%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : ANA029-2 : 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 : n018.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 0.55s 0.66s % Output : CNFRefutation 0.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : ANA029-2 : TPTP v8.2.0. Released v3.2.0. % 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n018.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 04:24:39 EDT 2024 % 0.13/0.34 % CPUTime : % 0.53/0.57 start to proof:theBenchmark % 0.55/0.65 %------------------------------------------- % 0.55/0.65 % File :CSE---1.7 % 0.55/0.65 % Problem :theBenchmark % 0.55/0.65 % Transform :cnf % 0.55/0.65 % Format :tptp:raw % 0.55/0.65 % Command :java -jar mcs_scs.jar %d %s % 0.55/0.65 % 0.55/0.65 % Result :Theorem 0.040000s % 0.55/0.65 % Output :CNFRefutation 0.040000s % 0.55/0.65 %------------------------------------------- % 0.55/0.65 %------------------------------------------------------------------------------ % 0.55/0.65 % File : ANA029-2 : TPTP v8.2.0. Released v3.2.0. % 0.55/0.65 % Domain : Analysis % 0.55/0.65 % Problem : Problem about Big-O notation % 0.55/0.65 % Version : [Pau06] axioms : Reduced > Especial. % 0.55/0.65 % English : % 0.55/0.65 % 0.55/0.65 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe % 0.55/0.65 % Source : [Pau06] % 0.55/0.65 % Names : % 0.55/0.65 % 0.55/0.65 % Status : Unsatisfiable % 0.55/0.65 % Rating : 0.00 v6.0.0, 0.14 v5.5.0, 0.12 v5.4.0, 0.10 v5.1.0, 0.09 v5.0.0, 0.07 v4.1.0, 0.12 v4.0.1, 0.00 v3.2.0 % 0.55/0.65 % Syntax : Number of clauses : 14 ( 3 unt; 1 nHn; 12 RR) % 0.55/0.65 % Number of literals : 33 ( 0 equ; 20 neg) % 0.55/0.65 % Maximal clause size : 4 ( 2 avg) % 0.55/0.65 % Maximal term depth : 4 ( 1 avg) % 0.55/0.65 % Number of predicates : 7 ( 7 usr; 0 prp; 1-3 aty) % 0.55/0.65 % Number of functors : 9 ( 9 usr; 3 con; 0-3 aty) % 0.55/0.65 % Number of variables : 26 ( 1 sgn) % 0.55/0.65 % SPC : CNF_UNS_RFO_NEQ_NHN % 0.55/0.65 % 0.55/0.65 % Comments : The problems in the [Pau06] collection each have very many axioms, % 0.55/0.65 % of which only a small selection are required for the refutation. % 0.55/0.65 % The mission is to find those few axioms, after which a refutation % 0.55/0.65 % can be quite easily found. This version has only the necessary % 0.55/0.65 % axioms. % 0.55/0.65 %------------------------------------------------------------------------------ % 0.55/0.65 cnf(cls_conjecture_2,negated_conjecture, % 0.55/0.65 ~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b) ). % 0.55/0.65 % 0.55/0.65 cnf(cls_conjecture_3,negated_conjecture, % 0.55/0.65 ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ). % 0.55/0.65 % 0.55/0.65 cnf(tfree_tcs,negated_conjecture, % 0.55/0.65 class_Ring__and__Field_Oordered__idom(t_b) ). % 0.55/0.65 % 0.55/0.65 cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom, % 0.55/0.65 ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) % 0.55/0.65 | c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ). % 0.55/0.65 % 0.55/0.65 cnf(cls_OrderedGroup_Odiff__le__0__iff__le_0,axiom, % 0.55/0.65 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.55/0.65 | ~ c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a) % 0.55/0.65 | c_lessequals(V_a,V_b,T_a) ) ). % 0.55/0.65 % 0.55/0.65 cnf(cls_OrderedGroup_Odiff__le__0__iff__le_1,axiom, % 0.55/0.65 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.55/0.65 | ~ c_lessequals(V_a,V_b,T_a) % 0.55/0.65 | c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a) ) ). % 0.55/0.65 % 0.55/0.65 cnf(cls_Orderings_Olinorder__not__le_0,axiom, % 0.55/0.65 ( ~ class_Orderings_Olinorder(T_a) % 0.55/0.65 | c_less(V_y,V_x,T_a) % 0.55/0.65 | c_lessequals(V_x,V_y,T_a) ) ). % 0.55/0.65 % 0.55/0.65 cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2,axiom, % 0.55/0.65 ( ~ class_Orderings_Olinorder(T_b) % 0.55/0.65 | ~ c_lessequals(V_y,V_z,T_b) % 0.55/0.65 | ~ c_lessequals(V_x,V_z,T_b) % 0.55/0.65 | c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ) ). % 0.55/0.65 % 0.55/0.65 cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom, % 0.55/0.65 ( ~ class_Orderings_Oorder(T_a) % 0.55/0.65 | ~ c_lessequals(V_y,V_z,T_a) % 0.55/0.65 | ~ c_lessequals(V_x,V_y,T_a) % 0.55/0.65 | c_lessequals(V_x,V_z,T_a) ) ). % 0.55/0.65 % 0.55/0.65 cnf(cls_Orderings_Oorder__less__imp__le_0,axiom, % 0.55/0.65 ( ~ class_Orderings_Oorder(T_a) % 0.55/0.65 | ~ c_less(V_x,V_y,T_a) % 0.55/0.65 | c_lessequals(V_x,V_y,T_a) ) ). % 0.55/0.65 % 0.55/0.65 cnf(clsrel_OrderedGroup_Opordered__ab__group__add_10,axiom, % 0.55/0.65 ( ~ class_OrderedGroup_Opordered__ab__group__add(T) % 0.55/0.65 | class_Orderings_Oorder(T) ) ). % 0.55/0.65 % 0.55/0.66 cnf(clsrel_Ring__and__Field_Oordered__idom_33,axiom, % 0.55/0.66 ( ~ class_Ring__and__Field_Oordered__idom(T) % 0.55/0.66 | class_Orderings_Olinorder(T) ) ). % 0.55/0.66 % 0.55/0.66 cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom, % 0.55/0.66 ( ~ class_Ring__and__Field_Oordered__idom(T) % 0.55/0.66 | class_OrderedGroup_Olordered__ab__group__abs(T) ) ). % 0.55/0.66 % 0.55/0.66 cnf(clsrel_Ring__and__Field_Oordered__idom_54,axiom, % 0.55/0.66 ( ~ class_Ring__and__Field_Oordered__idom(T) % 0.55/0.66 | class_OrderedGroup_Opordered__ab__group__add(T) ) ). % 0.55/0.66 % 0.55/0.66 %------------------------------------------------------------------------------ % 0.55/0.66 %------------------------------------------- % 0.55/0.66 % Proof found % 0.55/0.66 % SZS status Theorem for theBenchmark % 0.55/0.66 % SZS output start Proof % 0.55/0.66 %ClaNum:14(EqnAxiom:0) % 0.55/0.66 %VarNum:64(SingletonVarNum:26) % 0.55/0.66 %MaxLitNum:4 % 0.55/0.66 %MaxfuncDepth:3 % 0.55/0.66 %SharedTerms:13 % 0.55/0.66 %goalClause: 1 2 3 % 0.55/0.66 %singleGoalClaCount:3 % 0.55/0.66 [1]P1(a1) % 0.55/0.66 [2]~P2(a2,f3(f7(a6),f8(a6),a1),a1) % 0.55/0.66 [3]~P2(f4(f3(f7(a6),f8(a6),a1),a2,a1),f5(f3(f7(a6),f9(a6),a1),a1),a1) % 0.55/0.66 [4]~P1(x41)+P4(x41) % 0.55/0.66 [5]~P1(x51)+P5(x51) % 0.55/0.66 [6]~P1(x61)+P6(x61) % 0.55/0.66 [7]~P5(x71)+P7(x71) % 0.55/0.66 [8]~P4(x82)+P2(a2,f5(x81,x82),x82) % 0.55/0.66 [9]P3(x92,x91,x93)+~P6(x93)+P2(x91,x92,x93) % 0.55/0.66 [10]~P7(x103)+~P3(x101,x102,x103)+P2(x101,x102,x103) % 0.55/0.66 [12]~P5(x123)+~P2(x121,x122,x123)+P2(f3(x121,x122,x123),a2,x123) % 0.55/0.66 [13]~P5(x133)+P2(x131,x132,x133)+~P2(f3(x131,x132,x133),a2,x133) % 0.55/0.66 [11]~P7(x113)+~P2(x114,x112,x113)+P2(x111,x112,x113)+~P2(x111,x114,x113) % 0.55/0.66 [14]~P6(x143)+~P2(x141,x144,x143)+~P2(x142,x144,x143)+P2(f4(x141,x142,x143),x144,x143) % 0.55/0.66 %EqnAxiom % 0.55/0.66 % 0.55/0.66 %------------------------------------------- % 0.55/0.66 cnf(25,plain, % 0.55/0.66 (~P2(f3(f7(a6),f8(a6),a1),f5(f3(f7(a6),f9(a6),a1),a1),a1)+~P6(a1)+~P2(a2,f5(f3(f7(a6),f9(a6),a1),a1),a1)), % 0.55/0.66 inference(scs_inference,[],[3,14])). % 0.55/0.66 cnf(39,plain, % 0.55/0.66 (P2(a2,f5(x391,a1),a1)), % 0.55/0.66 inference(scs_inference,[],[1,4,8])). % 0.55/0.66 cnf(40,plain, % 0.55/0.66 (~P2(f3(f7(a6),f8(a6),a1),f5(f3(f7(a6),f9(a6),a1),a1),a1)+~P6(a1)), % 0.55/0.66 inference(scs_inference,[],[39,25])). % 0.55/0.66 cnf(43,plain, % 0.55/0.66 (~P5(a1)+~P2(f5(x431,a1),f3(f7(a6),f8(a6),a1),a1)), % 0.55/0.66 inference(scs_inference,[],[2,39,11,7])). % 0.55/0.66 cnf(47,plain, % 0.55/0.66 (P7(a1)), % 0.55/0.66 inference(scs_inference,[],[1,5,7])). % 0.55/0.66 cnf(51,plain, % 0.55/0.66 (~P2(f3(f7(a6),f8(a6),a1),f5(f3(f7(a6),f9(a6),a1),a1),a1)), % 0.55/0.66 inference(scs_inference,[],[1,6,40])). % 0.55/0.66 cnf(52,plain, % 0.55/0.66 (~P3(f3(f7(a6),f8(a6),a1),f5(f3(f7(a6),f9(a6),a1),a1),a1)), % 0.55/0.66 inference(scs_inference,[],[51,47,10])). % 0.55/0.66 cnf(57,plain, % 0.55/0.66 (~P6(a1)+~P5(a1)), % 0.55/0.66 inference(scs_inference,[],[52,43,9])). % 0.55/0.66 cnf(58,plain, % 0.55/0.66 (~P5(a1)), % 0.55/0.66 inference(scs_inference,[],[1,57,6])). % 0.55/0.66 cnf(59,plain, % 0.55/0.66 ($false), % 0.55/0.66 inference(scs_inference,[],[1,58,5]), % 0.55/0.66 ['proof']). % 0.55/0.66 % SZS output end Proof % 0.55/0.66 % Total time :0.040000s %------------------------------------------------------------------------------