%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : ANA027-2 : TPTP v8.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n019.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Jun 24 04:13:57 EDT 2024 % Result : Unsatisfiable 1.15s 1.23s % Output : CNFRefutation 1.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : ANA027-2 : TPTP v8.2.0. Released v3.2.0. % 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n019.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sun Jun 23 04:55:54 EDT 2024 % 0.13/0.34 % CPUTime : % 0.20/0.57 start to proof:theBenchmark % 1.15/1.23 %------------------------------------------- % 1.15/1.23 % File :CSE---1.7 % 1.15/1.23 % Problem :theBenchmark % 1.15/1.23 % Transform :cnf % 1.15/1.23 % Format :tptp:raw % 1.15/1.23 % Command :java -jar mcs_scs.jar %d %s % 1.15/1.23 % 1.15/1.23 % Result :Theorem 0.620000s % 1.15/1.23 % Output :CNFRefutation 0.620000s % 1.15/1.23 %------------------------------------------- % 1.15/1.23 %------------------------------------------------------------------------------ % 1.15/1.23 % File : ANA027-2 : TPTP v8.2.0. Released v3.2.0. % 1.15/1.23 % Domain : Analysis % 1.15/1.23 % Problem : Problem about Big-O notation % 1.15/1.23 % Version : [Pau06] axioms : Reduced > Especial. % 1.15/1.23 % English : % 1.15/1.23 % 1.15/1.23 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe % 1.15/1.23 % Source : [Pau06] % 1.15/1.23 % Names : % 1.15/1.23 % 1.15/1.23 % Status : Unsatisfiable % 1.15/1.23 % Rating : 0.00 v5.3.0, 0.08 v5.2.0, 0.00 v5.0.0, 0.14 v4.1.0, 0.11 v4.0.1, 0.17 v3.3.0, 0.14 v3.2.0 % 1.15/1.23 % Syntax : Number of clauses : 13 ( 4 unt; 0 nHn; 12 RR) % 1.15/1.23 % Number of literals : 26 ( 1 equ; 14 neg) % 1.15/1.23 % Maximal clause size : 4 ( 2 avg) % 1.15/1.23 % Maximal term depth : 3 ( 1 avg) % 1.15/1.23 % Number of predicates : 8 ( 7 usr; 0 prp; 1-3 aty) % 1.15/1.23 % Number of functors : 8 ( 8 usr; 3 con; 0-3 aty) % 1.15/1.23 % Number of variables : 19 ( 0 sgn) % 1.15/1.23 % SPC : CNF_UNS_RFO_SEQ_HRN % 1.15/1.23 % 1.15/1.23 % Comments : The problems in the [Pau06] collection each have very many axioms, % 1.15/1.23 % of which only a small selection are required for the refutation. % 1.15/1.23 % The mission is to find those few axioms, after which a refutation % 1.15/1.23 % can be quite easily found. This version has only the necessary % 1.15/1.23 % axioms. % 1.15/1.23 %------------------------------------------------------------------------------ % 1.15/1.23 cnf(cls_conjecture_1,negated_conjecture, % 1.15/1.23 c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b) ). % 1.15/1.23 % 1.15/1.23 cnf(cls_conjecture_2,negated_conjecture, % 1.15/1.23 c_lessequals(v_g(v_x),v_k(v_x),t_b) ). % 1.15/1.23 % 1.15/1.23 cnf(cls_conjecture_3,negated_conjecture, % 1.15/1.23 ~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ). % 1.15/1.23 % 1.15/1.23 cnf(tfree_tcs,negated_conjecture, % 1.15/1.23 class_Ring__and__Field_Oordered__idom(t_b) ). % 1.15/1.23 % 1.15/1.23 cnf(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom, % 1.15/1.23 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.15/1.23 | c_plus(c_0,V_y,T_a) = V_y ) ). % 1.15/1.23 % 1.15/1.23 cnf(cls_OrderedGroup_Ocompare__rls__9_0,axiom, % 1.15/1.23 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.15/1.23 | ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) % 1.15/1.23 | c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ) ). % 1.15/1.23 % 1.15/1.23 cnf(cls_OrderedGroup_Ocompare__rls__9_1,axiom, % 1.15/1.23 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.15/1.23 | ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) % 1.15/1.23 | c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ) ). % 1.15/1.23 % 1.15/1.23 cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom, % 1.15/1.23 ( ~ class_Orderings_Oorder(T_a) % 1.15/1.23 | ~ c_lessequals(V_y,V_z,T_a) % 1.15/1.23 | ~ c_lessequals(V_x,V_y,T_a) % 1.15/1.23 | c_lessequals(V_x,V_z,T_a) ) ). % 1.15/1.23 % 1.15/1.23 cnf(clsrel_LOrder_Ojoin__semilorder_1,axiom, % 1.15/1.23 ( ~ class_LOrder_Ojoin__semilorder(T) % 1.15/1.23 | class_Orderings_Oorder(T) ) ). % 1.15/1.23 % 1.15/1.23 cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_1,axiom, % 1.15/1.23 ( ~ class_OrderedGroup_Olordered__ab__group__abs(T) % 1.15/1.23 | class_OrderedGroup_Opordered__ab__group__add(T) ) ). % 1.15/1.23 % 1.15/1.23 cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_15,axiom, % 1.15/1.23 ( ~ class_OrderedGroup_Olordered__ab__group__abs(T) % 1.15/1.23 | class_LOrder_Ojoin__semilorder(T) ) ). % 1.15/1.23 % 1.15/1.23 cnf(clsrel_Ring__and__Field_Oordered__idom_23,axiom, % 1.15/1.23 ( ~ class_Ring__and__Field_Oordered__idom(T) % 1.15/1.23 | class_OrderedGroup_Ocomm__monoid__add(T) ) ). % 1.15/1.23 % 1.15/1.23 cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom, % 1.15/1.23 ( ~ class_Ring__and__Field_Oordered__idom(T) % 1.15/1.23 | class_OrderedGroup_Olordered__ab__group__abs(T) ) ). % 1.15/1.23 % 1.15/1.23 %------------------------------------------------------------------------------ % 1.15/1.23 %------------------------------------------- % 1.15/1.23 % Proof found % 1.15/1.23 % SZS status Theorem for theBenchmark % 1.15/1.23 % SZS output start Proof % 1.15/1.23 %ClaNum:34(EqnAxiom:21) % 1.15/1.23 %VarNum:46(SingletonVarNum:19) % 1.15/1.23 %MaxLitNum:4 % 1.15/1.23 %MaxfuncDepth:2 % 1.15/1.23 %SharedTerms:12 % 1.15/1.23 %goalClause: 22 23 24 25 % 1.15/1.23 %singleGoalClaCount:4 % 1.15/1.23 [22]P1(a1) % 1.15/1.23 [23]P2(f6(a5),f8(a5),a1) % 1.15/1.23 [24]P2(a2,f3(f7(a5),f8(a5),a1),a1) % 1.15/1.23 [25]~P2(a2,f3(f7(a5),f6(a5),a1),a1) % 1.15/1.23 [26]~P1(x261)+P3(x261) % 1.15/1.23 [27]~P6(x271)+P5(x271) % 1.15/1.23 [28]~P4(x281)+P7(x281) % 1.15/1.23 [29]~P6(x291)+P4(x291) % 1.15/1.23 [30]~P1(x301)+P6(x301) % 1.15/1.23 [31]~P3(x312)+E(f4(a2,x311,x312),x311) % 1.15/1.23 [33]~P5(x334)+~P2(f4(x331,x333,x334),x332,x334)+P2(x331,f3(x332,x333,x334),x334) % 1.15/1.23 [34]~P5(x343)+~P2(x341,f3(x344,x342,x343),x343)+P2(f4(x341,x342,x343),x344,x343) % 1.15/1.23 [32]~P7(x323)+~P2(x324,x322,x323)+P2(x321,x322,x323)+~P2(x321,x324,x323) % 1.15/1.23 %EqnAxiom % 1.15/1.23 [1]E(x11,x11) % 1.15/1.23 [2]E(x22,x21)+~E(x21,x22) % 1.15/1.23 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.15/1.23 [4]~E(x41,x42)+E(f6(x41),f6(x42)) % 1.15/1.23 [5]~E(x51,x52)+E(f8(x51),f8(x52)) % 1.15/1.24 [6]~E(x61,x62)+E(f7(x61),f7(x62)) % 1.15/1.24 [7]~E(x71,x72)+E(f4(x71,x73,x74),f4(x72,x73,x74)) % 1.15/1.24 [8]~E(x81,x82)+E(f4(x83,x81,x84),f4(x83,x82,x84)) % 1.15/1.24 [9]~E(x91,x92)+E(f4(x93,x94,x91),f4(x93,x94,x92)) % 1.15/1.24 [10]~E(x101,x102)+E(f3(x101,x103,x104),f3(x102,x103,x104)) % 1.15/1.24 [11]~E(x111,x112)+E(f3(x113,x111,x114),f3(x113,x112,x114)) % 1.15/1.24 [12]~E(x121,x122)+E(f3(x123,x124,x121),f3(x123,x124,x122)) % 1.15/1.24 [13]~P1(x131)+P1(x132)+~E(x131,x132) % 1.15/1.24 [14]P2(x142,x143,x144)+~E(x141,x142)+~P2(x141,x143,x144) % 1.15/1.24 [15]P2(x153,x152,x154)+~E(x151,x152)+~P2(x153,x151,x154) % 1.15/1.24 [16]P2(x163,x164,x162)+~E(x161,x162)+~P2(x163,x164,x161) % 1.15/1.24 [17]~P5(x171)+P5(x172)+~E(x171,x172) % 1.15/1.24 [18]~P7(x181)+P7(x182)+~E(x181,x182) % 1.15/1.24 [19]~P3(x191)+P3(x192)+~E(x191,x192) % 1.15/1.24 [20]~P4(x201)+P4(x202)+~E(x201,x202) % 1.15/1.24 [21]~P6(x211)+P6(x212)+~E(x211,x212) % 1.15/1.24 % 1.15/1.24 %------------------------------------------- % 1.15/1.24 cnf(37,plain, % 1.15/1.24 (~P5(a1)+~P2(f4(a2,f6(a5),a1),f7(a5),a1)), % 1.15/1.24 inference(scs_inference,[],[24,25,15,11,33])). % 1.15/1.24 cnf(50,plain, % 1.15/1.24 (P2(x501,f3(f7(a5),f8(a5),a1),a1)+~E(a2,x501)), % 1.15/1.24 inference(scs_inference,[],[24,14])). % 1.15/1.24 cnf(75,plain, % 1.15/1.24 (E(f4(a2,x751,a1),x751)), % 1.15/1.24 inference(scs_inference,[],[22,26,31])). % 1.15/1.24 cnf(76,plain, % 1.15/1.24 (E(x761,f4(a2,x761,a1))), % 1.15/1.24 inference(scs_inference,[],[75,2])). % 1.15/1.24 cnf(78,plain, % 1.15/1.24 (P2(f6(a5),f8(a5),f4(a2,a1,a1))), % 1.15/1.24 inference(scs_inference,[],[22,23,75,2,13,16])). % 1.15/1.24 cnf(85,plain, % 1.15/1.24 (E(x851,f4(a2,x851,a1))), % 1.15/1.24 inference(rename_variables,[],[76])). % 1.15/1.24 cnf(87,plain, % 1.15/1.24 (E(x871,f4(a2,x871,a1))), % 1.15/1.24 inference(rename_variables,[],[76])). % 1.15/1.24 cnf(88,plain, % 1.15/1.24 (P2(f6(a5),f4(a2,f8(a5),a1),a1)), % 1.15/1.24 inference(scs_inference,[],[23,76,85,87,50,14,15])). % 1.15/1.24 cnf(89,plain, % 1.15/1.24 (E(x891,f4(a2,x891,a1))), % 1.15/1.24 inference(rename_variables,[],[76])). % 1.15/1.24 cnf(92,plain, % 1.15/1.24 (~P6(f4(a2,x921,a1))+P6(x921)), % 1.15/1.24 inference(scs_inference,[],[23,75,76,85,87,89,50,14,15,16,21])). % 1.15/1.24 cnf(96,plain, % 1.15/1.24 (P2(f4(a2,f6(a5),a1),f8(a5),f4(a2,a1,a1))), % 1.15/1.24 inference(scs_inference,[],[78,76,14])). % 1.15/1.24 cnf(97,plain, % 1.15/1.24 (E(x971,f4(a2,x971,a1))), % 1.15/1.24 inference(rename_variables,[],[76])). % 1.15/1.24 cnf(100,plain, % 1.15/1.24 (~P5(f4(a2,x1001,a1))+P5(x1001)), % 1.15/1.24 inference(scs_inference,[],[78,75,76,97,14,15,17])). % 1.15/1.24 cnf(101,plain, % 1.15/1.24 (~P6(f4(a2,x1011,a1))+P5(x1011)), % 1.15/1.24 inference(scs_inference,[],[78,75,76,97,14,15,17,27])). % 1.15/1.24 cnf(108,plain, % 1.15/1.24 (P2(f4(a2,f6(a5),a1),f4(a2,f8(a5),a1),a1)), % 1.15/1.24 inference(scs_inference,[],[88,76,14])). % 1.15/1.24 cnf(109,plain, % 1.15/1.24 (E(x1091,f4(a2,x1091,a1))), % 1.15/1.24 inference(rename_variables,[],[76])). % 1.15/1.24 cnf(111,plain, % 1.15/1.24 (E(x1111,f4(a2,x1111,a1))), % 1.15/1.24 inference(rename_variables,[],[76])). % 1.15/1.24 cnf(112,plain, % 1.15/1.24 (~P5(x1121)+P5(f4(a2,x1121,a1))), % 1.15/1.24 inference(scs_inference,[],[88,96,76,109,111,14,15,17])). % 1.15/1.24 cnf(118,plain, % 1.15/1.24 (~P7(f4(a2,x1181,a1))+P7(x1181)), % 1.15/1.24 inference(scs_inference,[],[75,18])). % 1.15/1.24 cnf(134,plain, % 1.15/1.24 (~P6(x1341)+P7(f4(a2,x1341,a1))), % 1.15/1.24 inference(scs_inference,[],[76,18,28,29])). % 1.15/1.24 cnf(147,plain, % 1.15/1.24 (~P6(x1471)+P6(f4(a2,x1471,a1))), % 1.15/1.24 inference(scs_inference,[],[76,21])). % 1.15/1.24 cnf(185,plain, % 1.15/1.24 (~P2(f4(a2,f6(a5),a1),f7(a5),a1)+~P5(f4(a2,a1,a1))), % 1.15/1.24 inference(scs_inference,[],[100,37])). % 1.15/1.24 cnf(297,plain, % 1.15/1.24 (P7(f4(a2,a1,a1))), % 1.15/1.24 inference(scs_inference,[],[22,134,30])). % 1.15/1.24 cnf(299,plain, % 1.15/1.24 (P7(a1)), % 1.15/1.24 inference(scs_inference,[],[297,118])). % 1.15/1.24 cnf(367,plain, % 1.15/1.24 (~P6(f4(a2,a1,a1))+~P2(f4(a2,f8(a5),a1),f7(a5),a1)), % 1.15/1.24 inference(scs_inference,[],[108,299,32,185,112,27])). % 1.15/1.24 cnf(403,plain, % 1.15/1.24 (P6(f4(a2,a1,a1))), % 1.15/1.24 inference(scs_inference,[],[22,147,30])). % 1.15/1.24 cnf(406,plain, % 1.15/1.24 (~P2(f4(a2,f8(a5),a1),f7(a5),a1)), % 1.15/1.24 inference(scs_inference,[],[403,367])). % 1.15/1.24 cnf(408,plain, % 1.15/1.24 (P5(a1)), % 1.15/1.24 inference(scs_inference,[],[403,92,101])). % 1.15/1.24 cnf(429,plain, % 1.15/1.24 ($false), % 1.15/1.24 inference(scs_inference,[],[24,406,408,34]), % 1.15/1.24 ['proof']). % 1.15/1.24 % SZS output end Proof % 1.15/1.24 % Total time :0.620000s %------------------------------------------------------------------------------