% Time passed: 3698ms
% Effective reasoning time: 2359ms
% 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 (12): thm_2Epair_2ESND, logicdef_2E_3D, thm_2Ebool_2EREFL__CLAUSE, thm_2Ealist_2EMEM__fmap__to__alist__FLOOKUP, logicdef_2E_5C_2F, thm_2Epair_2EFST, quantdef_2E_21, thm_2Ebool_2ETRUTH, logicdef_2E_3D_3D_3E, logicdef_2E_2F_5C, logicdef_2E_7E, quantdef_2E_3F
% No. of inferences in proof: 64
% No. of processed clauses: 19
% No. of generated clauses: 4
% No. of forward subsumed clauses: 1
% No. of backward subsumed clauses: 0
% No. of ground rewrite rules in store: 15
% No. of non-ground rewrite rules in store: 1
% No. of positive (non-rewrite) units in store: 0
% No. of negative (non-rewrite) units in store: 1
% No. of choice functions detected: 0
% No. of choice instantiations: 0
% SZS status Theorem for /export/starexec/sandbox/benchmark/Problems/HL405179^3.p : 3698 ms resp. 2359 ms w/o parsing
% SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/Problems/HL405179^3.p
thf(tyop_2Emin_2Ebool_type, type, tyop_2Emin_2Ebool: $tType).
thf(c_2Ebool_2E_21_type, type, c_2Ebool_2E_21: !>[TA: $tType]: ((TA > $o) > $o)).
thf(c_2Epair_2E_2C_type, type, c_2Epair_2E_2C: !>[TA: $tType,TB: $tType]: (TA > (TB > (tyop_2Epair_2Eprod @ TA @ TB)))).
thf(c_2Ebool_2E_2F_5C_type, type, c_2Ebool_2E_2F_5C: ($o > ($o > $o))).
thf(c_2Emin_2E_3D_type, type, c_2Emin_2E_3D: !>[TA: $tType]: (TA > (TA > $o))).
thf(c_2Emin_2E_3D_3D_3E_type, type, c_2Emin_2E_3D_3D_3E: ($o > ($o > $o))).
thf(c_2Ebool_2E_3F_type, type, c_2Ebool_2E_3F: !>[TA: $tType]: ((TA > $o) > $o)).
thf(c_2Efinite__map_2EFLOOKUP_type, type, c_2Efinite__map_2EFLOOKUP: !>[TA: $tType,TB: $tType]: ((tyop_2Efinite__map_2Efmap @ TA @ TB) > (TA > (tyop_2Eoption_2Eoption @ TB)))).
thf(c_2Epair_2EFST_type, type, c_2Epair_2EFST: !>[TA: $tType,TB: $tType]: ((tyop_2Epair_2Eprod @ TA @ TB) > TA)).
thf(c_2Ebool_2EIN_type, type, c_2Ebool_2EIN: !>[TA: $tType]: (TA > ((TA > $o) > $o))).
thf(c_2Elist_2ELIST__TO__SET_type, type, c_2Elist_2ELIST__TO__SET: !>[TA: $tType]: ((tyop_2Elist_2Elist @ TA) > (TA > $o))).
thf(c_2Epair_2ESND_type, type, c_2Epair_2ESND: !>[TA: $tType,TB: $tType]: ((tyop_2Epair_2Eprod @ TA @ TB) > TB)).
thf(c_2Eoption_2ESOME_type, type, c_2Eoption_2ESOME: !>[TA: $tType]: (TA > (tyop_2Eoption_2Eoption @ TA))).
thf(c_2Ebool_2ET_type, type, c_2Ebool_2ET: $o).
thf(c_2Ebool_2E_5C_2F_type, type, c_2Ebool_2E_5C_2F: ($o > ($o > $o))).
thf(c_2Ealist_2Efmap__to__alist_type, type, c_2Ealist_2Efmap__to__alist: !>[TA: $tType,TB: $tType]: ((tyop_2Efinite__map_2Efmap @ TA @ TB) > (tyop_2Elist_2Elist @ (tyop_2Epair_2Eprod @ TA @ TB)))).
thf(c_2Ebool_2E_7E_type, type, c_2Ebool_2E_7E: ($o > $o)).
thf(skt1_type, type, skt1: $tType).
thf(skt2_type, type, skt2: $tType).
thf(sk1_type, type, sk1: skt1).
thf(sk2_type, type, sk2: skt2).
thf(sk3_type, type, sk3: (tyop_2Efinite__map_2Efmap @ skt1 @ skt2)).
thf(3,axiom,((! [A:$o,B:$o]: ((c_2Ebool_2E_2F_5C @ A @ B) = ((A) & (B))))),file('/export/starexec/sandbox/benchmark/Problems/HL405179^3.p',logicdef_2E_2F_5C)).
thf(18,plain,((! [A:$o,B:$o]: ((c_2Ebool_2E_2F_5C @ A @ B) = ((A) & (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
thf(23,plain,(((c_2Ebool_2E_2F_5C @ $false @ $true) = (($false) & ($true)))),inference(instance,[status(thm)],[18])).
thf(24,plain,((~ (c_2Ebool_2E_2F_5C @ $false @ $true))),inference(simp,[status(thm)],[23])).
thf(7,axiom,((! [TA: $tType]: (! [A:TA,B:TA]: ((c_2Emin_2E_3D @ TA @ A @ B) = (A = B))))),file('/export/starexec/sandbox/benchmark/Problems/HL405179^3.p',logicdef_2E_3D)).
thf(52,plain,((! [TA: $tType]: (! [A:TA,B:TA]: ((c_2Emin_2E_3D @ TA @ A @ B) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
thf(19,plain,(((c_2Ebool_2E_2F_5C @ $true @ $true) = (($true) & ($true)))),inference(instance,[status(thm)],[18])).
thf(20,plain,((c_2Ebool_2E_2F_5C @ $true @ $true)),inference(simp,[status(thm)],[19])).
thf(4,axiom,((! [A:$o,B:$o]: ((c_2Ebool_2E_5C_2F @ A @ B) = ((A) | (B))))),file('/export/starexec/sandbox/benchmark/Problems/HL405179^3.p',logicdef_2E_5C_2F)).
thf(27,plain,((! [A:$o,B:$o]: ((c_2Ebool_2E_5C_2F @ A @ B) = ((A) | (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
thf(28,plain,(((c_2Ebool_2E_5C_2F @ $true @ $true) = (($true) | ($true)))),inference(instance,[status(thm)],[27])).
thf(29,plain,((c_2Ebool_2E_5C_2F @ $true @ $true)),inference(simp,[status(thm)],[28])).
thf(1,conjecture,((! [TA: $tType,TB: $tType]: (! [A:TA,B:TB,C:(tyop_2Efinite__map_2Efmap @ TA @ TB)]: ((c_2Ebool_2EIN @ (tyop_2Epair_2Eprod @ TA @ TB) @ (c_2Epair_2E_2C @ TA @ TB @ A @ B) @ (c_2Elist_2ELIST__TO__SET @ (tyop_2Epair_2Eprod @ TA @ TB) @ (c_2Ealist_2Efmap__to__alist @ TA @ TB @ C))) = ((c_2Efinite__map_2EFLOOKUP @ TA @ TB @ C @ A) = (c_2Eoption_2ESOME @ TB @ B)))))),file('/export/starexec/sandbox/benchmark/Problems/HL405179^3.p',thm_2Ealist_2EMEM__pair__fmap__to__alist__FLOOKUP)).
thf(2,negated_conjecture,((~ (! [TA: $tType,TB: $tType]: (! [A:TA,B:TB,C:(tyop_2Efinite__map_2Efmap @ TA @ TB)]: ((c_2Ebool_2EIN @ (tyop_2Epair_2Eprod @ TA @ TB) @ (c_2Epair_2E_2C @ TA @ TB @ A @ B) @ (c_2Elist_2ELIST__TO__SET @ (tyop_2Epair_2Eprod @ TA @ TB) @ (c_2Ealist_2Efmap__to__alist @ TA @ TB @ C))) = ((c_2Efinite__map_2EFLOOKUP @ TA @ TB @ C @ A) = (c_2Eoption_2ESOME @ TB @ B))))))),inference(neg_conjecture,[status(cth)],[1])).
thf(15,plain,((~ (! [TA: $tType,TB: $tType]: (! [A:TA,B:TB,C:(tyop_2Efinite__map_2Efmap @ TA @ TB)]: ((c_2Ebool_2EIN @ (tyop_2Epair_2Eprod @ TA @ TB) @ (c_2Epair_2E_2C @ TA @ TB @ A @ B) @ (c_2Elist_2ELIST__TO__SET @ (tyop_2Epair_2Eprod @ TA @ TB) @ (c_2Ealist_2Efmap__to__alist @ TA @ TB @ C))) = ((c_2Efinite__map_2EFLOOKUP @ TA @ TB @ C @ A) = (c_2Eoption_2ESOME @ TB @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(16,plain,((~ ((c_2Ebool_2EIN @ (tyop_2Epair_2Eprod @ skt1 @ skt2) @ (c_2Epair_2E_2C @ skt1 @ skt2 @ sk1 @ sk2) @ (c_2Elist_2ELIST__TO__SET @ (tyop_2Epair_2Eprod @ skt1 @ skt2) @ (c_2Ealist_2Efmap__to__alist @ skt1 @ skt2 @ sk3))) = ((c_2Efinite__map_2EFLOOKUP @ skt1 @ skt2 @ sk3 @ sk1) = (c_2Eoption_2ESOME @ skt2 @ sk2))))),inference(cnf,[status(esa)],[15])).
thf(17,plain,(((c_2Ebool_2EIN @ (tyop_2Epair_2Eprod @ skt1 @ skt2) @ (c_2Epair_2E_2C @ skt1 @ skt2 @ sk1 @ sk2) @ (c_2Elist_2ELIST__TO__SET @ (tyop_2Epair_2Eprod @ skt1 @ skt2) @ (c_2Ealist_2Efmap__to__alist @ skt1 @ skt2 @ sk3))) != ((c_2Efinite__map_2EFLOOKUP @ skt1 @ skt2 @ sk3 @ sk1) = (c_2Eoption_2ESOME @ skt2 @ sk2)))),inference(lifteq,[status(thm)],[16])).
thf(82,plain,((~ (c_2Ebool_2EIN @ (tyop_2Epair_2Eprod @ skt1 @ skt2) @ (c_2Epair_2E_2C @ skt1 @ skt2 @ sk1 @ sk2) @ (c_2Elist_2ELIST__TO__SET @ (tyop_2Epair_2Eprod @ skt1 @ skt2) @ (c_2Ealist_2Efmap__to__alist @ skt1 @ skt2 @ sk3)))) | (~ ((c_2Efinite__map_2EFLOOKUP @ skt1 @ skt2 @ sk3 @ sk1) = (c_2Eoption_2ESOME @ skt2 @ sk2)))),inference(bool_ext,[status(thm)],[17])).
thf(84,plain,(((c_2Efinite__map_2EFLOOKUP @ skt1 @ skt2 @ sk3 @ sk1) != (c_2Eoption_2ESOME @ skt2 @ sk2)) | (~ (c_2Ebool_2EIN @ (tyop_2Epair_2Eprod @ skt1 @ skt2) @ (c_2Epair_2E_2C @ skt1 @ skt2 @ sk1 @ sk2) @ (c_2Elist_2ELIST__TO__SET @ (tyop_2Epair_2Eprod @ skt1 @ skt2) @ (c_2Ealist_2Efmap__to__alist @ skt1 @ skt2 @ sk3))))),inference(lifteq,[status(thm)],[82])).
thf(10,axiom,((! [TA: $tType,TB: $tType]: (! [A:(tyop_2Epair_2Eprod @ TA @ TB),B:(tyop_2Efinite__map_2Efmap @ TA @ TB)]: ((c_2Ebool_2EIN @ (tyop_2Epair_2Eprod @ TA @ TB) @ A @ (c_2Elist_2ELIST__TO__SET @ (tyop_2Epair_2Eprod @ TA @ TB) @ (c_2Ealist_2Efmap__to__alist @ TA @ TB @ B))) = ((c_2Efinite__map_2EFLOOKUP @ TA @ TB @ B @ (c_2Epair_2EFST @ TA @ TB @ A)) = (c_2Eoption_2ESOME @ TB @ (c_2Epair_2ESND @ TA @ TB @ A))))))),file('/export/starexec/sandbox/benchmark/Problems/HL405179^3.p',thm_2Ealist_2EMEM__fmap__to__alist__FLOOKUP)).
thf(61,plain,((! [TA: $tType,TB: $tType]: (! [A:(tyop_2Epair_2Eprod @ TA @ TB),B:(tyop_2Efinite__map_2Efmap @ TA @ TB)]: ((c_2Ebool_2EIN @ (tyop_2Epair_2Eprod @ TA @ TB) @ A @ (c_2Elist_2ELIST__TO__SET @ (tyop_2Epair_2Eprod @ TA @ TB) @ (c_2Ealist_2Efmap__to__alist @ TA @ TB @ B))) = ((c_2Efinite__map_2EFLOOKUP @ TA @ TB @ B @ (c_2Epair_2EFST @ TA @ TB @ A)) = (c_2Eoption_2ESOME @ TB @ (c_2Epair_2ESND @ TA @ TB @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
thf(83,plain,((c_2Ebool_2EIN @ (tyop_2Epair_2Eprod @ skt1 @ skt2) @ (c_2Epair_2E_2C @ skt1 @ skt2 @ sk1 @ sk2) @ (c_2Elist_2ELIST__TO__SET @ (tyop_2Epair_2Eprod @ skt1 @ skt2) @ (c_2Ealist_2Efmap__to__alist @ skt1 @ skt2 @ sk3))) | ((c_2Efinite__map_2EFLOOKUP @ skt1 @ skt2 @ sk3 @ sk1) = (c_2Eoption_2ESOME @ skt2 @ sk2))),inference(bool_ext,[status(thm)],[17])).
thf(85,plain,(((c_2Efinite__map_2EFLOOKUP @ skt1 @ skt2 @ sk3 @ sk1) = (c_2Eoption_2ESOME @ skt2 @ sk2)) | (c_2Ebool_2EIN @ (tyop_2Epair_2Eprod @ skt1 @ skt2) @ (c_2Epair_2E_2C @ skt1 @ skt2 @ sk1 @ sk2) @ (c_2Elist_2ELIST__TO__SET @ (tyop_2Epair_2Eprod @ skt1 @ skt2) @ (c_2Ealist_2Efmap__to__alist @ skt1 @ skt2 @ sk3)))),inference(lifteq,[status(thm)],[83])).
thf(5,axiom,((! [A:$o]: ((c_2Ebool_2E_7E @ A) = (~ (A))))),file('/export/starexec/sandbox/benchmark/Problems/HL405179^3.p',logicdef_2E_7E)).
thf(36,plain,((! [A:$o]: ((c_2Ebool_2E_7E @ A) = (~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
thf(37,plain,(((c_2Ebool_2E_7E @ $true) = (~ ($true)))),inference(instance,[status(thm)],[36])).
thf(38,plain,((~ (c_2Ebool_2E_7E @ $true))),inference(simp,[status(thm)],[37])).
thf(14,axiom,((! [TA: $tType,TB: $tType]: (! [A:TA,B:TB]: ((c_2Epair_2ESND @ TA @ TB @ (c_2Epair_2E_2C @ TA @ TB @ A @ B)) = B)))),file('/export/starexec/sandbox/benchmark/Problems/HL405179^3.p',thm_2Epair_2ESND)).
thf(70,plain,((! [TA: $tType,TB: $tType]: (! [A:TA,B:TB]: ((c_2Epair_2ESND @ TA @ TB @ (c_2Epair_2E_2C @ TA @ TB @ A @ B)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
thf(32,plain,(((c_2Ebool_2E_5C_2F @ $false @ $true) = (($false) | ($true)))),inference(instance,[status(thm)],[27])).
thf(33,plain,((c_2Ebool_2E_5C_2F @ $false @ $true)),inference(simp,[status(thm)],[32])).
thf(12,axiom,((! [TA: $tType]: (! [A:TA]: ((A = A) = c_2Ebool_2ET)))),file('/export/starexec/sandbox/benchmark/Problems/HL405179^3.p',thm_2Ebool_2EREFL__CLAUSE)).
thf(65,plain,((! [TA: $tType]: (c_2Ebool_2ET))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
thf(6,axiom,((! [A:$o,B:$o]: ((c_2Emin_2E_3D_3D_3E @ A @ B) = ((A) => (B))))),file('/export/starexec/sandbox/benchmark/Problems/HL405179^3.p',logicdef_2E_3D_3D_3E)).
thf(41,plain,((! [A:$o,B:$o]: ((c_2Emin_2E_3D_3D_3E @ A @ B) = ((A) => (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
thf(11,axiom,(c_2Ebool_2ET),file('/export/starexec/sandbox/benchmark/Problems/HL405179^3.p',thm_2Ebool_2ETRUTH)).
thf(64,plain,(c_2Ebool_2ET),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
thf(21,plain,(((c_2Ebool_2E_2F_5C @ $true @ $false) = (($true) & ($false)))),inference(instance,[status(thm)],[18])).
thf(22,plain,((~ (c_2Ebool_2E_2F_5C @ $true @ $false))),inference(simp,[status(thm)],[21])).
thf(48,plain,(((c_2Emin_2E_3D_3D_3E @ $false @ $false) = (($false) => ($false)))),inference(instance,[status(thm)],[41])).
thf(49,plain,((c_2Emin_2E_3D_3D_3E @ $false @ $false)),inference(simp,[status(thm)],[48])).
thf(34,plain,(((c_2Ebool_2E_5C_2F @ $false @ $false) = (($false) | ($false)))),inference(instance,[status(thm)],[27])).
thf(35,plain,((~ (c_2Ebool_2E_5C_2F @ $false @ $false))),inference(simp,[status(thm)],[34])).
thf(13,axiom,((! [TA: $tType,TB: $tType]: (! [A:TA,B:TB]: ((c_2Epair_2EFST @ TA @ TB @ (c_2Epair_2E_2C @ TA @ TB @ A @ B)) = A)))),file('/export/starexec/sandbox/benchmark/Problems/HL405179^3.p',thm_2Epair_2EFST)).
thf(67,plain,((! [TA: $tType,TB: $tType]: (! [A:TA,B:TB]: ((c_2Epair_2EFST @ TA @ TB @ (c_2Epair_2E_2C @ TA @ TB @ A @ B)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
thf(30,plain,(((c_2Ebool_2E_5C_2F @ $true @ $false) = (($true) | ($false)))),inference(instance,[status(thm)],[27])).
thf(31,plain,((c_2Ebool_2E_5C_2F @ $true @ $false)),inference(simp,[status(thm)],[30])).
thf(42,plain,(((c_2Emin_2E_3D_3D_3E @ $true @ $true) = (($true) => ($true)))),inference(instance,[status(thm)],[41])).
thf(43,plain,((c_2Emin_2E_3D_3D_3E @ $true @ $true)),inference(simp,[status(thm)],[42])).
thf(39,plain,(((c_2Ebool_2E_7E @ $false) = (~ ($false)))),inference(instance,[status(thm)],[36])).
thf(40,plain,((c_2Ebool_2E_7E @ $false)),inference(simp,[status(thm)],[39])).
thf(25,plain,(((c_2Ebool_2E_2F_5C @ $false @ $false) = (($false) & ($false)))),inference(instance,[status(thm)],[18])).
thf(26,plain,((~ (c_2Ebool_2E_2F_5C @ $false @ $false))),inference(simp,[status(thm)],[25])).
thf(8,axiom,((! [TA: $tType]: (! [A:(TA > $o)]: ((c_2Ebool_2E_21 @ TA @ A) = (! [B:TA]: (A @ B)))))),file('/export/starexec/sandbox/benchmark/Problems/HL405179^3.p',quantdef_2E_21)).
thf(55,plain,((! [TA: $tType]: (! [A:(TA > $o)]: ((c_2Ebool_2E_21 @ TA @ (A)) = (! [B:TA]: (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
thf(9,axiom,((! [TA: $tType]: (! [A:(TA > $o)]: ((c_2Ebool_2E_3F @ TA @ A) = (? [B:TA]: (A @ B)))))),file('/export/starexec/sandbox/benchmark/Problems/HL405179^3.p',quantdef_2E_3F)).
thf(58,plain,((! [TA: $tType]: (! [A:(TA > $o)]: ((c_2Ebool_2E_3F @ TA @ (A)) = (? [B:TA]: (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
thf(44,plain,(((c_2Emin_2E_3D_3D_3E @ $true @ $false) = (($true) => ($false)))),inference(instance,[status(thm)],[41])).
thf(45,plain,(((c_2Emin_2E_3D_3D_3E @ $true @ $false) = (~ ($true)))),inference(simp,[status(thm)],[44])).
thf(50,plain,(((c_2Emin_2E_3D_3D_3E @ $true @ $false) = (~ ($true)))),inference(lifteq,[status(thm)],[45])).
thf(51,plain,((~ (c_2Emin_2E_3D_3D_3E @ $true @ $false))),inference(simp,[status(thm)],[50])).
thf(46,plain,(((c_2Emin_2E_3D_3D_3E @ $false @ $true) = (($false) => ($true)))),inference(instance,[status(thm)],[41])).
thf(47,plain,((c_2Emin_2E_3D_3D_3E @ $false @ $true)),inference(simp,[status(thm)],[46])).
thf(125,plain,($false),inference(cvc4,[status(thm)],[24,52,20,29,84,61,85,38,70,33,65,41,64,17,22,27,49,35,18,67,31,43,40,26,55,58,36,51,47,15])).
% SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/Problems/HL405179^3.p

30.1100000000006/3.93999999999869	EOF