%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET848-2 : 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 14:22:44 EDT 2024 % Result : Unsatisfiable 0.57s 0.69s % Output : CNFRefutation 0.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET848-2 : TPTP v8.2.0. Released v3.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n018.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sun Jun 23 13:36:09 EDT 2024 % 0.12/0.33 % CPUTime : % 0.46/0.60 start to proof:theBenchmark % 0.57/0.68 %------------------------------------------- % 0.57/0.68 % File :CSE---1.7 % 0.57/0.68 % Problem :theBenchmark % 0.57/0.68 % Transform :cnf % 0.57/0.68 % Format :tptp:raw % 0.57/0.68 % Command :java -jar mcs_scs.jar %d %s % 0.57/0.68 % 0.57/0.68 % Result :Theorem 0.040000s % 0.57/0.68 % Output :CNFRefutation 0.040000s % 0.57/0.68 %------------------------------------------- % 0.57/0.68 %------------------------------------------------------------------------------ % 0.57/0.68 % File : SET848-2 : TPTP v8.2.0. Released v3.2.0. % 0.57/0.68 % Domain : Set Theory % 0.57/0.69 % Problem : Problem about Zorn's lemma % 0.57/0.69 % Version : [Pau06] axioms : Reduced > Especial. % 0.57/0.69 % English : % 0.57/0.69 % 0.57/0.69 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe % 0.57/0.69 % Source : [Pau06] % 0.57/0.69 % Names : % 0.57/0.69 % 0.57/0.69 % Status : Unsatisfiable % 0.57/0.69 % Rating : 0.10 v8.1.0, 0.00 v7.5.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.09 v6.2.0, 0.10 v6.1.0, 0.07 v6.0.0, 0.10 v5.5.0, 0.15 v5.3.0, 0.17 v5.2.0, 0.12 v5.1.0, 0.18 v5.0.0, 0.07 v4.1.0, 0.15 v4.0.1, 0.18 v4.0.0, 0.09 v3.7.0, 0.00 v3.4.0, 0.08 v3.3.0, 0.14 v3.2.0 % 0.57/0.69 % Syntax : Number of clauses : 7 ( 3 unt; 1 nHn; 5 RR) % 0.57/0.69 % Number of literals : 12 ( 2 equ; 6 neg) % 0.57/0.69 % Maximal clause size : 3 ( 1 avg) % 0.57/0.69 % Maximal term depth : 5 ( 2 avg) % 0.57/0.69 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty) % 0.57/0.69 % Number of functors : 9 ( 9 usr; 2 con; 0-3 aty) % 0.57/0.69 % Number of variables : 15 ( 1 sgn) % 0.57/0.69 % SPC : CNF_UNS_RFO_SEQ_NHN % 0.57/0.69 % 0.57/0.69 % Comments : The problems in the [Pau06] collection each have very many axioms, % 0.57/0.69 % of which only a small selection are required for the refutation. % 0.57/0.69 % The mission is to find those few axioms, after which a refutation % 0.57/0.69 % can be quite easily found. This version has only the necessary % 0.57/0.69 % axioms. % 0.57/0.69 %------------------------------------------------------------------------------ % 0.57/0.69 cnf(cls_Set_ODiffI_0,axiom, % 0.57/0.69 ( ~ c_in(V_c,V_A,T_a) % 0.57/0.69 | c_in(V_c,V_B,T_a) % 0.57/0.69 | c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a) ) ). % 0.57/0.69 % 0.57/0.69 cnf(cls_Set_Osubset__refl_0,axiom, % 0.57/0.69 c_lessequals(V_A,V_A,tc_set(T_a)) ). % 0.57/0.69 % 0.57/0.69 cnf(cls_Zorn_OTFin__UnionI_0,axiom, % 0.57/0.69 ( ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a)))) % 0.57/0.69 | c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ). % 0.57/0.69 % 0.57/0.69 cnf(cls_Zorn_OTFin__chain__lemma4_0,axiom, % 0.57/0.69 ( ~ c_in(V_c,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.57/0.69 | c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a))) ) ). % 0.57/0.69 % 0.57/0.69 cnf(cls_Zorn_Osucc__not__equals_0,axiom, % 0.57/0.69 ( ~ c_in(V_c,c_minus(c_Zorn_Ochain(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))),tc_set(tc_set(T_a))) % 0.57/0.69 | c_Zorn_Osucc(V_S,V_c,T_a) != V_c ) ). % 0.57/0.69 % 0.57/0.69 cnf(cls_conjecture_0,negated_conjecture, % 0.57/0.69 ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ). % 0.57/0.69 % 0.57/0.69 cnf(cls_conjecture_1,negated_conjecture, % 0.57/0.69 c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ). % 0.57/0.69 % 0.57/0.69 %------------------------------------------------------------------------------ % 0.57/0.69 %------------------------------------------- % 0.57/0.69 % Proof found % 0.57/0.69 % SZS status Theorem for theBenchmark % 0.57/0.69 % SZS output start Proof % 0.57/0.69 %ClaNum:31(EqnAxiom:24) % 0.57/0.69 %VarNum:42(SingletonVarNum:15) % 0.57/0.69 %MaxLitNum:3 % 0.57/0.69 %MaxfuncDepth:4 % 0.57/0.69 %SharedTerms:10 % 0.57/0.69 %goalClause: 26 27 % 0.57/0.69 %singleGoalClaCount:2 % 0.57/0.69 [27]~P2(f4(f3(a9,a2),f1(a2)),f6(a9,a2),f1(f1(a2))) % 0.57/0.69 [26]E(f5(a9,f4(f3(a9,a2),f1(a2)),a2),f4(f3(a9,a2),f1(a2))) % 0.57/0.69 [25]P1(x251,x251,f1(x252)) % 0.57/0.69 [28]~P2(x281,f3(x282,x283),f1(f1(x283)))+P2(x281,f7(x282,x283),f1(f1(x283))) % 0.57/0.69 [30]P2(f4(x301,f1(x302)),f3(x303,x302),f1(f1(x302)))+~P1(x301,f3(x303,x302),f1(f1(f1(x302)))) % 0.57/0.69 [31]~E(f5(x311,x312,x313),x312)+~P2(x312,f8(f7(x311,x313),f6(x311,x313),f1(f1(f1(x313)))),f1(f1(x313))) % 0.57/0.69 [29]~P2(x291,x294,x293)+P2(x291,x292,x293)+P2(x291,f8(x294,x292,f1(x293)),x293) % 0.57/0.69 %EqnAxiom % 0.57/0.69 [1]E(x11,x11) % 0.57/0.69 [2]E(x22,x21)+~E(x21,x22) % 0.57/0.69 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.57/0.69 [4]~E(x41,x42)+E(f1(x41),f1(x42)) % 0.57/0.69 [5]~E(x51,x52)+E(f3(x51,x53),f3(x52,x53)) % 0.57/0.69 [6]~E(x61,x62)+E(f3(x63,x61),f3(x63,x62)) % 0.57/0.69 [7]~E(x71,x72)+E(f8(x71,x73,x74),f8(x72,x73,x74)) % 0.57/0.69 [8]~E(x81,x82)+E(f8(x83,x81,x84),f8(x83,x82,x84)) % 0.57/0.69 [9]~E(x91,x92)+E(f8(x93,x94,x91),f8(x93,x94,x92)) % 0.57/0.69 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103)) % 0.57/0.69 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112)) % 0.57/0.69 [12]~E(x121,x122)+E(f5(x121,x123,x124),f5(x122,x123,x124)) % 0.57/0.69 [13]~E(x131,x132)+E(f5(x133,x131,x134),f5(x133,x132,x134)) % 0.57/0.69 [14]~E(x141,x142)+E(f5(x143,x144,x141),f5(x143,x144,x142)) % 0.57/0.69 [15]~E(x151,x152)+E(f7(x151,x153),f7(x152,x153)) % 0.57/0.69 [16]~E(x161,x162)+E(f7(x163,x161),f7(x163,x162)) % 0.57/0.69 [17]~E(x171,x172)+E(f6(x171,x173),f6(x172,x173)) % 0.57/0.69 [18]~E(x181,x182)+E(f6(x183,x181),f6(x183,x182)) % 0.57/0.69 [19]P1(x192,x193,x194)+~E(x191,x192)+~P1(x191,x193,x194) % 0.57/0.69 [20]P1(x203,x202,x204)+~E(x201,x202)+~P1(x203,x201,x204) % 0.57/0.69 [21]P1(x213,x214,x212)+~E(x211,x212)+~P1(x213,x214,x211) % 0.57/0.69 [22]P2(x222,x223,x224)+~E(x221,x222)+~P2(x221,x223,x224) % 0.57/0.69 [23]P2(x233,x232,x234)+~E(x231,x232)+~P2(x233,x231,x234) % 0.57/0.69 [24]P2(x243,x244,x242)+~E(x241,x242)+~P2(x243,x244,x241) % 0.57/0.69 % 0.57/0.69 %------------------------------------------- % 0.57/0.69 cnf(32,plain, % 0.57/0.69 (E(f4(f3(a9,a2),f1(a2)),f5(a9,f4(f3(a9,a2),f1(a2)),a2))), % 0.57/0.69 inference(scs_inference,[],[26,2])). % 0.57/0.69 cnf(34,plain, % 0.57/0.69 (P1(x341,x341,f1(x342))), % 0.57/0.69 inference(rename_variables,[],[25])). % 0.57/0.69 cnf(37,plain, % 0.57/0.69 (P1(x371,x371,f1(x372))), % 0.57/0.69 inference(rename_variables,[],[25])). % 0.57/0.69 cnf(40,plain, % 0.57/0.69 (P2(f5(a9,f4(f3(a9,a2),f1(a2)),a2),f3(a9,a2),f1(f1(a2)))), % 0.57/0.69 inference(scs_inference,[],[26,25,34,37,2,30,19,20,22])). % 0.57/0.69 cnf(64,plain, % 0.57/0.69 (P2(f4(f3(a9,a2),f1(a2)),f7(a9,a2),f1(f1(a2)))), % 0.57/0.69 inference(scs_inference,[],[40,26,28,22])). % 0.57/0.69 cnf(69,plain, % 0.57/0.69 (~P2(f4(f3(a9,a2),f1(a2)),f8(f7(a9,a2),f6(a9,a2),f1(f1(f1(a2)))),f1(f1(a2)))), % 0.57/0.69 inference(scs_inference,[],[32,31,2])). % 0.57/0.69 cnf(70,plain, % 0.57/0.69 ($false), % 0.57/0.69 inference(scs_inference,[],[27,69,64,29]), % 0.57/0.69 ['proof']). % 0.57/0.69 % SZS output end Proof % 0.57/0.69 % Total time :0.040000s %------------------------------------------------------------------------------