%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET841-2 : 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 14:22:41 EDT 2024 % Result : Unsatisfiable 0.49s 0.61s % Output : CNFRefutation 0.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET841-2 : 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 % 0.12/0.33 % Computer : n028.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 12:40:39 EDT 2024 % 0.12/0.33 % CPUTime : % 0.49/0.56 start to proof:theBenchmark % 0.49/0.60 %------------------------------------------- % 0.49/0.60 % File :CSE---1.7 % 0.49/0.60 % Problem :theBenchmark % 0.49/0.60 % Transform :cnf % 0.49/0.60 % Format :tptp:raw % 0.49/0.60 % Command :java -jar mcs_scs.jar %d %s % 0.49/0.60 % 0.49/0.60 % Result :Theorem 0.000000s % 0.49/0.60 % Output :CNFRefutation 0.000000s % 0.49/0.60 %------------------------------------------- % 0.49/0.60 %------------------------------------------------------------------------------ % 0.49/0.60 % File : SET841-2 : TPTP v8.2.0. Released v3.2.0. % 0.49/0.60 % Domain : Set Theory % 0.49/0.60 % Problem : Problem about Zorn's lemma % 0.49/0.60 % Version : [Pau06] axioms : Reduced > Especial. % 0.49/0.60 % English : % 0.49/0.60 % 0.49/0.60 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe % 0.49/0.60 % Source : [Pau06] % 0.49/0.60 % Names : % 0.49/0.60 % 0.49/0.60 % Status : Unsatisfiable % 0.49/0.60 % 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 v6.1.0, 0.07 v6.0.0, 0.00 v5.5.0, 0.10 v5.3.0, 0.06 v5.2.0, 0.00 v3.4.0, 0.08 v3.3.0, 0.14 v3.2.0 % 0.49/0.60 % Syntax : Number of clauses : 7 ( 6 unt; 1 nHn; 6 RR) % 0.49/0.60 % Number of literals : 11 ( 2 equ; 4 neg) % 0.49/0.60 % Maximal clause size : 5 ( 1 avg) % 0.49/0.60 % Maximal term depth : 3 ( 1 avg) % 0.49/0.60 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty) % 0.49/0.60 % Number of functors : 7 ( 7 usr; 4 con; 0-3 aty) % 0.49/0.60 % Number of variables : 6 ( 1 sgn) % 0.49/0.60 % SPC : CNF_UNS_RFO_SEQ_NHN % 0.49/0.60 % 0.49/0.60 % Comments : The problems in the [Pau06] collection each have very many axioms, % 0.49/0.60 % of which only a small selection are required for the refutation. % 0.49/0.60 % The mission is to find those few axioms, after which a refutation % 0.49/0.60 % can be quite easily found. This version has only the necessary % 0.49/0.60 % axioms. % 0.49/0.60 %------------------------------------------------------------------------------ % 0.49/0.60 cnf(cls_Set_Osubset__refl_0,axiom, % 0.49/0.60 c_lessequals(V_A,V_A,tc_set(T_a)) ). % 0.49/0.60 % 0.49/0.60 cnf(cls_Zorn_OTFin__subsetD_0,axiom, % 0.49/0.60 ( ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.49/0.60 | ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.49/0.60 | ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) % 0.49/0.60 | c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a))) % 0.49/0.60 | V_n = V_m ) ). % 0.49/0.60 % 0.49/0.60 cnf(cls_conjecture_0,negated_conjecture, % 0.49/0.60 c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ). % 0.49/0.60 % 0.49/0.60 cnf(cls_conjecture_1,negated_conjecture, % 0.49/0.60 v_m = c_Zorn_Osucc(v_S,v_m,t_a) ). % 0.49/0.60 % 0.49/0.60 cnf(cls_conjecture_2,negated_conjecture, % 0.49/0.60 c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ). % 0.49/0.61 % 0.49/0.61 cnf(cls_conjecture_3,negated_conjecture, % 0.49/0.61 c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ). % 0.49/0.61 % 0.49/0.61 cnf(cls_conjecture_4,negated_conjecture, % 0.49/0.61 ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ). % 0.49/0.61 % 0.49/0.61 %------------------------------------------------------------------------------ % 0.49/0.61 %------------------------------------------- % 0.49/0.61 % Proof found % 0.49/0.61 % SZS status Theorem for theBenchmark % 0.49/0.61 % SZS output start Proof % 0.49/0.61 %ClaNum:22(EqnAxiom:15) % 0.49/0.61 %VarNum:21(SingletonVarNum:6) % 0.49/0.61 %MaxLitNum:5 % 0.49/0.61 %MaxfuncDepth:2 % 0.49/0.61 %SharedTerms:14 % 0.49/0.61 %goalClause: 16 18 19 20 21 % 0.49/0.61 %singleGoalClaCount:5 % 0.49/0.61 [16]E(f3(a1,a6,a2),a6) % 0.49/0.61 [18]P1(a7,a6,f5(f5(a2))) % 0.49/0.61 [19]P2(a6,f4(a1,a2),f5(f5(a2))) % 0.49/0.61 [20]P2(a7,f4(a1,a2),f5(f5(a2))) % 0.49/0.61 [21]~P1(f3(a1,a7,a2),a6,f5(f5(a2))) % 0.49/0.61 [17]P1(x171,x171,f5(x172)) % 0.49/0.61 [22]E(x221,x222)+~P1(x221,x222,f5(f5(x224)))+~P2(x222,f4(x223,x224),f5(f5(x224)))+~P2(x221,f4(x223,x224),f5(f5(x224)))+P1(f3(x223,x221,x224),x222,f5(f5(x224))) % 0.49/0.61 %EqnAxiom % 0.49/0.61 [1]E(x11,x11) % 0.49/0.61 [2]E(x22,x21)+~E(x21,x22) % 0.49/0.61 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.49/0.61 [4]~E(x41,x42)+E(f3(x41,x43,x44),f3(x42,x43,x44)) % 0.49/0.61 [5]~E(x51,x52)+E(f3(x53,x51,x54),f3(x53,x52,x54)) % 0.49/0.61 [6]~E(x61,x62)+E(f3(x63,x64,x61),f3(x63,x64,x62)) % 0.49/0.61 [7]~E(x71,x72)+E(f5(x71),f5(x72)) % 0.49/0.61 [8]~E(x81,x82)+E(f4(x81,x83),f4(x82,x83)) % 0.49/0.61 [9]~E(x91,x92)+E(f4(x93,x91),f4(x93,x92)) % 0.49/0.61 [10]P1(x102,x103,x104)+~E(x101,x102)+~P1(x101,x103,x104) % 0.49/0.61 [11]P1(x113,x112,x114)+~E(x111,x112)+~P1(x113,x111,x114) % 0.49/0.61 [12]P1(x123,x124,x122)+~E(x121,x122)+~P1(x123,x124,x121) % 0.49/0.61 [13]P2(x132,x133,x134)+~E(x131,x132)+~P2(x131,x133,x134) % 0.49/0.61 [14]P2(x143,x142,x144)+~E(x141,x142)+~P2(x143,x141,x144) % 0.49/0.61 [15]P2(x153,x154,x152)+~E(x151,x152)+~P2(x153,x154,x151) % 0.49/0.61 % 0.49/0.61 %------------------------------------------- % 0.49/0.61 cnf(25,plain, % 0.49/0.61 (P1(a7,f3(a1,a6,a2),f5(f5(a2)))), % 0.49/0.61 inference(scs_inference,[],[16,21,18,2,10,11])). % 0.49/0.61 cnf(27,plain, % 0.49/0.61 (E(a7,a6)), % 0.49/0.61 inference(scs_inference,[],[16,20,19,21,18,2,10,11,13,22])). % 0.49/0.61 cnf(39,plain, % 0.49/0.61 ($false), % 0.49/0.61 inference(scs_inference,[],[16,21,25,17,27,2,11,3,10,5]), % 0.49/0.61 ['proof']). % 0.49/0.61 % SZS output end Proof % 0.49/0.61 % Total time :0.000000s %------------------------------------------------------------------------------