% Time passed: 3024ms
% Effective reasoning time: 1622ms
% 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): logicdef_2E_3D, thm_2Ebool_2EREFL__CLAUSE, thm_2Ecombin_2EFCOMM__DEF, logicdef_2E_5C_2F, quantdef_2E_21, thm_2Ebool_2ETRUTH, logicdef_2E_3D_3D_3E, thm_2Ebool_2EFORALL__SIMP, logicdef_2E_2F_5C, logicdef_2E_7E, thm_2Ecombin_2EASSOC__DEF, quantdef_2E_3F
% No. of inferences in proof: 51
% No. of processed clauses: 15
% No. of generated clauses: 2
% No. of forward subsumed clauses: 1
% No. of backward subsumed clauses: 0
% No. of ground rewrite rules in store: 13
% 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: 1
% No. of choice functions detected: 0
% No. of choice instantiations: 0
% SZS status Theorem for /export/starexec/sandbox/benchmark/Problems/HL400261^3.p : 3024 ms resp. 1622 ms w/o parsing
% SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/Problems/HL400261^3.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) > $o)).
thf(c_2Ebool_2E_2F_5C_type, type, c_2Ebool_2E_2F_5C: ($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_2Ecombin_2EASSOC_type, type, c_2Ecombin_2EASSOC: !>[TA: $tType]: ((TA > (TA > TA)) > $o)).
thf(c_2Ecombin_2EFCOMM_type, type, c_2Ecombin_2EFCOMM: !>[TA: $tType,TB: $tType,TC: $tType]: ((TA > (TB > TA)) > ((TC > (TA > TA)) > $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 > $o))).
thf(c_2Ebool_2E_7E_type, type, c_2Ebool_2E_7E: ($o > $o)).
thf(skt1_type, type, skt1: $tType).
thf(sk1_type, type, sk1: (skt1 > (skt1 > skt1))).
thf(14,axiom,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (TB > TA)),B:(TC > (TA > TA))]: ((c_2Ecombin_2EFCOMM @ TA @ TB @ TC @ A @ B) = (! [C:TC,D:TA,E:TB]: ((B @ C @ (A @ D @ E)) = (A @ (B @ C @ D) @ E))))))),file('/export/starexec/sandbox/benchmark/Problems/HL400261^3.p',thm_2Ecombin_2EFCOMM__DEF)).
thf(69,plain,((! [TA: $tType,TB: $tType,TC: $tType]: (! [A:(TA > (TB > TA)),B:(TC > (TA > TA))]: ((c_2Ecombin_2EFCOMM @ TA @ TB @ TC @ (A) @ (B)) = (! [C:TC,D:TA,E:TB]: ((B @ C @ (A @ D @ E)) = (A @ (B @ C @ D) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
thf(3,axiom,((! [A:$o,B:$o]: ((c_2Ebool_2E_2F_5C @ A @ B) = ((A) & (B))))),file('/export/starexec/sandbox/benchmark/Problems/HL400261^3.p',logicdef_2E_2F_5C)).
thf(18,plain,((! [A:$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/HL400261^3.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:$o]: ((c_2Ebool_2E_5C_2F @ A @ B) = ((A) | (B))))),file('/export/starexec/sandbox/benchmark/Problems/HL400261^3.p',logicdef_2E_5C_2F)).
thf(27,plain,((! [A:$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 @ $true)),inference(simp,[status(thm)],[28])).
thf(10,axiom,(c_2Ebool_2ET),file('/export/starexec/sandbox/benchmark/Problems/HL400261^3.p',thm_2Ebool_2ETRUTH)).
thf(61,plain,(c_2Ebool_2ET),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
thf(5,axiom,((! [A:$o]: ((c_2Ebool_2E_7E @ A) = (~ (A))))),file('/export/starexec/sandbox/benchmark/Problems/HL400261^3.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 @ $true)),inference(simp,[status(thm)],[32])).
thf(6,axiom,((! [A:$o,B:$o]: ((c_2Emin_2E_3D_3D_3E @ A @ B) = ((A) => (B))))),file('/export/starexec/sandbox/benchmark/Problems/HL400261^3.p',logicdef_2E_3D_3D_3E)).
thf(41,plain,((! [A:$o,B:$o]: ((c_2Emin_2E_3D_3D_3E @ A @ B) = ((A) => (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
thf(12,axiom,((! [TA: $tType]: (! [A:TA]: ((A = A) = c_2Ebool_2ET)))),file('/export/starexec/sandbox/benchmark/Problems/HL400261^3.p',thm_2Ebool_2EREFL__CLAUSE)).
thf(64,plain,((! [TA: $tType]: (c_2Ebool_2ET))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
thf(1,conjecture,((! [TA: $tType]: (! [A:(TA > (TA > TA))]: ((c_2Ecombin_2EFCOMM @ TA @ TA @ TA @ A @ A) = (c_2Ecombin_2EASSOC @ TA @ A))))),file('/export/starexec/sandbox/benchmark/Problems/HL400261^3.p',thm_2Ecombin_2EFCOMM__ASSOC)).
thf(2,negated_conjecture,((~ (! [TA: $tType]: (! [A:(TA > (TA > TA))]: ((c_2Ecombin_2EFCOMM @ TA @ TA @ TA @ A @ A) = (c_2Ecombin_2EASSOC @ TA @ A)))))),inference(neg_conjecture,[status(cth)],[1])).
thf(15,plain,((~ (! [TA: $tType]: (! [A:(TA > (TA > TA))]: ((c_2Ecombin_2EFCOMM @ TA @ TA @ TA @ (A) @ (A)) = (c_2Ecombin_2EASSOC @ TA @ (A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(16,plain,((~ ((c_2Ecombin_2EFCOMM @ skt1 @ skt1 @ skt1 @ (sk1) @ (sk1)) = (c_2Ecombin_2EASSOC @ skt1 @ (sk1))))),inference(cnf,[status(esa)],[15])).
thf(17,plain,(((c_2Ecombin_2EFCOMM @ skt1 @ skt1 @ skt1 @ (sk1) @ (sk1)) != (c_2Ecombin_2EASSOC @ skt1 @ (sk1)))),inference(lifteq,[status(thm)],[16])).
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(81,plain,((~ (c_2Ecombin_2EFCOMM @ skt1 @ skt1 @ skt1 @ (sk1) @ (sk1))) | (~ (c_2Ecombin_2EASSOC @ skt1 @ (sk1)))),inference(bool_ext,[status(thm)],[17])).
thf(13,axiom,((! [TA: $tType]: (! [A:(TA > (TA > TA))]: ((c_2Ecombin_2EASSOC @ TA @ A) = (! [B:TA,C:TA,D:TA]: ((A @ B @ (A @ C @ D)) = (A @ (A @ B @ C) @ D))))))),file('/export/starexec/sandbox/benchmark/Problems/HL400261^3.p',thm_2Ecombin_2EASSOC__DEF)).
thf(66,plain,((! [TA: $tType]: (! [A:(TA > (TA > TA))]: ((c_2Ecombin_2EASSOC @ TA @ (A)) = (! [B:TA,C:TA,D:TA]: ((A @ B @ (A @ C @ D)) = (A @ (A @ B @ C) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
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(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/HL400261^3.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/HL400261^3.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(11,axiom,((! [TA: $tType]: (! [A:$o]: ((! [B:TA]: (A)) = A)))),file('/export/starexec/sandbox/benchmark/Problems/HL400261^3.p',thm_2Ebool_2EFORALL__SIMP)).
thf(62,plain,((! [TA: $tType]: ($true))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
thf(98,plain,($false),inference(cvc4,[status(thm)],[69,24,52,20,29,61,38,33,41,64,17,22,27,81,66,35,18,31,40,26,55,58,36,15,62])).
% SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/Problems/HL400261^3.p

23.6099999999999/3.36000000000001	EOF