% Time passed: 6570ms
% Effective reasoning time: 4696ms
% Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(59),restrictUniAttempts(true),termOrdering(CPO)>
% Axioms used in derivation (10): thm_2Ebool_2ENOT__CLAUSES, thm_2Enum_2ENOT__SUC, thm_2Ebool_2EREFL__CLAUSE, thm_2Ebool_2EEQ__CLAUSES, thm_2Ebool_2EFALSITY, thm_2Elist_2ENULL__DEF, thm_2Ebool_2ETRUTH, thm_2Earithmetic_2Enum__CASES, thm_2Elist_2EGENLIST__CONS, thm_2Elist_2EGENLIST
% No. of inferences in proof: 100
% No. of processed clauses: 25
% No. of generated clauses: 505
% No. of forward subsumed clauses: 52
% No. of backward subsumed clauses: 2
% No. of ground rewrite rules in store: 7
% No. of non-ground rewrite rules in store: 5
% No. of positive (non-rewrite) units in store: 7
% No. of negative (non-rewrite) units in store: 5
% No. of choice functions detected: 0
% No. of choice instantiations: 0
% SZS status Theorem for /export/starexec/sandbox/benchmark/Problems/HL402239^3.p : 6570 ms resp. 4696 ms w/o parsing
% SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/Problems/HL402239^3.p
thf(tyop_2Emin_2Ebool_type, type, tyop_2Emin_2Ebool: $tType).
thf(tyop_2Enum_2Enum_type, type, tyop_2Enum_2Enum: $tType).
thf(c_2Enum_2E0_type, type, c_2Enum_2E0: tyop_2Enum_2Enum).
thf(c_2Elist_2ECONS_type, type, c_2Elist_2ECONS: !>[TA: $tType]: (TA > ((tyop_2Elist_2Elist @ TA) > (tyop_2Elist_2Elist @ TA)))).
thf(c_2Ebool_2EF_type, type, c_2Ebool_2EF: $o).
thf(c_2Elist_2EGENLIST_type, type, c_2Elist_2EGENLIST: !>[TA: $tType]: ((tyop_2Enum_2Enum > TA) > (tyop_2Enum_2Enum > (tyop_2Elist_2Elist @ TA)))).
thf(c_2Elist_2ENIL_type, type, c_2Elist_2ENIL: !>[TA: $tType]: (tyop_2Elist_2Elist @ TA)).
thf(c_2Elist_2ENULL_type, type, c_2Elist_2ENULL: !>[TA: $tType]: ((tyop_2Elist_2Elist @ TA) > $o)).
thf(c_2Elist_2ESNOC_type, type, c_2Elist_2ESNOC: !>[TA: $tType]: (TA > ((tyop_2Elist_2Elist @ TA) > (tyop_2Elist_2Elist @ TA)))).
thf(c_2Enum_2ESUC_type, type, c_2Enum_2ESUC: (tyop_2Enum_2Enum > tyop_2Enum_2Enum)).
thf(c_2Ebool_2ET_type, type, c_2Ebool_2ET: $o).
thf(c_2Ecombin_2Eo_type, type, c_2Ecombin_2Eo: !>[TA: $tType,TB: $tType,TC: $tType]: ((TC > TB) > ((TA > TC) > (TA > TB)))).
thf(skt1_type, type, skt1: $tType).
thf(sk1_type, type, sk1: tyop_2Enum_2Enum).
thf(sk2_type, type, sk2: (tyop_2Enum_2Enum > skt1)).
thf(sk3_type, type, sk3: (tyop_2Enum_2Enum > tyop_2Enum_2Enum)).
thf(12,axiom,((! [A:tyop_2Enum_2Enum]: ((A = c_2Enum_2E0) | ? [B:tyop_2Enum_2Enum]: (A = (c_2Enum_2ESUC @ B))))),file('/export/starexec/sandbox/benchmark/Problems/HL402239^3.p',thm_2Earithmetic_2Enum__CASES)).
thf(56,plain,((! [A:tyop_2Enum_2Enum]: ((A = c_2Enum_2E0) | ? [B:tyop_2Enum_2Enum]: (A = (c_2Enum_2ESUC @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
thf(8,axiom,((! [TA: $tType]: (! [A:(tyop_2Enum_2Enum > TA)]: ((c_2Elist_2EGENLIST @ TA @ A @ c_2Enum_2E0) = (c_2Elist_2ENIL @ TA)) & ! [A:(tyop_2Enum_2Enum > TA),B:tyop_2Enum_2Enum]: ((c_2Elist_2EGENLIST @ TA @ A @ (c_2Enum_2ESUC @ B)) = (c_2Elist_2ESNOC @ TA @ (A @ B) @ (c_2Elist_2EGENLIST @ TA @ A @ B)))))),file('/export/starexec/sandbox/benchmark/Problems/HL402239^3.p',thm_2Elist_2EGENLIST)).
thf(38,plain,((! [TA: $tType]: (! [A:(tyop_2Enum_2Enum > TA)]: ((c_2Elist_2EGENLIST @ TA @ (A) @ c_2Enum_2E0) = (c_2Elist_2ENIL @ TA)) & ! [A:(tyop_2Enum_2Enum > TA),B:tyop_2Enum_2Enum]: ((c_2Elist_2EGENLIST @ TA @ (A) @ (c_2Enum_2ESUC @ B)) = (c_2Elist_2ESNOC @ TA @ (A @ B) @ (c_2Elist_2EGENLIST @ TA @ (A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
thf(39,plain,(! [TA:$tType,B:tyop_2Enum_2Enum,A:(tyop_2Enum_2Enum > TA)] : (((c_2Elist_2EGENLIST @ TA @ (A) @ (c_2Enum_2ESUC @ B)) = (c_2Elist_2ESNOC @ TA @ (A @ B) @ (c_2Elist_2EGENLIST @ TA @ (A) @ B))))),inference(cnf,[status(esa)],[38])).
thf(41,plain,(! [TA:$tType,B:tyop_2Enum_2Enum,A:(tyop_2Enum_2Enum > TA)] : (((c_2Elist_2EGENLIST @ TA @ (A) @ (c_2Enum_2ESUC @ B)) = (c_2Elist_2ESNOC @ TA @ (A @ B) @ (c_2Elist_2EGENLIST @ TA @ (A) @ B))))),inference(lifteq,[status(thm)],[39])).
thf(42,plain,(! [TA:$tType,B:tyop_2Enum_2Enum,A:(tyop_2Enum_2Enum > TA)] : (((c_2Elist_2EGENLIST @ TA @ (A) @ (c_2Enum_2ESUC @ B)) = (c_2Elist_2ESNOC @ TA @ (A @ B) @ (c_2Elist_2EGENLIST @ TA @ (A) @ B))))),inference(simp,[status(thm)],[41])).
thf(6,axiom,((! [A:$o]: ((~ (~ (A))) = A) & ((~ (c_2Ebool_2ET)) = c_2Ebool_2EF) & ((~ (c_2Ebool_2EF)) = c_2Ebool_2ET))),file('/export/starexec/sandbox/benchmark/Problems/HL402239^3.p',thm_2Ebool_2ENOT__CLAUSES)).
thf(24,plain,((((~ (c_2Ebool_2ET)) = c_2Ebool_2EF) & ((~ (c_2Ebool_2EF)) = c_2Ebool_2ET))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
thf(11,axiom,((! [A:tyop_2Enum_2Enum]: ~ ((c_2Enum_2ESUC @ A) = c_2Enum_2E0))),file('/export/starexec/sandbox/benchmark/Problems/HL402239^3.p',thm_2Enum_2ENOT__SUC)).
thf(52,plain,((! [A:tyop_2Enum_2Enum]: ~ ((c_2Enum_2ESUC @ A) = c_2Enum_2E0))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
thf(3,axiom,((! [TA: $tType]: (! [A:TA]: ((A = A) = c_2Ebool_2ET)))),file('/export/starexec/sandbox/benchmark/Problems/HL402239^3.p',thm_2Ebool_2EREFL__CLAUSE)).
thf(16,plain,((! [TA: $tType]: (c_2Ebool_2ET))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
thf(17,plain,(c_2Ebool_2ET),inference(cnf,[status(esa)],[16])).
thf(40,plain,(! [TA:$tType,A:(tyop_2Enum_2Enum > TA)] : (((c_2Elist_2EGENLIST @ TA @ (A) @ c_2Enum_2E0) = (c_2Elist_2ENIL @ TA)))),inference(cnf,[status(esa)],[38])).
thf(43,plain,(! [TA:$tType,A:(tyop_2Enum_2Enum > TA)] : (((c_2Elist_2EGENLIST @ TA @ (A) @ c_2Enum_2E0) = (c_2Elist_2ENIL @ TA)))),inference(lifteq,[status(thm)],[40])).
thf(140,plain,(! [TB:$tType,C:tyop_2Enum_2Enum,B:(tyop_2Enum_2Enum > T@),A:(tyop_2Enum_2Enum > T@)] : (((c_2Elist_2ESNOC @ T@ @ (B @ C) @ (c_2Elist_2ENIL @ T@)) = (c_2Elist_2EGENLIST @ T@ @ (B) @ (c_2Enum_2ESUC @ C))) | ((c_2Elist_2EGENLIST @ T@ @ (A) @ c_2Enum_2E0) != (c_2Elist_2EGENLIST @ T@ @ (B) @ C)))),inference(paramod_ordered,[status(thm)],[43,42])).
thf(141,plain,(! [TB:$tType,A:(tyop_2Enum_2Enum > T@)] : (((c_2Elist_2ESNOC @ T@ @ (A @ c_2Enum_2E0) @ (c_2Elist_2ENIL @ T@)) = (c_2Elist_2EGENLIST @ T@ @ (A) @ (c_2Enum_2ESUC @ c_2Enum_2E0))))),inference(pattern_uni,[status(thm)],[140:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(c_2Enum_2E0))]])).
thf(161,plain,(! [TA:$tType,A:(tyop_2Enum_2Enum > TA)] : (((c_2Elist_2ESNOC @ TA @ (A @ c_2Enum_2E0) @ (c_2Elist_2ENIL @ TA)) = (c_2Elist_2EGENLIST @ TA @ (A) @ (c_2Enum_2ESUC @ c_2Enum_2E0))))),inference(simp,[status(thm)],[141])).
thf(201,plain,(! [A:(tyop_2Enum_2Enum > $o)] : (((c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ENIL @ $o)) = (c_2Elist_2EGENLIST @ $o @ (A) @ (c_2Enum_2ESUC @ c_2Enum_2E0))) | (c_2Ebool_2ET != (A @ c_2Enum_2E0)))),inference(paramod_ordered,[status(thm)],[17,161])).
thf(215,plain,(((c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ENIL @ $o)) = (c_2Elist_2EGENLIST @ $o @ (^ [A:tyop_2Enum_2Enum]: (c_2Ebool_2ET)) @ (c_2Enum_2ESUC @ c_2Enum_2E0)))),inference(pre_uni,[status(thm)],[201:[bind(A, $thf(^ [B:tyop_2Enum_2Enum]: (c_2Ebool_2ET)))]])).
thf(261,plain,(((c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ENIL @ $o)) = (c_2Elist_2EGENLIST @ $o @ (^ [A:tyop_2Enum_2Enum]: ($true)) @ (c_2Enum_2ESUC @ c_2Enum_2E0)))),inference(rewrite,[status(thm)],[215,17])).
thf(10,axiom,((! [TA: $tType]: (! [A:tyop_2Enum_2Enum,B:(tyop_2Enum_2Enum > TA)]: ((c_2Elist_2EGENLIST @ TA @ B @ (c_2Enum_2ESUC @ A)) = (c_2Elist_2ECONS @ TA @ (B @ c_2Enum_2E0) @ (c_2Elist_2EGENLIST @ TA @ (c_2Ecombin_2Eo @ tyop_2Enum_2Enum @ TA @ tyop_2Enum_2Enum @ B @ c_2Enum_2ESUC) @ A)))))),file('/export/starexec/sandbox/benchmark/Problems/HL402239^3.p',thm_2Elist_2EGENLIST__CONS)).
thf(49,plain,((! [TA: $tType]: (! [A:tyop_2Enum_2Enum,B:(tyop_2Enum_2Enum > TA)]: ((c_2Elist_2EGENLIST @ TA @ (B) @ (c_2Enum_2ESUC @ A)) = (c_2Elist_2ECONS @ TA @ (B @ c_2Enum_2E0) @ (c_2Elist_2EGENLIST @ TA @ (c_2Ecombin_2Eo @ tyop_2Enum_2Enum @ TA @ tyop_2Enum_2Enum @ B @ c_2Enum_2ESUC) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
thf(50,plain,(! [TA:$tType,B:(tyop_2Enum_2Enum > TA),A:tyop_2Enum_2Enum] : (((c_2Elist_2EGENLIST @ TA @ (B) @ (c_2Enum_2ESUC @ A)) = (c_2Elist_2ECONS @ TA @ (B @ c_2Enum_2E0) @ (c_2Elist_2EGENLIST @ TA @ (c_2Ecombin_2Eo @ tyop_2Enum_2Enum @ TA @ tyop_2Enum_2Enum @ B @ c_2Enum_2ESUC) @ A))))),inference(cnf,[status(esa)],[49])).
thf(51,plain,(! [TA:$tType,B:(tyop_2Enum_2Enum > TA),A:tyop_2Enum_2Enum] : (((c_2Elist_2EGENLIST @ TA @ (B) @ (c_2Enum_2ESUC @ A)) = (c_2Elist_2ECONS @ TA @ (B @ c_2Enum_2E0) @ (c_2Elist_2EGENLIST @ TA @ (c_2Ecombin_2Eo @ tyop_2Enum_2Enum @ TA @ tyop_2Enum_2Enum @ B @ c_2Enum_2ESUC) @ A))))),inference(lifteq,[status(thm)],[50])).
thf(326,plain,(! [B:(tyop_2Enum_2Enum > $o),A:tyop_2Enum_2Enum] : (((c_2Elist_2ECONS @ $o @ (B @ c_2Enum_2E0) @ (c_2Elist_2EGENLIST @ $o @ (c_2Ecombin_2Eo @ tyop_2Enum_2Enum @ $o @ tyop_2Enum_2Enum @ B @ c_2Enum_2ESUC) @ A)) = (c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ENIL @ $o))) | ((c_2Elist_2EGENLIST @ $o @ (B) @ (c_2Enum_2ESUC @ A)) != (c_2Elist_2EGENLIST @ $o @ (^ [C:tyop_2Enum_2Enum]: ($true)) @ (c_2Enum_2ESUC @ c_2Enum_2E0))))),inference(paramod_ordered,[status(thm)],[51,261])).
thf(327,plain,(((c_2Elist_2ECONS @ $o @ $true @ (c_2Elist_2EGENLIST @ $o @ (c_2Ecombin_2Eo @ tyop_2Enum_2Enum @ $o @ tyop_2Enum_2Enum @ (^ [A:tyop_2Enum_2Enum]: ($true)) @ c_2Enum_2ESUC) @ c_2Enum_2E0)) = (c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ENIL @ $o)))),inference(pattern_uni,[status(thm)],[326:[bind(A, $thf(c_2Enum_2E0)),bind(B, $thf(^ [C:tyop_2Enum_2Enum]: ($true)))]])).
thf(1028,plain,(! [A:(tyop_2Enum_2Enum > $o)] : (((c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ENIL @ $o)) = (c_2Elist_2ECONS @ $o @ $true @ (c_2Elist_2ENIL @ $o))) | ((c_2Elist_2EGENLIST @ $o @ (A) @ c_2Enum_2E0) != (c_2Elist_2EGENLIST @ $o @ (c_2Ecombin_2Eo @ tyop_2Enum_2Enum @ $o @ tyop_2Enum_2Enum @ (^ [B:tyop_2Enum_2Enum]: ($true)) @ c_2Enum_2ESUC) @ c_2Enum_2E0)))),inference(paramod_ordered,[status(thm)],[43,327])).
thf(1029,plain,(((c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ENIL @ $o)) = (c_2Elist_2ECONS @ $o @ $true @ (c_2Elist_2ENIL @ $o)))),inference(pattern_uni,[status(thm)],[1028:[bind(A, $thf(c_2Ecombin_2Eo @ tyop_2Enum_2Enum @ $o @ tyop_2Enum_2Enum @ (^ [B:tyop_2Enum_2Enum]: ($true)) @ c_2Enum_2ESUC))]])).
thf(1232,plain,(((c_2Elist_2ECONS @ $o @ $true @ (c_2Elist_2ENIL @ $o)) = (c_2Elist_2EGENLIST @ $o @ (^ [A:tyop_2Enum_2Enum]: ($true)) @ (c_2Enum_2ESUC @ c_2Enum_2E0)))),inference(rewrite,[status(thm)],[261,1029])).
thf(7,axiom,((! [A:$o]: (((c_2Ebool_2ET = A) = A) & ((A = c_2Ebool_2ET) = A) & ((c_2Ebool_2EF = A) = (~ (A))) & ((A = c_2Ebool_2EF) = (~ (A)))))),file('/export/starexec/sandbox/benchmark/Problems/HL402239^3.p',thm_2Ebool_2EEQ__CLAUSES)).
thf(29,plain,((! [A:$o]: (((c_2Ebool_2ET = A) = A) & ((A = c_2Ebool_2ET) = A) & ((c_2Ebool_2EF = A) = (~ (A))) & ((A = c_2Ebool_2EF) = (~ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
thf(9,axiom,((! [TA: $tType]: (((c_2Elist_2ENULL @ TA @ (c_2Elist_2ENIL @ TA)) = c_2Ebool_2ET) & ! [A:TA,B:(tyop_2Elist_2Elist @ TA)]: ((c_2Elist_2ENULL @ TA @ (c_2Elist_2ECONS @ TA @ A @ B)) = c_2Ebool_2EF)))),file('/export/starexec/sandbox/benchmark/Problems/HL402239^3.p',thm_2Elist_2ENULL__DEF)).
thf(44,plain,((! [TA: $tType]: (((c_2Elist_2ENULL @ TA @ (c_2Elist_2ENIL @ TA)) = c_2Ebool_2ET) & ! [A:TA,B:(tyop_2Elist_2Elist @ TA)]: ((c_2Elist_2ENULL @ TA @ (c_2Elist_2ECONS @ TA @ A @ B)) = c_2Ebool_2EF)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
thf(46,plain,(! [TA:$tType] : (((c_2Elist_2ENULL @ TA @ (c_2Elist_2ENIL @ TA)) = c_2Ebool_2ET))),inference(cnf,[status(esa)],[44])).
thf(48,plain,(! [TA:$tType] : ((c_2Ebool_2ET = (c_2Elist_2ENULL @ TA @ (c_2Elist_2ENIL @ TA))))),inference(lifteq,[status(thm)],[46])).
thf(85,plain,(! [TA:$tType] : ((c_2Elist_2ENULL @ TA @ (c_2Elist_2ENIL @ TA)))),inference(rewrite,[status(thm)],[48,17])).
thf(1,conjecture,((! [TA: $tType]: (! [A:tyop_2Enum_2Enum,B:(tyop_2Enum_2Enum > TA)]: ((c_2Elist_2ENULL @ TA @ (c_2Elist_2EGENLIST @ TA @ B @ A)) = (A = c_2Enum_2E0))))),file('/export/starexec/sandbox/benchmark/Problems/HL402239^3.p',thm_2Elist_2ENULL__GENLIST)).
thf(2,negated_conjecture,((~ (! [TA: $tType]: (! [A:tyop_2Enum_2Enum,B:(tyop_2Enum_2Enum > TA)]: ((c_2Elist_2ENULL @ TA @ (c_2Elist_2EGENLIST @ TA @ B @ A)) = (A = c_2Enum_2E0)))))),inference(neg_conjecture,[status(cth)],[1])).
thf(13,plain,((~ (! [TA: $tType]: (! [A:tyop_2Enum_2Enum,B:(tyop_2Enum_2Enum > TA)]: ((c_2Elist_2ENULL @ TA @ (c_2Elist_2EGENLIST @ TA @ (B) @ A)) = (A = c_2Enum_2E0)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(14,plain,((~ ((c_2Elist_2ENULL @ skt1 @ (c_2Elist_2EGENLIST @ skt1 @ (sk2) @ sk1)) = (sk1 = c_2Enum_2E0)))),inference(cnf,[status(esa)],[13])).
thf(15,plain,(((c_2Elist_2ENULL @ skt1 @ (c_2Elist_2EGENLIST @ skt1 @ (sk2) @ sk1)) != (sk1 = c_2Enum_2E0))),inference(lifteq,[status(thm)],[14])).
thf(63,plain,((c_2Elist_2ENULL @ skt1 @ (c_2Elist_2EGENLIST @ skt1 @ (sk2) @ sk1)) | (sk1 = c_2Enum_2E0)),inference(bool_ext,[status(thm)],[15])).
thf(65,plain,((sk1 = c_2Enum_2E0) | (c_2Elist_2ENULL @ skt1 @ (c_2Elist_2EGENLIST @ skt1 @ (sk2) @ sk1))),inference(lifteq,[status(thm)],[63])).
thf(62,plain,((~ (c_2Elist_2ENULL @ skt1 @ (c_2Elist_2EGENLIST @ skt1 @ (sk2) @ sk1))) | (~ (sk1 = c_2Enum_2E0))),inference(bool_ext,[status(thm)],[15])).
thf(64,plain,((sk1 != c_2Enum_2E0) | (~ (c_2Elist_2ENULL @ skt1 @ (c_2Elist_2EGENLIST @ skt1 @ (sk2) @ sk1)))),inference(lifteq,[status(thm)],[62])).
thf(107,plain,(! [A:(tyop_2Enum_2Enum > skt1)] : ((sk1 != c_2Enum_2E0) | (~ (c_2Elist_2ENULL @ skt1 @ (c_2Elist_2ENIL @ skt1))) | ((c_2Elist_2EGENLIST @ skt1 @ (A) @ c_2Enum_2E0) != (c_2Elist_2EGENLIST @ skt1 @ (sk2) @ sk1)))),inference(paramod_ordered,[status(thm)],[43,64])).
thf(114,plain,(! [A:(tyop_2Enum_2Enum > skt1)] : ((sk1 != c_2Enum_2E0) | (~ (c_2Elist_2ENULL @ skt1 @ (c_2Elist_2ENIL @ skt1))) | ((A) != (sk2)) | (sk1 != c_2Enum_2E0))),inference(simp,[status(thm)],[107])).
thf(116,plain,((sk1 != c_2Enum_2E0) | (~ (c_2Elist_2ENULL @ skt1 @ (c_2Elist_2ENIL @ skt1)))),inference(simp,[status(thm)],[114])).
thf(121,plain,((sk1 != c_2Enum_2E0) | ~ ($true)),inference(rewrite,[status(thm)],[116,85])).
thf(122,plain,((sk1 != c_2Enum_2E0)),inference(simp,[status(thm)],[121])).
thf(123,plain,((c_2Elist_2ENULL @ skt1 @ (c_2Elist_2EGENLIST @ skt1 @ (sk2) @ sk1))),inference(simplifyReflect,[status(thm)],[65,122])).
thf(136,plain,(! [B:tyop_2Enum_2Enum,A:(tyop_2Enum_2Enum > $o)] : (((c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2EGENLIST @ $o @ (A) @ B)) = (c_2Elist_2EGENLIST @ $o @ (A) @ (c_2Enum_2ESUC @ B))) | ((c_2Elist_2ENULL @ skt1 @ (c_2Elist_2EGENLIST @ skt1 @ (sk2) @ sk1)) != (A @ B)))),inference(paramod_ordered,[status(thm)],[123,42])).
thf(156,plain,(((c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2EGENLIST @ $o @ (^ [A:tyop_2Enum_2Enum]: (c_2Elist_2ENULL @ skt1 @ (c_2Elist_2EGENLIST @ skt1 @ sk2 @ A))) @ sk1)) = (c_2Elist_2EGENLIST @ $o @ (^ [A:tyop_2Enum_2Enum]: (c_2Elist_2ENULL @ skt1 @ (c_2Elist_2EGENLIST @ skt1 @ sk2 @ A))) @ (c_2Enum_2ESUC @ sk1)))),inference(pre_uni,[status(thm)],[136:[bind(A, $thf(^ [C:tyop_2Enum_2Enum]: (c_2Elist_2ENULL @ skt1 @ (c_2Elist_2EGENLIST @ skt1 @ sk2 @ C)))),bind(B, $thf(sk1))]])).
thf(57,plain,(! [A:tyop_2Enum_2Enum] : ((A = c_2Enum_2E0) | (A = (c_2Enum_2ESUC @ (sk3 @ A))))),inference(cnf,[status(esa)],[56])).
thf(58,plain,(! [A:tyop_2Enum_2Enum] : ((A = c_2Enum_2E0) | ((c_2Enum_2ESUC @ (sk3 @ A)) = A))),inference(lifteq,[status(thm)],[57])).
thf(204,plain,(! [A:(tyop_2Enum_2Enum > skt1)] : ((c_2Elist_2ENULL @ skt1 @ (c_2Elist_2ESNOC @ skt1 @ (A @ c_2Enum_2E0) @ (c_2Elist_2ENIL @ skt1))) | ((c_2Elist_2EGENLIST @ skt1 @ (A) @ (c_2Enum_2ESUC @ c_2Enum_2E0)) != (c_2Elist_2EGENLIST @ skt1 @ (sk2) @ sk1)))),inference(paramod_ordered,[status(thm)],[161,123])).
thf(220,plain,(! [A:(tyop_2Enum_2Enum > skt1)] : ((c_2Elist_2ENULL @ skt1 @ (c_2Elist_2ESNOC @ skt1 @ (A @ c_2Enum_2E0) @ (c_2Elist_2ENIL @ skt1))) | ((A) != (sk2)) | ((c_2Enum_2ESUC @ c_2Enum_2E0) != sk1))),inference(simp,[status(thm)],[204])).
thf(241,plain,((c_2Elist_2ENULL @ skt1 @ (c_2Elist_2ESNOC @ skt1 @ (sk2 @ c_2Enum_2E0) @ (c_2Elist_2ENIL @ skt1))) | ((c_2Enum_2ESUC @ c_2Enum_2E0) != sk1)),inference(simp,[status(thm)],[220])).
thf(45,plain,(! [TA:$tType,B:(tyop_2Elist_2Elist @ TA),A:TA] : (((c_2Elist_2ENULL @ TA @ (c_2Elist_2ECONS @ TA @ A @ B)) = c_2Ebool_2EF))),inference(cnf,[status(esa)],[44])).
thf(47,plain,(! [TA:$tType,B:(tyop_2Elist_2Elist @ TA),A:TA] : (((c_2Elist_2ENULL @ TA @ (c_2Elist_2ECONS @ TA @ A @ B)) = c_2Ebool_2EF))),inference(lifteq,[status(thm)],[45])).
thf(5,axiom,((! [A:$o]: ((c_2Ebool_2EF) => (A)))),file('/export/starexec/sandbox/benchmark/Problems/HL402239^3.p',thm_2Ebool_2EFALSITY)).
thf(19,plain,((! [A:$o]: ((c_2Ebool_2EF) => (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
thf(22,plain,(((c_2Ebool_2EF) => ($false))),inference(instance,[status(thm)],[19])).
thf(23,plain,(~ (c_2Ebool_2EF)),inference(simp,[status(thm)],[22])).
thf(182,plain,(! [TA:$tType,B:(tyop_2Elist_2Elist @ TA),A:TA] : ((~ (c_2Elist_2ENULL @ TA @ (c_2Elist_2ECONS @ TA @ A @ B))))),inference(rewrite,[status(thm)],[47,23])).
thf(349,plain,(! [TB:$tType,D:(tyop_2Elist_2Elist @ T@),C:T@,B:(tyop_2Enum_2Enum > T@),A:tyop_2Enum_2Enum] : ((~ (c_2Elist_2ENULL @ T@ @ (c_2Elist_2EGENLIST @ T@ @ (B) @ (c_2Enum_2ESUC @ A)))) | ((c_2Elist_2ECONS @ T@ @ (B @ c_2Enum_2E0) @ (c_2Elist_2EGENLIST @ T@ @ (c_2Ecombin_2Eo @ tyop_2Enum_2Enum @ T@ @ tyop_2Enum_2Enum @ B @ c_2Enum_2ESUC) @ A)) != (c_2Elist_2ECONS @ T@ @ C @ D)))),inference(paramod_ordered,[status(thm)],[51,182])).
thf(369,plain,(! [TB:$tType,B:(tyop_2Enum_2Enum > T@),A:tyop_2Enum_2Enum] : ((~ (c_2Elist_2ENULL @ T@ @ (c_2Elist_2EGENLIST @ T@ @ (B) @ (c_2Enum_2ESUC @ A)))))),inference(pre_uni,[status(thm)],[349:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(B @ c_2Enum_2E0)),bind(D, $thf(c_2Elist_2EGENLIST @ T? @ (c_2Ecombin_2Eo @ tyop_2Enum_2Enum @ T? @ tyop_2Enum_2Enum @ B @ c_2Enum_2ESUC) @ A))]])).
thf(418,plain,(! [TA:$tType,B:(tyop_2Enum_2Enum > TA),A:tyop_2Enum_2Enum] : ((~ (c_2Elist_2ENULL @ TA @ (c_2Elist_2EGENLIST @ TA @ (B) @ (c_2Enum_2ESUC @ A)))))),inference(simp,[status(thm)],[369])).
thf(582,plain,(! [TB:$tType,C:(tyop_2Enum_2Enum > T@),B:tyop_2Enum_2Enum,A:(tyop_2Enum_2Enum > T@)] : ((~ (c_2Elist_2ENULL @ T@ @ (c_2Elist_2ESNOC @ T@ @ (A @ c_2Enum_2E0) @ (c_2Elist_2ENIL @ T@)))) | ((c_2Elist_2EGENLIST @ T@ @ (A) @ (c_2Enum_2ESUC @ c_2Enum_2E0)) != (c_2Elist_2EGENLIST @ T@ @ (C) @ (c_2Enum_2ESUC @ B))))),inference(paramod_ordered,[status(thm)],[161,418])).
thf(583,plain,(! [TB:$tType,A:(tyop_2Enum_2Enum > T@)] : ((~ (c_2Elist_2ENULL @ T@ @ (c_2Elist_2ESNOC @ T@ @ (A @ c_2Enum_2E0) @ (c_2Elist_2ENIL @ T@)))))),inference(pattern_uni,[status(thm)],[582:[bind(A, $thf(A)),bind(B, $thf(c_2Enum_2E0)),bind(C, $thf(A))]])).
thf(594,plain,(! [TA:$tType,A:(tyop_2Enum_2Enum > TA)] : ((~ (c_2Elist_2ENULL @ TA @ (c_2Elist_2ESNOC @ TA @ (A @ c_2Enum_2E0) @ (c_2Elist_2ENIL @ TA)))))),inference(simp,[status(thm)],[583])).
thf(716,plain,($false | ((c_2Enum_2ESUC @ c_2Enum_2E0) != sk1)),inference(rewrite,[status(thm)],[241,594])).
thf(717,plain,(((c_2Enum_2ESUC @ c_2Enum_2E0) != sk1)),inference(simp,[status(thm)],[716])).
thf(796,plain,(! [A:tyop_2Enum_2Enum] : ((A = c_2Enum_2E0) | (A != sk1) | ((c_2Enum_2ESUC @ (sk3 @ A)) != (c_2Enum_2ESUC @ c_2Enum_2E0)))),inference(paramod_ordered,[status(thm)],[58,717])).
thf(797,plain,((sk1 = c_2Enum_2E0) | ((c_2Enum_2ESUC @ (sk3 @ sk1)) != (c_2Enum_2ESUC @ c_2Enum_2E0))),inference(simp,[status(thm)],[796])).
thf(805,plain,(((c_2Enum_2ESUC @ (sk3 @ sk1)) != (c_2Enum_2ESUC @ c_2Enum_2E0))),inference(simplifyReflect,[status(thm)],[797,122])).
thf(104,plain,(! [TB:$tType,A:(tyop_2Enum_2Enum > T@)] : ((c_2Elist_2ENULL @ T@ @ (c_2Elist_2EGENLIST @ T@ @ (A) @ c_2Enum_2E0)) | ((c_2Elist_2ENIL @ T@) != (c_2Elist_2ENIL @ T@)))),inference(paramod_ordered,[status(thm)],[43,85])).
thf(105,plain,(! [TB:$tType,A:(tyop_2Enum_2Enum > T@)] : ((c_2Elist_2ENULL @ T@ @ (c_2Elist_2EGENLIST @ T@ @ (A) @ c_2Enum_2E0)))),inference(pattern_uni,[status(thm)],[104:[]])).
thf(118,plain,(! [TA:$tType,A:(tyop_2Enum_2Enum > TA)] : ((c_2Elist_2ENULL @ TA @ (c_2Elist_2EGENLIST @ TA @ (A) @ c_2Enum_2E0)))),inference(simp,[status(thm)],[105])).
thf(798,plain,((sk1 = c_2Enum_2E0) | ((sk3 @ sk1) != c_2Enum_2E0)),inference(simp,[status(thm)],[796])).
thf(804,plain,(((sk3 @ sk1) != c_2Enum_2E0)),inference(simplifyReflect,[status(thm)],[798,122])).
thf(4,axiom,(c_2Ebool_2ET),file('/export/starexec/sandbox/benchmark/Problems/HL402239^3.p',thm_2Ebool_2ETRUTH)).
thf(18,plain,(c_2Ebool_2ET),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
thf(264,plain,(! [B:tyop_2Enum_2Enum,A:(tyop_2Enum_2Enum > $o)] : (((c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ENIL @ $o)) = (c_2Elist_2ESNOC @ $o @ (A @ B) @ (c_2Elist_2EGENLIST @ $o @ (A) @ B))) | ((c_2Elist_2EGENLIST @ $o @ (^ [C:tyop_2Enum_2Enum]: ($true)) @ (c_2Enum_2ESUC @ c_2Enum_2E0)) != (c_2Elist_2EGENLIST @ $o @ (A) @ (c_2Enum_2ESUC @ B))))),inference(paramod_ordered,[status(thm)],[261,42])).
thf(265,plain,(((c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ENIL @ $o)) = (c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2EGENLIST @ $o @ (^ [A:tyop_2Enum_2Enum]: ($true)) @ c_2Enum_2E0)))),inference(pattern_uni,[status(thm)],[264:[bind(A, $thf(^ [C:tyop_2Enum_2Enum]: ($true))),bind(B, $thf(c_2Enum_2E0))]])).
thf(432,plain,(((c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2EGENLIST @ $o @ (^ [A:tyop_2Enum_2Enum]: ($true)) @ c_2Enum_2E0)) = (c_2Elist_2EGENLIST @ $o @ (^ [A:tyop_2Enum_2Enum]: ($true)) @ (c_2Enum_2ESUC @ c_2Enum_2E0))) | ((c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ENIL @ $o)) != (c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ENIL @ $o)))),inference(paramod_ordered,[status(thm)],[265,261])).
thf(433,plain,(((c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2EGENLIST @ $o @ (^ [A:tyop_2Enum_2Enum]: ($true)) @ c_2Enum_2E0)) = (c_2Elist_2EGENLIST @ $o @ (^ [A:tyop_2Enum_2Enum]: ($true)) @ (c_2Enum_2ESUC @ c_2Enum_2E0)))),inference(pattern_uni,[status(thm)],[432:[]])).
thf(587,plain,(! [B:(tyop_2Enum_2Enum > $o),A:tyop_2Enum_2Enum] : ((~ (c_2Elist_2ENULL @ $o @ (c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2EGENLIST @ $o @ (^ [C:tyop_2Enum_2Enum]: ($true)) @ c_2Enum_2E0)))) | ((c_2Elist_2EGENLIST @ $o @ (^ [C:tyop_2Enum_2Enum]: ($true)) @ (c_2Enum_2ESUC @ c_2Enum_2E0)) != (c_2Elist_2EGENLIST @ $o @ (B) @ (c_2Enum_2ESUC @ A))))),inference(paramod_ordered,[status(thm)],[433,418])).
thf(588,plain,((~ (c_2Elist_2ENULL @ $o @ (c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2EGENLIST @ $o @ (^ [A:tyop_2Enum_2Enum]: ($true)) @ c_2Enum_2E0))))),inference(pattern_uni,[status(thm)],[587:[bind(A, $thf(c_2Enum_2E0)),bind(B, $thf(^ [C:tyop_2Enum_2Enum]: ($true)))]])).
thf(53,plain,((~ (? [A:tyop_2Enum_2Enum]: ((c_2Enum_2ESUC @ A) = c_2Enum_2E0)))),inference(miniscope,[status(thm)],[52])).
thf(54,plain,(! [A:tyop_2Enum_2Enum] : ((~ ((c_2Enum_2ESUC @ A) = c_2Enum_2E0)))),inference(cnf,[status(esa)],[53])).
thf(55,plain,(! [A:tyop_2Enum_2Enum] : (((c_2Enum_2ESUC @ A) != c_2Enum_2E0))),inference(lifteq,[status(thm)],[54])).
thf(267,plain,(! [B:tyop_2Enum_2Enum,A:(tyop_2Enum_2Enum > $o)] : (((c_2Elist_2ESNOC @ $o @ (A @ B) @ (c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ENIL @ $o))) = (c_2Elist_2EGENLIST @ $o @ (A) @ (c_2Enum_2ESUC @ B))) | ((c_2Elist_2EGENLIST @ $o @ (^ [C:tyop_2Enum_2Enum]: ($true)) @ (c_2Enum_2ESUC @ c_2Enum_2E0)) != (c_2Elist_2EGENLIST @ $o @ (A) @ B)))),inference(paramod_ordered,[status(thm)],[261,42])).
thf(268,plain,(((c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ENIL @ $o))) = (c_2Elist_2EGENLIST @ $o @ (^ [A:tyop_2Enum_2Enum]: ($true)) @ (c_2Enum_2ESUC @ (c_2Enum_2ESUC @ c_2Enum_2E0))))),inference(pattern_uni,[status(thm)],[267:[bind(A, $thf(^ [C:tyop_2Enum_2Enum]: ($true))),bind(B, $thf(c_2Enum_2ESUC @ c_2Enum_2E0))]])).
thf(859,plain,(! [B:(tyop_2Enum_2Enum > $o),A:tyop_2Enum_2Enum] : ((~ (c_2Elist_2ENULL @ $o @ (c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ENIL @ $o))))) | ((c_2Elist_2EGENLIST @ $o @ (^ [C:tyop_2Enum_2Enum]: ($true)) @ (c_2Enum_2ESUC @ (c_2Enum_2ESUC @ c_2Enum_2E0))) != (c_2Elist_2EGENLIST @ $o @ (B) @ (c_2Enum_2ESUC @ A))))),inference(paramod_ordered,[status(thm)],[268,418])).
thf(860,plain,((~ (c_2Elist_2ENULL @ $o @ (c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ENIL @ $o)))))),inference(pattern_uni,[status(thm)],[859:[bind(A, $thf(c_2Enum_2ESUC @ c_2Enum_2E0)),bind(B, $thf(^ [C:tyop_2Enum_2Enum]: ($true)))]])).
thf(1236,plain,((~ (c_2Elist_2ENULL @ $o @ (c_2Elist_2ESNOC @ $o @ $true @ (c_2Elist_2ECONS @ $o @ $true @ (c_2Elist_2ENIL @ $o)))))),inference(rewrite,[status(thm)],[860,1029])).
thf(1409,plain,($false),inference(cvc4,[status(thm)],[56,42,24,52,1232,29,85,38,156,13,805,161,17,44,118,49,804,594,1029,123,18,182,16,717,43,588,55,418,23,58,433,51,19,1236,122])).
% SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/Problems/HL402239^3.p

54.3199999999997/7.06999999999971	EOF