%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : ANA043-2 : 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 : n027.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 04:14:01 EDT 2024 % Result : Unsatisfiable 0.53s 0.65s % Output : CNFRefutation 0.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : ANA043-2 : TPTP v8.2.0. Released v3.2.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.11/0.32 % Computer : n027.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.33 % DateTime : Sun Jun 23 04:55:09 EDT 2024 % 0.11/0.33 % CPUTime : % 0.49/0.57 start to proof:theBenchmark % 0.53/0.64 %------------------------------------------- % 0.53/0.64 % File :CSE---1.7 % 0.53/0.64 % Problem :theBenchmark % 0.53/0.64 % Transform :cnf % 0.53/0.64 % Format :tptp:raw % 0.53/0.64 % Command :java -jar mcs_scs.jar %d %s % 0.53/0.64 % 0.53/0.64 % Result :Theorem 0.020000s % 0.53/0.64 % Output :CNFRefutation 0.020000s % 0.53/0.64 %------------------------------------------- % 0.53/0.65 %------------------------------------------------------------------------------ % 0.53/0.65 % File : ANA043-2 : TPTP v8.2.0. Released v3.2.0. % 0.53/0.65 % Domain : Analysis % 0.53/0.65 % Problem : Problem about Big-O notation % 0.53/0.65 % Version : [Pau06] axioms : Reduced > Especial. % 0.53/0.65 % English : % 0.53/0.65 % 0.53/0.65 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe % 0.53/0.65 % Source : [Pau06] % 0.53/0.65 % Names : % 0.53/0.65 % 0.53/0.65 % Status : Unsatisfiable % 0.53/0.65 % Rating : 0.06 v8.2.0, 0.00 v5.5.0, 0.06 v5.4.0, 0.00 v5.3.0, 0.08 v5.2.0, 0.00 v5.0.0, 0.14 v4.1.0, 0.22 v4.0.1, 0.17 v3.3.0, 0.29 v3.2.0 % 0.53/0.65 % Syntax : Number of clauses : 9 ( 3 unt; 0 nHn; 6 RR) % 0.53/0.65 % Number of literals : 17 ( 1 equ; 9 neg) % 0.53/0.65 % Maximal clause size : 4 ( 1 avg) % 0.53/0.65 % Maximal term depth : 7 ( 2 avg) % 0.53/0.65 % Number of predicates : 6 ( 5 usr; 0 prp; 1-3 aty) % 0.53/0.65 % Number of functors : 11 ( 11 usr; 3 con; 0-3 aty) % 0.53/0.65 % Number of variables : 15 ( 1 sgn) % 0.53/0.65 % SPC : CNF_UNS_RFO_SEQ_HRN % 0.53/0.65 % 0.53/0.65 % Comments : The problems in the [Pau06] collection each have very many axioms, % 0.53/0.65 % of which only a small selection are required for the refutation. % 0.53/0.65 % The mission is to find those few axioms, after which a refutation % 0.53/0.65 % can be quite easily found. This version has only the necessary % 0.53/0.65 % axioms. % 0.53/0.65 %------------------------------------------------------------------------------ % 0.53/0.65 cnf(cls_conjecture_0,negated_conjecture, % 0.53/0.65 c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) ). % 0.53/0.65 % 0.53/0.65 cnf(cls_conjecture_1,negated_conjecture, % 0.53/0.65 ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),t_b),t_b) ). % 0.53/0.65 % 0.53/0.65 cnf(tfree_tcs,negated_conjecture, % 0.53/0.65 class_Ring__and__Field_Oordered__idom(t_b) ). % 0.53/0.65 % 0.53/0.65 cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom, % 0.53/0.65 ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) % 0.53/0.65 | c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ). % 0.53/0.65 % 0.53/0.65 cnf(cls_OrderedGroup_Omult__left__commute_0,axiom, % 0.53/0.65 ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a) % 0.53/0.65 | c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ). % 0.53/0.65 % 0.53/0.65 cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom, % 0.53/0.65 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 0.53/0.65 | ~ c_lessequals(V_a,V_b,T_a) % 0.53/0.65 | ~ c_lessequals(c_0,V_c,T_a) % 0.53/0.65 | c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) ) ). % 0.53/0.65 % 0.53/0.65 cnf(clsrel_Ring__and__Field_Oordered__idom_17,axiom, % 0.53/0.65 ( ~ class_Ring__and__Field_Oordered__idom(T) % 0.53/0.65 | class_OrderedGroup_Oab__semigroup__mult(T) ) ). % 0.53/0.65 % 0.53/0.65 cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom, % 0.53/0.65 ( ~ class_Ring__and__Field_Oordered__idom(T) % 0.53/0.65 | class_Ring__and__Field_Opordered__semiring(T) ) ). % 0.53/0.65 % 0.53/0.65 cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom, % 0.53/0.65 ( ~ class_Ring__and__Field_Oordered__idom(T) % 0.53/0.65 | class_OrderedGroup_Olordered__ab__group__abs(T) ) ). % 0.53/0.65 % 0.53/0.65 %------------------------------------------------------------------------------ % 0.53/0.65 %------------------------------------------- % 0.53/0.65 % Proof found % 0.53/0.65 % SZS status Theorem for theBenchmark % 0.53/0.65 % SZS output start Proof % 0.53/0.65 %ClaNum:32(EqnAxiom:23) % 0.53/0.65 %VarNum:45(SingletonVarNum:15) % 0.53/0.65 %MaxLitNum:4 % 0.53/0.65 %MaxfuncDepth:6 % 0.53/0.65 %SharedTerms:4 % 0.53/0.65 %goalClause: 24 25 26 % 0.53/0.65 %singleGoalClaCount:3 % 0.53/0.65 [24]P1(a1) % 0.53/0.65 [25]P2(f2(f5(x251),a1),f4(a6,f2(f7(x251),a1),a1),a1) % 0.53/0.65 [26]~P2(f4(f2(f9(f8(x261),f11(x261)),a1),f2(f5(f10(f8(x261),f11(x261))),a1),a1),f4(x261,f4(f2(f9(f8(x261),f11(x261)),a1),f2(f7(f10(f8(x261),f11(x261))),a1),a1),a1),a1) % 0.53/0.65 [27]~P1(x271)+P3(x271) % 0.53/0.65 [28]~P1(x281)+P4(x281) % 0.53/0.65 [29]~P1(x291)+P5(x291) % 0.53/0.65 [30]~P3(x302)+P2(a3,f2(x301,x302),x302) % 0.53/0.65 [31]~P4(x314)+E(f4(x311,f4(x312,x313,x314),x314),f4(x312,f4(x311,x313,x314),x314)) % 0.53/0.65 [32]~P5(x323)+~P2(x322,x324,x323)+~P2(a3,x321,x323)+P2(f4(x321,x322,x323),f4(x321,x324,x323),x323) % 0.53/0.65 %EqnAxiom % 0.53/0.65 [1]E(x11,x11) % 0.53/0.65 [2]E(x22,x21)+~E(x21,x22) % 0.53/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.53/0.65 [4]~E(x41,x42)+E(f5(x41),f5(x42)) % 0.53/0.65 [5]~E(x51,x52)+E(f2(x51,x53),f2(x52,x53)) % 0.53/0.65 [6]~E(x61,x62)+E(f2(x63,x61),f2(x63,x62)) % 0.53/0.65 [7]~E(x71,x72)+E(f7(x71),f7(x72)) % 0.53/0.65 [8]~E(x81,x82)+E(f4(x81,x83,x84),f4(x82,x83,x84)) % 0.53/0.65 [9]~E(x91,x92)+E(f4(x93,x91,x94),f4(x93,x92,x94)) % 0.53/0.65 [10]~E(x101,x102)+E(f4(x103,x104,x101),f4(x103,x104,x102)) % 0.53/0.65 [11]~E(x111,x112)+E(f10(x111,x113),f10(x112,x113)) % 0.53/0.65 [12]~E(x121,x122)+E(f10(x123,x121),f10(x123,x122)) % 0.53/0.65 [13]~E(x131,x132)+E(f8(x131),f8(x132)) % 0.53/0.65 [14]~E(x141,x142)+E(f11(x141),f11(x142)) % 0.53/0.65 [15]~E(x151,x152)+E(f9(x151,x153),f9(x152,x153)) % 0.53/0.65 [16]~E(x161,x162)+E(f9(x163,x161),f9(x163,x162)) % 0.53/0.65 [17]~P1(x171)+P1(x172)+~E(x171,x172) % 0.53/0.65 [18]P2(x182,x183,x184)+~E(x181,x182)+~P2(x181,x183,x184) % 0.53/0.65 [19]P2(x193,x192,x194)+~E(x191,x192)+~P2(x193,x191,x194) % 0.53/0.65 [20]P2(x203,x204,x202)+~E(x201,x202)+~P2(x203,x204,x201) % 0.53/0.65 [21]~P4(x211)+P4(x212)+~E(x211,x212) % 0.53/0.65 [22]~P3(x221)+P3(x222)+~E(x221,x222) % 0.53/0.65 [23]~P5(x231)+P5(x232)+~E(x231,x232) % 0.53/0.65 % 0.53/0.65 %------------------------------------------- % 0.53/0.66 cnf(39,plain, % 0.53/0.66 (P2(a3,f2(x391,a1),a1)), % 0.53/0.66 inference(scs_inference,[],[24,27,30])). % 0.53/0.66 cnf(46,plain, % 0.53/0.66 (E(f4(x461,f4(x462,x463,a1),a1),f4(x462,f4(x461,x463,a1),a1))), % 0.53/0.66 inference(scs_inference,[],[24,28,31])). % 0.53/0.66 cnf(51,plain, % 0.53/0.66 (P2(f4(f2(x511,a1),f2(f5(x512),a1),a1),f4(f2(x511,a1),f4(a6,f2(f7(x512),a1),a1),a1),a1)), % 0.53/0.66 inference(scs_inference,[],[24,39,25,29,32])). % 0.53/0.66 cnf(52,plain, % 0.53/0.66 ($false), % 0.53/0.66 inference(scs_inference,[],[26,46,51,19]), % 0.53/0.66 ['proof']). % 0.53/0.66 % SZS output end Proof % 0.53/0.66 % Total time :0.020000s %------------------------------------------------------------------------------