% Time passed: 4068ms
% Effective reasoning time: 2153ms
% 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): logicdef_2E_3D, thm_2Ebool_2EEQ__CLAUSES, logicdef_2E_5C_2F, thm_2Ereal__topology_2ECONTINUOUS__ON__CLOSED__GEN, quantdef_2E_21, thm_2Ebool_2ETRUTH, logicdef_2E_3D_3D_3E, thm_2Epred__set_2ESUBSET__REFL, logicdef_2E_2F_5C, logicdef_2E_7E, quantdef_2E_3F
% No. of inferences in proof: 26
% No. of processed clauses: 2
% No. of generated clauses: 0
% No. of forward subsumed clauses: 0
% No. of backward subsumed clauses: 0
% No. of ground rewrite rules in store: 2
% No. of non-ground rewrite rules in store: 0
% No. of positive (non-rewrite) units in store: 0
% No. of negative (non-rewrite) units in store: 0
% No. of choice functions detected: 0
% No. of choice instantiations: 0
% SZS status Theorem for /export/starexec/sandbox/benchmark/Problems/HL411203^3.p : 4068 ms resp. 2153 ms w/o parsing
% SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/Problems/HL411203^3.p
thf(tyop_2Emin_2Ebool_type, type, tyop_2Emin_2Ebool: $tType).
thf(tyop_2Erealax_2Ereal_type, type, tyop_2Erealax_2Ereal: $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_2Ebool_2EF_type, type, c_2Ebool_2EF: $o).
thf(c_2Epred__set_2EGSPEC_type, type, c_2Epred__set_2EGSPEC: !>[TA: $tType,TB: $tType]: ((TB > (tyop_2Epair_2Eprod @ TA @ $o)) > (TA > $o))).
thf(c_2Epred__set_2EIMAGE_type, type, c_2Epred__set_2EIMAGE: !>[TA: $tType,TB: $tType]: ((TA > TB) > ((TA > $o) > (TB > $o)))).
thf(c_2Ebool_2EIN_type, type, c_2Ebool_2EIN: !>[TA: $tType]: (TA > ((TA > $o) > $o))).
thf(c_2Epred__set_2ESUBSET_type, type, c_2Epred__set_2ESUBSET: !>[TA: $tType]: ((TA > $o) > ((TA > $o) > $o))).
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_2Etopology_2Eclosed__in_type, type, c_2Etopology_2Eclosed__in: !>[TA: $tType]: ((tyop_2Etopology_2Etopology @ TA) > ((TA > $o) > $o))).
thf(c_2Ereal__topology_2Econtinuous__on_type, type, c_2Ereal__topology_2Econtinuous__on: ((tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal) > ((tyop_2Erealax_2Ereal > $o) > $o))).
thf(c_2Ereal__topology_2Eeuclidean_type, type, c_2Ereal__topology_2Eeuclidean: (tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal)).
thf(c_2Ereal__topology_2Esubtopology_type, type, c_2Ereal__topology_2Esubtopology: !>[TA: $tType]: ((tyop_2Etopology_2Etopology @ TA) > ((TA > $o) > (tyop_2Etopology_2Etopology @ TA)))).
thf(c_2Ebool_2E_7E_type, type, c_2Ebool_2E_7E: ($o > $o)).
thf(1,conjecture,((! [A:(tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal),B:(tyop_2Erealax_2Ereal > $o)]: ((c_2Ereal__topology_2Econtinuous__on @ A @ B) = (! [C:(tyop_2Erealax_2Ereal > $o)]: ((c_2Etopology_2Eclosed__in @ tyop_2Erealax_2Ereal @ (c_2Ereal__topology_2Esubtopology @ tyop_2Erealax_2Ereal @ c_2Ereal__topology_2Eeuclidean @ (c_2Epred__set_2EIMAGE @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B)) @ C) => (c_2Etopology_2Eclosed__in @ tyop_2Erealax_2Ereal @ (c_2Ereal__topology_2Esubtopology @ tyop_2Erealax_2Ereal @ c_2Ereal__topology_2Eeuclidean @ B) @ (c_2Epred__set_2EGSPEC @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ (^ [D:tyop_2Erealax_2Ereal]: (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ $o @ D @ (c_2Ebool_2E_2F_5C @ (c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ D @ B) @ (c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ (A @ D) @ C))))))))))),file('/export/starexec/sandbox/benchmark/Problems/HL411203^3.p',thm_2Ereal__topology_2ECONTINUOUS__ON__CLOSED)).
thf(2,negated_conjecture,((~ (! [A:(tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal),B:(tyop_2Erealax_2Ereal > $o)]: ((c_2Ereal__topology_2Econtinuous__on @ A @ B) = (! [C:(tyop_2Erealax_2Ereal > $o)]: ((c_2Etopology_2Eclosed__in @ tyop_2Erealax_2Ereal @ (c_2Ereal__topology_2Esubtopology @ tyop_2Erealax_2Ereal @ c_2Ereal__topology_2Eeuclidean @ (c_2Epred__set_2EIMAGE @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B)) @ C) => (c_2Etopology_2Eclosed__in @ tyop_2Erealax_2Ereal @ (c_2Ereal__topology_2Esubtopology @ tyop_2Erealax_2Ereal @ c_2Ereal__topology_2Eeuclidean @ B) @ (c_2Epred__set_2EGSPEC @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ (^ [D:tyop_2Erealax_2Ereal]: (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ $o @ D @ (c_2Ebool_2E_2F_5C @ (c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ D @ B) @ (c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ (A @ D) @ C)))))))))))),inference(neg_conjecture,[status(cth)],[1])).
thf(14,plain,((~ (! [A:(tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal),B:(tyop_2Erealax_2Ereal > $o)]: ((c_2Ereal__topology_2Econtinuous__on @ (A) @ (B)) = (! [C:(tyop_2Erealax_2Ereal > $o)]: ((c_2Etopology_2Eclosed__in @ tyop_2Erealax_2Ereal @ (c_2Ereal__topology_2Esubtopology @ tyop_2Erealax_2Ereal @ c_2Ereal__topology_2Eeuclidean @ (c_2Epred__set_2EIMAGE @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B)) @ (C)) => (c_2Etopology_2Eclosed__in @ tyop_2Erealax_2Ereal @ (c_2Ereal__topology_2Esubtopology @ tyop_2Erealax_2Ereal @ c_2Ereal__topology_2Eeuclidean @ (B)) @ (c_2Epred__set_2EGSPEC @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ (^ [D:tyop_2Erealax_2Ereal]: (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ $o @ D @ (c_2Ebool_2E_2F_5C @ (c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ D @ B) @ (c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ (A @ D) @ C)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(9,axiom,((! [TA: $tType]: (! [A:(TA > $o)]: ((c_2Ebool_2E_3F @ TA @ A) = (? [B:TA]: (A @ B)))))),file('/export/starexec/sandbox/benchmark/Problems/HL411203^3.p',quantdef_2E_3F)).
thf(57,plain,((! [TA: $tType]: (! [A:(TA > $o)]: ((c_2Ebool_2E_3F @ TA @ (A)) = (? [B:TA]: (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
thf(11,axiom,((! [A:$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/HL411203^3.p',thm_2Ebool_2EEQ__CLAUSES)).
thf(61,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)],[11])).
thf(10,axiom,(c_2Ebool_2ET),file('/export/starexec/sandbox/benchmark/Problems/HL411203^3.p',thm_2Ebool_2ETRUTH)).
thf(60,plain,(c_2Ebool_2ET),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
thf(12,axiom,((! [TA: $tType]: (! [A:(TA > $o)]: (c_2Epred__set_2ESUBSET @ TA @ A @ A)))),file('/export/starexec/sandbox/benchmark/Problems/HL411203^3.p',thm_2Epred__set_2ESUBSET__REFL)).
thf(70,plain,((! [TA: $tType]: (! [A:(TA > $o)]: (c_2Epred__set_2ESUBSET @ TA @ (A) @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
thf(3,axiom,((! [A:$o,B:$o]: ((c_2Ebool_2E_2F_5C @ A @ B) = ((A) & (B))))),file('/export/starexec/sandbox/benchmark/Problems/HL411203^3.p',logicdef_2E_2F_5C)).
thf(17,plain,((! [A:$o,B:$o]: ((c_2Ebool_2E_2F_5C @ A @ B) = ((A) & (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
thf(8,axiom,((! [TA: $tType]: (! [A:(TA > $o)]: ((c_2Ebool_2E_21 @ TA @ A) = (! [B:TA]: (A @ B)))))),file('/export/starexec/sandbox/benchmark/Problems/HL411203^3.p',quantdef_2E_21)).
thf(54,plain,((! [TA: $tType]: (! [A:(TA > $o)]: ((c_2Ebool_2E_21 @ TA @ (A)) = (! [B:TA]: (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
thf(5,axiom,((! [A:$o]: ((c_2Ebool_2E_7E @ A) = (~ (A))))),file('/export/starexec/sandbox/benchmark/Problems/HL411203^3.p',logicdef_2E_7E)).
thf(35,plain,((! [A:$o]: ((c_2Ebool_2E_7E @ A) = (~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
thf(13,axiom,((! [A:(tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal),B:(tyop_2Erealax_2Ereal > $o),C:(tyop_2Erealax_2Ereal > $o)]: ((c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ (c_2Epred__set_2EIMAGE @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B) @ C) => ((c_2Ereal__topology_2Econtinuous__on @ A @ B) = (! [D:(tyop_2Erealax_2Ereal > $o)]: ((c_2Etopology_2Eclosed__in @ tyop_2Erealax_2Ereal @ (c_2Ereal__topology_2Esubtopology @ tyop_2Erealax_2Ereal @ c_2Ereal__topology_2Eeuclidean @ C) @ D) => (c_2Etopology_2Eclosed__in @ tyop_2Erealax_2Ereal @ (c_2Ereal__topology_2Esubtopology @ tyop_2Erealax_2Ereal @ c_2Ereal__topology_2Eeuclidean @ B) @ (c_2Epred__set_2EGSPEC @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ (^ [E:tyop_2Erealax_2Ereal]: (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ $o @ E @ (c_2Ebool_2E_2F_5C @ (c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ E @ B) @ (c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ (A @ E) @ D)))))))))))),file('/export/starexec/sandbox/benchmark/Problems/HL411203^3.p',thm_2Ereal__topology_2ECONTINUOUS__ON__CLOSED__GEN)).
thf(72,plain,((! [A:(tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal),B:(tyop_2Erealax_2Ereal > $o),C:(tyop_2Erealax_2Ereal > $o)]: ((c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ (c_2Epred__set_2EIMAGE @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B) @ (C)) => ((c_2Ereal__topology_2Econtinuous__on @ (A) @ (B)) = (! [D:(tyop_2Erealax_2Ereal > $o)]: ((c_2Etopology_2Eclosed__in @ tyop_2Erealax_2Ereal @ (c_2Ereal__topology_2Esubtopology @ tyop_2Erealax_2Ereal @ c_2Ereal__topology_2Eeuclidean @ (C)) @ (D)) => (c_2Etopology_2Eclosed__in @ tyop_2Erealax_2Ereal @ (c_2Ereal__topology_2Esubtopology @ tyop_2Erealax_2Ereal @ c_2Ereal__topology_2Eeuclidean @ (B)) @ (c_2Epred__set_2EGSPEC @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ (^ [E:tyop_2Erealax_2Ereal]: (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ $o @ E @ (c_2Ebool_2E_2F_5C @ (c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ E @ B) @ (c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ (A @ E) @ D)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
thf(6,axiom,((! [A:$o,B:$o]: ((c_2Emin_2E_3D_3D_3E @ A @ B) = ((A) => (B))))),file('/export/starexec/sandbox/benchmark/Problems/HL411203^3.p',logicdef_2E_3D_3D_3E)).
thf(40,plain,((! [A:$o,B:$o]: ((c_2Emin_2E_3D_3D_3E @ A @ B) = ((A) => (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
thf(4,axiom,((! [A:$o,B:$o]: ((c_2Ebool_2E_5C_2F @ A @ B) = ((A) | (B))))),file('/export/starexec/sandbox/benchmark/Problems/HL411203^3.p',logicdef_2E_5C_2F)).
thf(26,plain,((! [A:$o,B:$o]: ((c_2Ebool_2E_5C_2F @ A @ B) = ((A) | (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
thf(7,axiom,((! [TA: $tType]: (! [A:TA,B:TA]: ((c_2Emin_2E_3D @ TA @ A @ B) = (A = B))))),file('/export/starexec/sandbox/benchmark/Problems/HL411203^3.p',logicdef_2E_3D)).
thf(51,plain,((! [TA: $tType]: (! [A:TA,B:TA]: ((c_2Emin_2E_3D @ TA @ A @ B) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
thf(75,plain,($false),inference(e,[status(thm)],[14,57,61,60,70,17,54,35,72,40,26,51])).
% SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/Problems/HL411203^3.p

30.2600000000093/4.57999999999811	EOF