0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.45 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.iJLAyqZ5Fu 0.48/0.66 % Computer : n013.cluster.edu 0.48/0.66 % Model : x86_64 x86_64 0.48/0.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.48/0.66 % Memory : 8042.1875MB 0.48/0.66 % OS : Linux 3.10.0-693.el7.x86_64 0.48/0.66 % CPULimit : 1200 0.48/0.66 % DateTime : Tue Jul 13 12:04:19 EDT 2021 0.48/0.67 % CPUTime : 0.48/0.67 % Running portfolio for 120 s 0.48/0.67 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.48/0.67 % Number of cores: 8 0.52/0.67 % Python version: Python 3.6.8 0.52/0.67 % Running in HO mode 0.52/0.93 % Estimated wc time : 1286 0.52/0.93 % Estimated cpu time (7 cpus) : 183.71428571428572 0.52/0.99 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.52/1.03 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.52/1.03 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.52/1.04 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.52/1.05 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.52/1.05 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 0.52/1.06 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 71.30/11.06 % /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s 105.99/16.06 % /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s 105.99/16.09 % /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s 147.45/22.14 % /export/starexec/sandbox2/solver/bin/lams/b.lsimp.sh running for 17s 147.45/22.25 % /export/starexec/sandbox2/solver/bin/lams/b.split.sh running for 31s 150.09/22.64 % Solved by lams/b.sh. 150.09/22.64 % Running : timeout 14 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.iJLAyqZ5Fu/e_inputd2bc6f --cpu-limit=12 --auto -s -p. 150.09/22.64 % done 251 iterations in 6.536s 150.09/22.64 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 150.09/22.64 % SZS output start Refutation 150.09/22.64 tff(thm_2Earithmetic_2EMOD__2, conjecture, 150.09/22.64 (![V0n:mono_2Etyop_2Enum_2Enum]: 150.09/22.64 (mono_2Ec_2Earithmetic_2EMOD(V0n, 150.09/22.64 mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT2( 150.09/22.64 mono_2Ec_2Earithmetic_2EZERO))) = 150.09/22.64 mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN( 150.09/22.64 V0n), 150.09/22.64 mono_2Ec_2Enum_2E0, 150.09/22.64 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.64 mono_2Ec_2Earithmetic_2EBIT1( 150.09/22.64 mono_2Ec_2Earithmetic_2EZERO)))))). 150.09/22.64 tff(zf_stmt_0, negated_conjecture, 150.09/22.64 (~ 150.09/22.64 (![V0n:mono_2Etyop_2Enum_2Enum]: 150.09/22.64 (mono_2Ec_2Earithmetic_2EMOD(V0n, 150.09/22.64 mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT2( 150.09/22.64 mono_2Ec_2Earithmetic_2EZERO))) = 150.09/22.64 mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN( 150.09/22.64 V0n), 150.09/22.64 mono_2Ec_2Enum_2E0, 150.09/22.64 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.64 mono_2Ec_2Earithmetic_2EBIT1( 150.09/22.64 mono_2Ec_2Earithmetic_2EZERO))))))). 150.09/22.64 tff('0', plain, 150.09/22.64 ~ (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.64 (mono_2Ec_2Earithmetic_2EMOD(Y0, 150.09/22.64 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.64 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Earithmetic_2EZERO))) = 150.09/22.64 mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum( 150.09/22.64 mono_2Ec_2Earithmetic_2EEVEN(Y0), mono_2Ec_2Enum_2E0, 150.09/22.64 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.64 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO))))))), 150.09/22.64 inference('cnf', [status(esa)], [zf_stmt_0])). 150.09/22.64 tff('1', plain, 150.09/22.64 mono_2Ec_2Earithmetic_2EMOD('#sk1', 150.09/22.64 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.64 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Earithmetic_2EZERO))) 150.09/22.64 != mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum( 150.09/22.64 mono_2Ec_2Earithmetic_2EEVEN('#sk1'), mono_2Ec_2Enum_2E0, 150.09/22.64 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.64 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO))), 150.09/22.64 inference('lazy_cnf_exists', [status(thm)], ['0'])). 150.09/22.64 tff(thm_2Earithmetic_2EALT__ZERO, axiom, 150.09/22.64 (mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0)). 150.09/22.64 tff('2', plain, mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0, 150.09/22.64 inference('cnf', [status(esa)], [thm_2Earithmetic_2EALT__ZERO])). 150.09/22.64 tff('3', plain, mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0, 150.09/22.64 inference('cnf', [status(esa)], [thm_2Earithmetic_2EALT__ZERO])). 150.09/22.64 tff(thm_2Earithmetic_2EONE, axiom, 150.09/22.64 (mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO)) = 150.09/22.64 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0))). 150.09/22.64 tff('4', plain, 150.09/22.64 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.64 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO)) 150.09/22.64 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0), 150.09/22.64 inference('cnf', [status(esa)], [thm_2Earithmetic_2EONE])). 150.09/22.64 tff('5', plain, mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0, 150.09/22.64 inference('cnf', [status(esa)], [thm_2Earithmetic_2EALT__ZERO])). 150.09/22.64 tff('6', plain, 150.09/22.64 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.64 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0)) 150.09/22.64 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0), 150.09/22.64 inference('demod', [status(thm)], ['4', '5'])). 150.09/22.64 tff('7', plain, 150.09/22.64 mono_2Ec_2Earithmetic_2EMOD('#sk1', 150.09/22.64 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.64 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Enum_2E0))) 150.09/22.64 != mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum( 150.09/22.64 mono_2Ec_2Earithmetic_2EEVEN('#sk1'), mono_2Ec_2Enum_2E0, 150.09/22.64 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0)), 150.09/22.64 inference('demod', [status(thm)], ['1', '2', '3', '6'])). 150.09/22.64 tff(thm_2Earithmetic_2ENUMERAL__DEF, axiom, 150.09/22.64 (![V0x:mono_2Etyop_2Enum_2Enum]: 150.09/22.64 (mono_2Ec_2Earithmetic_2ENUMERAL(V0x) = V0x))). 150.09/22.64 tff('8', plain, 150.09/22.64 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.64 (mono_2Ec_2Earithmetic_2ENUMERAL(Y0) = Y0)))), 150.09/22.64 inference('cnf', [status(esa)], [thm_2Earithmetic_2ENUMERAL__DEF])). 150.09/22.64 tff('9', plain, 150.09/22.64 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.64 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.64 tff('10', plain, 150.09/22.64 mono_2Ec_2Earithmetic_2EMOD('#sk1', 150.09/22.64 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Enum_2E0)) 150.09/22.64 != mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum( 150.09/22.64 mono_2Ec_2Earithmetic_2EEVEN('#sk1'), mono_2Ec_2Enum_2E0, 150.09/22.64 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0)), 150.09/22.64 inference('demod', [status(thm)], ['7', '9'])). 150.09/22.64 tff('11', plain, 150.09/22.64 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.64 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0)) 150.09/22.64 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0), 150.09/22.64 inference('demod', [status(thm)], ['4', '5'])). 150.09/22.64 tff('12', plain, 150.09/22.64 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.64 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.64 tff('13', plain, 150.09/22.64 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0) 150.09/22.64 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0), 150.09/22.64 inference('demod', [status(thm)], ['11', '12'])). 150.09/22.64 tff('14', plain, 150.09/22.64 mono_2Ec_2Earithmetic_2EMOD('#sk1', 150.09/22.64 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Enum_2E0)) 150.09/22.64 != mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum( 150.09/22.64 mono_2Ec_2Earithmetic_2EEVEN('#sk1'), mono_2Ec_2Enum_2E0, 150.09/22.64 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0)), 150.09/22.64 inference('demod', [status(thm)], ['10', '13'])). 150.09/22.64 tff('15', plain, 150.09/22.64 ( mono_2Ec_2Earithmetic_2EEVEN('#sk1') 150.09/22.64 | mono_2Ec_2Earithmetic_2EMOD('#sk1', 150.09/22.64 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Enum_2E0)) 150.09/22.64 != mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum($false, 150.09/22.64 mono_2Ec_2Enum_2E0, 150.09/22.64 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0))), 150.09/22.64 inference('bool_inf', [status(thm)], ['14'])). 150.09/22.64 tff(thm_2Earithmetic_2EEVEN__MULT, axiom, 150.09/22.64 (![V0m:mono_2Etyop_2Enum_2Enum,V1n:mono_2Etyop_2Enum_2Enum]: 150.09/22.64 ((mono_2Ec_2Earithmetic_2EEVEN(V0m) | mono_2Ec_2Earithmetic_2EEVEN(V1n)) <=> 150.09/22.64 mono_2Ec_2Earithmetic_2EEVEN(mono_2Ec_2Earithmetic_2E_2A(V0m,V1n))))). 150.09/22.64 tff('16', plain, 150.09/22.64 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.64 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.64 ((mono_2Ec_2Earithmetic_2EEVEN(Y0) | 150.09/22.64 mono_2Ec_2Earithmetic_2EEVEN(Y1)) <=> 150.09/22.64 mono_2Ec_2Earithmetic_2EEVEN( 150.09/22.64 mono_2Ec_2Earithmetic_2E_2A(Y0, Y1))))))))), 150.09/22.64 inference('cnf', [status(esa)], [thm_2Earithmetic_2EEVEN__MULT])). 150.09/22.64 tff('17', plain, 150.09/22.64 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.64 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.64 ((mono_2Ec_2Earithmetic_2EEVEN(X1) | 150.09/22.64 mono_2Ec_2Earithmetic_2EEVEN(Y0)) <=> 150.09/22.64 mono_2Ec_2Earithmetic_2EEVEN( 150.09/22.64 mono_2Ec_2Earithmetic_2E_2A(X1, Y0)))))), 150.09/22.64 inference('lazy_cnf_forall', [status(thm)], ['16'])). 150.09/22.64 tff('18', plain, 150.09/22.64 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.64 ((mono_2Ec_2Earithmetic_2EEVEN(X1) | mono_2Ec_2Earithmetic_2EEVEN(X2)) <=> 150.09/22.64 mono_2Ec_2Earithmetic_2EEVEN(mono_2Ec_2Earithmetic_2E_2A(X1, X2))), 150.09/22.64 inference('lazy_cnf_forall', [status(thm)], ['17'])). 150.09/22.64 tff('19', plain, 150.09/22.64 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.64 (mono_2Ec_2Earithmetic_2EEVEN(X1) | mono_2Ec_2Earithmetic_2EEVEN(X2)) 150.09/22.64 = mono_2Ec_2Earithmetic_2EEVEN(mono_2Ec_2Earithmetic_2E_2A(X1, X2)), 150.09/22.64 inference('simplify nested equalities', [status(thm)], ['18'])). 150.09/22.64 tff(thm_2Earithmetic_2EMOD__SUC, axiom, 150.09/22.64 (![V0y:mono_2Etyop_2Enum_2Enum,V1x:mono_2Etyop_2Enum_2Enum]: 150.09/22.64 ((mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Enum_2E0,V0y) & 150.09/22.64 (mono_2Ec_2Enum_2ESUC(V1x) != 150.09/22.64 mono_2Ec_2Earithmetic_2E_2A(mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2EDIV( 150.09/22.64 V1x,V0y)), 150.09/22.64 V0y))) => 150.09/22.64 (mono_2Ec_2Earithmetic_2EMOD(mono_2Ec_2Enum_2ESUC(V1x),V0y) = 150.09/22.64 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2EMOD(V1x,V0y)))))). 150.09/22.64 tff('20', plain, 150.09/22.64 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.64 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.64 ((mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Enum_2E0, Y0) & 150.09/22.64 (mono_2Ec_2Enum_2ESUC(Y1) != 150.09/22.64 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.64 mono_2Ec_2Enum_2ESUC( 150.09/22.64 mono_2Ec_2Earithmetic_2EDIV(Y1, Y0)), Y0))) => 150.09/22.64 (mono_2Ec_2Earithmetic_2EMOD(mono_2Ec_2Enum_2ESUC(Y1), 150.09/22.64 Y0) = 150.09/22.64 mono_2Ec_2Enum_2ESUC( 150.09/22.64 mono_2Ec_2Earithmetic_2EMOD(Y1, Y0)))))))))), 150.09/22.64 inference('cnf', [status(esa)], [thm_2Earithmetic_2EMOD__SUC])). 150.09/22.64 tff('21', plain, 150.09/22.64 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.64 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.64 ((mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Enum_2E0, X1) & 150.09/22.64 (mono_2Ec_2Enum_2ESUC(Y0) != 150.09/22.64 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.64 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2EDIV(Y0, X1)), 150.09/22.64 X1))) => 150.09/22.64 (mono_2Ec_2Earithmetic_2EMOD(mono_2Ec_2Enum_2ESUC(Y0), X1) = 150.09/22.64 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2EMOD(Y0, X1))))))), 150.09/22.64 inference('lazy_cnf_forall', [status(thm)], ['20'])). 150.09/22.64 tff('22', plain, 150.09/22.64 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.64 ((mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Enum_2E0, X1) & 150.09/22.64 (mono_2Ec_2Enum_2ESUC(X2) != 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2EDIV(X2, X1)), X1))) => 150.09/22.65 (mono_2Ec_2Earithmetic_2EMOD(mono_2Ec_2Enum_2ESUC(X2), X1) = 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2EMOD(X2, X1)))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['21'])). 150.09/22.65 tff('23', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (~ (mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Enum_2E0, X1) & 150.09/22.65 (mono_2Ec_2Enum_2ESUC(X2) != 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2EDIV(X2, X1)), X1))) 150.09/22.65 | mono_2Ec_2Earithmetic_2EMOD(mono_2Ec_2Enum_2ESUC(X2), X1) 150.09/22.65 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2EMOD(X2, X1))), 150.09/22.65 inference('lazy_cnf_imply', [status(thm)], ['22'])). 150.09/22.65 tff('24', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (~ mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Enum_2E0, X1) 150.09/22.65 | mono_2Ec_2Enum_2ESUC(X2) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2EDIV(X2, X1)), X1) 150.09/22.65 | mono_2Ec_2Earithmetic_2EMOD(mono_2Ec_2Enum_2ESUC(X2), X1) 150.09/22.65 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2EMOD(X2, X1))), 150.09/22.65 inference('lazy_cnf_and', [status(thm)], ['23'])). 150.09/22.65 tff(thm_2Earithmetic_2EMULT__SYM, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum,V1n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2A(V0m,V1n) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A(V1n,V0m)))). 150.09/22.65 tff('25', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2A(Y0, Y1) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A(Y1, Y0)))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EMULT__SYM])). 150.09/22.65 tff('26', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2A(X1, Y0) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A(Y0, X1))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['25'])). 150.09/22.65 tff('27', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A(X1, X2) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2A(X2, X1), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['26'])). 150.09/22.65 tff('28', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (~ mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Enum_2E0, X1) 150.09/22.65 | mono_2Ec_2Enum_2ESUC(X2) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2A(X1, 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2EDIV(X2, X1))) 150.09/22.65 | mono_2Ec_2Earithmetic_2EMOD(mono_2Ec_2Enum_2ESUC(X2), X1) 150.09/22.65 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2EMOD(X2, X1))), 150.09/22.65 inference('demod', [status(thm)], ['24', '27'])). 150.09/22.65 tff(thm_2Earithmetic_2EMAX__0, axiom, 150.09/22.65 (![V0n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2EMAX(V0n,mono_2Ec_2Enum_2E0) = V0n) & 150.09/22.65 (mono_2Ec_2Earithmetic_2EMAX(mono_2Ec_2Enum_2E0,V0n) = V0n)))). 150.09/22.65 tff('29', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2EMAX(Y0, mono_2Ec_2Enum_2E0) = Y0) & 150.09/22.65 (mono_2Ec_2Earithmetic_2EMAX(mono_2Ec_2Enum_2E0, Y0) = Y0))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EMAX__0])). 150.09/22.65 tff('30', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2EMAX(X1, mono_2Ec_2Enum_2E0) = X1) & 150.09/22.65 (mono_2Ec_2Earithmetic_2EMAX(mono_2Ec_2Enum_2E0, X1) = X1)), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['29'])). 150.09/22.65 tff('31', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2EMAX(X1, mono_2Ec_2Enum_2E0) = X1, 150.09/22.65 inference('lazy_cnf_and', [status(thm)], ['30'])). 150.09/22.65 tff(thm_2Earithmetic_2EEVEN__ODD, axiom, 150.09/22.65 (![V0n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EEVEN(V0n) <=> 150.09/22.65 (~mono_2Ec_2Earithmetic_2EODD(V0n))))). 150.09/22.65 tff('32', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EEVEN(Y0) <=> 150.09/22.65 (~(mono_2Ec_2Earithmetic_2EODD(Y0))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EEVEN__ODD])). 150.09/22.65 tff('33', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EEVEN(X1) <=> 150.09/22.65 (~(mono_2Ec_2Earithmetic_2EODD(X1)))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['32'])). 150.09/22.65 tff('34', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2EEVEN(X1) != mono_2Ec_2Earithmetic_2EODD(X1), 150.09/22.65 inference('simplify nested equalities', [status(thm)], ['33'])). 150.09/22.65 tff(thm_2Earithmetic_2EODD__OR__EVEN, axiom, 150.09/22.65 (![V0n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (?[V1m:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((V0n = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(mono_2Ec_2Earithmetic_2E_2A(mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Enum_2E0)), 150.09/22.65 V1m), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO)))) | 150.09/22.65 (V0n = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A(mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Enum_2E0)), 150.09/22.65 V1m)))))). 150.09/22.65 tff('35', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (??((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((Y0 = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0)), Y1), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO)))) | 150.09/22.65 (Y0 = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0)), Y1))))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EODD__OR__EVEN])). 150.09/22.65 tff('36', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (??((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((X1 = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0)), Y0), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO)))) | 150.09/22.65 (X1 = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0)), Y0)))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['35'])). 150.09/22.65 tff('37', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((X1 = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0)), 150.09/22.65 '#sk175'(X1)), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO)))) | 150.09/22.65 (X1 = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0)), 150.09/22.65 '#sk175'(X1)))), 150.09/22.65 inference('lazy_cnf_exists', [status(thm)], ['36'])). 150.09/22.65 tff('38', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (X1 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2B( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0)), 150.09/22.65 '#sk175'(X1)), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO))) 150.09/22.65 | X1 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0)), 150.09/22.65 '#sk175'(X1))), 150.09/22.65 inference('lazy_cnf_or', [status(thm)], ['37'])). 150.09/22.65 tff('39', plain, 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0) 150.09/22.65 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0), 150.09/22.65 inference('demod', [status(thm)], ['11', '12'])). 150.09/22.65 tff(thm_2Earithmetic_2ETWO, axiom, 150.09/22.65 (mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Earithmetic_2EZERO)) = 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT1( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO))))). 150.09/22.65 tff('40', plain, 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Earithmetic_2EZERO)) 150.09/22.65 = mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2ETWO])). 150.09/22.65 tff('41', plain, mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0, 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EALT__ZERO])). 150.09/22.65 tff('42', plain, mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0, 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EALT__ZERO])). 150.09/22.65 tff('43', plain, 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0)) 150.09/22.65 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0), 150.09/22.65 inference('demod', [status(thm)], ['4', '5'])). 150.09/22.65 tff('44', plain, 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Enum_2E0)) 150.09/22.65 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0)), 150.09/22.65 inference('demod', [status(thm)], ['40', '41', '42', '43'])). 150.09/22.65 tff('45', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff('46', plain, 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Enum_2E0) 150.09/22.65 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0)), 150.09/22.65 inference('demod', [status(thm)], ['44', '45'])). 150.09/22.65 tff('47', plain, 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0) 150.09/22.65 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0), 150.09/22.65 inference('demod', [status(thm)], ['11', '12'])). 150.09/22.65 tff('48', plain, 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Enum_2E0) 150.09/22.65 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0)), 150.09/22.65 inference('demod', [status(thm)], ['46', '47'])). 150.09/22.65 tff('49', plain, mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0, 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EALT__ZERO])). 150.09/22.65 tff('50', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff(thm_2Earithmetic_2EADD1, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Enum_2ESUC(V0m) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(V0m, 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT1( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO)))))). 150.09/22.65 tff('51', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Enum_2ESUC(Y0) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(Y0, 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EADD1])). 150.09/22.65 tff('52', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Enum_2ESUC(X1) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2B(X1, 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['51'])). 150.09/22.65 tff('53', plain, mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0, 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EALT__ZERO])). 150.09/22.65 tff('54', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff('55', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Enum_2ESUC(X1) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2B(X1, 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0)), 150.09/22.65 inference('demod', [status(thm)], ['52', '53', '54'])). 150.09/22.65 tff('56', plain, 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0) 150.09/22.65 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0), 150.09/22.65 inference('demod', [status(thm)], ['11', '12'])). 150.09/22.65 tff('57', plain, 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Enum_2E0) 150.09/22.65 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0)), 150.09/22.65 inference('demod', [status(thm)], ['46', '47'])). 150.09/22.65 tff('58', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (X1 150.09/22.65 = mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Enum_2E0), '#sk175'(X1))) 150.09/22.65 | X1 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Enum_2E0), '#sk175'(X1))), 150.09/22.65 inference('demod', [status(thm)], 150.09/22.65 ['38', '39', '48', '49', '50', '55', '56', '57'])). 150.09/22.65 tff(thm_2Earithmetic_2ELESS__CASES, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum,V1n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_3C_3D(V1n,V0m) | 150.09/22.65 mono_2Ec_2Eprim__rec_2E_3C(V0m,V1n)))). 150.09/22.65 tff('59', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_3C_3D(Y1, Y0) | 150.09/22.65 mono_2Ec_2Eprim__rec_2E_3C(Y0, Y1)))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2ELESS__CASES])). 150.09/22.65 tff('60', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_3C_3D(Y0, X1) | 150.09/22.65 mono_2Ec_2Eprim__rec_2E_3C(X1, Y0))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['59'])). 150.09/22.65 tff('61', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_3C_3D(X2, X1) | 150.09/22.65 mono_2Ec_2Eprim__rec_2E_3C(X1, X2)), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['60'])). 150.09/22.65 tff('62', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ( mono_2Ec_2Earithmetic_2E_3C_3D(X2, X1) 150.09/22.65 | mono_2Ec_2Eprim__rec_2E_3C(X1, X2)), 150.09/22.65 inference('lazy_cnf_or', [status(thm)], ['61'])). 150.09/22.65 tff(thm_2Earithmetic_2EADD__EQ__1, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum,V1n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_2B(V0m,V1n) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO))) <=> 150.09/22.65 (((V1n = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT1( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO))) & 150.09/22.65 (V0m = mono_2Ec_2Enum_2E0)) | 150.09/22.65 ((V1n = mono_2Ec_2Enum_2E0) & 150.09/22.65 (V0m = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT1( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO)))))))). 150.09/22.65 tff('63', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_2B(Y0, Y1) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO))) <=> 150.09/22.65 (((Y1 = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO))) & 150.09/22.65 (Y0 = mono_2Ec_2Enum_2E0)) | 150.09/22.65 ((Y1 = mono_2Ec_2Enum_2E0) & 150.09/22.65 (Y0 = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO)))))))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EADD__EQ__1])). 150.09/22.65 tff('64', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_2B(X1, Y0) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO))) <=> 150.09/22.65 (((Y0 = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO))) & 150.09/22.65 (X1 = mono_2Ec_2Enum_2E0)) | 150.09/22.65 ((Y0 = mono_2Ec_2Enum_2E0) & 150.09/22.65 (X1 = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO))))))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['63'])). 150.09/22.65 tff('65', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_2B(X1, X2) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO))) <=> 150.09/22.65 (((X2 = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO))) & 150.09/22.65 (X1 = mono_2Ec_2Enum_2E0)) | 150.09/22.65 ((X2 = mono_2Ec_2Enum_2E0) & 150.09/22.65 (X1 = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO)))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['64'])). 150.09/22.65 tff('66', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(X1, X2) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO))) 150.09/22.65 = (((X2 = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO))) & 150.09/22.65 (X1 = mono_2Ec_2Enum_2E0)) | 150.09/22.65 ((X2 = mono_2Ec_2Enum_2E0) & 150.09/22.65 (X1 = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO))))), 150.09/22.65 inference('simplify nested equalities', [status(thm)], ['65'])). 150.09/22.65 tff('67', plain, mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0, 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EALT__ZERO])). 150.09/22.65 tff('68', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff('69', plain, mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0, 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EALT__ZERO])). 150.09/22.65 tff('70', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff('71', plain, mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0, 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EALT__ZERO])). 150.09/22.65 tff('72', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff('73', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(X1, X2) = 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0)) 150.09/22.65 = (((X2 = mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0)) & 150.09/22.65 (X1 = mono_2Ec_2Enum_2E0)) | 150.09/22.65 ((X2 = mono_2Ec_2Enum_2E0) & 150.09/22.65 (X1 = mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0)))), 150.09/22.65 inference('demod', [status(thm)], 150.09/22.65 ['66', '67', '68', '69', '70', '71', '72'])). 150.09/22.65 tff(thm_2Earithmetic_2ENOT__SUC__ADD__LESS__EQ, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum,V1n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (~ 150.09/22.65 mono_2Ec_2Earithmetic_2E_3C_3D(mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2E_2B( 150.09/22.65 V0m,V1n)), 150.09/22.65 V0m)))). 150.09/22.65 tff('74', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (~(mono_2Ec_2Earithmetic_2E_3C_3D( 150.09/22.65 mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(Y0, Y1)), Y0))))))))), 150.09/22.65 inference('cnf', [status(esa)], 150.09/22.65 [thm_2Earithmetic_2ENOT__SUC__ADD__LESS__EQ])). 150.09/22.65 tff('75', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (~(mono_2Ec_2Earithmetic_2E_3C_3D( 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2E_2B(X1, Y0)), 150.09/22.65 X1)))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['74'])). 150.09/22.65 tff('76', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ~ mono_2Ec_2Earithmetic_2E_3C_3D( 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2E_2B(X1, X2)), X1), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['75'])). 150.09/22.65 tff(thm_2Earithmetic_2ELESS__EQ, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum,V1n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Eprim__rec_2E_3C(V0m,V1n) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_3C_3D(mono_2Ec_2Enum_2ESUC(V0m),V1n)))). 150.09/22.65 tff('77', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Eprim__rec_2E_3C(Y0, Y1) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_3C_3D(mono_2Ec_2Enum_2ESUC(Y0), 150.09/22.65 Y1)))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2ELESS__EQ])). 150.09/22.65 tff('78', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Eprim__rec_2E_3C(X1, Y0) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_3C_3D(mono_2Ec_2Enum_2ESUC(X1), Y0))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['77'])). 150.09/22.65 tff('79', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Eprim__rec_2E_3C(X1, X2) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_3C_3D(mono_2Ec_2Enum_2ESUC(X1), X2), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['78'])). 150.09/22.65 tff('80', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ~ mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Earithmetic_2E_2B(X1, X2), X1), 150.09/22.65 inference('demod', [status(thm)], ['76', '79'])). 150.09/22.65 tff(thm_2Earithmetic_2EMIN__0, axiom, 150.09/22.65 (![V0n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2EMIN(mono_2Ec_2Enum_2E0,V0n) = 150.09/22.65 mono_2Ec_2Enum_2E0) & 150.09/22.65 (mono_2Ec_2Earithmetic_2EMIN(V0n,mono_2Ec_2Enum_2E0) = 150.09/22.65 mono_2Ec_2Enum_2E0)))). 150.09/22.65 tff('81', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2EMIN(mono_2Ec_2Enum_2E0, Y0) = 150.09/22.65 mono_2Ec_2Enum_2E0) & 150.09/22.65 (mono_2Ec_2Earithmetic_2EMIN(Y0, mono_2Ec_2Enum_2E0) = 150.09/22.65 mono_2Ec_2Enum_2E0))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EMIN__0])). 150.09/22.65 tff('82', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2EMIN(mono_2Ec_2Enum_2E0, X1) = 150.09/22.65 mono_2Ec_2Enum_2E0) & 150.09/22.65 (mono_2Ec_2Earithmetic_2EMIN(X1, mono_2Ec_2Enum_2E0) = 150.09/22.65 mono_2Ec_2Enum_2E0)), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['81'])). 150.09/22.65 tff('83', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2EMIN(mono_2Ec_2Enum_2E0, X1) 150.09/22.65 = mono_2Ec_2Enum_2E0, 150.09/22.65 inference('lazy_cnf_and', [status(thm)], ['82'])). 150.09/22.65 tff(thm_2Earithmetic_2EMAX__DEF, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum,V1n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EMAX(V0m,V1n) = 150.09/22.65 mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2E_3C( 150.09/22.65 V0m,V1n),V1n,V0m)))). 150.09/22.65 tff('84', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EMAX(Y0, Y1) = 150.09/22.65 mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum( 150.09/22.65 mono_2Ec_2Eprim__rec_2E_3C(Y0, Y1), Y1, Y0)))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EMAX__DEF])). 150.09/22.65 tff('85', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EMAX(X1, Y0) = 150.09/22.65 mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum( 150.09/22.65 mono_2Ec_2Eprim__rec_2E_3C(X1, Y0), Y0, X1))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['84'])). 150.09/22.65 tff('86', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2EMAX(X1, X2) 150.09/22.65 = mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum( 150.09/22.65 mono_2Ec_2Eprim__rec_2E_3C(X1, X2), X2, X1), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['85'])). 150.09/22.65 tff(thm_2Earithmetic_2ELESS__EQUAL__ANTISYM, axiom, 150.09/22.65 (![V0n:mono_2Etyop_2Enum_2Enum,V1m:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_3C_3D(V0n,V1m) & 150.09/22.65 mono_2Ec_2Earithmetic_2E_3C_3D(V1m,V0n)) => 150.09/22.65 (V0n = V1m)))). 150.09/22.65 tff('87', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_3C_3D(Y0, Y1) & 150.09/22.65 mono_2Ec_2Earithmetic_2E_3C_3D(Y1, Y0)) => 150.09/22.65 (Y0 = Y1)))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2ELESS__EQUAL__ANTISYM])). 150.09/22.65 tff('88', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_3C_3D(X1, Y0) & 150.09/22.65 mono_2Ec_2Earithmetic_2E_3C_3D(Y0, X1)) => 150.09/22.65 (X1 = Y0))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['87'])). 150.09/22.65 tff('89', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_3C_3D(X1, X2) & 150.09/22.65 mono_2Ec_2Earithmetic_2E_3C_3D(X2, X1)) => 150.09/22.65 (X1 = X2)), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['88'])). 150.09/22.65 tff('90', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (~ (mono_2Ec_2Earithmetic_2E_3C_3D(X1, X2) & 150.09/22.65 mono_2Ec_2Earithmetic_2E_3C_3D(X2, X1)) 150.09/22.65 | X1 = X2), 150.09/22.65 inference('lazy_cnf_imply', [status(thm)], ['89'])). 150.09/22.65 tff('91', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (~ mono_2Ec_2Earithmetic_2E_3C_3D(X1, X2) 150.09/22.65 | ~ mono_2Ec_2Earithmetic_2E_3C_3D(X2, X1) 150.09/22.65 | X1 = X2), 150.09/22.65 inference('lazy_cnf_and', [status(thm)], ['90'])). 150.09/22.65 tff(thm_2Earithmetic_2EEVEN__ODD__EXISTS, axiom, 150.09/22.65 (![V0n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2EODD(V0n) => 150.09/22.65 (?[V2m:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (V0n = 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2E_2A(mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO)), 150.09/22.65 V2m))))) & 150.09/22.65 (mono_2Ec_2Earithmetic_2EEVEN(V0n) => 150.09/22.65 (?[V1m:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (V0n = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A(mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Earithmetic_2EZERO)), 150.09/22.65 V1m))))))). 150.09/22.65 tff('92', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2EODD(Y0) => 150.09/22.65 (??((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (Y0 = 150.09/22.65 mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO)), Y1))))))) & 150.09/22.65 (mono_2Ec_2Earithmetic_2EEVEN(Y0) => 150.09/22.65 (??((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (Y0 = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO)), Y1)))))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EEVEN__ODD__EXISTS])). 150.09/22.65 tff('93', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2EODD(X1) => 150.09/22.65 (??((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (X1 = 150.09/22.65 mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO)), Y0))))))) & 150.09/22.65 (mono_2Ec_2Earithmetic_2EEVEN(X1) => 150.09/22.65 (??((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (X1 = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO)), Y0))))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['92'])). 150.09/22.65 tff('94', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EEVEN(X1) => 150.09/22.65 (??((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (X1 = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO)), Y0)))))), 150.09/22.65 inference('lazy_cnf_and', [status(thm)], ['93'])). 150.09/22.65 tff('95', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (~ mono_2Ec_2Earithmetic_2EEVEN(X1) 150.09/22.65 | (??((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (X1 = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO)), Y0)))))), 150.09/22.65 inference('lazy_cnf_imply', [status(thm)], ['94'])). 150.09/22.65 tff('96', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (X1 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Earithmetic_2EZERO)), 150.09/22.65 '#sk210'(X1)) 150.09/22.65 | ~ mono_2Ec_2Earithmetic_2EEVEN(X1)), 150.09/22.65 inference('lazy_cnf_exists', [status(thm)], ['95'])). 150.09/22.65 tff('97', plain, mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0, 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EALT__ZERO])). 150.09/22.65 tff('98', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff('99', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (X1 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Enum_2E0), '#sk210'(X1)) 150.09/22.65 | ~ mono_2Ec_2Earithmetic_2EEVEN(X1)), 150.09/22.65 inference('demod', [status(thm)], ['96', '97', '98'])). 150.09/22.65 tff(thm_2Earithmetic_2EZERO__LT__EXP, axiom, 150.09/22.65 (![V0y:mono_2Etyop_2Enum_2Enum,V1x:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Enum_2E0, 150.09/22.65 mono_2Ec_2Earithmetic_2EEXP(V1x,V0y)) <=> 150.09/22.65 ((V0y = mono_2Ec_2Enum_2E0) | 150.09/22.65 mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Enum_2E0,V1x))))). 150.09/22.65 tff('100', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Enum_2E0, 150.09/22.65 mono_2Ec_2Earithmetic_2EEXP(Y1, Y0)) <=> 150.09/22.65 ((Y0 = mono_2Ec_2Enum_2E0) | 150.09/22.65 mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Enum_2E0, Y1))))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EZERO__LT__EXP])). 150.09/22.65 tff('101', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Enum_2E0, 150.09/22.65 mono_2Ec_2Earithmetic_2EEXP(Y0, X1)) <=> 150.09/22.65 ((X1 = mono_2Ec_2Enum_2E0) | 150.09/22.65 mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Enum_2E0, Y0)))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['100'])). 150.09/22.65 tff('102', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Enum_2E0, 150.09/22.65 mono_2Ec_2Earithmetic_2EEXP(X2, X1)) <=> 150.09/22.65 ((X1 = mono_2Ec_2Enum_2E0) | 150.09/22.65 mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Enum_2E0, X2))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['101'])). 150.09/22.65 tff('103', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Enum_2E0, 150.09/22.65 mono_2Ec_2Earithmetic_2EEXP(X2, X1)) 150.09/22.65 = ((X1 = mono_2Ec_2Enum_2E0) | 150.09/22.65 mono_2Ec_2Eprim__rec_2E_3C(mono_2Ec_2Enum_2E0, X2)), 150.09/22.65 inference('simplify nested equalities', [status(thm)], ['102'])). 150.09/22.65 tff(thm_2Earithmetic_2EMIN__DEF, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum,V1n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EMIN(V0m,V1n) = 150.09/22.65 mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2E_3C( 150.09/22.65 V0m,V1n),V0m,V1n)))). 150.09/22.65 tff('104', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EMIN(Y0, Y1) = 150.09/22.65 mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum( 150.09/22.65 mono_2Ec_2Eprim__rec_2E_3C(Y0, Y1), Y0, Y1)))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EMIN__DEF])). 150.09/22.65 tff('105', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EMIN(X1, Y0) = 150.09/22.65 mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum( 150.09/22.65 mono_2Ec_2Eprim__rec_2E_3C(X1, Y0), X1, Y0))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['104'])). 150.09/22.65 tff('106', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2EMIN(X1, X2) 150.09/22.65 = mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum( 150.09/22.65 mono_2Ec_2Eprim__rec_2E_3C(X1, X2), X1, X2), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['105'])). 150.09/22.65 tff('107', plain, 150.09/22.65 mono_2Ec_2Earithmetic_2EMOD('#sk1', 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Enum_2E0)) 150.09/22.65 != mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum( 150.09/22.65 mono_2Ec_2Earithmetic_2EEVEN('#sk1'), mono_2Ec_2Enum_2E0, 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0)), 150.09/22.65 inference('demod', [status(thm)], ['10', '13'])). 150.09/22.65 tff(thm_2Earithmetic_2EADD__INV__0, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum,V1n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_2B(V0m,V1n) = V0m) => 150.09/22.65 (V1n = mono_2Ec_2Enum_2E0)))). 150.09/22.65 tff('108', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_2B(Y0, Y1) = Y0) => 150.09/22.65 (Y1 = mono_2Ec_2Enum_2E0)))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EADD__INV__0])). 150.09/22.65 tff('109', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_2B(X1, Y0) = X1) => 150.09/22.65 (Y0 = mono_2Ec_2Enum_2E0))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['108'])). 150.09/22.65 tff('110', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_2B(X1, X2) = X1) => 150.09/22.65 (X2 = mono_2Ec_2Enum_2E0)), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['109'])). 150.09/22.65 tff('111', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(X1, X2) != X1 | X2 = mono_2Ec_2Enum_2E0), 150.09/22.65 inference('lazy_cnf_imply', [status(thm)], ['110'])). 150.09/22.65 tff(thm_2Earithmetic_2ELESS__EQ__ADD, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum,V1n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2E_3C_3D(V0m,mono_2Ec_2Earithmetic_2E_2B(V0m,V1n)))). 150.09/22.65 tff('112', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2E_3C_3D(Y0, 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(Y0, Y1)))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2ELESS__EQ__ADD])). 150.09/22.65 tff('113', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2E_3C_3D(X1, 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(X1, Y0))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['112'])). 150.09/22.65 tff('114', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2E_3C_3D(X1, 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(X1, X2)), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['113'])). 150.09/22.65 tff(thm_2Earithmetic_2Enum__CASES, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((?[V1n:mono_2Etyop_2Enum_2Enum]: (V0m = mono_2Ec_2Enum_2ESUC(V1n))) | 150.09/22.65 (V0m = mono_2Ec_2Enum_2E0)))). 150.09/22.65 tff('115', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((??((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (Y0 = mono_2Ec_2Enum_2ESUC(Y1))))) | 150.09/22.65 (Y0 = mono_2Ec_2Enum_2E0))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2Enum__CASES])). 150.09/22.65 tff('116', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((??((^[Y0 : mono_2Etyop_2Enum_2Enum]: (X1 = mono_2Ec_2Enum_2ESUC(Y0))))) | 150.09/22.65 (X1 = mono_2Ec_2Enum_2E0)), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['115'])). 150.09/22.65 tff('117', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ( (??((^[Y0 : mono_2Etyop_2Enum_2Enum]: (X1 = mono_2Ec_2Enum_2ESUC(Y0))))) 150.09/22.65 | X1 = mono_2Ec_2Enum_2E0), 150.09/22.65 inference('lazy_cnf_or', [status(thm)], ['116'])). 150.09/22.65 tff('118', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (X1 = mono_2Ec_2Enum_2ESUC('#sk24'(X1)) | X1 = mono_2Ec_2Enum_2E0), 150.09/22.65 inference('lazy_cnf_exists', [status(thm)], ['117'])). 150.09/22.65 tff(thm_2Earithmetic_2ENUMERAL__MULT__EQ__DIV, axiom, 150.09/22.65 (![V0z:mono_2Etyop_2Enum_2Enum,V1y:mono_2Etyop_2Enum_2Enum, 150.09/22.65 V2x:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((((mono_2Ec_2Earithmetic_2EMOD(mono_2Ec_2Earithmetic_2ENUMERAL(V0z), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(V2x))) = 150.09/22.65 mono_2Ec_2Enum_2E0) & 150.09/22.65 (V1y = 150.09/22.65 mono_2Ec_2Earithmetic_2EDIV(mono_2Ec_2Earithmetic_2ENUMERAL(V0z), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(V2x))))) <=> 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2A(mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT1( 150.09/22.65 V2x)), 150.09/22.65 V1y) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(V0z))) & 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_2A(mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT2( 150.09/22.65 V2x)), 150.09/22.65 V1y) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(V0z)) <=> 150.09/22.65 ((mono_2Ec_2Earithmetic_2EMOD(mono_2Ec_2Earithmetic_2ENUMERAL(V0z), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(V2x))) = 150.09/22.65 mono_2Ec_2Enum_2E0) & 150.09/22.65 (V1y = 150.09/22.65 mono_2Ec_2Earithmetic_2EDIV(mono_2Ec_2Earithmetic_2ENUMERAL(V0z), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(V2x))))))))). 150.09/22.65 tff('119', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((((mono_2Ec_2Earithmetic_2EMOD( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(Y0), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(Y2))) = 150.09/22.65 mono_2Ec_2Enum_2E0) & 150.09/22.65 (Y1 = 150.09/22.65 mono_2Ec_2Earithmetic_2EDIV( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(Y0), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(Y2))))) <=> 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(Y2)), Y1) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(Y0))) & 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(Y2)), Y1) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(Y0)) <=> 150.09/22.65 ((mono_2Ec_2Earithmetic_2EMOD( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(Y0), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(Y2))) = 150.09/22.65 mono_2Ec_2Enum_2E0) & 150.09/22.65 (Y1 = 150.09/22.65 mono_2Ec_2Earithmetic_2EDIV( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(Y0), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(Y2)))))))))))))))), 150.09/22.65 inference('cnf', [status(esa)], 150.09/22.65 [thm_2Earithmetic_2ENUMERAL__MULT__EQ__DIV])). 150.09/22.65 tff('120', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((((mono_2Ec_2Earithmetic_2EMOD( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(X1), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(Y1))) = 150.09/22.65 mono_2Ec_2Enum_2E0) & 150.09/22.65 (Y0 = 150.09/22.65 mono_2Ec_2Earithmetic_2EDIV( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(X1), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(Y1))))) <=> 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(Y1)), Y0) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(X1))) & 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(Y1)), Y0) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(X1)) <=> 150.09/22.65 ((mono_2Ec_2Earithmetic_2EMOD( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(X1), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(Y1))) = 150.09/22.65 mono_2Ec_2Enum_2E0) & 150.09/22.65 (Y0 = 150.09/22.65 mono_2Ec_2Earithmetic_2EDIV( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(X1), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(Y1))))))))))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['119'])). 150.09/22.65 tff('121', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((((mono_2Ec_2Earithmetic_2EMOD( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(X1), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(Y0))) = 150.09/22.65 mono_2Ec_2Enum_2E0) & 150.09/22.65 (X2 = 150.09/22.65 mono_2Ec_2Earithmetic_2EDIV( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(X1), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(Y0))))) <=> 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(Y0)), X2) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(X1))) & 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(Y0)), X2) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(X1)) <=> 150.09/22.65 ((mono_2Ec_2Earithmetic_2EMOD( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(X1), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(Y0))) = 150.09/22.65 mono_2Ec_2Enum_2E0) & 150.09/22.65 (X2 = 150.09/22.65 mono_2Ec_2Earithmetic_2EDIV( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(X1), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(Y0)))))))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['120'])). 150.09/22.65 tff('122', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum, 150.09/22.65 X3 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((((mono_2Ec_2Earithmetic_2EMOD(mono_2Ec_2Earithmetic_2ENUMERAL(X1), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(X3))) = 150.09/22.65 mono_2Ec_2Enum_2E0) & 150.09/22.65 (X2 = 150.09/22.65 mono_2Ec_2Earithmetic_2EDIV(mono_2Ec_2Earithmetic_2ENUMERAL(X1), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(X3))))) <=> 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT1(X3)), 150.09/22.65 X2) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(X1))) & 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT2(X3)), 150.09/22.65 X2) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(X1)) <=> 150.09/22.65 ((mono_2Ec_2Earithmetic_2EMOD(mono_2Ec_2Earithmetic_2ENUMERAL(X1), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(X3))) = 150.09/22.65 mono_2Ec_2Enum_2E0) & 150.09/22.65 (X2 = 150.09/22.65 mono_2Ec_2Earithmetic_2EDIV(mono_2Ec_2Earithmetic_2ENUMERAL(X1), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(X3))))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['121'])). 150.09/22.65 tff('123', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum, 150.09/22.65 X3 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT2(X3)), 150.09/22.65 X2) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(X1)) <=> 150.09/22.65 ((mono_2Ec_2Earithmetic_2EMOD(mono_2Ec_2Earithmetic_2ENUMERAL(X1), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT2(X3))) = 150.09/22.65 mono_2Ec_2Enum_2E0) & 150.09/22.65 (X2 = 150.09/22.65 mono_2Ec_2Earithmetic_2EDIV(mono_2Ec_2Earithmetic_2ENUMERAL(X1), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT2(X3)))))), 150.09/22.65 inference('lazy_cnf_and', [status(thm)], ['122'])). 150.09/22.65 tff('124', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum, 150.09/22.65 X3 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT2(X3)), 150.09/22.65 X2) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(X1)) 150.09/22.65 = ((mono_2Ec_2Earithmetic_2EMOD(mono_2Ec_2Earithmetic_2ENUMERAL(X1), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(X3))) = 150.09/22.65 mono_2Ec_2Enum_2E0) & 150.09/22.65 (X2 = 150.09/22.65 mono_2Ec_2Earithmetic_2EDIV(mono_2Ec_2Earithmetic_2ENUMERAL(X1), 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(X3))))), 150.09/22.65 inference('simplify nested equalities', [status(thm)], ['123'])). 150.09/22.65 tff('125', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff('126', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff('127', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff('128', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff('129', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff('130', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff('131', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum, 150.09/22.65 X3 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2A(mono_2Ec_2Earithmetic_2EBIT2(X3), X2) = X1) 150.09/22.65 = ((mono_2Ec_2Earithmetic_2EMOD(X1, mono_2Ec_2Earithmetic_2EBIT2(X3)) = 150.09/22.65 mono_2Ec_2Enum_2E0) & 150.09/22.65 (X2 = 150.09/22.65 mono_2Ec_2Earithmetic_2EDIV(X1, mono_2Ec_2Earithmetic_2EBIT2(X3)))), 150.09/22.65 inference('demod', [status(thm)], 150.09/22.65 ['124', '125', '126', '127', '128', '129', '130'])). 150.09/22.65 tff(thm_2Earithmetic_2EADD, axiom, 150.09/22.65 ((![V0n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(mono_2Ec_2Enum_2E0,V0n) = V0n)) & 150.09/22.65 (![V1m:mono_2Etyop_2Enum_2Enum,V2n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(mono_2Ec_2Enum_2ESUC(V1m),V2n) = 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2E_2B(V1m,V2n)))))). 150.09/22.65 tff('132', plain, 150.09/22.65 ((!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(mono_2Ec_2Enum_2E0, Y0) = Y0)))) & 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(mono_2Ec_2Enum_2ESUC(Y0), 150.09/22.65 Y1) = 150.09/22.65 mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(Y0, Y1)))))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EADD])). 150.09/22.65 tff('133', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(mono_2Ec_2Enum_2ESUC(Y0), Y1) = 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2E_2B(Y0, Y1))))))))), 150.09/22.65 inference('lazy_cnf_and', [status(thm)], ['132'])). 150.09/22.65 tff('134', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(mono_2Ec_2Enum_2ESUC(X1), Y0) = 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2E_2B(X1, Y0)))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['133'])). 150.09/22.65 tff('135', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(mono_2Ec_2Enum_2ESUC(X1), X2) 150.09/22.65 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2E_2B(X1, X2)), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['134'])). 150.09/22.65 tff(thm_2Earithmetic_2ETIMES2, axiom, 150.09/22.65 (![V0n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2A(mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT2( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO)), 150.09/22.65 V0n) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(V0n,V0n)))). 150.09/22.65 tff('136', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Earithmetic_2EZERO)), 150.09/22.65 Y0) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(Y0, Y0))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2ETIMES2])). 150.09/22.65 tff('137', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Earithmetic_2EZERO)), X1) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2B(X1, X1), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['136'])). 150.09/22.65 tff('138', plain, mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0, 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EALT__ZERO])). 150.09/22.65 tff('139', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff('140', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Enum_2E0), X1) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2B(X1, X1), 150.09/22.65 inference('demod', [status(thm)], ['137', '138', '139'])). 150.09/22.65 tff(thm_2Earithmetic_2EODD__MULT, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum,V1n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EODD(mono_2Ec_2Earithmetic_2E_2A(V0m,V1n)) <=> 150.09/22.65 (mono_2Ec_2Earithmetic_2EODD(V1n) & mono_2Ec_2Earithmetic_2EODD(V0m))))). 150.09/22.65 tff('141', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EODD( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A(Y0, Y1)) <=> 150.09/22.65 (mono_2Ec_2Earithmetic_2EODD(Y1) & 150.09/22.65 mono_2Ec_2Earithmetic_2EODD(Y0))))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EODD__MULT])). 150.09/22.65 tff('142', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EODD( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A(X1, Y0)) <=> 150.09/22.65 (mono_2Ec_2Earithmetic_2EODD(Y0) & 150.09/22.65 mono_2Ec_2Earithmetic_2EODD(X1)))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['141'])). 150.09/22.65 tff('143', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EODD(mono_2Ec_2Earithmetic_2E_2A(X1, X2)) <=> 150.09/22.65 (mono_2Ec_2Earithmetic_2EODD(X2) & mono_2Ec_2Earithmetic_2EODD(X1))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['142'])). 150.09/22.65 tff('144', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2EODD(mono_2Ec_2Earithmetic_2E_2A(X1, X2)) 150.09/22.65 = (mono_2Ec_2Earithmetic_2EODD(X2) & mono_2Ec_2Earithmetic_2EODD(X1)), 150.09/22.65 inference('simplify nested equalities', [status(thm)], ['143'])). 150.09/22.65 tff(thm_2Earithmetic_2EBIT2, axiom, 150.09/22.65 (![V0n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EBIT2(V0n) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(V0n, 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(V0n, 150.09/22.65 mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Enum_2E0))))))). 150.09/22.65 tff('145', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EBIT2(Y0) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(Y0, 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(Y0, 150.09/22.65 mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0)))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EBIT2])). 150.09/22.65 tff('146', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(X1) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2B(X1, 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(X1, 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0)))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['145'])). 150.09/22.65 tff('147', plain, 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0) 150.09/22.65 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0), 150.09/22.65 inference('demod', [status(thm)], ['11', '12'])). 150.09/22.65 tff('148', plain, 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Enum_2E0) 150.09/22.65 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0)), 150.09/22.65 inference('demod', [status(thm)], ['46', '47'])). 150.09/22.65 tff('149', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(X1) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2B(X1, 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(X1, 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Enum_2E0))), 150.09/22.65 inference('demod', [status(thm)], ['146', '147', '148'])). 150.09/22.65 tff(thm_2Earithmetic_2EADD__ASSOC, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum,V1n:mono_2Etyop_2Enum_2Enum, 150.09/22.65 V2p:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(V0m,mono_2Ec_2Earithmetic_2E_2B(V1n,V2p)) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(mono_2Ec_2Earithmetic_2E_2B(V0m,V1n),V2p)))). 150.09/22.65 tff('150', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(Y0, 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(Y1, Y2)) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(Y0, Y1), Y2))))))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EADD__ASSOC])). 150.09/22.65 tff('151', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(X1, 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(Y0, Y1)) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(X1, Y0), Y1)))))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['150'])). 150.09/22.65 tff('152', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(X1, 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(X2, Y0)) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(X1, X2), Y0))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['151'])). 150.09/22.65 tff('153', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum, 150.09/22.65 X3 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(X1, mono_2Ec_2Earithmetic_2E_2B(X2, X3)) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2B(mono_2Ec_2Earithmetic_2E_2B(X1, X2), X3), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['152'])). 150.09/22.65 tff(thm_2Earithmetic_2EEQ__ADD__LCANCEL, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum,V1n:mono_2Etyop_2Enum_2Enum, 150.09/22.65 V2p:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((V1n = V2p) <=> 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(V0m,V1n) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(V0m,V2p))))). 150.09/22.65 tff('154', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((Y1 = Y2) <=> 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(Y0, Y1) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(Y0, Y2)))))))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EEQ__ADD__LCANCEL])). 150.09/22.65 tff('155', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((Y0 = Y1) <=> 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(X1, Y0) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(X1, Y1))))))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['154'])). 150.09/22.65 tff('156', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((X2 = Y0) <=> 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(X1, X2) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(X1, Y0)))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['155'])). 150.09/22.65 tff('157', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum, 150.09/22.65 X3 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 ((X2 = X3) <=> 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2B(X1, X2) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(X1, X3))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['156'])). 150.09/22.65 tff('158', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum, 150.09/22.65 X3 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (X2 = X3) 150.09/22.65 = (mono_2Ec_2Earithmetic_2E_2B(X1, X2) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(X1, X3)), 150.09/22.65 inference('simplify nested equalities', [status(thm)], ['157'])). 150.09/22.65 tff('159', plain, 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0) 150.09/22.65 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0), 150.09/22.65 inference('demod', [status(thm)], ['11', '12'])). 150.09/22.65 tff(thm_2Earithmetic_2ESUC__NOT, axiom, 150.09/22.65 (![V0n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Enum_2E0 != mono_2Ec_2Enum_2ESUC(V0n)))). 150.09/22.65 tff('160', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Enum_2E0 != mono_2Ec_2Enum_2ESUC(Y0))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2ESUC__NOT])). 150.09/22.65 tff('161', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Enum_2E0 != mono_2Ec_2Enum_2ESUC(X1), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['160'])). 150.09/22.65 tff('162', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Enum_2ESUC(X1) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2B(X1, 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0)), 150.09/22.65 inference('demod', [status(thm)], ['52', '53', '54'])). 150.09/22.65 tff(thm_2Earithmetic_2EADD__SUC, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum,V1n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2E_2B(V0m,V1n)) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(V0m,mono_2Ec_2Enum_2ESUC(V1n))))). 150.09/22.65 tff('163', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2E_2B(Y0, Y1)) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(Y0, mono_2Ec_2Enum_2ESUC(Y1))))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EADD__SUC])). 150.09/22.65 tff('164', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2E_2B(X1, Y0)) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(X1, mono_2Ec_2Enum_2ESUC(Y0)))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['163'])). 150.09/22.65 tff('165', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2E_2B(X1, X2)) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2B(X1, mono_2Ec_2Enum_2ESUC(X2)), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['164'])). 150.09/22.65 tff(thm_2Earithmetic_2EEXP, axiom, 150.09/22.65 ((![V1m:mono_2Etyop_2Enum_2Enum,V2n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EEXP(V1m,mono_2Ec_2Enum_2ESUC(V2n)) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A(V1m,mono_2Ec_2Earithmetic_2EEXP(V1m,V2n)))) & 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EEXP(V0m,mono_2Ec_2Enum_2E0) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO)))))). 150.09/22.65 tff('166', plain, 150.09/22.65 ((!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EEXP(Y0, 150.09/22.65 mono_2Ec_2Enum_2ESUC(Y1)) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A(Y0, 150.09/22.65 mono_2Ec_2Earithmetic_2EEXP(Y0, Y1))))))))) & 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EEXP(Y0, mono_2Ec_2Enum_2E0) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EEXP])). 150.09/22.65 tff('167', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EEXP(Y0, mono_2Ec_2Enum_2E0) = 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO)))))), 150.09/22.65 inference('lazy_cnf_and', [status(thm)], ['166'])). 150.09/22.65 tff('168', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2EEXP(X1, mono_2Ec_2Enum_2E0) 150.09/22.65 = mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO)), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['167'])). 150.09/22.65 tff('169', plain, mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0, 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EALT__ZERO])). 150.09/22.65 tff('170', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff('171', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2EEXP(X1, mono_2Ec_2Enum_2E0) 150.09/22.65 = mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0), 150.09/22.65 inference('demod', [status(thm)], ['168', '169', '170'])). 150.09/22.65 tff(thm_2Earithmetic_2EMULT__0, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2A(V0m,mono_2Ec_2Enum_2E0) = 150.09/22.65 mono_2Ec_2Enum_2E0))). 150.09/22.65 tff('172', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2A(Y0, mono_2Ec_2Enum_2E0) = 150.09/22.65 mono_2Ec_2Enum_2E0)))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EMULT__0])). 150.09/22.65 tff('173', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A(X1, mono_2Ec_2Enum_2E0) 150.09/22.65 = mono_2Ec_2Enum_2E0, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['172'])). 150.09/22.65 tff('174', plain, 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Enum_2E0) 150.09/22.65 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0)), 150.09/22.65 inference('demod', [status(thm)], ['46', '47'])). 150.09/22.65 tff(thm_2Earithmetic_2EODD__ADD, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum,V1n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EODD(mono_2Ec_2Earithmetic_2E_2B(V0m,V1n)) <=> 150.09/22.65 (~ 150.09/22.65 (mono_2Ec_2Earithmetic_2EODD(V0m) <=> 150.09/22.65 mono_2Ec_2Earithmetic_2EODD(V1n)))))). 150.09/22.65 tff('175', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EODD( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(Y0, Y1)) <=> 150.09/22.65 (~((mono_2Ec_2Earithmetic_2EODD(Y0) <=> 150.09/22.65 mono_2Ec_2Earithmetic_2EODD(Y1))))))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EODD__ADD])). 150.09/22.65 tff('176', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EODD( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(X1, Y0)) <=> 150.09/22.65 (~((mono_2Ec_2Earithmetic_2EODD(X1) <=> 150.09/22.65 mono_2Ec_2Earithmetic_2EODD(Y0)))))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['175'])). 150.09/22.65 tff('177', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EODD(mono_2Ec_2Earithmetic_2E_2B(X1, X2)) <=> 150.09/22.65 (~((mono_2Ec_2Earithmetic_2EODD(X1) <=> 150.09/22.65 mono_2Ec_2Earithmetic_2EODD(X2))))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['176'])). 150.09/22.65 tff('178', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum, X2 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2EODD(mono_2Ec_2Earithmetic_2E_2B(X1, X2)) 150.09/22.65 != (mono_2Ec_2Earithmetic_2EODD(X1) <=> 150.09/22.65 mono_2Ec_2Earithmetic_2EODD(X2)), 150.09/22.65 inference('simplify nested equalities', [status(thm)], ['177'])). 150.09/22.65 tff(thm_2Earithmetic_2EBIT1, axiom, 150.09/22.65 (![V0n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EBIT1(V0n) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(V0n, 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(V0n, 150.09/22.65 mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Enum_2E0)))))). 150.09/22.65 tff('179', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2EBIT1(Y0) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(Y0, 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(Y0, 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0))))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EBIT1])). 150.09/22.65 tff('180', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(X1) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2B(X1, 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(X1, 150.09/22.65 mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['179'])). 150.09/22.65 tff('181', plain, 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0) 150.09/22.65 = mono_2Ec_2Enum_2ESUC(mono_2Ec_2Enum_2E0), 150.09/22.65 inference('demod', [status(thm)], ['11', '12'])). 150.09/22.65 tff('182', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Enum_2ESUC(X1) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2B(X1, 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0)), 150.09/22.65 inference('demod', [status(thm)], ['52', '53', '54'])). 150.09/22.65 tff('183', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(X1) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2B(X1, mono_2Ec_2Enum_2ESUC(X1)), 150.09/22.65 inference('demod', [status(thm)], ['180', '181', '182'])). 150.09/22.65 tff(thm_2Earithmetic_2ESUC__ONE__ADD, axiom, 150.09/22.65 (![V0n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Enum_2ESUC(V0n) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B(mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT1( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO)), 150.09/22.65 V0n)))). 150.09/22.65 tff('184', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Enum_2ESUC(Y0) = 150.09/22.65 mono_2Ec_2Earithmetic_2E_2B( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO)), 150.09/22.65 Y0))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2ESUC__ONE__ADD])). 150.09/22.65 tff('185', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Enum_2ESUC(X1) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2B( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO)), X1), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['184'])). 150.09/22.65 tff('186', plain, mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0, 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EALT__ZERO])). 150.09/22.65 tff('187', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff('188', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Enum_2ESUC(X1) 150.09/22.65 = mono_2Ec_2Earithmetic_2E_2B( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0), X1), 150.09/22.65 inference('demod', [status(thm)], ['185', '186', '187'])). 150.09/22.65 tff(thm_2Earithmetic_2EMULT__RIGHT__1, axiom, 150.09/22.65 (![V0m:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2A(V0m, 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL(mono_2Ec_2Earithmetic_2EBIT1( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO))) = 150.09/22.65 V0m))). 150.09/22.65 tff('189', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 (mono_2Ec_2Earithmetic_2E_2A(Y0, 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO))) = 150.09/22.65 Y0)))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EMULT__RIGHT__1])). 150.09/22.65 tff('190', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A(X1, 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Earithmetic_2EZERO))) 150.09/22.65 = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['189'])). 150.09/22.65 tff('191', plain, mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0, 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EALT__ZERO])). 150.09/22.65 tff('192', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff('193', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A(X1, 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT1(mono_2Ec_2Enum_2E0)) 150.09/22.65 = X1, 150.09/22.65 inference('demod', [status(thm)], ['190', '191', '192'])). 150.09/22.65 tff(thm_2Earithmetic_2EODD__DOUBLE, axiom, 150.09/22.65 (![V0n:mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2EODD(mono_2Ec_2Enum_2ESUC(mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO)), 150.09/22.65 V0n))))). 150.09/22.65 tff('194', plain, 150.09/22.65 (!!((^[Y0 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2EODD( 150.09/22.65 mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2( 150.09/22.65 mono_2Ec_2Earithmetic_2EZERO)), Y0)))))), 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EODD__DOUBLE])). 150.09/22.65 tff('195', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2EODD( 150.09/22.65 mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2ENUMERAL( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Earithmetic_2EZERO)), 150.09/22.65 X1))), 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['194'])). 150.09/22.65 tff('196', plain, mono_2Ec_2Earithmetic_2EZERO = mono_2Ec_2Enum_2E0, 150.09/22.65 inference('cnf', [status(esa)], [thm_2Earithmetic_2EALT__ZERO])). 150.09/22.65 tff('197', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: mono_2Ec_2Earithmetic_2ENUMERAL(X1) = X1, 150.09/22.65 inference('lazy_cnf_forall', [status(thm)], ['8'])). 150.09/22.65 tff('198', plain, 150.09/22.65 ![X1 : mono_2Etyop_2Enum_2Enum]: 150.09/22.65 mono_2Ec_2Earithmetic_2EODD( 150.09/22.65 mono_2Ec_2Enum_2ESUC( 150.09/22.65 mono_2Ec_2Earithmetic_2E_2A( 150.09/22.65 mono_2Ec_2Earithmetic_2EBIT2(mono_2Ec_2Enum_2E0), X1))), 150.09/22.65 inference('demod', [status(thm)], ['195', '196', '197'])). 150.09/22.65 tff('199', plain, $false, 150.09/22.65 inference('eprover', [status(thm)], 150.09/22.65 ['15', '19', '28', '31', '34', '58', '62', '73', '80', '83', 150.09/22.65 '86', '91', '99', '103', '106', '107', '111', '114', '118', 150.09/22.65 '131', '135', '140', '144', '149', '153', '158', '159', 150.09/22.65 '161', '162', '165', '171', '173', '174', '178', '183', 150.09/22.65 '188', '193', '198'])). 150.09/22.65 150.09/22.65 % SZS output end Refutation 150.09/22.65 150.09/22.65 150.09/22.65 % Terminating... 150.41/22.69 % Runner terminated. 150.41/22.71 % Zipperpin 1.5 exiting 150.41/22.71 EOF