%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET844-2 : 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 : n025.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 14:22:42 EDT 2024 % Result : Unsatisfiable 0.61s 0.67s % Output : CNFRefutation 0.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SET844-2 : TPTP v8.2.0. Released v3.2.0. % 0.04/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n025.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sun Jun 23 16:15:24 EDT 2024 % 0.12/0.34 % CPUTime : % 0.50/0.62 start to proof:theBenchmark % 0.61/0.66 %------------------------------------------- % 0.61/0.66 % File :CSE---1.7 % 0.61/0.66 % Problem :theBenchmark % 0.61/0.66 % Transform :cnf % 0.61/0.66 % Format :tptp:raw % 0.61/0.66 % Command :java -jar mcs_scs.jar %d %s % 0.61/0.67 % 0.61/0.67 % Result :Theorem 0.000000s % 0.61/0.67 % Output :CNFRefutation 0.000000s % 0.61/0.67 %------------------------------------------- % 0.61/0.67 %------------------------------------------------------------------------------ % 0.61/0.67 % File : SET844-2 : TPTP v8.2.0. Released v3.2.0. % 0.61/0.67 % Domain : Set Theory % 0.61/0.67 % Problem : Problem about Zorn's lemma % 0.61/0.67 % Version : [Pau06] axioms : Reduced > Especial. % 0.61/0.67 % English : % 0.61/0.67 % 0.61/0.67 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe % 0.61/0.67 % Source : [Pau06] % 0.61/0.67 % Names : % 0.61/0.67 % 0.61/0.67 % Status : Unsatisfiable % 0.61/0.67 % Rating : 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 % 0.61/0.67 % Syntax : Number of clauses : 6 ( 4 unt; 0 nHn; 5 RR) % 0.61/0.67 % Number of literals : 10 ( 2 equ; 5 neg) % 0.61/0.67 % Maximal clause size : 4 ( 1 avg) % 0.61/0.67 % Maximal term depth : 4 ( 2 avg) % 0.61/0.67 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty) % 0.61/0.67 % Number of functors : 7 ( 7 usr; 3 con; 0-3 aty) % 0.61/0.67 % Number of variables : 9 ( 1 sgn) % 0.61/0.67 % SPC : CNF_UNS_RFO_SEQ_HRN % 0.61/0.67 % 0.61/0.67 % Comments : The problems in the [Pau06] collection each have very many axioms, % 0.61/0.67 % of which only a small selection are required for the refutation. % 0.61/0.67 % The mission is to find those few axioms, after which a refutation % 0.61/0.67 % can be quite easily found. This version has only the necessary % 0.61/0.67 % axioms. % 0.61/0.67 %------------------------------------------------------------------------------ % 0.61/0.67 cnf(cls_Set_Osubset__refl_0,axiom, % 0.61/0.67 c_lessequals(V_A,V_A,tc_set(T_a)) ). % 0.61/0.67 % 0.61/0.67 cnf(cls_Zorn_OTFin__UnionI_0,axiom, % 0.61/0.67 ( ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a)))) % 0.61/0.67 | c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ). % 0.61/0.67 % 0.61/0.67 cnf(cls_Zorn_Oeq__succ__upper_0,axiom, % 0.61/0.67 ( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.61/0.67 | ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.61/0.67 | V_m != c_Zorn_Osucc(V_S,V_m,T_a) % 0.61/0.67 | c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) ) ). % 0.61/0.67 % 0.61/0.67 cnf(cls_conjecture_0,negated_conjecture, % 0.61/0.67 c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ). % 0.61/0.67 % 0.61/0.67 cnf(cls_conjecture_1,negated_conjecture, % 0.61/0.67 v_m = c_Zorn_Osucc(v_S,v_m,t_a) ). % 0.61/0.67 % 0.61/0.67 cnf(cls_conjecture_2,negated_conjecture, % 0.61/0.67 ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ). % 0.61/0.67 % 0.61/0.67 %------------------------------------------------------------------------------ % 0.61/0.67 %------------------------------------------- % 0.61/0.67 % Proof found % 0.61/0.67 % SZS status Theorem for theBenchmark % 0.61/0.67 % SZS output start Proof % 0.61/0.67 %ClaNum:23(EqnAxiom:17) % 0.61/0.67 %VarNum:27(SingletonVarNum:9) % 0.61/0.67 %MaxLitNum:4 % 0.61/0.67 %MaxfuncDepth:3 % 0.61/0.67 %SharedTerms:11 % 0.61/0.67 %goalClause: 18 20 21 % 0.61/0.67 %singleGoalClaCount:3 % 0.61/0.67 [18]E(f3(a1,a7,a2),a7) % 0.61/0.67 [20]P2(a7,f4(a1,a2),f6(f6(a2))) % 0.61/0.67 [21]~P1(f5(f4(a1,a2),f6(a2)),a7,f6(f6(a2))) % 0.61/0.67 [19]P1(x191,x191,f6(x192)) % 0.61/0.67 [22]P2(f5(x221,f6(x222)),f4(x223,x222),f6(f6(x222)))+~P1(x221,f4(x223,x222),f6(f6(f6(x222)))) % 0.61/0.67 [23]~E(f3(x234,x232,x233),x232)+~P2(x231,f4(x234,x233),f6(f6(x233)))+~P2(x232,f4(x234,x233),f6(f6(x233)))+P1(x231,x232,f6(f6(x233))) % 0.61/0.67 %EqnAxiom % 0.61/0.67 [1]E(x11,x11) % 0.61/0.67 [2]E(x22,x21)+~E(x21,x22) % 0.61/0.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.61/0.67 [4]~E(x41,x42)+E(f3(x41,x43,x44),f3(x42,x43,x44)) % 0.61/0.67 [5]~E(x51,x52)+E(f3(x53,x51,x54),f3(x53,x52,x54)) % 0.61/0.67 [6]~E(x61,x62)+E(f3(x63,x64,x61),f3(x63,x64,x62)) % 0.61/0.67 [7]~E(x71,x72)+E(f6(x71),f6(x72)) % 0.61/0.67 [8]~E(x81,x82)+E(f4(x81,x83),f4(x82,x83)) % 0.61/0.67 [9]~E(x91,x92)+E(f4(x93,x91),f4(x93,x92)) % 0.61/0.67 [10]~E(x101,x102)+E(f5(x101,x103),f5(x102,x103)) % 0.61/0.67 [11]~E(x111,x112)+E(f5(x113,x111),f5(x113,x112)) % 0.61/0.67 [12]P1(x122,x123,x124)+~E(x121,x122)+~P1(x121,x123,x124) % 0.61/0.67 [13]P1(x133,x132,x134)+~E(x131,x132)+~P1(x133,x131,x134) % 0.61/0.67 [14]P1(x143,x144,x142)+~E(x141,x142)+~P1(x143,x144,x141) % 0.61/0.67 [15]P2(x152,x153,x154)+~E(x151,x152)+~P2(x151,x153,x154) % 0.61/0.67 [16]P2(x163,x162,x164)+~E(x161,x162)+~P2(x163,x161,x164) % 0.61/0.67 [17]P2(x173,x174,x172)+~E(x171,x172)+~P2(x173,x174,x171) % 0.61/0.67 % 0.61/0.67 %------------------------------------------- % 0.61/0.68 cnf(26,plain, % 0.61/0.68 (P1(x261,x261,f6(x262))), % 0.61/0.68 inference(rename_variables,[],[19])). % 0.61/0.68 cnf(29,plain, % 0.61/0.68 (P1(x291,x291,f6(x292))), % 0.61/0.68 inference(rename_variables,[],[19])). % 0.61/0.68 cnf(33,plain, % 0.61/0.68 ($false), % 0.61/0.68 inference(scs_inference,[],[18,21,20,19,26,29,2,22,12,13,15,23]), % 0.61/0.68 ['proof']). % 0.61/0.68 % SZS output end Proof % 0.61/0.68 % Total time :0.000000s %------------------------------------------------------------------------------