0.13/0.14 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.13/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.VEjeBMG3uu true 0.15/0.37 % Computer : n007.cluster.edu 0.15/0.37 % Model : x86_64 x86_64 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.37 % Memory : 8042.1875MB 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.37 % CPULimit : 960 0.15/0.37 % WCLimit : 120 0.15/0.37 % DateTime : Tue Aug 9 03:05:12 EDT 2022 0.15/0.37 % CPUTime : 0.15/0.37 % Running portfolio for 960 s 0.15/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.15/0.37 % Number of cores: 8 0.22/0.38 % Python version: Python 3.6.8 0.22/0.38 % Running in HO mode 0.46/0.65 % Total configuration time : 828 0.46/0.65 % Estimated wc time : 1656 0.46/0.65 % Estimated cpu time (8 cpus) : 207.0 0.48/0.68 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.48/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.48/0.77 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.48/0.77 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.48/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.48/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.48/0.80 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.50/0.84 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 33.31/7.43 % Solved by lams/20_acsne_simpl.sh. 33.31/7.43 % done 70 iterations in 6.474s 33.31/7.43 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 33.31/7.43 % SZS output start Refutation 33.31/7.43 thf('#sk347_type', type, '#sk347': (($i > $o) > ($i > $o) > $i > $o) > 33.31/7.43 (($i > $o) > ($i > $o) > $i > $o) > $i > $o). 33.31/7.43 thf(p_type, type, p: $o). 33.31/7.43 thf('#sk717_type', type, '#sk717': (($i > $o) > ($i > $o) > $i > $o) > 33.31/7.43 (($i > $o) > ($i > $o) > $i > $o) > $i). 33.31/7.43 thf('#sk171_type', type, '#sk171': (($i > $o) > ($i > $o) > $i > $o) > 33.31/7.43 (($i > $o) > ($i > $o) > $i > $o) > $i > $o). 33.31/7.43 thf('#sk106_type', type, '#sk106': (($i > $o) > ($i > $o) > $i > $o) > 33.31/7.43 (($i > $o) > ($i > $o) > $i > $o) > $i > $o). 33.31/7.43 thf('#form346_type', type, '#form346': (($i > $o) > ($i > $o) > $i > $o) > 33.31/7.43 (($i > $o) > ($i > $o) > $i > $o) > $o). 33.31/7.43 thf('#sk61_type', type, '#sk61': (($i > $o) > ($i > $o) > $i > $o) > 33.31/7.43 (($i > $o) > ($i > $o) > $i > $o) > $i > $o). 33.31/7.43 thf('#sk478_type', type, '#sk478': (($i > $o) > ($i > $o) > $i > $o) > 33.31/7.43 (($i > $o) > ($i > $o) > $i > $o) > $i). 33.31/7.43 thf(cTHM120F_pme, conjecture, 33.31/7.43 (?[Xr_28:( ( $i > $o ) > ( $i > $o ) > $i > $o ), 33.31/7.43 Xr_27:( ( $i > $o ) > ( $i > $o ) > $i > $o )]: 33.31/7.43 ( ( ![Xx:( $i > $o ),Xy:( $i > $o ),Xz:( $i > $o )]: 33.31/7.43 ( ( ( ![Xw_2:$i]: 33.31/7.43 ( ( Xr_28 @ Xy @ Xz @ Xw_2 ) | ( Xr_27 @ Xy @ Xz @ Xw_2 ) ) ) & 33.31/7.43 ( ![Xw_2:$i]: 33.31/7.43 ( ( Xr_27 @ Xx @ Xy @ Xw_2 ) | ( Xr_28 @ Xx @ Xy @ Xw_2 ) ) ) ) => 33.31/7.43 ( ![Xw_2:$i]: 33.31/7.43 ( ( Xr_27 @ Xx @ Xz @ Xw_2 ) | ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) ) ) ) & 33.31/7.43 ( ~( ![Xw_2:$i]: 33.31/7.43 ( ( Xr_28 @ 33.31/7.43 ( ^[Xx:$i]: ( ( p ) | ( ~( p ) ) ) ) @ 33.31/7.43 ( ^[Xx:$i]: ( ( p ) & ( ~( p ) ) ) ) @ Xw_2 ) | 33.31/7.43 ( Xr_27 @ 33.31/7.43 ( ^[Xx:$i]: ( ( p ) | ( ~( p ) ) ) ) @ 33.31/7.43 ( ^[Xx:$i]: ( ( p ) & ( ~( p ) ) ) ) @ Xw_2 ) ) ) ) & 33.31/7.43 ( ![Xx:( $i > $o ),Xw_2:$i]: 33.31/7.43 ( ( Xr_28 @ Xx @ Xx @ Xw_2 ) | ( Xr_27 @ Xx @ Xx @ Xw_2 ) ) ) ))). 33.31/7.43 thf(zf_stmt_0, negated_conjecture, 33.31/7.43 (~( ?[Xr_28:( ( $i > $o ) > ( $i > $o ) > $i > $o ), 33.31/7.43 Xr_27:( ( $i > $o ) > ( $i > $o ) > $i > $o )]: 33.31/7.43 ( ( ![Xx:( $i > $o ),Xy:( $i > $o ),Xz:( $i > $o )]: 33.31/7.43 ( ( ( ![Xw_2:$i]: 33.31/7.43 ( ( Xr_28 @ Xy @ Xz @ Xw_2 ) | ( Xr_27 @ Xy @ Xz @ Xw_2 ) ) ) & 33.31/7.43 ( ![Xw_2:$i]: 33.31/7.43 ( ( Xr_27 @ Xx @ Xy @ Xw_2 ) | ( Xr_28 @ Xx @ Xy @ Xw_2 ) ) ) ) => 33.31/7.43 ( ![Xw_2:$i]: 33.31/7.43 ( ( Xr_27 @ Xx @ Xz @ Xw_2 ) | ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) ) ) ) & 33.31/7.43 ( ~( ![Xw_2:$i]: 33.31/7.43 ( ( Xr_28 @ 33.31/7.43 ( ^[Xx:$i]: ( ( p ) | ( ~( p ) ) ) ) @ 33.31/7.43 ( ^[Xx:$i]: ( ( p ) & ( ~( p ) ) ) ) @ Xw_2 ) | 33.31/7.43 ( Xr_27 @ 33.31/7.43 ( ^[Xx:$i]: ( ( p ) | ( ~( p ) ) ) ) @ 33.31/7.43 ( ^[Xx:$i]: ( ( p ) & ( ~( p ) ) ) ) @ Xw_2 ) ) ) ) & 33.31/7.43 ( ![Xx:( $i > $o ),Xw_2:$i]: 33.31/7.43 ( ( Xr_28 @ Xx @ Xx @ Xw_2 ) | ( Xr_27 @ Xx @ Xx @ Xw_2 ) ) ) ) )), 33.31/7.43 inference('cnf.neg', [status(esa)], [cTHM120F_pme])). 33.31/7.43 thf(zip_derived_cl0, plain, 33.31/7.43 (~ (((??) @ (^[Y0 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (((??) @ (^[Y1 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (((((!!) @ (^[Y2 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y3 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y4 : $i > $o]: 33.31/7.43 (( 33.31/7.43 (( 33.31/7.43 (( 33.31/7.43 (!!) @ ( 33.31/7.43 ^[Y5 : $i]: 33.31/7.43 (( 33.31/7.43 (Y0 @ 33.31/7.43 Y3 @ 33.31/7.43 Y4 @ 33.31/7.43 Y5) | 33.31/7.43 (Y1 @ 33.31/7.43 Y3 @ 33.31/7.43 Y4 @ Y5)))))) & 33.31/7.43 (( 33.31/7.43 (!!) @ ( 33.31/7.43 ^[Y5 : $i]: 33.31/7.43 (( 33.31/7.43 (Y1 @ 33.31/7.43 Y2 @ 33.31/7.43 Y3 @ 33.31/7.43 Y5) | 33.31/7.43 (Y0 @ 33.31/7.43 Y2 @ 33.31/7.43 Y3 @ Y5)))))))) => 33.31/7.43 (( 33.31/7.43 (!!) @ ( 33.31/7.43 ^[Y5 : $i]: 33.31/7.43 (( 33.31/7.43 (Y1 @ 33.31/7.43 Y2 @ 33.31/7.43 Y4 @ 33.31/7.43 Y5) | 33.31/7.43 (Y0 @ 33.31/7.43 Y2 @ 33.31/7.43 Y4 @ Y5))))))))))))))))) & 33.31/7.43 (((~) @ (((!!) @ (^[Y2 : $i]: 33.31/7.43 (((Y0 @ 33.31/7.43 (^[Y3 : $i]: 33.31/7.43 (((p) | (((~) @ p))))) @ 33.31/7.43 (^[Y3 : $i]: 33.31/7.43 (((p) & (((~) @ p))))) @ 33.31/7.43 Y2) | (Y1 @ 33.31/7.43 (^[Y3 : $i]: 33.31/7.43 (((p) | (((~) @ p))))) @ 33.31/7.43 (^[Y3 : $i]: 33.31/7.43 (((p) & (((~) @ p))))) @ 33.31/7.43 Y2)))))))) & 33.31/7.43 (((!!) @ (^[Y2 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y3 : $i]: 33.31/7.43 (((Y0 @ Y2 @ Y2 @ 33.31/7.43 Y3) | (Y1 @ Y2 @ 33.31/7.43 Y2 @ Y3)))))))))))))))))), 33.31/7.43 inference('cnf', [status(esa)], [zf_stmt_0])). 33.31/7.43 thf(zip_derived_cl1, plain, 33.31/7.43 (~ (((??) @ (^[Y0 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (((??) @ (^[Y1 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (((((!!) @ (^[Y2 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y3 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y4 : $i > $o]: 33.31/7.43 (( 33.31/7.43 (( 33.31/7.43 (( 33.31/7.43 (!!) @ ( 33.31/7.43 ^[Y5 : $i]: 33.31/7.43 (( 33.31/7.43 (Y0 @ 33.31/7.43 Y3 @ 33.31/7.43 Y4 @ 33.31/7.43 Y5) | 33.31/7.43 (Y1 @ 33.31/7.43 Y3 @ 33.31/7.43 Y4 @ Y5)))))) & 33.31/7.43 (( 33.31/7.43 (!!) @ ( 33.31/7.43 ^[Y5 : $i]: 33.31/7.43 (( 33.31/7.43 (Y1 @ 33.31/7.43 Y2 @ 33.31/7.43 Y3 @ 33.31/7.43 Y5) | 33.31/7.43 (Y0 @ 33.31/7.43 Y2 @ 33.31/7.43 Y3 @ Y5)))))))) => 33.31/7.43 (( 33.31/7.43 (!!) @ ( 33.31/7.43 ^[Y5 : $i]: 33.31/7.43 (( 33.31/7.43 (Y1 @ 33.31/7.43 Y2 @ 33.31/7.43 Y4 @ 33.31/7.43 Y5) | 33.31/7.43 (Y0 @ 33.31/7.43 Y2 @ 33.31/7.43 Y4 @ Y5))))))))))))))))) & 33.31/7.43 (((~) @ (((!!) @ (^[Y2 : $i]: 33.31/7.43 (((Y0 @ 33.31/7.43 (^[Y3 : $i]: ($true)) @ 33.31/7.43 (^[Y3 : $i]: ($false)) @ 33.31/7.43 Y2) | (Y1 @ 33.31/7.43 (^[Y3 : $i]: ($true)) @ 33.31/7.43 (^[Y3 : $i]: ($false)) @ 33.31/7.43 Y2)))))))) & 33.31/7.43 (((!!) @ (^[Y2 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y3 : $i]: 33.31/7.43 (((Y0 @ Y2 @ Y2 @ 33.31/7.43 Y3) | (Y1 @ Y2 @ 33.31/7.43 Y2 @ Y3)))))))))))))))))), 33.31/7.43 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl0])). 33.31/7.43 thf(zip_derived_cl2, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 ~ (((??) @ (^[Y0 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (((((!!) @ (^[Y1 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y2 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y3 : $i > $o]: 33.31/7.43 (((((((!!) @ ( 33.31/7.43 ^[Y4 : $i]: 33.31/7.43 (( 33.31/7.43 (X2 @ 33.31/7.43 Y2 @ 33.31/7.43 Y3 @ 33.31/7.43 Y4) | 33.31/7.43 (Y0 @ 33.31/7.43 Y2 @ 33.31/7.43 Y3 @ Y4)))))) & 33.31/7.43 (((!!) @ ( 33.31/7.43 ^[Y4 : $i]: 33.31/7.43 (( 33.31/7.43 (Y0 @ 33.31/7.43 Y1 @ 33.31/7.43 Y2 @ 33.31/7.43 Y4) | 33.31/7.43 (X2 @ 33.31/7.43 Y1 @ 33.31/7.43 Y2 @ Y4)))))))) => 33.31/7.43 (((!!) @ ( 33.31/7.43 ^[Y4 : $i]: 33.31/7.43 (((Y0 @ 33.31/7.43 Y1 @ Y3 @ 33.31/7.43 Y4) | 33.31/7.43 (X2 @ 33.31/7.43 Y1 @ Y3 @ 33.31/7.43 Y4))))))))))))))))) & 33.31/7.43 (((~) @ (((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X2 @ (^[Y2 : $i]: ($true)) @ 33.31/7.43 (^[Y2 : $i]: ($false)) @ Y1) | 33.31/7.43 (Y0 @ (^[Y2 : $i]: ($true)) @ 33.31/7.43 (^[Y2 : $i]: ($false)) @ Y1)))))))) & 33.31/7.43 (((!!) @ (^[Y1 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y2 : $i]: 33.31/7.43 (((X2 @ Y1 @ Y1 @ Y2) | (Y0 @ 33.31/7.43 Y1 @ Y1 @ Y2))))))))))))))), 33.31/7.43 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 33.31/7.43 thf(zip_derived_cl3, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 ~ (((((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y1 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y2 : $i > $o]: 33.31/7.43 (((((((!!) @ (^[Y3 : $i]: 33.31/7.43 (((X2 @ Y1 @ 33.31/7.43 Y2 @ Y3) | 33.31/7.43 (X4 @ Y1 @ 33.31/7.43 Y2 @ Y3)))))) & 33.31/7.43 (((!!) @ (^[Y3 : $i]: 33.31/7.43 (((X4 @ Y0 @ 33.31/7.43 Y1 @ Y3) | 33.31/7.43 (X2 @ Y0 @ 33.31/7.43 Y1 @ Y3)))))))) => 33.31/7.43 (((!!) @ (^[Y3 : $i]: 33.31/7.43 (((X4 @ Y0 @ 33.31/7.43 Y2 @ Y3) | 33.31/7.43 (X2 @ Y0 @ 33.31/7.43 Y2 @ Y3))))))))))))))))) & 33.31/7.43 (((~) @ (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ (^[Y1 : $i]: ($true)) @ 33.31/7.43 (^[Y1 : $i]: ($false)) @ Y0) | (X4 @ 33.31/7.43 (^[Y1 : $i]: ($true)) @ 33.31/7.43 (^[Y1 : $i]: ($false)) @ Y0)))))))) & 33.31/7.43 (((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X2 @ Y0 @ Y0 @ Y1) | (X4 @ Y0 @ Y0 @ 33.31/7.43 Y1)))))))))))), 33.31/7.43 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 33.31/7.43 thf(zip_derived_cl4, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (~ (((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y1 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y2 : $i > $o]: 33.31/7.43 (((((((!!) @ (^[Y3 : $i]: 33.31/7.43 (((X2 @ Y1 @ 33.31/7.43 Y2 @ Y3) | 33.31/7.43 (X4 @ Y1 @ 33.31/7.43 Y2 @ Y3)))))) & 33.31/7.43 (((!!) @ (^[Y3 : $i]: 33.31/7.43 (((X4 @ Y0 @ 33.31/7.43 Y1 @ Y3) | 33.31/7.43 (X2 @ Y0 @ 33.31/7.43 Y1 @ Y3)))))))) => 33.31/7.43 (((!!) @ (^[Y3 : $i]: 33.31/7.43 (((X4 @ Y0 @ 33.31/7.43 Y2 @ Y3) | 33.31/7.43 (X2 @ Y0 @ 33.31/7.43 Y2 @ Y3))))))))))))))))) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ (^[Y1 : $i]: ($true)) @ 33.31/7.43 (^[Y1 : $i]: ($false)) @ Y0) | (X4 @ 33.31/7.43 (^[Y1 : $i]: ($true)) @ (^[Y1 : $i]: ($false)) @ Y0)))))) 33.31/7.43 | ~ (((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X2 @ Y0 @ Y0 @ Y1) | (X4 @ Y0 @ Y0 @ 33.31/7.43 Y1))))))))))), 33.31/7.43 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])). 33.31/7.43 thf(zip_derived_cl5, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (~ (((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y1 : $i > $o]: 33.31/7.43 (((((((!!) @ (^[Y2 : $i]: 33.31/7.43 (((X2 @ Y0 @ Y1 @ Y2) | 33.31/7.43 (X4 @ Y0 @ Y1 @ Y2)))))) & 33.31/7.43 (((!!) @ (^[Y2 : $i]: 33.31/7.43 (((X4 @ 33.31/7.43 ('#sk61' @ X2 @ X4) @ 33.31/7.43 Y0 @ Y2) | (X2 @ 33.31/7.43 ('#sk61' @ X2 @ X4) @ 33.31/7.43 Y0 @ Y2)))))))) => 33.31/7.43 (((!!) @ (^[Y2 : $i]: 33.31/7.43 (((X4 @ 33.31/7.43 ('#sk61' @ X2 @ X4) @ Y1 @ 33.31/7.43 Y2) | (X2 @ 33.31/7.43 ('#sk61' @ X2 @ X4) @ Y1 @ 33.31/7.43 Y2)))))))))))))) 33.31/7.43 | ~ (((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X2 @ Y0 @ Y0 @ Y1) | (X4 @ Y0 @ Y0 @ 33.31/7.43 Y1))))))))) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ (^[Y1 : $i]: ($true)) @ 33.31/7.43 (^[Y1 : $i]: ($false)) @ Y0) | (X4 @ 33.31/7.43 (^[Y1 : $i]: ($true)) @ (^[Y1 : $i]: ($false)) @ Y0)))))))), 33.31/7.43 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl4])). 33.31/7.43 thf(zip_derived_cl6, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (~ (((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((((((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X2 @ ('#sk106' @ X2 @ X4) @ Y0 @ 33.31/7.43 Y1) | (X4 @ ('#sk106' @ X2 @ X4) @ 33.31/7.43 Y0 @ Y1)))))) & 33.31/7.43 (((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X4 @ ('#sk61' @ X2 @ X4) @ 33.31/7.43 ('#sk106' @ X2 @ X4) @ Y1) | (X2 @ 33.31/7.43 ('#sk61' @ X2 @ X4) @ 33.31/7.43 ('#sk106' @ X2 @ X4) @ Y1)))))))) => 33.31/7.43 (((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X4 @ ('#sk61' @ X2 @ X4) @ Y0 @ Y1) | 33.31/7.43 (X2 @ ('#sk61' @ X2 @ X4) @ Y0 @ Y1))))))))))) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ (^[Y1 : $i]: ($true)) @ 33.31/7.43 (^[Y1 : $i]: ($false)) @ Y0) | (X4 @ 33.31/7.43 (^[Y1 : $i]: ($true)) @ (^[Y1 : $i]: ($false)) @ Y0)))))) 33.31/7.43 | ~ (((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X2 @ Y0 @ Y0 @ Y1) | (X4 @ Y0 @ Y0 @ 33.31/7.43 Y1))))))))))), 33.31/7.43 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl5])). 33.31/7.43 thf(zip_derived_cl7, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (~ (((((((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ ('#sk106' @ X2 @ X4) @ 33.31/7.43 ('#sk171' @ X2 @ X4) @ Y0) | (X4 @ 33.31/7.43 ('#sk106' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ Y0)))))) & 33.31/7.43 (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X4 @ ('#sk61' @ X2 @ X4) @ 33.31/7.43 ('#sk106' @ X2 @ X4) @ Y0) | (X2 @ 33.31/7.43 ('#sk61' @ X2 @ X4) @ ('#sk106' @ X2 @ X4) @ Y0)))))))) => 33.31/7.43 (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X4 @ ('#sk61' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ 33.31/7.43 Y0) | (X2 @ ('#sk61' @ X2 @ X4) @ 33.31/7.43 ('#sk171' @ X2 @ X4) @ Y0)))))))) 33.31/7.43 | ~ (((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X2 @ Y0 @ Y0 @ Y1) | (X4 @ Y0 @ Y0 @ 33.31/7.43 Y1))))))))) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ (^[Y1 : $i]: ($true)) @ 33.31/7.43 (^[Y1 : $i]: ($false)) @ Y0) | (X4 @ 33.31/7.43 (^[Y1 : $i]: ($true)) @ (^[Y1 : $i]: ($false)) @ Y0)))))))), 33.31/7.43 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 33.31/7.43 thf(zip_derived_cl9, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (~ (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X4 @ ('#sk61' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ 33.31/7.43 Y0) | (X2 @ ('#sk61' @ X2 @ X4) @ 33.31/7.43 ('#sk171' @ X2 @ X4) @ Y0)))))) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ (^[Y1 : $i]: ($true)) @ 33.31/7.43 (^[Y1 : $i]: ($false)) @ Y0) | (X4 @ 33.31/7.43 (^[Y1 : $i]: ($true)) @ (^[Y1 : $i]: ($false)) @ Y0)))))) 33.31/7.43 | ~ (((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X2 @ Y0 @ Y0 @ Y1) | (X4 @ Y0 @ Y0 @ 33.31/7.43 Y1))))))))))), 33.31/7.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 33.31/7.43 thf(zip_derived_cl12, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 ( ('#form346' @ X2 @ X4) 33.31/7.43 | ~ (((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X2 @ Y0 @ Y0 @ Y1) | (X4 @ Y0 @ Y0 @ 33.31/7.43 Y1))))))))))), 33.31/7.43 define([status(thm)])). 33.31/7.43 thf(zip_derived_cl13, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (~ (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ ('#sk347' @ X2 @ X4) @ ('#sk347' @ X2 @ X4) @ 33.31/7.43 Y0) | (X4 @ ('#sk347' @ X2 @ X4) @ 33.31/7.43 ('#sk347' @ X2 @ X4) @ Y0)))))) 33.31/7.43 | ('#form346' @ X2 @ X4))), 33.31/7.43 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 33.31/7.43 thf(zip_derived_cl18, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (~ (((X2 @ ('#sk347' @ X2 @ X4) @ ('#sk347' @ X2 @ X4) @ 33.31/7.43 ('#sk478' @ X2 @ X4)) | (X4 @ ('#sk347' @ X2 @ X4) @ 33.31/7.43 ('#sk347' @ X2 @ X4) @ ('#sk478' @ X2 @ X4)))) 33.31/7.43 | ('#form346' @ X2 @ X4))), 33.31/7.43 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl13])). 33.31/7.43 thf(zip_derived_cl22, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (~ (X2 @ ('#sk347' @ X2 @ X4) @ ('#sk347' @ X2 @ X4) @ 33.31/7.43 ('#sk478' @ X2 @ X4)) 33.31/7.43 | ('#form346' @ X2 @ X4))), 33.31/7.43 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl18])). 33.31/7.43 thf(zip_derived_cl9, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (~ (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X4 @ ('#sk61' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ 33.31/7.43 Y0) | (X2 @ ('#sk61' @ X2 @ X4) @ 33.31/7.43 ('#sk171' @ X2 @ X4) @ Y0)))))) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ (^[Y1 : $i]: ($true)) @ 33.31/7.43 (^[Y1 : $i]: ($false)) @ Y0) | (X4 @ 33.31/7.43 (^[Y1 : $i]: ($true)) @ (^[Y1 : $i]: ($false)) @ Y0)))))) 33.31/7.43 | ~ (((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X2 @ Y0 @ Y0 @ Y1) | (X4 @ Y0 @ Y0 @ 33.31/7.43 Y1))))))))))), 33.31/7.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 33.31/7.43 thf(zip_derived_cl12, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 ( ('#form346' @ X2 @ X4) 33.31/7.43 | ~ (((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X2 @ Y0 @ Y0 @ Y1) | (X4 @ Y0 @ Y0 @ 33.31/7.43 Y1))))))))))), 33.31/7.43 define([status(thm)])). 33.31/7.43 thf(zip_derived_cl14, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (~ ('#form346' @ X2 @ X4) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ (^[Y1 : $i]: ($true)) @ 33.31/7.43 (^[Y1 : $i]: ($false)) @ Y0) | (X4 @ 33.31/7.43 (^[Y1 : $i]: ($true)) @ (^[Y1 : $i]: ($false)) @ Y0)))))) 33.31/7.43 | ~ (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X4 @ ('#sk61' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ 33.31/7.43 Y0) | (X2 @ ('#sk61' @ X2 @ X4) @ 33.31/7.43 ('#sk171' @ X2 @ X4) @ Y0)))))))), 33.31/7.43 inference('renaming', [status(thm)], [zip_derived_cl9, zip_derived_cl12])). 33.31/7.43 thf(zip_derived_cl17, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o, X6 : $i]: 33.31/7.43 ( (((X2 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) | 33.31/7.43 (X4 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6))) 33.31/7.43 | ~ (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X4 @ ('#sk61' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ 33.31/7.43 Y0) | (X2 @ ('#sk61' @ X2 @ X4) @ 33.31/7.43 ('#sk171' @ X2 @ X4) @ Y0)))))) 33.31/7.43 | ~ ('#form346' @ X2 @ X4))), 33.31/7.43 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 33.31/7.43 thf(zip_derived_cl21, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o, X6 : $i]: 33.31/7.43 ( (X2 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) 33.31/7.43 | (X4 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) 33.31/7.43 | ~ ('#form346' @ X2 @ X4) 33.31/7.43 | ~ (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X4 @ ('#sk61' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ 33.31/7.43 Y0) | (X2 @ ('#sk61' @ X2 @ X4) @ 33.31/7.43 ('#sk171' @ X2 @ X4) @ Y0)))))))), 33.31/7.43 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl17])). 33.31/7.43 thf(zip_derived_cl26, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o, X6 : $i]: 33.31/7.43 (~ (((X4 @ ('#sk61' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ 33.31/7.43 ('#sk717' @ X2 @ X4)) | (X2 @ ('#sk61' @ X2 @ X4) @ 33.31/7.43 ('#sk171' @ X2 @ X4) @ ('#sk717' @ X2 @ X4)))) 33.31/7.43 | ~ ('#form346' @ X2 @ X4) 33.31/7.43 | (X4 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) 33.31/7.43 | (X2 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6))), 33.31/7.43 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl21])). 33.31/7.43 thf(zip_derived_cl30, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o, X6 : $i]: 33.31/7.43 (~ (X2 @ ('#sk61' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ 33.31/7.43 ('#sk717' @ X2 @ X4)) 33.31/7.43 | (X2 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) 33.31/7.43 | (X4 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) 33.31/7.43 | ~ ('#form346' @ X2 @ X4))), 33.31/7.43 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl26])). 33.31/7.43 thf(zip_derived_cl610, plain, 33.31/7.43 (![X0 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X1 : ($i > $o) > ($i > $o) > $i > $o, X2 : $i]: 33.31/7.43 (~ (X1 @ ('#sk347' @ X1 @ X0) @ ('#sk347' @ X1 @ X0) @ 33.31/7.43 ('#sk478' @ X1 @ X0)) 33.31/7.43 | (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) 33.31/7.43 | (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) 33.31/7.43 | ~ (X1 @ ('#sk61' @ X1 @ X0) @ ('#sk171' @ X1 @ X0) @ 33.31/7.43 ('#sk717' @ X1 @ X0)))), 33.31/7.43 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl30])). 33.31/7.43 thf(zip_derived_cl22, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (~ (X2 @ ('#sk347' @ X2 @ X4) @ ('#sk347' @ X2 @ X4) @ 33.31/7.43 ('#sk478' @ X2 @ X4)) 33.31/7.43 | ('#form346' @ X2 @ X4))), 33.31/7.43 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl18])). 33.31/7.43 thf(zip_derived_cl8, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 ( (((((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ ('#sk106' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ 33.31/7.43 Y0) | (X4 @ ('#sk106' @ X2 @ X4) @ 33.31/7.43 ('#sk171' @ X2 @ X4) @ Y0)))))) & 33.31/7.43 (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X4 @ ('#sk61' @ X2 @ X4) @ ('#sk106' @ X2 @ X4) @ 33.31/7.43 Y0) | (X2 @ ('#sk61' @ X2 @ X4) @ 33.31/7.43 ('#sk106' @ X2 @ X4) @ Y0)))))))) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ (^[Y1 : $i]: ($true)) @ 33.31/7.43 (^[Y1 : $i]: ($false)) @ Y0) | (X4 @ 33.31/7.43 (^[Y1 : $i]: ($true)) @ (^[Y1 : $i]: ($false)) @ Y0)))))) 33.31/7.43 | ~ (((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X2 @ Y0 @ Y0 @ Y1) | (X4 @ Y0 @ Y0 @ 33.31/7.43 Y1))))))))))), 33.31/7.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 33.31/7.43 thf(zip_derived_cl10, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 ( (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ ('#sk106' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ 33.31/7.43 Y0) | (X4 @ ('#sk106' @ X2 @ X4) @ 33.31/7.43 ('#sk171' @ X2 @ X4) @ Y0)))))) 33.31/7.43 | ~ (((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X2 @ Y0 @ Y0 @ Y1) | (X4 @ Y0 @ Y0 @ 33.31/7.43 Y1))))))))) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ (^[Y1 : $i]: ($true)) @ 33.31/7.43 (^[Y1 : $i]: ($false)) @ Y0) | (X4 @ 33.31/7.43 (^[Y1 : $i]: ($true)) @ (^[Y1 : $i]: ($false)) @ Y0)))))))), 33.31/7.43 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl8])). 33.31/7.43 thf(zip_derived_cl12, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 ( ('#form346' @ X2 @ X4) 33.31/7.43 | ~ (((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X2 @ Y0 @ Y0 @ Y1) | (X4 @ Y0 @ Y0 @ 33.31/7.43 Y1))))))))))), 33.31/7.43 define([status(thm)])). 33.31/7.43 thf(zip_derived_cl15, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (~ ('#form346' @ X2 @ X4) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ (^[Y1 : $i]: ($true)) @ 33.31/7.43 (^[Y1 : $i]: ($false)) @ Y0) | (X4 @ 33.31/7.43 (^[Y1 : $i]: ($true)) @ (^[Y1 : $i]: ($false)) @ Y0)))))) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ ('#sk106' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ 33.31/7.43 Y0) | (X4 @ ('#sk106' @ X2 @ X4) @ 33.31/7.43 ('#sk171' @ X2 @ X4) @ Y0)))))))), 33.31/7.43 inference('renaming', [status(thm)], [zip_derived_cl10, zip_derived_cl12])). 33.31/7.43 thf(zip_derived_cl19, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o, X6 : $i]: 33.31/7.43 ( (((X2 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) | 33.31/7.43 (X4 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6))) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ ('#sk106' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ 33.31/7.43 Y0) | (X4 @ ('#sk106' @ X2 @ X4) @ 33.31/7.43 ('#sk171' @ X2 @ X4) @ Y0)))))) 33.31/7.43 | ~ ('#form346' @ X2 @ X4))), 33.31/7.43 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 33.31/7.43 thf(zip_derived_cl24, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o, X6 : $i]: 33.31/7.43 ( (X2 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) 33.31/7.43 | (X4 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) 33.31/7.43 | ~ ('#form346' @ X2 @ X4) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ ('#sk106' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ 33.31/7.43 Y0) | (X4 @ ('#sk106' @ X2 @ X4) @ 33.31/7.43 ('#sk171' @ X2 @ X4) @ Y0)))))))), 33.31/7.43 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 33.31/7.43 thf(zip_derived_cl27, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o, X6 : $i, X8 : $i]: 33.31/7.43 ( (((X2 @ ('#sk106' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ X8) | (X4 @ 33.31/7.43 ('#sk106' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ X8))) 33.31/7.43 | ~ ('#form346' @ X2 @ X4) 33.31/7.43 | (X4 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) 33.31/7.43 | (X2 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6))), 33.31/7.43 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl24])). 33.31/7.43 thf(zip_derived_cl31, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o, X6 : $i, X8 : $i]: 33.31/7.43 ( (X2 @ ('#sk106' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ X8) 33.31/7.43 | (X4 @ ('#sk106' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ X8) 33.31/7.43 | (X2 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) 33.31/7.43 | (X4 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) 33.31/7.43 | ~ ('#form346' @ X2 @ X4))), 33.31/7.43 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl27])). 33.31/7.43 thf(zip_derived_cl31, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o, X6 : $i, X8 : $i]: 33.31/7.43 ( (X2 @ ('#sk106' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ X8) 33.31/7.43 | (X4 @ ('#sk106' @ X2 @ X4) @ ('#sk171' @ X2 @ X4) @ X8) 33.31/7.43 | (X2 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) 33.31/7.43 | (X4 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) 33.31/7.43 | ~ ('#form346' @ X2 @ X4))), 33.31/7.43 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl27])). 33.31/7.43 thf(zip_derived_cl1097, plain, 33.31/7.43 (![X0 : $o, X1 : ($i > $o) > ($i > $o) > $i > $i, 33.31/7.43 X2 : ($i > $o) > ($i > $o) > $i > $i > $o, 33.31/7.43 X3 : ($i > $o) > ($i > $o) > $i > $i > $o, X4 : $i, 33.31/7.43 X5 : ($i > $o) > ($i > $o) > $i > $i, 33.31/7.43 X6 : ($i > $o) > ($i > $o) > $i > $i > $o, 33.31/7.43 X7 : ($i > $o) > ($i > $o) > $i > $i > $o, X8 : $i]: 33.31/7.43 (~ ('#form346' @ 33.31/7.43 (^[Y0 : $i > $o,Y1 : $i > $o,Y2 : $i]: 33.31/7.43 ((^[Y3 : $i > $o,Y4 : $i > $o,Y5 : $i,Y6 : $i > $o, 33.31/7.43 Y7 : $i > $o,Y8 : $i]: 33.31/7.43 (X0)) @ 33.31/7.43 (X7 @ Y0 @ Y1 @ Y2) @ (X6 @ Y0 @ Y1 @ Y2) @ 33.31/7.43 (X5 @ Y0 @ Y1 @ Y2) @ Y0 @ Y1 @ Y2)) @ 33.31/7.43 (^[Y0 : $i > $o,Y1 : $i > $o,Y2 : $i]: 33.31/7.43 ((^[Y3 : $i > $o,Y4 : $i > $o,Y5 : $i,Y6 : $i > $o, 33.31/7.43 Y7 : $i > $o,Y8 : $i]: 33.31/7.43 (X0)) @ 33.31/7.43 Y0 @ Y1 @ Y2 @ (X3 @ Y0 @ Y1 @ Y2) @ (X2 @ Y0 @ Y1 @ Y2) @ 33.31/7.43 (X1 @ Y0 @ Y1 @ Y2)))) 33.31/7.43 | ((^[Y0 : $i > $o,Y1 : $i > $o,Y2 : $i]: 33.31/7.43 ((^[Y3 : $i > $o,Y4 : $i > $o,Y5 : $i,Y6 : $i > $o, 33.31/7.43 Y7 : $i > $o,Y8 : $i]: 33.31/7.43 (X0)) @ 33.31/7.43 (X7 @ Y0 @ Y1 @ Y2) @ (X6 @ Y0 @ Y1 @ Y2) @ 33.31/7.43 (X5 @ Y0 @ Y1 @ Y2) @ Y0 @ Y1 @ Y2)) @ 33.31/7.43 (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) 33.31/7.43 | ((^[Y0 : $i > $o,Y1 : $i > $o,Y2 : $i]: 33.31/7.43 ((^[Y3 : $i > $o,Y4 : $i > $o,Y5 : $i,Y6 : $i > $o, 33.31/7.43 Y7 : $i > $o,Y8 : $i]: 33.31/7.43 (X0)) @ 33.31/7.43 Y0 @ Y1 @ Y2 @ (X3 @ Y0 @ Y1 @ Y2) @ (X2 @ Y0 @ Y1 @ Y2) @ 33.31/7.43 (X1 @ Y0 @ Y1 @ Y2))) @ 33.31/7.43 ('#sk106' @ 33.31/7.43 (^[Y0 : $i > $o,Y1 : $i > $o,Y2 : $i]: 33.31/7.43 ((^[Y3 : $i > $o,Y4 : $i > $o,Y5 : $i,Y6 : $i > $o, 33.31/7.43 Y7 : $i > $o,Y8 : $i]: 33.31/7.43 (X0)) @ 33.31/7.43 (X7 @ Y0 @ Y1 @ Y2) @ (X6 @ Y0 @ Y1 @ Y2) @ 33.31/7.43 (X5 @ Y0 @ Y1 @ Y2) @ Y0 @ Y1 @ Y2)) @ 33.31/7.43 (^[Y0 : $i > $o,Y1 : $i > $o,Y2 : $i]: 33.31/7.43 ((^[Y3 : $i > $o,Y4 : $i > $o,Y5 : $i,Y6 : $i > $o, 33.31/7.43 Y7 : $i > $o,Y8 : $i]: 33.31/7.43 (X0)) @ 33.31/7.43 Y0 @ Y1 @ Y2 @ (X3 @ Y0 @ Y1 @ Y2) @ (X2 @ Y0 @ Y1 @ Y2) @ 33.31/7.43 (X1 @ Y0 @ Y1 @ Y2)))) @ 33.31/7.43 ('#sk171' @ 33.31/7.43 (^[Y0 : $i > $o,Y1 : $i > $o,Y2 : $i]: 33.31/7.43 ((^[Y3 : $i > $o,Y4 : $i > $o,Y5 : $i,Y6 : $i > $o, 33.31/7.43 Y7 : $i > $o,Y8 : $i]: 33.31/7.43 (X0)) @ 33.31/7.43 (X7 @ Y0 @ Y1 @ Y2) @ (X6 @ Y0 @ Y1 @ Y2) @ 33.31/7.43 (X5 @ Y0 @ Y1 @ Y2) @ Y0 @ Y1 @ Y2)) @ 33.31/7.43 (^[Y0 : $i > $o,Y1 : $i > $o,Y2 : $i]: 33.31/7.43 ((^[Y3 : $i > $o,Y4 : $i > $o,Y5 : $i,Y6 : $i > $o, 33.31/7.43 Y7 : $i > $o,Y8 : $i]: 33.31/7.43 (X0)) @ 33.31/7.43 Y0 @ Y1 @ Y2 @ (X3 @ Y0 @ Y1 @ Y2) @ (X2 @ Y0 @ Y1 @ Y2) @ 33.31/7.43 (X1 @ Y0 @ Y1 @ Y2)))) @ 33.31/7.43 X8) 33.31/7.43 | ((^[Y0 : $i > $o,Y1 : $i > $o,Y2 : $i]: 33.31/7.43 ((^[Y3 : $i > $o,Y4 : $i > $o,Y5 : $i,Y6 : $i > $o, 33.31/7.43 Y7 : $i > $o,Y8 : $i]: 33.31/7.43 (X0)) @ 33.31/7.43 (X7 @ Y0 @ Y1 @ Y2) @ (X6 @ Y0 @ Y1 @ Y2) @ 33.31/7.43 (X5 @ Y0 @ Y1 @ Y2) @ Y0 @ Y1 @ Y2)) @ 33.31/7.43 ('#sk106' @ 33.31/7.43 (^[Y0 : $i > $o,Y1 : $i > $o,Y2 : $i]: 33.31/7.43 ((^[Y3 : $i > $o,Y4 : $i > $o,Y5 : $i,Y6 : $i > $o, 33.31/7.43 Y7 : $i > $o,Y8 : $i]: 33.31/7.43 (X0)) @ 33.31/7.43 (X7 @ Y0 @ Y1 @ Y2) @ (X6 @ Y0 @ Y1 @ Y2) @ 33.31/7.43 (X5 @ Y0 @ Y1 @ Y2) @ Y0 @ Y1 @ Y2)) @ 33.31/7.43 (^[Y0 : $i > $o,Y1 : $i > $o,Y2 : $i]: 33.31/7.43 ((^[Y3 : $i > $o,Y4 : $i > $o,Y5 : $i,Y6 : $i > $o, 33.31/7.43 Y7 : $i > $o,Y8 : $i]: 33.31/7.43 (X0)) @ 33.31/7.43 Y0 @ Y1 @ Y2 @ (X3 @ Y0 @ Y1 @ Y2) @ (X2 @ Y0 @ Y1 @ Y2) @ 33.31/7.43 (X1 @ Y0 @ Y1 @ Y2)))) @ 33.31/7.43 ('#sk171' @ 33.31/7.43 (^[Y0 : $i > $o,Y1 : $i > $o,Y2 : $i]: 33.31/7.43 ((^[Y3 : $i > $o,Y4 : $i > $o,Y5 : $i,Y6 : $i > $o, 33.31/7.43 Y7 : $i > $o,Y8 : $i]: 33.31/7.43 (X0)) @ 33.31/7.43 (X7 @ Y0 @ Y1 @ Y2) @ (X6 @ Y0 @ Y1 @ Y2) @ 33.31/7.43 (X5 @ Y0 @ Y1 @ Y2) @ Y0 @ Y1 @ Y2)) @ 33.31/7.43 (^[Y0 : $i > $o,Y1 : $i > $o,Y2 : $i]: 33.31/7.43 ((^[Y3 : $i > $o,Y4 : $i > $o,Y5 : $i,Y6 : $i > $o, 33.31/7.43 Y7 : $i > $o,Y8 : $i]: 33.31/7.43 (X0)) @ 33.31/7.43 Y0 @ Y1 @ Y2 @ (X3 @ Y0 @ Y1 @ Y2) @ (X2 @ Y0 @ Y1 @ Y2) @ 33.31/7.43 (X1 @ Y0 @ Y1 @ Y2)))) @ 33.31/7.43 X8))), 33.31/7.43 inference('eq_fact', [status(thm)], [zip_derived_cl31])). 33.31/7.43 thf(zip_derived_cl1146, plain, 33.31/7.43 (![X0 : $o]: 33.31/7.43 (~ ('#form346' @ (^[Y0 : $i > $o,Y1 : $i > $o,Y2 : $i]: (X0)) @ 33.31/7.43 (^[Y0 : $i > $o,Y1 : $i > $o,Y2 : $i]: (X0))) 33.31/7.43 | (X0) 33.31/7.43 | (X0) 33.31/7.43 | (X0))), 33.31/7.43 inference('ho_norm', [status(thm)], [zip_derived_cl1097])). 33.31/7.43 thf(zip_derived_cl1147, plain, 33.31/7.43 (![X0 : $o]: 33.31/7.43 ( (X0) 33.31/7.43 | ~ ('#form346' @ (^[Y0 : $i > $o,Y1 : $i > $o,Y2 : $i]: (X0)) @ 33.31/7.43 (^[Y0 : $i > $o,Y1 : $i > $o,Y2 : $i]: (X0))))), 33.31/7.43 inference('simplify', [status(thm)], [zip_derived_cl1146])). 33.31/7.43 thf(zip_derived_cl11, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 ( (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X4 @ ('#sk61' @ X2 @ X4) @ ('#sk106' @ X2 @ X4) @ 33.31/7.43 Y0) | (X2 @ ('#sk61' @ X2 @ X4) @ 33.31/7.43 ('#sk106' @ X2 @ X4) @ Y0)))))) 33.31/7.43 | ~ (((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X2 @ Y0 @ Y0 @ Y1) | (X4 @ Y0 @ Y0 @ 33.31/7.43 Y1))))))))) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ (^[Y1 : $i]: ($true)) @ 33.31/7.43 (^[Y1 : $i]: ($false)) @ Y0) | (X4 @ 33.31/7.43 (^[Y1 : $i]: ($true)) @ (^[Y1 : $i]: ($false)) @ Y0)))))))), 33.31/7.43 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl8])). 33.31/7.43 thf(zip_derived_cl12, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 ( ('#form346' @ X2 @ X4) 33.31/7.43 | ~ (((!!) @ (^[Y0 : $i > $o]: 33.31/7.43 (((!!) @ (^[Y1 : $i]: 33.31/7.43 (((X2 @ Y0 @ Y0 @ Y1) | (X4 @ Y0 @ Y0 @ 33.31/7.43 Y1))))))))))), 33.31/7.43 define([status(thm)])). 33.31/7.43 thf(zip_derived_cl16, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (~ ('#form346' @ X2 @ X4) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X2 @ (^[Y1 : $i]: ($true)) @ 33.31/7.43 (^[Y1 : $i]: ($false)) @ Y0) | (X4 @ 33.31/7.43 (^[Y1 : $i]: ($true)) @ (^[Y1 : $i]: ($false)) @ Y0)))))) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X4 @ ('#sk61' @ X2 @ X4) @ ('#sk106' @ X2 @ X4) @ 33.31/7.43 Y0) | (X2 @ ('#sk61' @ X2 @ X4) @ 33.31/7.43 ('#sk106' @ X2 @ X4) @ Y0)))))))), 33.31/7.43 inference('renaming', [status(thm)], [zip_derived_cl11, zip_derived_cl12])). 33.31/7.43 thf(zip_derived_cl20, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o, X6 : $i]: 33.31/7.43 ( (((X2 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) | 33.31/7.43 (X4 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6))) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X4 @ ('#sk61' @ X2 @ X4) @ ('#sk106' @ X2 @ X4) @ 33.31/7.43 Y0) | (X2 @ ('#sk61' @ X2 @ X4) @ 33.31/7.43 ('#sk106' @ X2 @ X4) @ Y0)))))) 33.31/7.43 | ~ ('#form346' @ X2 @ X4))), 33.31/7.43 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 33.31/7.43 thf(zip_derived_cl25, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o, X6 : $i]: 33.31/7.43 ( (X2 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) 33.31/7.43 | (X4 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) 33.31/7.43 | ~ ('#form346' @ X2 @ X4) 33.31/7.43 | (((!!) @ (^[Y0 : $i]: 33.31/7.43 (((X4 @ ('#sk61' @ X2 @ X4) @ ('#sk106' @ X2 @ X4) @ 33.31/7.43 Y0) | (X2 @ ('#sk61' @ X2 @ X4) @ 33.31/7.43 ('#sk106' @ X2 @ X4) @ Y0)))))))), 33.31/7.43 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 33.31/7.43 thf(zip_derived_cl28, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o, X6 : $i, X8 : $i]: 33.31/7.43 ( (((X4 @ ('#sk61' @ X2 @ X4) @ ('#sk106' @ X2 @ X4) @ X8) | (X2 @ 33.31/7.43 ('#sk61' @ X2 @ X4) @ ('#sk106' @ X2 @ X4) @ X8))) 33.31/7.43 | ~ ('#form346' @ X2 @ X4) 33.31/7.43 | (X4 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) 33.31/7.43 | (X2 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6))), 33.31/7.43 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl25])). 33.31/7.43 thf(zip_derived_cl32, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o, X6 : $i, X8 : $i]: 33.31/7.43 ( (X4 @ ('#sk61' @ X2 @ X4) @ ('#sk106' @ X2 @ X4) @ X8) 33.31/7.43 | (X2 @ ('#sk61' @ X2 @ X4) @ ('#sk106' @ X2 @ X4) @ X8) 33.31/7.43 | (X2 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) 33.31/7.43 | (X4 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X6) 33.31/7.43 | ~ ('#form346' @ X2 @ X4))), 33.31/7.43 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl28])). 33.31/7.43 thf(zip_derived_cl23, plain, 33.31/7.43 (![X2 : ($i > $o) > ($i > $o) > $i > $o, 33.31/7.43 X4 : ($i > $o) > ($i > $o) > $i > $o]: 33.31/7.43 (~ (X4 @ ('#sk347' @ X2 @ X4) @ ('#sk347' @ X2 @ X4) @ 33.31/7.43 ('#sk478' @ X2 @ X4)) 33.31/7.43 | ('#form346' @ X2 @ X4))), 33.31/7.43 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl18])). 33.31/7.43 thf(zip_derived_cl3737, plain, ($false), 33.31/7.43 inference('eprover', [status(thm)], 33.31/7.43 [zip_derived_cl610, zip_derived_cl22, zip_derived_cl31, 33.31/7.43 zip_derived_cl1147, zip_derived_cl32, zip_derived_cl23])). 33.31/7.43 33.31/7.43 % SZS output end Refutation 33.31/7.43 33.31/7.43 33.31/7.43 % Terminating... 33.82/7.59 % Runner terminated. 33.82/7.60 % Zipperpin 1.5 exiting 33.82/7.62 EOF