%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET847-2 : 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 14:22:43 EDT 2024 % Result : Unsatisfiable 0.72s 0.85s % Output : CNFRefutation 0.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET847-2 : TPTP v8.2.0. Released v3.2.0. % 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.32 % Computer : n027.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Sun Jun 23 12:06:39 EDT 2024 % 0.12/0.33 % CPUTime : % 0.18/0.55 start to proof:theBenchmark % 0.72/0.85 %------------------------------------------- % 0.72/0.85 % File :CSE---1.7 % 0.72/0.85 % Problem :theBenchmark % 0.72/0.85 % Transform :cnf % 0.72/0.85 % Format :tptp:raw % 0.72/0.85 % Command :java -jar mcs_scs.jar %d %s % 0.72/0.85 % 0.72/0.85 % Result :Theorem 0.260000s % 0.72/0.85 % Output :CNFRefutation 0.260000s % 0.72/0.85 %------------------------------------------- % 0.72/0.85 %------------------------------------------------------------------------------ % 0.72/0.85 % File : SET847-2 : TPTP v8.2.0. Released v3.2.0. % 0.72/0.85 % Domain : Set Theory % 0.72/0.85 % Problem : Problem about Zorn's lemma % 0.72/0.85 % Version : [Pau06] axioms : Reduced > Especial. % 0.72/0.85 % English : % 0.72/0.85 % 0.72/0.85 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe % 0.72/0.85 % Source : [Pau06] % 0.72/0.85 % Names : % 0.72/0.85 % 0.72/0.85 % Status : Unsatisfiable % 0.72/0.85 % 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, 0.07 v6.4.0, 0.00 v6.3.0, 0.09 v6.2.0, 0.00 v6.1.0, 0.14 v6.0.0, 0.00 v5.5.0, 0.30 v5.4.0, 0.25 v5.3.0, 0.33 v5.2.0, 0.12 v5.1.0, 0.18 v5.0.0, 0.21 v4.1.0, 0.31 v4.0.1, 0.36 v3.7.0, 0.10 v3.5.0, 0.18 v3.4.0, 0.25 v3.3.0, 0.29 v3.2.0 % 0.72/0.85 % Syntax : Number of clauses : 11 ( 4 unt; 2 nHn; 7 RR) % 0.72/0.85 % Number of literals : 20 ( 3 equ; 10 neg) % 0.72/0.85 % Maximal clause size : 3 ( 1 avg) % 0.72/0.85 % Maximal term depth : 5 ( 2 avg) % 0.72/0.85 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty) % 0.72/0.85 % Number of functors : 11 ( 11 usr; 3 con; 0-3 aty) % 0.72/0.85 % Number of variables : 28 ( 6 sgn) % 0.72/0.85 % SPC : CNF_UNS_RFO_SEQ_NHN % 0.72/0.85 % 0.72/0.85 % Comments : The problems in the [Pau06] collection each have very many axioms, % 0.72/0.85 % of which only a small selection are required for the refutation. % 0.72/0.85 % The mission is to find those few axioms, after which a refutation % 0.72/0.85 % can be quite easily found. This version has only the necessary % 0.72/0.85 % axioms. % 0.72/0.85 %------------------------------------------------------------------------------ % 0.72/0.85 cnf(cls_Set_ODiffI_0,axiom, % 0.72/0.85 ( ~ c_in(V_c,V_A,T_a) % 0.72/0.85 | c_in(V_c,V_B,T_a) % 0.72/0.85 | c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a) ) ). % 0.72/0.85 % 0.72/0.85 cnf(cls_Set_OemptyE_0,axiom, % 0.72/0.85 ~ c_in(V_a,c_emptyset,T_a) ). % 0.72/0.85 % 0.72/0.85 cnf(cls_Set_Oempty__subsetI_0,axiom, % 0.72/0.85 c_lessequals(c_emptyset,V_A,tc_set(T_a)) ). % 0.72/0.85 % 0.72/0.85 cnf(cls_Set_OsubsetI_0,axiom, % 0.72/0.85 ( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) % 0.72/0.85 | c_lessequals(V_A,V_B,tc_set(T_a)) ) ). % 0.72/0.85 % 0.72/0.85 cnf(cls_Set_Osubset__antisym_0,axiom, % 0.72/0.85 ( ~ c_lessequals(V_B,V_A,tc_set(T_a)) % 0.72/0.85 | ~ c_lessequals(V_A,V_B,tc_set(T_a)) % 0.72/0.85 | V_A = V_B ) ). % 0.72/0.85 % 0.72/0.85 cnf(cls_Set_Osubset__refl_0,axiom, % 0.72/0.85 c_lessequals(V_A,V_A,tc_set(T_a)) ). % 0.72/0.85 % 0.72/0.85 cnf(cls_Zorn_OTFin__UnionI_0,axiom, % 0.72/0.85 ( ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a)))) % 0.72/0.85 | c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ). % 0.72/0.85 % 0.72/0.85 cnf(cls_Zorn_OTFin__chain__lemma4_0,axiom, % 0.72/0.85 ( ~ c_in(V_c,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.72/0.85 | c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a))) ) ). % 0.72/0.85 % 0.72/0.85 cnf(cls_Zorn_Oequal__succ__Union_1,axiom, % 0.72/0.85 ( ~ c_in(c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.72/0.85 | c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)) = c_Zorn_Osucc(V_S,c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)),T_a) ) ). % 0.72/0.85 % 0.72/0.85 cnf(cls_Zorn_Osucc__not__equals_0,axiom, % 0.72/0.85 ( ~ 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))) % 0.72/0.85 | c_Zorn_Osucc(V_S,V_c,T_a) != V_c ) ). % 0.72/0.85 % 0.72/0.85 cnf(cls_conjecture_0,negated_conjecture, % 0.72/0.85 ~ c_in(V_U,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ). % 0.72/0.85 % 0.72/0.85 %------------------------------------------------------------------------------ % 0.72/0.85 %------------------------------------------- % 0.72/0.85 % Proof found % 0.72/0.85 % SZS status Theorem for theBenchmark % 0.72/0.85 % SZS output start Proof % 0.72/0.85 %ClaNum:38(EqnAxiom:27) % 0.72/0.85 %VarNum:77(SingletonVarNum:28) % 0.72/0.85 %MaxLitNum:3 % 0.72/0.85 %MaxfuncDepth:4 % 0.72/0.85 %SharedTerms:6 % 0.72/0.85 %goalClause: 31 % 0.72/0.85 %singleGoalClaCount:1 % 0.72/0.85 [31]~P2(x311,f2(a11,a9),f8(f8(a9))) % 0.72/0.85 [30]~P2(x301,a1,x302) % 0.72/0.85 [28]P1(a1,x281,f8(x282)) % 0.72/0.85 [29]P1(x291,x291,f8(x292)) % 0.72/0.85 [37]~P2(f6(f5(x371,x372),f8(x372)),f5(x371,x372),f8(f8(x372)))+E(f7(x371,f6(f5(x371,x372),f8(x372)),x372),f6(f5(x371,x372),f8(x372))) % 0.72/0.85 [33]P2(f3(x331,x332,x333),x331,x333)+P1(x331,x332,f8(x333)) % 0.72/0.85 [34]~P2(x341,f5(x342,x343),f8(f8(x343)))+P2(x341,f4(x342,x343),f8(f8(x343))) % 0.72/0.85 [36]P2(f6(x361,f8(x362)),f5(x363,x362),f8(f8(x362)))+~P1(x361,f5(x363,x362),f8(f8(f8(x362)))) % 0.72/0.85 [38]~E(f7(x381,x382,x383),x382)+~P2(x382,f10(f4(x381,x383),f2(x381,x383),f8(f8(f8(x383)))),f8(f8(x383))) % 0.72/0.85 [32]E(x321,x322)+~P1(x322,x321,f8(x323))+~P1(x321,x322,f8(x323)) % 0.72/0.85 [35]~P2(x351,x354,x353)+P2(x351,x352,x353)+P2(x351,f10(x354,x352,f8(x353)),x353) % 0.72/0.85 %EqnAxiom % 0.72/0.85 [1]E(x11,x11) % 0.72/0.85 [2]E(x22,x21)+~E(x21,x22) % 0.72/0.85 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.72/0.85 [4]~E(x41,x42)+E(f8(x41),f8(x42)) % 0.72/0.85 [5]~E(x51,x52)+E(f10(x51,x53,x54),f10(x52,x53,x54)) % 0.72/0.85 [6]~E(x61,x62)+E(f10(x63,x61,x64),f10(x63,x62,x64)) % 0.72/0.85 [7]~E(x71,x72)+E(f10(x73,x74,x71),f10(x73,x74,x72)) % 0.72/0.85 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83)) % 0.72/0.85 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92)) % 0.72/0.85 [10]~E(x101,x102)+E(f5(x101,x103),f5(x102,x103)) % 0.72/0.85 [11]~E(x111,x112)+E(f5(x113,x111),f5(x113,x112)) % 0.72/0.85 [12]~E(x121,x122)+E(f4(x121,x123),f4(x122,x123)) % 0.72/0.86 [13]~E(x131,x132)+E(f4(x133,x131),f4(x133,x132)) % 0.72/0.86 [14]~E(x141,x142)+E(f7(x141,x143,x144),f7(x142,x143,x144)) % 0.72/0.86 [15]~E(x151,x152)+E(f7(x153,x151,x154),f7(x153,x152,x154)) % 0.72/0.86 [16]~E(x161,x162)+E(f7(x163,x164,x161),f7(x163,x164,x162)) % 0.72/0.86 [17]~E(x171,x172)+E(f6(x171,x173),f6(x172,x173)) % 0.72/0.86 [18]~E(x181,x182)+E(f6(x183,x181),f6(x183,x182)) % 0.72/0.86 [19]~E(x191,x192)+E(f3(x191,x193,x194),f3(x192,x193,x194)) % 0.72/0.86 [20]~E(x201,x202)+E(f3(x203,x201,x204),f3(x203,x202,x204)) % 0.72/0.86 [21]~E(x211,x212)+E(f3(x213,x214,x211),f3(x213,x214,x212)) % 0.72/0.86 [22]P1(x222,x223,x224)+~E(x221,x222)+~P1(x221,x223,x224) % 0.72/0.86 [23]P1(x233,x232,x234)+~E(x231,x232)+~P1(x233,x231,x234) % 0.72/0.86 [24]P1(x243,x244,x242)+~E(x241,x242)+~P1(x243,x244,x241) % 0.72/0.86 [25]P2(x252,x253,x254)+~E(x251,x252)+~P2(x251,x253,x254) % 0.72/0.86 [26]P2(x263,x262,x264)+~E(x261,x262)+~P2(x263,x261,x264) % 0.72/0.86 [27]P2(x273,x274,x272)+~E(x271,x272)+~P2(x273,x274,x271) % 0.72/0.86 % 0.72/0.86 %------------------------------------------- % 0.72/0.86 cnf(39,plain, % 0.72/0.86 (P2(f6(f5(x391,x392),f8(x392)),f5(x391,x392),f8(f8(x392)))), % 0.72/0.86 inference(scs_inference,[],[29,36])). % 0.72/0.86 cnf(40,plain, % 0.72/0.86 (P1(x401,x401,f8(x402))), % 0.72/0.86 inference(rename_variables,[],[29])). % 0.72/0.86 cnf(46,plain, % 0.72/0.86 (P1(x461,x462,f8(x463))+~E(x462,x461)), % 0.72/0.86 inference(scs_inference,[],[31,29,40,36,26,25,27,22])). % 0.72/0.86 cnf(47,plain, % 0.72/0.86 (P1(x471,x472,f8(x473))+~E(x471,x472)), % 0.72/0.86 inference(scs_inference,[],[31,29,40,36,26,25,27,22,23])). % 0.72/0.86 cnf(75,plain, % 0.72/0.86 (E(f6(f5(x751,x752),f8(x752)),f7(x751,f6(f5(x751,x752),f8(x752)),x752))), % 0.72/0.86 inference(scs_inference,[],[39,2,37])). % 0.72/0.86 cnf(78,plain, % 0.72/0.86 (E(f7(x781,f6(f5(x781,x782),f8(x782)),x782),f6(f5(x781,x782),f8(x782)))), % 0.72/0.86 inference(scs_inference,[],[75,46,47,2])). % 0.72/0.86 cnf(79,plain, % 0.72/0.86 (P2(f7(x791,f6(f5(x791,x792),f8(x792)),x792),f5(x791,x792),f8(f8(x792)))), % 0.72/0.86 inference(scs_inference,[],[39,75,46,47,2,25])). % 0.72/0.86 cnf(98,plain, % 0.72/0.86 (P2(f6(f2(a11,a9),f8(a9)),f5(x981,a9),f8(f8(a9)))), % 0.72/0.86 inference(scs_inference,[],[31,33,36])). % 0.72/0.86 cnf(105,plain, % 0.72/0.86 (P2(f6(f5(x1051,x1052),f8(x1052)),f4(x1051,x1052),f8(f8(x1052)))), % 0.72/0.86 inference(scs_inference,[],[79,78,34,25])). % 0.72/0.86 cnf(123,plain, % 0.72/0.86 (P2(f6(f2(a11,a9),f8(a9)),f10(f4(x1231,a9),f2(a11,a9),f8(f8(f8(a9)))),f8(f8(a9)))), % 0.72/0.86 inference(scs_inference,[],[31,98,35,34])). % 0.72/0.86 cnf(125,plain, % 0.72/0.86 (P2(f6(f2(a11,a9),f8(a9)),f10(f4(x1251,a9),f2(a11,a9),f8(f8(f8(a9)))),f8(f8(a9)))), % 0.72/0.86 inference(rename_variables,[],[123])). % 0.72/0.86 cnf(130,plain, % 0.72/0.86 (P2(x1301,f10(f4(x1302,a9),f2(a11,a9),f8(f8(f8(a9)))),f8(f8(a9)))+~E(f6(f2(a11,a9),f8(a9)),x1301)), % 0.72/0.86 inference(scs_inference,[],[31,123,125,38,26,27,25])). % 0.72/0.86 cnf(165,plain, % 0.72/0.86 (~P2(f6(f5(x1651,x1652),f8(x1652)),f10(f4(x1651,x1652),f2(x1651,x1652),f8(f8(f8(x1652)))),f8(f8(x1652)))), % 0.72/0.86 inference(scs_inference,[],[75,2,38])). % 0.72/0.86 cnf(167,plain, % 0.72/0.86 (~P2(f6(f5(x1671,x1672),f8(x1672)),f10(f4(x1671,x1672),f2(x1671,x1672),f8(f8(f8(x1672)))),f8(f8(x1672)))), % 0.72/0.86 inference(rename_variables,[],[165])). % 0.72/0.86 cnf(168,plain, % 0.72/0.86 ($false), % 0.72/0.86 inference(scs_inference,[],[31,105,165,167,130,35]), % 0.72/0.86 ['proof']). % 0.82/0.86 % SZS output end Proof % 0.82/0.86 % Total time :0.260000s 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