0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.05 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.uWcOj7R7dh true 0.12/0.38 % Computer : n015.cluster.edu 0.12/0.38 % Model : x86_64 x86_64 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.38 % Memory : 8046.5625MB 0.12/0.38 % OS : Linux 6.8.0-71-generic 0.12/0.38 % CPULimit : 1440 0.12/0.38 % WCLimit : 180 0.12/0.38 % DateTime : Mon Jul 27 13:39:49 UTC 2026 0.12/0.38 % CPUTime : 0.12/0.38 % Running portfolio for 1440 s 0.12/0.38 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.12/0.39 % Number of cores: 8 0.12/0.39 % Python version: Python 3.12.3 0.12/0.39 % Running in HO mode 0.43/0.68 % Total configuration time : 828 0.43/0.68 % Estimated wc time : 1656 0.43/0.68 % Estimated cpu time (8 cpus) : 207.0 0.47/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.49/0.80 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.49/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.49/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.49/0.80 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.49/0.82 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.49/0.82 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.49/0.88 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 4.05/1.19 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 89.61/13.74 % Solved by lams/40_c_ic.sh. 89.61/13.74 % done 374 iterations in 12.811s 89.61/13.74 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 89.61/13.74 % SZS output start Refutation 89.61/13.74 thf(du_type, type, du: $tType). 89.61/13.74 thf(d_type, type, d: $tType). 89.61/13.74 thf(u_type, type, u: $tType). 89.61/13.74 thf(c_2Eoption_2EIS__NONE_2E1_type, type, c_2Eoption_2EIS__NONE_2E1: du > u). 89.61/13.74 thf(tyop_2Emin_2Efun_type, type, tyop_2Emin_2Efun: d > d > d). 89.61/13.74 thf(j_mono_2Etyop_2Emin_2Ebool_type, type, j_mono_2Etyop_2Emin_2Ebool: 89.61/13.74 du > $o). 89.61/13.74 thf(mono_2Ec_2Ebool_2EF_type, type, mono_2Ec_2Ebool_2EF: $o). 89.61/13.74 thf(sk__4_type, type, sk__4: u). 89.61/13.74 thf(c_2Eoption_2EOPTREL_2E3_type, type, c_2Eoption_2EOPTREL_2E3: du > du > du > u). 89.61/13.74 thf(sk__5_type, type, sk__5: u). 89.61/13.74 thf(combin_i_2E0_type, type, combin_i_2E0: u). 89.61/13.74 thf(c_2Eoption_2Eoption__CASE_2E3_type, type, c_2Eoption_2Eoption__CASE_2E3: 89.61/13.74 du > du > du > u). 89.61/13.74 thf(c_2Eoption_2ESOME_2E0_type, type, c_2Eoption_2ESOME_2E0: u). 89.61/13.74 thf(sk__6_type, type, sk__6: u). 89.61/13.74 thf(s_type, type, s: d > u > du). 89.61/13.74 thf(app_2E2_type, type, app_2E2: du > du > u). 89.61/13.74 thf(zip_tseitin_0_type, type, zip_tseitin_0: u > u > d > d > $o). 89.61/13.74 thf(c_2Eoption_2EOPTION__MAP_2E2_type, type, c_2Eoption_2EOPTION__MAP_2E2: 89.61/13.74 du > du > u). 89.61/13.74 thf(c_2Eoption_2EOPTION__JOIN_2E1_type, type, c_2Eoption_2EOPTION__JOIN_2E1: 89.61/13.74 du > u). 89.61/13.74 thf(sk__1_type, type, sk__1: u > u > u > d > d > u). 89.61/13.74 thf(tyop_2Eoption_2Eoption_type, type, tyop_2Eoption_2Eoption: d > d). 89.61/13.74 thf(sk__3_type, type, sk__3: d). 89.61/13.74 thf(tyop_2Emin_2Ebool_type, type, tyop_2Emin_2Ebool: d). 89.61/13.74 thf(mono_2Ec_2Ebool_2ET_type, type, mono_2Ec_2Ebool_2ET: $o). 89.61/13.74 thf(c_2Eoption_2ENONE_2E0_type, type, c_2Eoption_2ENONE_2E0: u). 89.61/13.74 thf(sk__2_type, type, sk__2: u > u > u > d > d > u). 89.61/13.74 thf(c_2Eoption_2ETHE_2E1_type, type, c_2Eoption_2ETHE_2E1: du > u). 89.61/13.74 thf(c_2Eoption_2ESOME_2E1_type, type, c_2Eoption_2ESOME_2E1: du > u). 89.61/13.74 thf(c_2Eoption_2EIS__SOME_2E1_type, type, c_2Eoption_2EIS__SOME_2E1: du > u). 89.61/13.74 thf(zip_tseitin_1_type, type, zip_tseitin_1: u > u > u > u > u > d > d > $o). 89.61/13.74 thf(thm_2Eoption_2EOPTREL__def, axiom, 89.61/13.74 (![A_27a:d,A_27b:d,V0R_2E0:u,V1x_2E0:u,V2y_2E0:u]: 89.61/13.74 ( ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ 89.61/13.74 A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ 89.61/13.74 V0R_2E0 ) @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 ) @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 ) ) ) ) <=> 89.61/13.74 ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 ) = 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) & 89.61/13.74 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 ) = 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) | 89.61/13.74 ( ?[V3x0_2E0:u,V4y0_2E0:u]: 89.61/13.74 ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 ) = 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3x0_2E0 ) ) ) ) & 89.61/13.74 ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( app_2E2 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ 89.61/13.74 ( app_2E2 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ 89.61/13.74 A_27a @ 89.61/13.74 ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ 89.61/13.74 V0R_2E0 ) @ 89.61/13.74 ( s @ A_27a @ V3x0_2E0 ) ) ) @ 89.61/13.74 ( s @ A_27b @ V4y0_2E0 ) ) ) ) & 89.61/13.74 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 ) = 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27b ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V4y0_2E0 ) ) ) ) ) ) ) ))). 89.61/13.74 thf(zf_stmt_0, type, zip_tseitin_1 : u > u > u > u > u > d > d > $o). 89.61/13.74 thf(zf_stmt_1, axiom, 89.61/13.74 (![V4y0_2E0:u,V3x0_2E0:u,V2y_2E0:u,V1x_2E0:u,V0R_2E0:u,A_27b:d,A_27a:d]: 89.61/13.74 ( ( zip_tseitin_1 @ 89.61/13.74 V4y0_2E0 @ V3x0_2E0 @ V2y_2E0 @ V1x_2E0 @ V0R_2E0 @ A_27b @ A_27a ) <=> 89.61/13.74 ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 ) = 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27b ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V4y0_2E0 ) ) ) ) & 89.61/13.74 ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( app_2E2 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ 89.61/13.74 ( app_2E2 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ 89.61/13.74 A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ 89.61/13.74 V0R_2E0 ) @ 89.61/13.74 ( s @ A_27a @ V3x0_2E0 ) ) ) @ 89.61/13.74 ( s @ A_27b @ V4y0_2E0 ) ) ) ) & 89.61/13.74 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 ) = 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3x0_2E0 ) ) ) ) ) ))). 89.61/13.74 thf(zf_stmt_2, type, zip_tseitin_0 : u > u > d > d > $o). 89.61/13.74 thf(zf_stmt_3, axiom, 89.61/13.74 (![V2y_2E0:u,V1x_2E0:u,A_27b:d,A_27a:d]: 89.61/13.74 ( ( zip_tseitin_0 @ V2y_2E0 @ V1x_2E0 @ A_27b @ A_27a ) <=> 89.61/13.74 ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 ) = 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) & 89.61/13.74 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 ) = 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) ))). 89.61/13.74 thf(zf_stmt_4, axiom, 89.61/13.74 (![A_27a:d,A_27b:d,V0R_2E0:u,V1x_2E0:u,V2y_2E0:u]: 89.61/13.74 ( ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ 89.61/13.74 A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ 89.61/13.74 V0R_2E0 ) @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 ) @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 ) ) ) ) <=> 89.61/13.74 ( ( ?[V3x0_2E0:u,V4y0_2E0:u]: 89.61/13.74 ( zip_tseitin_1 @ 89.61/13.74 V4y0_2E0 @ V3x0_2E0 @ V2y_2E0 @ V1x_2E0 @ V0R_2E0 @ A_27b @ A_27a ) ) | 89.61/13.74 ( zip_tseitin_0 @ V2y_2E0 @ V1x_2E0 @ A_27b @ A_27a ) ) ))). 89.61/13.74 thf(zip_derived_cl30, plain, 89.61/13.74 (![X0 : d, X1 : d, X2 : u, X3 : u, X4 : u, X5 : u, X6 : u]: 89.61/13.74 ( (j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 (s @ tyop_2Emin_2Ebool @ 89.61/13.74 (c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 (s @ 89.61/13.74 (tyop_2Emin_2Efun @ X0 @ 89.61/13.74 (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ 89.61/13.74 X2) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ X1) @ X4)))) 89.61/13.74 | ~ (zip_tseitin_1 @ X5 @ X6 @ X4 @ X3 @ X2 @ X1 @ X0))), 89.61/13.74 inference('cnf', [status(esa)], [zf_stmt_4])). 89.61/13.74 thf(thm_2Equotient__option_2EOPTION__REL__def, conjecture, 89.61/13.74 (![A_27a:d,V0y_2E0:u,V1x_2E0:u,V2R_2E0:u]: 89.61/13.74 ( ( ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ 89.61/13.74 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 89.61/13.74 V2R_2E0 ) @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) <=> 89.61/13.74 ( mono_2Ec_2Ebool_2EF ) ) & 89.61/13.74 ( ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ 89.61/13.74 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 89.61/13.74 V2R_2E0 ) @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) ) <=> 89.61/13.74 ( mono_2Ec_2Ebool_2EF ) ) & 89.61/13.74 ( ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ 89.61/13.74 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 89.61/13.74 V2R_2E0 ) @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) ) <=> 89.61/13.74 ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( app_2E2 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ 89.61/13.74 ( app_2E2 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ 89.61/13.74 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 89.61/13.74 V2R_2E0 ) @ 89.61/13.74 ( s @ A_27a @ V1x_2E0 ) ) ) @ 89.61/13.74 ( s @ A_27a @ V0y_2E0 ) ) ) ) ) & 89.61/13.74 ( ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ 89.61/13.74 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 89.61/13.74 V2R_2E0 ) @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) <=> 89.61/13.74 ( mono_2Ec_2Ebool_2ET ) ) ))). 89.61/13.74 thf(zf_stmt_5, negated_conjecture, 89.61/13.74 (~( ![A_27a:d,V0y_2E0:u,V1x_2E0:u,V2R_2E0:u]: 89.61/13.74 ( ( ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ 89.61/13.74 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 89.61/13.74 V2R_2E0 ) @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) <=> 89.61/13.74 ( mono_2Ec_2Ebool_2EF ) ) & 89.61/13.74 ( ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ 89.61/13.74 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 89.61/13.74 V2R_2E0 ) @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) ) <=> 89.61/13.74 ( mono_2Ec_2Ebool_2EF ) ) & 89.61/13.74 ( ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ 89.61/13.74 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 89.61/13.74 V2R_2E0 ) @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) ) <=> 89.61/13.74 ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( app_2E2 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ 89.61/13.74 ( app_2E2 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ 89.61/13.74 A_27a @ 89.61/13.74 ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 89.61/13.74 V2R_2E0 ) @ 89.61/13.74 ( s @ A_27a @ V1x_2E0 ) ) ) @ 89.61/13.74 ( s @ A_27a @ V0y_2E0 ) ) ) ) ) & 89.61/13.74 ( ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ 89.61/13.74 A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 89.61/13.74 V2R_2E0 ) @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) <=> 89.61/13.74 ( mono_2Ec_2Ebool_2ET ) ) ) )), 89.61/13.74 inference('cnf.neg', [status(esa)], 89.61/13.74 [thm_2Equotient__option_2EOPTION__REL__def])). 89.61/13.74 thf(zip_derived_cl99, plain, 89.61/13.74 (( (j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 (s @ tyop_2Emin_2Ebool @ 89.61/13.74 (c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 (s @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ tyop_2Emin_2Ebool)) @ 89.61/13.74 sk__6) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ sk__3) @ 89.61/13.74 (c_2Eoption_2ESOME_2E1 @ (s @ sk__3 @ sk__5))) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ sk__3) @ c_2Eoption_2ENONE_2E0)))) 89.61/13.74 | (mono_2Ec_2Ebool_2EF) 89.61/13.74 | (j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 (s @ tyop_2Emin_2Ebool @ 89.61/13.74 (c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 (s @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ tyop_2Emin_2Ebool)) @ 89.61/13.74 sk__6) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ sk__3) @ c_2Eoption_2ENONE_2E0) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ sk__3) @ 89.61/13.74 (c_2Eoption_2ESOME_2E1 @ (s @ sk__3 @ sk__4)))))) 89.61/13.74 | (mono_2Ec_2Ebool_2EF) 89.61/13.74 | ~ (j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 (s @ tyop_2Emin_2Ebool @ 89.61/13.74 (c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 (s @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ tyop_2Emin_2Ebool)) @ 89.61/13.74 sk__6) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ sk__3) @ 89.61/13.74 (c_2Eoption_2ESOME_2E1 @ (s @ sk__3 @ sk__5))) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ sk__3) @ 89.61/13.74 (c_2Eoption_2ESOME_2E1 @ (s @ sk__3 @ sk__4)))))) 89.61/13.74 | ~ (j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 (s @ tyop_2Emin_2Ebool @ 89.61/13.74 (app_2E2 @ 89.61/13.74 (s @ (tyop_2Emin_2Efun @ sk__3 @ tyop_2Emin_2Ebool) @ 89.61/13.74 (app_2E2 @ 89.61/13.74 (s @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ tyop_2Emin_2Ebool)) @ 89.61/13.74 sk__6) @ 89.61/13.74 (s @ sk__3 @ sk__5))) @ 89.61/13.74 (s @ sk__3 @ sk__4)))) 89.61/13.74 | ~ (mono_2Ec_2Ebool_2ET) 89.61/13.74 | ~ (j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 (s @ tyop_2Emin_2Ebool @ 89.61/13.74 (c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 (s @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ tyop_2Emin_2Ebool)) @ 89.61/13.74 sk__6) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ sk__3) @ c_2Eoption_2ENONE_2E0) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ sk__3) @ c_2Eoption_2ENONE_2E0)))))), 89.61/13.74 inference('cnf', [status(esa)], [zf_stmt_5])). 89.61/13.74 thf(zip_derived_cl26, plain, 89.61/13.74 (![X0 : d, X1 : d, X2 : u, X3 : u, X4 : u, X5 : u, X6 : u]: 89.61/13.74 ( (j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 (s @ tyop_2Emin_2Ebool @ 89.61/13.74 (app_2E2 @ 89.61/13.74 (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ 89.61/13.74 (app_2E2 @ 89.61/13.74 (s @ 89.61/13.74 (tyop_2Emin_2Efun @ X1 @ 89.61/13.74 (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ 89.61/13.74 X2) @ 89.61/13.74 (s @ X1 @ X3))) @ 89.61/13.74 (s @ X0 @ X4)))) 89.61/13.74 | ~ (zip_tseitin_1 @ X4 @ X3 @ X5 @ X6 @ X2 @ X0 @ X1))), 89.61/13.74 inference('cnf', [status(esa)], [zf_stmt_1])). 89.61/13.74 thf(zip_derived_cl23, plain, 89.61/13.74 (![X0 : d, X1 : u, X2 : u, X3 : d]: 89.61/13.74 (((s @ (tyop_2Eoption_2Eoption @ X0) @ X1) 89.61/13.74 = (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)) 89.61/13.74 | ~ (zip_tseitin_0 @ X1 @ X2 @ X0 @ X3))), 89.61/13.74 inference('cnf', [status(esa)], [zf_stmt_3])). 89.61/13.74 thf(reserved_2Eho_2Ei__thm, axiom, 89.61/13.74 (![A_27a:d,V0x_2E0:u]: 89.61/13.74 ( ( s @ 89.61/13.74 A_27a @ 89.61/13.74 ( app_2E2 @ 89.61/13.74 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ 89.61/13.74 ( s @ A_27a @ V0x_2E0 ) ) ) = 89.61/13.74 ( s @ A_27a @ V0x_2E0 ) ))). 89.61/13.74 thf(zip_derived_cl90, plain, 89.61/13.74 (![X0 : d, X1 : u]: 89.61/13.74 ((s @ X0 @ 89.61/13.74 (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X0) @ combin_i_2E0) @ 89.61/13.74 (s @ X0 @ X1))) 89.61/13.74 = (s @ X0 @ X1))), 89.61/13.74 inference('cnf', [status(esa)], [reserved_2Eho_2Ei__thm])). 89.61/13.74 thf(zip_derived_cl22, plain, 89.61/13.74 (![X0 : d, X1 : u, X2 : u, X3 : d]: 89.61/13.74 (((s @ (tyop_2Eoption_2Eoption @ X0) @ X1) 89.61/13.74 = (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)) 89.61/13.74 | ~ (zip_tseitin_0 @ X2 @ X1 @ X3 @ X0))), 89.61/13.74 inference('cnf', [status(esa)], [zf_stmt_3])). 89.61/13.74 thf(thm_2Eoption_2Eoption__CLAUSES, axiom, 89.61/13.74 (![A_27a:d,A_27b:d,V0f_2E0:u,V1e_2E0:u,V2e_2E0:u]: 89.61/13.74 ( ( ![V3x_2E0:u,V4y_2E0:u]: 89.61/13.74 ( ( ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3x_2E0 ) ) ) = 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V4y_2E0 ) ) ) ) <=> 89.61/13.74 ( ( s @ A_27a @ V3x_2E0 ) = ( s @ A_27a @ V4y_2E0 ) ) ) ) & 89.61/13.74 ( ![V6x_2E0:u]: 89.61/13.74 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) != 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V6x_2E0 ) ) ) ) ) & 89.61/13.74 ( ![V7x_2E0:u]: 89.61/13.74 ( ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V7x_2E0 ) ) ) != 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) & 89.61/13.74 ( ![V8x_2E0:u]: 89.61/13.74 ( ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EIS__SOME_2E1 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V8x_2E0 ) ) ) ) ) ) <=> 89.61/13.74 ( mono_2Ec_2Ebool_2ET ) ) ) & 89.61/13.74 ( ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EIS__SOME_2E1 @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) <=> 89.61/13.74 ( mono_2Ec_2Ebool_2EF ) ) & 89.61/13.74 ( ![V9x_2E0:u]: 89.61/13.74 ( ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EIS__NONE_2E1 @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V9x_2E0 ) ) ) ) <=> 89.61/13.74 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V9x_2E0 ) = 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) & 89.61/13.74 ( ![V10x_2E0:u]: 89.61/13.74 ( ( ~( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EIS__SOME_2E1 @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V10x_2E0 ) ) ) ) ) <=> 89.61/13.74 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V10x_2E0 ) = 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) & 89.61/13.74 ( ![V14x_2E0:u]: 89.61/13.74 ( ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EIS__NONE_2E1 @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V14x_2E0 ) ) ) ) => 89.61/13.74 ( ( s @ 89.61/13.74 A_27b @ 89.61/13.74 ( c_2Eoption_2Eoption__CASE_2E3 @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V14x_2E0 ) @ 89.61/13.74 ( s @ A_27b @ V2e_2E0 ) @ 89.61/13.74 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) = 89.61/13.74 ( s @ A_27b @ V2e_2E0 ) ) ) ) & 89.61/13.74 ( ![V16x_2E0:u]: 89.61/13.74 ( ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EIS__SOME_2E1 @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V16x_2E0 ) ) ) ) => 89.61/13.74 ( ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2Eoption__CASE_2E3 @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V16x_2E0 ) @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1e_2E0 ) @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ 89.61/13.74 A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ 89.61/13.74 c_2Eoption_2ESOME_2E0 ) ) ) = 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V16x_2E0 ) ) ) ) & 89.61/13.74 ( ![V22f_2E0:u,V23x_2E0:u]: 89.61/13.74 ( ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27b ) @ 89.61/13.74 ( c_2Eoption_2EOPTION__MAP_2E2 @ 89.61/13.74 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V22f_2E0 ) @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V23x_2E0 ) ) ) ) ) = 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27b ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ 89.61/13.74 ( s @ 89.61/13.74 A_27b @ 89.61/13.74 ( app_2E2 @ 89.61/13.74 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V22f_2E0 ) @ 89.61/13.74 ( s @ A_27a @ V23x_2E0 ) ) ) ) ) ) ) & 89.61/13.74 ( ![V24f_2E0:u]: 89.61/13.74 ( ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27b ) @ 89.61/13.74 ( c_2Eoption_2EOPTION__MAP_2E2 @ 89.61/13.74 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V24f_2E0 ) @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) = 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) & 89.61/13.74 ( ![V25x_2E0:u]: 89.61/13.74 ( ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2EOPTION__JOIN_2E1 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V25x_2E0 ) ) ) ) ) = 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V25x_2E0 ) ) ) & 89.61/13.74 ( ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2EOPTION__JOIN_2E1 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ 89.61/13.74 c_2Eoption_2ENONE_2E0 ) ) ) = 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) & 89.61/13.74 ( ![V19x_2E0:u,V20v_2E0:u,V21f_2E0:u]: 89.61/13.74 ( ( s @ 89.61/13.74 A_27b @ 89.61/13.74 ( c_2Eoption_2Eoption__CASE_2E3 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V19x_2E0 ) ) ) @ 89.61/13.74 ( s @ A_27b @ V20v_2E0 ) @ 89.61/13.74 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V21f_2E0 ) ) ) = 89.61/13.74 ( s @ 89.61/13.74 A_27b @ 89.61/13.74 ( app_2E2 @ 89.61/13.74 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V21f_2E0 ) @ 89.61/13.74 ( s @ A_27a @ V19x_2E0 ) ) ) ) ) & 89.61/13.74 ( ![V17v_2E0:u,V18f_2E0:u]: 89.61/13.74 ( ( s @ 89.61/13.74 A_27b @ 89.61/13.74 ( c_2Eoption_2Eoption__CASE_2E3 @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ 89.61/13.74 ( s @ A_27b @ V17v_2E0 ) @ 89.61/13.74 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V18f_2E0 ) ) ) = 89.61/13.74 ( s @ A_27b @ V17v_2E0 ) ) ) & 89.61/13.74 ( ![V15x_2E0:u]: 89.61/13.74 ( ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EIS__SOME_2E1 @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V15x_2E0 ) ) ) ) => 89.61/13.74 ( ( s @ 89.61/13.74 A_27b @ 89.61/13.74 ( c_2Eoption_2Eoption__CASE_2E3 @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V15x_2E0 ) @ 89.61/13.74 ( s @ A_27b @ V2e_2E0 ) @ 89.61/13.74 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) = 89.61/13.74 ( s @ 89.61/13.74 A_27b @ 89.61/13.74 ( app_2E2 @ 89.61/13.74 ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ 89.61/13.74 ( s @ 89.61/13.74 A_27a @ 89.61/13.74 ( c_2Eoption_2ETHE_2E1 @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V15x_2E0 ) ) ) ) ) ) ) ) & 89.61/13.74 ( ![V13x_2E0:u]: 89.61/13.74 ( ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2Eoption__CASE_2E3 @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V13x_2E0 ) @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V13x_2E0 ) @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ 89.61/13.74 A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ 89.61/13.74 c_2Eoption_2ESOME_2E0 ) ) ) = 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V13x_2E0 ) ) ) & 89.61/13.74 ( ![V12x_2E0:u]: 89.61/13.74 ( ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2Eoption__CASE_2E3 @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V12x_2E0 ) @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Emin_2Efun @ 89.61/13.74 A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ 89.61/13.74 c_2Eoption_2ESOME_2E0 ) ) ) = 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V12x_2E0 ) ) ) & 89.61/13.74 ( ![V11x_2E0:u]: 89.61/13.74 ( ( j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 ( s @ 89.61/13.74 tyop_2Emin_2Ebool @ 89.61/13.74 ( c_2Eoption_2EIS__SOME_2E1 @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V11x_2E0 ) ) ) ) => 89.61/13.74 ( ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ 89.61/13.74 ( s @ 89.61/13.74 A_27a @ 89.61/13.74 ( c_2Eoption_2ETHE_2E1 @ 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V11x_2E0 ) ) ) ) ) = 89.61/13.74 ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V11x_2E0 ) ) ) ) & 89.61/13.74 ( ![V5x_2E0:u]: 89.61/13.74 ( ( s @ 89.61/13.74 A_27a @ 89.61/13.74 ( c_2Eoption_2ETHE_2E1 @ 89.61/13.74 ( s @ 89.61/13.74 ( tyop_2Eoption_2Eoption @ A_27a ) @ 89.61/13.74 ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V5x_2E0 ) ) ) ) ) = 89.61/13.74 ( s @ A_27a @ V5x_2E0 ) ) ) ))). 89.61/13.74 thf(zip_derived_cl45, plain, 89.61/13.74 (![X0 : d, X1 : d, X2 : u, X3 : u]: 89.61/13.74 ((s @ (tyop_2Eoption_2Eoption @ X0) @ 89.61/13.74 (c_2Eoption_2EOPTION__MAP_2E2 @ 89.61/13.74 (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X2) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ X1) @ 89.61/13.74 (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X3))))) 89.61/13.74 = (s @ (tyop_2Eoption_2Eoption @ X0) @ 89.61/13.74 (c_2Eoption_2ESOME_2E1 @ 89.61/13.74 (s @ X0 @ 89.61/13.74 (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X2) @ 89.61/13.74 (s @ X1 @ X3))))))), 89.61/13.74 inference('cnf', [status(esa)], [thm_2Eoption_2Eoption__CLAUSES])). 89.61/13.74 thf(zip_derived_cl56, plain, 89.61/13.74 (![X0 : d, X1 : u]: 89.61/13.74 ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) 89.61/13.74 != (s @ (tyop_2Eoption_2Eoption @ X0) @ 89.61/13.74 (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X1))))), 89.61/13.74 inference('cnf', [status(esa)], [thm_2Eoption_2Eoption__CLAUSES])). 89.61/13.74 thf(zip_derived_cl36, plain, 89.61/13.74 (![X0 : d, X1 : u]: 89.61/13.74 ((s @ X0 @ 89.61/13.74 (c_2Eoption_2ETHE_2E1 @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ X0) @ 89.61/13.74 (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X1))))) 89.61/13.74 = (s @ X0 @ X1))), 89.61/13.74 inference('cnf', [status(esa)], [thm_2Eoption_2Eoption__CLAUSES])). 89.61/13.74 thf(zip_derived_cl28, plain, 89.61/13.74 (![X0 : u, X1 : u, X2 : u, X3 : u, X4 : u, X5 : d, X6 : d]: 89.61/13.74 ( (zip_tseitin_1 @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6) 89.61/13.74 | ((s @ (tyop_2Eoption_2Eoption @ X6) @ X3) 89.61/13.74 != (s @ (tyop_2Eoption_2Eoption @ X6) @ 89.61/13.74 (c_2Eoption_2ESOME_2E1 @ (s @ X6 @ X1)))) 89.61/13.74 | ~ (j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 (s @ tyop_2Emin_2Ebool @ 89.61/13.74 (app_2E2 @ 89.61/13.74 (s @ (tyop_2Emin_2Efun @ X5 @ tyop_2Emin_2Ebool) @ 89.61/13.74 (app_2E2 @ 89.61/13.74 (s @ 89.61/13.74 (tyop_2Emin_2Efun @ X6 @ 89.61/13.74 (tyop_2Emin_2Efun @ X5 @ tyop_2Emin_2Ebool)) @ 89.61/13.74 X4) @ 89.61/13.74 (s @ X6 @ X1))) @ 89.61/13.74 (s @ X5 @ X0)))) 89.61/13.74 | ((s @ (tyop_2Eoption_2Eoption @ X5) @ X2) 89.61/13.74 != (s @ (tyop_2Eoption_2Eoption @ X5) @ 89.61/13.74 (c_2Eoption_2ESOME_2E1 @ (s @ X5 @ X0)))))), 89.61/13.74 inference('cnf', [status(esa)], [zf_stmt_1])). 89.61/13.74 thf(zip_derived_cl25, plain, 89.61/13.74 (![X0 : d, X1 : u, X2 : u, X3 : u, X4 : u, X5 : u, X6 : d]: 89.61/13.74 (((s @ (tyop_2Eoption_2Eoption @ X0) @ X2) 89.61/13.74 = (s @ (tyop_2Eoption_2Eoption @ X0) @ 89.61/13.74 (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X1)))) 89.61/13.74 | ~ (zip_tseitin_1 @ X1 @ X3 @ X2 @ X4 @ X5 @ X0 @ X6))), 89.61/13.74 inference('cnf', [status(esa)], [zf_stmt_1])). 89.61/13.74 thf(thm_2Ebool_2EREFL__CLAUSE, axiom, 89.61/13.74 (![A_27a:d,V0x_2E0:u]: 89.61/13.74 ( ( ( s @ A_27a @ V0x_2E0 ) = ( s @ A_27a @ V0x_2E0 ) ) <=> 89.61/13.74 ( mono_2Ec_2Ebool_2ET ) ))). 89.61/13.74 thf(zip_derived_cl88, plain, ( (mono_2Ec_2Ebool_2ET)), 89.61/13.74 inference('cnf', [status(esa)], [thm_2Ebool_2EREFL__CLAUSE])). 89.61/13.74 thf(zip_derived_cl44, plain, 89.61/13.74 (![X0 : d, X1 : d, X2 : u]: 89.61/13.74 ((s @ (tyop_2Eoption_2Eoption @ X0) @ 89.61/13.74 (c_2Eoption_2EOPTION__MAP_2E2 @ 89.61/13.74 (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X2) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0))) 89.61/13.74 = (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))), 89.61/13.74 inference('cnf', [status(esa)], [thm_2Eoption_2Eoption__CLAUSES])). 89.61/13.74 thf(zip_derived_cl29, plain, 89.61/13.74 (![X0 : u, X1 : u, X2 : d, X3 : d, X4 : u]: 89.61/13.74 ( (zip_tseitin_0 @ X0 @ X1 @ X2 @ X3) 89.61/13.74 | (zip_tseitin_1 @ (sk__2 @ X0 @ X1 @ X4 @ X2 @ X3) @ 89.61/13.74 (sk__1 @ X0 @ X1 @ X4 @ X2 @ X3) @ X0 @ X1 @ X4 @ X2 @ X3) 89.61/13.74 | ~ (j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 (s @ tyop_2Emin_2Ebool @ 89.61/13.74 (c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 (s @ 89.61/13.74 (tyop_2Emin_2Efun @ X3 @ 89.61/13.74 (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ 89.61/13.74 X4) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ X3) @ X1) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ X2) @ X0)))))), 89.61/13.74 inference('cnf', [status(esa)], [zf_stmt_4])). 89.61/13.74 thf(zip_derived_cl27, plain, 89.61/13.74 (![X0 : d, X1 : u, X2 : u, X3 : u, X4 : u, X5 : u, X6 : d]: 89.61/13.74 (((s @ (tyop_2Eoption_2Eoption @ X0) @ X2) 89.61/13.74 = (s @ (tyop_2Eoption_2Eoption @ X0) @ 89.61/13.74 (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X1)))) 89.61/13.74 | ~ (zip_tseitin_1 @ X3 @ X1 @ X4 @ X2 @ X5 @ X6 @ X0))), 89.61/13.74 inference('cnf', [status(esa)], [zf_stmt_1])). 89.61/13.74 thf(zip_derived_cl24, plain, 89.61/13.74 (![X0 : u, X1 : u, X2 : d, X3 : d]: 89.61/13.74 ( (zip_tseitin_0 @ X0 @ X1 @ X2 @ X3) 89.61/13.74 | ((s @ (tyop_2Eoption_2Eoption @ X2) @ X0) 89.61/13.74 != (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) 89.61/13.74 | ((s @ (tyop_2Eoption_2Eoption @ X3) @ X1) 89.61/13.74 != (s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0)))), 89.61/13.74 inference('cnf', [status(esa)], [zf_stmt_3])). 89.61/13.74 thf(thm_2Ebool_2EEQ__CLAUSES, axiom, 89.61/13.74 (![V0t:$o]: 89.61/13.74 ( ( ( ( mono_2Ec_2Ebool_2EF ) <=> ( V0t ) ) <=> ( ~( V0t ) ) ) & 89.61/13.74 ( ( ( V0t ) <=> ( mono_2Ec_2Ebool_2EF ) ) <=> ( ~( V0t ) ) ) & 89.61/13.74 ( ( ( V0t ) <=> ( mono_2Ec_2Ebool_2ET ) ) <=> ( V0t ) ) & 89.61/13.74 ( ( ( mono_2Ec_2Ebool_2ET ) <=> ( V0t ) ) <=> ( V0t ) ) ))). 89.61/13.74 thf(zip_derived_cl85, plain, 89.61/13.74 (![X0 : $o]: (~ (X0) | ~ (X0) | ~ (mono_2Ec_2Ebool_2EF))), 89.61/13.74 inference('cnf', [status(esa)], [thm_2Ebool_2EEQ__CLAUSES])). 89.61/13.74 thf(zip_derived_cl101, plain, 89.61/13.74 (( (j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 (s @ tyop_2Emin_2Ebool @ 89.61/13.74 (c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 (s @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ tyop_2Emin_2Ebool)) @ 89.61/13.74 sk__6) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ sk__3) @ 89.61/13.74 (c_2Eoption_2ESOME_2E1 @ (s @ sk__3 @ sk__5))) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ sk__3) @ c_2Eoption_2ENONE_2E0)))) 89.61/13.74 | (mono_2Ec_2Ebool_2EF) 89.61/13.74 | (j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 (s @ tyop_2Emin_2Ebool @ 89.61/13.74 (c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 (s @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ tyop_2Emin_2Ebool)) @ 89.61/13.74 sk__6) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ sk__3) @ c_2Eoption_2ENONE_2E0) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ sk__3) @ 89.61/13.74 (c_2Eoption_2ESOME_2E1 @ (s @ sk__3 @ sk__4)))))) 89.61/13.74 | (mono_2Ec_2Ebool_2EF) 89.61/13.74 | (j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 (s @ tyop_2Emin_2Ebool @ 89.61/13.74 (c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 (s @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ tyop_2Emin_2Ebool)) @ 89.61/13.74 sk__6) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ sk__3) @ 89.61/13.74 (c_2Eoption_2ESOME_2E1 @ (s @ sk__3 @ sk__5))) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ sk__3) @ 89.61/13.74 (c_2Eoption_2ESOME_2E1 @ (s @ sk__3 @ sk__4)))))) 89.61/13.74 | (j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 (s @ tyop_2Emin_2Ebool @ 89.61/13.74 (app_2E2 @ 89.61/13.74 (s @ (tyop_2Emin_2Efun @ sk__3 @ tyop_2Emin_2Ebool) @ 89.61/13.74 (app_2E2 @ 89.61/13.74 (s @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ tyop_2Emin_2Ebool)) @ 89.61/13.74 sk__6) @ 89.61/13.74 (s @ sk__3 @ sk__5))) @ 89.61/13.74 (s @ sk__3 @ sk__4)))) 89.61/13.74 | ~ (mono_2Ec_2Ebool_2ET) 89.61/13.74 | ~ (j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 (s @ tyop_2Emin_2Ebool @ 89.61/13.74 (c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 (s @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ 89.61/13.74 (tyop_2Emin_2Efun @ sk__3 @ tyop_2Emin_2Ebool)) @ 89.61/13.74 sk__6) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ sk__3) @ c_2Eoption_2ENONE_2E0) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ sk__3) @ c_2Eoption_2ENONE_2E0)))))), 89.61/13.74 inference('cnf', [status(esa)], [zf_stmt_5])). 89.61/13.74 thf(zip_derived_cl42, plain, 89.61/13.74 (![X0 : d]: 89.61/13.74 ((s @ (tyop_2Eoption_2Eoption @ X0) @ 89.61/13.74 (c_2Eoption_2EOPTION__JOIN_2E1 @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X0)) @ 89.61/13.74 c_2Eoption_2ENONE_2E0))) 89.61/13.74 = (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))), 89.61/13.74 inference('cnf', [status(esa)], [thm_2Eoption_2Eoption__CLAUSES])). 89.61/13.74 thf(zip_derived_cl31, plain, 89.61/13.74 (![X0 : d, X1 : d, X2 : u, X3 : u, X4 : u]: 89.61/13.74 ( (j_mono_2Etyop_2Emin_2Ebool @ 89.61/13.74 (s @ tyop_2Emin_2Ebool @ 89.61/13.74 (c_2Eoption_2EOPTREL_2E3 @ 89.61/13.74 (s @ 89.61/13.74 (tyop_2Emin_2Efun @ X0 @ 89.61/13.74 (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ 89.61/13.74 X2) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ 89.61/13.74 (s @ (tyop_2Eoption_2Eoption @ X1) @ X4)))) 89.61/13.74 | ~ (zip_tseitin_0 @ X4 @ X3 @ X1 @ X0))), 89.61/13.74 inference('cnf', [status(esa)], [zf_stmt_4])). 89.61/13.74 thf(zip_derived_cl5788, plain, ($false), 89.61/13.74 inference('eprover', [status(thm)], 89.61/13.74 [zip_derived_cl30, zip_derived_cl99, zip_derived_cl26, 89.61/13.74 zip_derived_cl23, zip_derived_cl90, zip_derived_cl22, 89.61/13.74 zip_derived_cl45, zip_derived_cl56, zip_derived_cl36, 89.61/13.74 zip_derived_cl28, zip_derived_cl25, zip_derived_cl88, 89.61/13.74 zip_derived_cl44, zip_derived_cl29, zip_derived_cl27, 89.61/13.74 zip_derived_cl24, zip_derived_cl85, zip_derived_cl101, 89.61/13.74 zip_derived_cl42, zip_derived_cl31])). 89.61/13.74 89.61/13.74 % SZS output end Refutation 89.61/13.74 89.61/13.74 89.61/13.74 % Terminating... 14.79/13.81 % Runner terminated. 14.79/13.85 % Zipperpin 1.5 exiting 14.79/13.86 EOF