% Time passed: 4358ms
% Effective reasoning time: 3243ms
% 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 (11): thm_2Earithmetic_2ESUB__ADD, logicdef_2E_3D, logicdef_2E_5C_2F, thm_2Earithmetic_2ELESS__EQ__REFL, quantdef_2E_21, logicdef_2E_3D_3D_3E, thm_2Erich__list_2EEVERY__SEG, thm_2Erich__list_2EDROP__SEG, logicdef_2E_2F_5C, logicdef_2E_7E, quantdef_2E_3F
% No. of inferences in proof: 101
% No. of processed clauses: 36
% No. of generated clauses: 112
% No. of forward subsumed clauses: 2
% No. of backward subsumed clauses: 0
% No. of ground rewrite rules in store: 19
% No. of non-ground rewrite rules in store: 5
% No. of positive (non-rewrite) units in store: 0
% No. of negative (non-rewrite) units in store: 2
% No. of choice functions detected: 0
% No. of choice instantiations: 0
% SZS status Theorem for /export/starexec/sandbox/benchmark/Problems/HL402756^3.p : 4358 ms resp. 3243 ms w/o parsing
% SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/Problems/HL402756^3.p
thf(tyop_2Emin_2Ebool_type, type, tyop_2Emin_2Ebool: $tType).
thf(tyop_2Enum_2Enum_type, type, tyop_2Enum_2Enum: $tType).
thf(c_2Ebool_2E_21_type, type, c_2Ebool_2E_21: !>[TA: $tType]: ((TA > $o) > $o)).
thf(c_2Earithmetic_2E_2B_type, type, c_2Earithmetic_2E_2B: (tyop_2Enum_2Enum > (tyop_2Enum_2Enum > tyop_2Enum_2Enum))).
thf(c_2Earithmetic_2E_2D_type, type, c_2Earithmetic_2E_2D: (tyop_2Enum_2Enum > (tyop_2Enum_2Enum > tyop_2Enum_2Enum))).
thf(c_2Ebool_2E_2F_5C_type, type, c_2Ebool_2E_2F_5C: ($o > ($o > $o))).
thf(c_2Earithmetic_2E_3C_3D_type, type, c_2Earithmetic_2E_3C_3D: (tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $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_2Elist_2EDROP_type, type, c_2Elist_2EDROP: !>[TA: $tType]: (tyop_2Enum_2Enum > ((tyop_2Elist_2Elist @ TA) > (tyop_2Elist_2Elist @ TA)))).
thf(c_2Elist_2EEVERY_type, type, c_2Elist_2EEVERY: !>[TA: $tType]: ((TA > $o) > ((tyop_2Elist_2Elist @ TA) > $o))).
thf(c_2Elist_2ELENGTH_type, type, c_2Elist_2ELENGTH: !>[TA: $tType]: ((tyop_2Elist_2Elist @ TA) > tyop_2Enum_2Enum)).
thf(c_2Erich__list_2ESEG_type, type, c_2Erich__list_2ESEG: !>[TA: $tType]: (tyop_2Enum_2Enum > (tyop_2Enum_2Enum > ((tyop_2Elist_2Elist @ TA) > (tyop_2Elist_2Elist @ TA))))).
thf(c_2Ebool_2E_5C_2F_type, type, c_2Ebool_2E_5C_2F: ($o > ($o > $o))).
thf(c_2Ebool_2E_7E_type, type, c_2Ebool_2E_7E: ($o > $o)).
thf(skt1_type, type, skt1: $tType).
thf(sk1_type, type, sk1: (skt1 > $o)).
thf(sk2_type, type, sk2: (tyop_2Elist_2Elist @ skt1)).
thf(sk3_type, type, sk3: tyop_2Enum_2Enum).
thf(13,axiom,((! [TA: $tType]: (! [A:(TA > $o),B:(tyop_2Elist_2Elist @ TA)]: ((c_2Elist_2EEVERY @ TA @ A @ B) => (! [C:tyop_2Enum_2Enum,D:tyop_2Enum_2Enum]: ((c_2Earithmetic_2E_3C_3D @ (c_2Earithmetic_2E_2B @ C @ D) @ (c_2Elist_2ELENGTH @ TA @ B)) => (c_2Elist_2EEVERY @ TA @ A @ (c_2Erich__list_2ESEG @ TA @ C @ D @ B)))))))),file('/export/starexec/sandbox/benchmark/Problems/HL402756^3.p',thm_2Erich__list_2EEVERY__SEG)).
thf(69,plain,((! [TA: $tType]: (! [A:(TA > $o),B:(tyop_2Elist_2Elist @ TA)]: ((c_2Elist_2EEVERY @ TA @ (A) @ B) => (! [C:tyop_2Enum_2Enum,D:tyop_2Enum_2Enum]: ((c_2Earithmetic_2E_3C_3D @ (c_2Earithmetic_2E_2B @ C @ D) @ (c_2Elist_2ELENGTH @ TA @ B)) => (c_2Elist_2EEVERY @ TA @ (A) @ (c_2Erich__list_2ESEG @ TA @ C @ D @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
thf(1,conjecture,((! [TA: $tType]: (! [A:(TA > $o),B:(tyop_2Elist_2Elist @ TA)]: ((c_2Elist_2EEVERY @ TA @ A @ B) => (! [C:tyop_2Enum_2Enum]: ((c_2Earithmetic_2E_3C_3D @ C @ (c_2Elist_2ELENGTH @ TA @ B)) => (c_2Elist_2EEVERY @ TA @ A @ (c_2Elist_2EDROP @ TA @ C @ B)))))))),file('/export/starexec/sandbox/benchmark/Problems/HL402756^3.p',thm_2Erich__list_2EEVERY__DROP)).
thf(2,negated_conjecture,((~ (! [TA: $tType]: (! [A:(TA > $o),B:(tyop_2Elist_2Elist @ TA)]: ((c_2Elist_2EEVERY @ TA @ A @ B) => (! [C:tyop_2Enum_2Enum]: ((c_2Earithmetic_2E_3C_3D @ C @ (c_2Elist_2ELENGTH @ TA @ B)) => (c_2Elist_2EEVERY @ TA @ A @ (c_2Elist_2EDROP @ TA @ C @ B))))))))),inference(neg_conjecture,[status(cth)],[1])).
thf(14,plain,((~ (! [TA: $tType]: (! [A:(TA > $o),B:(tyop_2Elist_2Elist @ TA)]: ((c_2Elist_2EEVERY @ TA @ (A) @ B) => (! [C:tyop_2Enum_2Enum]: ((c_2Earithmetic_2E_3C_3D @ C @ (c_2Elist_2ELENGTH @ TA @ B)) => (c_2Elist_2EEVERY @ TA @ (A) @ (c_2Elist_2EDROP @ TA @ C @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(16,plain,((c_2Earithmetic_2E_3C_3D @ sk3 @ (c_2Elist_2ELENGTH @ skt1 @ sk2))),inference(cnf,[status(esa)],[14])).
thf(70,plain,(! [TA:$tType,D:tyop_2Enum_2Enum,C:tyop_2Enum_2Enum,B:(tyop_2Elist_2Elist @ TA),A:(TA > $o)] : ((~ (c_2Elist_2EEVERY @ TA @ (A) @ B)) | (~ (c_2Earithmetic_2E_3C_3D @ (c_2Earithmetic_2E_2B @ C @ D) @ (c_2Elist_2ELENGTH @ TA @ B))) | (c_2Elist_2EEVERY @ TA @ (A) @ (c_2Erich__list_2ESEG @ TA @ C @ D @ B)))),inference(cnf,[status(esa)],[69])).
thf(125,plain,(! [TA:$tType,D:tyop_2Enum_2Enum,C:tyop_2Enum_2Enum,B:(tyop_2Elist_2Elist @ TA),A:(TA > $o)] : ((~ (c_2Elist_2EEVERY @ TA @ (A) @ B)) | (c_2Elist_2EEVERY @ TA @ (A) @ (c_2Erich__list_2ESEG @ TA @ C @ D @ B)) | ((c_2Earithmetic_2E_3C_3D @ (c_2Earithmetic_2E_2B @ C @ D) @ (c_2Elist_2ELENGTH @ TA @ B)) != (c_2Earithmetic_2E_3C_3D @ sk3 @ (c_2Elist_2ELENGTH @ skt1 @ sk2))))),inference(paramod_ordered,[status(thm)],[16,70])).
thf(127,plain,(! [TA:$tType,D:tyop_2Enum_2Enum,C:tyop_2Enum_2Enum,B:(tyop_2Elist_2Elist @ TA),A:(TA > $o)] : ((c_2Elist_2EEVERY @ TA @ (A) @ (c_2Erich__list_2ESEG @ TA @ C @ D @ B)) | (~ (c_2Elist_2EEVERY @ TA @ (A) @ B)) | ((c_2Earithmetic_2E_2B @ C @ D) != sk3) | ((c_2Elist_2ELENGTH @ TA @ B) != (c_2Elist_2ELENGTH @ skt1 @ sk2)))),inference(simp,[status(thm)],[125])).
thf(138,plain,(! [TA:$tType,TB:$tType,H:tyop_2Enum_2Enum,G:tyop_2Enum_2Enum,F:(tyop_2Elist_2Elist @ TA),E:(TA > $o),D:tyop_2Enum_2Enum,C:tyop_2Enum_2Enum,B:(tyop_2Elist_2Elist @ TB),A:(TB > $o)] : ((~ (c_2Elist_2EEVERY @ TB @ (A) @ B)) | ((c_2Earithmetic_2E_2B @ C @ D) != sk3) | ((c_2Elist_2ELENGTH @ TB @ B) != (c_2Elist_2ELENGTH @ skt1 @ sk2)) | (c_2Elist_2EEVERY @ TA @ (E) @ (c_2Erich__list_2ESEG @ TA @ G @ H @ F)) | ((c_2Earithmetic_2E_2B @ G @ H) != sk3) | ((c_2Elist_2ELENGTH @ TA @ F) != (c_2Elist_2ELENGTH @ skt1 @ sk2)) | ((c_2Elist_2EEVERY @ TB @ (A) @ (c_2Erich__list_2ESEG @ TB @ C @ D @ B)) != (c_2Elist_2EEVERY @ TA @ (E) @ F)))),inference(paramod_ordered,[status(thm)],[127,127])).
thf(139,plain,(! [TB:$tType,F:(tyop_2Elist_2Elist @ T@),E:tyop_2Enum_2Enum,D:tyop_2Enum_2Enum,C:tyop_2Enum_2Enum,B:tyop_2Enum_2Enum,A:(T@ > $o)] : ((~ (c_2Elist_2EEVERY @ T@ @ (A) @ F)) | ((c_2Earithmetic_2E_2B @ D @ E) != sk3) | ((c_2Elist_2ELENGTH @ T@ @ F) != (c_2Elist_2ELENGTH @ skt1 @ sk2)) | (c_2Elist_2EEVERY @ T@ @ (A) @ (c_2Erich__list_2ESEG @ T@ @ B @ C @ (c_2Erich__list_2ESEG @ T@ @ D @ E @ F))) | ((c_2Earithmetic_2E_2B @ B @ C) != sk3) | ((c_2Elist_2ELENGTH @ T@ @ (c_2Erich__list_2ESEG @ T@ @ D @ E @ F)) != (c_2Elist_2ELENGTH @ skt1 @ sk2)))),inference(pattern_uni,[status(thm)],[138:[bind(A, $thf(A)),bind(B, $thf(K)),bind(C, $thf(I)),bind(D, $thf(J)),bind(E, $thf(A)),bind(F, $thf(c_2Erich__list_2ESEG @ T? @ I @ J @ K))]])).
thf(142,plain,(! [TA:$tType,F:(tyop_2Elist_2Elist @ TA),E:tyop_2Enum_2Enum,D:tyop_2Enum_2Enum,C:tyop_2Enum_2Enum,B:tyop_2Enum_2Enum,A:(TA > $o)] : ((~ (c_2Elist_2EEVERY @ TA @ (A) @ F)) | ((c_2Earithmetic_2E_2B @ D @ E) != sk3) | ((c_2Elist_2ELENGTH @ TA @ F) != (c_2Elist_2ELENGTH @ skt1 @ sk2)) | (c_2Elist_2EEVERY @ TA @ (A) @ (c_2Erich__list_2ESEG @ TA @ B @ C @ (c_2Erich__list_2ESEG @ TA @ D @ E @ F))) | ((c_2Earithmetic_2E_2B @ B @ C) != sk3) | ((c_2Elist_2ELENGTH @ TA @ (c_2Erich__list_2ESEG @ TA @ D @ E @ F)) != (c_2Elist_2ELENGTH @ skt1 @ sk2)))),inference(simp,[status(thm)],[139])).
thf(3,axiom,((! [A:$o,B:$o]: ((c_2Ebool_2E_2F_5C @ A @ B) = ((A) & (B))))),file('/export/starexec/sandbox/benchmark/Problems/HL402756^3.p',logicdef_2E_2F_5C)).
thf(18,plain,((! [A:$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/HL402756^3.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(8,axiom,((! [TA: $tType]: (! [A:(TA > $o)]: ((c_2Ebool_2E_21 @ TA @ A) = (! [B:TA]: (A @ B)))))),file('/export/starexec/sandbox/benchmark/Problems/HL402756^3.p',quantdef_2E_21)).
thf(55,plain,((! [TA: $tType]: (! [A:(TA > $o)]: ((c_2Ebool_2E_21 @ TA @ (A)) = (! [B:TA]: (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
thf(56,plain,(! [TA:$tType,A:(TA > $o)] : (((c_2Ebool_2E_21 @ TA @ (A)) = (! [B:TA]: (A @ B))))),inference(cnf,[status(esa)],[55])).
thf(57,plain,(! [TA:$tType,A:(TA > $o)] : (((c_2Ebool_2E_21 @ TA @ (A)) = (! [B:TA]: (A @ B))))),inference(lifteq,[status(thm)],[56])).
thf(4,axiom,((! [A:$o,B:$o]: ((c_2Ebool_2E_5C_2F @ A @ B) = ((A) | (B))))),file('/export/starexec/sandbox/benchmark/Problems/HL402756^3.p',logicdef_2E_5C_2F)).
thf(27,plain,((! [A:$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(10,axiom,((! [A:tyop_2Enum_2Enum,B:tyop_2Enum_2Enum]: ((c_2Earithmetic_2E_3C_3D @ B @ A) => ((c_2Earithmetic_2E_2B @ (c_2Earithmetic_2E_2D @ A @ B) @ B) = A)))),file('/export/starexec/sandbox/benchmark/Problems/HL402756^3.p',thm_2Earithmetic_2ESUB__ADD)).
thf(61,plain,((! [A:tyop_2Enum_2Enum,B:tyop_2Enum_2Enum]: ((c_2Earithmetic_2E_3C_3D @ B @ A) => ((c_2Earithmetic_2E_2B @ (c_2Earithmetic_2E_2D @ A @ B) @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
thf(9,axiom,((! [TA: $tType]: (! [A:(TA > $o)]: ((c_2Ebool_2E_3F @ TA @ A) = (? [B:TA]: (A @ B)))))),file('/export/starexec/sandbox/benchmark/Problems/HL402756^3.p',quantdef_2E_3F)).
thf(58,plain,((! [TA: $tType]: (! [A:(TA > $o)]: ((c_2Ebool_2E_3F @ TA @ (A)) = (? [B:TA]: (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
thf(59,plain,(! [TA:$tType,A:(TA > $o)] : (((c_2Ebool_2E_3F @ TA @ (A)) = (? [B:TA]: (A @ B))))),inference(cnf,[status(esa)],[58])).
thf(60,plain,(! [TA:$tType,A:(TA > $o)] : (((c_2Ebool_2E_3F @ TA @ (A)) = (? [B:TA]: (A @ B))))),inference(lifteq,[status(thm)],[59])).
thf(5,axiom,((! [A:$o]: ((c_2Ebool_2E_7E @ A) = (~ (A))))),file('/export/starexec/sandbox/benchmark/Problems/HL402756^3.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(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(11,axiom,((! [A:tyop_2Enum_2Enum]: (c_2Earithmetic_2E_3C_3D @ A @ A))),file('/export/starexec/sandbox/benchmark/Problems/HL402756^3.p',thm_2Earithmetic_2ELESS__EQ__REFL)).
thf(64,plain,((! [A:tyop_2Enum_2Enum]: (c_2Earithmetic_2E_3C_3D @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
thf(65,plain,(! [A:tyop_2Enum_2Enum] : ((c_2Earithmetic_2E_3C_3D @ A @ A))),inference(cnf,[status(esa)],[64])).
thf(62,plain,(! [B:tyop_2Enum_2Enum,A:tyop_2Enum_2Enum] : ((~ (c_2Earithmetic_2E_3C_3D @ B @ A)) | ((c_2Earithmetic_2E_2B @ (c_2Earithmetic_2E_2D @ A @ B) @ B) = A))),inference(cnf,[status(esa)],[61])).
thf(63,plain,(! [B:tyop_2Enum_2Enum,A:tyop_2Enum_2Enum] : (((c_2Earithmetic_2E_2B @ (c_2Earithmetic_2E_2D @ A @ B) @ B) = A) | (~ (c_2Earithmetic_2E_3C_3D @ B @ A)))),inference(lifteq,[status(thm)],[62])).
thf(155,plain,(! [C:tyop_2Enum_2Enum,B:tyop_2Enum_2Enum,A:tyop_2Enum_2Enum] : (((c_2Earithmetic_2E_2B @ (c_2Earithmetic_2E_2D @ B @ C) @ C) = B) | ((c_2Earithmetic_2E_3C_3D @ A @ A) != (c_2Earithmetic_2E_3C_3D @ C @ B)))),inference(paramod_ordered,[status(thm)],[65,63])).
thf(156,plain,(! [A:tyop_2Enum_2Enum] : (((c_2Earithmetic_2E_2B @ (c_2Earithmetic_2E_2D @ A @ A) @ A) = A))),inference(pattern_uni,[status(thm)],[155:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(A))]])).
thf(6,axiom,((! [A:$o,B:$o]: ((c_2Emin_2E_3D_3D_3E @ A @ B) = ((A) => (B))))),file('/export/starexec/sandbox/benchmark/Problems/HL402756^3.p',logicdef_2E_3D_3D_3E)).
thf(41,plain,((! [A:$o,B:$o]: ((c_2Emin_2E_3D_3D_3E @ A @ B) = ((A) => (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
thf(17,plain,((c_2Elist_2EEVERY @ skt1 @ (sk1) @ sk2)),inference(cnf,[status(esa)],[14])).
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 @ $false))),inference(simp,[status(thm)],[21])).
thf(53,plain,(! [TA:$tType,B:TA,A:TA] : (((c_2Emin_2E_3D @ TA @ A @ B) = (A = B)))),inference(cnf,[status(esa)],[52])).
thf(54,plain,(! [TA:$tType,B:TA,A:TA] : (((c_2Emin_2E_3D @ TA @ A @ B) = (A = B)))),inference(lifteq,[status(thm)],[53])).
thf(136,plain,(! [TA:$tType,D:tyop_2Enum_2Enum,C:tyop_2Enum_2Enum,B:(tyop_2Elist_2Elist @ TA),A:(TA > $o)] : ((c_2Elist_2EEVERY @ TA @ (A) @ (c_2Erich__list_2ESEG @ TA @ C @ D @ B)) | ((c_2Earithmetic_2E_2B @ C @ D) != sk3) | ((c_2Elist_2ELENGTH @ TA @ B) != (c_2Elist_2ELENGTH @ skt1 @ sk2)) | ((c_2Elist_2EEVERY @ skt1 @ (sk1) @ sk2) != (c_2Elist_2EEVERY @ TA @ (A) @ B)))),inference(paramod_ordered,[status(thm)],[17,127])).
thf(137,plain,(! [B:tyop_2Enum_2Enum,A:tyop_2Enum_2Enum] : ((c_2Elist_2EEVERY @ skt1 @ (sk1) @ (c_2Erich__list_2ESEG @ skt1 @ A @ B @ sk2)) | ((c_2Earithmetic_2E_2B @ A @ B) != sk3) | ((c_2Elist_2ELENGTH @ skt1 @ sk2) != (c_2Elist_2ELENGTH @ skt1 @ sk2)))),inference(pattern_uni,[status(thm)],[136:[bind(A, $thf(sk1)),bind(B, $thf(sk2)),bind(C, $thf(C)),bind(D, $thf(D))]])).
thf(144,plain,(! [B:tyop_2Enum_2Enum,A:tyop_2Enum_2Enum] : ((c_2Elist_2EEVERY @ skt1 @ (sk1) @ (c_2Erich__list_2ESEG @ skt1 @ A @ B @ sk2)) | ((c_2Earithmetic_2E_2B @ A @ B) != sk3))),inference(simp,[status(thm)],[137])).
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(161,plain,(! [B:tyop_2Enum_2Enum,A:tyop_2Enum_2Enum] : (((c_2Earithmetic_2E_2B @ (c_2Earithmetic_2E_2D @ A @ B) @ B) = A) | ((c_2Earithmetic_2E_3C_3D @ sk3 @ (c_2Elist_2ELENGTH @ skt1 @ sk2)) != (c_2Earithmetic_2E_3C_3D @ B @ A)))),inference(paramod_ordered,[status(thm)],[16,63])).
thf(162,plain,(((c_2Earithmetic_2E_2B @ (c_2Earithmetic_2E_2D @ (c_2Elist_2ELENGTH @ skt1 @ sk2) @ sk3) @ sk3) = (c_2Elist_2ELENGTH @ skt1 @ sk2))),inference(pattern_uni,[status(thm)],[161:[bind(A, $thf(c_2Elist_2ELENGTH @ skt1 @ sk2)),bind(B, $thf(sk3))]])).
thf(171,plain,(! [B:tyop_2Enum_2Enum,A:tyop_2Enum_2Enum] : ((c_2Elist_2EEVERY @ skt1 @ (sk1) @ (c_2Erich__list_2ESEG @ skt1 @ A @ B @ sk2)) | (sk3 != (c_2Elist_2ELENGTH @ skt1 @ sk2)) | ((c_2Earithmetic_2E_2B @ (c_2Earithmetic_2E_2D @ (c_2Elist_2ELENGTH @ skt1 @ sk2) @ sk3) @ sk3) != (c_2Earithmetic_2E_2B @ A @ B)))),inference(paramod_ordered,[status(thm)],[162,144])).
thf(172,plain,((c_2Elist_2EEVERY @ skt1 @ (sk1) @ (c_2Erich__list_2ESEG @ skt1 @ (c_2Earithmetic_2E_2D @ (c_2Elist_2ELENGTH @ skt1 @ sk2) @ sk3) @ sk3 @ sk2)) | (sk3 != (c_2Elist_2ELENGTH @ skt1 @ sk2))),inference(pattern_uni,[status(thm)],[171:[bind(A, $thf(c_2Earithmetic_2E_2D @ (c_2Elist_2ELENGTH @ skt1 @ sk2) @ sk3)),bind(B, $thf(sk3))]])).
thf(15,plain,((~ (c_2Elist_2EEVERY @ skt1 @ (sk1) @ (c_2Elist_2EDROP @ skt1 @ sk3 @ sk2)))),inference(cnf,[status(esa)],[14])).
thf(79,plain,(((c_2Elist_2EEVERY @ skt1 @ (sk1) @ (c_2Elist_2EDROP @ skt1 @ sk3 @ sk2)) != (c_2Elist_2EEVERY @ skt1 @ (sk1) @ sk2))),inference(paramod_ordered,[status(thm)],[17,15])).
thf(80,plain,(((sk1) != (sk1)) | ((c_2Elist_2EDROP @ skt1 @ sk3 @ sk2) != sk2)),inference(simp,[status(thm)],[79])).
thf(81,plain,(((c_2Elist_2EDROP @ skt1 @ sk3 @ sk2) != sk2)),inference(simp,[status(thm)],[80])).
thf(12,axiom,((! [TA: $tType]: (! [A:tyop_2Enum_2Enum,B:(tyop_2Elist_2Elist @ TA)]: ((c_2Earithmetic_2E_3C_3D @ A @ (c_2Elist_2ELENGTH @ TA @ B)) => ((c_2Elist_2EDROP @ TA @ A @ B) = (c_2Erich__list_2ESEG @ TA @ (c_2Earithmetic_2E_2D @ (c_2Elist_2ELENGTH @ TA @ B) @ A) @ A @ B)))))),file('/export/starexec/sandbox/benchmark/Problems/HL402756^3.p',thm_2Erich__list_2EDROP__SEG)).
thf(66,plain,((! [TA: $tType]: (! [A:tyop_2Enum_2Enum,B:(tyop_2Elist_2Elist @ TA)]: ((c_2Earithmetic_2E_3C_3D @ A @ (c_2Elist_2ELENGTH @ TA @ B)) => ((c_2Elist_2EDROP @ TA @ A @ B) = (c_2Erich__list_2ESEG @ TA @ (c_2Earithmetic_2E_2D @ (c_2Elist_2ELENGTH @ TA @ B) @ A) @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
thf(183,plain,(! [C:tyop_2Enum_2Enum,B:tyop_2Enum_2Enum,A:tyop_2Enum_2Enum] : ((c_2Elist_2EEVERY @ skt1 @ (sk1) @ (c_2Erich__list_2ESEG @ skt1 @ B @ C @ sk2)) | (A != sk3) | ((c_2Earithmetic_2E_2B @ (c_2Earithmetic_2E_2D @ A @ A) @ A) != (c_2Earithmetic_2E_2B @ B @ C)))),inference(paramod_ordered,[status(thm)],[156,144])).
thf(184,plain,(! [A:tyop_2Enum_2Enum] : ((c_2Elist_2EEVERY @ skt1 @ (sk1) @ (c_2Erich__list_2ESEG @ skt1 @ (c_2Earithmetic_2E_2D @ A @ A) @ A @ sk2)) | (A != sk3))),inference(pattern_uni,[status(thm)],[183:[bind(A, $thf(E)),bind(B, $thf(c_2Earithmetic_2E_2D @ E @ E)),bind(C, $thf(E))]])).
thf(198,plain,((c_2Elist_2EEVERY @ skt1 @ (sk1) @ (c_2Erich__list_2ESEG @ skt1 @ (c_2Earithmetic_2E_2D @ sk3 @ sk3) @ sk3 @ sk2))),inference(simp,[status(thm)],[184])).
thf(123,plain,(! [TA:$tType,D:tyop_2Enum_2Enum,C:tyop_2Enum_2Enum,B:(tyop_2Elist_2Elist @ TA),A:(TA > $o)] : ((~ (c_2Earithmetic_2E_3C_3D @ (c_2Earithmetic_2E_2B @ C @ D) @ (c_2Elist_2ELENGTH @ TA @ B))) | (c_2Elist_2EEVERY @ TA @ (A) @ (c_2Erich__list_2ESEG @ TA @ C @ D @ B)) | ((c_2Elist_2EEVERY @ skt1 @ (sk1) @ sk2) != (c_2Elist_2EEVERY @ TA @ (A) @ B)))),inference(paramod_ordered,[status(thm)],[17,70])).
thf(124,plain,(! [B:tyop_2Enum_2Enum,A:tyop_2Enum_2Enum] : ((~ (c_2Earithmetic_2E_3C_3D @ (c_2Earithmetic_2E_2B @ A @ B) @ (c_2Elist_2ELENGTH @ skt1 @ sk2))) | (c_2Elist_2EEVERY @ skt1 @ (sk1) @ (c_2Erich__list_2ESEG @ skt1 @ A @ B @ sk2)))),inference(pattern_uni,[status(thm)],[123:[bind(A, $thf(sk1)),bind(B, $thf(sk2)),bind(C, $thf(C)),bind(D, $thf(D))]])).
thf(130,plain,(! [B:tyop_2Enum_2Enum,A:tyop_2Enum_2Enum] : ((~ (c_2Earithmetic_2E_3C_3D @ (c_2Earithmetic_2E_2B @ A @ B) @ (c_2Elist_2ELENGTH @ skt1 @ sk2))) | (c_2Elist_2EEVERY @ skt1 @ (sk1) @ (c_2Erich__list_2ESEG @ skt1 @ A @ B @ sk2)))),inference(simp,[status(thm)],[124])).
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(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 @ $true)),inference(simp,[status(thm)],[42])).
thf(212,plain,(! [TA:$tType,TB:$tType,L:(tyop_2Elist_2Elist @ TA),K:tyop_2Enum_2Enum,J:tyop_2Enum_2Enum,I:tyop_2Enum_2Enum,H:tyop_2Enum_2Enum,G:(TA > $o),F:(tyop_2Elist_2Elist @ TB),E:tyop_2Enum_2Enum,D:tyop_2Enum_2Enum,C:tyop_2Enum_2Enum,B:tyop_2Enum_2Enum,A:(TB > $o)] : ((~ (c_2Elist_2EEVERY @ TB @ (A) @ F)) | ((c_2Earithmetic_2E_2B @ D @ E) != sk3) | ((c_2Elist_2ELENGTH @ TB @ F) != (c_2Elist_2ELENGTH @ skt1 @ sk2)) | ((c_2Earithmetic_2E_2B @ B @ C) != sk3) | ((c_2Elist_2ELENGTH @ TB @ (c_2Erich__list_2ESEG @ TB @ D @ E @ F)) != (c_2Elist_2ELENGTH @ skt1 @ sk2)) | ((c_2Earithmetic_2E_2B @ J @ K) != sk3) | ((c_2Elist_2ELENGTH @ TA @ L) != (c_2Elist_2ELENGTH @ skt1 @ sk2)) | (c_2Elist_2EEVERY @ TA @ (G) @ (c_2Erich__list_2ESEG @ TA @ H @ I @ (c_2Erich__list_2ESEG @ TA @ J @ K @ L))) | ((c_2Earithmetic_2E_2B @ H @ I) != sk3) | ((c_2Elist_2ELENGTH @ TA @ (c_2Erich__list_2ESEG @ TA @ J @ K @ L)) != (c_2Elist_2ELENGTH @ skt1 @ sk2)) | ((c_2Elist_2EEVERY @ TB @ (A) @ (c_2Erich__list_2ESEG @ TB @ B @ C @ (c_2Erich__list_2ESEG @ TB @ D @ E @ F))) != (c_2Elist_2EEVERY @ TA @ (G) @ L)))),inference(paramod_ordered,[status(thm)],[142,142])).
thf(213,plain,(! [TB:$tType,J:(tyop_2Elist_2Elist @ T@),I:tyop_2Enum_2Enum,H:tyop_2Enum_2Enum,G:tyop_2Enum_2Enum,F:tyop_2Enum_2Enum,E:tyop_2Enum_2Enum,D:tyop_2Enum_2Enum,C:tyop_2Enum_2Enum,B:tyop_2Enum_2Enum,A:(T@ > $o)] : ((~ (c_2Elist_2EEVERY @ T@ @ (A) @ J)) | ((c_2Earithmetic_2E_2B @ H @ I) != sk3) | ((c_2Elist_2ELENGTH @ T@ @ J) != (c_2Elist_2ELENGTH @ skt1 @ sk2)) | ((c_2Earithmetic_2E_2B @ F @ G) != sk3) | ((c_2Elist_2ELENGTH @ T@ @ (c_2Erich__list_2ESEG @ T@ @ H @ I @ J)) != (c_2Elist_2ELENGTH @ skt1 @ sk2)) | ((c_2Earithmetic_2E_2B @ D @ E) != sk3) | ((c_2Elist_2ELENGTH @ T@ @ (c_2Erich__list_2ESEG @ T@ @ F @ G @ (c_2Erich__list_2ESEG @ T@ @ H @ I @ J))) != (c_2Elist_2ELENGTH @ skt1 @ sk2)) | (c_2Elist_2EEVERY @ T@ @ (A) @ (c_2Erich__list_2ESEG @ T@ @ B @ C @ (c_2Erich__list_2ESEG @ T@ @ D @ E @ (c_2Erich__list_2ESEG @ T@ @ F @ G @ (c_2Erich__list_2ESEG @ T@ @ H @ I @ J))))) | ((c_2Earithmetic_2E_2B @ B @ C) != sk3) | ((c_2Elist_2ELENGTH @ T@ @ (c_2Erich__list_2ESEG @ T@ @ D @ E @ (c_2Erich__list_2ESEG @ T@ @ F @ G @ (c_2Erich__list_2ESEG @ T@ @ H @ I @ J)))) != (c_2Elist_2ELENGTH @ skt1 @ sk2)))),inference(pattern_uni,[status(thm)],[212:[bind(A, $thf(A)),bind(B, $thf(M)),bind(C, $thf(N)),bind(D, $thf(P)),bind(E, $thf(Q)),bind(F, $thf(R)),bind(G, $thf(A)),bind(H, $thf(H)),bind(I, $thf(I)),bind(J, $thf(J)),bind(K, $thf(K)),bind(L, $thf(c_2Erich__list_2ESEG @ T? @ M @ N @ (c_2Erich__list_2ESEG @ T? @ P @ Q @ R)))]])).
thf(250,plain,(! [TA:$tType,J:(tyop_2Elist_2Elist @ TA),I:tyop_2Enum_2Enum,H:tyop_2Enum_2Enum,G:tyop_2Enum_2Enum,F:tyop_2Enum_2Enum,E:tyop_2Enum_2Enum,D:tyop_2Enum_2Enum,C:tyop_2Enum_2Enum,B:tyop_2Enum_2Enum,A:(TA > $o)] : ((~ (c_2Elist_2EEVERY @ TA @ (A) @ J)) | ((c_2Earithmetic_2E_2B @ H @ I) != sk3) | ((c_2Elist_2ELENGTH @ TA @ J) != (c_2Elist_2ELENGTH @ skt1 @ sk2)) | ((c_2Earithmetic_2E_2B @ F @ G) != sk3) | ((c_2Elist_2ELENGTH @ TA @ (c_2Erich__list_2ESEG @ TA @ H @ I @ J)) != (c_2Elist_2ELENGTH @ skt1 @ sk2)) | ((c_2Earithmetic_2E_2B @ D @ E) != sk3) | ((c_2Elist_2ELENGTH @ TA @ (c_2Erich__list_2ESEG @ TA @ F @ G @ (c_2Erich__list_2ESEG @ TA @ H @ I @ J))) != (c_2Elist_2ELENGTH @ skt1 @ sk2)) | (c_2Elist_2EEVERY @ TA @ (A) @ (c_2Erich__list_2ESEG @ TA @ B @ C @ (c_2Erich__list_2ESEG @ TA @ D @ E @ (c_2Erich__list_2ESEG @ TA @ F @ G @ (c_2Erich__list_2ESEG @ TA @ H @ I @ J))))) | ((c_2Earithmetic_2E_2B @ B @ C) != sk3) | ((c_2Elist_2ELENGTH @ TA @ (c_2Erich__list_2ESEG @ TA @ D @ E @ (c_2Erich__list_2ESEG @ TA @ F @ G @ (c_2Erich__list_2ESEG @ TA @ H @ I @ J)))) != (c_2Elist_2ELENGTH @ skt1 @ sk2)))),inference(simp,[status(thm)],[213])).
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(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(207,plain,(((c_2Elist_2EEVERY @ skt1 @ (sk1) @ (c_2Erich__list_2ESEG @ skt1 @ (c_2Earithmetic_2E_2D @ sk3 @ sk3) @ sk3 @ sk2)) != (c_2Elist_2EEVERY @ skt1 @ (sk1) @ (c_2Elist_2EDROP @ skt1 @ sk3 @ sk2)))),inference(paramod_ordered,[status(thm)],[198,15])).
thf(208,plain,(((sk1) != (sk1)) | ((c_2Erich__list_2ESEG @ skt1 @ (c_2Earithmetic_2E_2D @ sk3 @ sk3) @ sk3 @ sk2) != (c_2Elist_2EDROP @ skt1 @ sk3 @ sk2))),inference(simp,[status(thm)],[207])).
thf(210,plain,(((c_2Erich__list_2ESEG @ skt1 @ (c_2Earithmetic_2E_2D @ sk3 @ sk3) @ sk3 @ sk2) != (c_2Elist_2EDROP @ skt1 @ sk3 @ sk2))),inference(simp,[status(thm)],[208])).
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 @ $true)),inference(simp,[status(thm)],[46])).
thf(188,plain,(! [A:tyop_2Enum_2Enum] : (((c_2Elist_2ELENGTH @ skt1 @ sk2) = A) | ((c_2Earithmetic_2E_2B @ (c_2Earithmetic_2E_2D @ (c_2Elist_2ELENGTH @ skt1 @ sk2) @ sk3) @ sk3) != (c_2Earithmetic_2E_2B @ (c_2Earithmetic_2E_2D @ A @ A) @ A)))),inference(paramod_ordered,[status(thm)],[162,156])).
thf(195,plain,(! [A:tyop_2Enum_2Enum] : (((c_2Elist_2ELENGTH @ skt1 @ sk2) = A) | ((c_2Earithmetic_2E_2D @ (c_2Elist_2ELENGTH @ skt1 @ sk2) @ sk3) != (c_2Earithmetic_2E_2D @ A @ A)) | (sk3 != A))),inference(simp,[status(thm)],[188])).
thf(200,plain,((sk3 = (c_2Elist_2ELENGTH @ skt1 @ sk2)) | ((c_2Earithmetic_2E_2D @ sk3 @ sk3) != (c_2Earithmetic_2E_2D @ (c_2Elist_2ELENGTH @ skt1 @ sk2) @ sk3))),inference(simp,[status(thm)],[195])).
thf(431,plain,($false),inference(cvc4,[status(thm)],[69,142,24,52,14,20,57,29,61,60,38,70,33,65,156,41,64,17,22,27,54,144,49,172,81,66,198,130,35,162,63,18,16,127,31,43,250,40,26,55,58,36,51,210,47,15,200])).
% SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/Problems/HL402756^3.p

34.5800000000017/4.64000000000033	EOF