%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET865-2 : 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 : 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 14:22:50 EDT 2024 % Result : Unsatisfiable 0.81s 0.88s % Output : CNFRefutation 0.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET865-2 : TPTP v8.2.0. Released v3.2.0. % 0.11/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n027.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 11:26:39 EDT 2024 % 0.12/0.33 % CPUTime : % 0.19/0.56 start to proof:theBenchmark % 0.81/0.87 %------------------------------------------- % 0.81/0.87 % File :CSE---1.7 % 0.81/0.87 % Problem :theBenchmark % 0.81/0.87 % Transform :cnf % 0.81/0.87 % Format :tptp:raw % 0.81/0.87 % Command :java -jar mcs_scs.jar %d %s % 0.81/0.87 % 0.81/0.87 % Result :Theorem 0.280000s % 0.81/0.88 % Output :CNFRefutation 0.280000s % 0.81/0.88 %------------------------------------------- % 0.81/0.88 %------------------------------------------------------------------------------ % 0.81/0.88 % File : SET865-2 : TPTP v8.2.0. Released v3.2.0. % 0.81/0.88 % Domain : Set Theory % 0.81/0.88 % Problem : Problem about Zorn's lemma % 0.81/0.88 % Version : [Pau06] axioms : Reduced > Especial. % 0.81/0.88 % English : % 0.81/0.88 % 0.81/0.88 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe % 0.81/0.88 % Source : [Pau06] % 0.81/0.88 % Names : % 0.81/0.88 % 0.81/0.88 % Status : Unsatisfiable % 0.81/0.88 % Rating : 0.06 v8.2.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.00 v5.3.0, 0.08 v5.2.0, 0.00 v5.1.0, 0.14 v4.1.0, 0.22 v4.0.1, 0.33 v3.7.0, 0.17 v3.3.0, 0.14 v3.2.0 % 0.81/0.88 % Syntax : Number of clauses : 8 ( 2 unt; 0 nHn; 6 RR) % 0.81/0.88 % Number of literals : 17 ( 2 equ; 10 neg) % 0.81/0.88 % Maximal clause size : 4 ( 2 avg) % 0.81/0.88 % Maximal term depth : 4 ( 1 avg) % 0.81/0.88 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty) % 0.81/0.88 % Number of functors : 8 ( 8 usr; 2 con; 0-2 aty) % 0.81/0.88 % Number of variables : 16 ( 0 sgn) % 0.81/0.88 % SPC : CNF_UNS_RFO_SEQ_HRN % 0.81/0.88 % 0.81/0.88 % Comments : The problems in the [Pau06] collection each have very many axioms, % 0.81/0.88 % of which only a small selection are required for the refutation. % 0.81/0.88 % The mission is to find those few axioms, after which a refutation % 0.81/0.88 % can be quite easily found. This version has only the necessary % 0.81/0.88 % axioms. % 0.81/0.88 %------------------------------------------------------------------------------ % 0.81/0.88 cnf(cls_conjecture_0,negated_conjecture, % 0.81/0.88 ( c_in(c_Union(V_U,t_a),v_S,tc_set(t_a)) % 0.81/0.88 | ~ c_in(V_U,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ) ). % 0.81/0.88 % 0.81/0.88 cnf(cls_conjecture_1,negated_conjecture, % 0.81/0.88 ( c_in(v_x(V_U),v_S,tc_set(t_a)) % 0.81/0.88 | ~ c_in(V_U,v_S,tc_set(t_a)) ) ). % 0.81/0.88 % 0.81/0.88 cnf(cls_conjecture_2,negated_conjecture, % 0.81/0.88 ( c_lessequals(V_U,v_x(V_U),tc_set(t_a)) % 0.81/0.88 | ~ c_in(V_U,v_S,tc_set(t_a)) ) ). % 0.81/0.88 % 0.81/0.88 cnf(cls_conjecture_3,negated_conjecture, % 0.81/0.88 ( V_U != v_x(V_U) % 0.81/0.88 | ~ c_in(V_U,v_S,tc_set(t_a)) ) ). % 0.81/0.88 % 0.81/0.88 cnf(cls_Set_OsubsetD_0,axiom, % 0.81/0.88 ( ~ c_in(V_c,V_A,T_a) % 0.81/0.88 | ~ c_lessequals(V_A,V_B,tc_set(T_a)) % 0.81/0.88 | c_in(V_c,V_B,T_a) ) ). % 0.81/0.88 % 0.81/0.88 cnf(cls_Zorn_OHausdorff_0,axiom, % 0.81/0.88 c_in(c_Zorn_OHausdorff__1(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a))) ). % 0.81/0.88 % 0.81/0.88 cnf(cls_Zorn_Omaxchain__Zorn_0,axiom, % 0.81/0.88 ( ~ c_in(V_u,V_S,tc_set(T_a)) % 0.81/0.88 | ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a))) % 0.81/0.88 | ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a)) % 0.81/0.88 | c_Union(V_c,T_a) = V_u ) ). % 0.81/0.88 % 0.81/0.88 cnf(cls_Zorn_Omaxchain__subset__chain_0,axiom, % 0.81/0.88 c_lessequals(c_Zorn_Omaxchain(V_S,T_a),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))) ). % 0.81/0.88 % 0.81/0.88 %------------------------------------------------------------------------------ % 0.81/0.88 %------------------------------------------- % 0.81/0.88 % Proof found % 0.81/0.88 % SZS status Theorem for theBenchmark % 0.81/0.88 % SZS output start Proof % 0.81/0.88 %ClaNum:27(EqnAxiom:19) % 0.81/0.88 %VarNum:43(SingletonVarNum:16) % 0.81/0.88 %MaxLitNum:4 % 0.81/0.88 %MaxfuncDepth:3 % 0.81/0.88 %SharedTerms:5 % 0.81/0.88 %goalClause: 22 23 24 25 % 0.81/0.88 [20]P1(f1(x201,x202),f3(x201,x202),f5(f5(x202))) % 0.81/0.88 [21]P2(f3(x211,x212),f4(x211,x212),f5(f5(f5(x212)))) % 0.81/0.88 [22]~E(f7(x221),x221)+~P1(x221,a8,f5(a6)) % 0.81/0.88 [23]~P1(x231,a8,f5(a6))+P1(f7(x231),a8,f5(a6)) % 0.81/0.88 [24]P2(x241,f7(x241),f5(a6))+~P1(x241,a8,f5(a6)) % 0.81/0.88 [25]~P1(x251,f4(a8,a6),f5(f5(a6)))+P1(f2(x251,a6),a8,f5(a6)) % 0.81/0.88 [26]P1(x261,x262,x263)+~P1(x261,x264,x263)+~P2(x264,x262,f5(x263)) % 0.81/0.88 [27]~P2(f2(x271,x272),x273,f5(x272))+~P1(x273,x274,f5(x272))+E(f2(x271,x272),x273)+~P1(x271,f3(x274,x272),f5(f5(x272))) % 0.81/0.88 %EqnAxiom % 0.81/0.88 [1]E(x11,x11) % 0.81/0.88 [2]E(x22,x21)+~E(x21,x22) % 0.81/0.88 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.81/0.88 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43)) % 0.81/0.88 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52)) % 0.81/0.88 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63)) % 0.81/0.88 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72)) % 0.81/0.88 [8]~E(x81,x82)+E(f5(x81),f5(x82)) % 0.81/0.88 [9]~E(x91,x92)+E(f2(x91,x93),f2(x92,x93)) % 0.81/0.88 [10]~E(x101,x102)+E(f2(x103,x101),f2(x103,x102)) % 0.81/0.88 [11]~E(x111,x112)+E(f7(x111),f7(x112)) % 0.81/0.88 [12]~E(x121,x122)+E(f4(x121,x123),f4(x122,x123)) % 0.81/0.88 [13]~E(x131,x132)+E(f4(x133,x131),f4(x133,x132)) % 0.81/0.88 [14]P1(x142,x143,x144)+~E(x141,x142)+~P1(x141,x143,x144) % 0.81/0.88 [15]P1(x153,x152,x154)+~E(x151,x152)+~P1(x153,x151,x154) % 0.81/0.88 [16]P1(x163,x164,x162)+~E(x161,x162)+~P1(x163,x164,x161) % 0.81/0.88 [17]P2(x172,x173,x174)+~E(x171,x172)+~P2(x171,x173,x174) % 0.81/0.88 [18]P2(x183,x182,x184)+~E(x181,x182)+~P2(x183,x181,x184) % 0.81/0.88 [19]P2(x193,x194,x192)+~E(x191,x192)+~P2(x193,x194,x191) % 0.81/0.88 % 0.81/0.88 %------------------------------------------- % 0.81/0.88 cnf(28,plain, % 0.81/0.88 (P1(f1(x281,x282),f4(x281,x282),f5(f5(x282)))), % 0.81/0.88 inference(scs_inference,[],[20,21,26])). % 0.81/0.88 cnf(74,plain, % 0.81/0.88 (~E(f7(f2(f1(a8,a6),a6)),f2(f1(a8,a6),a6))), % 0.81/0.88 inference(scs_inference,[],[28,25,22])). % 0.81/0.88 cnf(151,plain, % 0.81/0.88 (~P2(f2(f1(a8,a6),a6),f7(f2(f1(a8,a6),a6)),f5(a6))+~P1(f7(f2(f1(a8,a6),a6)),a8,f5(a6))), % 0.81/0.88 inference(scs_inference,[],[74,20,2,27])). % 0.81/0.88 cnf(152,plain, % 0.81/0.88 (~P1(f7(f2(f1(a8,a6),a6)),a8,f5(a6))+~P1(f2(f1(a8,a6),a6),a8,f5(a6))), % 0.81/0.88 inference(scs_inference,[],[151,24])). % 0.81/0.88 cnf(153,plain, % 0.81/0.88 (~P1(f7(f2(f1(a8,a6),a6)),a8,f5(a6))), % 0.81/0.88 inference(scs_inference,[],[28,152,25])). % 0.81/0.88 cnf(156,plain, % 0.81/0.88 ($false), % 0.81/0.88 inference(scs_inference,[],[28,153,23,25]), % 0.81/0.88 ['proof']). % 0.81/0.88 % SZS output end Proof % 0.81/0.88 % Total time :0.280000s %------------------------------------------------------------------------------