0.13/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.15/0.15 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.2p0OAvFln5 0.15/0.36 % Computer : n011.cluster.edu 0.15/0.36 % Model : x86_64 x86_64 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.36 % Memory : 8042.1875MB 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.36 % CPULimit : 1200 0.15/0.36 % DateTime : Tue Jul 13 14:07:55 EDT 2021 0.15/0.37 % CPUTime : 0.15/0.37 % Running portfolio for 120 s 0.15/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.15/0.37 % Number of cores: 8 0.15/0.37 % Python version: Python 3.6.8 0.15/0.37 % Running in HO mode 0.54/0.64 % Estimated wc time : 1286 0.54/0.64 % Estimated cpu time (7 cpus) : 183.71428571428572 0.56/0.71 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.56/0.74 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.56/0.75 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.56/0.75 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.56/0.76 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.56/0.77 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 0.56/0.77 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 12.77/2.50 % Solved by lams/old_b3.avatar.sh. 12.77/2.50 % done 208 iterations in 1.698s 12.77/2.50 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 12.77/2.50 % SZS output start Refutation 12.77/2.50 tff(thm_2Ewords_2En2w__sub, conjecture, 12.77/2.50 (![A_27a:d,V0a:mono_2Etyop_2Enum_2Enum,V1b:mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (mono_2Ec_2Earithmetic_2E_3C_3D(V1b,V0a) => 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a), 12.77/2.50 c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D( 12.77/2.50 V0a,V1b))))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a), 12.77/2.50 c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, 12.77/2.50 A_27a), 12.77/2.50 c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 V0a)))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, 12.77/2.50 A_27a), 12.77/2.50 c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 V1b)))))))))). 12.77/2.50 tff(zf_stmt_0, negated_conjecture, 12.77/2.50 (~ 12.77/2.50 (![A_27a:d,V0a:mono_2Etyop_2Enum_2Enum,V1b:mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (mono_2Ec_2Earithmetic_2E_3C_3D(V1b,V0a) => 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a), 12.77/2.50 c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D( 12.77/2.50 V0a,V1b))))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a), 12.77/2.50 c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, 12.77/2.50 A_27a), 12.77/2.50 c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 V0a)))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, 12.77/2.50 A_27a), 12.77/2.50 c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 V1b))))))))))). 12.77/2.50 tff('0', plain, 12.77/2.50 ~ (!!((^[Y0 : d]: 12.77/2.50 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (!!((^[Y2 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (mono_2Ec_2Earithmetic_2E_3C_3D(Y2, Y1) => 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D(Y1, Y2))))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2Eword__sub_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum(Y1)))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum(Y2))))))))))))))))), 12.77/2.50 inference('cnf', [status(esa)], [zf_stmt_0])). 12.77/2.50 tff('1', plain, 12.77/2.50 ~ (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (mono_2Ec_2Earithmetic_2E_3C_3D(Y1, Y0) => 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D(Y0, Y1))))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2Eword__sub_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum(Y0)))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum(Y1)))))))))))))), 12.77/2.50 inference('lazy_cnf_exists', [status(thm)], ['0'])). 12.77/2.50 tff('2', plain, 12.77/2.50 ~ (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (mono_2Ec_2Earithmetic_2E_3C_3D(Y0, '#sk2') => 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D('#sk2', Y0))))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2Eword__sub_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk2')))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum(Y0))))))))))), 12.77/2.50 inference('lazy_cnf_exists', [status(thm)], ['1'])). 12.77/2.50 tff('3', plain, 12.77/2.50 ~ (mono_2Ec_2Earithmetic_2E_3C_3D('#sk3', '#sk2') => 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D('#sk2', '#sk3'))))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2Eword__sub_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk2')))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk3')))))))), 12.77/2.50 inference('lazy_cnf_exists', [status(thm)], ['2'])). 12.77/2.50 tff('4', plain, 12.77/2.50 ~ (mono_2Ec_2Earithmetic_2E_3C_3D('#sk3', '#sk2') => 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D('#sk2', '#sk3'))))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2Eword__sub_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk2')))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk3')))))))), 12.77/2.50 inference('lazy_cnf_exists', [status(thm)], ['2'])). 12.77/2.50 tff('5', plain, mono_2Ec_2Earithmetic_2E_3C_3D('#sk3', '#sk2'), 12.77/2.50 inference('lazy_cnf_imply', [status(thm)], ['4'])). 12.77/2.50 tff('6', plain, 12.77/2.50 ~ ($true => 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D('#sk2', '#sk3'))))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2Eword__sub_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk2')))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk3')))))))), 12.77/2.50 inference('demod', [status(thm)], ['3', '5'])). 12.77/2.50 tff('7', plain, 12.77/2.50 ~ (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D('#sk2', '#sk3'))))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2Eword__sub_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk2')))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk3'))))))), 12.77/2.50 inference('simplify boolean subterms', [status(thm)], ['6'])). 12.77/2.50 tff('8', plain, 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D('#sk2', '#sk3'))))) 12.77/2.50 != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2Eword__sub_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk2')))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk3')))))), 12.77/2.50 inference('simplify nested equalities', [status(thm)], ['7'])). 12.77/2.50 tff(thm_2Ewords_2Eword__sub__def, axiom, 12.77/2.50 (![A_27a:d,V0v_2E0:u,V1w_2E0:u]: 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a), 12.77/2.50 c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a), 12.77/2.50 V0v_2E0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a), 12.77/2.50 V1w_2E0))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a), 12.77/2.50 c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a), 12.77/2.50 V0v_2E0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, 12.77/2.50 A_27a), 12.77/2.50 V1w_2E0)))))))). 12.77/2.50 tff('9', plain, 12.77/2.50 (!!((^[Y0 : d]: 12.77/2.50 (!!((^[Y1 : u]: 12.77/2.50 (!!((^[Y2 : u]: 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2Eword__sub_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 Y1), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 Y2))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 Y1), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 Y2))))))))))))))), 12.77/2.50 inference('cnf', [status(esa)], [thm_2Ewords_2Eword__sub__def])). 12.77/2.50 tff('10', plain, 12.77/2.50 ![X1 : d]: 12.77/2.50 (!!((^[Y0 : u]: 12.77/2.50 (!!((^[Y1 : u]: 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__sub_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), Y0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), Y1))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), Y0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), Y1)))))))))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['9'])). 12.77/2.50 tff('11', plain, 12.77/2.50 ![X1 : d, X2 : u]: 12.77/2.50 (!!((^[Y0 : u]: 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__sub_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), X2), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), Y0))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), X2), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), Y0))))))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['10'])). 12.77/2.50 tff('12', plain, 12.77/2.50 ![X1 : d, X2 : u, X3 : u]: 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__sub_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), X2), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), X3))) 12.77/2.50 = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), X2), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), X3))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['11'])). 12.77/2.50 tff('13', plain, 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D('#sk2', '#sk3'))))) 12.77/2.50 != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk2')))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk3')))))))), 12.77/2.50 inference('demod', [status(thm)], ['8', '12'])). 12.77/2.50 tff(arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27b, axiom, 12.77/2.50 (![A_27b:d,X0_2E0:u,X1_2E0:u]: 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b), 12.77/2.50 c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b), 12.77/2.50 X0_2E0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b), 12.77/2.50 X1_2E0))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b), 12.77/2.50 app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)), 12.77/2.50 app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, 12.77/2.50 A_27b), 12.77/2.50 tyop_2Emin_2Efun(tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, 12.77/2.50 A_27b), 12.77/2.50 tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, 12.77/2.50 A_27b))), 12.77/2.50 c_2Ewords_2Eword__add_2E0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X0_2E0))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X1_2E0)))))). 12.77/2.50 tff('14', plain, 12.77/2.50 (!!((^[Y0 : d]: 12.77/2.50 (!!((^[Y1 : u]: 12.77/2.50 (!!((^[Y2 : u]: 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 Y1), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 Y2))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0)), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, 12.77/2.50 Y0), 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, Y0), 12.77/2.50 tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, Y0))), 12.77/2.50 c_2Ewords_2Eword__add_2E0), 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 Y1))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 Y2))))))))))))), 12.77/2.50 inference('cnf', [status(esa)], 12.77/2.50 [arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27b])). 12.77/2.50 tff('15', plain, 12.77/2.50 ![X1 : d]: 12.77/2.50 (!!((^[Y0 : u]: 12.77/2.50 (!!((^[Y1 : u]: 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), Y0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), Y1))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1)), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1))), 12.77/2.50 c_2Ewords_2Eword__add_2E0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), Y0))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), Y1)))))))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['14'])). 12.77/2.50 tff('16', plain, 12.77/2.50 ![X1 : d, X2 : u]: 12.77/2.50 (!!((^[Y0 : u]: 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), X2), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), Y0))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1)), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1))), 12.77/2.50 c_2Ewords_2Eword__add_2E0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), X2))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), Y0))))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['15'])). 12.77/2.50 tff('17', plain, 12.77/2.50 ![X1 : d, X2 : u, X3 : u]: 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), X2), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), X3))) 12.77/2.50 = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1)), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1))), 12.77/2.50 c_2Ewords_2Eword__add_2E0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), X2))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), X3))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['16'])). 12.77/2.50 tff('18', plain, 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D('#sk2', '#sk3'))))) 12.77/2.50 != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1')), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'))), 12.77/2.50 c_2Ewords_2Eword__add_2E0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk2')))))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk3')))))))), 12.77/2.50 inference('demod', [status(thm)], ['13', '17'])). 12.77/2.50 tff('19', plain, mono_2Ec_2Earithmetic_2E_3C_3D('#sk3', '#sk2'), 12.77/2.50 inference('lazy_cnf_imply', [status(thm)], ['4'])). 12.77/2.50 tff(thm_2Ewords_2EWORD__LITERAL__ADD, axiom, 12.77/2.50 (![A_27a:d,A_27b:d]: 12.77/2.50 ((![V2m:mono_2Etyop_2Enum_2Enum,V3n:mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b), 12.77/2.50 c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, 12.77/2.50 A_27b), 12.77/2.50 c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 V2m)))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, 12.77/2.50 A_27b), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1(s( 12.77/2.50 tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, 12.77/2.50 A_27b), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s( 12.77/2.50 tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 V3n)))))))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b), 12.77/2.50 c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2E_3C_3D( 12.77/2.50 V3n,V2m))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b), 12.77/2.50 c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D( 12.77/2.50 V2m,V3n))))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, 12.77/2.50 A_27b), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D( 12.77/2.50 V3n,V2m))))))))))) & 12.77/2.50 (![V0m:mono_2Etyop_2Enum_2Enum,V1n:mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a), 12.77/2.50 c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, 12.77/2.50 A_27a), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1(s( 12.77/2.50 tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, 12.77/2.50 A_27a), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s( 12.77/2.50 tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 V0m)))))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, 12.77/2.50 A_27a), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1(s( 12.77/2.50 tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, 12.77/2.50 A_27a), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s( 12.77/2.50 tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 V1n)))))))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, 12.77/2.50 A_27a), 12.77/2.50 c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2B( 12.77/2.50 V0m,V1n)))))))))))). 12.77/2.50 tff('20', plain, 12.77/2.50 (!!((^[Y0 : d]: 12.77/2.50 (!!((^[Y1 : d]: 12.77/2.50 ((!!((^[Y2 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (!!((^[Y3 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (s( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y1), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, Y1), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum(Y2)))), 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, Y1), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, Y1), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 Y3)))))))) = 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y1), 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 mono_2Ec_2Earithmetic_2E_3C_3D( 12.77/2.50 Y3, Y2))), 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, Y1), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D( 12.77/2.50 Y2, Y3))))), 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, Y1), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, Y1), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D( 12.77/2.50 Y3, Y2)))))))))))))))) & 12.77/2.50 (!!((^[Y2 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (!!((^[Y3 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (s( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 Y2)))))), 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 Y3)))))))) = 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart( 12.77/2.50 tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2B( 12.77/2.50 Y2, Y3))))))))))))))))))))), 12.77/2.50 inference('cnf', [status(esa)], [thm_2Ewords_2EWORD__LITERAL__ADD])). 12.77/2.50 tff('21', plain, 12.77/2.50 ![X1 : d]: 12.77/2.50 (!!((^[Y0 : d]: 12.77/2.50 ((!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (!!((^[Y2 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum(Y1)))), 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, 12.77/2.50 Y0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum(Y2)))))))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 mono_2Ec_2Earithmetic_2E_3C_3D(Y2, Y1))), 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D(Y1, Y2))))), 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, Y0), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, 12.77/2.50 Y0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D( 12.77/2.50 Y2, Y1)))))))))))))))) & 12.77/2.50 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (!!((^[Y2 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, 12.77/2.50 X1), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum(Y1)))))), 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, 12.77/2.50 X1), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum(Y2)))))))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2B(Y1, Y2)))))))))))))))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['20'])). 12.77/2.50 tff('22', plain, 12.77/2.50 ![X1 : d, X2 : d]: 12.77/2.50 ((!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum(Y0)))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum(Y1)))))))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 mono_2Ec_2Earithmetic_2E_3C_3D(Y1, Y0))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D(Y0, Y1))))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D(Y1, Y0)))))))))))))))) & 12.77/2.50 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum(Y0)))))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum(Y1)))))))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2B(Y0, Y1))))))))))))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['21'])). 12.77/2.50 tff('23', plain, 12.77/2.50 ![X2 : d]: 12.77/2.50 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum(Y0)))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum(Y1)))))))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 mono_2Ec_2Earithmetic_2E_3C_3D(Y1, Y0))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D(Y0, Y1))))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D(Y1, Y0)))))))))))))))), 12.77/2.50 inference('lazy_cnf_and', [status(thm)], ['22'])). 12.77/2.50 tff('24', plain, 12.77/2.50 ![X2 : d, X3 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum(X3)))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum(Y0)))))))) = 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 mono_2Ec_2Earithmetic_2E_3C_3D(Y0, X3))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D(X3, Y0))))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D(Y0, X3))))))))))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['23'])). 12.77/2.50 tff('25', plain, 12.77/2.50 ![X2 : d, X3 : mono_2Etyop_2Enum_2Enum, X4 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum(X3)))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum(X4)))))))) 12.77/2.50 = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 mono_2Ec_2Earithmetic_2E_3C_3D(X4, X3))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D(X3, X4))))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D(X4, X3))))))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['24'])). 12.77/2.50 tff('26', plain, 12.77/2.50 ![X1 : d, X2 : u, X3 : u]: 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 c_2Ewords_2Eword__add_2E2( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), X2), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), X3))) 12.77/2.50 = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1)), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1))), 12.77/2.50 c_2Ewords_2Eword__add_2E0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), X2))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X1), X3))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['16'])). 12.77/2.50 tff('27', plain, 12.77/2.50 ![X2 : d, X3 : mono_2Etyop_2Enum_2Enum, X4 : mono_2Etyop_2Enum_2Enum]: 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2)), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2))), 12.77/2.50 c_2Ewords_2Eword__add_2E0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum(X3)))))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum(X4)))))))) 12.77/2.50 = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 mono_2Ec_2Earithmetic_2E_3C_3D(X4, X3))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D(X3, X4))))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X2), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D(X4, X3))))))))), 12.77/2.50 inference('demod', [status(thm)], ['25', '26'])). 12.77/2.50 tff('28', plain, 12.77/2.50 ![X0 : d]: 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0)), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0))), 12.77/2.50 c_2Ewords_2Eword__add_2E0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk2')))))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk3')))))))) 12.77/2.50 = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool($true)), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D('#sk2', '#sk3'))))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D('#sk3', '#sk2'))))))))), 12.77/2.50 inference('sup+', [status(thm)], ['19', '27'])). 12.77/2.50 tff(thm_2Ebool_2ECOND__CONG, axiom, 12.77/2.50 (![A_27a:d,V0P:$o,V1Q:$o,V2x_2E0:u,V3x_27_2E0:u,V4y_2E0:u,V5y_27_2E0:u]: 12.77/2.50 (((V0P <=> V1Q) & (V1Q => (s(A_27a,V2x_2E0) = s(A_27a,V3x_27_2E0))) & 12.77/2.50 ((~V1Q) => (s(A_27a,V4y_2E0) = s(A_27a,V5y_27_2E0)))) => 12.77/2.50 (s(A_27a, 12.77/2.50 c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(V0P)), 12.77/2.50 s(A_27a,V2x_2E0),s(A_27a,V4y_2E0))) = 12.77/2.50 s(A_27a, 12.77/2.50 c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(V1Q)), 12.77/2.50 s(A_27a,V3x_27_2E0),s(A_27a,V5y_27_2E0))))))). 12.77/2.50 tff('29', plain, 12.77/2.50 (!!((^[Y0 : d]: 12.77/2.50 (!!((^[Y1 : $o]: 12.77/2.50 (!!((^[Y2 : $o]: 12.77/2.50 (!!((^[Y3 : u]: 12.77/2.50 (!!((^[Y4 : u]: 12.77/2.50 (!!((^[Y5 : u]: 12.77/2.50 (!!((^[Y6 : u]: 12.77/2.50 (((Y1 <=> Y2)& 12.77/2.50 (Y2 => 12.77/2.50 (s(Y0, Y3) = 12.77/2.50 s(Y0, Y4)))& 12.77/2.50 ((~(Y2)) => 12.77/2.50 (s(Y0, Y5) = 12.77/2.50 s(Y0, Y6)))) => 12.77/2.50 (s(Y0, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 Y1)), 12.77/2.50 s(Y0, Y3), 12.77/2.50 s(Y0, Y5))) = 12.77/2.50 s(Y0, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 Y2)), 12.77/2.50 s(Y0, Y4), 12.77/2.50 s(Y0, Y6)))))))))))))))))))))))))), 12.77/2.50 inference('cnf', [status(esa)], [thm_2Ebool_2ECOND__CONG])). 12.77/2.50 tff('30', plain, 12.77/2.50 ![X1 : d]: 12.77/2.50 (!!((^[Y0 : $o]: 12.77/2.50 (!!((^[Y1 : $o]: 12.77/2.50 (!!((^[Y2 : u]: 12.77/2.50 (!!((^[Y3 : u]: 12.77/2.50 (!!((^[Y4 : u]: 12.77/2.50 (!!((^[Y5 : u]: 12.77/2.50 (((Y0 <=> Y1)& 12.77/2.50 (Y1 => 12.77/2.50 (s(X1, Y2) = s(X1, Y3)))& 12.77/2.50 ((~(Y1)) => 12.77/2.50 (s(X1, Y4) = s(X1, Y5)))) => 12.77/2.50 (s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 Y0)), s(X1, Y2), 12.77/2.50 s(X1, Y4))) = 12.77/2.50 s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 Y1)), s(X1, Y3), 12.77/2.50 s(X1, Y5))))))))))))))))))))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['29'])). 12.77/2.50 tff('31', plain, 12.77/2.50 ![X1 : d, X2 : $o]: 12.77/2.50 (!!((^[Y0 : $o]: 12.77/2.50 (!!((^[Y1 : u]: 12.77/2.50 (!!((^[Y2 : u]: 12.77/2.50 (!!((^[Y3 : u]: 12.77/2.50 (!!((^[Y4 : u]: 12.77/2.50 (((X2 <=> Y0)& 12.77/2.50 (Y0 => (s(X1, Y1) = s(X1, Y2)))& 12.77/2.50 ((~(Y0)) => 12.77/2.50 (s(X1, Y3) = s(X1, Y4)))) => 12.77/2.50 (s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 X2)), s(X1, Y1), 12.77/2.50 s(X1, Y3))) = 12.77/2.50 s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 Y0)), s(X1, Y2), 12.77/2.50 s(X1, Y4)))))))))))))))))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['30'])). 12.77/2.50 tff('32', plain, 12.77/2.50 ![X1 : d, X2 : $o, X3 : $o]: 12.77/2.50 (!!((^[Y0 : u]: 12.77/2.50 (!!((^[Y1 : u]: 12.77/2.50 (!!((^[Y2 : u]: 12.77/2.50 (!!((^[Y3 : u]: 12.77/2.50 (((X2 <=> X3)& 12.77/2.50 (X3 => (s(X1, Y0) = s(X1, Y1)))& 12.77/2.50 ((~(X3)) => (s(X1, Y2) = s(X1, Y3)))) => 12.77/2.50 (s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(X2)), 12.77/2.50 s(X1, Y0), s(X1, Y2))) = 12.77/2.50 s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(X3)), 12.77/2.50 s(X1, Y1), s(X1, Y3))))))))))))))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['31'])). 12.77/2.50 tff('33', plain, 12.77/2.50 ![X1 : d, X2 : $o, X3 : $o, X4 : u]: 12.77/2.50 (!!((^[Y0 : u]: 12.77/2.50 (!!((^[Y1 : u]: 12.77/2.50 (!!((^[Y2 : u]: 12.77/2.50 (((X2 <=> X3)&(X3 => (s(X1, X4) = s(X1, Y0)))& 12.77/2.50 ((~(X3)) => (s(X1, Y1) = s(X1, Y2)))) => 12.77/2.50 (s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(X2)), 12.77/2.50 s(X1, X4), s(X1, Y1))) = 12.77/2.50 s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(X3)), 12.77/2.50 s(X1, Y0), s(X1, Y2)))))))))))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['32'])). 12.77/2.50 tff('34', plain, 12.77/2.50 ![X1 : d, X2 : $o, X3 : $o, X4 : u, X5 : u]: 12.77/2.50 (!!((^[Y0 : u]: 12.77/2.50 (!!((^[Y1 : u]: 12.77/2.50 (((X2 <=> X3)&(X3 => (s(X1, X4) = s(X1, X5)))& 12.77/2.50 ((~(X3)) => (s(X1, Y0) = s(X1, Y1)))) => 12.77/2.50 (s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(X2)), s(X1, X4), 12.77/2.50 s(X1, Y0))) = 12.77/2.50 s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(X3)), s(X1, X5), 12.77/2.50 s(X1, Y1))))))))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['33'])). 12.77/2.50 tff('35', plain, 12.77/2.50 ![X1 : d, X2 : $o, X3 : $o, X4 : u, X5 : u, X6 : u]: 12.77/2.50 (!!((^[Y0 : u]: 12.77/2.50 (((X2 <=> X3)&(X3 => (s(X1, X4) = s(X1, X5)))& 12.77/2.50 ((~(X3)) => (s(X1, X6) = s(X1, Y0)))) => 12.77/2.50 (s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X2)), 12.77/2.50 s(X1, X4), s(X1, X6))) = 12.77/2.50 s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X3)), 12.77/2.50 s(X1, X5), s(X1, Y0)))))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['34'])). 12.77/2.50 tff('36', plain, 12.77/2.50 ![X1 : d, X2 : $o, X3 : $o, X4 : u, X5 : u, X6 : u, X7 : u]: 12.77/2.50 (((X2 <=> X3)&(X3 => (s(X1, X4) = s(X1, X5)))& 12.77/2.50 ((~(X3)) => (s(X1, X6) = s(X1, X7)))) => 12.77/2.50 (s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X2)), 12.77/2.50 s(X1, X4), s(X1, X6))) = 12.77/2.50 s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X3)), 12.77/2.50 s(X1, X5), s(X1, X7))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['35'])). 12.77/2.50 tff('37', plain, 12.77/2.50 ![X1 : d, X2 : $o, X3 : $o, X4 : u, X5 : u, X6 : u, X7 : u]: 12.77/2.50 (~ ((X2 <=> X3)&(X3 => (s(X1, X4) = s(X1, X5)))& 12.77/2.50 ((~(X3)) => (s(X1, X6) = s(X1, X7)))) 12.77/2.50 | s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X2)), 12.77/2.50 s(X1, X4), s(X1, X6))) 12.77/2.50 = s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X3)), 12.77/2.50 s(X1, X5), s(X1, X7)))), 12.77/2.50 inference('lazy_cnf_imply', [status(thm)], ['36'])). 12.77/2.50 tff('38', plain, 12.77/2.50 ![X1 : d, X2 : $o, X3 : $o, X4 : u, X5 : u, X6 : u, X7 : u]: 12.77/2.50 (~ (X2 <=> X3) 12.77/2.50 | ~ (X3 => (s(X1, X4) = s(X1, X5))) 12.77/2.50 | ~ ((~(X3)) => (s(X1, X6) = s(X1, X7))) 12.77/2.50 | s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X2)), 12.77/2.50 s(X1, X4), s(X1, X6))) 12.77/2.50 = s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X3)), 12.77/2.50 s(X1, X5), s(X1, X7)))), 12.77/2.50 inference('lazy_cnf_and', [status(thm)], ['37'])). 12.77/2.50 tff('39', plain, 12.77/2.50 ![X1 : d, X2 : $o, X3 : $o, X4 : u, X5 : u, X6 : u, X7 : u]: 12.77/2.50 (X2 != X3 12.77/2.50 | ~ (X3 => (s(X1, X4) = s(X1, X5))) 12.77/2.50 | ~ ((~(X3)) => (s(X1, X6) = s(X1, X7))) 12.77/2.50 | s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X2)), 12.77/2.50 s(X1, X4), s(X1, X6))) 12.77/2.50 = s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X3)), 12.77/2.50 s(X1, X5), s(X1, X7)))), 12.77/2.50 inference('simplify nested equalities', [status(thm)], ['38'])). 12.77/2.50 tff('40', plain, 12.77/2.50 ![X1 : d, X3 : $o, X4 : u, X5 : u, X6 : u, X7 : u]: 12.77/2.50 (s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X3)), s(X1, X4), 12.77/2.50 s(X1, X6))) 12.77/2.50 = s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X3)), 12.77/2.50 s(X1, X5), s(X1, X7))) 12.77/2.50 | ~ ((~(X3)) => (s(X1, X6) = s(X1, X7))) 12.77/2.50 | ~ (X3 => (s(X1, X4) = s(X1, X5)))), 12.77/2.50 inference('simplify', [status(thm)], ['39'])). 12.77/2.50 tff('41', plain, 12.77/2.50 ![X1 : d, X3 : $o, X4 : u, X5 : u, X6 : u, X7 : u]: 12.77/2.50 (~ X3 12.77/2.50 | ~ (X3 => (s(X1, X4) = s(X1, X5))) 12.77/2.50 | s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X3)), 12.77/2.50 s(X1, X4), s(X1, X6))) 12.77/2.50 = s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X3)), 12.77/2.50 s(X1, X5), s(X1, X7)))), 12.77/2.50 inference('lazy_cnf_imply', [status(thm)], ['40'])). 12.77/2.50 tff('42', plain, 12.77/2.50 ![X0 : u, X1 : d, X2 : u, X3 : u, X4 : u]: 12.77/2.50 (~ ($true => (s(X1, X2) = s(X1, X0))) 12.77/2.50 | s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool($true)), 12.77/2.50 s(X1, X2), s(X1, X3))) 12.77/2.50 = s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool($true)), 12.77/2.50 s(X1, X0), s(X1, X4)))), 12.77/2.50 inference('elim_bool_vars', [status(thm)], ['41'])). 12.77/2.50 tff('43', plain, 12.77/2.50 ![X0 : u, X1 : d, X2 : u, X3 : u, X4 : u]: 12.77/2.50 (~ (s(X1, X2) = s(X1, X0)) 12.77/2.50 | s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool($true)), 12.77/2.50 s(X1, X2), s(X1, X3))) 12.77/2.50 = s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool($true)), 12.77/2.50 s(X1, X0), s(X1, X4)))), 12.77/2.50 inference('simplify boolean subterms', [status(thm)], ['42'])). 12.77/2.50 tff('44', plain, 12.77/2.50 ![X0 : u, X1 : d, X2 : u, X3 : u, X4 : u]: 12.77/2.50 (s(X1, X2) != s(X1, X0) 12.77/2.50 | s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool($true)), 12.77/2.50 s(X1, X2), s(X1, X3))) 12.77/2.50 = s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool($true)), 12.77/2.50 s(X1, X0), s(X1, X4)))), 12.77/2.50 inference('simplify nested equalities', [status(thm)], ['43'])). 12.77/2.50 tff('45', plain, 12.77/2.50 ![X0 : u, X1 : d, X2 : u, X3 : u]: 12.77/2.50 s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool($true)), 12.77/2.50 s(X1, X2), s(X1, X0))) 12.77/2.50 = s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool($true)), 12.77/2.50 s(X1, X2), s(X1, X3))), 12.77/2.50 inference('eq_res', [status(thm)], ['44'])). 12.77/2.50 tff('46', plain, 12.77/2.50 ![X0 : d, X1 : u]: 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool($true)), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D('#sk2', '#sk3'))))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), X1))) 12.77/2.50 = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0)), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0))), 12.77/2.50 c_2Ewords_2Eword__add_2E0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk2')))))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk3')))))))), 12.77/2.50 inference('sup+', [status(thm)], ['28', '45'])). 12.77/2.50 tff(thm_2Ebool_2Ebool__case__thm, axiom, 12.77/2.50 (![A_27a:d]: 12.77/2.50 ((![V0t1_2E0:u,V1t2_2E0:u]: 12.77/2.50 (s(A_27a, 12.77/2.50 c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET)), 12.77/2.50 s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0))) = 12.77/2.50 s(A_27a,V0t1_2E0))) & 12.77/2.50 (![V2t1_2E0:u,V3t2_2E0:u]: 12.77/2.50 (s(A_27a, 12.77/2.50 c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF)), 12.77/2.50 s(A_27a,V2t1_2E0),s(A_27a,V3t2_2E0))) = 12.77/2.50 s(A_27a,V3t2_2E0)))))). 12.77/2.50 tff('47', plain, 12.77/2.50 (!!((^[Y0 : d]: 12.77/2.50 ((!!((^[Y1 : u]: 12.77/2.50 (!!((^[Y2 : u]: 12.77/2.50 (s(Y0, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 mono_2Ec_2Ebool_2ET)), s(Y0, Y1), 12.77/2.50 s(Y0, Y2))) = 12.77/2.50 s(Y0, Y1)))))))) & 12.77/2.50 (!!((^[Y1 : u]: 12.77/2.50 (!!((^[Y2 : u]: 12.77/2.50 (s(Y0, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 mono_2Ec_2Ebool_2EF)), s(Y0, Y1), 12.77/2.50 s(Y0, Y2))) = 12.77/2.50 s(Y0, Y2)))))))))))), 12.77/2.50 inference('cnf', [status(esa)], [thm_2Ebool_2Ebool__case__thm])). 12.77/2.50 tff('48', plain, 12.77/2.50 ![X1 : d]: 12.77/2.50 ((!!((^[Y0 : u]: 12.77/2.50 (!!((^[Y1 : u]: 12.77/2.50 (s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET)), 12.77/2.50 s(X1, Y0), s(X1, Y1))) = 12.77/2.50 s(X1, Y0)))))))) & 12.77/2.50 (!!((^[Y0 : u]: 12.77/2.50 (!!((^[Y1 : u]: 12.77/2.50 (s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF)), 12.77/2.50 s(X1, Y0), s(X1, Y1))) = 12.77/2.50 s(X1, Y1))))))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['47'])). 12.77/2.50 tff('49', plain, 12.77/2.50 ![X1 : d]: 12.77/2.50 (!!((^[Y0 : u]: 12.77/2.50 (!!((^[Y1 : u]: 12.77/2.50 (s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET)), 12.77/2.50 s(X1, Y0), s(X1, Y1))) = 12.77/2.50 s(X1, Y0)))))))), 12.77/2.50 inference('lazy_cnf_and', [status(thm)], ['48'])). 12.77/2.50 tff('50', plain, 12.77/2.50 ![X1 : d, X2 : u]: 12.77/2.50 (!!((^[Y0 : u]: 12.77/2.50 (s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET)), 12.77/2.50 s(X1, X2), s(X1, Y0))) = 12.77/2.50 s(X1, X2))))), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['49'])). 12.77/2.50 tff('51', plain, 12.77/2.50 ![X1 : d, X2 : u, X3 : u]: 12.77/2.50 s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET)), s(X1, X2), 12.77/2.50 s(X1, X3))) 12.77/2.50 = s(X1, X2), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['50'])). 12.77/2.50 tff('52', plain, 12.77/2.50 ![X1 : d, X2 : u, X3 : u]: 12.77/2.50 s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET)), s(X1, X2), 12.77/2.50 s(X1, X3))) 12.77/2.50 = s(X1, X2), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['50'])). 12.77/2.50 tff('53', plain, 12.77/2.50 ![X1 : d, X3 : $o, X4 : u, X5 : u, X6 : u, X7 : u]: 12.77/2.50 (s(X1, X6) != s(X1, X7) 12.77/2.50 | ~ (X3 => (s(X1, X4) = s(X1, X5))) 12.77/2.50 | s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X3)), 12.77/2.50 s(X1, X4), s(X1, X6))) 12.77/2.50 = s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X3)), 12.77/2.50 s(X1, X5), s(X1, X7)))), 12.77/2.50 inference('lazy_cnf_imply', [status(thm)], ['40'])). 12.77/2.50 tff('54', plain, 12.77/2.50 ![X1 : d, X3 : $o, X4 : u, X5 : u, X6 : u, X7 : u]: 12.77/2.50 ( X3 12.77/2.50 | s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X3)), 12.77/2.50 s(X1, X4), s(X1, X6))) 12.77/2.50 = s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X3)), 12.77/2.50 s(X1, X5), s(X1, X7))) 12.77/2.50 | s(X1, X6) != s(X1, X7)), 12.77/2.50 inference('lazy_cnf_imply', [status(thm)], ['53'])). 12.77/2.50 tff('55', plain, 12.77/2.50 ![X0 : u, X1 : d, X2 : u, X3 : $o, X4 : u]: 12.77/2.50 (s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X3)), s(X1, X2), 12.77/2.50 s(X1, X0))) 12.77/2.50 = s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X3)), 12.77/2.50 s(X1, X4), s(X1, X0))) 12.77/2.50 | X3), 12.77/2.50 inference('eq_res', [status(thm)], ['54'])). 12.77/2.50 tff('56', plain, 12.77/2.50 ![X0 : u, X1 : d, X2 : u, X3 : u]: 12.77/2.50 (s(X1, X0) 12.77/2.50 = s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET)), s(X1, X3), 12.77/2.50 s(X1, X2))) 12.77/2.50 | mono_2Ec_2Ebool_2ET), 12.77/2.50 inference('sup+', [status(thm)], ['52', '55'])). 12.77/2.50 tff('57', plain, 12.77/2.50 ![X1 : d, X2 : u, X3 : u]: 12.77/2.50 s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET)), s(X1, X2), 12.77/2.50 s(X1, X3))) 12.77/2.50 = s(X1, X2), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['50'])). 12.77/2.50 tff('58', plain, 12.77/2.50 ![X0 : u, X1 : d, X3 : u]: (s(X1, X0) = s(X1, X3) | mono_2Ec_2Ebool_2ET), 12.77/2.50 inference('demod', [status(thm)], ['56', '57'])). 12.77/2.50 tff(ji_2Emono_2Etyop_2Emin_2Ebool, axiom, 12.77/2.50 (![V0:$o]: 12.77/2.50 (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 12.77/2.50 i_mono_2Etyop_2Emin_2Ebool(V0))) <=> 12.77/2.50 V0))). 12.77/2.50 tff('59', plain, 12.77/2.50 (!!((^[Y0 : $o]: 12.77/2.50 (j_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(Y0))) <=> 12.77/2.50 Y0)))), 12.77/2.50 inference('cnf', [status(esa)], [ji_2Emono_2Etyop_2Emin_2Ebool])). 12.77/2.50 tff('60', plain, 12.77/2.50 ![X1 : $o]: 12.77/2.50 (j_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X1))) <=> 12.77/2.50 X1), 12.77/2.50 inference('lazy_cnf_forall', [status(thm)], ['59'])). 12.77/2.50 tff('61', plain, 12.77/2.50 ![X1 : $o]: 12.77/2.50 j_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X1))) 12.77/2.50 = X1, 12.77/2.50 inference('simplify nested equalities', [status(thm)], ['60'])). 12.77/2.50 tff('62', plain, 12.77/2.50 ![X1 : $o]: 12.77/2.50 ( j_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X1))) 12.77/2.50 | ~ X1), 12.77/2.50 inference('lazy_cnf_equiv', [status(thm)], ['61'])). 12.77/2.50 tff('63', plain, 12.77/2.50 ![X0 : u, X1 : $o]: 12.77/2.50 ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, X0)) 12.77/2.50 | mono_2Ec_2Ebool_2ET 12.77/2.50 | ~ X1), 12.77/2.50 inference('sup+', [status(thm)], ['58', '62'])). 12.77/2.50 tff('64', plain, 12.77/2.50 ![X0 : u]: 12.77/2.50 ( mono_2Ec_2Ebool_2ET 12.77/2.50 | j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, X0))), 12.77/2.50 inference('ho_elim_pred', [status(thm)], ['63'])). 12.77/2.50 tff('65', plain, 12.77/2.50 ![X1 : $o]: 12.77/2.50 j_mono_2Etyop_2Emin_2Ebool( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool(X1))) 12.77/2.50 = X1, 12.77/2.50 inference('simplify nested equalities', [status(thm)], ['60'])). 12.77/2.50 tff('66', plain, ![X0 : $o]: ( X0 | mono_2Ec_2Ebool_2ET), 12.77/2.50 inference('sup+', [status(thm)], ['64', '65'])). 12.77/2.50 tff('67', plain, mono_2Ec_2Ebool_2ET, 12.77/2.50 inference('condensation', [status(thm)], ['66'])). 12.77/2.50 tff('68', plain, 12.77/2.50 ![X1 : d, X2 : u, X3 : u]: 12.77/2.50 s(X1, 12.77/2.50 c_2Ebool_2ECOND_2E3( 12.77/2.50 s(tyop_2Emin_2Ebool, i_mono_2Etyop_2Emin_2Ebool($true)), 12.77/2.50 s(X1, X2), s(X1, X3))) 12.77/2.50 = s(X1, X2), 12.77/2.50 inference('demod', [status(thm)], ['51', '67'])). 12.77/2.50 tff('69', plain, 12.77/2.50 ![X0 : d]: 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, 12.77/2.50 i_mono_2Etyop_2Enum_2Enum( 12.77/2.50 mono_2Ec_2Earithmetic_2E_2D('#sk2', '#sk3'))))) 12.77/2.50 = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0)), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0))), 12.77/2.50 c_2Ewords_2Eword__add_2E0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk2')))))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X0), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk3')))))))), 12.77/2.50 inference('demod', [status(thm)], ['46', '68'])). 12.77/2.50 tff('70', plain, 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1')), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'))), 12.77/2.50 c_2Ewords_2Eword__add_2E0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk2')))))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk3')))))))) 12.77/2.50 != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1')), 12.77/2.50 app_2E2( 12.77/2.50 s( 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 tyop_2Emin_2Efun( 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'))), 12.77/2.50 c_2Ewords_2Eword__add_2E0), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk2')))))), 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2Eword__2comp_2E1( 12.77/2.50 s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, '#sk1'), 12.77/2.50 c_2Ewords_2En2w_2E1( 12.77/2.50 s(tyop_2Enum_2Enum, i_mono_2Etyop_2Enum_2Enum('#sk3')))))))), 12.77/2.50 inference('demod', [status(thm)], ['18', '69'])). 12.77/2.50 tff('71', plain, $false, inference('simplify', [status(thm)], ['70'])). 12.77/2.50 12.77/2.50 % SZS output end Refutation 12.77/2.50 12.77/2.50 12.77/2.50 % Terminating... 13.30/2.57 % Runner terminated. 13.30/2.58 % Zipperpin 1.5 exiting 13.30/2.59 EOF