% Time passed: 2736ms
% Effective reasoning time: 1727ms
% 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): thm_2Equotient_2Erespects__def, logicdef_2E_3D, thm_2Ebool_2EREFL__CLAUSE, logicdef_2E_5C_2F, quantdef_2E_21, thm_2Ecombin_2EW__THM, thm_2Ebool_2ETRUTH, logicdef_2E_3D_3D_3E, logicdef_2E_2F_5C, logicdef_2E_7E, thm_2Equotient_2EFUN__REL, quantdef_2E_3F
% No. of inferences in proof: 46
% No. of processed clauses: 11
% No. of generated clauses: 5
% No. of forward subsumed clauses: 1
% No. of backward subsumed clauses: 0
% No. of ground rewrite rules in store: 8
% 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/HL403996^3.p : 2736 ms resp. 1727 ms w/o parsing
% SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/Problems/HL403996^3.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_2Equotient_2E_3D_3D_3D_3E_type, type, c_2Equotient_2E_3D_3D_3D_3E: !>[TA: $tType,TB: $tType]: ((TA > (TA > $o)) > ((TB > (TB > $o)) > ((TA > TB) > ((TA > TB) > $o))))).
thf(c_2Emin_2E_3D_3D_3E_type, type, c_2Emin_2E_3D_3D_3E: ($o > ($o > $o))).
thf(c_2Ebool_2E_3F_type, type, c_2Ebool_2E_3F: !>[TA: $tType]: ((TA > $o) > $o)).
thf(c_2Ebool_2ET_type, type, c_2Ebool_2ET: $o).
thf(c_2Ecombin_2EW_type, type, c_2Ecombin_2EW: !>[TA: $tType,TB: $tType]: ((TA > (TA > TB)) > (TA > TB))).
thf(c_2Ebool_2E_5C_2F_type, type, c_2Ebool_2E_5C_2F: ($o > ($o > $o))).
thf(c_2Equotient_2Erespects_type, type, c_2Equotient_2Erespects: !>[TA: $tType,TB: $tType]: ((TA > (TA > TB)) > (TA > TB))).
thf(c_2Ebool_2E_7E_type, type, c_2Ebool_2E_7E: ($o > $o)).
thf(skt1_type, type, skt1: $tType).
thf(skt2_type, type, skt2: $tType).
thf(sk1_type, type, sk1: (skt1 > (skt1 > $o))).
thf(sk2_type, type, sk2: (skt2 > (skt2 > $o))).
thf(sk3_type, type, sk3: (skt1 > skt2)).
thf(sk4_type, type, sk4: skt1).
thf(sk5_type, type, sk5: skt1).
thf(3,axiom,((! [A:$o,B:$o]: ((c_2Ebool_2E_2F_5C @ A @ B) = ((A) & (B))))),file('/export/starexec/sandbox/benchmark/Problems/HL403996^3.p',logicdef_2E_2F_5C)).
thf(18,plain,((! [A:$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/HL403996^3.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 @ $true)),inference(simp,[status(thm)],[19])).
thf(10,axiom,(c_2Ebool_2ET),file('/export/starexec/sandbox/benchmark/Problems/HL403996^3.p',thm_2Ebool_2ETRUTH)).
thf(61,plain,(c_2Ebool_2ET),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
thf(5,axiom,((! [A:$o]: ((c_2Ebool_2E_7E @ A) = (~ (A))))),file('/export/starexec/sandbox/benchmark/Problems/HL403996^3.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(14,axiom,((! [TA: $tType,TB: $tType]: ((c_2Equotient_2Erespects @ TA @ TB) = (c_2Ecombin_2EW @ TA @ TB)))),file('/export/starexec/sandbox/benchmark/Problems/HL403996^3.p',thm_2Equotient_2Erespects__def)).
thf(70,plain,((! [TA: $tType,TB: $tType]: ((c_2Equotient_2Erespects @ TA @ TB) = (c_2Ecombin_2EW @ TA @ TB)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
thf(6,axiom,((! [A:$o,B:$o]: ((c_2Emin_2E_3D_3D_3E @ A @ B) = ((A) => (B))))),file('/export/starexec/sandbox/benchmark/Problems/HL403996^3.p',logicdef_2E_3D_3D_3E)).
thf(41,plain,((! [A:$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,TB: $tType]: (! [A:(TA > (TA > TB)),B:TA]: ((c_2Ecombin_2EW @ TA @ TB @ A @ B) = (A @ B @ B))))),file('/export/starexec/sandbox/benchmark/Problems/HL403996^3.p',thm_2Ecombin_2EW__THM)).
thf(64,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (TA > TB)),B:TA]: ((c_2Ecombin_2EW @ TA @ TB @ (A) @ B) = (A @ B @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
thf(1,conjecture,((! [TA: $tType,TB: $tType]: (! [A:(TA > (TA > $o)),B:(TB > (TB > $o)),C:(TA > TB)]: ((c_2Equotient_2Erespects @ (TA > TB) @ $o @ (c_2Equotient_2E_3D_3D_3D_3E @ TA @ TB @ A @ B) @ C) = (! [D:TA,E:TA]: ((A @ D @ E) => (B @ (C @ D) @ (C @ E)))))))),file('/export/starexec/sandbox/benchmark/Problems/HL403996^3.p',thm_2Equotient_2ERESPECTS__THM)).
thf(2,negated_conjecture,((~ (! [TA: $tType,TB: $tType]: (! [A:(TA > (TA > $o)),B:(TB > (TB > $o)),C:(TA > TB)]: ((c_2Equotient_2Erespects @ (TA > TB) @ $o @ (c_2Equotient_2E_3D_3D_3D_3E @ TA @ TB @ A @ B) @ C) = (! [D:TA,E:TA]: ((A @ D @ E) => (B @ (C @ D) @ (C @ E))))))))),inference(neg_conjecture,[status(cth)],[1])).
thf(15,plain,((~ (! [TA: $tType,TB: $tType]: (! [A:(TA > (TA > $o)),B:(TB > (TB > $o)),C:(TA > TB)]: ((c_2Equotient_2Erespects @ (TA > TB) @ $o @ (c_2Equotient_2E_3D_3D_3D_3E @ TA @ TB @ A @ B) @ (C)) = (! [D:TA,E:TA]: ((A @ D @ E) => (B @ (C @ D) @ (C @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(16,plain,((~ ((c_2Equotient_2Erespects @ (skt1 > skt2) @ $o @ (c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk2) @ (sk3)) = (! [A:skt1,B:skt1]: ((sk1 @ A @ B) => (sk2 @ (sk3 @ A) @ (sk3 @ B))))))),inference(cnf,[status(esa)],[15])).
thf(17,plain,(((c_2Equotient_2Erespects @ (skt1 > skt2) @ $o @ (c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk2) @ (sk3)) != (! [A:skt1,B:skt1]: ((sk1 @ A @ B) => (sk2 @ (sk3 @ A) @ (sk3 @ B)))))),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 @ $false))),inference(simp,[status(thm)],[21])).
thf(4,axiom,((! [A:$o,B:$o]: ((c_2Ebool_2E_5C_2F @ A @ B) = ((A) | (B))))),file('/export/starexec/sandbox/benchmark/Problems/HL403996^3.p',logicdef_2E_5C_2F)).
thf(27,plain,((! [A:$o,B:$o]: ((c_2Ebool_2E_5C_2F @ A @ B) = ((A) | (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
thf(78,plain,((~ (c_2Equotient_2Erespects @ (skt1 > skt2) @ $o @ (c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk2) @ (sk3))) | (~ (! [A:skt1,B:skt1]: ((sk1 @ A @ B) => (sk2 @ (sk3 @ A) @ (sk3 @ B)))))),inference(bool_ext,[status(thm)],[17])).
thf(81,plain,((sk1 @ sk4 @ sk5) | (~ (c_2Equotient_2Erespects @ (skt1 > skt2) @ $o @ (c_2Equotient_2E_3D_3D_3D_3E @ skt1 @ skt2 @ sk1 @ sk2) @ (sk3)))),inference(cnf,[status(esa)],[78])).
thf(13,axiom,((! [TA: $tType,TB: $tType]: (! [A:(TA > (TA > $o)),B:(TB > (TB > $o)),C:(TA > TB),D:(TA > TB)]: ((c_2Equotient_2E_3D_3D_3D_3E @ TA @ TB @ A @ B @ C @ D) = (! [E:TA,F:TA]: ((A @ E @ F) => (B @ (C @ E) @ (D @ F)))))))),file('/export/starexec/sandbox/benchmark/Problems/HL403996^3.p',thm_2Equotient_2EFUN__REL)).
thf(67,plain,((! [TA: $tType,TB: $tType]: (! [A:(TA > (TA > $o)),B:(TB > (TB > $o)),C:(TA > TB),D:(TA > TB)]: ((c_2Equotient_2E_3D_3D_3D_3E @ TA @ TB @ (A) @ (B) @ (C) @ (D)) = (! [E:TA,F:TA]: ((A @ E @ F) => (B @ (C @ E) @ (D @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
thf(71,plain,(! [TA:$tType,TB:$tType] : (((c_2Equotient_2Erespects @ TB @ TA) = (c_2Ecombin_2EW @ TB @ TA)))),inference(cnf,[status(esa)],[70])).
thf(72,plain,(! [TA:$tType,TB:$tType] : (((c_2Equotient_2Erespects @ TB @ TA) = (c_2Ecombin_2EW @ TB @ TA)))),inference(lifteq,[status(thm)],[71])).
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/HL403996^3.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/HL403996^3.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:TA]: ((A = A) = c_2Ebool_2ET)))),file('/export/starexec/sandbox/benchmark/Problems/HL403996^3.p',thm_2Ebool_2EREFL__CLAUSE)).
thf(62,plain,((! [TA: $tType]: (c_2Ebool_2ET))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
thf(92,plain,($false),inference(cvc4,[status(thm)],[24,52,20,61,38,70,41,64,17,22,27,81,18,67,72,40,26,55,58,36,15,62])).
% SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/Problems/HL403996^3.p

16.4400000000023/3.09000000000015	EOF