0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.13/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.6UqNIxMiCA true 0.13/0.35 % Computer : n021.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 1200 0.13/0.35 % WCLimit : 120 0.13/0.35 % DateTime : Tue Jul 13 16:03:41 EDT 2021 0.20/0.35 % CPUTime : 0.20/0.35 % Running portfolio for 120 s 0.20/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.20/0.35 % Number of cores: 8 0.20/0.35 % Python version: Python 3.6.8 0.20/0.35 % Running in HO mode 0.49/0.62 % Total configuration time : 828 0.49/0.62 % Estimated wc time : 983 0.49/0.62 % Estimated cpu time (8 cpus) : 122.875 0.54/0.69 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 47s 0.54/0.72 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 47s 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 18s 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 47s 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 53s 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 41s 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 35s 0.55/0.90 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 53s 66.69/9.08 % Solved by lams/30_b.l.sh. 66.69/9.08 % running E: timeout 14 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.6UqNIxMiCA/e_input6e295f --cpu-limit=12 --auto -s -p 66.69/9.08 % done 1423 iterations in 8.078s 66.69/9.08 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 66.69/9.08 % SZS output start Refutation 66.69/9.08 thf(du_type, type, du: $tType). 66.69/9.08 thf(d_type, type, d: $tType). 66.69/9.08 thf(u_type, type, u: $tType). 66.69/9.08 thf(c_2Eoption_2EOPTION__JOIN_2E1_type, type, c_2Eoption_2EOPTION__JOIN_2E1: 66.69/9.08 du > u). 66.69/9.08 thf(tyop_2Emin_2Ebool_type, type, tyop_2Emin_2Ebool: d). 66.69/9.08 thf(app_2E2_type, type, app_2E2: du > du > u). 66.69/9.08 thf('#sk4_type', type, '#sk4': u). 66.69/9.08 thf(c_2Eoption_2EIS__NONE_2E1_type, type, c_2Eoption_2EIS__NONE_2E1: du > u). 66.69/9.08 thf(j_mono_2Etyop_2Emin_2Ebool_type, type, j_mono_2Etyop_2Emin_2Ebool: 66.69/9.08 du > $o). 66.69/9.08 thf(c_2Eoption_2EOPTREL_2E3_type, type, c_2Eoption_2EOPTREL_2E3: du > du > du > u). 66.69/9.08 thf(tyop_2Eoption_2Eoption_type, type, tyop_2Eoption_2Eoption: d > d). 66.69/9.08 thf(s_type, type, s: d > u > du). 66.69/9.08 thf(mono_2Ec_2Ebool_2ET_type, type, mono_2Ec_2Ebool_2ET: $o). 66.69/9.08 thf('#sk2_type', type, '#sk2': d). 66.69/9.08 thf(tyop_2Emin_2Efun_type, type, tyop_2Emin_2Efun: d > d > d). 66.69/9.08 thf('#sk3_type', type, '#sk3': u). 66.69/9.08 thf(mono_2Ec_2Ebool_2EF_type, type, mono_2Ec_2Ebool_2EF: $o). 66.69/9.08 thf(c_2Eoption_2EIS__SOME_2E1_type, type, c_2Eoption_2EIS__SOME_2E1: du > u). 66.69/9.08 thf(c_2Eoption_2ETHE_2E1_type, type, c_2Eoption_2ETHE_2E1: du > u). 66.69/9.08 thf(c_2Eoption_2ESOME_2E0_type, type, c_2Eoption_2ESOME_2E0: u). 66.69/9.08 thf('#sk5_type', type, '#sk5': u). 66.69/9.08 thf(c_2Eoption_2ENONE_2E0_type, type, c_2Eoption_2ENONE_2E0: u). 66.69/9.08 thf(c_2Eoption_2Eoption__CASE_2E3_type, type, c_2Eoption_2Eoption__CASE_2E3: 66.69/9.08 du > du > du > u). 66.69/9.08 thf(c_2Eoption_2ESOME_2E1_type, type, c_2Eoption_2ESOME_2E1: du > u). 66.69/9.08 thf(c_2Eoption_2EOPTION__MAP_2E2_type, type, c_2Eoption_2EOPTION__MAP_2E2: 66.69/9.08 du > du > u). 66.69/9.08 thf(thm_2Eoption_2Eoption__CLAUSES, axiom, 66.69/9.08 (![A_27a:d,A_27b:d,V0f_2E0:u,V1e_2E0:u,V2e_2E0:u]: 66.69/9.08 ( ( ![V5x_2E0:u]: 66.69/9.08 ( ( s @ 66.69/9.08 A_27a @ 66.69/9.08 ( c_2Eoption_2ETHE_2E1 @ 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.08 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V5x_2E0 ) ) ) ) ) = 66.69/9.08 ( s @ A_27a @ V5x_2E0 ) ) ) & 66.69/9.08 ( ![V8x_2E0:u]: 66.69/9.08 ( ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.08 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V8x_2E0 ) ) ) ) ) ) = 66.69/9.08 ( mono_2Ec_2Ebool_2ET ) ) ) & 66.69/9.08 ( ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) = 66.69/9.08 ( mono_2Ec_2Ebool_2EF ) ) & 66.69/9.08 ( ![V9x_2E0:u]: 66.69/9.08 ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V9x_2E0 ) = 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) <=> 66.69/9.08 ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V9x_2E0 ) ) ) ) ) ) & 66.69/9.08 ( ![V10x_2E0:u]: 66.69/9.08 ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V10x_2E0 ) = 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) <=> 66.69/9.08 ( ~( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V10x_2E0 ) ) ) ) ) ) ) & 66.69/9.08 ( ![V11x_2E0:u]: 66.69/9.08 ( ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V11x_2E0 ) ) ) ) => 66.69/9.08 ( ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.08 ( c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( s @ 66.69/9.08 A_27a @ 66.69/9.08 ( c_2Eoption_2ETHE_2E1 @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V11x_2E0 ) ) ) ) ) = 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V11x_2E0 ) ) ) ) & 66.69/9.08 ( ![V12x_2E0:u]: 66.69/9.08 ( ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.08 ( c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V12x_2E0 ) @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Emin_2Efun @ 66.69/9.08 A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ 66.69/9.08 c_2Eoption_2ESOME_2E0 ) ) ) = 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V12x_2E0 ) ) ) & 66.69/9.08 ( ![V16x_2E0:u]: 66.69/9.08 ( ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V16x_2E0 ) ) ) ) => 66.69/9.08 ( ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.08 ( c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V16x_2E0 ) @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1e_2E0 ) @ 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Emin_2Efun @ 66.69/9.08 A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ 66.69/9.08 c_2Eoption_2ESOME_2E0 ) ) ) = 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V16x_2E0 ) ) ) ) & 66.69/9.08 ( ![V17v_2E0:u,V18f_2E0:u]: 66.69/9.08 ( ( s @ 66.69/9.08 A_27b @ 66.69/9.08 ( c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ 66.69/9.08 ( s @ A_27b @ V17v_2E0 ) @ 66.69/9.08 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V18f_2E0 ) ) ) = 66.69/9.08 ( s @ A_27b @ V17v_2E0 ) ) ) & 66.69/9.08 ( ![V19x_2E0:u,V20v_2E0:u,V21f_2E0:u]: 66.69/9.08 ( ( s @ 66.69/9.08 A_27b @ 66.69/9.08 ( c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.08 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V19x_2E0 ) ) ) @ 66.69/9.08 ( s @ A_27b @ V20v_2E0 ) @ 66.69/9.08 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V21f_2E0 ) ) ) = 66.69/9.08 ( s @ 66.69/9.08 A_27b @ 66.69/9.08 ( app_2E2 @ 66.69/9.08 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V21f_2E0 ) @ 66.69/9.08 ( s @ A_27a @ V19x_2E0 ) ) ) ) ) & 66.69/9.08 ( ![V22f_2E0:u,V23x_2E0:u]: 66.69/9.08 ( ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27b ) @ 66.69/9.08 ( c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V22f_2E0 ) @ 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.08 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V23x_2E0 ) ) ) ) ) = 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27b ) @ 66.69/9.08 ( c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( s @ 66.69/9.08 A_27b @ 66.69/9.08 ( app_2E2 @ 66.69/9.08 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V22f_2E0 ) @ 66.69/9.08 ( s @ A_27a @ V23x_2E0 ) ) ) ) ) ) ) & 66.69/9.08 ( ![V24f_2E0:u]: 66.69/9.08 ( ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27b ) @ 66.69/9.08 ( c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V24f_2E0 ) @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) = 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) & 66.69/9.08 ( ![V25x_2E0:u]: 66.69/9.08 ( ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.08 ( c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ 66.69/9.08 ( c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V25x_2E0 ) ) ) ) ) = 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V25x_2E0 ) ) ) & 66.69/9.08 ( ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.08 ( c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ 66.69/9.08 c_2Eoption_2ENONE_2E0 ) ) ) = 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) & 66.69/9.08 ( ![V15x_2E0:u]: 66.69/9.08 ( ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V15x_2E0 ) ) ) ) => 66.69/9.08 ( ( s @ 66.69/9.08 A_27b @ 66.69/9.08 ( c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V15x_2E0 ) @ 66.69/9.08 ( s @ A_27b @ V2e_2E0 ) @ 66.69/9.08 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) = 66.69/9.08 ( s @ 66.69/9.08 A_27b @ 66.69/9.08 ( app_2E2 @ 66.69/9.08 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ 66.69/9.08 ( s @ 66.69/9.08 A_27a @ 66.69/9.08 ( c_2Eoption_2ETHE_2E1 @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V15x_2E0 ) ) ) ) ) ) ) ) & 66.69/9.08 ( ![V14x_2E0:u]: 66.69/9.08 ( ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V14x_2E0 ) ) ) ) => 66.69/9.08 ( ( s @ 66.69/9.08 A_27b @ 66.69/9.08 ( c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V14x_2E0 ) @ 66.69/9.08 ( s @ A_27b @ V2e_2E0 ) @ 66.69/9.08 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) = 66.69/9.08 ( s @ A_27b @ V2e_2E0 ) ) ) ) & 66.69/9.08 ( ![V13x_2E0:u]: 66.69/9.08 ( ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.08 ( c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V13x_2E0 ) @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V13x_2E0 ) @ 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Emin_2Efun @ 66.69/9.08 A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ 66.69/9.08 c_2Eoption_2ESOME_2E0 ) ) ) = 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V13x_2E0 ) ) ) & 66.69/9.08 ( ![V7x_2E0:u]: 66.69/9.08 ( ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.08 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V7x_2E0 ) ) ) != 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) & 66.69/9.08 ( ![V6x_2E0:u]: 66.69/9.08 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) != 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.08 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V6x_2E0 ) ) ) ) ) & 66.69/9.08 ( ![V3x_2E0:u,V4y_2E0:u]: 66.69/9.08 ( ( ( s @ A_27a @ V3x_2E0 ) = ( s @ A_27a @ V4y_2E0 ) ) <=> 66.69/9.08 ( ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.08 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3x_2E0 ) ) ) = 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.08 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V4y_2E0 ) ) ) ) ) ) ))). 66.69/9.08 thf(zip_derived_cl5, plain, 66.69/9.08 ( (((!!) @ (^[Y0 : d]: 66.69/9.08 (((!!) @ (^[Y1 : d]: 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 ((( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 Y0 @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ETHE_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ Y0 @ 66.69/9.08 Y5))))) = 66.69/9.08 (s @ 66.69/9.08 Y0 @ Y5)))))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ Y0 @ 66.69/9.08 Y5)))))) = 66.69/9.08 (mono_2Ec_2Ebool_2ET)))))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))) = 66.69/9.08 (mono_2Ec_2Ebool_2EF))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 Y5) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) <=> 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5))))))))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 Y5) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) <=> 66.69/9.08 (( 66.69/9.08 (~) @ ( 66.69/9.08 j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5))))))))))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5)))) => 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ Y0 @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ETHE_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5))))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5)))))))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 Y0 @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5)))))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5)))) => 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y3) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 Y0 @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5)))))))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y6 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 Y1 @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) @ 66.69/9.08 ( 66.69/9.08 s @ Y1 @ 66.69/9.08 Y5) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 Y0 @ Y1) @ 66.69/9.08 Y6))) = 66.69/9.08 (s @ 66.69/9.08 Y1 @ Y5))))))))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y6 : u]: 66.69/9.08 (( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y7 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 Y1 @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ Y0 @ 66.69/9.08 Y5))) @ 66.69/9.08 ( 66.69/9.08 s @ Y1 @ 66.69/9.08 Y6) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 Y0 @ Y1) @ 66.69/9.08 Y7))) = 66.69/9.08 (s @ 66.69/9.08 Y1 @ 66.69/9.08 ( 66.69/9.08 app_2E2 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 Y0 @ Y1) @ 66.69/9.08 Y7) @ 66.69/9.08 ( 66.69/9.08 s @ Y0 @ 66.69/9.08 Y5)))))))))))))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y6 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y1) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 Y0 @ Y1) @ 66.69/9.08 Y5) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ Y0 @ 66.69/9.08 Y6))))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y1) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ Y1 @ 66.69/9.08 ( 66.69/9.08 app_2E2 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 Y0 @ Y1) @ 66.69/9.08 Y5) @ 66.69/9.08 ( 66.69/9.08 s @ Y0 @ 66.69/9.08 Y6))))))))))))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y1) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 Y0 @ Y1) @ 66.69/9.08 Y5) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y1) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0)) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5))))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5)))))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0)) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5)))) => 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 Y1 @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5) @ 66.69/9.08 ( 66.69/9.08 s @ Y1 @ 66.69/9.08 Y4) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 Y0 @ Y1) @ 66.69/9.08 Y2))) = 66.69/9.08 (s @ 66.69/9.08 Y1 @ 66.69/9.08 ( 66.69/9.08 app_2E2 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 Y0 @ Y1) @ 66.69/9.08 Y2) @ 66.69/9.08 ( 66.69/9.08 s @ Y0 @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ETHE_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5)))))))))))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5)))) => 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 Y1 @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5) @ 66.69/9.08 ( 66.69/9.08 s @ Y1 @ 66.69/9.08 Y4) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 Y0 @ Y1) @ 66.69/9.08 Y2))) = 66.69/9.08 (s @ 66.69/9.08 Y1 @ Y4)))))))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 Y0 @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ Y5)))))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ Y0 @ 66.69/9.08 Y5))) != 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) != 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ Y0 @ 66.69/9.08 Y5)))))))) & 66.69/9.08 ( 66.69/9.08 ( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y6 : u]: 66.69/9.08 (( 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 Y0 @ 66.69/9.08 Y5) = 66.69/9.08 (s @ 66.69/9.08 Y0 @ Y6))) <=> 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ Y0 @ 66.69/9.08 Y5))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ Y0 @ 66.69/9.08 Y6))))))))))))))))))))))))))))))), 66.69/9.08 inference('cnf', [status(esa)], [thm_2Eoption_2Eoption__CLAUSES])). 66.69/9.08 thf(zip_derived_cl113, plain, 66.69/9.08 (![X2 : d]: 66.69/9.08 (((!!) @ (^[Y0 : d]: 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 X2 @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ETHE_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y4))))) = 66.69/9.08 (s @ 66.69/9.08 X2 @ Y4)))))) & 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y4)))))) = 66.69/9.08 (mono_2Ec_2Ebool_2ET)))))) & 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))) = 66.69/9.08 (mono_2Ec_2Ebool_2EF))) & 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y4) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) <=> 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4))))))))) & 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y4) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) <=> 66.69/9.08 (( 66.69/9.08 (~) @ ( 66.69/9.08 j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4))))))))))) & 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4)))) => 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ETHE_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4))))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4)))))))) & 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4)))))) & 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4)))) => 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y2) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4)))))))) & 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 Y0 @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) @ 66.69/9.08 ( 66.69/9.08 s @ Y0 @ 66.69/9.08 Y4) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ Y0) @ 66.69/9.08 Y5))) = 66.69/9.08 (s @ 66.69/9.08 Y0 @ Y4))))))))) & 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y6 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 Y0 @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y4))) @ 66.69/9.08 ( 66.69/9.08 s @ Y0 @ 66.69/9.08 Y5) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ Y0) @ 66.69/9.08 Y6))) = 66.69/9.08 (s @ 66.69/9.08 Y0 @ 66.69/9.08 ( 66.69/9.08 app_2E2 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ Y0) @ 66.69/9.08 Y6) @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y4)))))))))))))) & 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ Y0) @ 66.69/9.08 Y4) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y5))))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ Y0 @ 66.69/9.08 ( 66.69/9.08 app_2E2 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ Y0) @ 66.69/9.08 Y4) @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y5))))))))))))) & 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ Y0) @ 66.69/9.08 Y4) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 Y0) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2)) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4))))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4)))))) & 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2)) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) & 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4)))) => 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 Y0 @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4) @ 66.69/9.08 ( 66.69/9.08 s @ Y0 @ 66.69/9.08 Y3) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ Y0) @ 66.69/9.08 Y1))) = 66.69/9.08 (s @ 66.69/9.08 Y0 @ 66.69/9.08 ( 66.69/9.08 app_2E2 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ Y0) @ 66.69/9.08 Y1) @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ETHE_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4)))))))))))) & 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4)))) => 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 Y0 @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4) @ 66.69/9.08 ( 66.69/9.08 s @ Y0 @ 66.69/9.08 Y3) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ Y0) @ 66.69/9.08 Y1))) = 66.69/9.08 (s @ 66.69/9.08 Y0 @ Y3)))))))) & 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ Y4)))))) & 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y4))) != 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) != 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y4)))))))) & 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 X2 @ 66.69/9.08 Y4) = 66.69/9.08 (s @ 66.69/9.08 X2 @ Y5))) <=> 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y4))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y5)))))))))))))))))))))))))))), 66.69/9.08 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 66.69/9.08 thf(zip_derived_cl114, plain, 66.69/9.08 (![X2 : d, X4 : d]: 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((((!!) @ (^[Y3 : u]: 66.69/9.08 (((s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y3))))) = 66.69/9.08 (s @ X2 @ Y3)))))) & 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y3)))))) = 66.69/9.08 (mono_2Ec_2Ebool_2ET)))))) & 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))) = 66.69/9.08 (mono_2Ec_2Ebool_2EF))) & 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3) = (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) <=> 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3))))))))) & 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3) = (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) <=> 66.69/9.08 (((~) @ ( 66.69/9.08 j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3))))))))))) & 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3)))) => 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3))))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3)))))))) & 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ 66.69/9.08 X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3)))))) & 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3)))) => 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y1) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ 66.69/9.08 X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3)))))))) & 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 X4 @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) @ 66.69/9.08 ( 66.69/9.08 s @ X4 @ 66.69/9.08 Y3) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ X4) @ 66.69/9.08 Y4))) = 66.69/9.08 (s @ 66.69/9.08 X4 @ Y3))))))))) & 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (!!) @ ( 66.69/9.08 ^[Y5 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 X4 @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y3))) @ 66.69/9.08 ( 66.69/9.08 s @ X4 @ 66.69/9.08 Y4) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ X4) @ 66.69/9.08 Y5))) = 66.69/9.08 (s @ 66.69/9.08 X4 @ 66.69/9.08 ( 66.69/9.08 app_2E2 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ X4) @ 66.69/9.08 Y5) @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y3)))))))))))))) & 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X4) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ X4) @ 66.69/9.08 Y3) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y4))))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X4) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ X4 @ 66.69/9.08 ( 66.69/9.08 app_2E2 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ X4) @ 66.69/9.08 Y3) @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y4))))))))))))) & 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X4) @ 66.69/9.08 (c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ 66.69/9.08 X2 @ X4) @ 66.69/9.08 Y3) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X4) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2)) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3))))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3)))))) & 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2)) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) & 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3)))) => 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3) @ 66.69/9.08 (s @ X4 @ Y2) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ 66.69/9.08 X2 @ X4) @ 66.69/9.08 Y0))) = 66.69/9.08 (s @ X4 @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ 66.69/9.08 X2 @ X4) @ 66.69/9.08 Y0) @ 66.69/9.08 (s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3)))))))))))) & 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3)))) => 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3) @ 66.69/9.08 (s @ X4 @ Y2) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ 66.69/9.08 X2 @ X4) @ 66.69/9.08 Y0))) = 66.69/9.08 (s @ X4 @ Y2)))))))) & 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ 66.69/9.08 X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y3)))))) & 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y3))) != 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) != 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y3)))))))) & 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 X2 @ 66.69/9.08 Y3) = 66.69/9.08 (s @ 66.69/9.08 X2 @ Y4))) <=> 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y3))) = 66.69/9.08 (s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y4))))))))))))))))))))))))), 66.69/9.08 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl113])). 66.69/9.08 thf(zip_derived_cl115, plain, 66.69/9.08 (![X2 : d, X4 : d, X6 : u]: 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((((!!) @ (^[Y2 : u]: 66.69/9.08 (((s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y2))))) = 66.69/9.08 (s @ X2 @ Y2)))))) & 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y2)))))) = 66.69/9.08 (mono_2Ec_2Ebool_2ET)))))) & 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))) = 66.69/9.08 (mono_2Ec_2Ebool_2EF))) & 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2) = (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) <=> 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2))))))))) & 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2) = (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) <=> 66.69/9.08 (((~) @ (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2))))))))))) & 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2)))) => 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2))))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2)))))))) & 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 Y2)))))) & 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2)))) => 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y0) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2)))))))) & 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) @ 66.69/9.08 (s @ X4 @ Y2) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ 66.69/9.08 X2 @ X4) @ 66.69/9.08 Y3))) = 66.69/9.08 (s @ X4 @ Y2))))))))) & 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((!!) @ (^[Y4 : u]: 66.69/9.08 (( 66.69/9.08 (s @ 66.69/9.08 X4 @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 ( 66.69/9.08 c_2Eoption_2ESOME_2E1 @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y2))) @ 66.69/9.08 ( 66.69/9.08 s @ X4 @ 66.69/9.08 Y3) @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ X4) @ 66.69/9.08 Y4))) = 66.69/9.08 (s @ 66.69/9.08 X4 @ 66.69/9.08 ( 66.69/9.08 app_2E2 @ 66.69/9.08 ( 66.69/9.08 s @ 66.69/9.08 ( 66.69/9.08 tyop_2Emin_2Efun @ 66.69/9.08 X2 @ X4) @ 66.69/9.08 Y4) @ 66.69/9.08 ( 66.69/9.08 s @ X2 @ 66.69/9.08 Y2)))))))))))))) & 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X4) @ 66.69/9.08 (c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ 66.69/9.08 X2 @ X4) @ 66.69/9.08 Y2) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y3))))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X4) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X4 @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ 66.69/9.08 X2 @ X4) @ 66.69/9.08 Y2) @ 66.69/9.08 (s @ X2 @ Y3))))))))))))) & 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 (c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ X4) @ 66.69/9.08 Y2) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2)) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2))))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 Y2)))))) & 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) & 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2)))) => 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2) @ 66.69/9.08 (s @ X4 @ Y1) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 X4) @ 66.69/9.08 X6))) = 66.69/9.08 (s @ X4 @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 X4) @ 66.69/9.08 X6) @ 66.69/9.08 (s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2)))))))))))) & 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2)))) => 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2) @ 66.69/9.08 (s @ X4 @ Y1) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 X4) @ 66.69/9.08 X6))) = 66.69/9.08 (s @ X4 @ Y1)))))))) & 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 Y2) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 Y2)))))) & 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y2))) != 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) != 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y2)))))))) & 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((((s @ X2 @ Y2) = 66.69/9.08 (s @ X2 @ Y3))) <=> 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y2))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y3)))))))))))))))))))))), 66.69/9.08 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl114])). 66.69/9.08 thf(zip_derived_cl116, plain, 66.69/9.08 (![X2 : d, X4 : d, X6 : u, X8 : u]: 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((((!!) @ (^[Y1 : u]: 66.69/9.08 (((s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y1))))) = 66.69/9.08 (s @ X2 @ Y1)))))) & 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y1)))))) = 66.69/9.08 (mono_2Ec_2Ebool_2ET)))))) & 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))) = 66.69/9.08 (mono_2Ec_2Ebool_2EF))) & 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 Y1) = (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) <=> 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y1))))))))) & 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 Y1) = (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) <=> 66.69/9.08 (((~) @ (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 Y1))))))))))) & 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y1)))) => 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ Y1))))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 Y1)))))))) & 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y1) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y1)))))) & 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y1)))) => 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 Y1) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 X8) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 Y1)))))))) & 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) @ 66.69/9.08 (s @ X4 @ Y1) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ X4) @ 66.69/9.08 Y2))) = 66.69/9.08 (s @ X4 @ Y1))))))))) & 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((!!) @ (^[Y3 : u]: 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y1))) @ 66.69/9.08 (s @ X4 @ Y2) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ 66.69/9.08 X2 @ X4) @ 66.69/9.08 Y3))) = 66.69/9.08 (s @ X4 @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ 66.69/9.08 X2 @ X4) @ 66.69/9.08 Y3) @ 66.69/9.08 (s @ X2 @ Y1)))))))))))))) & 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 (c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ X4) @ 66.69/9.08 Y1) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y2))))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X4 @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 X4) @ 66.69/9.08 Y1) @ 66.69/9.08 (s @ X2 @ Y2))))))))))))) & 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 (c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ Y1) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 Y1))))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y1)))))) & 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) & 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y1)))) => 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 Y1) @ 66.69/9.08 (s @ X4 @ Y0) @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X6))) = 66.69/9.08 (s @ X4 @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X6) @ 66.69/9.08 (s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ Y1)))))))))))) & 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y1)))) => 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 Y1) @ 66.69/9.08 (s @ X4 @ Y0) @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X6))) = 66.69/9.08 (s @ X4 @ Y0)))))))) & 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y1) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y1) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y1)))))) & 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y1))) != 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) != (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y1)))))))) & 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((((s @ X2 @ Y1) = (s @ X2 @ 66.69/9.08 Y2))) <=> 66.69/9.08 (((s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y1))) = 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y2))))))))))))))))))), 66.69/9.08 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl115])). 66.69/9.08 thf(zip_derived_cl117, plain, 66.69/9.08 (![X2 : d, X4 : d, X6 : u, X8 : u, X10 : u]: 66.69/9.08 (((((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0))))) = 66.69/9.08 (s @ X2 @ Y0)))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0)))))) = 66.69/9.08 (mono_2Ec_2Ebool_2ET)))))) & 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))) = 66.69/9.08 (mono_2Ec_2Ebool_2EF))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((((s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) = (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) <=> 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((((s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) = (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) <=> 66.69/9.08 (((~) @ (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0))))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))) => 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0))))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))) => 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ X8) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) @ 66.69/9.08 (s @ X4 @ Y0) @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ Y1))) = 66.69/9.08 (s @ X4 @ Y0))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y0))) @ 66.69/9.08 (s @ X4 @ Y1) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ X4) @ 66.69/9.08 Y2))) = 66.69/9.08 (s @ X4 @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ X4) @ 66.69/9.08 Y2) @ 66.69/9.08 (s @ X2 @ Y0)))))))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 (c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ Y0) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y1))))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X4 @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ Y0) @ 66.69/9.08 (s @ X2 @ Y1))))))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 (c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ Y0) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0))))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))) & 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))) => 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ X4 @ X10) @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X6))) = 66.69/9.08 (s @ X4 @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X6) @ 66.69/9.08 (s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))) => 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ X4 @ X10) @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X6))) = 66.69/9.08 (s @ X4 @ X10)))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0))) != (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) != (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0)))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((((s @ X2 @ Y0) = (s @ X2 @ Y1))) <=> 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y1)))))))))))))))), 66.69/9.08 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl116])). 66.69/9.08 thf(thm_2Ebool_2ENOT__CLAUSES, axiom, 66.69/9.08 (( ( ~( mono_2Ec_2Ebool_2EF ) ) <=> ( mono_2Ec_2Ebool_2ET ) ) & 66.69/9.08 ( ( ~( mono_2Ec_2Ebool_2ET ) ) <=> ( mono_2Ec_2Ebool_2EF ) ) & 66.69/9.08 ( ![V0t:$o]: ( ( V0t ) <=> ( V0t ) ) ))). 66.69/9.08 thf(zip_derived_cl1, plain, 66.69/9.08 ( (((((((~) @ mono_2Ec_2Ebool_2EF)) <=> (mono_2Ec_2Ebool_2ET))) & 66.69/9.08 (((((~) @ mono_2Ec_2Ebool_2ET)) <=> (mono_2Ec_2Ebool_2EF))) & 66.69/9.08 (((!!) @ (^[Y0 : $o]: (((Y0) <=> (Y0))))))))), 66.69/9.08 inference('cnf', [status(esa)], [thm_2Ebool_2ENOT__CLAUSES])). 66.69/9.08 thf(zip_derived_cl29, plain, 66.69/9.08 ( (((((((~) @ mono_2Ec_2Ebool_2EF)) <=> (mono_2Ec_2Ebool_2ET))) & 66.69/9.08 (((((~) @ mono_2Ec_2Ebool_2ET)) <=> (mono_2Ec_2Ebool_2EF)))))), 66.69/9.08 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl1])). 66.69/9.08 thf(thm_2Ebool_2ETRUTH, axiom, (mono_2Ec_2Ebool_2ET)). 66.69/9.08 thf(zip_derived_cl20, plain, ( (mono_2Ec_2Ebool_2ET)), 66.69/9.08 inference('cnf', [status(esa)], [thm_2Ebool_2ETRUTH])). 66.69/9.08 thf(zip_derived_cl20, plain, ( (mono_2Ec_2Ebool_2ET)), 66.69/9.08 inference('cnf', [status(esa)], [thm_2Ebool_2ETRUTH])). 66.69/9.08 thf(zip_derived_cl30, plain, 66.69/9.08 ( (((((((~) @ mono_2Ec_2Ebool_2EF)) <=> ($true))) & 66.69/9.08 (((((~) @ ($true))) <=> (mono_2Ec_2Ebool_2EF)))))), 66.69/9.08 inference('demod', [status(thm)], 66.69/9.08 [zip_derived_cl29, zip_derived_cl20, zip_derived_cl20])). 66.69/9.08 thf(zip_derived_cl31, plain, ( (((~) @ mono_2Ec_2Ebool_2EF))), 66.69/9.08 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl30])). 66.69/9.08 thf(zip_derived_cl32, plain, (~ (mono_2Ec_2Ebool_2EF)), 66.69/9.08 inference('simplify nested equalities', [status(thm)], [zip_derived_cl31])). 66.69/9.08 thf(zip_derived_cl118, plain, 66.69/9.08 (![X2 : d, X4 : d, X6 : u, X8 : u, X10 : u]: 66.69/9.08 (((((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0))))) = 66.69/9.08 (s @ X2 @ Y0)))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0)))))) = 66.69/9.08 (mono_2Ec_2Ebool_2ET)))))) & 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))) = 66.69/9.08 ($false))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((((s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) = (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) <=> 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((((s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) = (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) <=> 66.69/9.08 (((~) @ (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0))))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))) => 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0))))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))) => 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ X8) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) @ 66.69/9.08 (s @ X4 @ Y0) @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ Y1))) = 66.69/9.08 (s @ X4 @ Y0))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y0))) @ 66.69/9.08 (s @ X4 @ Y1) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ X4) @ 66.69/9.08 Y2))) = 66.69/9.08 (s @ X4 @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ X4) @ 66.69/9.08 Y2) @ 66.69/9.08 (s @ X2 @ Y0)))))))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 (c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ Y0) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y1))))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X4 @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ Y0) @ 66.69/9.08 (s @ X2 @ Y1))))))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 (c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ Y0) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0))))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))) & 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))) => 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ X4 @ X10) @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X6))) = 66.69/9.08 (s @ X4 @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X6) @ 66.69/9.08 (s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))) => 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ X4 @ X10) @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X6))) = 66.69/9.08 (s @ X4 @ X10)))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0))) != (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) != (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0)))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((((s @ X2 @ Y0) = (s @ X2 @ Y1))) <=> 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y1)))))))))))))))), 66.69/9.08 inference('demod', [status(thm)], [zip_derived_cl117, zip_derived_cl32])). 66.69/9.08 thf(zip_derived_cl119, plain, 66.69/9.08 (![X2 : d, X4 : d, X6 : u, X8 : u, X10 : u]: 66.69/9.08 (((((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0))))) = 66.69/9.08 (s @ X2 @ Y0)))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0)))))) = 66.69/9.08 (mono_2Ec_2Ebool_2ET)))))) & 66.69/9.08 (((~) @ (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((((s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) = (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) <=> 66.69/9.08 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((((s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) = (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) <=> 66.69/9.08 (((~) @ (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0))))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))) => 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0))))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))) => 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ X8) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) @ 66.69/9.08 (s @ X4 @ Y0) @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ Y1))) = 66.69/9.08 (s @ X4 @ Y0))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((!!) @ (^[Y2 : u]: 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X2 @ Y0))) @ 66.69/9.08 (s @ X4 @ Y1) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ X4) @ 66.69/9.08 Y2))) = 66.69/9.08 (s @ X4 @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ X4) @ 66.69/9.08 Y2) @ 66.69/9.08 (s @ X2 @ Y0)))))))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 (c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ Y0) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y1))))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ X4 @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ Y0) @ 66.69/9.08 (s @ X2 @ Y1))))))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 (c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ Y0) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0))))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))) & 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2EOPTION__JOIN_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ENONE_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__SOME_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))) => 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ X4 @ X10) @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X6))) = 66.69/9.08 (s @ X4 @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X6) @ 66.69/9.08 (s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 (s @ tyop_2Emin_2Ebool @ 66.69/9.08 (c_2Eoption_2EIS__NONE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))) => 66.69/9.08 (((s @ X4 @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ X4 @ X10) @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X6))) = 66.69/9.08 (s @ X4 @ X10)))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2Eoption__CASE_2E3 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0)))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0))) != (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 c_2Eoption_2ENONE_2E0) != (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0)))))))) & 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((((s @ X2 @ Y0) = (s @ X2 @ Y1))) <=> 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y1)))))))))))))))), 66.69/9.08 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl118])). 66.69/9.08 thf(zip_derived_cl120, plain, 66.69/9.08 (![X2 : d]: 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0))))) = 66.69/9.08 (s @ X2 @ Y0))))))), 66.69/9.08 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl119])). 66.69/9.08 thf(zip_derived_cl140, plain, 66.69/9.08 (![X2 : d, X4 : u]: 66.69/9.08 (((s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X4))))) = 66.69/9.08 (s @ X2 @ X4)))), 66.69/9.08 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl120])). 66.69/9.08 thf(zip_derived_cl159, plain, 66.69/9.08 (![X2 : d, X4 : u]: 66.69/9.08 ((s @ X2 @ 66.69/9.08 (c_2Eoption_2ETHE_2E1 @ 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X4))))) 66.69/9.08 = (s @ X2 @ X4))), 66.69/9.08 inference('simplify nested equalities', [status(thm)], 66.69/9.08 [zip_derived_cl140])). 66.69/9.08 thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b, axiom, 66.69/9.08 (![A_27b:d,X0_2E0:u]: 66.69/9.08 ( ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27b ) @ 66.69/9.08 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ X0_2E0 ) ) ) = 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27b ) @ 66.69/9.08 ( app_2E2 @ 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ 66.69/9.08 c_2Eoption_2ESOME_2E0 ) @ 66.69/9.08 ( s @ A_27b @ X0_2E0 ) ) ) ))). 66.69/9.08 thf(zip_derived_cl3, plain, 66.69/9.08 ( (((!!) @ (^[Y0 : d]: 66.69/9.08 (((!!) @ (^[Y1 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ Y0) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ Y0 @ Y1))) = 66.69/9.08 (s @ (tyop_2Eoption_2Eoption @ Y0) @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ Y0 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ Y0)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0) @ 66.69/9.08 (s @ Y0 @ Y1)))))))))))), 66.69/9.08 inference('cnf', [status(esa)], 66.69/9.08 [arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b])). 66.69/9.08 thf(zip_derived_cl40, plain, 66.69/9.08 (![X2 : d]: 66.69/9.08 (((!!) @ (^[Y0 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0))) = (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ 66.69/9.08 (tyop_2Emin_2Efun @ X2 @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0) @ 66.69/9.08 (s @ X2 @ Y0))))))))), 66.69/9.08 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 66.69/9.08 thf(zip_derived_cl41, plain, 66.69/9.08 (![X2 : d, X4 : u]: 66.69/9.08 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X4))) = (s @ 66.69/9.08 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0) @ 66.69/9.08 (s @ X2 @ X4)))))), 66.69/9.08 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl40])). 66.69/9.08 thf(zip_derived_cl42, plain, 66.69/9.08 (![X2 : d, X4 : u]: 66.69/9.08 ((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X4))) 66.69/9.08 = (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.08 (app_2E2 @ 66.69/9.08 (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ 66.69/9.08 c_2Eoption_2ESOME_2E0) @ 66.69/9.08 (s @ X2 @ X4))))), 66.69/9.08 inference('simplify nested equalities', [status(thm)], [zip_derived_cl41])). 66.69/9.08 thf(thm_2Equotient__option_2EOPTION__REL__def, conjecture, 66.69/9.08 (![A_27a:d,V0y_2E0:u,V1x_2E0:u,V2R_2E0:u]: 66.69/9.08 ( ( ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( c_2Eoption_2EOPTREL_2E3 @ 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Emin_2Efun @ 66.69/9.08 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 66.69/9.08 V2R_2E0 ) @ 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.08 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) = 66.69/9.08 ( mono_2Ec_2Ebool_2EF ) ) & 66.69/9.08 ( ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.08 ( s @ 66.69/9.08 tyop_2Emin_2Ebool @ 66.69/9.08 ( c_2Eoption_2EOPTREL_2E3 @ 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Emin_2Efun @ 66.69/9.08 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 66.69/9.08 V2R_2E0 ) @ 66.69/9.08 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ 66.69/9.08 ( s @ 66.69/9.08 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.08 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) ) = 66.69/9.08 ( mono_2Ec_2Ebool_2EF ) ) & 66.69/9.09 ( ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 ( s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 ( c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Emin_2Efun @ 66.69/9.09 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 66.69/9.09 V2R_2E0 ) @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.09 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.09 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) ) = 66.69/9.09 ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 ( s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 ( app_2E2 @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ 66.69/9.09 ( app_2E2 @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Emin_2Efun @ 66.69/9.09 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 66.69/9.09 V2R_2E0 ) @ 66.69/9.09 ( s @ A_27a @ V1x_2E0 ) ) ) @ 66.69/9.09 ( s @ A_27a @ V0y_2E0 ) ) ) ) ) & 66.69/9.09 ( ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 ( s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 ( c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Emin_2Efun @ 66.69/9.09 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 66.69/9.09 V2R_2E0 ) @ 66.69/9.09 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ 66.69/9.09 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) = 66.69/9.09 ( mono_2Ec_2Ebool_2ET ) ) ))). 66.69/9.09 thf(zf_stmt_0, negated_conjecture, 66.69/9.09 (~( ![A_27a:d,V0y_2E0:u,V1x_2E0:u,V2R_2E0:u]: 66.69/9.09 ( ( ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 ( s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 ( c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Emin_2Efun @ 66.69/9.09 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 66.69/9.09 V2R_2E0 ) @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.09 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) = 66.69/9.09 ( mono_2Ec_2Ebool_2EF ) ) & 66.69/9.09 ( ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 ( s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 ( c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Emin_2Efun @ 66.69/9.09 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 66.69/9.09 V2R_2E0 ) @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.09 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) ) = 66.69/9.09 ( mono_2Ec_2Ebool_2EF ) ) & 66.69/9.09 ( ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 ( s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 ( c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Emin_2Efun @ 66.69/9.09 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 66.69/9.09 V2R_2E0 ) @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.09 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.09 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) ) = 66.69/9.09 ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 ( s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 ( app_2E2 @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ 66.69/9.09 ( app_2E2 @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Emin_2Efun @ 66.69/9.09 A_27a @ 66.69/9.09 ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 66.69/9.09 V2R_2E0 ) @ 66.69/9.09 ( s @ A_27a @ V1x_2E0 ) ) ) @ 66.69/9.09 ( s @ A_27a @ V0y_2E0 ) ) ) ) ) & 66.69/9.09 ( ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 ( s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 ( c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Emin_2Efun @ 66.69/9.09 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 66.69/9.09 V2R_2E0 ) @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) = 66.69/9.09 ( mono_2Ec_2Ebool_2ET ) ) ) )), 66.69/9.09 inference('cnf.neg', [status(esa)], 66.69/9.09 [thm_2Equotient__option_2EOPTION__REL__def])). 66.69/9.09 thf(zip_derived_cl23, plain, 66.69/9.09 (~ (((!!) @ (^[Y0 : d]: 66.69/9.09 (((!!) @ (^[Y1 : u]: 66.69/9.09 (((!!) @ (^[Y2 : u]: 66.69/9.09 (((!!) @ (^[Y3 : u]: 66.69/9.09 (((((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 Y0 @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 Y0 @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y3) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ Y0 @ Y2))) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ 66.69/9.09 c_2Eoption_2ENONE_2E0)))) = 66.69/9.09 (mono_2Ec_2Ebool_2EF))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 Y0 @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 Y0 @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y3) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ 66.69/9.09 c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ Y0 @ Y1)))))) = 66.69/9.09 (mono_2Ec_2Ebool_2EF))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 Y0 @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 Y0 @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y3) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ Y0 @ Y2))) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ Y0 @ Y1)))))) = 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 Y0 @ 66.69/9.09 tyop_2Emin_2Ebool) @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 Y0 @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 Y0 @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y3) @ 66.69/9.09 (s @ Y0 @ Y2))) @ 66.69/9.09 (s @ Y0 @ Y1)))))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 Y0 @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 Y0 @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y3) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ 66.69/9.09 c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ 66.69/9.09 c_2Eoption_2ENONE_2E0)))) = 66.69/9.09 (mono_2Ec_2Ebool_2ET)))))))))))))))))), 66.69/9.09 inference('cnf', [status(esa)], [zf_stmt_0])). 66.69/9.09 thf(zip_derived_cl77, plain, 66.69/9.09 (~ (((!!) @ (^[Y0 : u]: 66.69/9.09 (((!!) @ (^[Y1 : u]: 66.69/9.09 (((!!) @ (^[Y2 : u]: 66.69/9.09 (((((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 '#sk2' @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y2) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ '#sk2' @ Y1))) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 '#sk2') @ 66.69/9.09 c_2Eoption_2ENONE_2E0)))) = 66.69/9.09 (mono_2Ec_2Ebool_2EF))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 '#sk2' @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y2) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 '#sk2') @ 66.69/9.09 c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ '#sk2' @ Y0)))))) = 66.69/9.09 (mono_2Ec_2Ebool_2EF))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 '#sk2' @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y2) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ '#sk2' @ Y1))) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ '#sk2' @ Y0)))))) = 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 '#sk2' @ tyop_2Emin_2Ebool) @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 '#sk2' @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y2) @ 66.69/9.09 (s @ '#sk2' @ Y1))) @ 66.69/9.09 (s @ '#sk2' @ Y0)))))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 '#sk2' @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y2) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 '#sk2') @ 66.69/9.09 c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 '#sk2') @ 66.69/9.09 c_2Eoption_2ENONE_2E0)))) = 66.69/9.09 (mono_2Ec_2Ebool_2ET))))))))))))))), 66.69/9.09 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl23])). 66.69/9.09 thf(zip_derived_cl78, plain, 66.69/9.09 (~ (((!!) @ (^[Y0 : u]: 66.69/9.09 (((!!) @ (^[Y1 : u]: 66.69/9.09 (((((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y1) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ '#sk2' @ Y0))) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 c_2Eoption_2ENONE_2E0)))) = 66.69/9.09 (mono_2Ec_2Ebool_2EF))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y1) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ '#sk2' @ '#sk3')))))) = 66.69/9.09 (mono_2Ec_2Ebool_2EF))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y1) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ '#sk2' @ Y0))) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ '#sk2' @ '#sk3')))))) = 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 tyop_2Emin_2Ebool) @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y1) @ 66.69/9.09 (s @ '#sk2' @ Y0))) @ 66.69/9.09 (s @ '#sk2' @ '#sk3')))))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y1) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 c_2Eoption_2ENONE_2E0)))) = 66.69/9.09 (mono_2Ec_2Ebool_2ET)))))))))))), 66.69/9.09 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl77])). 66.69/9.09 thf(zip_derived_cl79, plain, 66.69/9.09 (~ (((!!) @ (^[Y0 : u]: 66.69/9.09 (((((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 Y0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 c_2Eoption_2ENONE_2E0)))) = 66.69/9.09 (mono_2Ec_2Ebool_2EF))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 Y0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk3')))))) = 66.69/9.09 (mono_2Ec_2Ebool_2EF))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 Y0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk3')))))) = 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool) @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 Y0) @ 66.69/9.09 (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ '#sk2' @ '#sk3')))))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 Y0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 c_2Eoption_2ENONE_2E0)))) = 66.69/9.09 (mono_2Ec_2Ebool_2ET))))))))), 66.69/9.09 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl78])). 66.69/9.09 thf(zip_derived_cl80, plain, 66.69/9.09 (~ (((((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0)))) = 66.69/9.09 (mono_2Ec_2Ebool_2EF))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk3')))))) = 66.69/9.09 (mono_2Ec_2Ebool_2EF))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk3')))))) = 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool) @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ '#sk2' @ '#sk3')))))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0)))) = 66.69/9.09 (mono_2Ec_2Ebool_2ET)))))), 66.69/9.09 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl79])). 66.69/9.09 thf(zip_derived_cl32, plain, (~ (mono_2Ec_2Ebool_2EF)), 66.69/9.09 inference('simplify nested equalities', [status(thm)], [zip_derived_cl31])). 66.69/9.09 thf(zip_derived_cl32, plain, (~ (mono_2Ec_2Ebool_2EF)), 66.69/9.09 inference('simplify nested equalities', [status(thm)], [zip_derived_cl31])). 66.69/9.09 thf(zip_derived_cl20, plain, ( (mono_2Ec_2Ebool_2ET)), 66.69/9.09 inference('cnf', [status(esa)], [thm_2Ebool_2ETRUTH])). 66.69/9.09 thf(zip_derived_cl81, plain, 66.69/9.09 (~ (((((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0)))) = 66.69/9.09 ($false))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk3')))))) = 66.69/9.09 ($false))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk3')))))) = 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool) @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ '#sk2' @ '#sk3')))))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0)))) = 66.69/9.09 ($true)))))), 66.69/9.09 inference('demod', [status(thm)], 66.69/9.09 [zip_derived_cl80, zip_derived_cl32, zip_derived_cl32, 66.69/9.09 zip_derived_cl20])). 66.69/9.09 thf(zip_derived_cl82, plain, 66.69/9.09 (~ (((((~) @ (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 c_2Eoption_2ENONE_2E0)))))) & 66.69/9.09 (((~) @ (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk3')))))))) & 66.69/9.09 (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk3')))))) = 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool) @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ '#sk2' @ '#sk3')))))) & 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0))))))), 66.69/9.09 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl81])). 66.69/9.09 thf(zip_derived_cl83, plain, 66.69/9.09 (( (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0)))) 66.69/9.09 | (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk3')))))) 66.69/9.09 | ~ (((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk3')))))) = 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool) @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ '#sk2' @ '#sk3')))))) 66.69/9.09 | ~ (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0)))))), 66.69/9.09 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl82])). 66.69/9.09 thf(zip_derived_cl84, plain, 66.69/9.09 (( (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0)))) 66.69/9.09 | (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk3')))))) 66.69/9.09 | ((j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ '#sk2' @ '#sk3')))))) 66.69/9.09 != (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool) @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ '#sk2' @ '#sk4'))) @ 66.69/9.09 (s @ '#sk2' @ '#sk3'))))) 66.69/9.09 | ~ (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ 66.69/9.09 (tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool)) @ 66.69/9.09 '#sk5') @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ '#sk2') @ c_2Eoption_2ENONE_2E0)))))), 66.69/9.09 inference('simplify nested equalities', [status(thm)], [zip_derived_cl83])). 66.69/9.09 thf(zip_derived_cl137, plain, 66.69/9.09 (![X2 : d]: 66.69/9.09 (((!!) @ (^[Y0 : u]: 66.69/9.09 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0))) != (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))))))), 66.69/9.09 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl119])). 66.69/9.09 thf(zip_derived_cl156, plain, 66.69/9.09 (![X2 : d, X4 : u]: 66.69/9.09 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X4))) != (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))), 66.69/9.09 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl137])). 66.69/9.09 thf(zip_derived_cl175, plain, 66.69/9.09 (![X2 : d, X4 : u]: 66.69/9.09 ((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X4))) 66.69/9.09 != (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))), 66.69/9.09 inference('simplify nested equalities', [status(thm)], 66.69/9.09 [zip_derived_cl156])). 66.69/9.09 thf(zip_derived_cl131, plain, 66.69/9.09 (![X2 : d, X4 : d]: 66.69/9.09 (((!!) @ (^[Y0 : u]: 66.69/9.09 (((s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.09 (c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.09 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ Y0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.09 c_2Eoption_2ENONE_2E0))) = 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.09 c_2Eoption_2ENONE_2E0))))))), 66.69/9.09 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl119])). 66.69/9.09 thf(zip_derived_cl150, plain, 66.69/9.09 (![X2 : d, X4 : d, X6 : u]: 66.69/9.09 (((s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.09 (c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.09 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X6) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))) = 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0)))), 66.69/9.09 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl131])). 66.69/9.09 thf(zip_derived_cl170, plain, 66.69/9.09 (![X2 : d, X4 : d, X6 : u]: 66.69/9.09 ((s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.09 (c_2Eoption_2EOPTION__MAP_2E2 @ 66.69/9.09 (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X6) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))) 66.69/9.09 = (s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0))), 66.69/9.09 inference('simplify nested equalities', [status(thm)], 66.69/9.09 [zip_derived_cl150])). 66.69/9.09 thf(thm_2Eoption_2EOPTREL__def, axiom, 66.69/9.09 (![A_27a:d,A_27b:d,V0R_2E0:u,V1x_2E0:u,V2y_2E0:u]: 66.69/9.09 ( ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 ) = 66.69/9.09 ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) & 66.69/9.09 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 ) = 66.69/9.09 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) | 66.69/9.09 ( ?[V3x0_2E0:u,V4y0_2E0:u]: 66.69/9.09 ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 ) = 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Eoption_2Eoption @ A_27a ) @ 66.69/9.09 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3x0_2E0 ) ) ) ) & 66.69/9.09 ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 ( s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 ( app_2E2 @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ 66.69/9.09 ( app_2E2 @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Emin_2Efun @ 66.69/9.09 A_27a @ 66.69/9.09 ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ 66.69/9.09 V0R_2E0 ) @ 66.69/9.09 ( s @ A_27a @ V3x0_2E0 ) ) ) @ 66.69/9.09 ( s @ A_27b @ V4y0_2E0 ) ) ) ) & 66.69/9.09 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 ) = 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Eoption_2Eoption @ A_27b ) @ 66.69/9.09 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V4y0_2E0 ) ) ) ) ) ) ) <=> 66.69/9.09 ( j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 ( s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 ( c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 ( s @ 66.69/9.09 ( tyop_2Emin_2Efun @ 66.69/9.09 A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ 66.69/9.09 V0R_2E0 ) @ 66.69/9.09 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 ) @ 66.69/9.09 ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 ) ) ) ) ))). 66.69/9.09 thf(zip_derived_cl13, plain, 66.69/9.09 ( (((!!) @ (^[Y0 : d]: 66.69/9.09 (((!!) @ (^[Y1 : d]: 66.69/9.09 (((!!) @ (^[Y2 : u]: 66.69/9.09 (((!!) @ (^[Y3 : u]: 66.69/9.09 (((!!) @ (^[Y4 : u]: 66.69/9.09 (((( 66.69/9.09 (( 66.69/9.09 (( 66.69/9.09 (s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 Y1) @ 66.69/9.09 Y4) = 66.69/9.09 (s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 Y1) @ 66.69/9.09 c_2Eoption_2ENONE_2E0))) & 66.69/9.09 (( 66.69/9.09 (s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ 66.69/9.09 Y3) = 66.69/9.09 (s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ 66.69/9.09 c_2Eoption_2ENONE_2E0))))) | 66.69/9.09 (( 66.69/9.09 (??) @ ( 66.69/9.09 ^[Y5 : u]: 66.69/9.09 (( 66.69/9.09 (??) @ ( 66.69/9.09 ^[Y6 : u]: 66.69/9.09 (( 66.69/9.09 ( 66.69/9.09 ( 66.69/9.09 (s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ 66.69/9.09 Y3) = 66.69/9.09 (s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ 66.69/9.09 ( 66.69/9.09 c_2Eoption_2ESOME_2E1 @ 66.69/9.09 ( 66.69/9.09 s @ Y0 @ 66.69/9.09 Y5))))) & 66.69/9.09 ( 66.69/9.09 j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 ( 66.69/9.09 s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 ( 66.69/9.09 app_2E2 @ 66.69/9.09 ( 66.69/9.09 s @ 66.69/9.09 ( 66.69/9.09 tyop_2Emin_2Efun @ 66.69/9.09 Y1 @ 66.69/9.09 tyop_2Emin_2Ebool) @ 66.69/9.09 ( 66.69/9.09 app_2E2 @ 66.69/9.09 ( 66.69/9.09 s @ 66.69/9.09 ( 66.69/9.09 tyop_2Emin_2Efun @ 66.69/9.09 Y0 @ 66.69/9.09 ( 66.69/9.09 tyop_2Emin_2Efun @ 66.69/9.09 Y1 @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y2) @ 66.69/9.09 ( 66.69/9.09 s @ Y0 @ 66.69/9.09 Y5))) @ 66.69/9.09 ( 66.69/9.09 s @ Y1 @ 66.69/9.09 Y6)))) & 66.69/9.09 ( 66.69/9.09 ( 66.69/9.09 (s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 Y1) @ 66.69/9.09 Y4) = 66.69/9.09 (s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 Y1) @ 66.69/9.09 ( 66.69/9.09 c_2Eoption_2ESOME_2E1 @ 66.69/9.09 ( 66.69/9.09 s @ Y1 @ 66.69/9.09 Y6))))))))))))))) <=> 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 ( 66.69/9.09 s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 ( 66.69/9.09 c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 ( 66.69/9.09 s @ 66.69/9.09 ( 66.69/9.09 tyop_2Emin_2Efun @ 66.69/9.09 Y0 @ 66.69/9.09 ( 66.69/9.09 tyop_2Emin_2Efun @ 66.69/9.09 Y1 @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y2) @ 66.69/9.09 ( 66.69/9.09 s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ Y3) @ 66.69/9.09 ( 66.69/9.09 s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 Y1) @ Y4)))))))))))))))))))))), 66.69/9.09 inference('cnf', [status(esa)], [thm_2Eoption_2EOPTREL__def])). 66.69/9.09 thf(zip_derived_cl107, plain, 66.69/9.09 (![X2 : d]: 66.69/9.09 (((!!) @ (^[Y0 : d]: 66.69/9.09 (((!!) @ (^[Y1 : u]: 66.69/9.09 (((!!) @ (^[Y2 : u]: 66.69/9.09 (((!!) @ (^[Y3 : u]: 66.69/9.09 (((((((((s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ 66.69/9.09 Y3) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ 66.69/9.09 c_2Eoption_2ENONE_2E0))) & 66.69/9.09 (((s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 X2) @ 66.69/9.09 Y2) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 X2) @ 66.69/9.09 c_2Eoption_2ENONE_2E0))))) | 66.69/9.09 (((??) @ ( 66.69/9.09 ^[Y4 : u]: 66.69/9.09 (((??) @ ( 66.69/9.09 ^[Y5 : u]: 66.69/9.09 ( 66.69/9.09 ( 66.69/9.09 ( 66.69/9.09 ( 66.69/9.09 (s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 X2) @ 66.69/9.09 Y2) = 66.69/9.09 (s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 X2) @ 66.69/9.09 ( 66.69/9.09 c_2Eoption_2ESOME_2E1 @ 66.69/9.09 ( 66.69/9.09 s @ X2 @ 66.69/9.09 Y4))))) & 66.69/9.09 ( 66.69/9.09 j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 ( 66.69/9.09 s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 ( 66.69/9.09 app_2E2 @ 66.69/9.09 ( 66.69/9.09 s @ 66.69/9.09 ( 66.69/9.09 tyop_2Emin_2Efun @ 66.69/9.09 Y0 @ 66.69/9.09 tyop_2Emin_2Ebool) @ 66.69/9.09 ( 66.69/9.09 app_2E2 @ 66.69/9.09 ( 66.69/9.09 s @ 66.69/9.09 ( 66.69/9.09 tyop_2Emin_2Efun @ 66.69/9.09 X2 @ 66.69/9.09 ( 66.69/9.09 tyop_2Emin_2Efun @ 66.69/9.09 Y0 @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y1) @ 66.69/9.09 ( 66.69/9.09 s @ X2 @ 66.69/9.09 Y4))) @ 66.69/9.09 ( 66.69/9.09 s @ Y0 @ 66.69/9.09 Y5)))) & 66.69/9.09 ( 66.69/9.09 ( 66.69/9.09 (s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ 66.69/9.09 Y3) = 66.69/9.09 (s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ 66.69/9.09 ( 66.69/9.09 c_2Eoption_2ESOME_2E1 @ 66.69/9.09 ( 66.69/9.09 s @ Y0 @ 66.69/9.09 Y5))))))))))))))) <=> 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 X2 @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 Y0 @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y1) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 X2) @ 66.69/9.09 Y2) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 Y0) @ 66.69/9.09 Y3))))))))))))))))))), 66.69/9.09 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 66.69/9.09 thf(zip_derived_cl108, plain, 66.69/9.09 (![X2 : d, X4 : d]: 66.69/9.09 (((!!) @ (^[Y0 : u]: 66.69/9.09 (((!!) @ (^[Y1 : u]: 66.69/9.09 (((!!) @ (^[Y2 : u]: 66.69/9.09 (((((((((s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 X4) @ 66.69/9.09 Y2) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 X4) @ 66.69/9.09 c_2Eoption_2ENONE_2E0))) & 66.69/9.09 (((s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 X2) @ 66.69/9.09 Y1) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 X2) @ 66.69/9.09 c_2Eoption_2ENONE_2E0))))) | 66.69/9.09 (((??) @ (^[Y3 : u]: 66.69/9.09 (((??) @ ( 66.69/9.09 ^[Y4 : u]: 66.69/9.09 (((((s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 X2) @ 66.69/9.09 Y1) = 66.69/9.09 (s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 X2) @ 66.69/9.09 ( 66.69/9.09 c_2Eoption_2ESOME_2E1 @ 66.69/9.09 ( 66.69/9.09 s @ X2 @ 66.69/9.09 Y3))))) & 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 ( 66.69/9.09 app_2E2 @ 66.69/9.09 ( 66.69/9.09 s @ 66.69/9.09 ( 66.69/9.09 tyop_2Emin_2Efun @ 66.69/9.09 X4 @ 66.69/9.09 tyop_2Emin_2Ebool) @ 66.69/9.09 ( 66.69/9.09 app_2E2 @ 66.69/9.09 ( 66.69/9.09 s @ 66.69/9.09 ( 66.69/9.09 tyop_2Emin_2Efun @ 66.69/9.09 X2 @ 66.69/9.09 ( 66.69/9.09 tyop_2Emin_2Efun @ 66.69/9.09 X4 @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y0) @ 66.69/9.09 ( 66.69/9.09 s @ X2 @ 66.69/9.09 Y3))) @ 66.69/9.09 ( 66.69/9.09 s @ X4 @ 66.69/9.09 Y4)))) & 66.69/9.09 (((s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 X4) @ 66.69/9.09 Y2) = 66.69/9.09 (s @ 66.69/9.09 ( 66.69/9.09 tyop_2Eoption_2Eoption @ 66.69/9.09 X4) @ 66.69/9.09 ( 66.69/9.09 c_2Eoption_2ESOME_2E1 @ 66.69/9.09 ( 66.69/9.09 s @ X4 @ 66.69/9.09 Y4))))))))))))))) <=> 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ X2 @ 66.69/9.09 (tyop_2Emin_2Efun @ X4 @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 Y0) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.09 Y1) @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.09 Y2)))))))))))))))), 66.69/9.09 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl107])). 66.69/9.09 thf(zip_derived_cl109, plain, 66.69/9.09 (![X2 : d, X4 : d, X6 : u]: 66.69/9.09 (((!!) @ (^[Y0 : u]: 66.69/9.09 (((!!) @ (^[Y1 : u]: 66.69/9.09 (((((((((s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.09 Y1) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.09 c_2Eoption_2ENONE_2E0))) & 66.69/9.09 (((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.09 Y0) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.09 c_2Eoption_2ENONE_2E0))))) | 66.69/9.09 (((??) @ (^[Y2 : u]: 66.69/9.09 (((??) @ (^[Y3 : u]: 66.69/9.09 (((((s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 X2) @ 66.69/9.09 Y0) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 X2) @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ X2 @ Y2))))) & 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ 66.69/9.09 tyop_2Emin_2Ebool @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 X4 @ 66.69/9.09 tyop_2Emin_2Ebool) @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 ( 66.69/9.09 tyop_2Emin_2Efun @ 66.69/9.09 X2 @ 66.69/9.09 ( 66.69/9.09 tyop_2Emin_2Efun @ 66.69/9.09 X4 @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 X6) @ 66.69/9.09 (s @ X2 @ 66.69/9.09 Y2))) @ 66.69/9.09 (s @ X4 @ Y3)))) & 66.69/9.09 (((s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 X4) @ 66.69/9.09 Y1) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 X4) @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ X4 @ Y3))))))))))))))) <=> 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ X2 @ 66.69/9.09 (tyop_2Emin_2Efun @ X4 @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 X6) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ X2) @ Y0) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ X4) @ Y1))))))))))))), 66.69/9.09 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl108])). 66.69/9.09 thf(zip_derived_cl110, plain, 66.69/9.09 (![X2 : d, X4 : d, X6 : u, X8 : u]: 66.69/9.09 (((!!) @ (^[Y0 : u]: 66.69/9.09 (((((((((s @ (tyop_2Eoption_2Eoption @ X4) @ Y0) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.09 c_2Eoption_2ENONE_2E0))) & 66.69/9.09 (((s @ (tyop_2Eoption_2Eoption @ X2) @ X8) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.09 c_2Eoption_2ENONE_2E0))))) | 66.69/9.09 (((??) @ (^[Y1 : u]: 66.69/9.09 (((??) @ (^[Y2 : u]: 66.69/9.09 (((((s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 X2) @ 66.69/9.09 X8) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 X2) @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ X2 @ Y1))))) & 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 X4 @ tyop_2Emin_2Ebool) @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 X2 @ 66.69/9.09 (tyop_2Emin_2Efun @ 66.69/9.09 X4 @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 X6) @ 66.69/9.09 (s @ X2 @ Y1))) @ 66.69/9.09 (s @ X4 @ Y2)))) & 66.69/9.09 (((s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 X4) @ 66.69/9.09 Y0) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ 66.69/9.09 X4) @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ X4 @ Y2))))))))))))))) <=> 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ X2 @ 66.69/9.09 (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool)) @ 66.69/9.09 X6) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ X2) @ X8) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ X4) @ Y0)))))))))), 66.69/9.09 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl109])). 66.69/9.09 thf(zip_derived_cl111, plain, 66.69/9.09 (![X2 : d, X4 : d, X6 : u, X8 : u, X10 : u]: 66.69/9.09 (((((((((s @ (tyop_2Eoption_2Eoption @ X4) @ X10) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0))) & 66.69/9.09 (((s @ (tyop_2Eoption_2Eoption @ X2) @ X8) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))))) | 66.69/9.09 (((??) @ (^[Y0 : u]: 66.69/9.09 (((??) @ (^[Y1 : u]: 66.69/9.09 (((((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.09 X8) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ X2 @ Y0))))) & 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ X4 @ 66.69/9.09 tyop_2Emin_2Ebool) @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ X2 @ 66.69/9.09 (tyop_2Emin_2Efun @ X4 @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 X6) @ 66.69/9.09 (s @ X2 @ Y0))) @ 66.69/9.09 (s @ X4 @ Y1)))) & 66.69/9.09 (((s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.09 X10) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ 66.69/9.09 (s @ X4 @ Y1))))))))))))))) <=> 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ X2 @ 66.69/9.09 (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool)) @ 66.69/9.09 X6) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ X2) @ X8) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ X4) @ X10))))))), 66.69/9.09 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl110])). 66.69/9.09 thf(zip_derived_cl112, plain, 66.69/9.09 (![X2 : d, X4 : d, X6 : u, X8 : u, X10 : u]: 66.69/9.09 ((((((((s @ (tyop_2Eoption_2Eoption @ X4) @ X10) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0))) & 66.69/9.09 (((s @ (tyop_2Eoption_2Eoption @ X2) @ X8) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))))) | 66.69/9.09 (((??) @ (^[Y0 : u]: 66.69/9.09 (((??) @ (^[Y1 : u]: 66.69/9.09 (((((s @ (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.09 X8) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ X2) @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ Y0))))) & 66.69/9.09 (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ X4 @ 66.69/9.09 tyop_2Emin_2Ebool) @ 66.69/9.09 (app_2E2 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ X2 @ 66.69/9.09 (tyop_2Emin_2Efun @ X4 @ 66.69/9.09 tyop_2Emin_2Ebool)) @ 66.69/9.09 X6) @ 66.69/9.09 (s @ X2 @ Y0))) @ 66.69/9.09 (s @ X4 @ Y1)))) & 66.69/9.09 (((s @ (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.09 X10) = (s @ 66.69/9.09 (tyop_2Eoption_2Eoption @ X4) @ 66.69/9.09 (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ Y1))))))))))))))) 66.69/9.09 = (j_mono_2Etyop_2Emin_2Ebool @ 66.69/9.09 (s @ tyop_2Emin_2Ebool @ 66.69/9.09 (c_2Eoption_2EOPTREL_2E3 @ 66.69/9.09 (s @ 66.69/9.09 (tyop_2Emin_2Efun @ X2 @ 66.69/9.09 (tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool)) @ 66.69/9.09 X6) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ X2) @ X8) @ 66.69/9.09 (s @ (tyop_2Eoption_2Eoption @ X4) @ X10)))))), 66.69/9.09 inference('simplify nested equalities', [status(thm)], 66.69/9.09 [zip_derived_cl111])). 66.69/9.09 thf(zip_derived_cl18206, plain, ($false), 66.69/9.09 inference('eprover', [status(thm)], 66.69/9.09 [zip_derived_cl159, zip_derived_cl42, zip_derived_cl84, 66.69/9.09 zip_derived_cl175, zip_derived_cl170, zip_derived_cl112])). 66.69/9.09 66.69/9.09 % SZS output end Refutation 66.69/9.09 66.69/9.09 66.69/9.09 % Terminating... 67.22/9.16 % Runner terminated. 67.22/9.16 % Zipperpin 1.5 exiting 67.22/9.16 EOF