ X1) = ('#sk20' @ ('#sk1' @ '#sk2') @ X1)) 23.42/3.55 | ~ ('#sk20' @ ('#sk1' @ '#sk2') @ X0))), 23.42/3.55 inference('eq_elim', [status(thm)], [zip_derived_cl316])). 23.42/3.55 thf(zip_derived_cl485, plain, 23.42/3.55 (![X0 : a]: 23.42/3.55 ( ('#sk1' @ '#sk2' @ X0) 23.42/3.55 | ~ ('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ X0))), 23.42/3.55 inference('sup-', [status(thm)], [zip_derived_cl471, zip_derived_cl22])). 23.42/3.55 thf(zip_derived_cl2233, plain, 23.42/3.55 (![X0 : a, X1 : a]: 23.42/3.55 (~ ('#sk20' @ ('#sk1' @ '#sk2') @ X0) 23.42/3.55 | (('#sk1' @ X0 @ X1) = ('#sk20' @ ('#sk1' @ '#sk2') @ X1)) 23.42/3.55 | ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))))), 23.42/3.55 inference('clc', [status(thm)], [zip_derived_cl418, zip_derived_cl485])). 23.42/3.55 thf(zip_derived_cl489, plain, 23.42/3.55 (![X0 : a]: 23.42/3.55 ( ('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ X0) 23.42/3.55 | ~ ('#sk1' @ '#sk2' @ X0))), 23.42/3.55 inference('sup-', [status(thm)], [zip_derived_cl486, zip_derived_cl22])). 23.42/3.55 thf(zip_derived_cl316, plain, 23.42/3.55 (![X0 : a, X1 : a]: 23.42/3.55 (~ ('#sk20' @ ('#sk1' @ '#sk2') @ X0) 23.42/3.55 | (('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ 23.42/3.55 ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.55 != ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2')))) 23.42/3.55 | (('#sk1' @ X0 @ X1) = ('#sk20' @ ('#sk1' @ '#sk2') @ X1)))), 23.42/3.55 inference('ho_norm', [status(thm)], [zip_derived_cl311])). 23.42/3.55 thf(zip_derived_cl541, plain, 23.42/3.55 (![X0 : a, X1 : a]: 23.42/3.55 (~ ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.55 | ~ ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.55 | (('#sk1' @ X1 @ X0) = ('#sk20' @ ('#sk1' @ '#sk2') @ X0)) 23.42/3.55 | ~ ('#sk20' @ ('#sk1' @ '#sk2') @ X1))), 23.42/3.55 inference('sup-', [status(thm)], [zip_derived_cl489, zip_derived_cl316])). 23.42/3.55 thf(zip_derived_cl562, plain, 23.42/3.55 (![X0 : a, X1 : a]: 23.42/3.55 (~ ('#sk20' @ ('#sk1' @ '#sk2') @ X1) 23.42/3.55 | (('#sk1' @ X1 @ X0) = ('#sk20' @ ('#sk1' @ '#sk2') @ X0)) 23.42/3.55 | ~ ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))))), 23.42/3.55 inference('simplify', [status(thm)], [zip_derived_cl541])). 23.42/3.55 thf(zip_derived_cl2234, plain, 23.42/3.55 (![X0 : a, X1 : a]: 23.42/3.55 ((('#sk1' @ X0 @ X1) = ('#sk20' @ ('#sk1' @ '#sk2') @ X1)) 23.42/3.55 | ~ ('#sk20' @ ('#sk1' @ '#sk2') @ X0))), 23.42/3.55 inference('clc', [status(thm)], [zip_derived_cl2233, zip_derived_cl562])). 23.42/3.55 thf(zip_derived_cl2239, plain, 23.42/3.55 (![X0 : a]: (('#sk1' @ '#sk2' @ X0) = ('#sk20' @ ('#sk1' @ '#sk2') @ X0))), 23.42/3.55 inference('sup-', [status(thm)], [zip_derived_cl571, zip_derived_cl2234])). 23.42/3.55 thf(zip_derived_cl2257, plain, 23.42/3.55 (((('#sk1' @ '#sk2' @ ('#_fresh_sk125' @ ('#sk1' @ '#sk2'))) 23.42/3.55 != ('#sk1' @ '#sk2' @ ('#_fresh_sk125' @ ('#sk1' @ '#sk2')))) 23.42/3.55 | ~ ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.55 | ~ ('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ 23.42/3.55 ('#sk25' @ ('#sk1' @ '#sk2'))))), 23.42/3.55 inference('demod', [status(thm)], [zip_derived_cl195, zip_derived_cl2239])). 23.42/3.55 thf(zip_derived_cl2258, plain, 23.42/3.55 ((~ ('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ 23.42/3.55 ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.55 | ~ ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))))), 23.42/3.55 inference('simplify', [status(thm)], [zip_derived_cl2257])). 23.42/3.55 thf(zip_derived_cl11, plain, (![X2 : a]: ('#sk1' @ X2 @ X2)), 23.42/3.55 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 23.42/3.55 thf(zip_derived_cl51, plain, 23.42/3.55 (![X0 : a > $o]: 23.42/3.55 ((('#sk20' @ X0 @ ('#_fresh_sk125' @ X0)) 23.42/3.55 != (X0 @ ('#_fresh_sk125' @ X0))) 23.42/3.55 | (('#sk1' @ ('#sk11' @ X0) @ ('#sk25' @ X0)) 23.42/3.55 != (X0 @ ('#sk25' @ X0))) 23.42/3.55 | ~ (X0 @ '#sk2'))), 23.42/3.55 inference('neg_ext_simpl', [status(thm)], [zip_derived_cl50])). 23.42/3.55 thf(zip_derived_cl171, plain, 23.42/3.55 (((('#sk1' @ 23.42/3.55 ('#sk11' @ 23.42/3.55 (^[Y0 : a]: 23.42/3.55 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.55 ((^[Y1 : a]: (Y1)) @ Y0)))) @ 23.42/3.55 ('#sk25' @ 23.42/3.55 (^[Y0 : a]: 23.42/3.55 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.55 ((^[Y1 : a]: (Y1)) @ Y0))))) 23.42/3.55 != ((^[Y0 : a]: 23.42/3.55 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.55 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.55 ('#sk25' @ 23.42/3.55 (^[Y0 : a]: 23.42/3.55 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.55 ((^[Y1 : a]: (Y1)) @ Y0)))))) 23.42/3.55 | (('#sk20' @ 23.42/3.55 (^[Y0 : a]: 23.42/3.55 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.55 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.55 ('#_fresh_sk125' @ 23.42/3.55 (^[Y0 : a]: 23.42/3.55 ('#sk1' @ ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.55 ((^[Y1 : a]: (Y1)) @ Y0))))) 23.42/3.55 != ((^[Y0 : a]: 23.42/3.55 ('#sk1' @ 23.42/3.55 ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.55 ((^[Y1 : a]: (Y1)) @ Y0))) @ 23.42/3.55 ('#_fresh_sk125' @ 23.42/3.55 (^[Y0 : a]: 23.42/3.55 ('#sk1' @ 23.42/3.55 ((^[Y1 : a]: ((^[Y2 : a]: ('#sk2')) @ Y1)) @ Y0) @ 23.42/3.55 ((^[Y1 : a]: (Y1)) @ Y0)))))))), 23.42/3.55 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl51])). 23.42/3.55 thf(zip_derived_cl180, plain, 23.42/3.55 (((('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ 23.42/3.55 ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.55 != ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2')))) 23.42/3.55 | (('#sk20' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk125' @ ('#sk1' @ '#sk2'))) 23.42/3.55 != ('#sk1' @ '#sk2' @ ('#_fresh_sk125' @ ('#sk1' @ '#sk2')))))), 23.42/3.55 inference('ho_norm', [status(thm)], [zip_derived_cl171])). 23.42/3.55 thf(zip_derived_cl196, plain, 23.42/3.55 (( ('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ 23.42/3.55 ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.55 | ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))) 23.42/3.55 | (('#sk20' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk125' @ ('#sk1' @ '#sk2'))) 23.42/3.55 != ('#sk1' @ '#sk2' @ ('#_fresh_sk125' @ ('#sk1' @ '#sk2')))))), 23.42/3.55 inference('eq_elim', [status(thm)], [zip_derived_cl180])). 23.42/3.55 thf(zip_derived_cl485, plain, 23.42/3.55 (![X0 : a]: 23.42/3.55 ( ('#sk1' @ '#sk2' @ X0) 23.42/3.55 | ~ ('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ X0))), 23.42/3.55 inference('sup-', [status(thm)], [zip_derived_cl471, zip_derived_cl22])). 23.42/3.55 thf(zip_derived_cl1032, plain, 23.42/3.55 (((('#sk20' @ ('#sk1' @ '#sk2') @ ('#_fresh_sk125' @ ('#sk1' @ '#sk2'))) 23.42/3.55 != ('#sk1' @ '#sk2' @ ('#_fresh_sk125' @ ('#sk1' @ '#sk2')))) 23.42/3.55 | ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))))), 23.42/3.55 inference('clc', [status(thm)], [zip_derived_cl196, zip_derived_cl485])). 23.42/3.55 thf(zip_derived_cl2239, plain, 23.42/3.55 (![X0 : a]: (('#sk1' @ '#sk2' @ X0) = ('#sk20' @ ('#sk1' @ '#sk2') @ X0))), 23.42/3.55 inference('sup-', [status(thm)], [zip_derived_cl571, zip_derived_cl2234])). 23.42/3.55 thf(zip_derived_cl2263, plain, 23.42/3.55 (((('#sk1' @ '#sk2' @ ('#_fresh_sk125' @ ('#sk1' @ '#sk2'))) 23.42/3.55 != ('#sk1' @ '#sk2' @ ('#_fresh_sk125' @ ('#sk1' @ '#sk2')))) 23.42/3.55 | ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2'))))), 23.42/3.55 inference('demod', [status(thm)], 23.42/3.55 [zip_derived_cl1032, zip_derived_cl2239])). 23.42/3.55 thf(zip_derived_cl2264, plain, 23.42/3.55 ( ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2')))), 23.42/3.55 inference('simplify', [status(thm)], [zip_derived_cl2263])). 23.42/3.55 thf(zip_derived_cl2409, plain, 23.42/3.55 (~ ('#sk1' @ ('#sk11' @ ('#sk1' @ '#sk2')) @ 23.42/3.55 ('#sk25' @ ('#sk1' @ '#sk2')))), 23.42/3.55 inference('demod', [status(thm)], 23.42/3.55 [zip_derived_cl2258, zip_derived_cl2264])). 23.42/3.55 thf(zip_derived_cl2410, plain, 23.42/3.55 (~ ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2')))), 23.42/3.55 inference('sup-', [status(thm)], [zip_derived_cl489, zip_derived_cl2409])). 23.42/3.55 thf(zip_derived_cl2264, plain, 23.42/3.55 ( ('#sk1' @ '#sk2' @ ('#sk25' @ ('#sk1' @ '#sk2')))), 23.42/3.55 inference('simplify', [status(thm)], [zip_derived_cl2263])). 23.42/3.55 thf(zip_derived_cl2411, plain, ($false), 23.42/3.55 inference('demod', [status(thm)], 23.42/3.55 [zip_derived_cl2410, zip_derived_cl2264])). 23.42/3.55 23.42/3.55 % SZS output end Refutation 23.42/3.55 23.42/3.55 23.42/3.55 % Terminating... 24.13/3.62 % Runner terminated. 24.13/3.63 % Zipperpin 1.5 exiting 24.13/3.63 EOF