%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : ANA017-2 : TPTP v8.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n028.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 04:13:54 EDT 2024 % Result : Unsatisfiable 58.57s 58.65s % Output : CNFRefutation 58.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ANA017-2 : TPTP v8.2.0. Released v3.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.33 % Computer : n028.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Sun Jun 23 04:23:09 EDT 2024 % 0.13/0.34 % CPUTime : % 0.21/0.58 start to proof:theBenchmark % 58.57/58.63 %------------------------------------------- % 58.57/58.63 % File :CSE---1.7 % 58.57/58.63 % Problem :theBenchmark % 58.57/58.63 % Transform :cnf % 58.57/58.63 % Format :tptp:raw % 58.57/58.63 % Command :java -jar mcs_scs.jar %d %s % 58.57/58.63 % 58.57/58.63 % Result :Theorem 58.010000s % 58.57/58.63 % Output :CNFRefutation 58.010000s % 58.57/58.63 %------------------------------------------- % 58.57/58.64 %------------------------------------------------------------------------------ % 58.57/58.64 % File : ANA017-2 : TPTP v8.2.0. Released v3.2.0. % 58.57/58.64 % Domain : Analysis % 58.57/58.64 % Problem : Problem about Big-O notation % 58.57/58.64 % Version : [Pau06] axioms : Reduced > Especial. % 58.57/58.64 % English : % 58.57/58.64 % 58.57/58.64 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe % 58.57/58.64 % Source : [Pau06] % 58.57/58.64 % Names : % 58.57/58.64 % 58.57/58.64 % Status : Unsatisfiable % 58.57/58.64 % Rating : 0.12 v8.2.0, 0.08 v8.1.0, 0.11 v7.5.0, 0.10 v7.4.0, 0.22 v7.3.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.14 v6.3.0, 0.00 v6.0.0, 0.11 v5.5.0, 0.06 v5.4.0, 0.07 v5.3.0, 0.17 v5.2.0, 0.12 v5.1.0, 0.14 v4.1.0, 0.22 v4.0.1, 0.17 v3.3.0, 0.29 v3.2.0 % 58.57/58.64 % Syntax : Number of clauses : 10 ( 3 unt; 0 nHn; 6 RR) % 58.57/58.64 % Number of literals : 19 ( 2 equ; 10 neg) % 58.57/58.64 % Maximal clause size : 4 ( 1 avg) % 58.57/58.64 % Maximal term depth : 5 ( 2 avg) % 58.57/58.64 % Number of predicates : 6 ( 5 usr; 0 prp; 1-3 aty) % 58.57/58.64 % Number of functors : 9 ( 9 usr; 4 con; 0-3 aty) % 58.57/58.64 % Number of variables : 18 ( 1 sgn) % 58.57/58.64 % SPC : CNF_UNS_RFO_SEQ_HRN % 58.57/58.64 % 58.57/58.64 % Comments : The problems in the [Pau06] collection each have very many axioms, % 58.57/58.64 % of which only a small selection are required for the refutation. % 58.57/58.64 % The mission is to find those few axioms, after which a refutation % 58.57/58.64 % can be quite easily found. This version has only the necessary % 58.57/58.64 % axioms. % 58.57/58.64 %------------------------------------------------------------------------------ % 58.57/58.64 cnf(cls_conjecture_0,negated_conjecture, % 58.57/58.64 c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),t_b) ). % 58.57/58.64 % 58.57/58.64 cnf(cls_conjecture_1,negated_conjecture, % 58.57/58.64 ~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(V_U)),t_b),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b) ). % 58.57/58.64 % 58.57/58.64 cnf(tfree_tcs,negated_conjecture, % 58.57/58.64 class_Ring__and__Field_Oordered__idom(t_b) ). % 58.57/58.64 % 58.57/58.64 cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom, % 58.57/58.64 ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) % 58.57/58.64 | c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ). % 58.57/58.64 % 58.57/58.64 cnf(cls_OrderedGroup_Omult__ac__1_0,axiom, % 58.57/58.64 ( ~ class_OrderedGroup_Osemigroup__mult(T_a) % 58.57/58.64 | c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ). % 58.57/58.64 % 58.57/58.64 cnf(cls_Ring__and__Field_Oabs__mult_0,axiom, % 58.57/58.64 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 58.57/58.64 | c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) ). % 58.57/58.64 % 58.57/58.64 cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom, % 58.57/58.64 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 58.57/58.64 | ~ c_lessequals(V_a,V_b,T_a) % 58.57/58.64 | ~ c_lessequals(c_0,V_c,T_a) % 58.57/58.64 | c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) ) ). % 58.57/58.64 % 58.57/58.64 cnf(clsrel_Ring__and__Field_Oordered__idom_21,axiom, % 58.57/58.64 ( ~ class_Ring__and__Field_Oordered__idom(T) % 58.57/58.64 | class_OrderedGroup_Osemigroup__mult(T) ) ). % 58.57/58.64 % 58.57/58.64 cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom, % 58.57/58.64 ( ~ class_Ring__and__Field_Oordered__idom(T) % 58.57/58.65 | class_Ring__and__Field_Opordered__semiring(T) ) ). % 58.57/58.65 % 58.57/58.65 cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom, % 58.57/58.65 ( ~ class_Ring__and__Field_Oordered__idom(T) % 58.57/58.65 | class_OrderedGroup_Olordered__ab__group__abs(T) ) ). % 58.57/58.65 % 58.57/58.65 %------------------------------------------------------------------------------ % 58.57/58.65 %------------------------------------------- % 58.57/58.65 % Proof found % 58.57/58.65 % SZS status Theorem for theBenchmark % 58.57/58.65 % SZS output start Proof % 58.57/58.65 %ClaNum:28(EqnAxiom:18) % 58.57/58.65 %VarNum:49(SingletonVarNum:18) % 58.57/58.65 %MaxLitNum:4 % 58.57/58.65 %MaxfuncDepth:4 % 58.57/58.65 %SharedTerms:5 % 58.57/58.65 %goalClause: 19 20 21 % 58.57/58.65 %singleGoalClaCount:3 % 58.57/58.65 [19]P1(a1) % 58.57/58.65 [20]P2(f2(f5(x201),a1),f4(a6,f2(f8(x201),a1),a1),a1) % 58.57/58.65 [21]~P2(f2(f4(a7,f5(f9(x211)),a1),a1),f4(x211,f2(f8(f9(x211)),a1),a1),a1) % 58.57/58.65 [22]~P1(x221)+P3(x221) % 58.57/58.65 [23]~P1(x231)+P4(x231) % 58.57/58.65 [24]~P1(x241)+P5(x241) % 58.57/58.65 [25]~P3(x252)+P2(a3,f2(x251,x252),x252) % 58.57/58.65 [26]~P1(x262)+E(f4(f2(x261,x262),f2(x263,x262),x262),f2(f4(x261,x263,x262),x262)) % 58.57/58.65 [27]~P4(x273)+E(f4(f4(x271,x272,x273),x274,x273),f4(x271,f4(x272,x274,x273),x273)) % 58.57/58.65 [28]~P5(x283)+~P2(x282,x284,x283)+~P2(a3,x281,x283)+P2(f4(x281,x282,x283),f4(x281,x284,x283),x283) % 58.57/58.65 %EqnAxiom % 58.57/58.65 [1]E(x11,x11) % 58.57/58.65 [2]E(x22,x21)+~E(x21,x22) % 58.57/58.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 58.57/58.65 [4]~E(x41,x42)+E(f5(x41),f5(x42)) % 58.57/58.65 [5]~E(x51,x52)+E(f2(x51,x53),f2(x52,x53)) % 58.57/58.65 [6]~E(x61,x62)+E(f2(x63,x61),f2(x63,x62)) % 58.57/58.65 [7]~E(x71,x72)+E(f8(x71),f8(x72)) % 58.57/58.65 [8]~E(x81,x82)+E(f4(x81,x83,x84),f4(x82,x83,x84)) % 58.57/58.65 [9]~E(x91,x92)+E(f4(x93,x91,x94),f4(x93,x92,x94)) % 58.57/58.65 [10]~E(x101,x102)+E(f4(x103,x104,x101),f4(x103,x104,x102)) % 58.57/58.65 [11]~E(x111,x112)+E(f9(x111),f9(x112)) % 58.57/58.65 [12]~P1(x121)+P1(x122)+~E(x121,x122) % 58.57/58.65 [13]P2(x132,x133,x134)+~E(x131,x132)+~P2(x131,x133,x134) % 58.57/58.65 [14]P2(x143,x142,x144)+~E(x141,x142)+~P2(x143,x141,x144) % 58.57/58.65 [15]P2(x153,x154,x152)+~E(x151,x152)+~P2(x153,x154,x151) % 58.57/58.65 [16]~P4(x161)+P4(x162)+~E(x161,x162) % 58.57/58.65 [17]~P3(x171)+P3(x172)+~E(x171,x172) % 58.57/58.65 [18]~P5(x181)+P5(x182)+~E(x181,x182) % 58.57/58.65 % 58.57/58.65 %------------------------------------------- % 58.57/58.67 cnf(32,plain, % 58.57/58.67 (~E(f5(f9(a6)),f4(a7,f5(f9(a6)),a1))), % 58.57/58.67 inference(scs_inference,[],[20,21,13,5])). % 58.57/58.67 cnf(37,plain, % 58.57/58.67 (P2(a3,f2(x371,a1),a1)), % 58.57/58.67 inference(scs_inference,[],[19,22,25])). % 58.57/58.67 cnf(42,plain, % 58.57/58.67 (E(f4(f4(x421,x422,a1),x423,a1),f4(x421,f4(x422,x423,a1),a1))), % 58.57/58.67 inference(scs_inference,[],[19,23,27])). % 58.57/58.67 cnf(43,plain, % 58.57/58.67 (E(f4(x431,f4(x432,x433,a1),a1),f4(f4(x431,x432,a1),x433,a1))), % 58.57/58.67 inference(scs_inference,[],[42,2])). % 58.57/58.67 cnf(142,plain, % 58.57/58.67 (E(f4(f4(x1421,f4(f4(x1422,x1423,a1),x1424,a1),x1425),x1426,x1427),f4(f4(x1421,f4(x1422,f4(x1423,x1424,a1),a1),x1425),x1426,x1427))), % 58.57/58.67 inference(scs_inference,[],[42,8,9])). % 58.57/58.67 cnf(143,plain, % 58.57/58.67 (E(f4(f4(x1431,f4(x1432,f4(x1433,x1434,a1),a1),x1435),x1436,x1437),f4(f4(x1431,f4(f4(x1432,x1433,a1),x1434,a1),x1435),x1436,x1437))), % 58.57/58.67 inference(scs_inference,[],[142,2])). % 58.57/58.67 cnf(1653,plain, % 58.57/58.67 (P2(f4(f2(x16531,a1),f2(f5(x16532),a1),a1),f4(f2(x16531,a1),f4(a6,f2(f8(x16532),a1),a1),a1),a1)), % 58.57/58.67 inference(scs_inference,[],[19,37,20,24,28])). % 58.57/58.67 cnf(1654,plain, % 58.57/58.67 (P2(f4(f2(x16541,a1),f2(f5(x16542),a1),a1),f4(f4(f2(x16541,a1),a6,a1),f2(f8(x16542),a1),a1),a1)), % 58.57/58.67 inference(scs_inference,[],[43,1653,14])). % 58.57/58.67 cnf(1657,plain, % 58.57/58.67 (P2(x16571,f4(f2(x16572,a1),f4(a6,f2(f8(x16573),a1),a1),a1),a1)+~E(f4(f2(x16572,a1),f2(f5(x16573),a1),a1),x16571)), % 58.57/58.67 inference(scs_inference,[],[43,1653,14,15,13])). % 58.57/58.67 cnf(1931,plain, % 58.57/58.67 (E(f4(f4(f4(x19311,f4(x19312,f4(x19313,x19314,a1),a1),x19315),x19316,a1),x19317,a1),f4(f4(x19311,f4(f4(x19312,x19313,a1),x19314,a1),x19315),f4(x19316,x19317,a1),a1))), % 58.57/58.67 inference(scs_inference,[],[42,143,3])). % 58.57/58.67 cnf(1963,plain, % 58.57/58.67 (E(f4(f4(f4(x19631,f4(f4(x19632,x19633,a1),x19634,a1),x19635),x19636,a1),x19637,a1),f4(f4(x19631,f4(x19632,f4(x19633,x19634,a1),a1),x19635),f4(x19636,x19637,a1),a1))), % 58.57/58.67 inference(scs_inference,[],[42,142,3])). % 58.57/58.67 cnf(2006,plain, % 58.57/58.67 ($false), % 58.57/58.67 inference(scs_inference,[],[19,32,1963,1931,21,1654,4,7,11,6,8,9,10,26,1657,5,24,2,3,13]), % 58.57/58.67 ['proof']). % 58.57/58.67 % SZS output end Proof % 58.57/58.67 % Total time :58.010000s %------------------------------------------------------------------------------