% Time passed: 3899ms % Effective reasoning time: 2498ms % Solved by strategy % Axioms used in derivation (8): thm_2Ebool_2ENOT__CLAUSES, thm_2EquantHeuristics_2EIS__SOME__EQ__NOT__NONE, thm_2Ebool_2EREFL__CLAUSE, thm_2Ebool_2EEQ__CLAUSES, thm_2Ebool_2ETRUTH, thm_2Elist_2EEXISTS__DEF, thm_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE__def, thm_2Ebool_2EAND__CLAUSES % No. of inferences in proof: 32 % No. of processed clauses: 6 % No. of generated clauses: 11 % No. of forward subsumed clauses: 8 % 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: 0 % No. of choice functions detected: 0 % No. of choice instantiations: 0 % SZS status Theorem for /export/starexec/sandbox/benchmark/Problems/HL402978^3.p : 3899 ms resp. 2498 ms w/o parsing % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/Problems/HL402978^3.p thf(tyop_2Emin_2Ebool_type, type, tyop_2Emin_2Ebool: $tType). thf(c_2Elist_2ECONS_type, type, c_2Elist_2ECONS: !>[TA: $tType]: (TA > ((tyop_2Elist_2Elist @ TA) > (tyop_2Elist_2Elist @ TA)))). thf(c_2Elist_2EEXISTS_type, type, c_2Elist_2EEXISTS: !>[TA: $tType]: ((TA > $o) > ((tyop_2Elist_2Elist @ TA) > $o))). thf(c_2Ebool_2EF_type, type, c_2Ebool_2EF: $o). thf(c_2Eoption_2EIS__SOME_type, type, c_2Eoption_2EIS__SOME: !>[TA: $tType]: ((tyop_2Eoption_2Eoption @ TA) > $o)). thf(c_2Elist_2ENIL_type, type, c_2Elist_2ENIL: !>[TA: $tType]: (tyop_2Elist_2Elist @ TA)). thf(c_2Eoption_2ENONE_type, type, c_2Eoption_2ENONE: !>[TA: $tType]: (tyop_2Eoption_2Eoption @ TA)). thf(c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_type, type, c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE: !>[TA: $tType,TB: $tType]: (TA > ((tyop_2Elist_2Elist @ (TA > (tyop_2Eoption_2Eoption @ TB))) > $o))). thf(c_2Ebool_2ET_type, type, c_2Ebool_2ET: $o). thf(skt1_type, type, skt1: $tType). thf(skt2_type, type, skt2: $tType). thf(skt3_type, type, skt3: $tType). thf(skt4_type, type, skt4: $tType). thf(sk1_type, type, sk1: skt1). thf(sk2_type, type, sk2: skt3). thf(sk3_type, type, sk3: (skt3 > (tyop_2Eoption_2Eoption @ skt4))). thf(sk4_type, type, sk4: (tyop_2Elist_2Elist @ (skt3 > (tyop_2Eoption_2Eoption @ skt4)))). thf(6,axiom,((! [TA: $tType]: (! [A:(TA > $o)]: ((c_2Elist_2EEXISTS @ TA @ A @ (c_2Elist_2ENIL @ TA)) = c_2Ebool_2EF) & ! [A:(TA > $o),B:TA,C:(tyop_2Elist_2Elist @ TA)]: ((c_2Elist_2EEXISTS @ TA @ A @ (c_2Elist_2ECONS @ TA @ B @ C)) = ((A @ B) | (c_2Elist_2EEXISTS @ TA @ A @ C)))))),file('/export/starexec/sandbox/benchmark/Problems/HL402978^3.p',thm_2Elist_2EEXISTS__DEF)). thf(24,plain,((! [TA: $tType]: (! [A:(TA > $o)]: ((c_2Elist_2EEXISTS @ TA @ (A) @ (c_2Elist_2ENIL @ TA)) = c_2Ebool_2EF) & ! [A:(TA > $o),B:TA,C:(tyop_2Elist_2Elist @ TA)]: ((c_2Elist_2EEXISTS @ TA @ (A) @ (c_2Elist_2ECONS @ TA @ B @ C)) = ((A @ B) | (c_2Elist_2EEXISTS @ TA @ (A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). thf(3,axiom,((! [TA: $tType]: (! [A:TA]: ((A = A) = c_2Ebool_2ET)))),file('/export/starexec/sandbox/benchmark/Problems/HL402978^3.p',thm_2Ebool_2EREFL__CLAUSE)). thf(14,plain,((! [TA: $tType]: (c_2Ebool_2ET))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). thf(25,plain,(! [TA:$tType,C:(tyop_2Elist_2Elist @ TA),B:TA,A:(TA > $o)] : (((c_2Elist_2EEXISTS @ TA @ (A) @ (c_2Elist_2ECONS @ TA @ B @ C)) = ((A @ B) | (c_2Elist_2EEXISTS @ TA @ (A) @ C))))),inference(cnf,[status(esa)],[24])). thf(27,plain,(! [TA:$tType,C:(tyop_2Elist_2Elist @ TA),B:TA,A:(TA > $o)] : ((((A @ B) | (c_2Elist_2EEXISTS @ TA @ (A) @ C)) = (c_2Elist_2EEXISTS @ TA @ (A) @ (c_2Elist_2ECONS @ TA @ B @ C))))),inference(lifteq,[status(thm)],[25])). thf(28,plain,(! [TA:$tType,C:(tyop_2Elist_2Elist @ TA),B:TA,A:(TA > $o)] : ((((A @ B) | (c_2Elist_2EEXISTS @ TA @ (A) @ C)) = (c_2Elist_2EEXISTS @ TA @ (A) @ (c_2Elist_2ECONS @ TA @ B @ C))))),inference(simp,[status(thm)],[27])). thf(9,axiom,((! [A:$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/HL402978^3.p',thm_2Ebool_2EEQ__CLAUSES)). thf(38,plain,((! [A:$o]: (((c_2Ebool_2ET = A) = A) & ((A = c_2Ebool_2ET) = A) & ((c_2Ebool_2EF = A) = (~ (A))) & ((A = c_2Ebool_2EF) = (~ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). thf(8,axiom,((! [A:$o]: ((~ (~ (A))) = A) & ((~ (c_2Ebool_2ET)) = c_2Ebool_2EF) & ((~ (c_2Ebool_2EF)) = c_2Ebool_2ET))),file('/export/starexec/sandbox/benchmark/Problems/HL402978^3.p',thm_2Ebool_2ENOT__CLAUSES)). thf(33,plain,((((~ (c_2Ebool_2ET)) = c_2Ebool_2EF) & ((~ (c_2Ebool_2EF)) = c_2Ebool_2ET))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). thf(5,axiom,((! [A:$o]: ((((c_2Ebool_2ET) & (A)) = A) & (((A) & (c_2Ebool_2ET)) = A) & (((c_2Ebool_2EF) & (A)) = c_2Ebool_2EF) & (((A) & (c_2Ebool_2EF)) = c_2Ebool_2EF) & (((A) & (A)) = A)))),file('/export/starexec/sandbox/benchmark/Problems/HL402978^3.p',thm_2Ebool_2EAND__CLAUSES)). thf(17,plain,((! [A:$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(20,plain,(((((c_2Ebool_2ET) & ($false)) = $false) & ((($false) & (c_2Ebool_2ET)) = $false) & (((c_2Ebool_2EF) & ($false)) = c_2Ebool_2EF) & ((($false) & (c_2Ebool_2EF)) = c_2Ebool_2EF))),inference(instance,[status(thm)],[17])). thf(21,plain,((~ ($false) & ~ (c_2Ebool_2EF) & ~ (c_2Ebool_2EF))),inference(simp,[status(thm)],[20])). thf(22,plain,(~ (c_2Ebool_2EF)),inference(cnf,[status(esa)],[21])). thf(4,axiom,(c_2Ebool_2ET),file('/export/starexec/sandbox/benchmark/Problems/HL402978^3.p',thm_2Ebool_2ETRUTH)). thf(16,plain,(c_2Ebool_2ET),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). thf(1,conjecture,((! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:TA]: ((c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ TA @ TB @ A @ (c_2Elist_2ENIL @ (TA > (tyop_2Eoption_2Eoption @ TB)))) = c_2Ebool_2EF) & ! [A:TC,B:(TC > (tyop_2Eoption_2Eoption @ TD)),C:(tyop_2Elist_2Elist @ (TC > (tyop_2Eoption_2Eoption @ TD)))]: ((c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ TC @ TD @ A @ (c_2Elist_2ECONS @ (TC > (tyop_2Eoption_2Eoption @ TD)) @ B @ C)) = (~ ((B @ A) = (c_2Eoption_2ENONE @ TD)) | (c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ TC @ TD @ A @ C)))))),file('/export/starexec/sandbox/benchmark/Problems/HL402978^3.p',thm_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE__REWRITES)). thf(2,negated_conjecture,((~ (! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:TA]: ((c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ TA @ TB @ A @ (c_2Elist_2ENIL @ (TA > (tyop_2Eoption_2Eoption @ TB)))) = c_2Ebool_2EF) & ! [A:TC,B:(TC > (tyop_2Eoption_2Eoption @ TD)),C:(tyop_2Elist_2Elist @ (TC > (tyop_2Eoption_2Eoption @ TD)))]: ((c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ TC @ TD @ A @ (c_2Elist_2ECONS @ (TC > (tyop_2Eoption_2Eoption @ TD)) @ B @ C)) = (~ ((B @ A) = (c_2Eoption_2ENONE @ TD)) | (c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ TC @ TD @ A @ C))))))),inference(neg_conjecture,[status(cth)],[1])). thf(11,plain,((~ (! [TA: $tType,TB: $tType,TC: $tType,TD: $tType]: (! [A:TA]: ((c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ TA @ TB @ A @ (c_2Elist_2ENIL @ (TA > (tyop_2Eoption_2Eoption @ TB)))) = c_2Ebool_2EF) & ! [A:TC,B:(TC > (tyop_2Eoption_2Eoption @ TD)),C:(tyop_2Elist_2Elist @ (TC > (tyop_2Eoption_2Eoption @ TD)))]: ((c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ TC @ TD @ A @ (c_2Elist_2ECONS @ (TC > (tyop_2Eoption_2Eoption @ TD)) @ (B) @ C)) = (~ ((B @ A) = (c_2Eoption_2ENONE @ TD)) | (c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ TC @ TD @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). thf(12,plain,((~ ((c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ skt1 @ skt2 @ sk1 @ (c_2Elist_2ENIL @ (skt1 > (tyop_2Eoption_2Eoption @ skt2)))) = c_2Ebool_2EF)) | (~ ((c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ skt3 @ skt4 @ sk2 @ (c_2Elist_2ECONS @ (skt3 > (tyop_2Eoption_2Eoption @ skt4)) @ (sk3) @ sk4)) = (~ ((sk3 @ sk2) = (c_2Eoption_2ENONE @ skt4)) | (c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ skt3 @ skt4 @ sk2 @ sk4))))),inference(cnf,[status(esa)],[11])). thf(13,plain,(((c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ skt1 @ skt2 @ sk1 @ (c_2Elist_2ENIL @ (skt1 > (tyop_2Eoption_2Eoption @ skt2)))) != c_2Ebool_2EF) | ((~ ((sk3 @ sk2) = (c_2Eoption_2ENONE @ skt4)) | (c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ skt3 @ skt4 @ sk2 @ sk4)) != (c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ skt3 @ skt4 @ sk2 @ (c_2Elist_2ECONS @ (skt3 > (tyop_2Eoption_2Eoption @ skt4)) @ (sk3) @ sk4)))),inference(lifteq,[status(thm)],[12])). thf(55,plain,((c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ skt1 @ skt2 @ sk1 @ (c_2Elist_2ENIL @ (skt1 > (tyop_2Eoption_2Eoption @ skt2)))) | ((~ ((sk3 @ sk2) = (c_2Eoption_2ENONE @ skt4)) | (c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ skt3 @ skt4 @ sk2 @ sk4)) != (c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ skt3 @ skt4 @ sk2 @ (c_2Elist_2ECONS @ (skt3 > (tyop_2Eoption_2Eoption @ skt4)) @ (sk3) @ sk4)))),inference(rewrite,[status(thm)],[13,22])). thf(56,plain,((c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ skt1 @ skt2 @ sk1 @ (c_2Elist_2ENIL @ (skt1 > (tyop_2Eoption_2Eoption @ skt2)))) | (~ (~ ((sk3 @ sk2) = (c_2Eoption_2ENONE @ skt4)) | (c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ skt3 @ skt4 @ sk2 @ sk4))) | (~ (c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ skt3 @ skt4 @ sk2 @ (c_2Elist_2ECONS @ (skt3 > (tyop_2Eoption_2Eoption @ skt4)) @ (sk3) @ sk4)))),inference(bool_ext,[status(thm)],[55])). thf(58,plain,((~ (c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ skt3 @ skt4 @ sk2 @ (c_2Elist_2ECONS @ (skt3 > (tyop_2Eoption_2Eoption @ skt4)) @ (sk3) @ sk4))) | (~ (c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ skt3 @ skt4 @ sk2 @ sk4)) | (c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ skt1 @ skt2 @ sk1 @ (c_2Elist_2ENIL @ (skt1 > (tyop_2Eoption_2Eoption @ skt2))))),inference(cnf,[status(esa)],[56])). thf(7,axiom,((! [TA: $tType,TB: $tType]: (! [A:TA,B:(tyop_2Elist_2Elist @ (TA > (tyop_2Eoption_2Eoption @ TB)))]: ((c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ TA @ TB @ A @ B) = (c_2Elist_2EEXISTS @ (TA > (tyop_2Eoption_2Eoption @ TB)) @ (^ [C:(TA > (tyop_2Eoption_2Eoption @ TB))]: (c_2Eoption_2EIS__SOME @ TB @ (C @ A))) @ B))))),file('/export/starexec/sandbox/benchmark/Problems/HL402978^3.p',thm_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE__def)). thf(30,plain,((! [TA: $tType,TB: $tType]: (! [A:TA,B:(tyop_2Elist_2Elist @ (TA > (tyop_2Eoption_2Eoption @ TB)))]: ((c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE @ TA @ TB @ A @ B) = (c_2Elist_2EEXISTS @ (TA > (tyop_2Eoption_2Eoption @ TB)) @ (^ [C:(TA > (tyop_2Eoption_2Eoption @ TB))]: (c_2Eoption_2EIS__SOME @ TB @ (C @ A))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). thf(10,axiom,((! [TA: $tType]: (! [A:(tyop_2Eoption_2Eoption @ TA)]: ((c_2Eoption_2EIS__SOME @ TA @ A) = (~ (A = (c_2Eoption_2ENONE @ TA))))))),file('/export/starexec/sandbox/benchmark/Problems/HL402978^3.p',thm_2EquantHeuristics_2EIS__SOME__EQ__NOT__NONE)). thf(47,plain,((! [TA: $tType]: (! [A:(tyop_2Eoption_2Eoption @ TA)]: ((c_2Eoption_2EIS__SOME @ TA @ A) = (~ (A = (c_2Eoption_2ENONE @ TA))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). thf(15,plain,(c_2Ebool_2ET),inference(cnf,[status(esa)],[14])). thf(87,plain,($false),inference(cvc4,[status(thm)],[24,14,28,38,33,17,22,16,11,55,58,30,47,15])). % SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/Problems/HL402978^3.p 32.3000000000029/4.16000000000076 EOF