0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.AsQCpRwUU7 true 0.14/0.35 % Computer : n007.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 1440 0.14/0.35 % WCLimit : 180 0.14/0.35 % DateTime : Thu Jul 4 10:20:39 EDT 2024 0.14/0.35 % CPUTime : 0.14/0.35 % Running portfolio for 1440 s 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.14/0.35 % Number of cores: 8 0.14/0.35 % Python version: Python 3.6.8 0.14/0.35 % Running in HO mode 0.55/0.67 % Total configuration time : 828 0.55/0.67 % Estimated wc time : 1656 0.55/0.67 % Estimated cpu time (8 cpus) : 207.0 0.55/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.55/0.73 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.55/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.55/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.55/0.77 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.56/0.79 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.56/0.85 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 237.55/30.54 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s 477.86/60.87 % /export/starexec/sandbox/solver/bin/lams/15_old_s4.sh running for 30s 560.37/71.52 % /export/starexec/sandbox/solver/bin/lams/15_lifting3.sh running for 30s 633.36/80.65 % /export/starexec/sandbox/solver/bin/lams/33_shallow_sine.sh running for 66s 634.03/80.82 % /export/starexec/sandbox/solver/bin/lams/40_e_lift.sh running for 80s 634.03/80.82 % /export/starexec/sandbox/solver/bin/lams/15_lifting1.sh running for 30s 680.35/86.64 % /export/starexec/sandbox/solver/bin/lams/8_new_cnf.sh running for 16s 680.35/86.72 % /export/starexec/sandbox/solver/bin/lams/10_e_short2.sh running for 20s 712.00/90.68 % /export/starexec/sandbox/solver/bin/lams/8_add_var_l_av.sh running for 16s 712.00/90.74 % /export/starexec/sandbox/solver/bin/lams/8_new_sh_or.sh running for 16s 713.81/91.11 % /export/starexec/sandbox/solver/bin/lams/30_old_zip1.sh running for 36s 796.58/101.56 % /export/starexec/sandbox/solver/bin/lams/10_shallow_lift.sh running for 30s 836.10/106.54 % /export/starexec/sandbox/solver/bin/lams/15_lcnf_noform.sh running for 30s 836.81/106.72 % /export/starexec/sandbox/solver/bin/lams/8_sh.eqenc2.sh running for 10s 836.81/106.74 % /export/starexec/sandbox/solver/bin/lams/8_cmb.lcnf4.sh running for 10s 869.88/110.88 % /export/starexec/sandbox/solver/bin/lams/8_new_l_av.sh running for 24s 880.82/112.32 % Solved by lams/8_new_l_av.sh. 880.82/112.32 % done 854 iterations in 1.316s 880.82/112.32 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 880.82/112.32 % SZS output start Refutation 880.82/112.32 thf(del_type, type, del: $tType). 880.82/112.32 thf(c_2Eoption_2EOPTION__JOIN_type, type, c_2Eoption_2EOPTION__JOIN: del > $i). 880.82/112.32 thf(mem_type, type, mem: $i > del > $o). 880.82/112.32 thf('#sk8_type', type, '#sk8': del > del > $i > $i > $i > $i). 880.82/112.32 thf(c_2Eoption_2ENONE_type, type, c_2Eoption_2ENONE: del > $i). 880.82/112.32 thf('#sk7_type', type, '#sk7': del > del > $i > $i > $i > $i). 880.82/112.32 thf(c_2Eoption_2EIS__NONE_type, type, c_2Eoption_2EIS__NONE: del > $i). 880.82/112.32 thf('#sk4_type', type, '#sk4': $i). 880.82/112.32 thf(p_type, type, p: $i > $o). 880.82/112.32 thf('#sk6_type', type, '#sk6': $i). 880.82/112.32 thf(c_2Eoption_2EIS__SOME_type, type, c_2Eoption_2EIS__SOME: del > $i). 880.82/112.32 thf(c_2Eoption_2EOPTION__MAP_type, type, c_2Eoption_2EOPTION__MAP: del > del > $i). 880.82/112.32 thf('#sk3_type', type, '#sk3': del). 880.82/112.32 thf(ty_2Eoption_2Eoption_type, type, ty_2Eoption_2Eoption: del > del). 880.82/112.32 thf(ap_type, type, ap: $i > $i > $i). 880.82/112.32 thf('#sk5_type', type, '#sk5': $i). 880.82/112.32 thf(arr_type, type, arr: del > del > del). 880.82/112.32 thf(bool_type, type, bool: del). 880.82/112.32 thf(c_2Eoption_2ETHE_type, type, c_2Eoption_2ETHE: del > $i). 880.82/112.32 thf(c_2Eoption_2EOPTREL_type, type, c_2Eoption_2EOPTREL: del > del > $i). 880.82/112.32 thf(c_2Eoption_2ESOME_type, type, c_2Eoption_2ESOME: del > $i). 880.82/112.32 thf(c_2Eoption_2Eoption__CASE_type, type, c_2Eoption_2Eoption__CASE: 880.82/112.32 del > del > $i). 880.82/112.32 thf(conj_thm_2Equotient__option_2EOPTION__REL__def, conjecture, 880.82/112.32 (![A_27a:del,V0R:$i]: 880.82/112.32 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) => 880.82/112.32 ( ![V1x:$i]: 880.82/112.32 ( ( mem @ V1x @ A_27a ) => 880.82/112.32 ( ![V2y:$i]: 880.82/112.32 ( ( mem @ V2y @ A_27a ) => 880.82/112.32 ( ( ( p @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27a ) @ V0R ) @ 880.82/112.32 ( c_2Eoption_2ENONE @ A_27a ) ) @ 880.82/112.32 ( c_2Eoption_2ENONE @ A_27a ) ) ) <=> 880.82/112.32 ( $true ) ) & 880.82/112.32 ( ( $false ) <=> 880.82/112.32 ( p @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27a ) @ V0R ) @ 880.82/112.32 ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) ) @ 880.82/112.32 ( c_2Eoption_2ENONE @ A_27a ) ) ) ) & 880.82/112.32 ( ( $false ) <=> 880.82/112.32 ( p @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27a ) @ V0R ) @ 880.82/112.32 ( c_2Eoption_2ENONE @ A_27a ) ) @ 880.82/112.32 ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2y ) ) ) ) & 880.82/112.32 ( ( p @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27a ) @ V0R ) @ 880.82/112.32 ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) ) @ 880.82/112.32 ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2y ) ) ) <=> 880.82/112.32 ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) ) ) ) ) ) ) ) ))). 880.82/112.32 thf(zf_stmt_0, negated_conjecture, 880.82/112.32 (~( ![A_27a:del,V0R:$i]: 880.82/112.32 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) => 880.82/112.32 ( ![V1x:$i]: 880.82/112.32 ( ( mem @ V1x @ A_27a ) => 880.82/112.32 ( ![V2y:$i]: 880.82/112.32 ( ( mem @ V2y @ A_27a ) => 880.82/112.32 ( ( ( p @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ 880.82/112.32 ( c_2Eoption_2EOPTREL @ A_27a @ A_27a ) @ V0R ) @ 880.82/112.32 ( c_2Eoption_2ENONE @ A_27a ) ) @ 880.82/112.32 ( c_2Eoption_2ENONE @ A_27a ) ) ) <=> 880.82/112.32 ( $true ) ) & 880.82/112.32 ( ( $false ) <=> 880.82/112.32 ( p @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ 880.82/112.32 ( c_2Eoption_2EOPTREL @ A_27a @ A_27a ) @ V0R ) @ 880.82/112.32 ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) ) @ 880.82/112.32 ( c_2Eoption_2ENONE @ A_27a ) ) ) ) & 880.82/112.32 ( ( $false ) <=> 880.82/112.32 ( p @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ 880.82/112.32 ( c_2Eoption_2EOPTREL @ A_27a @ A_27a ) @ V0R ) @ 880.82/112.32 ( c_2Eoption_2ENONE @ A_27a ) ) @ 880.82/112.32 ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2y ) ) ) ) & 880.82/112.32 ( ( p @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ 880.82/112.32 ( c_2Eoption_2EOPTREL @ A_27a @ A_27a ) @ V0R ) @ 880.82/112.32 ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) ) @ 880.82/112.32 ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2y ) ) ) <=> 880.82/112.32 ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) ) ) ) ) ) ) ) ) )), 880.82/112.32 inference('cnf.neg', [status(esa)], 880.82/112.32 [conj_thm_2Equotient__option_2EOPTION__REL__def])). 880.82/112.32 thf(zip_derived_cl21, plain, 880.82/112.32 (~ (((!!) @ (^[Y0 : del]: 880.82/112.32 (((!!) @ (^[Y1 : $i]: 880.82/112.32 (((mem @ Y1 @ 880.82/112.32 (arr @ Y0 @ (arr @ Y0 @ bool))) => 880.82/112.32 (((!!) @ (^[Y2 : $i]: 880.82/112.32 (((mem @ Y2 @ Y0) => 880.82/112.32 (((!!) @ (^[Y3 : $i]: 880.82/112.32 (((mem @ Y3 @ 880.82/112.32 Y0) => 880.82/112.32 (((((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2EOPTREL @ 880.82/112.32 Y0 @ Y0) @ 880.82/112.32 Y1) @ 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 Y0)) @ 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 Y0))) <=> 880.82/112.32 ($true))) & 880.82/112.32 ((($false) <=> 880.82/112.32 (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2EOPTREL @ 880.82/112.32 Y0 @ Y0) @ 880.82/112.32 Y1) @ 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2ESOME @ 880.82/112.32 Y0) @ Y2)) @ 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 Y0))))) & 880.82/112.32 ((($false) <=> 880.82/112.32 (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2EOPTREL @ 880.82/112.32 Y0 @ Y0) @ 880.82/112.32 Y1) @ 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 Y0)) @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ 880.82/112.32 Y0) @ 880.82/112.32 Y3))))) & 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2EOPTREL @ 880.82/112.32 Y0 @ Y0) @ 880.82/112.32 Y1) @ 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2ESOME @ 880.82/112.32 Y0) @ Y2)) @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ 880.82/112.32 Y0) @ 880.82/112.32 Y3))) <=> 880.82/112.32 (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ Y1 @ 880.82/112.32 Y2) @ 880.82/112.32 Y3))))))))))))))))))))))))), 880.82/112.32 inference('cnf', [status(esa)], [zf_stmt_0])). 880.82/112.32 thf(zip_derived_cl253, plain, 880.82/112.32 (~ (((!!) @ (^[Y0 : del]: 880.82/112.32 (((!!) @ (^[Y1 : $i]: 880.82/112.32 (((mem @ Y1 @ 880.82/112.32 (arr @ Y0 @ (arr @ Y0 @ bool))) => 880.82/112.32 (((!!) @ (^[Y2 : $i]: 880.82/112.32 (((mem @ Y2 @ Y0) => 880.82/112.32 (((!!) @ (^[Y3 : $i]: 880.82/112.32 (((mem @ Y3 @ 880.82/112.32 Y0) => 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ 880.82/112.32 Y0 @ Y0) @ 880.82/112.32 Y1) @ 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 Y0)) @ 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 Y0))) & 880.82/112.32 (((~) @ ( 880.82/112.32 p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2EOPTREL @ 880.82/112.32 Y0 @ Y0) @ 880.82/112.32 Y1) @ 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2ESOME @ 880.82/112.32 Y0) @ Y2)) @ 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 Y0))))) & 880.82/112.32 (((~) @ ( 880.82/112.32 p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2EOPTREL @ 880.82/112.32 Y0 @ Y0) @ 880.82/112.32 Y1) @ 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 Y0)) @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ 880.82/112.32 Y0) @ 880.82/112.32 Y3))))) & 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2EOPTREL @ 880.82/112.32 Y0 @ Y0) @ 880.82/112.32 Y1) @ 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2ESOME @ 880.82/112.32 Y0) @ Y2)) @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ 880.82/112.32 Y0) @ 880.82/112.32 Y3))) <=> 880.82/112.32 (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ Y1 @ 880.82/112.32 Y2) @ 880.82/112.32 Y3))))))))))))))))))))))))), 880.82/112.32 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl21])). 880.82/112.32 thf(zip_derived_cl254, plain, 880.82/112.32 (~ (((!!) @ (^[Y0 : $i]: 880.82/112.32 (((mem @ Y0 @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool))) => 880.82/112.32 (((!!) @ (^[Y1 : $i]: 880.82/112.32 (((mem @ Y1 @ '#sk3') => 880.82/112.32 (((!!) @ (^[Y2 : $i]: 880.82/112.32 (((mem @ Y2 @ '#sk3') => 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ 880.82/112.32 '#sk3' @ '#sk3') @ 880.82/112.32 Y0) @ 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 '#sk3')) @ 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 '#sk3'))) & 880.82/112.32 (((~) @ (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ 880.82/112.32 '#sk3' @ 880.82/112.32 '#sk3') @ 880.82/112.32 Y0) @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ 880.82/112.32 '#sk3') @ 880.82/112.32 Y1)) @ 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 '#sk3'))))) & 880.82/112.32 (((~) @ (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ 880.82/112.32 '#sk3' @ 880.82/112.32 '#sk3') @ 880.82/112.32 Y0) @ 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 '#sk3')) @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ 880.82/112.32 '#sk3') @ 880.82/112.32 Y2))))) & 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ 880.82/112.32 '#sk3' @ '#sk3') @ 880.82/112.32 Y0) @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ 880.82/112.32 '#sk3') @ 880.82/112.32 Y1)) @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ 880.82/112.32 '#sk3') @ 880.82/112.32 Y2))) <=> 880.82/112.32 (p @ 880.82/112.32 (ap @ (ap @ Y0 @ Y1) @ 880.82/112.32 Y2)))))))))))))))))))))), 880.82/112.32 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl253])). 880.82/112.32 thf(zip_derived_cl255, plain, 880.82/112.32 (~ (((mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool))) => 880.82/112.32 (((!!) @ (^[Y0 : $i]: 880.82/112.32 (((mem @ Y0 @ '#sk3') => 880.82/112.32 (((!!) @ (^[Y1 : $i]: 880.82/112.32 (((mem @ Y1 @ '#sk3') => 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ '#sk3' @ 880.82/112.32 '#sk3') @ 880.82/112.32 '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3'))) & 880.82/112.32 (((~) @ (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ 880.82/112.32 '#sk3' @ '#sk3') @ 880.82/112.32 '#sk4') @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ 880.82/112.32 '#sk3') @ 880.82/112.32 Y0)) @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3'))))) & 880.82/112.32 (((~) @ (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ 880.82/112.32 '#sk3' @ '#sk3') @ 880.82/112.32 '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.32 Y1))))) & 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ '#sk3' @ 880.82/112.32 '#sk3') @ 880.82/112.32 '#sk4') @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ '#sk3') @ Y0)) @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ '#sk3') @ Y1))) <=> 880.82/112.32 (p @ (ap @ (ap @ '#sk4' @ Y0) @ Y1))))))))))))))))))), 880.82/112.32 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl254])). 880.82/112.32 thf(zip_derived_cl257, plain, 880.82/112.32 (~ (((!!) @ (^[Y0 : $i]: 880.82/112.32 (((mem @ Y0 @ '#sk3') => 880.82/112.32 (((!!) @ (^[Y1 : $i]: 880.82/112.32 (((mem @ Y1 @ '#sk3') => 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ '#sk3' @ 880.82/112.32 '#sk3') @ 880.82/112.32 '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3'))) & 880.82/112.32 (((~) @ (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ 880.82/112.32 '#sk3' @ '#sk3') @ 880.82/112.32 '#sk4') @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.32 Y0)) @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3'))))) & 880.82/112.32 (((~) @ (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ 880.82/112.32 '#sk3' @ '#sk3') @ 880.82/112.32 '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.32 Y1))))) & 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ '#sk3' @ 880.82/112.32 '#sk3') @ 880.82/112.32 '#sk4') @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ '#sk3') @ Y0)) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.32 Y1))) <=> 880.82/112.32 (p @ (ap @ (ap @ '#sk4' @ Y0) @ Y1))))))))))))))))), 880.82/112.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl255])). 880.82/112.32 thf(zip_derived_cl258, plain, 880.82/112.32 (~ (((mem @ '#sk5' @ '#sk3') => 880.82/112.32 (((!!) @ (^[Y0 : $i]: 880.82/112.32 (((mem @ Y0 @ '#sk3') => 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ 880.82/112.32 '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3'))) & 880.82/112.32 (((~) @ (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ 880.82/112.32 '#sk4') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.32 '#sk5')) @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3'))))) & 880.82/112.32 (((~) @ (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ 880.82/112.32 '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ Y0))))) & 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ 880.82/112.32 '#sk4') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ Y0))) <=> 880.82/112.32 (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ Y0)))))))))))))), 880.82/112.32 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl257])). 880.82/112.32 thf(zip_derived_cl260, plain, 880.82/112.32 (~ (((!!) @ (^[Y0 : $i]: 880.82/112.32 (((mem @ Y0 @ '#sk3') => 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ 880.82/112.32 '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3'))) & 880.82/112.32 (((~) @ (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ 880.82/112.32 '#sk4') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3'))))) & 880.82/112.32 (((~) @ (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ 880.82/112.32 '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ Y0))))) & 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ 880.82/112.32 '#sk4') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ Y0))) <=> 880.82/112.32 (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ Y0)))))))))))), 880.82/112.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl258])). 880.82/112.32 thf(zip_derived_cl261, plain, 880.82/112.32 (~ (((mem @ '#sk6' @ '#sk3') => 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3'))) & 880.82/112.32 (((~) @ (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3'))))) & 880.82/112.32 (((~) @ (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))) & 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) <=> 880.82/112.32 (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6'))))))))), 880.82/112.32 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl260])). 880.82/112.32 thf(zip_derived_cl263, plain, 880.82/112.32 (~ (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3'))) & 880.82/112.32 (((~) @ (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3'))))) & 880.82/112.32 (((~) @ (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))) & 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) <=> 880.82/112.32 (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6'))))))), 880.82/112.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl261])). 880.82/112.32 thf(zip_derived_cl264, plain, 880.82/112.32 ((~ (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3'))) 880.82/112.32 | (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3'))) 880.82/112.32 | (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.32 | ~ (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) <=> 880.82/112.32 (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.32 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl263])). 880.82/112.32 thf(zip_derived_cl265, plain, 880.82/112.32 ((~ (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3'))) 880.82/112.32 | (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3'))) 880.82/112.32 | (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.32 | ((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.32 != (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6'))))), 880.82/112.32 inference('simplify nested equalities', [status(thm)], 880.82/112.32 [zip_derived_cl264])). 880.82/112.32 thf(zip_derived_cl266, plain, 880.82/112.32 ((((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.32 != (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))) 880.82/112.32 <= (~ 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.32 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.32 inference('split', [status(esa)], [zip_derived_cl265])). 880.82/112.32 thf(zip_derived_cl281, plain, 880.82/112.32 (((~ (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.32 | ~ (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))) 880.82/112.32 <= (~ 880.82/112.32 (((p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.32 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.32 inference('eq_elim', [status(thm)], [zip_derived_cl266])). 880.82/112.32 thf(zip_derived_cl282, plain, 880.82/112.32 ((~ (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6'))) 880.82/112.32 <= (~ ( (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6'))))), 880.82/112.32 inference('split', [status(esa)], [zip_derived_cl281])). 880.82/112.32 thf(zip_derived_cl267, plain, 880.82/112.32 (( (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.32 <= (( (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.32 inference('split', [status(esa)], [zip_derived_cl265])). 880.82/112.32 thf(ax_thm_2Eoption_2EOPTREL__def, axiom, 880.82/112.32 (![A_27a:del,A_27b:del,V0R:$i]: 880.82/112.32 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) => 880.82/112.32 ( ![V1x:$i]: 880.82/112.32 ( ( mem @ V1x @ ( ty_2Eoption_2Eoption @ A_27a ) ) => 880.82/112.32 ( ![V2y:$i]: 880.82/112.32 ( ( mem @ V2y @ ( ty_2Eoption_2Eoption @ A_27b ) ) => 880.82/112.32 ( ( ( ?[V3x0:$i]: 880.82/112.32 ( ( ?[V4y0:$i]: 880.82/112.32 ( ( mem @ V4y0 @ A_27b ) & 880.82/112.32 ( ( V1x ) = 880.82/112.32 ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3x0 ) ) & 880.82/112.32 ( ( V2y ) = 880.82/112.32 ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V4y0 ) ) & 880.82/112.32 ( p @ ( ap @ ( ap @ V0R @ V3x0 ) @ V4y0 ) ) ) ) & 880.82/112.32 ( mem @ V3x0 @ A_27a ) ) ) | 880.82/112.32 ( ( ( V2y ) = ( c_2Eoption_2ENONE @ A_27b ) ) & 880.82/112.32 ( ( V1x ) = ( c_2Eoption_2ENONE @ A_27a ) ) ) ) <=> 880.82/112.32 ( p @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ 880.82/112.32 ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27b ) @ V0R ) @ 880.82/112.32 V1x ) @ 880.82/112.32 V2y ) ) ) ) ) ) ) ))). 880.82/112.32 thf(zip_derived_cl19, plain, 880.82/112.32 ( (((!!) @ (^[Y0 : del]: 880.82/112.32 (((!!) @ (^[Y1 : del]: 880.82/112.32 (((!!) @ (^[Y2 : $i]: 880.82/112.32 (((mem @ Y2 @ 880.82/112.32 (arr @ Y0 @ (arr @ Y1 @ bool))) => 880.82/112.32 (((!!) @ (^[Y3 : $i]: 880.82/112.32 (((mem @ Y3 @ 880.82/112.32 (ty_2Eoption_2Eoption @ 880.82/112.32 Y0)) => 880.82/112.32 (((!!) @ (^[Y4 : $i]: 880.82/112.32 (( 880.82/112.32 (mem @ 880.82/112.32 Y4 @ 880.82/112.32 ( 880.82/112.32 ty_2Eoption_2Eoption @ 880.82/112.32 Y1)) => 880.82/112.32 (( 880.82/112.32 (( 880.82/112.32 (( 880.82/112.32 (??) @ ( 880.82/112.32 ^[Y5 : $i]: 880.82/112.32 (( 880.82/112.32 (( 880.82/112.32 (??) @ ( 880.82/112.32 ^[Y6 : $i]: 880.82/112.32 (( 880.82/112.32 ( 880.82/112.32 mem @ 880.82/112.32 Y6 @ Y1) & 880.82/112.32 ( 880.82/112.32 ( 880.82/112.32 (Y3) = 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2ESOME @ 880.82/112.32 Y0) @ Y5))) & 880.82/112.32 ( 880.82/112.32 ( 880.82/112.32 (Y4) = 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2ESOME @ 880.82/112.32 Y1) @ Y6))) & 880.82/112.32 ( 880.82/112.32 p @ 880.82/112.32 ( 880.82/112.32 ap @ 880.82/112.32 ( 880.82/112.32 ap @ 880.82/112.32 Y2 @ Y5) @ 880.82/112.32 Y6))))))) & 880.82/112.32 (mem @ 880.82/112.32 Y5 @ Y0)))))) | 880.82/112.32 (( 880.82/112.32 (( 880.82/112.32 (Y4) = 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 Y1))) & 880.82/112.32 (( 880.82/112.32 (Y3) = 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 Y0))))))) <=> 880.82/112.32 (p @ 880.82/112.32 ( 880.82/112.32 ap @ 880.82/112.32 ( 880.82/112.32 ap @ 880.82/112.32 ( 880.82/112.32 ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2EOPTREL @ 880.82/112.32 Y0 @ Y1) @ 880.82/112.32 Y2) @ Y3) @ 880.82/112.32 Y4)))))))))))))))))))))))))), 880.82/112.32 inference('cnf', [status(esa)], [ax_thm_2Eoption_2EOPTREL__def])). 880.82/112.32 thf(zip_derived_cl225, plain, 880.82/112.32 (![X2 : del]: 880.82/112.32 (((!!) @ (^[Y0 : del]: 880.82/112.32 (((!!) @ (^[Y1 : $i]: 880.82/112.32 (((mem @ Y1 @ 880.82/112.32 (arr @ X2 @ (arr @ Y0 @ bool))) => 880.82/112.32 (((!!) @ (^[Y2 : $i]: 880.82/112.32 (((mem @ Y2 @ 880.82/112.32 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.32 (((!!) @ (^[Y3 : $i]: 880.82/112.32 (((mem @ Y3 @ 880.82/112.32 (ty_2Eoption_2Eoption @ 880.82/112.32 Y0)) => 880.82/112.32 (((((((??) @ ( 880.82/112.32 ^[Y4 : $i]: 880.82/112.32 (( 880.82/112.32 (( 880.82/112.32 (??) @ ( 880.82/112.32 ^[Y5 : $i]: 880.82/112.32 (( 880.82/112.32 ( 880.82/112.32 mem @ 880.82/112.32 Y5 @ Y0) & 880.82/112.32 ( 880.82/112.32 ( 880.82/112.32 (Y2) = 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2ESOME @ 880.82/112.32 X2) @ Y4))) & 880.82/112.32 ( 880.82/112.32 ( 880.82/112.32 (Y3) = 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2ESOME @ 880.82/112.32 Y0) @ Y5))) & 880.82/112.32 ( 880.82/112.32 p @ 880.82/112.32 ( 880.82/112.32 ap @ 880.82/112.32 ( 880.82/112.32 ap @ 880.82/112.32 Y1 @ Y4) @ 880.82/112.32 Y5))))))) & 880.82/112.32 (mem @ 880.82/112.32 Y4 @ X2)))))) | 880.82/112.32 (((( 880.82/112.32 (Y3) = 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 Y0))) & 880.82/112.32 (( 880.82/112.32 (Y2) = 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 X2))))))) <=> 880.82/112.32 (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ 880.82/112.32 X2 @ Y0) @ 880.82/112.32 Y1) @ 880.82/112.32 Y2) @ 880.82/112.32 Y3))))))))))))))))))))))), 880.82/112.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 880.82/112.32 thf(zip_derived_cl226, plain, 880.82/112.32 (![X2 : del, X4 : del]: 880.82/112.32 (((!!) @ (^[Y0 : $i]: 880.82/112.32 (((mem @ Y0 @ (arr @ X2 @ (arr @ X4 @ bool))) => 880.82/112.32 (((!!) @ (^[Y1 : $i]: 880.82/112.32 (((mem @ Y1 @ 880.82/112.32 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.32 (((!!) @ (^[Y2 : $i]: 880.82/112.32 (((mem @ Y2 @ 880.82/112.32 (ty_2Eoption_2Eoption @ X4)) => 880.82/112.32 (((((((??) @ (^[Y3 : $i]: 880.82/112.32 (((( 880.82/112.32 (??) @ ( 880.82/112.32 ^[Y4 : $i]: 880.82/112.32 (( 880.82/112.32 ( 880.82/112.32 mem @ 880.82/112.32 Y4 @ X4) & 880.82/112.32 ( 880.82/112.32 ( 880.82/112.32 (Y1) = 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2ESOME @ 880.82/112.32 X2) @ Y3))) & 880.82/112.32 ( 880.82/112.32 ( 880.82/112.32 (Y2) = 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2ESOME @ 880.82/112.32 X4) @ Y4))) & 880.82/112.32 ( 880.82/112.32 p @ 880.82/112.32 ( 880.82/112.32 ap @ 880.82/112.32 ( 880.82/112.32 ap @ 880.82/112.32 Y0 @ Y3) @ 880.82/112.32 Y4))))))) & 880.82/112.32 (mem @ 880.82/112.32 Y3 @ X2)))))) | 880.82/112.32 (((((Y2) = 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 X4))) & 880.82/112.32 (((Y1) = 880.82/112.32 (c_2Eoption_2ENONE @ 880.82/112.32 X2))))))) <=> 880.82/112.32 (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ 880.82/112.32 X2 @ X4) @ 880.82/112.32 Y0) @ 880.82/112.32 Y1) @ 880.82/112.32 Y2)))))))))))))))))))), 880.82/112.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl225])). 880.82/112.32 thf(zip_derived_cl227, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i]: 880.82/112.32 (((mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) => 880.82/112.32 (((!!) @ (^[Y0 : $i]: 880.82/112.32 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.32 (((!!) @ (^[Y1 : $i]: 880.82/112.32 (((mem @ Y1 @ 880.82/112.32 (ty_2Eoption_2Eoption @ X4)) => 880.82/112.32 (((((((??) @ (^[Y2 : $i]: 880.82/112.32 (((((??) @ (^[Y3 : $i]: 880.82/112.32 ( 880.82/112.32 ( 880.82/112.32 ( 880.82/112.32 mem @ 880.82/112.32 Y3 @ X4) & 880.82/112.32 ( 880.82/112.32 ( 880.82/112.32 (Y0) = 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2ESOME @ 880.82/112.32 X2) @ Y2))) & 880.82/112.32 ( 880.82/112.32 ( 880.82/112.32 (Y1) = 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2ESOME @ 880.82/112.32 X4) @ Y3))) & 880.82/112.32 ( 880.82/112.32 p @ 880.82/112.32 ( 880.82/112.32 ap @ 880.82/112.32 ( 880.82/112.32 ap @ 880.82/112.32 X6 @ Y2) @ 880.82/112.32 Y3))))))) & 880.82/112.32 (mem @ Y2 @ X2)))))) | 880.82/112.32 (((((Y1) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.32 (((Y0) = (c_2Eoption_2ENONE @ X2))))))) <=> 880.82/112.32 (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ X2 @ X4) @ 880.82/112.32 X6) @ 880.82/112.32 Y0) @ 880.82/112.32 Y1))))))))))))))))), 880.82/112.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl226])). 880.82/112.32 thf(zip_derived_cl228, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i]: 880.82/112.32 (~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.32 | (((!!) @ (^[Y0 : $i]: 880.82/112.32 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.32 (((!!) @ (^[Y1 : $i]: 880.82/112.32 (((mem @ Y1 @ 880.82/112.32 (ty_2Eoption_2Eoption @ X4)) => 880.82/112.32 (((((((??) @ (^[Y2 : $i]: 880.82/112.32 (((((??) @ (^[Y3 : $i]: 880.82/112.32 (( 880.82/112.32 ( 880.82/112.32 mem @ 880.82/112.32 Y3 @ X4) & 880.82/112.32 ( 880.82/112.32 ( 880.82/112.32 (Y0) = 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2ESOME @ 880.82/112.32 X2) @ Y2))) & 880.82/112.32 ( 880.82/112.32 ( 880.82/112.32 (Y1) = 880.82/112.32 (ap @ 880.82/112.32 ( 880.82/112.32 c_2Eoption_2ESOME @ 880.82/112.32 X4) @ Y3))) & 880.82/112.32 ( 880.82/112.32 p @ 880.82/112.32 ( 880.82/112.32 ap @ 880.82/112.32 ( 880.82/112.32 ap @ 880.82/112.32 X6 @ Y2) @ 880.82/112.32 Y3))))))) & 880.82/112.32 (mem @ Y2 @ X2)))))) | 880.82/112.32 (((((Y1) = (c_2Eoption_2ENONE @ 880.82/112.32 X4))) & 880.82/112.32 (((Y0) = (c_2Eoption_2ENONE @ 880.82/112.32 X2))))))) <=> 880.82/112.32 (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (c_2Eoption_2EOPTREL @ X2 @ X4) @ 880.82/112.32 X6) @ 880.82/112.32 Y0) @ 880.82/112.32 Y1)))))))))))))))), 880.82/112.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl227])). 880.82/112.32 thf(zip_derived_cl229, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 880.82/112.32 ( (((mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.32 (((!!) @ (^[Y0 : $i]: 880.82/112.32 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X4)) => 880.82/112.32 (((((((??) @ (^[Y1 : $i]: 880.82/112.32 (((((??) @ (^[Y2 : $i]: 880.82/112.32 (((mem @ Y2 @ X4) & 880.82/112.32 (((X8) = (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ 880.82/112.32 X2) @ 880.82/112.32 Y1))) & 880.82/112.32 (((Y0) = (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ 880.82/112.32 X4) @ 880.82/112.32 Y2))) & 880.82/112.32 (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ X6 @ Y1) @ 880.82/112.32 Y2))))))) & 880.82/112.32 (mem @ Y1 @ X2)))))) | 880.82/112.32 (((((Y0) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.32 (((X8) = (c_2Eoption_2ENONE @ X2))))))) <=> 880.82/112.32 (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.32 Y0))))))))))) 880.82/112.32 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))))), 880.82/112.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl228])). 880.82/112.32 thf(zip_derived_cl230, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 880.82/112.32 (~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.32 | (((!!) @ (^[Y0 : $i]: 880.82/112.32 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X4)) => 880.82/112.32 (((((((??) @ (^[Y1 : $i]: 880.82/112.32 (((((??) @ (^[Y2 : $i]: 880.82/112.32 (((mem @ Y2 @ X4) & 880.82/112.32 (((X8) = (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ 880.82/112.32 X2) @ 880.82/112.32 Y1))) & 880.82/112.32 (((Y0) = (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ 880.82/112.32 X4) @ 880.82/112.32 Y2))) & 880.82/112.32 (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ X6 @ Y1) @ 880.82/112.32 Y2))))))) & 880.82/112.32 (mem @ Y1 @ X2)))))) | 880.82/112.32 (((((Y0) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.32 (((X8) = (c_2Eoption_2ENONE @ X2))))))) <=> 880.82/112.32 (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.32 Y0))))))))) 880.82/112.32 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))))), 880.82/112.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl229])). 880.82/112.32 thf(zip_derived_cl231, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.32 ( (((mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) => 880.82/112.32 (((((((??) @ (^[Y0 : $i]: 880.82/112.32 (((((??) @ (^[Y1 : $i]: 880.82/112.32 (((mem @ Y1 @ X4) & 880.82/112.32 (((X8) = (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ X2) @ Y0))) & 880.82/112.32 (((X10) = (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ X4) @ Y1))) & 880.82/112.32 (p @ (ap @ (ap @ X6 @ Y0) @ Y1))))))) & 880.82/112.32 (mem @ Y0 @ X2)))))) | 880.82/112.32 (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.32 (((X8) = (c_2Eoption_2ENONE @ X2))))))) <=> 880.82/112.32 (p @ 880.82/112.32 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.32 X10)))))) 880.82/112.32 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.32 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)))), 880.82/112.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl230])). 880.82/112.32 thf(zip_derived_cl232, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.32 (~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.32 | (((((((??) @ (^[Y0 : $i]: 880.82/112.32 (((((??) @ (^[Y1 : $i]: 880.82/112.32 (((mem @ Y1 @ X4) & 880.82/112.32 (((X8) = (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ X2) @ Y0))) & 880.82/112.32 (((X10) = (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ X4) @ Y1))) & 880.82/112.32 (p @ (ap @ (ap @ X6 @ Y0) @ Y1))))))) & 880.82/112.32 (mem @ Y0 @ X2)))))) | 880.82/112.32 (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.32 (((X8) = (c_2Eoption_2ENONE @ X2))))))) <=> 880.82/112.32 (p @ 880.82/112.32 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.32 X10)))) 880.82/112.32 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.32 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))))), 880.82/112.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl231])). 880.82/112.32 thf(zip_derived_cl233, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.32 (~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.32 | ((((((??) @ (^[Y0 : $i]: 880.82/112.32 (((((??) @ (^[Y1 : $i]: 880.82/112.32 (((mem @ Y1 @ X4) & 880.82/112.32 (((X8) = (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ X2) @ Y0))) & 880.82/112.32 (((X10) = (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ X4) @ Y1))) & 880.82/112.32 (p @ (ap @ (ap @ X6 @ Y0) @ Y1))))))) & 880.82/112.32 (mem @ Y0 @ X2)))))) | 880.82/112.32 (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.32 (((X8) = (c_2Eoption_2ENONE @ X2))))))) 880.82/112.32 = (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ X10))) 880.82/112.32 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.32 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))))), 880.82/112.32 inference('simplify nested equalities', [status(thm)], 880.82/112.32 [zip_derived_cl232])). 880.82/112.32 thf(zip_derived_cl234, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.32 ( (((((??) @ (^[Y0 : $i]: 880.82/112.32 (((((??) @ (^[Y1 : $i]: 880.82/112.32 (((mem @ Y1 @ X4) & 880.82/112.32 (((X8) = (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ X2) @ Y0))) & 880.82/112.32 (((X10) = (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ X4) @ Y1))) & 880.82/112.32 (p @ (ap @ (ap @ X6 @ Y0) @ Y1))))))) & 880.82/112.32 (mem @ Y0 @ X2)))))) | 880.82/112.32 (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.32 (((X8) = (c_2Eoption_2ENONE @ X2))))))) 880.82/112.32 | ~ (p @ 880.82/112.32 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.32 X10)) 880.82/112.32 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.32 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.32 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)))), 880.82/112.32 inference('eq_elim', [status(thm)], [zip_derived_cl233])). 880.82/112.32 thf(zip_derived_cl286, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.32 ( (((??) @ (^[Y0 : $i]: 880.82/112.32 (((((??) @ (^[Y1 : $i]: 880.82/112.32 (((mem @ Y1 @ X4) & 880.82/112.32 (((X8) = (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ X2) @ Y0))) & 880.82/112.32 (((X10) = (ap @ 880.82/112.32 (c_2Eoption_2ESOME @ X4) @ Y1))) & 880.82/112.32 (p @ (ap @ (ap @ X6 @ Y0) @ Y1))))))) & 880.82/112.32 (mem @ Y0 @ X2)))))) 880.82/112.32 | (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.32 (((X8) = (c_2Eoption_2ENONE @ X2))))) 880.82/112.32 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.32 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.32 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.32 | ~ (p @ 880.82/112.32 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.32 X10)))), 880.82/112.32 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl234])). 880.82/112.32 thf(zip_derived_cl287, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.32 ( (((((??) @ (^[Y0 : $i]: 880.82/112.32 (((mem @ Y0 @ X4) & 880.82/112.32 (((X8) = (ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.32 ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10)))) & 880.82/112.32 (((X10) = (ap @ (c_2Eoption_2ESOME @ X4) @ Y0))) & 880.82/112.32 (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ X6 @ ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10)) @ 880.82/112.32 Y0))))))) & 880.82/112.32 (mem @ ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10) @ X2))) 880.82/112.32 | ~ (p @ 880.82/112.32 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.32 X10)) 880.82/112.32 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.32 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.32 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.32 | (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.32 (((X8) = (c_2Eoption_2ENONE @ X2))))))), 880.82/112.32 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl286])). 880.82/112.32 thf(zip_derived_cl288, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.32 ( (((??) @ (^[Y0 : $i]: 880.82/112.32 (((mem @ Y0 @ X4) & 880.82/112.32 (((X8) = (ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.32 ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10)))) & 880.82/112.32 (((X10) = (ap @ (c_2Eoption_2ESOME @ X4) @ Y0))) & 880.82/112.32 (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ X6 @ ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10)) @ Y0))))))) 880.82/112.32 | (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.32 (((X8) = (c_2Eoption_2ENONE @ X2))))) 880.82/112.32 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.32 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.32 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.32 | ~ (p @ 880.82/112.32 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.32 X10)))), 880.82/112.32 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl287])). 880.82/112.32 thf(zip_derived_cl290, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.32 ( (((mem @ ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10) @ X4) & 880.82/112.32 (((X8) = (ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.32 ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10)))) & 880.82/112.32 (((X10) = (ap @ (c_2Eoption_2ESOME @ X4) @ 880.82/112.32 ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10)))) & 880.82/112.32 (p @ 880.82/112.32 (ap @ (ap @ X6 @ ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10)) @ 880.82/112.32 ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10))))) 880.82/112.32 | ~ (p @ 880.82/112.32 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.32 X10)) 880.82/112.32 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.32 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.32 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.32 | (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.32 (((X8) = (c_2Eoption_2ENONE @ X2))))))), 880.82/112.32 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl288])). 880.82/112.32 thf(zip_derived_cl294, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.32 ( (((X8) = (ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.32 ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10)))) 880.82/112.32 | (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.32 (((X8) = (c_2Eoption_2ENONE @ X2))))) 880.82/112.32 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.32 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.32 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.32 | ~ (p @ 880.82/112.32 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.32 X10)))), 880.82/112.32 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl290])). 880.82/112.32 thf(zip_derived_cl301, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.32 (((X8) 880.82/112.32 = (ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.32 ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10))) 880.82/112.32 | (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.32 (((X8) = (c_2Eoption_2ENONE @ X2))))) 880.82/112.32 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.32 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.32 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.32 | ~ (p @ 880.82/112.32 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.32 X10)))), 880.82/112.32 inference('simplify nested equalities', [status(thm)], 880.82/112.32 [zip_derived_cl294])). 880.82/112.32 thf(zip_derived_cl302, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.32 ( (((X10) = (c_2Eoption_2ENONE @ X4))) 880.82/112.32 | ~ (p @ 880.82/112.32 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.32 X10)) 880.82/112.32 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.32 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.32 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.32 | ((X8) 880.82/112.32 = (ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.32 ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10))))), 880.82/112.32 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl301])). 880.82/112.32 thf(zip_derived_cl311, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.32 (((X10) = (c_2Eoption_2ENONE @ X4)) 880.82/112.32 | ~ (p @ 880.82/112.32 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.32 X10)) 880.82/112.32 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.32 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.32 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.32 | ((X8) 880.82/112.32 = (ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.32 ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10))))), 880.82/112.32 inference('simplify nested equalities', [status(thm)], 880.82/112.32 [zip_derived_cl302])). 880.82/112.32 thf(zip_derived_cl2658, plain, 880.82/112.32 (((((c_2Eoption_2ENONE @ '#sk3') 880.82/112.32 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.32 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.32 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.32 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.32 | ~ (mem @ (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.32 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.32 | ~ (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool))) 880.82/112.32 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.32 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.32 <= (( (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.32 inference('sup-', [status(thm)], [zip_derived_cl267, zip_derived_cl311])). 880.82/112.32 thf(mem_c_2Eoption_2ENONE, axiom, 880.82/112.32 (![A_27a:del]: 880.82/112.32 ( mem @ ( c_2Eoption_2ENONE @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27a ) ))). 880.82/112.32 thf(zip_derived_cl6, plain, 880.82/112.32 ( (((!!) @ (^[Y0 : del]: 880.82/112.32 (mem @ (c_2Eoption_2ENONE @ Y0) @ 880.82/112.32 (ty_2Eoption_2Eoption @ Y0)))))), 880.82/112.32 inference('cnf', [status(esa)], [mem_c_2Eoption_2ENONE])). 880.82/112.32 thf(zip_derived_cl27, plain, 880.82/112.32 (![X2 : del]: 880.82/112.32 (mem @ (c_2Eoption_2ENONE @ X2) @ (ty_2Eoption_2Eoption @ X2))), 880.82/112.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 880.82/112.32 thf(zip_derived_cl256, plain, 880.82/112.32 ( (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool)))), 880.82/112.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl255])). 880.82/112.32 thf(zip_derived_cl2672, plain, 880.82/112.32 (((((c_2Eoption_2ENONE @ '#sk3') 880.82/112.32 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.32 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.32 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.32 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.32 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.32 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.32 <= (( (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.32 inference('demod', [status(thm)], 880.82/112.32 [zip_derived_cl2658, zip_derived_cl27, zip_derived_cl256])). 880.82/112.32 thf('0', plain, 880.82/112.32 ((((c_2Eoption_2ENONE @ '#sk3') 880.82/112.32 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.32 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))) | 880.82/112.32 (((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.32 = (c_2Eoption_2ENONE @ '#sk3'))) | 880.82/112.32 ~ 880.82/112.32 ( (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) | 880.82/112.32 ~ 880.82/112.32 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.32 (ty_2Eoption_2Eoption @ '#sk3')))), 880.82/112.32 inference('split', [status(esa)], [zip_derived_cl2672])). 880.82/112.32 thf(zip_derived_cl267, plain, 880.82/112.32 (( (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.32 <= (( (p @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ 880.82/112.32 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.32 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.32 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.32 inference('split', [status(esa)], [zip_derived_cl265])). 880.82/112.32 thf(zip_derived_cl289, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.32 ( (mem @ ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10) @ X2) 880.82/112.32 | (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.32 (((X8) = (c_2Eoption_2ENONE @ X2))))) 880.82/112.32 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.32 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.32 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.32 | ~ (p @ 880.82/112.32 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.32 X10)))), 880.82/112.32 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl287])). 880.82/112.32 thf(zip_derived_cl291, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.32 ( (((X10) = (c_2Eoption_2ENONE @ X4))) 880.82/112.32 | ~ (p @ 880.82/112.32 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.32 X10)) 880.82/112.32 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.32 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.32 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.32 | (mem @ ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10) @ X2))), 880.82/112.32 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl289])). 880.82/112.32 thf(zip_derived_cl297, plain, 880.82/112.32 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.32 (((X10) = (c_2Eoption_2ENONE @ X4)) 880.82/112.32 | ~ (p @ 880.82/112.32 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.32 X10)) 880.82/112.32 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.32 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.32 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.32 | (mem @ ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10) @ X2))), 880.82/112.33 inference('simplify nested equalities', [status(thm)], 880.82/112.33 [zip_derived_cl291])). 880.82/112.33 thf(zip_derived_cl317, plain, 880.82/112.33 ((( (mem @ 880.82/112.33 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.33 '#sk3') 880.82/112.33 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.33 | ~ (mem @ (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.33 | ~ (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool))) 880.82/112.33 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.33 <= (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl267, zip_derived_cl297])). 880.82/112.33 thf(zip_derived_cl27, plain, 880.82/112.33 (![X2 : del]: 880.82/112.33 (mem @ (c_2Eoption_2ENONE @ X2) @ (ty_2Eoption_2Eoption @ X2))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 880.82/112.33 thf(zip_derived_cl256, plain, 880.82/112.33 ( (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool)))), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl255])). 880.82/112.33 thf(zip_derived_cl319, plain, 880.82/112.33 ((( (mem @ 880.82/112.33 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.33 '#sk3') 880.82/112.33 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.33 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.33 <= (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.33 inference('demod', [status(thm)], 880.82/112.33 [zip_derived_cl317, zip_derived_cl27, zip_derived_cl256])). 880.82/112.33 thf('1', plain, 880.82/112.33 (~ 880.82/112.33 ( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) | 880.82/112.33 ( (mem @ 880.82/112.33 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.33 '#sk3')) | 880.82/112.33 (((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3'))) | 880.82/112.33 ~ 880.82/112.33 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl319])). 880.82/112.33 thf(zip_derived_cl371, plain, 880.82/112.33 ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3'))) 880.82/112.33 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3'))))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl319])). 880.82/112.33 thf(zip_derived_cl27, plain, 880.82/112.33 (![X2 : del]: 880.82/112.33 (mem @ (c_2Eoption_2ENONE @ X2) @ (ty_2Eoption_2Eoption @ X2))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 880.82/112.33 thf(zip_derived_cl27, plain, 880.82/112.33 (![X2 : del]: 880.82/112.33 (mem @ (c_2Eoption_2ENONE @ X2) @ (ty_2Eoption_2Eoption @ X2))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 880.82/112.33 thf(mem_c_2Eoption_2ETHE, axiom, 880.82/112.33 (![A_27a:del]: 880.82/112.33 ( mem @ 880.82/112.33 ( c_2Eoption_2ETHE @ A_27a ) @ 880.82/112.33 ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ A_27a ) ))). 880.82/112.33 thf(zip_derived_cl11, plain, 880.82/112.33 ( (((!!) @ (^[Y0 : del]: 880.82/112.33 (mem @ (c_2Eoption_2ETHE @ Y0) @ 880.82/112.33 (arr @ (ty_2Eoption_2Eoption @ Y0) @ Y0)))))), 880.82/112.33 inference('cnf', [status(esa)], [mem_c_2Eoption_2ETHE])). 880.82/112.33 thf(zip_derived_cl30, plain, 880.82/112.33 (![X2 : del]: 880.82/112.33 (mem @ (c_2Eoption_2ETHE @ X2) @ 880.82/112.33 (arr @ (ty_2Eoption_2Eoption @ X2) @ X2))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl11])). 880.82/112.33 thf(ap_tp, axiom, 880.82/112.33 (![A:del,B:del,F:$i]: 880.82/112.33 ( ( mem @ F @ ( arr @ A @ B ) ) => 880.82/112.33 ( ![X:$i]: ( ( mem @ X @ A ) => ( mem @ ( ap @ F @ X ) @ B ) ) ) ))). 880.82/112.33 thf(zip_derived_cl0, plain, 880.82/112.33 ( (((!!) @ (^[Y0 : del]: 880.82/112.33 (((!!) @ (^[Y1 : del]: 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ (arr @ Y0 @ Y1)) => 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ Y3 @ Y0) => 880.82/112.33 (mem @ 880.82/112.33 (ap @ Y2 @ Y3) @ 880.82/112.33 Y1)))))))))))))))))), 880.82/112.33 inference('cnf', [status(esa)], [ap_tp])). 880.82/112.33 thf(zip_derived_cl31, plain, 880.82/112.33 (![X2 : del]: 880.82/112.33 (((!!) @ (^[Y0 : del]: 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ (arr @ X2 @ Y0)) => 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X2) => (mem @ 880.82/112.33 (ap @ Y1 @ Y2) @ Y0))))))))))))))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])). 880.82/112.33 thf(zip_derived_cl32, plain, 880.82/112.33 (![X2 : del, X4 : del]: 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (arr @ X2 @ X4)) => 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X2) => (mem @ 880.82/112.33 (ap @ Y0 @ Y1) @ X4)))))))))))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl31])). 880.82/112.33 thf(zip_derived_cl33, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i]: 880.82/112.33 (((mem @ X6 @ (arr @ X2 @ X4)) => 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X2) => (mem @ (ap @ X6 @ Y0) @ X4))))))))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 880.82/112.33 thf(zip_derived_cl34, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i]: 880.82/112.33 (~ (mem @ X6 @ (arr @ X2 @ X4)) 880.82/112.33 | (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X2) => (mem @ (ap @ X6 @ Y0) @ X4)))))))), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])). 880.82/112.33 thf(zip_derived_cl35, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 880.82/112.33 ( (((mem @ X8 @ X2) => (mem @ (ap @ X6 @ X8) @ X4))) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ X4)))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 880.82/112.33 thf(zip_derived_cl36, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 880.82/112.33 (~ (mem @ X8 @ X2) 880.82/112.33 | (mem @ (ap @ X6 @ X8) @ X4) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ X4)))), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 880.82/112.33 thf(zip_derived_cl37, plain, 880.82/112.33 (![X0 : del, X1 : $i]: 880.82/112.33 ( (mem @ (ap @ (c_2Eoption_2ETHE @ X0) @ X1) @ X0) 880.82/112.33 | ~ (mem @ X1 @ (ty_2Eoption_2Eoption @ X0)))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl36])). 880.82/112.33 thf(zip_derived_cl284, plain, 880.82/112.33 (![X0 : del]: 880.82/112.33 (mem @ (ap @ (c_2Eoption_2ETHE @ X0) @ (c_2Eoption_2ENONE @ X0)) @ X0)), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl37])). 880.82/112.33 thf(conj_thm_2Eoption_2Eoption__CLAUSES, axiom, 880.82/112.33 (![A_27a:del,A_27b:del,V0e:$i]: 880.82/112.33 ( ( mem @ V0e @ A_27b ) => 880.82/112.33 ( ![V1f:$i]: 880.82/112.33 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) ) => 880.82/112.33 ( ![V2e:$i]: 880.82/112.33 ( ( mem @ V2e @ ( ty_2Eoption_2Eoption @ A_27a ) ) => 880.82/112.33 ( ( ![V3x:$i]: 880.82/112.33 ( ( mem @ V3x @ A_27a ) => 880.82/112.33 ( ![V4y:$i]: 880.82/112.33 ( ( mem @ V4y @ A_27a ) => 880.82/112.33 ( ( ( V3x ) = ( V4y ) ) <=> 880.82/112.33 ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3x ) = 880.82/112.33 ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V4y ) ) ) ) ) ) ) & 880.82/112.33 ( ![V5x:$i]: 880.82/112.33 ( ( mem @ V5x @ A_27a ) => 880.82/112.33 ( ( ap @ 880.82/112.33 ( c_2Eoption_2ETHE @ A_27a ) @ 880.82/112.33 ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V5x ) ) = 880.82/112.33 ( V5x ) ) ) ) & 880.82/112.33 ( ![V6x:$i]: 880.82/112.33 ( ( mem @ V6x @ A_27a ) => 880.82/112.33 ( ( c_2Eoption_2ENONE @ A_27a ) != 880.82/112.33 ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V6x ) ) ) ) & 880.82/112.33 ( ![V7x:$i]: 880.82/112.33 ( ( mem @ V7x @ A_27a ) => 880.82/112.33 ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V7x ) != 880.82/112.33 ( c_2Eoption_2ENONE @ A_27a ) ) ) ) & 880.82/112.33 ( ![V8x:$i]: 880.82/112.33 ( ( mem @ V8x @ A_27a ) => 880.82/112.33 ( ( p @ 880.82/112.33 ( ap @ 880.82/112.33 ( c_2Eoption_2EIS__SOME @ A_27a ) @ 880.82/112.33 ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V8x ) ) ) <=> 880.82/112.33 ( $true ) ) ) ) & 880.82/112.33 ( ( p @ 880.82/112.33 ( ap @ 880.82/112.33 ( c_2Eoption_2EIS__SOME @ A_27a ) @ 880.82/112.33 ( c_2Eoption_2ENONE @ A_27a ) ) ) <=> 880.82/112.33 ( $false ) ) & 880.82/112.33 ( ![V11x:$i]: 880.82/112.33 ( ( mem @ V11x @ ( ty_2Eoption_2Eoption @ A_27a ) ) => 880.82/112.33 ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V11x ) ) => 880.82/112.33 ( ( ap @ 880.82/112.33 ( c_2Eoption_2ESOME @ A_27a ) @ 880.82/112.33 ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ V11x ) ) = 880.82/112.33 ( V11x ) ) ) ) ) & 880.82/112.33 ( ![V14x:$i]: 880.82/112.33 ( ( mem @ V14x @ ( ty_2Eoption_2Eoption @ A_27a ) ) => 880.82/112.33 ( ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ V14x ) ) => 880.82/112.33 ( ( ap @ 880.82/112.33 ( ap @ 880.82/112.33 ( ap @ 880.82/112.33 ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ 880.82/112.33 V14x ) @ 880.82/112.33 V0e ) @ 880.82/112.33 V1f ) = 880.82/112.33 ( V0e ) ) ) ) ) & 880.82/112.33 ( ![V15x:$i]: 880.82/112.33 ( ( mem @ V15x @ ( ty_2Eoption_2Eoption @ A_27a ) ) => 880.82/112.33 ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V15x ) ) => 880.82/112.33 ( ( ap @ 880.82/112.33 ( ap @ 880.82/112.33 ( ap @ 880.82/112.33 ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ 880.82/112.33 V15x ) @ 880.82/112.33 V0e ) @ 880.82/112.33 V1f ) = 880.82/112.33 ( ap @ 880.82/112.33 V1f @ ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ V15x ) ) ) ) ) ) & 880.82/112.33 ( ![V19x:$i]: 880.82/112.33 ( ( mem @ V19x @ A_27a ) => 880.82/112.33 ( ![V20v:$i]: 880.82/112.33 ( ( mem @ V20v @ A_27b ) => 880.82/112.33 ( ![V21f:$i]: 880.82/112.33 ( ( mem @ V21f @ ( arr @ A_27a @ A_27b ) ) => 880.82/112.33 ( ( ap @ 880.82/112.33 ( ap @ 880.82/112.33 ( ap @ 880.82/112.33 ( c_2Eoption_2Eoption__CASE @ 880.82/112.33 A_27a @ A_27b ) @ 880.82/112.33 ( ap @ 880.82/112.33 ( c_2Eoption_2ESOME @ A_27a ) @ V19x ) ) @ 880.82/112.33 V20v ) @ 880.82/112.33 V21f ) = 880.82/112.33 ( ap @ V21f @ V19x ) ) ) ) ) ) ) ) & 880.82/112.33 ( ![V22f:$i]: 880.82/112.33 ( ( mem @ V22f @ ( arr @ A_27a @ A_27b ) ) => 880.82/112.33 ( ![V23x:$i]: 880.82/112.33 ( ( mem @ V23x @ A_27a ) => 880.82/112.33 ( ( ap @ 880.82/112.33 ( ap @ 880.82/112.33 ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ 880.82/112.33 V22f ) @ 880.82/112.33 ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V23x ) ) = 880.82/112.33 ( ap @ 880.82/112.33 ( c_2Eoption_2ESOME @ A_27b ) @ 880.82/112.33 ( ap @ V22f @ V23x ) ) ) ) ) ) ) & 880.82/112.33 ( ( ap @ 880.82/112.33 ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ 880.82/112.33 ( c_2Eoption_2ENONE @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) = 880.82/112.33 ( c_2Eoption_2ENONE @ A_27a ) ) & 880.82/112.33 ( ![V25x:$i]: 880.82/112.33 ( ( mem @ V25x @ ( ty_2Eoption_2Eoption @ A_27a ) ) => 880.82/112.33 ( ( ap @ 880.82/112.33 ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ 880.82/112.33 ( ap @ 880.82/112.33 ( c_2Eoption_2ESOME @ 880.82/112.33 ( ty_2Eoption_2Eoption @ A_27a ) ) @ 880.82/112.33 V25x ) ) = 880.82/112.33 ( V25x ) ) ) ) & 880.82/112.33 ( ![V24f:$i]: 880.82/112.33 ( ( mem @ V24f @ ( arr @ A_27a @ A_27b ) ) => 880.82/112.33 ( ( ap @ 880.82/112.33 ( ap @ 880.82/112.33 ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V24f ) @ 880.82/112.33 ( c_2Eoption_2ENONE @ A_27a ) ) = 880.82/112.33 ( c_2Eoption_2ENONE @ A_27b ) ) ) ) & 880.82/112.33 ( ![V17v:$i]: 880.82/112.33 ( ( mem @ V17v @ A_27b ) => 880.82/112.33 ( ![V18f:$i]: 880.82/112.33 ( ( mem @ V18f @ ( arr @ A_27a @ A_27b ) ) => 880.82/112.33 ( ( ap @ 880.82/112.33 ( ap @ 880.82/112.33 ( ap @ 880.82/112.33 ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ 880.82/112.33 ( c_2Eoption_2ENONE @ A_27a ) ) @ 880.82/112.33 V17v ) @ 880.82/112.33 V18f ) = 880.82/112.33 ( V17v ) ) ) ) ) ) & 880.82/112.33 ( ![V16x:$i]: 880.82/112.33 ( ( mem @ V16x @ ( ty_2Eoption_2Eoption @ A_27a ) ) => 880.82/112.33 ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V16x ) ) => 880.82/112.33 ( ( ap @ 880.82/112.33 ( ap @ 880.82/112.33 ( ap @ 880.82/112.33 ( c_2Eoption_2Eoption__CASE @ 880.82/112.33 A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ 880.82/112.33 V16x ) @ 880.82/112.33 V2e ) @ 880.82/112.33 ( c_2Eoption_2ESOME @ A_27a ) ) = 880.82/112.33 ( V16x ) ) ) ) ) & 880.82/112.33 ( ![V13x:$i]: 880.82/112.33 ( ( mem @ V13x @ ( ty_2Eoption_2Eoption @ A_27a ) ) => 880.82/112.33 ( ( ap @ 880.82/112.33 ( ap @ 880.82/112.33 ( ap @ 880.82/112.33 ( c_2Eoption_2Eoption__CASE @ 880.82/112.33 A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ 880.82/112.33 V13x ) @ 880.82/112.33 V13x ) @ 880.82/112.33 ( c_2Eoption_2ESOME @ A_27a ) ) = 880.82/112.33 ( V13x ) ) ) ) & 880.82/112.33 ( ![V12x:$i]: 880.82/112.33 ( ( mem @ V12x @ ( ty_2Eoption_2Eoption @ A_27a ) ) => 880.82/112.33 ( ( ap @ 880.82/112.33 ( ap @ 880.82/112.33 ( ap @ 880.82/112.33 ( c_2Eoption_2Eoption__CASE @ 880.82/112.33 A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ 880.82/112.33 V12x ) @ 880.82/112.33 ( c_2Eoption_2ENONE @ A_27a ) ) @ 880.82/112.33 ( c_2Eoption_2ESOME @ A_27a ) ) = 880.82/112.33 ( V12x ) ) ) ) & 880.82/112.33 ( ![V10x:$i]: 880.82/112.33 ( ( mem @ V10x @ ( ty_2Eoption_2Eoption @ A_27a ) ) => 880.82/112.33 ( ( ~( p @ 880.82/112.33 ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V10x ) ) ) <=> 880.82/112.33 ( ( V10x ) = ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ) & 880.82/112.33 ( ![V9x:$i]: 880.82/112.33 ( ( mem @ V9x @ ( ty_2Eoption_2Eoption @ A_27a ) ) => 880.82/112.33 ( ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ V9x ) ) <=> 880.82/112.33 ( ( V9x ) = ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ) ) ) ) ) ) ))). 880.82/112.33 thf(zip_derived_cl14, plain, 880.82/112.33 ( (((!!) @ (^[Y0 : del]: 880.82/112.33 (((!!) @ (^[Y1 : del]: 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ Y1) => 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ Y3 @ 880.82/112.33 (arr @ Y0 @ Y1)) => 880.82/112.33 (((!!) @ (^[Y4 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 Y0) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y6 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y6 @ 880.82/112.33 Y0) => 880.82/112.33 (( 880.82/112.33 (( 880.82/112.33 (Y5) = 880.82/112.33 (Y6))) <=> 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ 880.82/112.33 Y5) = 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ Y6))))))))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 Y0) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ETHE @ 880.82/112.33 Y0) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ Y5)) = 880.82/112.33 (Y5)))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 Y0) => 880.82/112.33 (( 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 Y0) != 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ Y5)))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 Y0) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ 880.82/112.33 Y5) != 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 Y0)))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 Y0) => 880.82/112.33 (( 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 Y0) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ Y5))) <=> 880.82/112.33 ($true)))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 Y0) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 Y0))) <=> 880.82/112.33 ($false))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 Y0) @ Y5)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ETHE @ 880.82/112.33 Y0) @ Y5)) = 880.82/112.33 (Y5)))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__NONE @ 880.82/112.33 Y0) @ Y5)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 Y0 @ Y1) @ 880.82/112.33 Y5) @ Y2) @ 880.82/112.33 Y3) = 880.82/112.33 (Y2)))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 Y0) @ Y5)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 Y0 @ Y1) @ 880.82/112.33 Y5) @ Y2) @ 880.82/112.33 Y3) = 880.82/112.33 (ap @ 880.82/112.33 Y3 @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ETHE @ 880.82/112.33 Y0) @ Y5))))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 Y0) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y6 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y6 @ 880.82/112.33 Y1) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y7 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y7 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 Y0 @ Y1)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 Y0 @ Y1) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ Y5)) @ 880.82/112.33 Y6) @ 880.82/112.33 Y7) = 880.82/112.33 (ap @ 880.82/112.33 Y7 @ Y5)))))))))))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 Y0 @ Y1)) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y6 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y6 @ 880.82/112.33 Y0) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EOPTION__MAP @ 880.82/112.33 Y0 @ Y1) @ 880.82/112.33 Y5) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ Y6)) = 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y1) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 Y5 @ Y6)))))))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EOPTION__JOIN @ 880.82/112.33 Y0) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0))) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 Y0))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EOPTION__JOIN @ 880.82/112.33 Y0) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) @ Y5)) = 880.82/112.33 (Y5)))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 Y0 @ Y1)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EOPTION__MAP @ 880.82/112.33 Y0 @ Y1) @ 880.82/112.33 Y5) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 Y0)) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 Y1)))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 Y1) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y6 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y6 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 Y0 @ Y1)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 Y0 @ Y1) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 Y0)) @ Y5) @ 880.82/112.33 Y6) = 880.82/112.33 (Y5))))))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 Y0) @ Y5)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 Y0 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) @ Y5) @ 880.82/112.33 Y4) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0)) = 880.82/112.33 (Y5)))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 Y0 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) @ Y5) @ 880.82/112.33 Y5) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0)) = 880.82/112.33 (Y5)))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 Y0 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) @ Y5) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 Y0)) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0)) = 880.82/112.33 (Y5)))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (( 880.82/112.33 (~) @ ( 880.82/112.33 p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 Y0) @ Y5)))) <=> 880.82/112.33 (( 880.82/112.33 (Y5) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 Y0)))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__NONE @ 880.82/112.33 Y0) @ Y5)) <=> 880.82/112.33 (( 880.82/112.33 (Y5) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 Y0)))))))))))))))))))))))))))))))))), 880.82/112.33 inference('cnf', [status(esa)], [conj_thm_2Eoption_2Eoption__CLAUSES])). 880.82/112.33 thf(zip_derived_cl114, plain, 880.82/112.33 ( (((!!) @ (^[Y0 : del]: 880.82/112.33 (((!!) @ (^[Y1 : del]: 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ Y1) => 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ Y3 @ 880.82/112.33 (arr @ Y0 @ Y1)) => 880.82/112.33 (((!!) @ (^[Y4 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 Y0) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y6 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y6 @ 880.82/112.33 Y0) => 880.82/112.33 (( 880.82/112.33 (( 880.82/112.33 (Y5) = 880.82/112.33 (Y6))) <=> 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ 880.82/112.33 Y5) = 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ Y6))))))))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 Y0) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ETHE @ 880.82/112.33 Y0) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ Y5)) = 880.82/112.33 (Y5)))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 Y0) => 880.82/112.33 (( 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 Y0) != 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ Y5)))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 Y0) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ 880.82/112.33 Y5) != 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 Y0)))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 Y0) => 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 Y0) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ Y5)))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (~) @ ( 880.82/112.33 p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 Y0) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 Y0))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 Y0) @ Y5)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ETHE @ 880.82/112.33 Y0) @ Y5)) = 880.82/112.33 (Y5)))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__NONE @ 880.82/112.33 Y0) @ Y5)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 Y0 @ Y1) @ 880.82/112.33 Y5) @ Y2) @ 880.82/112.33 Y3) = 880.82/112.33 (Y2)))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 Y0) @ Y5)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 Y0 @ Y1) @ 880.82/112.33 Y5) @ Y2) @ 880.82/112.33 Y3) = 880.82/112.33 (ap @ 880.82/112.33 Y3 @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ETHE @ 880.82/112.33 Y0) @ Y5))))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 Y0) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y6 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y6 @ 880.82/112.33 Y1) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y7 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y7 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 Y0 @ Y1)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 Y0 @ Y1) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ Y5)) @ 880.82/112.33 Y6) @ 880.82/112.33 Y7) = 880.82/112.33 (ap @ 880.82/112.33 Y7 @ Y5)))))))))))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 Y0 @ Y1)) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y6 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y6 @ 880.82/112.33 Y0) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EOPTION__MAP @ 880.82/112.33 Y0 @ Y1) @ 880.82/112.33 Y5) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ Y6)) = 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y1) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 Y5 @ Y6)))))))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EOPTION__JOIN @ 880.82/112.33 Y0) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0))) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 Y0))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EOPTION__JOIN @ 880.82/112.33 Y0) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) @ Y5)) = 880.82/112.33 (Y5)))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 Y0 @ Y1)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EOPTION__MAP @ 880.82/112.33 Y0 @ Y1) @ 880.82/112.33 Y5) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 Y0)) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 Y1)))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 Y1) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y6 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y6 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 Y0 @ Y1)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 Y0 @ Y1) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 Y0)) @ Y5) @ 880.82/112.33 Y6) = 880.82/112.33 (Y5))))))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 Y0) @ Y5)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 Y0 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) @ Y5) @ 880.82/112.33 Y4) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0)) = 880.82/112.33 (Y5)))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 Y0 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) @ Y5) @ 880.82/112.33 Y5) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0)) = 880.82/112.33 (Y5)))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 Y0 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) @ Y5) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 Y0)) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0)) = 880.82/112.33 (Y5)))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (( 880.82/112.33 (~) @ ( 880.82/112.33 p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 Y0) @ Y5)))) <=> 880.82/112.33 (( 880.82/112.33 (Y5) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 Y0)))))))))) & 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 Y0)) => 880.82/112.33 (( 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__NONE @ 880.82/112.33 Y0) @ Y5)) <=> 880.82/112.33 (( 880.82/112.33 (Y5) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 Y0)))))))))))))))))))))))))))))))))), 880.82/112.33 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl14])). 880.82/112.33 thf(zip_derived_cl115, plain, 880.82/112.33 (![X2 : del]: 880.82/112.33 (((!!) @ (^[Y0 : del]: 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ Y0) => 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (arr @ X2 @ Y0)) => 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ Y3 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 X2) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 X2) => 880.82/112.33 (( 880.82/112.33 (( 880.82/112.33 (Y4) = 880.82/112.33 (Y5))) <=> 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y4) = 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y5))))))))))))))) & 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 X2) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ETHE @ 880.82/112.33 X2) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y4)) = 880.82/112.33 (Y4)))))))) & 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 X2) => 880.82/112.33 (( 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2) != 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y4)))))))) & 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 X2) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y4) != 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2)))))))) & 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 X2) => 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y4)))))))) & 880.82/112.33 (((~) @ ( 880.82/112.33 p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2))))) & 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (( 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ Y4)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ETHE @ 880.82/112.33 X2) @ Y4)) = 880.82/112.33 (Y4)))))))))) & 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (( 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__NONE @ 880.82/112.33 X2) @ Y4)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ Y0) @ 880.82/112.33 Y4) @ Y1) @ 880.82/112.33 Y2) = 880.82/112.33 (Y1)))))))))) & 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (( 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ Y4)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ Y0) @ 880.82/112.33 Y4) @ Y1) @ 880.82/112.33 Y2) = 880.82/112.33 (ap @ 880.82/112.33 Y2 @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ETHE @ 880.82/112.33 X2) @ Y4))))))))))) & 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 X2) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 Y0) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y6 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y6 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 X2 @ Y0)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ Y0) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y4)) @ 880.82/112.33 Y5) @ 880.82/112.33 Y6) = 880.82/112.33 (ap @ 880.82/112.33 Y6 @ Y4)))))))))))))))))) & 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 X2 @ Y0)) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 X2) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EOPTION__MAP @ 880.82/112.33 X2 @ Y0) @ 880.82/112.33 Y4) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y5)) = 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 Y0) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 Y4 @ Y5)))))))))))))) & 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2EOPTION__JOIN @ 880.82/112.33 X2) @ 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2))) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2))) & 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EOPTION__JOIN @ 880.82/112.33 X2) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 X2)) @ Y4)) = 880.82/112.33 (Y4)))))))) & 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 X2 @ Y0)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EOPTION__MAP @ 880.82/112.33 X2 @ Y0) @ 880.82/112.33 Y4) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 X2)) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 Y0)))))))) & 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 Y0) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 X2 @ Y0)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ Y0) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 X2)) @ Y4) @ 880.82/112.33 Y5) = 880.82/112.33 (Y4))))))))))))) & 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (( 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ Y4)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 X2)) @ Y4) @ 880.82/112.33 Y3) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2)) = 880.82/112.33 (Y4)))))))))) & 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 X2)) @ Y4) @ 880.82/112.33 Y4) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2)) = 880.82/112.33 (Y4)))))))) & 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 X2)) @ Y4) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 X2)) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2)) = 880.82/112.33 (Y4)))))))) & 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (( 880.82/112.33 (( 880.82/112.33 (~) @ ( 880.82/112.33 p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ Y4)))) <=> 880.82/112.33 (( 880.82/112.33 (Y4) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2)))))))))) & 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 ( 880.82/112.33 ( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (( 880.82/112.33 (p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__NONE @ 880.82/112.33 X2) @ Y4)) <=> 880.82/112.33 (( 880.82/112.33 (Y4) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2))))))))))))))))))))))))))))))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl114])). 880.82/112.33 thf(zip_derived_cl116, plain, 880.82/112.33 (![X2 : del, X4 : del]: 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X4) => 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ (arr @ X2 @ X4)) => 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ X2) => 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 X2) => 880.82/112.33 (( 880.82/112.33 (( 880.82/112.33 (Y3) = 880.82/112.33 (Y4))) <=> 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y3) = 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y4))))))))))))))) & 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ X2) => 880.82/112.33 (((ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ETHE @ 880.82/112.33 X2) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y3)) = 880.82/112.33 (Y3)))))))) & 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ X2) => 880.82/112.33 (((c_2Eoption_2ENONE @ 880.82/112.33 X2) != 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y3)))))))) & 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ X2) => 880.82/112.33 (((ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y3) != 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2)))))))) & 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ X2) => 880.82/112.33 (p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y3)))))))) & 880.82/112.33 (((~) @ (p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2))))) & 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ Y3)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ETHE @ 880.82/112.33 X2) @ Y3)) = 880.82/112.33 (Y3)))))))))) & 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__NONE @ 880.82/112.33 X2) @ Y3)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y3) @ Y0) @ 880.82/112.33 Y1) = 880.82/112.33 (Y0)))))))))) & 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ Y3)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y3) @ Y0) @ 880.82/112.33 Y1) = 880.82/112.33 (ap @ 880.82/112.33 Y1 @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ETHE @ 880.82/112.33 X2) @ Y3))))))))))) & 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ X2) => 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 X4) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y5 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y5 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 X2 @ X4)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y3)) @ 880.82/112.33 Y4) @ 880.82/112.33 Y5) = 880.82/112.33 (ap @ 880.82/112.33 Y5 @ Y3)))))))))))))))))) & 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ 880.82/112.33 (arr @ 880.82/112.33 X2 @ X4)) => 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 X2) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EOPTION__MAP @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y3) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y4)) = 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X4) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 Y3 @ Y4)))))))))))))) & 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2EOPTION__JOIN @ 880.82/112.33 X2) @ 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2))) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2))) & 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EOPTION__JOIN @ 880.82/112.33 X2) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 X2)) @ Y3)) = 880.82/112.33 (Y3)))))))) & 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ 880.82/112.33 (arr @ 880.82/112.33 X2 @ X4)) => 880.82/112.33 (((ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EOPTION__MAP @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y3) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 X2)) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X4)))))))) & 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ X4) => 880.82/112.33 (((!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 X2 @ X4)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 X2)) @ Y3) @ 880.82/112.33 Y4) = 880.82/112.33 (Y3))))))))))))) & 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ Y3)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 X2)) @ Y3) @ 880.82/112.33 Y2) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2)) = 880.82/112.33 (Y3)))))))))) & 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 X2)) @ Y3) @ 880.82/112.33 Y3) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2)) = 880.82/112.33 (Y3)))))))) & 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 ( 880.82/112.33 ty_2Eoption_2Eoption @ 880.82/112.33 X2)) @ Y3) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 X2)) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2)) = 880.82/112.33 (Y3)))))))) & 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((( 880.82/112.33 (~) @ ( 880.82/112.33 p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ Y3)))) <=> 880.82/112.33 (( 880.82/112.33 (Y3) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2)))))))))) & 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((p @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EIS__NONE @ 880.82/112.33 X2) @ Y3)) <=> 880.82/112.33 (( 880.82/112.33 (Y3) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2)))))))))))))))))))))))))))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl115])). 880.82/112.33 thf(zip_derived_cl117, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i]: 880.82/112.33 (((mem @ X6 @ X4) => 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (arr @ X2 @ X4)) => 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X2) => 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ 880.82/112.33 X2) => 880.82/112.33 (( 880.82/112.33 (( 880.82/112.33 (Y2) = 880.82/112.33 (Y3))) <=> 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2) = 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y3))))))))))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X2) => 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2ETHE @ 880.82/112.33 X2) @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2)) = 880.82/112.33 (Y2)))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X2) => 880.82/112.33 (((c_2Eoption_2ENONE @ 880.82/112.33 X2) != (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2)))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X2) => 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2) != 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2)))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X2) => 880.82/112.33 (p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2)))))))) & 880.82/112.33 (((~) @ (p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ X2) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2)) => 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ETHE @ 880.82/112.33 X2) @ 880.82/112.33 Y2)) = 880.82/112.33 (Y2)))))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__NONE @ 880.82/112.33 X2) @ 880.82/112.33 Y2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y2) @ 880.82/112.33 X6) @ 880.82/112.33 Y0) = (X6)))))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y2) @ 880.82/112.33 X6) @ 880.82/112.33 Y0) = (ap @ Y0 @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ETHE @ 880.82/112.33 X2) @ 880.82/112.33 Y2))))))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X2) => 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ 880.82/112.33 X4) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 X2 @ X4)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y2)) @ 880.82/112.33 Y3) @ 880.82/112.33 Y4) = 880.82/112.33 (ap @ 880.82/112.33 Y4 @ Y2)))))))))))))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (arr @ X2 @ X4)) => 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ 880.82/112.33 X2) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EOPTION__MAP @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y2) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y3)) = 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X4) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 Y2 @ Y3)))))))))))))) & 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2EOPTION__JOIN @ X2) @ 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2))) = 880.82/112.33 (c_2Eoption_2ENONE @ X2))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2EOPTION__JOIN @ 880.82/112.33 X2) @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) @ 880.82/112.33 Y2)) = 880.82/112.33 (Y2)))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (arr @ X2 @ X4)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EOPTION__MAP @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y2) @ 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2)) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X4)))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X4) => 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (((mem @ 880.82/112.33 Y3 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 X2 @ X4)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 X2)) @ Y2) @ 880.82/112.33 Y3) = 880.82/112.33 (Y2))))))))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) @ 880.82/112.33 Y2) @ 880.82/112.33 Y1) @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2)) = 880.82/112.33 (Y2)))))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) @ 880.82/112.33 Y2) @ 880.82/112.33 Y2) @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2)) = 880.82/112.33 (Y2)))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) @ 880.82/112.33 Y2) @ 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2)) @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2)) = 880.82/112.33 (Y2)))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((((~) @ (p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2)))) <=> 880.82/112.33 (((Y2) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2)))))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__NONE @ 880.82/112.33 X2) @ 880.82/112.33 Y2)) <=> 880.82/112.33 (((Y2) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2))))))))))))))))))))))))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl116])). 880.82/112.33 thf(zip_derived_cl118, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i]: 880.82/112.33 (~ (mem @ X6 @ X4) 880.82/112.33 | (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (arr @ X2 @ X4)) => 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X2) => 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y3 @ 880.82/112.33 X2) => 880.82/112.33 (( 880.82/112.33 (( 880.82/112.33 (Y2) = 880.82/112.33 (Y3))) <=> 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2) = 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y3))))))))))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X2) => 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2ETHE @ 880.82/112.33 X2) @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2)) = 880.82/112.33 (Y2)))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X2) => 880.82/112.33 (((c_2Eoption_2ENONE @ 880.82/112.33 X2) != (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2)))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X2) => 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2) != 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2)))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X2) => 880.82/112.33 (p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2)))))))) & 880.82/112.33 (((~) @ (p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2)) => 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ETHE @ 880.82/112.33 X2) @ 880.82/112.33 Y2)) = 880.82/112.33 (Y2)))))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__NONE @ 880.82/112.33 X2) @ 880.82/112.33 Y2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y2) @ 880.82/112.33 X6) @ 880.82/112.33 Y0) = (X6)))))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y2) @ 880.82/112.33 X6) @ 880.82/112.33 Y0) = (ap @ Y0 @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ETHE @ 880.82/112.33 X2) @ 880.82/112.33 Y2))))))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X2) => 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y3 @ 880.82/112.33 X4) => 880.82/112.33 (( 880.82/112.33 (!!) @ ( 880.82/112.33 ^[Y4 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y4 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 X2 @ X4)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y2)) @ 880.82/112.33 Y3) @ 880.82/112.33 Y4) = 880.82/112.33 (ap @ 880.82/112.33 Y4 @ Y2)))))))))))))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (arr @ X2 @ X4)) => 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y3 @ 880.82/112.33 X2) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2EOPTION__MAP @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y2) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y3)) = 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X4) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 Y2 @ Y3)))))))))))))) & 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2EOPTION__JOIN @ X2) @ 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2))) = 880.82/112.33 (c_2Eoption_2ENONE @ X2))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2EOPTION__JOIN @ 880.82/112.33 X2) @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) @ 880.82/112.33 Y2)) = 880.82/112.33 (Y2)))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (arr @ X2 @ X4)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EOPTION__MAP @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y2) @ 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2)) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X4)))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X4) => 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y3 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 X2 @ X4)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ENONE @ 880.82/112.33 X2)) @ Y2) @ 880.82/112.33 Y3) = 880.82/112.33 (Y2))))))))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) @ 880.82/112.33 Y2) @ 880.82/112.33 Y1) @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2)) = 880.82/112.33 (Y2)))))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) @ 880.82/112.33 Y2) @ 880.82/112.33 Y2) @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2)) = 880.82/112.33 (Y2)))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) @ 880.82/112.33 Y2) @ 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2)) @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2)) = 880.82/112.33 (Y2)))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((((~) @ (p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2)))) <=> 880.82/112.33 (((Y2) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2)))))))))) & 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ 880.82/112.33 X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__NONE @ 880.82/112.33 X2) @ 880.82/112.33 Y2)) <=> 880.82/112.33 (((Y2) = 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2)))))))))))))))))))))))), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl117])). 880.82/112.33 thf(zip_derived_cl119, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 880.82/112.33 ( (((mem @ X8 @ (arr @ X2 @ X4)) => 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X2) => 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X2) => 880.82/112.33 (((((Y1) = (Y2))) <=> 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y1) = (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2))))))))))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X2) => 880.82/112.33 (((ap @ (c_2Eoption_2ETHE @ X2) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.33 Y1)) = 880.82/112.33 (Y1)))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X2) => 880.82/112.33 (((c_2Eoption_2ENONE @ X2) != (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ X2) @ Y1)))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X2) => 880.82/112.33 (((ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.33 Y1) != (c_2Eoption_2ENONE @ X2)))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X2) => (p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ X2) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X2) @ Y1)))))))) & 880.82/112.33 (((~) @ (p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__SOME @ X2) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ X2) @ Y1)) => 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2ESOME @ X2) @ 880.82/112.33 (ap @ (c_2Eoption_2ETHE @ X2) @ 880.82/112.33 Y1)) = 880.82/112.33 (Y1)))))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__NONE @ X2) @ Y1)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y1) @ 880.82/112.33 X6) @ 880.82/112.33 X8) = (X6)))))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ X2) @ Y1)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y1) @ 880.82/112.33 X6) @ 880.82/112.33 X8) = (ap @ X8 @ 880.82/112.33 (ap @ (c_2Eoption_2ETHE @ X2) @ 880.82/112.33 Y1))))))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X2) => 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X4) => 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y3 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 X2 @ X4)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y1)) @ 880.82/112.33 Y2) @ 880.82/112.33 Y3) = 880.82/112.33 (ap @ 880.82/112.33 Y3 @ Y1)))))))))))))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ (arr @ X2 @ X4)) => 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X2) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EOPTION__MAP @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y1) @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2)) = 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X4) @ 880.82/112.33 (ap @ Y1 @ Y2)))))))))))))) & 880.82/112.33 (((ap @ (c_2Eoption_2EOPTION__JOIN @ X2) @ 880.82/112.33 (c_2Eoption_2ENONE @ (ty_2Eoption_2Eoption @ X2))) = 880.82/112.33 (c_2Eoption_2ENONE @ X2))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2EOPTION__JOIN @ X2) @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) @ 880.82/112.33 Y1)) = 880.82/112.33 (Y1)))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ (arr @ X2 @ X4)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EOPTION__MAP @ X2 @ 880.82/112.33 X4) @ 880.82/112.33 Y1) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2)) = 880.82/112.33 (c_2Eoption_2ENONE @ X4)))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X4) => 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (arr @ X2 @ X4)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2)) @ 880.82/112.33 Y1) @ 880.82/112.33 Y2) = (Y1))))))))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ X2) @ Y1)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) @ 880.82/112.33 Y1) @ 880.82/112.33 Y0) @ 880.82/112.33 (c_2Eoption_2ESOME @ X2)) = (Y1)))))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) @ 880.82/112.33 Y1) @ 880.82/112.33 Y1) @ 880.82/112.33 (c_2Eoption_2ESOME @ X2)) = (Y1)))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) @ 880.82/112.33 Y1) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2)) @ 880.82/112.33 (c_2Eoption_2ESOME @ X2)) = (Y1)))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((((~) @ (p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ 880.82/112.33 Y1)))) <=> 880.82/112.33 (((Y1) = (c_2Eoption_2ENONE @ X2)))))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__NONE @ X2) @ Y1)) <=> 880.82/112.33 (((Y1) = (c_2Eoption_2ENONE @ X2))))))))))))))))))) 880.82/112.33 | ~ (mem @ X6 @ X4))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl118])). 880.82/112.33 thf(zip_derived_cl120, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 880.82/112.33 (~ (mem @ X8 @ (arr @ X2 @ X4)) 880.82/112.33 | (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X2) => 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X2) => 880.82/112.33 (((((Y1) = (Y2))) <=> 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y1) = (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2))))))))))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X2) => 880.82/112.33 (((ap @ (c_2Eoption_2ETHE @ X2) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.33 Y1)) = 880.82/112.33 (Y1)))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X2) => 880.82/112.33 (((c_2Eoption_2ENONE @ X2) != (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ X2) @ Y1)))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X2) => 880.82/112.33 (((ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.33 Y1) != (c_2Eoption_2ENONE @ X2)))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X2) => (p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ X2) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X2) @ Y1)))))))) & 880.82/112.33 (((~) @ (p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__SOME @ X2) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ X2) @ Y1)) => 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2ESOME @ X2) @ 880.82/112.33 (ap @ (c_2Eoption_2ETHE @ X2) @ 880.82/112.33 Y1)) = 880.82/112.33 (Y1)))))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__NONE @ X2) @ Y1)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y1) @ 880.82/112.33 X6) @ 880.82/112.33 X8) = (X6)))))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ X2) @ Y1)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y1) @ 880.82/112.33 X6) @ 880.82/112.33 X8) = (ap @ X8 @ 880.82/112.33 (ap @ (c_2Eoption_2ETHE @ X2) @ 880.82/112.33 Y1))))))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X2) => 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X4) => 880.82/112.33 (((!!) @ (^[Y3 : $i]: 880.82/112.33 (( 880.82/112.33 (mem @ 880.82/112.33 Y3 @ 880.82/112.33 ( 880.82/112.33 arr @ 880.82/112.33 X2 @ X4)) => 880.82/112.33 (( 880.82/112.33 (ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 ( 880.82/112.33 ap @ 880.82/112.33 ( 880.82/112.33 c_2Eoption_2ESOME @ 880.82/112.33 X2) @ Y1)) @ 880.82/112.33 Y2) @ 880.82/112.33 Y3) = 880.82/112.33 (ap @ 880.82/112.33 Y3 @ Y1)))))))))))))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ (arr @ X2 @ X4)) => 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ X2) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EOPTION__MAP @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 Y1) @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y2)) = 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X4) @ 880.82/112.33 (ap @ Y1 @ Y2)))))))))))))) & 880.82/112.33 (((ap @ (c_2Eoption_2EOPTION__JOIN @ X2) @ 880.82/112.33 (c_2Eoption_2ENONE @ (ty_2Eoption_2Eoption @ X2))) = 880.82/112.33 (c_2Eoption_2ENONE @ X2))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2EOPTION__JOIN @ X2) @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) @ 880.82/112.33 Y1)) = 880.82/112.33 (Y1)))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ (arr @ X2 @ X4)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EOPTION__MAP @ X2 @ 880.82/112.33 X4) @ 880.82/112.33 Y1) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2)) = 880.82/112.33 (c_2Eoption_2ENONE @ X4)))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X4) => 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (arr @ X2 @ X4)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 (c_2Eoption_2ENONE @ 880.82/112.33 X2)) @ 880.82/112.33 Y1) @ 880.82/112.33 Y2) = (Y1))))))))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ X2) @ Y1)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) @ 880.82/112.33 Y1) @ 880.82/112.33 Y0) @ 880.82/112.33 (c_2Eoption_2ESOME @ X2)) = (Y1)))))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) @ 880.82/112.33 Y1) @ 880.82/112.33 Y1) @ 880.82/112.33 (c_2Eoption_2ESOME @ X2)) = (Y1)))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) @ 880.82/112.33 Y1) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2)) @ 880.82/112.33 (c_2Eoption_2ESOME @ X2)) = (Y1)))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((((~) @ (p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__SOME @ 880.82/112.33 X2) @ 880.82/112.33 Y1)))) <=> 880.82/112.33 (((Y1) = (c_2Eoption_2ENONE @ X2)))))))))) & 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EIS__NONE @ X2) @ Y1)) <=> 880.82/112.33 (((Y1) = (c_2Eoption_2ENONE @ X2))))))))))))))))) 880.82/112.33 | ~ (mem @ X6 @ X4))), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl119])). 880.82/112.33 thf(zip_derived_cl121, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 ( (((mem @ X10 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X2) => 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X2) => 880.82/112.33 (((((Y0) = (Y1))) <=> 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2ESOME @ X2) @ Y0) = 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ X2) @ Y1))))))))))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X2) => 880.82/112.33 (((ap @ (c_2Eoption_2ETHE @ X2) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X2) @ Y0)) = (Y0)))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X2) => 880.82/112.33 (((c_2Eoption_2ENONE @ X2) != (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ X2) @ Y0)))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X2) => 880.82/112.33 (((ap @ (c_2Eoption_2ESOME @ X2) @ Y0) != 880.82/112.33 (c_2Eoption_2ENONE @ X2)))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X2) => (p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__SOME @ X2) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X2) @ Y0)))))))) & 880.82/112.33 (((~) @ (p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__SOME @ X2) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__SOME @ X2) @ Y0)) => 880.82/112.33 (((ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.33 (ap @ (c_2Eoption_2ETHE @ X2) @ Y0)) = (Y0)))))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__NONE @ X2) @ Y0)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ X2 @ X4) @ Y0) @ 880.82/112.33 X6) @ 880.82/112.33 X8) = (X6)))))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__SOME @ X2) @ Y0)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ X2 @ X4) @ Y0) @ 880.82/112.33 X6) @ 880.82/112.33 X8) = (ap @ X8 @ 880.82/112.33 (ap @ (c_2Eoption_2ETHE @ X2) @ Y0))))))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X2) => 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X4) => 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (arr @ X2 @ X4)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y0)) @ 880.82/112.33 Y1) @ 880.82/112.33 Y2) = (ap @ Y2 @ Y0)))))))))))))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (arr @ X2 @ X4)) => 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X2) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EOPTION__MAP @ X2 @ 880.82/112.33 X4) @ 880.82/112.33 Y0) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.33 Y1)) = 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X4) @ 880.82/112.33 (ap @ Y0 @ Y1)))))))))))))) & 880.82/112.33 (((ap @ (c_2Eoption_2EOPTION__JOIN @ X2) @ 880.82/112.33 (c_2Eoption_2ENONE @ (ty_2Eoption_2Eoption @ X2))) = 880.82/112.33 (c_2Eoption_2ENONE @ X2))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((ap @ (c_2Eoption_2EOPTION__JOIN @ X2) @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) @ 880.82/112.33 Y0)) = 880.82/112.33 (Y0)))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (arr @ X2 @ X4)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTION__MAP @ X2 @ X4) @ Y0) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2)) = 880.82/112.33 (c_2Eoption_2ENONE @ X4)))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X4) => 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ (arr @ X2 @ X4)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2)) @ 880.82/112.33 Y0) @ 880.82/112.33 Y1) = (Y0))))))))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__SOME @ X2) @ Y0)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) @ 880.82/112.33 Y0) @ 880.82/112.33 X10) @ 880.82/112.33 (c_2Eoption_2ESOME @ X2)) = (Y0)))))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) @ 880.82/112.33 Y0) @ 880.82/112.33 Y0) @ 880.82/112.33 (c_2Eoption_2ESOME @ X2)) = (Y0)))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) @ 880.82/112.33 Y0) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2)) @ 880.82/112.33 (c_2Eoption_2ESOME @ X2)) = (Y0)))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((((~) @ (p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__SOME @ X2) @ Y0)))) <=> 880.82/112.33 (((Y0) = (c_2Eoption_2ENONE @ X2)))))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__NONE @ X2) @ Y0)) <=> 880.82/112.33 (((Y0) = (c_2Eoption_2ENONE @ X2)))))))))))))) 880.82/112.33 | ~ (mem @ X6 @ X4) 880.82/112.33 | ~ (mem @ X8 @ (arr @ X2 @ X4)))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl120])). 880.82/112.33 thf(zip_derived_cl122, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 (~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | (((((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X2) => 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X2) => 880.82/112.33 (((((Y0) = (Y1))) <=> 880.82/112.33 (((ap @ 880.82/112.33 (c_2Eoption_2ESOME @ X2) @ Y0) = 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ X2) @ Y1))))))))))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X2) => 880.82/112.33 (((ap @ (c_2Eoption_2ETHE @ X2) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X2) @ Y0)) = (Y0)))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X2) => 880.82/112.33 (((c_2Eoption_2ENONE @ X2) != (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ X2) @ Y0)))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X2) => 880.82/112.33 (((ap @ (c_2Eoption_2ESOME @ X2) @ Y0) != 880.82/112.33 (c_2Eoption_2ENONE @ X2)))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X2) => (p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__SOME @ X2) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X2) @ Y0)))))))) & 880.82/112.33 (((~) @ (p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__SOME @ X2) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__SOME @ X2) @ Y0)) => 880.82/112.33 (((ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.33 (ap @ (c_2Eoption_2ETHE @ X2) @ Y0)) = (Y0)))))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__NONE @ X2) @ Y0)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ X2 @ X4) @ Y0) @ 880.82/112.33 X6) @ 880.82/112.33 X8) = (X6)))))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__SOME @ X2) @ Y0)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ X2 @ X4) @ Y0) @ 880.82/112.33 X6) @ 880.82/112.33 X8) = (ap @ X8 @ 880.82/112.33 (ap @ (c_2Eoption_2ETHE @ X2) @ Y0))))))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X2) => 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X4) => 880.82/112.33 (((!!) @ (^[Y2 : $i]: 880.82/112.33 (((mem @ Y2 @ 880.82/112.33 (arr @ X2 @ X4)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 X2) @ 880.82/112.33 Y0)) @ 880.82/112.33 Y1) @ 880.82/112.33 Y2) = (ap @ Y2 @ Y0)))))))))))))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (arr @ X2 @ X4)) => 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X2) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2EOPTION__MAP @ X2 @ 880.82/112.33 X4) @ 880.82/112.33 Y0) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.33 Y1)) = 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X4) @ 880.82/112.33 (ap @ Y0 @ Y1)))))))))))))) & 880.82/112.33 (((ap @ (c_2Eoption_2EOPTION__JOIN @ X2) @ 880.82/112.33 (c_2Eoption_2ENONE @ (ty_2Eoption_2Eoption @ X2))) = 880.82/112.33 (c_2Eoption_2ENONE @ X2))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((ap @ (c_2Eoption_2EOPTION__JOIN @ X2) @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) @ 880.82/112.33 Y0)) = 880.82/112.33 (Y0)))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (arr @ X2 @ X4)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTION__MAP @ X2 @ X4) @ Y0) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2)) = 880.82/112.33 (c_2Eoption_2ENONE @ X4)))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X4) => 880.82/112.33 (((!!) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ (arr @ X2 @ X4)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ 880.82/112.33 X2 @ X4) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2)) @ 880.82/112.33 Y0) @ 880.82/112.33 Y1) = (Y0))))))))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__SOME @ X2) @ Y0)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) @ 880.82/112.33 Y0) @ 880.82/112.33 X10) @ 880.82/112.33 (c_2Eoption_2ESOME @ X2)) = (Y0)))))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) @ 880.82/112.33 Y0) @ 880.82/112.33 Y0) @ 880.82/112.33 (c_2Eoption_2ESOME @ X2)) = (Y0)))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (c_2Eoption_2Eoption__CASE @ X2 @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) @ 880.82/112.33 Y0) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2)) @ 880.82/112.33 (c_2Eoption_2ESOME @ X2)) = (Y0)))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((((~) @ (p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__SOME @ X2) @ Y0)))) <=> 880.82/112.33 (((Y0) = (c_2Eoption_2ENONE @ X2)))))))))) & 880.82/112.33 (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__NONE @ X2) @ Y0)) <=> 880.82/112.33 (((Y0) = (c_2Eoption_2ENONE @ X2)))))))))))) 880.82/112.33 | ~ (mem @ X8 @ (arr @ X2 @ X4)) 880.82/112.33 | ~ (mem @ X6 @ X4))), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl121])). 880.82/112.33 thf(zip_derived_cl125, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 ( (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X2) => 880.82/112.33 (((c_2Eoption_2ENONE @ X2) != (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ X2) @ Y0)))))))) 880.82/112.33 | ~ (mem @ X6 @ X4) 880.82/112.33 | ~ (mem @ X8 @ (arr @ X2 @ X4)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X2)))), 880.82/112.33 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl122])). 880.82/112.33 thf(zip_derived_cl145, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 880.82/112.33 ( (((mem @ X12 @ X2) => 880.82/112.33 (((c_2Eoption_2ENONE @ X2) != (ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.33 X12))))) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X8 @ (arr @ X2 @ X4)) 880.82/112.33 | ~ (mem @ X6 @ X4))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl125])). 880.82/112.33 thf(zip_derived_cl164, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 880.82/112.33 (~ (mem @ X12 @ X2) 880.82/112.33 | (((c_2Eoption_2ENONE @ X2) != (ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.33 X12))) 880.82/112.33 | ~ (mem @ X6 @ X4) 880.82/112.33 | ~ (mem @ X8 @ (arr @ X2 @ X4)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X2)))), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl145])). 880.82/112.33 thf(zip_derived_cl182, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 880.82/112.33 (~ (mem @ X12 @ X2) 880.82/112.33 | ((c_2Eoption_2ENONE @ X2) != (ap @ (c_2Eoption_2ESOME @ X2) @ X12)) 880.82/112.33 | ~ (mem @ X6 @ X4) 880.82/112.33 | ~ (mem @ X8 @ (arr @ X2 @ X4)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X2)))), 880.82/112.33 inference('simplify nested equalities', [status(thm)], 880.82/112.33 [zip_derived_cl164])). 880.82/112.33 thf(zip_derived_cl758, plain, 880.82/112.33 (![X0 : del, X1 : del, X2 : $i, X3 : $i, X4 : $i]: 880.82/112.33 (~ (mem @ X2 @ (ty_2Eoption_2Eoption @ X1)) 880.82/112.33 | ~ (mem @ X3 @ X0) 880.82/112.33 | ((c_2Eoption_2ENONE @ X1) != (ap @ (c_2Eoption_2ESOME @ X1) @ X4)) 880.82/112.33 | ~ (mem @ X4 @ X1))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl284, zip_derived_cl182])). 880.82/112.33 thf(zip_derived_cl776, plain, 880.82/112.33 (![X0 : del, X1 : $i, X2 : $i]: 880.82/112.33 (~ (mem @ X1 @ (ty_2Eoption_2Eoption @ X0)) 880.82/112.33 | ~ (mem @ X2 @ X0) 880.82/112.33 | ((c_2Eoption_2ENONE @ X0) != (ap @ (c_2Eoption_2ESOME @ X0) @ X2)))), 880.82/112.33 inference('condensation', [status(thm)], [zip_derived_cl758])). 880.82/112.33 thf(zip_derived_cl783, plain, 880.82/112.33 (![X0 : del, X1 : $i]: 880.82/112.33 (((c_2Eoption_2ENONE @ X0) != (ap @ (c_2Eoption_2ESOME @ X0) @ X1)) 880.82/112.33 | ~ (mem @ X1 @ X0))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl776])). 880.82/112.33 thf(zip_derived_cl801, plain, 880.82/112.33 (((((c_2Eoption_2ENONE @ '#sk3') != (c_2Eoption_2ENONE @ '#sk3')) 880.82/112.33 | ~ (mem @ '#sk6' @ '#sk3'))) 880.82/112.33 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3'))))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl371, zip_derived_cl783])). 880.82/112.33 thf(zip_derived_cl262, plain, ( (mem @ '#sk6' @ '#sk3')), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl261])). 880.82/112.33 thf(zip_derived_cl803, plain, 880.82/112.33 ((((c_2Eoption_2ENONE @ '#sk3') != (c_2Eoption_2ENONE @ '#sk3'))) 880.82/112.33 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3'))))), 880.82/112.33 inference('demod', [status(thm)], [zip_derived_cl801, zip_derived_cl262])). 880.82/112.33 thf('2', plain, 880.82/112.33 (~ 880.82/112.33 (((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3')))), 880.82/112.33 inference('simplify', [status(thm)], [zip_derived_cl803])). 880.82/112.33 thf(zip_derived_cl370, plain, 880.82/112.33 ((~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3'))) 880.82/112.33 <= (~ 880.82/112.33 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3'))))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl319])). 880.82/112.33 thf(mem_c_2Eoption_2ESOME, axiom, 880.82/112.33 (![A_27a:del]: 880.82/112.33 ( mem @ 880.82/112.33 ( c_2Eoption_2ESOME @ A_27a ) @ 880.82/112.33 ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) ))). 880.82/112.33 thf(zip_derived_cl20, plain, 880.82/112.33 ( (((!!) @ (^[Y0 : del]: 880.82/112.33 (mem @ (c_2Eoption_2ESOME @ Y0) @ 880.82/112.33 (arr @ Y0 @ (ty_2Eoption_2Eoption @ Y0))))))), 880.82/112.33 inference('cnf', [status(esa)], [mem_c_2Eoption_2ESOME])). 880.82/112.33 thf(zip_derived_cl63, plain, 880.82/112.33 (![X2 : del]: 880.82/112.33 (mem @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.33 (arr @ X2 @ (ty_2Eoption_2Eoption @ X2)))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])). 880.82/112.33 thf(zip_derived_cl36, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 880.82/112.33 (~ (mem @ X8 @ X2) 880.82/112.33 | (mem @ (ap @ X6 @ X8) @ X4) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ X4)))), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 880.82/112.33 thf(zip_derived_cl65, plain, 880.82/112.33 (![X0 : del, X1 : $i]: 880.82/112.33 ( (mem @ (ap @ (c_2Eoption_2ESOME @ X0) @ X1) @ 880.82/112.33 (ty_2Eoption_2Eoption @ X0)) 880.82/112.33 | ~ (mem @ X1 @ X0))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl36])). 880.82/112.33 thf(zip_derived_cl445, plain, 880.82/112.33 ((~ (mem @ '#sk6' @ '#sk3')) 880.82/112.33 <= (~ 880.82/112.33 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3'))))), 880.82/112.33 inference('sup+', [status(thm)], [zip_derived_cl370, zip_derived_cl65])). 880.82/112.33 thf(zip_derived_cl262, plain, ( (mem @ '#sk6' @ '#sk3')), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl261])). 880.82/112.33 thf('3', plain, 880.82/112.33 (( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')))), 880.82/112.33 inference('demod', [status(thm)], [zip_derived_cl445, zip_derived_cl262])). 880.82/112.33 thf(zip_derived_cl2773, plain, 880.82/112.33 ((((c_2Eoption_2ENONE @ '#sk3') 880.82/112.33 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.33 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))) 880.82/112.33 <= ((((c_2Eoption_2ENONE @ '#sk3') 880.82/112.33 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.33 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl2672])). 880.82/112.33 thf(zip_derived_cl284, plain, 880.82/112.33 (![X0 : del]: 880.82/112.33 (mem @ (ap @ (c_2Eoption_2ETHE @ X0) @ (c_2Eoption_2ENONE @ X0)) @ X0)), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl37])). 880.82/112.33 thf(zip_derived_cl142, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 ( (((!!) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ (ap @ (c_2Eoption_2EIS__NONE @ X2) @ Y0)) <=> 880.82/112.33 (((Y0) = (c_2Eoption_2ENONE @ X2)))))))))) 880.82/112.33 | ~ (mem @ X6 @ X4) 880.82/112.33 | ~ (mem @ X8 @ (arr @ X2 @ X4)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X2)))), 880.82/112.33 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl122])). 880.82/112.33 thf(zip_derived_cl161, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 880.82/112.33 ( (((mem @ X12 @ (ty_2Eoption_2Eoption @ X2)) => 880.82/112.33 (((p @ (ap @ (c_2Eoption_2EIS__NONE @ X2) @ X12)) <=> 880.82/112.33 (((X12) = (c_2Eoption_2ENONE @ X2))))))) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X8 @ (arr @ X2 @ X4)) 880.82/112.33 | ~ (mem @ X6 @ X4))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl142])). 880.82/112.33 thf(zip_derived_cl179, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 880.82/112.33 (~ (mem @ X12 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | (((p @ (ap @ (c_2Eoption_2EIS__NONE @ X2) @ X12)) <=> 880.82/112.33 (((X12) = (c_2Eoption_2ENONE @ X2))))) 880.82/112.33 | ~ (mem @ X6 @ X4) 880.82/112.33 | ~ (mem @ X8 @ (arr @ X2 @ X4)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X2)))), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl161])). 880.82/112.33 thf(zip_derived_cl206, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 880.82/112.33 (~ (mem @ X12 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ((p @ (ap @ (c_2Eoption_2EIS__NONE @ X2) @ X12)) 880.82/112.33 = (((X12) = (c_2Eoption_2ENONE @ X2)))) 880.82/112.33 | ~ (mem @ X6 @ X4) 880.82/112.33 | ~ (mem @ X8 @ (arr @ X2 @ X4)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X2)))), 880.82/112.33 inference('simplify nested equalities', [status(thm)], 880.82/112.33 [zip_derived_cl179])). 880.82/112.33 thf(zip_derived_cl207, plain, 880.82/112.33 (![X0 : del, X1 : $i, X2 : del, X3 : $i, X4 : $i]: 880.82/112.33 (~ (mem @ X1 @ (ty_2Eoption_2Eoption @ X0)) 880.82/112.33 | ((p @ (ap @ (c_2Eoption_2EIS__NONE @ X0) @ X1)) 880.82/112.33 = (((X1) = (c_2Eoption_2ENONE @ X0)))) 880.82/112.33 | ~ (mem @ X3 @ X2) 880.82/112.33 | ~ (mem @ X4 @ (arr @ X0 @ X2)))), 880.82/112.33 inference('condensation', [status(thm)], [zip_derived_cl206])). 880.82/112.33 thf(zip_derived_cl821, plain, 880.82/112.33 (![X0 : del, X1 : del, X2 : $i, X3 : $i]: 880.82/112.33 (~ (mem @ X2 @ X0) 880.82/112.33 | ((p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ X3)) 880.82/112.33 = (((X3) = (c_2Eoption_2ENONE @ X1)))) 880.82/112.33 | ~ (mem @ X3 @ (ty_2Eoption_2Eoption @ X1)))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl284, zip_derived_cl207])). 880.82/112.33 thf(zip_derived_cl1510, plain, 880.82/112.33 (![X0 : del, X1 : $i]: 880.82/112.33 (~ (mem @ X1 @ (ty_2Eoption_2Eoption @ X0)) 880.82/112.33 | ((p @ (ap @ (c_2Eoption_2EIS__NONE @ X0) @ X1)) 880.82/112.33 = (((X1) = (c_2Eoption_2ENONE @ X0)))))), 880.82/112.33 inference('condensation', [status(thm)], [zip_derived_cl821])). 880.82/112.33 thf(zip_derived_cl1536, plain, 880.82/112.33 (![X0 : del, X1 : $i]: 880.82/112.33 (~ (p @ (ap @ (c_2Eoption_2EIS__NONE @ X0) @ X1)) 880.82/112.33 | (((X1) = (c_2Eoption_2ENONE @ X0))) 880.82/112.33 | ~ (mem @ X1 @ (ty_2Eoption_2Eoption @ X0)))), 880.82/112.33 inference('eq_elim', [status(thm)], [zip_derived_cl1510])). 880.82/112.33 thf(zip_derived_cl1539, plain, 880.82/112.33 (![X0 : del, X1 : $i]: 880.82/112.33 (~ (p @ (ap @ (c_2Eoption_2EIS__NONE @ X0) @ X1)) 880.82/112.33 | ((X1) = (c_2Eoption_2ENONE @ X0)) 880.82/112.33 | ~ (mem @ X1 @ (ty_2Eoption_2Eoption @ X0)))), 880.82/112.33 inference('simplify nested equalities', [status(thm)], 880.82/112.33 [zip_derived_cl1536])). 880.82/112.33 thf(zip_derived_cl65, plain, 880.82/112.33 (![X0 : del, X1 : $i]: 880.82/112.33 ( (mem @ (ap @ (c_2Eoption_2ESOME @ X0) @ X1) @ 880.82/112.33 (ty_2Eoption_2Eoption @ X0)) 880.82/112.33 | ~ (mem @ X1 @ X0))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl36])). 880.82/112.33 thf(zip_derived_cl1580, plain, 880.82/112.33 (![X0 : del, X1 : $i]: 880.82/112.33 (((ap @ (c_2Eoption_2ESOME @ X0) @ X1) = (c_2Eoption_2ENONE @ X0)) 880.82/112.33 | ~ (p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__NONE @ X0) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X0) @ X1))) 880.82/112.33 | ~ (mem @ X1 @ X0))), 880.82/112.33 inference('sup+', [status(thm)], [zip_derived_cl1539, zip_derived_cl65])). 880.82/112.33 thf(zip_derived_cl783, plain, 880.82/112.33 (![X0 : del, X1 : $i]: 880.82/112.33 (((c_2Eoption_2ENONE @ X0) != (ap @ (c_2Eoption_2ESOME @ X0) @ X1)) 880.82/112.33 | ~ (mem @ X1 @ X0))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl776])). 880.82/112.33 thf(zip_derived_cl1702, plain, 880.82/112.33 (![X0 : del, X1 : $i]: 880.82/112.33 (~ (mem @ X1 @ X0) 880.82/112.33 | ~ (p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__NONE @ X0) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X0) @ X1))))), 880.82/112.33 inference('clc', [status(thm)], [zip_derived_cl1580, zip_derived_cl783])). 880.82/112.33 thf(zip_derived_cl2777, plain, 880.82/112.33 (((~ (p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__NONE @ '#sk3') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3'))) 880.82/112.33 | ~ (mem @ 880.82/112.33 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.33 '#sk3'))) 880.82/112.33 <= ((((c_2Eoption_2ENONE @ '#sk3') 880.82/112.33 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.33 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl2773, zip_derived_cl1702])). 880.82/112.33 thf(zip_derived_cl262, plain, ( (mem @ '#sk6' @ '#sk3')), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl261])). 880.82/112.33 thf(zip_derived_cl284, plain, 880.82/112.33 (![X0 : del]: 880.82/112.33 (mem @ (ap @ (c_2Eoption_2ETHE @ X0) @ (c_2Eoption_2ENONE @ X0)) @ X0)), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl37])). 880.82/112.33 thf(zip_derived_cl207, plain, 880.82/112.33 (![X0 : del, X1 : $i, X2 : del, X3 : $i, X4 : $i]: 880.82/112.33 (~ (mem @ X1 @ (ty_2Eoption_2Eoption @ X0)) 880.82/112.33 | ((p @ (ap @ (c_2Eoption_2EIS__NONE @ X0) @ X1)) 880.82/112.33 = (((X1) = (c_2Eoption_2ENONE @ X0)))) 880.82/112.33 | ~ (mem @ X3 @ X2) 880.82/112.33 | ~ (mem @ X4 @ (arr @ X0 @ X2)))), 880.82/112.33 inference('condensation', [status(thm)], [zip_derived_cl206])). 880.82/112.33 thf(zip_derived_cl823, plain, 880.82/112.33 (![X0 : del, X1 : $i, X2 : del, X3 : $i, X4 : $i]: 880.82/112.33 ( (p @ (ap @ (c_2Eoption_2EIS__NONE @ X0) @ X1)) 880.82/112.33 | ~ (((X1) = (c_2Eoption_2ENONE @ X0))) 880.82/112.33 | ~ (mem @ X4 @ (arr @ X0 @ X2)) 880.82/112.33 | ~ (mem @ X3 @ X2) 880.82/112.33 | ~ (mem @ X1 @ (ty_2Eoption_2Eoption @ X0)))), 880.82/112.33 inference('eq_elim', [status(thm)], [zip_derived_cl207])). 880.82/112.33 thf(zip_derived_cl825, plain, 880.82/112.33 (![X0 : del, X1 : $i, X2 : del, X3 : $i, X4 : $i]: 880.82/112.33 ( (p @ (ap @ (c_2Eoption_2EIS__NONE @ X0) @ X1)) 880.82/112.33 | ((X1) != (c_2Eoption_2ENONE @ X0)) 880.82/112.33 | ~ (mem @ X4 @ (arr @ X0 @ X2)) 880.82/112.33 | ~ (mem @ X3 @ X2) 880.82/112.33 | ~ (mem @ X1 @ (ty_2Eoption_2Eoption @ X0)))), 880.82/112.33 inference('simplify nested equalities', [status(thm)], 880.82/112.33 [zip_derived_cl823])). 880.82/112.33 thf(zip_derived_cl826, plain, 880.82/112.33 (![X0 : del, X2 : del, X3 : $i, X4 : $i]: 880.82/112.33 (~ (mem @ (c_2Eoption_2ENONE @ X0) @ (ty_2Eoption_2Eoption @ X0)) 880.82/112.33 | ~ (mem @ X3 @ X2) 880.82/112.33 | ~ (mem @ X4 @ (arr @ X0 @ X2)) 880.82/112.33 | (p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__NONE @ X0) @ (c_2Eoption_2ENONE @ X0))))), 880.82/112.33 inference('simplify', [status(thm)], [zip_derived_cl825])). 880.82/112.33 thf(zip_derived_cl27, plain, 880.82/112.33 (![X2 : del]: 880.82/112.33 (mem @ (c_2Eoption_2ENONE @ X2) @ (ty_2Eoption_2Eoption @ X2))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 880.82/112.33 thf(zip_derived_cl844, plain, 880.82/112.33 (![X0 : del, X2 : del, X3 : $i, X4 : $i]: 880.82/112.33 (~ (mem @ X3 @ X2) 880.82/112.33 | ~ (mem @ X4 @ (arr @ X0 @ X2)) 880.82/112.33 | (p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__NONE @ X0) @ (c_2Eoption_2ENONE @ X0))))), 880.82/112.33 inference('demod', [status(thm)], [zip_derived_cl826, zip_derived_cl27])). 880.82/112.33 thf(zip_derived_cl1015, plain, 880.82/112.33 (![X0 : del, X1 : del, X2 : $i]: 880.82/112.33 ( (p @ (ap @ (c_2Eoption_2EIS__NONE @ X1) @ (c_2Eoption_2ENONE @ X1))) 880.82/112.33 | ~ (mem @ X2 @ X0))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl284, zip_derived_cl844])). 880.82/112.33 thf(zip_derived_cl1076, plain, 880.82/112.33 (![X0 : del]: 880.82/112.33 (p @ (ap @ (c_2Eoption_2EIS__NONE @ X0) @ (c_2Eoption_2ENONE @ X0)))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl262, zip_derived_cl1015])). 880.82/112.33 thf(zip_derived_cl2787, plain, 880.82/112.33 ((~ (mem @ 880.82/112.33 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.33 '#sk3')) 880.82/112.33 <= ((((c_2Eoption_2ENONE @ '#sk3') 880.82/112.33 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.33 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.33 inference('demod', [status(thm)], 880.82/112.33 [zip_derived_cl2777, zip_derived_cl1076])). 880.82/112.33 thf(zip_derived_cl369, plain, 880.82/112.33 (( (mem @ 880.82/112.33 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.33 '#sk3')) 880.82/112.33 <= (( (mem @ 880.82/112.33 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.33 '#sk3')))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl319])). 880.82/112.33 thf('4', plain, 880.82/112.33 (~ 880.82/112.33 ( (mem @ 880.82/112.33 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.33 '#sk3')) | 880.82/112.33 ~ 880.82/112.33 (((c_2Eoption_2ENONE @ '#sk3') 880.82/112.33 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.33 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.33 inference('sup+', [status(thm)], [zip_derived_cl2787, zip_derived_cl369])). 880.82/112.33 thf(zip_derived_cl256, plain, 880.82/112.33 ( (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool)))), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl255])). 880.82/112.33 thf(zip_derived_cl233, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 (~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | ((((((??) @ (^[Y0 : $i]: 880.82/112.33 (((((??) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X4) & 880.82/112.33 (((X8) = (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ X2) @ Y0))) & 880.82/112.33 (((X10) = (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ X4) @ Y1))) & 880.82/112.33 (p @ (ap @ (ap @ X6 @ Y0) @ Y1))))))) & 880.82/112.33 (mem @ Y0 @ X2)))))) | 880.82/112.33 (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.33 (((X8) = (c_2Eoption_2ENONE @ X2))))))) 880.82/112.33 = (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ X10))) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))))), 880.82/112.33 inference('simplify nested equalities', [status(thm)], 880.82/112.33 [zip_derived_cl232])). 880.82/112.33 thf(zip_derived_cl235, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 (~ (((((??) @ (^[Y0 : $i]: 880.82/112.33 (((((??) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X4) & 880.82/112.33 (((X8) = (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ X2) @ Y0))) & 880.82/112.33 (((X10) = (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ X4) @ Y1))) & 880.82/112.33 (p @ (ap @ (ap @ X6 @ Y0) @ Y1))))))) & 880.82/112.33 (mem @ Y0 @ X2)))))) | 880.82/112.33 (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.33 (((X8) = (c_2Eoption_2ENONE @ X2))))))) 880.82/112.33 | (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)))), 880.82/112.33 inference('eq_elim', [status(thm)], [zip_derived_cl233])). 880.82/112.33 thf(zip_derived_cl240, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 (~ (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.33 (((X8) = (c_2Eoption_2ENONE @ X2))))) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)))), 880.82/112.33 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl235])). 880.82/112.33 thf(zip_derived_cl242, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 (~ (((X10) = (c_2Eoption_2ENONE @ X4))) 880.82/112.33 | ~ (((X8) = (c_2Eoption_2ENONE @ X2))) 880.82/112.33 | (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)))), 880.82/112.33 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl240])). 880.82/112.33 thf(zip_derived_cl244, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 (((X10) != (c_2Eoption_2ENONE @ X4)) 880.82/112.33 | ((X8) != (c_2Eoption_2ENONE @ X2)) 880.82/112.33 | (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)))), 880.82/112.33 inference('simplify nested equalities', [status(thm)], 880.82/112.33 [zip_derived_cl242])). 880.82/112.33 thf(zip_derived_cl245, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i]: 880.82/112.33 (~ (mem @ (c_2Eoption_2ENONE @ X4) @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | ~ (mem @ (c_2Eoption_2ENONE @ X2) @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2)) @ 880.82/112.33 (c_2Eoption_2ENONE @ X4))))), 880.82/112.33 inference('simplify', [status(thm)], [zip_derived_cl244])). 880.82/112.33 thf(zip_derived_cl27, plain, 880.82/112.33 (![X2 : del]: 880.82/112.33 (mem @ (c_2Eoption_2ENONE @ X2) @ (ty_2Eoption_2Eoption @ X2))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 880.82/112.33 thf(zip_derived_cl246, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i]: 880.82/112.33 ( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ 880.82/112.33 (c_2Eoption_2ENONE @ X2)) @ 880.82/112.33 (c_2Eoption_2ENONE @ X4))) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))))), 880.82/112.33 inference('simplify_reflect+', [status(thm)], 880.82/112.33 [zip_derived_cl245, zip_derived_cl27])). 880.82/112.33 thf(zip_derived_cl270, plain, 880.82/112.33 ( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl256, zip_derived_cl246])). 880.82/112.33 thf(zip_derived_cl269, plain, 880.82/112.33 ((~ (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.33 <= (~ 880.82/112.33 ( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl265])). 880.82/112.33 thf('5', plain, 880.82/112.33 (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3'))))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl270, zip_derived_cl269])). 880.82/112.33 thf(zip_derived_cl268, plain, 880.82/112.33 (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.33 <= (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl265])). 880.82/112.33 thf(zip_derived_cl295, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 ( (((X10) = (ap @ (c_2Eoption_2ESOME @ X4) @ 880.82/112.33 ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10)))) 880.82/112.33 | (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.33 (((X8) = (c_2Eoption_2ENONE @ X2))))) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | ~ (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)))), 880.82/112.33 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl290])). 880.82/112.33 thf(zip_derived_cl304, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 (((X10) 880.82/112.33 = (ap @ (c_2Eoption_2ESOME @ X4) @ 880.82/112.33 ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10))) 880.82/112.33 | (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.33 (((X8) = (c_2Eoption_2ENONE @ X2))))) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | ~ (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)))), 880.82/112.33 inference('simplify nested equalities', [status(thm)], 880.82/112.33 [zip_derived_cl295])). 880.82/112.33 thf(zip_derived_cl306, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 ( (((X8) = (c_2Eoption_2ENONE @ X2))) 880.82/112.33 | ~ (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | ((X10) 880.82/112.33 = (ap @ (c_2Eoption_2ESOME @ X4) @ 880.82/112.33 ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10))))), 880.82/112.33 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl304])). 880.82/112.33 thf(zip_derived_cl314, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 (((X8) = (c_2Eoption_2ENONE @ X2)) 880.82/112.33 | ~ (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | ((X10) 880.82/112.33 = (ap @ (c_2Eoption_2ESOME @ X4) @ 880.82/112.33 ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10))))), 880.82/112.33 inference('simplify nested equalities', [status(thm)], 880.82/112.33 [zip_derived_cl306])). 880.82/112.33 thf(zip_derived_cl2887, plain, 880.82/112.33 (((((c_2Eoption_2ENONE @ '#sk3') 880.82/112.33 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.33 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.33 | ~ (mem @ (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.33 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.33 | ~ (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool))) 880.82/112.33 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.33 <= (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl268, zip_derived_cl314])). 880.82/112.33 thf(zip_derived_cl27, plain, 880.82/112.33 (![X2 : del]: 880.82/112.33 (mem @ (c_2Eoption_2ENONE @ X2) @ (ty_2Eoption_2Eoption @ X2))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 880.82/112.33 thf(zip_derived_cl256, plain, 880.82/112.33 ( (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool)))), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl255])). 880.82/112.33 thf(zip_derived_cl2899, plain, 880.82/112.33 (((((c_2Eoption_2ENONE @ '#sk3') 880.82/112.33 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.33 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.33 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.33 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.33 <= (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))))), 880.82/112.33 inference('demod', [status(thm)], 880.82/112.33 [zip_derived_cl2887, zip_derived_cl27, zip_derived_cl256])). 880.82/112.33 thf('6', plain, 880.82/112.33 ((((c_2Eoption_2ENONE @ '#sk3') 880.82/112.33 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.33 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3'))))) | 880.82/112.33 (((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3'))) | 880.82/112.33 ~ 880.82/112.33 ( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))) | 880.82/112.33 ~ 880.82/112.33 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl2899])). 880.82/112.33 thf(zip_derived_cl266, plain, 880.82/112.33 ((((p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.33 != (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))) 880.82/112.33 <= (~ 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.33 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl265])). 880.82/112.33 thf(zip_derived_cl280, plain, 880.82/112.33 ((( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.33 | (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))) 880.82/112.33 <= (~ 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.33 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.33 inference('eq_elim', [status(thm)], [zip_derived_cl266])). 880.82/112.33 thf(zip_derived_cl346, plain, 880.82/112.33 (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.33 <= (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl280])). 880.82/112.33 thf(zip_derived_cl297, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 (((X10) = (c_2Eoption_2ENONE @ X4)) 880.82/112.33 | ~ (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | (mem @ ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10) @ X2))), 880.82/112.33 inference('simplify nested equalities', [status(thm)], 880.82/112.33 [zip_derived_cl291])). 880.82/112.33 thf(zip_derived_cl357, plain, 880.82/112.33 ((( (mem @ 880.82/112.33 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.33 '#sk3') 880.82/112.33 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.33 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.33 | ~ (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool))) 880.82/112.33 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.33 <= (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl346, zip_derived_cl297])). 880.82/112.33 thf(zip_derived_cl256, plain, 880.82/112.33 ( (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool)))), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl255])). 880.82/112.33 thf(zip_derived_cl363, plain, 880.82/112.33 ((( (mem @ 880.82/112.33 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.33 '#sk3') 880.82/112.33 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.33 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.33 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.33 <= (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.33 inference('demod', [status(thm)], [zip_derived_cl357, zip_derived_cl256])). 880.82/112.33 thf(zip_derived_cl430, plain, 880.82/112.33 ((~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3'))) 880.82/112.33 <= (~ 880.82/112.33 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3'))))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl363])). 880.82/112.33 thf(zip_derived_cl65, plain, 880.82/112.33 (![X0 : del, X1 : $i]: 880.82/112.33 ( (mem @ (ap @ (c_2Eoption_2ESOME @ X0) @ X1) @ 880.82/112.33 (ty_2Eoption_2Eoption @ X0)) 880.82/112.33 | ~ (mem @ X1 @ X0))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl36])). 880.82/112.33 thf(zip_derived_cl446, plain, 880.82/112.33 ((~ (mem @ '#sk5' @ '#sk3')) 880.82/112.33 <= (~ 880.82/112.33 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3'))))), 880.82/112.33 inference('sup+', [status(thm)], [zip_derived_cl430, zip_derived_cl65])). 880.82/112.33 thf(zip_derived_cl259, plain, ( (mem @ '#sk5' @ '#sk3')), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl258])). 880.82/112.33 thf('7', plain, 880.82/112.33 (( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')))), 880.82/112.33 inference('demod', [status(thm)], [zip_derived_cl446, zip_derived_cl259])). 880.82/112.33 thf(zip_derived_cl268, plain, 880.82/112.33 (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.33 <= (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl265])). 880.82/112.33 thf(zip_derived_cl292, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 ( (((X8) = (c_2Eoption_2ENONE @ X2))) 880.82/112.33 | ~ (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | (mem @ ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10) @ X2))), 880.82/112.33 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl289])). 880.82/112.33 thf(zip_derived_cl298, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 (((X8) = (c_2Eoption_2ENONE @ X2)) 880.82/112.33 | ~ (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | (mem @ ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10) @ X2))), 880.82/112.33 inference('simplify nested equalities', [status(thm)], 880.82/112.33 [zip_derived_cl292])). 880.82/112.33 thf(zip_derived_cl2465, plain, 880.82/112.33 ((( (mem @ 880.82/112.33 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 '#sk3') 880.82/112.33 | ~ (mem @ (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.33 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.33 | ~ (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool))) 880.82/112.33 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.33 <= (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl268, zip_derived_cl298])). 880.82/112.33 thf(zip_derived_cl27, plain, 880.82/112.33 (![X2 : del]: 880.82/112.33 (mem @ (c_2Eoption_2ENONE @ X2) @ (ty_2Eoption_2Eoption @ X2))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 880.82/112.33 thf(zip_derived_cl256, plain, 880.82/112.33 ( (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool)))), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl255])). 880.82/112.33 thf(zip_derived_cl2479, plain, 880.82/112.33 ((( (mem @ 880.82/112.33 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 '#sk3') 880.82/112.33 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.33 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.33 <= (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))))), 880.82/112.33 inference('demod', [status(thm)], 880.82/112.33 [zip_derived_cl2465, zip_derived_cl27, zip_derived_cl256])). 880.82/112.33 thf(zip_derived_cl2499, plain, 880.82/112.33 ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3'))) 880.82/112.33 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3'))))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl2479])). 880.82/112.33 thf(zip_derived_cl1702, plain, 880.82/112.33 (![X0 : del, X1 : $i]: 880.82/112.33 (~ (mem @ X1 @ X0) 880.82/112.33 | ~ (p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__NONE @ X0) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X0) @ X1))))), 880.82/112.33 inference('clc', [status(thm)], [zip_derived_cl1580, zip_derived_cl783])). 880.82/112.33 thf(zip_derived_cl2510, plain, 880.82/112.33 (((~ (p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__NONE @ '#sk3') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3'))) 880.82/112.33 | ~ (mem @ '#sk5' @ '#sk3'))) 880.82/112.33 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3'))))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl2499, zip_derived_cl1702])). 880.82/112.33 thf(zip_derived_cl1076, plain, 880.82/112.33 (![X0 : del]: 880.82/112.33 (p @ (ap @ (c_2Eoption_2EIS__NONE @ X0) @ (c_2Eoption_2ENONE @ X0)))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl262, zip_derived_cl1015])). 880.82/112.33 thf(zip_derived_cl259, plain, ( (mem @ '#sk5' @ '#sk3')), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl258])). 880.82/112.33 thf('8', plain, 880.82/112.33 (~ 880.82/112.33 (((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3')))), 880.82/112.33 inference('demod', [status(thm)], 880.82/112.33 [zip_derived_cl2510, zip_derived_cl1076, zip_derived_cl259])). 880.82/112.33 thf(zip_derived_cl268, plain, 880.82/112.33 (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.33 <= (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl265])). 880.82/112.33 thf(zip_derived_cl293, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 ( (mem @ ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10) @ X4) 880.82/112.33 | (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.33 (((X8) = (c_2Eoption_2ENONE @ X2))))) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | ~ (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)))), 880.82/112.33 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl290])). 880.82/112.33 thf(zip_derived_cl300, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 ( (((X8) = (c_2Eoption_2ENONE @ X2))) 880.82/112.33 | ~ (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | (mem @ ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10) @ X4))), 880.82/112.33 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl293])). 880.82/112.33 thf(zip_derived_cl310, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 (((X8) = (c_2Eoption_2ENONE @ X2)) 880.82/112.33 | ~ (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | (mem @ ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10) @ X4))), 880.82/112.33 inference('simplify nested equalities', [status(thm)], 880.82/112.33 [zip_derived_cl300])). 880.82/112.33 thf(zip_derived_cl2600, plain, 880.82/112.33 ((( (mem @ 880.82/112.33 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 '#sk3') 880.82/112.33 | ~ (mem @ (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.33 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.33 | ~ (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool))) 880.82/112.33 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.33 <= (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl268, zip_derived_cl310])). 880.82/112.33 thf(zip_derived_cl27, plain, 880.82/112.33 (![X2 : del]: 880.82/112.33 (mem @ (c_2Eoption_2ENONE @ X2) @ (ty_2Eoption_2Eoption @ X2))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 880.82/112.33 thf(zip_derived_cl256, plain, 880.82/112.33 ( (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool)))), 880.82/112.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl255])). 880.82/112.33 thf(zip_derived_cl2614, plain, 880.82/112.33 ((( (mem @ 880.82/112.33 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 '#sk3') 880.82/112.33 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.33 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.33 <= (( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))))), 880.82/112.33 inference('demod', [status(thm)], 880.82/112.33 [zip_derived_cl2600, zip_derived_cl27, zip_derived_cl256])). 880.82/112.33 thf('9', plain, 880.82/112.33 (( (mem @ 880.82/112.33 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 '#sk3')) | 880.82/112.33 (((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.33 = (c_2Eoption_2ENONE @ '#sk3'))) | 880.82/112.33 ~ 880.82/112.33 ( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))) | 880.82/112.33 ~ 880.82/112.33 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (ty_2Eoption_2Eoption @ '#sk3')))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl2614])). 880.82/112.33 thf(zip_derived_cl2972, plain, 880.82/112.33 ((((c_2Eoption_2ENONE @ '#sk3') 880.82/112.33 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.33 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3'))))) 880.82/112.33 <= ((((c_2Eoption_2ENONE @ '#sk3') 880.82/112.33 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.33 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3'))))))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl2899])). 880.82/112.33 thf(zip_derived_cl1702, plain, 880.82/112.33 (![X0 : del, X1 : $i]: 880.82/112.33 (~ (mem @ X1 @ X0) 880.82/112.33 | ~ (p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__NONE @ X0) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X0) @ X1))))), 880.82/112.33 inference('clc', [status(thm)], [zip_derived_cl1580, zip_derived_cl783])). 880.82/112.33 thf(zip_derived_cl2976, plain, 880.82/112.33 (((~ (p @ 880.82/112.33 (ap @ (c_2Eoption_2EIS__NONE @ '#sk3') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3'))) 880.82/112.33 | ~ (mem @ 880.82/112.33 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 '#sk3'))) 880.82/112.33 <= ((((c_2Eoption_2ENONE @ '#sk3') 880.82/112.33 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.33 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3'))))))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl2972, zip_derived_cl1702])). 880.82/112.33 thf(zip_derived_cl1076, plain, 880.82/112.33 (![X0 : del]: 880.82/112.33 (p @ (ap @ (c_2Eoption_2EIS__NONE @ X0) @ (c_2Eoption_2ENONE @ X0)))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl262, zip_derived_cl1015])). 880.82/112.33 thf(zip_derived_cl2992, plain, 880.82/112.33 ((~ (mem @ 880.82/112.33 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 '#sk3')) 880.82/112.33 <= ((((c_2Eoption_2ENONE @ '#sk3') 880.82/112.33 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.33 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3'))))))), 880.82/112.33 inference('demod', [status(thm)], 880.82/112.33 [zip_derived_cl2976, zip_derived_cl1076])). 880.82/112.33 thf(zip_derived_cl2643, plain, 880.82/112.33 (( (mem @ 880.82/112.33 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 '#sk3')) 880.82/112.33 <= (( (mem @ 880.82/112.33 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 '#sk3')))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl2614])). 880.82/112.33 thf('10', plain, 880.82/112.33 (~ 880.82/112.33 ( (mem @ 880.82/112.33 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 '#sk3')) | 880.82/112.33 ~ 880.82/112.33 (((c_2Eoption_2ENONE @ '#sk3') 880.82/112.33 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.33 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))))), 880.82/112.33 inference('sup+', [status(thm)], [zip_derived_cl2992, zip_derived_cl2643])). 880.82/112.33 thf('11', plain, 880.82/112.33 (~ 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.33 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))) | 880.82/112.33 ( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))) | 880.82/112.33 ~ 880.82/112.33 ( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')))) | 880.82/112.33 ( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (c_2Eoption_2ENONE @ '#sk3')) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl265])). 880.82/112.33 thf(zip_derived_cl239, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.33 (~ (((??) @ (^[Y0 : $i]: 880.82/112.33 (((((??) @ (^[Y1 : $i]: 880.82/112.33 (((mem @ Y1 @ X4) & 880.82/112.33 (((X8) = (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ X2) @ Y0))) & 880.82/112.33 (((X10) = (ap @ 880.82/112.33 (c_2Eoption_2ESOME @ X4) @ Y1))) & 880.82/112.33 (p @ (ap @ (ap @ X6 @ Y0) @ Y1))))))) & 880.82/112.33 (mem @ Y0 @ X2)))))) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)))), 880.82/112.33 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl235])). 880.82/112.33 thf(zip_derived_cl241, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 880.82/112.33 (~ (((((??) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X4) & 880.82/112.33 (((X8) = (ap @ (c_2Eoption_2ESOME @ X2) @ X12))) & 880.82/112.33 (((X10) = (ap @ (c_2Eoption_2ESOME @ X4) @ Y0))) & 880.82/112.33 (p @ (ap @ (ap @ X6 @ X12) @ Y0))))))) & 880.82/112.33 (mem @ X12 @ X2))) 880.82/112.33 | (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl239])). 880.82/112.33 thf(zip_derived_cl243, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 880.82/112.33 (~ (((??) @ (^[Y0 : $i]: 880.82/112.33 (((mem @ Y0 @ X4) & 880.82/112.33 (((X8) = (ap @ (c_2Eoption_2ESOME @ X2) @ X12))) & 880.82/112.33 (((X10) = (ap @ (c_2Eoption_2ESOME @ X4) @ Y0))) & 880.82/112.33 (p @ (ap @ (ap @ X6 @ X12) @ Y0))))))) 880.82/112.33 | ~ (mem @ X12 @ X2) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)))), 880.82/112.33 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl241])). 880.82/112.33 thf(zip_derived_cl247, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 880.82/112.33 (~ (((mem @ X14 @ X4) & 880.82/112.33 (((X8) = (ap @ (c_2Eoption_2ESOME @ X2) @ X12))) & 880.82/112.33 (((X10) = (ap @ (c_2Eoption_2ESOME @ X4) @ X14))) & 880.82/112.33 (p @ (ap @ (ap @ X6 @ X12) @ X14)))) 880.82/112.33 | (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | ~ (mem @ X12 @ X2))), 880.82/112.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl243])). 880.82/112.33 thf(zip_derived_cl248, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 880.82/112.33 (~ (mem @ X14 @ X4) 880.82/112.33 | ~ (((X8) = (ap @ (c_2Eoption_2ESOME @ X2) @ X12))) 880.82/112.33 | ~ (((X10) = (ap @ (c_2Eoption_2ESOME @ X4) @ X14))) 880.82/112.33 | ~ (p @ (ap @ (ap @ X6 @ X12) @ X14)) 880.82/112.33 | ~ (mem @ X12 @ X2) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)))), 880.82/112.33 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl247])). 880.82/112.33 thf(zip_derived_cl249, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 880.82/112.33 (~ (mem @ X14 @ X4) 880.82/112.33 | ((X8) != (ap @ (c_2Eoption_2ESOME @ X2) @ X12)) 880.82/112.33 | ((X10) != (ap @ (c_2Eoption_2ESOME @ X4) @ X14)) 880.82/112.33 | ~ (p @ (ap @ (ap @ X6 @ X12) @ X14)) 880.82/112.33 | ~ (mem @ X12 @ X2) 880.82/112.33 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | (p @ 880.82/112.33 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.33 X10)))), 880.82/112.33 inference('simplify nested equalities', [status(thm)], 880.82/112.33 [zip_derived_cl248])). 880.82/112.33 thf(zip_derived_cl250, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X12 : $i, X14 : $i]: 880.82/112.33 ( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X2) @ X12)) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X4) @ X14))) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ X2) @ X12) @ 880.82/112.33 (ty_2Eoption_2Eoption @ X2)) 880.82/112.33 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ X4) @ X14) @ 880.82/112.33 (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | ~ (mem @ X12 @ X2) 880.82/112.33 | ~ (p @ (ap @ (ap @ X6 @ X12) @ X14)) 880.82/112.33 | ~ (mem @ X14 @ X4))), 880.82/112.33 inference('simplify', [status(thm)], [zip_derived_cl249])). 880.82/112.33 thf(zip_derived_cl65, plain, 880.82/112.33 (![X0 : del, X1 : $i]: 880.82/112.33 ( (mem @ (ap @ (c_2Eoption_2ESOME @ X0) @ X1) @ 880.82/112.33 (ty_2Eoption_2Eoption @ X0)) 880.82/112.33 | ~ (mem @ X1 @ X0))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl36])). 880.82/112.33 thf(zip_derived_cl2301, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X12 : $i, X14 : $i]: 880.82/112.33 (~ (mem @ X14 @ X4) 880.82/112.33 | ~ (p @ (ap @ (ap @ X6 @ X12) @ X14)) 880.82/112.33 | ~ (mem @ X12 @ X2) 880.82/112.33 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ X4) @ X14) @ 880.82/112.33 (ty_2Eoption_2Eoption @ X4)) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X2) @ X12)) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X4) @ X14))))), 880.82/112.33 inference('clc', [status(thm)], [zip_derived_cl250, zip_derived_cl65])). 880.82/112.33 thf(zip_derived_cl65, plain, 880.82/112.33 (![X0 : del, X1 : $i]: 880.82/112.33 ( (mem @ (ap @ (c_2Eoption_2ESOME @ X0) @ X1) @ 880.82/112.33 (ty_2Eoption_2Eoption @ X0)) 880.82/112.33 | ~ (mem @ X1 @ X0))), 880.82/112.33 inference('sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl36])). 880.82/112.33 thf(zip_derived_cl2302, plain, 880.82/112.33 (![X2 : del, X4 : del, X6 : $i, X12 : $i, X14 : $i]: 880.82/112.33 ( (p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X2) @ X12)) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ X4) @ X14))) 880.82/112.33 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.33 | ~ (mem @ X12 @ X2) 880.82/112.33 | ~ (p @ (ap @ (ap @ X6 @ X12) @ X14)) 880.82/112.33 | ~ (mem @ X14 @ X4))), 880.82/112.33 inference('clc', [status(thm)], [zip_derived_cl2301, zip_derived_cl65])). 880.82/112.33 thf(zip_derived_cl266, plain, 880.82/112.33 ((((p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.33 != (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))) 880.82/112.33 <= (~ 880.82/112.33 (((p @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ 880.82/112.33 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.33 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.33 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.33 inference('split', [status(esa)], [zip_derived_cl265])). 880.82/112.34 thf(zip_derived_cl2304, plain, 880.82/112.34 (((~ (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')) 880.82/112.34 | ~ (mem @ '#sk6' @ '#sk3') 880.82/112.34 | ~ (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')) 880.82/112.34 | ~ (mem @ '#sk5' @ '#sk3') 880.82/112.34 | ~ (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool))))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('sup-', [status(thm)], [zip_derived_cl2302, zip_derived_cl266])). 880.82/112.34 thf(zip_derived_cl262, plain, ( (mem @ '#sk6' @ '#sk3')), 880.82/112.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl261])). 880.82/112.34 thf(zip_derived_cl259, plain, ( (mem @ '#sk5' @ '#sk3')), 880.82/112.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl258])). 880.82/112.34 thf(zip_derived_cl256, plain, 880.82/112.34 ( (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool)))), 880.82/112.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl255])). 880.82/112.34 thf(zip_derived_cl2317, plain, 880.82/112.34 (((~ (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')) 880.82/112.34 | ~ (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('demod', [status(thm)], 880.82/112.34 [zip_derived_cl2304, zip_derived_cl262, zip_derived_cl259, 880.82/112.34 zip_derived_cl256])). 880.82/112.34 thf(zip_derived_cl2318, plain, 880.82/112.34 ((~ (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6'))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('simplify', [status(thm)], [zip_derived_cl2317])). 880.82/112.34 thf(zip_derived_cl345, plain, 880.82/112.34 (( (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6'))) 880.82/112.34 <= (( (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6'))))), 880.82/112.34 inference('split', [status(esa)], [zip_derived_cl280])). 880.82/112.34 thf('12', plain, 880.82/112.34 (~ ( (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6'))) | 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6'))))), 880.82/112.34 inference('sup+', [status(thm)], [zip_derived_cl2318, zip_derived_cl345])). 880.82/112.34 thf('13', plain, (~ ( (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))), 880.82/112.34 inference('sat_resolution*', [status(thm)], 880.82/112.34 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', 880.82/112.34 '12'])). 880.82/112.34 thf(zip_derived_cl3089, plain, 880.82/112.34 (~ (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6'))), 880.82/112.34 inference('simpl_trail', [status(thm)], [zip_derived_cl282, '13'])). 880.82/112.34 thf(zip_derived_cl65, plain, 880.82/112.34 (![X0 : del, X1 : $i]: 880.82/112.34 ( (mem @ (ap @ (c_2Eoption_2ESOME @ X0) @ X1) @ 880.82/112.34 (ty_2Eoption_2Eoption @ X0)) 880.82/112.34 | ~ (mem @ X1 @ X0))), 880.82/112.34 inference('sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl36])). 880.82/112.34 thf(zip_derived_cl284, plain, 880.82/112.34 (![X0 : del]: 880.82/112.34 (mem @ (ap @ (c_2Eoption_2ETHE @ X0) @ (c_2Eoption_2ENONE @ X0)) @ X0)), 880.82/112.34 inference('sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl37])). 880.82/112.34 thf(zip_derived_cl124, plain, 880.82/112.34 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.34 ( (((!!) @ (^[Y0 : $i]: 880.82/112.34 (((mem @ Y0 @ X2) => 880.82/112.34 (((ap @ (c_2Eoption_2ETHE @ X2) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ X2) @ Y0)) = (Y0)))))))) 880.82/112.34 | ~ (mem @ X6 @ X4) 880.82/112.34 | ~ (mem @ X8 @ (arr @ X2 @ X4)) 880.82/112.34 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X2)))), 880.82/112.34 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl122])). 880.82/112.34 thf(zip_derived_cl144, plain, 880.82/112.34 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 880.82/112.34 ( (((mem @ X12 @ X2) => 880.82/112.34 (((ap @ (c_2Eoption_2ETHE @ X2) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ X2) @ X12)) = (X12))))) 880.82/112.34 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.34 | ~ (mem @ X8 @ (arr @ X2 @ X4)) 880.82/112.34 | ~ (mem @ X6 @ X4))), 880.82/112.34 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl124])). 880.82/112.34 thf(zip_derived_cl163, plain, 880.82/112.34 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 880.82/112.34 (~ (mem @ X12 @ X2) 880.82/112.34 | (((ap @ (c_2Eoption_2ETHE @ X2) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ X2) @ X12)) = (X12))) 880.82/112.34 | ~ (mem @ X6 @ X4) 880.82/112.34 | ~ (mem @ X8 @ (arr @ X2 @ X4)) 880.82/112.34 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X2)))), 880.82/112.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl144])). 880.82/112.34 thf(zip_derived_cl181, plain, 880.82/112.34 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 880.82/112.34 (~ (mem @ X12 @ X2) 880.82/112.34 | ((ap @ (c_2Eoption_2ETHE @ X2) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ X2) @ X12)) = (X12)) 880.82/112.34 | ~ (mem @ X6 @ X4) 880.82/112.34 | ~ (mem @ X8 @ (arr @ X2 @ X4)) 880.82/112.34 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X2)))), 880.82/112.34 inference('simplify nested equalities', [status(thm)], 880.82/112.34 [zip_derived_cl163])). 880.82/112.34 thf(zip_derived_cl1287, plain, 880.82/112.34 (![X0 : del, X1 : del, X2 : $i, X3 : $i, X4 : $i]: 880.82/112.34 (~ (mem @ X2 @ (ty_2Eoption_2Eoption @ X1)) 880.82/112.34 | ~ (mem @ X3 @ X0) 880.82/112.34 | ((ap @ (c_2Eoption_2ETHE @ X1) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ X1) @ X4)) = (X4)) 880.82/112.34 | ~ (mem @ X4 @ X1))), 880.82/112.34 inference('sup-', [status(thm)], [zip_derived_cl284, zip_derived_cl181])). 880.82/112.34 thf(zip_derived_cl1456, plain, 880.82/112.34 (![X0 : del, X1 : $i, X2 : $i]: 880.82/112.34 (~ (mem @ X1 @ (ty_2Eoption_2Eoption @ X0)) 880.82/112.34 | ~ (mem @ X2 @ X0) 880.82/112.34 | ((ap @ (c_2Eoption_2ETHE @ X0) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ X0) @ X2)) = (X2)))), 880.82/112.34 inference('condensation', [status(thm)], [zip_derived_cl1287])). 880.82/112.34 thf(zip_derived_cl1464, plain, 880.82/112.34 (![X0 : del, X1 : $i, X2 : $i]: 880.82/112.34 (~ (mem @ X1 @ X0) 880.82/112.34 | ((ap @ (c_2Eoption_2ETHE @ X0) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ X0) @ X2)) = (X2)) 880.82/112.34 | ~ (mem @ X2 @ X0))), 880.82/112.34 inference('sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl1456])). 880.82/112.34 thf(zip_derived_cl1697, plain, 880.82/112.34 (![X0 : del, X1 : $i]: 880.82/112.34 (~ (mem @ X1 @ X0) 880.82/112.34 | ((ap @ (c_2Eoption_2ETHE @ X0) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ X0) @ X1)) = (X1)))), 880.82/112.34 inference('condensation', [status(thm)], [zip_derived_cl1464])). 880.82/112.34 thf(zip_derived_cl1697, plain, 880.82/112.34 (![X0 : del, X1 : $i]: 880.82/112.34 (~ (mem @ X1 @ X0) 880.82/112.34 | ((ap @ (c_2Eoption_2ETHE @ X0) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ X0) @ X1)) = (X1)))), 880.82/112.34 inference('condensation', [status(thm)], [zip_derived_cl1464])). 880.82/112.34 thf(zip_derived_cl266, plain, 880.82/112.34 ((((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 != (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('split', [status(esa)], [zip_derived_cl265])). 880.82/112.34 thf(zip_derived_cl2318, plain, 880.82/112.34 ((~ (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6'))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('simplify', [status(thm)], [zip_derived_cl2317])). 880.82/112.34 thf(zip_derived_cl2332, plain, 880.82/112.34 (( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('demod', [status(thm)], [zip_derived_cl266, zip_derived_cl2318])). 880.82/112.34 thf(zip_derived_cl305, plain, 880.82/112.34 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.34 ( (((X10) = (c_2Eoption_2ENONE @ X4))) 880.82/112.34 | ~ (p @ 880.82/112.34 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.34 X10)) 880.82/112.34 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.34 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.34 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.34 | ((X10) 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ X4) @ 880.82/112.34 ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10))))), 880.82/112.34 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl304])). 880.82/112.34 thf(zip_derived_cl313, plain, 880.82/112.34 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.34 (((X10) = (c_2Eoption_2ENONE @ X4)) 880.82/112.34 | ~ (p @ 880.82/112.34 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.34 X10)) 880.82/112.34 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.34 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.34 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.34 | ((X10) 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ X4) @ 880.82/112.34 ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10))))), 880.82/112.34 inference('simplify nested equalities', [status(thm)], 880.82/112.34 [zip_derived_cl305])). 880.82/112.34 thf(zip_derived_cl2859, plain, 880.82/112.34 (((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool))) 880.82/112.34 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('sup-', [status(thm)], [zip_derived_cl2332, zip_derived_cl313])). 880.82/112.34 thf(zip_derived_cl256, plain, 880.82/112.34 ( (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool)))), 880.82/112.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl255])). 880.82/112.34 thf(zip_derived_cl2871, plain, 880.82/112.34 (((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('demod', [status(thm)], [zip_derived_cl2859, zip_derived_cl256])). 880.82/112.34 thf(zip_derived_cl2332, plain, 880.82/112.34 (( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('demod', [status(thm)], [zip_derived_cl266, zip_derived_cl2318])). 880.82/112.34 thf(zip_derived_cl311, plain, 880.82/112.34 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.34 (((X10) = (c_2Eoption_2ENONE @ X4)) 880.82/112.34 | ~ (p @ 880.82/112.34 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.34 X10)) 880.82/112.34 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.34 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.34 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.34 | ((X8) 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ X2) @ 880.82/112.34 ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10))))), 880.82/112.34 inference('simplify nested equalities', [status(thm)], 880.82/112.34 [zip_derived_cl302])). 880.82/112.34 thf(zip_derived_cl2656, plain, 880.82/112.34 (((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool))) 880.82/112.34 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('sup-', [status(thm)], [zip_derived_cl2332, zip_derived_cl311])). 880.82/112.34 thf(zip_derived_cl256, plain, 880.82/112.34 ( (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool)))), 880.82/112.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl255])). 880.82/112.34 thf(zip_derived_cl2670, plain, 880.82/112.34 (((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('demod', [status(thm)], [zip_derived_cl2656, zip_derived_cl256])). 880.82/112.34 thf('14', plain, 880.82/112.34 (~ 880.82/112.34 (((c_2Eoption_2ENONE @ '#sk3') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))) | 880.82/112.34 ~ 880.82/112.34 ( (mem @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ (c_2Eoption_2ENONE @ '#sk3') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3'))), 880.82/112.34 inference('sup+', [status(thm)], [zip_derived_cl2787, zip_derived_cl369])). 880.82/112.34 thf('15', plain, 880.82/112.34 (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6'))))), 880.82/112.34 inference('sat_resolution*', [status(thm)], 880.82/112.34 ['0', '1', '2', '3', '14', '5', '6', '7', '8', '9', '10', '11'])). 880.82/112.34 thf(zip_derived_cl4155, plain, 880.82/112.34 ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3')))), 880.82/112.34 inference('simpl_trail', [status(thm)], [zip_derived_cl2670, '15'])). 880.82/112.34 thf(zip_derived_cl4159, plain, 880.82/112.34 ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))) 880.82/112.34 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.34 inference('split', [status(esa)], [zip_derived_cl4155])). 880.82/112.34 thf(zip_derived_cl65, plain, 880.82/112.34 (![X0 : del, X1 : $i]: 880.82/112.34 ( (mem @ (ap @ (c_2Eoption_2ESOME @ X0) @ X1) @ 880.82/112.34 (ty_2Eoption_2Eoption @ X0)) 880.82/112.34 | ~ (mem @ X1 @ X0))), 880.82/112.34 inference('sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl36])). 880.82/112.34 thf(zip_derived_cl4168, plain, 880.82/112.34 ((( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3'))) 880.82/112.34 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.34 inference('sup+', [status(thm)], [zip_derived_cl4159, zip_derived_cl65])). 880.82/112.34 thf(zip_derived_cl429, plain, 880.82/112.34 (( (mem @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3')) 880.82/112.34 <= (( (mem @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3')))), 880.82/112.34 inference('split', [status(esa)], [zip_derived_cl363])). 880.82/112.34 thf(zip_derived_cl2332, plain, 880.82/112.34 (( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('demod', [status(thm)], [zip_derived_cl266, zip_derived_cl2318])). 880.82/112.34 thf(zip_derived_cl298, plain, 880.82/112.34 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.34 (((X8) = (c_2Eoption_2ENONE @ X2)) 880.82/112.34 | ~ (p @ 880.82/112.34 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.34 X10)) 880.82/112.34 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.34 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.34 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.34 | (mem @ ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10) @ X2))), 880.82/112.34 inference('simplify nested equalities', [status(thm)], 880.82/112.34 [zip_derived_cl292])). 880.82/112.34 thf(zip_derived_cl2468, plain, 880.82/112.34 ((( (mem @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3') 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool))) 880.82/112.34 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('sup-', [status(thm)], [zip_derived_cl2332, zip_derived_cl298])). 880.82/112.34 thf(zip_derived_cl256, plain, 880.82/112.34 ( (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool)))), 880.82/112.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl255])). 880.82/112.34 thf(zip_derived_cl2482, plain, 880.82/112.34 ((( (mem @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3') 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('demod', [status(thm)], [zip_derived_cl2468, zip_derived_cl256])). 880.82/112.34 thf('16', plain, 880.82/112.34 ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3'))) | 880.82/112.34 ( (mem @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3')) | 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))) | 880.82/112.34 ~ 880.82/112.34 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3'))) | 880.82/112.34 ~ 880.82/112.34 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')))), 880.82/112.34 inference('split', [status(esa)], [zip_derived_cl2482])). 880.82/112.34 thf('17', plain, 880.82/112.34 (( (mem @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3'))), 880.82/112.34 inference('sat_resolution*', [status(thm)], 880.82/112.34 ['0', '1', '2', '4', '5', '6', '9', '10', '11', '7', '3', '8', 880.82/112.34 '16'])). 880.82/112.34 thf(zip_derived_cl3091, plain, 880.82/112.34 ( (mem @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3')), 880.82/112.34 inference('simpl_trail', [status(thm)], [zip_derived_cl429, '17'])). 880.82/112.34 thf(zip_derived_cl4193, plain, 880.82/112.34 (( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3'))) 880.82/112.34 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.34 inference('demod', [status(thm)], 880.82/112.34 [zip_derived_cl4168, zip_derived_cl3091])). 880.82/112.34 thf('18', plain, 880.82/112.34 ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))) | 880.82/112.34 (((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3'))) | 880.82/112.34 ~ 880.82/112.34 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3'))) | 880.82/112.34 ~ 880.82/112.34 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')))), 880.82/112.34 inference('split', [status(esa)], [zip_derived_cl4155])). 880.82/112.34 thf('19', plain, 880.82/112.34 ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.34 inference('sat_resolution*', [status(thm)], ['7', '3', '2', '18'])). 880.82/112.34 thf(zip_derived_cl4194, plain, 880.82/112.34 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3'))), 880.82/112.34 inference('simpl_trail', [status(thm)], [zip_derived_cl4193, '19'])). 880.82/112.34 thf(zip_derived_cl4831, plain, 880.82/112.34 (((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('demod', [status(thm)], 880.82/112.34 [zip_derived_cl2871, zip_derived_cl4194])). 880.82/112.34 thf('20', plain, 880.82/112.34 (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6'))))), 880.82/112.34 inference('sat_resolution*', [status(thm)], 880.82/112.34 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11'])). 880.82/112.34 thf(zip_derived_cl4832, plain, 880.82/112.34 ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3')))), 880.82/112.34 inference('simpl_trail', [status(thm)], [zip_derived_cl4831, '20'])). 880.82/112.34 thf(zip_derived_cl4834, plain, 880.82/112.34 ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))) 880.82/112.34 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.34 inference('split', [status(esa)], [zip_derived_cl4832])). 880.82/112.34 thf(zip_derived_cl1697, plain, 880.82/112.34 (![X0 : del, X1 : $i]: 880.82/112.34 (~ (mem @ X1 @ X0) 880.82/112.34 | ((ap @ (c_2Eoption_2ETHE @ X0) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ X0) @ X1)) = (X1)))), 880.82/112.34 inference('condensation', [status(thm)], [zip_derived_cl1464])). 880.82/112.34 thf(zip_derived_cl4840, plain, 880.82/112.34 (((((ap @ (c_2Eoption_2ETHE @ '#sk3') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) 880.82/112.34 = ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 | ~ (mem @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3'))) 880.82/112.34 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.34 inference('sup+', [status(thm)], [zip_derived_cl4834, zip_derived_cl1697])). 880.82/112.34 thf(zip_derived_cl346, plain, 880.82/112.34 (( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 <= (( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.34 inference('split', [status(esa)], [zip_derived_cl280])). 880.82/112.34 thf(zip_derived_cl299, plain, 880.82/112.34 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.34 ( (((X10) = (c_2Eoption_2ENONE @ X4))) 880.82/112.34 | ~ (p @ 880.82/112.34 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.34 X10)) 880.82/112.34 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.34 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.34 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.34 | (mem @ ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10) @ X4))), 880.82/112.34 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl293])). 880.82/112.34 thf(zip_derived_cl309, plain, 880.82/112.34 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.34 (((X10) = (c_2Eoption_2ENONE @ X4)) 880.82/112.34 | ~ (p @ 880.82/112.34 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.34 X10)) 880.82/112.34 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.34 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.34 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.34 | (mem @ ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10) @ X4))), 880.82/112.34 inference('simplify nested equalities', [status(thm)], 880.82/112.34 [zip_derived_cl299])). 880.82/112.34 thf(zip_derived_cl2558, plain, 880.82/112.34 ((( (mem @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3') 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool))) 880.82/112.34 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.34 <= (( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.34 inference('sup-', [status(thm)], [zip_derived_cl346, zip_derived_cl309])). 880.82/112.34 thf(zip_derived_cl256, plain, 880.82/112.34 ( (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool)))), 880.82/112.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl255])). 880.82/112.34 thf(zip_derived_cl2572, plain, 880.82/112.34 ((( (mem @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3') 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.34 <= (( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.34 inference('demod', [status(thm)], [zip_derived_cl2558, zip_derived_cl256])). 880.82/112.34 thf(zip_derived_cl2332, plain, 880.82/112.34 (( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('demod', [status(thm)], [zip_derived_cl266, zip_derived_cl2318])). 880.82/112.34 thf(zip_derived_cl283, plain, 880.82/112.34 ((~ (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 <= (~ 880.82/112.34 ( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.34 inference('split', [status(esa)], [zip_derived_cl281])). 880.82/112.34 thf('21', plain, 880.82/112.34 (( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) | 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6'))))), 880.82/112.34 inference('sup-', [status(thm)], [zip_derived_cl2332, zip_derived_cl283])). 880.82/112.34 thf('22', plain, 880.82/112.34 (( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))), 880.82/112.34 inference('sat_resolution*', [status(thm)], 880.82/112.34 ['0', '1', '2', '3', '14', '5', '6', '7', '8', '9', '10', 880.82/112.34 '11', '21'])). 880.82/112.34 thf(zip_derived_cl3724, plain, 880.82/112.34 (( (mem @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3') 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3')))), 880.82/112.34 inference('simpl_trail', [status(thm)], [zip_derived_cl2572, '22'])). 880.82/112.34 thf(zip_derived_cl3725, plain, 880.82/112.34 (( (mem @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3')) 880.82/112.34 <= (( (mem @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3')))), 880.82/112.34 inference('split', [status(esa)], [zip_derived_cl3724])). 880.82/112.34 thf(zip_derived_cl2332, plain, 880.82/112.34 (( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('demod', [status(thm)], [zip_derived_cl266, zip_derived_cl2318])). 880.82/112.34 thf(zip_derived_cl309, plain, 880.82/112.34 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.34 (((X10) = (c_2Eoption_2ENONE @ X4)) 880.82/112.34 | ~ (p @ 880.82/112.34 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.34 X10)) 880.82/112.34 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.34 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.34 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.34 | (mem @ ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10) @ X4))), 880.82/112.34 inference('simplify nested equalities', [status(thm)], 880.82/112.34 [zip_derived_cl299])). 880.82/112.34 thf(zip_derived_cl2557, plain, 880.82/112.34 ((( (mem @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3') 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool))) 880.82/112.34 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('sup-', [status(thm)], [zip_derived_cl2332, zip_derived_cl309])). 880.82/112.34 thf(zip_derived_cl256, plain, 880.82/112.34 ( (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool)))), 880.82/112.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl255])). 880.82/112.34 thf(zip_derived_cl2571, plain, 880.82/112.34 ((( (mem @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3') 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3')))) 880.82/112.34 <= (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')))))), 880.82/112.34 inference('demod', [status(thm)], [zip_derived_cl2557, zip_derived_cl256])). 880.82/112.34 thf('23', plain, 880.82/112.34 (~ 880.82/112.34 (((p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 = (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6'))))), 880.82/112.34 inference('sat_resolution*', [status(thm)], 880.82/112.34 ['0', '1', '2', '3', '14', '5', '6', '7', '8', '9', '10', '11'])). 880.82/112.34 thf(zip_derived_cl3719, plain, 880.82/112.34 (( (mem @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3') 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3')))), 880.82/112.34 inference('simpl_trail', [status(thm)], [zip_derived_cl2571, '23'])). 880.82/112.34 thf('24', plain, 880.82/112.34 (( (mem @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3')) | 880.82/112.34 (((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3'))) | 880.82/112.34 ~ 880.82/112.34 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3'))) | 880.82/112.34 ~ 880.82/112.34 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')))), 880.82/112.34 inference('split', [status(esa)], [zip_derived_cl3719])). 880.82/112.34 thf('25', plain, 880.82/112.34 (( (mem @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3'))), 880.82/112.34 inference('sat_resolution*', [status(thm)], ['7', '3', '2', '24'])). 880.82/112.34 thf(zip_derived_cl3729, plain, 880.82/112.34 ( (mem @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3')), 880.82/112.34 inference('simpl_trail', [status(thm)], [zip_derived_cl3725, '25'])). 880.82/112.34 thf(zip_derived_cl4861, plain, 880.82/112.34 ((((ap @ (c_2Eoption_2ETHE @ '#sk3') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) 880.82/112.34 = ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.34 inference('demod', [status(thm)], 880.82/112.34 [zip_derived_cl4840, zip_derived_cl3729])). 880.82/112.34 thf('26', plain, 880.82/112.34 ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))) | 880.82/112.34 (((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3'))) | 880.82/112.34 ~ 880.82/112.34 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')))), 880.82/112.34 inference('split', [status(esa)], [zip_derived_cl4832])). 880.82/112.34 thf('27', plain, 880.82/112.34 ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.34 inference('sat_resolution*', [status(thm)], ['3', '2', '26'])). 880.82/112.34 thf(zip_derived_cl4862, plain, 880.82/112.34 (((ap @ (c_2Eoption_2ETHE @ '#sk3') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) 880.82/112.34 = ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))), 880.82/112.34 inference('simpl_trail', [status(thm)], [zip_derived_cl4861, '27'])). 880.82/112.34 thf(zip_derived_cl296, plain, 880.82/112.34 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.34 ( (p @ 880.82/112.34 (ap @ (ap @ X6 @ ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10)) @ 880.82/112.34 ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10))) 880.82/112.34 | (((((X10) = (c_2Eoption_2ENONE @ X4))) & 880.82/112.34 (((X8) = (c_2Eoption_2ENONE @ X2))))) 880.82/112.34 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.34 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.34 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.34 | ~ (p @ 880.82/112.34 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.34 X10)))), 880.82/112.34 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl290])). 880.82/112.34 thf(zip_derived_cl308, plain, 880.82/112.34 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.34 ( (((X8) = (c_2Eoption_2ENONE @ X2))) 880.82/112.34 | ~ (p @ 880.82/112.34 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.34 X10)) 880.82/112.34 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.34 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.34 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.34 | (p @ 880.82/112.34 (ap @ (ap @ X6 @ ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10)) @ 880.82/112.34 ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10))))), 880.82/112.34 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl296])). 880.82/112.34 thf(zip_derived_cl316, plain, 880.82/112.34 (![X2 : del, X4 : del, X6 : $i, X8 : $i, X10 : $i]: 880.82/112.34 (((X8) = (c_2Eoption_2ENONE @ X2)) 880.82/112.34 | ~ (p @ 880.82/112.34 (ap @ (ap @ (ap @ (c_2Eoption_2EOPTREL @ X2 @ X4) @ X6) @ X8) @ 880.82/112.34 X10)) 880.82/112.34 | ~ (mem @ X6 @ (arr @ X2 @ (arr @ X4 @ bool))) 880.82/112.34 | ~ (mem @ X8 @ (ty_2Eoption_2Eoption @ X2)) 880.82/112.34 | ~ (mem @ X10 @ (ty_2Eoption_2Eoption @ X4)) 880.82/112.34 | (p @ 880.82/112.34 (ap @ (ap @ X6 @ ('#sk7' @ X2 @ X4 @ X6 @ X8 @ X10)) @ 880.82/112.34 ('#sk8' @ X2 @ X4 @ X6 @ X8 @ X10))))), 880.82/112.34 inference('simplify nested equalities', [status(thm)], 880.82/112.34 [zip_derived_cl308])). 880.82/112.34 thf(zip_derived_cl5076, plain, 880.82/112.34 (( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ '#sk4' @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) @ 880.82/112.34 (ap @ (c_2Eoption_2ETHE @ '#sk3') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool))) 880.82/112.34 | ~ (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3')))), 880.82/112.34 inference('sup+', [status(thm)], [zip_derived_cl4862, zip_derived_cl316])). 880.82/112.34 thf(zip_derived_cl4159, plain, 880.82/112.34 ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))) 880.82/112.34 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.34 inference('split', [status(esa)], [zip_derived_cl4155])). 880.82/112.34 thf(zip_derived_cl1697, plain, 880.82/112.34 (![X0 : del, X1 : $i]: 880.82/112.34 (~ (mem @ X1 @ X0) 880.82/112.34 | ((ap @ (c_2Eoption_2ETHE @ X0) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ X0) @ X1)) = (X1)))), 880.82/112.34 inference('condensation', [status(thm)], [zip_derived_cl1464])). 880.82/112.34 thf(zip_derived_cl4164, plain, 880.82/112.34 (((((ap @ (c_2Eoption_2ETHE @ '#sk3') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) 880.82/112.34 = ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))) 880.82/112.34 | ~ (mem @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3'))) 880.82/112.34 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.34 inference('sup+', [status(thm)], [zip_derived_cl4159, zip_derived_cl1697])). 880.82/112.34 thf(zip_derived_cl3091, plain, 880.82/112.34 ( (mem @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3')), 880.82/112.34 inference('simpl_trail', [status(thm)], [zip_derived_cl429, '17'])). 880.82/112.34 thf(zip_derived_cl4185, plain, 880.82/112.34 ((((ap @ (c_2Eoption_2ETHE @ '#sk3') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) 880.82/112.34 = ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.34 inference('demod', [status(thm)], 880.82/112.34 [zip_derived_cl4164, zip_derived_cl3091])). 880.82/112.34 thf('28', plain, 880.82/112.34 ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.34 inference('sat_resolution*', [status(thm)], ['7', '3', '2', '18'])). 880.82/112.34 thf(zip_derived_cl4186, plain, 880.82/112.34 (((ap @ (c_2Eoption_2ETHE @ '#sk3') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) 880.82/112.34 = ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))), 880.82/112.34 inference('simpl_trail', [status(thm)], [zip_derived_cl4185, '28'])). 880.82/112.34 thf(zip_derived_cl4834, plain, 880.82/112.34 ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))) 880.82/112.34 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.34 inference('split', [status(esa)], [zip_derived_cl4832])). 880.82/112.34 thf(zip_derived_cl65, plain, 880.82/112.34 (![X0 : del, X1 : $i]: 880.82/112.34 ( (mem @ (ap @ (c_2Eoption_2ESOME @ X0) @ X1) @ 880.82/112.34 (ty_2Eoption_2Eoption @ X0)) 880.82/112.34 | ~ (mem @ X1 @ X0))), 880.82/112.34 inference('sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl36])). 880.82/112.34 thf(zip_derived_cl4844, plain, 880.82/112.34 ((( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3')) 880.82/112.34 | ~ (mem @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3'))) 880.82/112.34 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.34 inference('sup+', [status(thm)], [zip_derived_cl4834, zip_derived_cl65])). 880.82/112.34 thf(zip_derived_cl3729, plain, 880.82/112.34 ( (mem @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3')), 880.82/112.34 inference('simpl_trail', [status(thm)], [zip_derived_cl3725, '25'])). 880.82/112.34 thf(zip_derived_cl4869, plain, 880.82/112.34 (( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3'))) 880.82/112.34 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.34 inference('demod', [status(thm)], 880.82/112.34 [zip_derived_cl4844, zip_derived_cl3729])). 880.82/112.34 thf('29', plain, 880.82/112.34 ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk8' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.34 inference('sat_resolution*', [status(thm)], ['3', '2', '26'])). 880.82/112.34 thf(zip_derived_cl4870, plain, 880.82/112.34 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3'))), 880.82/112.34 inference('simpl_trail', [status(thm)], [zip_derived_cl4869, '29'])). 880.82/112.34 thf(zip_derived_cl4194, plain, 880.82/112.34 ( (mem @ (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ty_2Eoption_2Eoption @ '#sk3'))), 880.82/112.34 inference('simpl_trail', [status(thm)], [zip_derived_cl4193, '19'])). 880.82/112.34 thf(zip_derived_cl256, plain, 880.82/112.34 ( (mem @ '#sk4' @ (arr @ '#sk3' @ (arr @ '#sk3' @ bool)))), 880.82/112.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl255])). 880.82/112.34 thf(zip_derived_cl346, plain, 880.82/112.34 (( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 <= (( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.34 inference('split', [status(esa)], [zip_derived_cl280])). 880.82/112.34 thf('30', plain, 880.82/112.34 (( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))), 880.82/112.34 inference('sat_resolution*', [status(thm)], 880.82/112.34 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', 880.82/112.34 '21'])). 880.82/112.34 thf(zip_derived_cl3090, plain, 880.82/112.34 ( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ (ap @ (c_2Eoption_2EOPTREL @ '#sk3' @ '#sk3') @ '#sk4') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))), 880.82/112.34 inference('simpl_trail', [status(thm)], [zip_derived_cl346, '30'])). 880.82/112.34 thf(zip_derived_cl5080, plain, 880.82/112.34 (( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ETHE @ '#sk3') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5'))) @ 880.82/112.34 (ap @ (c_2Eoption_2ETHE @ '#sk3') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 | ((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (c_2Eoption_2ENONE @ '#sk3')))), 880.82/112.34 inference('demod', [status(thm)], 880.82/112.34 [zip_derived_cl5076, zip_derived_cl4186, zip_derived_cl4870, 880.82/112.34 zip_derived_cl4194, zip_derived_cl256, zip_derived_cl3090])). 880.82/112.34 thf(zip_derived_cl4159, plain, 880.82/112.34 ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))) 880.82/112.34 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.34 inference('split', [status(esa)], [zip_derived_cl4155])). 880.82/112.34 thf(zip_derived_cl783, plain, 880.82/112.34 (![X0 : del, X1 : $i]: 880.82/112.34 (((c_2Eoption_2ENONE @ X0) != (ap @ (c_2Eoption_2ESOME @ X0) @ X1)) 880.82/112.34 | ~ (mem @ X1 @ X0))), 880.82/112.34 inference('sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl776])). 880.82/112.34 thf(zip_derived_cl4166, plain, 880.82/112.34 (((((c_2Eoption_2ENONE @ '#sk3') 880.82/112.34 != (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5')) 880.82/112.34 | ~ (mem @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3'))) 880.82/112.34 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.34 inference('sup-', [status(thm)], [zip_derived_cl4159, zip_derived_cl783])). 880.82/112.34 thf(zip_derived_cl3091, plain, 880.82/112.34 ( (mem @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')) @ 880.82/112.34 '#sk3')), 880.82/112.34 inference('simpl_trail', [status(thm)], [zip_derived_cl429, '17'])). 880.82/112.34 thf(zip_derived_cl4189, plain, 880.82/112.34 ((((c_2Eoption_2ENONE @ '#sk3') 880.82/112.34 != (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5'))) 880.82/112.34 <= ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))))), 880.82/112.34 inference('demod', [status(thm)], 880.82/112.34 [zip_derived_cl4166, zip_derived_cl3091])). 880.82/112.34 thf('31', plain, 880.82/112.34 ((((ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') 880.82/112.34 = (ap @ (c_2Eoption_2ESOME @ '#sk3') @ 880.82/112.34 ('#sk7' @ '#sk3' @ '#sk3' @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))))), 880.82/112.34 inference('sat_resolution*', [status(thm)], ['7', '3', '2', '18'])). 880.82/112.34 thf(zip_derived_cl4190, plain, 880.82/112.34 (((c_2Eoption_2ENONE @ '#sk3') 880.82/112.34 != (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5'))), 880.82/112.34 inference('simpl_trail', [status(thm)], [zip_derived_cl4189, '31'])). 880.82/112.34 thf(zip_derived_cl5081, plain, 880.82/112.34 ( (p @ 880.82/112.34 (ap @ 880.82/112.34 (ap @ '#sk4' @ 880.82/112.34 (ap @ (c_2Eoption_2ETHE @ '#sk3') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk5'))) @ 880.82/112.34 (ap @ (c_2Eoption_2ETHE @ '#sk3') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))), 880.82/112.34 inference('simplify_reflect-', [status(thm)], 880.82/112.34 [zip_derived_cl5080, zip_derived_cl4190])). 880.82/112.34 thf(zip_derived_cl5186, plain, 880.82/112.34 (( (p @ 880.82/112.34 (ap @ (ap @ '#sk4' @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ETHE @ '#sk3') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6')))) 880.82/112.34 | ~ (mem @ '#sk5' @ '#sk3'))), 880.82/112.34 inference('sup+', [status(thm)], [zip_derived_cl1697, zip_derived_cl5081])). 880.82/112.34 thf(zip_derived_cl259, plain, ( (mem @ '#sk5' @ '#sk3')), 880.82/112.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl258])). 880.82/112.34 thf(zip_derived_cl5190, plain, 880.82/112.34 ( (p @ 880.82/112.34 (ap @ (ap @ '#sk4' @ '#sk5') @ 880.82/112.34 (ap @ (c_2Eoption_2ETHE @ '#sk3') @ 880.82/112.34 (ap @ (c_2Eoption_2ESOME @ '#sk3') @ '#sk6'))))), 880.82/112.34 inference('demod', [status(thm)], [zip_derived_cl5186, zip_derived_cl259])). 880.82/112.34 thf(zip_derived_cl5194, plain, 880.82/112.34 (( (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6')) 880.82/112.34 | ~ (mem @ '#sk6' @ '#sk3'))), 880.82/112.34 inference('sup+', [status(thm)], [zip_derived_cl1697, zip_derived_cl5190])). 880.82/112.34 thf(zip_derived_cl262, plain, ( (mem @ '#sk6' @ '#sk3')), 880.82/112.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl261])). 880.82/112.34 thf(zip_derived_cl5196, plain, 880.82/112.34 ( (p @ (ap @ (ap @ '#sk4' @ '#sk5') @ '#sk6'))), 880.82/112.34 inference('demod', [status(thm)], [zip_derived_cl5194, zip_derived_cl262])). 880.82/112.34 thf(zip_derived_cl5198, plain, ($false), 880.82/112.34 inference('demod', [status(thm)], 880.82/112.34 [zip_derived_cl3089, zip_derived_cl5196])). 880.82/112.34 880.82/112.34 % SZS output end Refutation 880.82/112.34 880.82/112.34 880.82/112.34 % Terminating... 880.82/112.34 % /export/starexec/sandbox/solver/bin/lams/10_forms1.sh running for 20s 881.32/112.43 % Runner terminated. 881.32/112.44 % Zipperpin 1.5 exiting 881.32/112.45 EOF