% Time passed: 3555ms
% Effective reasoning time: 1962ms
% 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 (9): thm_2Ebool_2ENOT__CLAUSES, thm_2Ebool_2EREFL__CLAUSE, thm_2Efinite__map_2EFDOM__DOMSUB, thm_2Ebool_2ECOND__CONG, thm_2Efinite__map_2EFLOOKUP__DEF, thm_2Ebool_2ETRUTH, thm_2Epred__set_2EIN__DELETE, thm_2Ebool_2EAND__CLAUSES, thm_2Ebool_2Ebool__case__thm
% No. of inferences in proof: 31
% No. of processed clauses: 5
% No. of generated clauses: 13
% No. of forward subsumed clauses: 4
% No. of backward subsumed clauses: 0
% No. of ground rewrite rules in store: 2
% 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/HL404725^3.p : 3555 ms resp. 1962 ms w/o parsing
% SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/Problems/HL404725^3.p
thf(tyop_2Emin_2Ebool_type, type, tyop_2Emin_2Ebool: $tType).
thf(c_2Ebool_2ECOND_type, type, c_2Ebool_2ECOND: !>[TA: $tType]: ($o > (TA > (TA > TA)))).
thf(c_2Epred__set_2EDELETE_type, type, c_2Epred__set_2EDELETE: !>[TA: $tType]: ((TA > $o) > (TA > (TA > $o)))).
thf(c_2Ebool_2EF_type, type, c_2Ebool_2EF: $o).
thf(c_2Efinite__map_2EFAPPLY_type, type, c_2Efinite__map_2EFAPPLY: !>[TA: $tType,TB: $tType]: ((tyop_2Efinite__map_2Efmap @ TA @ TB) > (TA > TB))).
thf(c_2Efinite__map_2EFDOM_type, type, c_2Efinite__map_2EFDOM: !>[TA: $tType,TB: $tType]: ((tyop_2Efinite__map_2Efmap @ TA @ TB) > (TA > $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_2Ebool_2EIN_type, type, c_2Ebool_2EIN: !>[TA: $tType]: (TA > ((TA > $o) > $o))).
thf(c_2Eoption_2ENONE_type, type, c_2Eoption_2ENONE: !>[TA: $tType]: (tyop_2Eoption_2Eoption @ TA)).
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_2Efinite__map_2Efdomsub_type, type, c_2Efinite__map_2Efdomsub: !>[TA: $tType,TB: $tType]: ((tyop_2Efinite__map_2Efmap @ TA @ TB) > (TA > (tyop_2Efinite__map_2Efmap @ TA @ TB)))).
thf(skt1_type, type, skt1: $tType).
thf(skt2_type, type, skt2: $tType).
thf(sk1_type, type, sk1: (tyop_2Efinite__map_2Efmap @ skt1 @ skt2)).
thf(sk2_type, type, sk2: skt1).
thf(6,axiom,((! [A:$o]: ((~ (~ (A))) = A) & ((~ (c_2Ebool_2ET)) = c_2Ebool_2EF) & ((~ (c_2Ebool_2EF)) = c_2Ebool_2ET))),file('/export/starexec/sandbox/benchmark/Problems/HL404725^3.p',thm_2Ebool_2ENOT__CLAUSES)).
thf(25,plain,((((~ (c_2Ebool_2ET)) = c_2Ebool_2EF) & ((~ (c_2Ebool_2EF)) = c_2Ebool_2ET))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
thf(10,axiom,((! [TA: $tType,TB: $tType]: (! [A:(tyop_2Efinite__map_2Efmap @ TA @ TB),B:TA]: ((c_2Efinite__map_2EFDOM @ TA @ TB @ (c_2Efinite__map_2Efdomsub @ TA @ TB @ A @ B)) = (c_2Epred__set_2EDELETE @ TA @ (c_2Efinite__map_2EFDOM @ TA @ TB @ A) @ B))))),file('/export/starexec/sandbox/benchmark/Problems/HL404725^3.p',thm_2Efinite__map_2EFDOM__DOMSUB)).
thf(52,plain,((! [TA: $tType,TB: $tType]: (! [A:(tyop_2Efinite__map_2Efmap @ TA @ TB),B:TA]: ((c_2Efinite__map_2EFDOM @ TA @ TB @ (c_2Efinite__map_2Efdomsub @ TA @ TB @ A @ B)) = (c_2Epred__set_2EDELETE @ TA @ (c_2Efinite__map_2EFDOM @ TA @ TB @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
thf(1,conjecture,((! [TA: $tType,TB: $tType]: (! [A:(tyop_2Efinite__map_2Efmap @ TA @ TB),B:TA]: ((c_2Efinite__map_2EFLOOKUP @ TA @ TB @ (c_2Efinite__map_2Efdomsub @ TA @ TB @ A @ B) @ B) = (c_2Eoption_2ENONE @ TB))))),file('/export/starexec/sandbox/benchmark/Problems/HL404725^3.p',thm_2Efinite__map_2EDOMSUB__FLOOKUP)).
thf(2,negated_conjecture,((~ (! [TA: $tType,TB: $tType]: (! [A:(tyop_2Efinite__map_2Efmap @ TA @ TB),B:TA]: ((c_2Efinite__map_2EFLOOKUP @ TA @ TB @ (c_2Efinite__map_2Efdomsub @ TA @ TB @ A @ B) @ B) = (c_2Eoption_2ENONE @ TB)))))),inference(neg_conjecture,[status(cth)],[1])).
thf(12,plain,((~ (! [TA: $tType,TB: $tType]: (! [A:(tyop_2Efinite__map_2Efmap @ TA @ TB),B:TA]: ((c_2Efinite__map_2EFLOOKUP @ TA @ TB @ (c_2Efinite__map_2Efdomsub @ TA @ TB @ A @ B) @ B) = (c_2Eoption_2ENONE @ TB)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(13,plain,((~ ((c_2Efinite__map_2EFLOOKUP @ skt1 @ skt2 @ (c_2Efinite__map_2Efdomsub @ skt1 @ skt2 @ sk1 @ sk2) @ sk2) = (c_2Eoption_2ENONE @ skt2)))),inference(cnf,[status(esa)],[12])).
thf(14,plain,(((c_2Efinite__map_2EFLOOKUP @ skt1 @ skt2 @ (c_2Efinite__map_2Efdomsub @ skt1 @ skt2 @ sk1 @ sk2) @ sk2) != (c_2Eoption_2ENONE @ skt2))),inference(lifteq,[status(thm)],[13])).
thf(9,axiom,((! [TA: $tType]: (! [A:TA,B:TA]: ((c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B) = A) & ! [A:TA,B:TA]: ((c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/Problems/HL404725^3.p',thm_2Ebool_2Ebool__case__thm)).
thf(46,plain,((! [TA: $tType]: (! [A:TA,B:TA]: ((c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B) = A) & ! [A:TA,B:TA]: ((c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
thf(8,axiom,((! [TA: $tType]: (! [A:$o,B:$o,C:TA,D:TA,E:TA,F:TA]: (((A = B) & ((B) => (C = D)) & ((~ (B)) => (E = F))) => ((c_2Ebool_2ECOND @ TA @ A @ C @ E) = (c_2Ebool_2ECOND @ TA @ B @ D @ F)))))),file('/export/starexec/sandbox/benchmark/Problems/HL404725^3.p',thm_2Ebool_2ECOND__CONG)).
thf(33,plain,((! [TA: $tType]: (! [A:$o,B:$o,C:TA,D:TA,E:TA,F:TA]: (((A = B) & ((B) => (C = D)) & ((~ (B)) => (E = F))) => ((c_2Ebool_2ECOND @ TA @ A @ C @ E) = (c_2Ebool_2ECOND @ TA @ B @ D @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
thf(37,plain,(! [TA:$tType,F:TA,E:TA,D:TA,C:TA,B:$o,A:$o] : ((~ (A = B)) | (~ (C = D)) | ~ (B) | ((c_2Ebool_2ECOND @ TA @ A @ C @ E) = (c_2Ebool_2ECOND @ TA @ B @ D @ F)))),inference(cnf,[status(esa)],[33])).
thf(44,plain,(! [TA:$tType,F:TA,E:TA,D:TA,C:TA,B:$o,A:$o] : ((A != B) | (C != D) | ((c_2Ebool_2ECOND @ TA @ A @ C @ E) = (c_2Ebool_2ECOND @ TA @ B @ D @ F)) | ~ (B))),inference(lifteq,[status(thm)],[37])).
thf(45,plain,(! [TA:$tType,D:TA,C:TA,B:TA,A:$o] : (((c_2Ebool_2ECOND @ TA @ A @ B @ C) = (c_2Ebool_2ECOND @ TA @ A @ B @ D)) | ~ (A))),inference(simp,[status(thm)],[44])).
thf(4,axiom,(c_2Ebool_2ET),file('/export/starexec/sandbox/benchmark/Problems/HL404725^3.p',thm_2Ebool_2ETRUTH)).
thf(17,plain,(c_2Ebool_2ET),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
thf(5,axiom,((! [A:$o]: ((((c_2Ebool_2ET) & (A)) = A) & (((A) & (c_2Ebool_2ET)) = A) & (((c_2Ebool_2EF) & (A)) = c_2Ebool_2EF) & (((A) & (c_2Ebool_2EF)) = c_2Ebool_2EF) & (((A) & (A)) = A)))),file('/export/starexec/sandbox/benchmark/Problems/HL404725^3.p',thm_2Ebool_2EAND__CLAUSES)).
thf(18,plain,((! [A:$o]: ((((c_2Ebool_2ET) & (A)) = A) & (((A) & (c_2Ebool_2ET)) = A) & (((c_2Ebool_2EF) & (A)) = c_2Ebool_2EF) & (((A) & (c_2Ebool_2EF)) = c_2Ebool_2EF)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
thf(3,axiom,((! [TA: $tType]: (! [A:TA]: ((A = A) = c_2Ebool_2ET)))),file('/export/starexec/sandbox/benchmark/Problems/HL404725^3.p',thm_2Ebool_2EREFL__CLAUSE)).
thf(15,plain,((! [TA: $tType]: (c_2Ebool_2ET))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
thf(16,plain,(c_2Ebool_2ET),inference(cnf,[status(esa)],[15])).
thf(11,axiom,((! [TA: $tType,TB: $tType]: (! [A:(tyop_2Efinite__map_2Efmap @ TA @ TB),B:TA]: ((c_2Efinite__map_2EFLOOKUP @ TA @ TB @ A @ B) = (c_2Ebool_2ECOND @ (tyop_2Eoption_2Eoption @ TB) @ (c_2Ebool_2EIN @ TA @ B @ (c_2Efinite__map_2EFDOM @ TA @ TB @ A)) @ (c_2Eoption_2ESOME @ TB @ (c_2Efinite__map_2EFAPPLY @ TA @ TB @ A @ B)) @ (c_2Eoption_2ENONE @ TB)))))),file('/export/starexec/sandbox/benchmark/Problems/HL404725^3.p',thm_2Efinite__map_2EFLOOKUP__DEF)).
thf(55,plain,((! [TA: $tType,TB: $tType]: (! [A:(tyop_2Efinite__map_2Efmap @ TA @ TB),B:TA]: ((c_2Efinite__map_2EFLOOKUP @ TA @ TB @ A @ B) = (c_2Ebool_2ECOND @ (tyop_2Eoption_2Eoption @ TB) @ (c_2Ebool_2EIN @ TA @ B @ (c_2Efinite__map_2EFDOM @ TA @ TB @ A)) @ (c_2Eoption_2ESOME @ TB @ (c_2Efinite__map_2EFAPPLY @ TA @ TB @ A @ B)) @ (c_2Eoption_2ENONE @ TB)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
thf(21,plain,(((((c_2Ebool_2ET) & ($false)) = $false) & ((($false) & (c_2Ebool_2ET)) = $false) & (((c_2Ebool_2EF) & ($false)) = c_2Ebool_2EF) & ((($false) & (c_2Ebool_2EF)) = c_2Ebool_2EF))),inference(instance,[status(thm)],[18])).
thf(22,plain,((~ ($false) & ~ (c_2Ebool_2EF) & ~ (c_2Ebool_2EF))),inference(simp,[status(thm)],[21])).
thf(23,plain,(~ (c_2Ebool_2EF)),inference(cnf,[status(esa)],[22])).
thf(7,axiom,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:TA]: ((c_2Ebool_2EIN @ TA @ B @ (c_2Epred__set_2EDELETE @ TA @ A @ C)) = ((c_2Ebool_2EIN @ TA @ B @ A) & ~ (B = C)))))),file('/export/starexec/sandbox/benchmark/Problems/HL404725^3.p',thm_2Epred__set_2EIN__DELETE)).
thf(30,plain,((! [TA: $tType]: (! [A:(TA > $o),B:TA,C:TA]: ((c_2Ebool_2EIN @ TA @ B @ (c_2Epred__set_2EDELETE @ TA @ A @ C)) = ((c_2Ebool_2EIN @ TA @ B @ (A)) & ~ (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
thf(102,plain,($false),inference(e,[status(thm)],[25,52,14,46,33,45,17,12,18,16,55,23,30,15])).
% SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/Problems/HL404725^3.p

25.4899999999907/3.84000000000015	EOF