%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET845-2 : 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 : n023.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 0.55s 0.61s % Output : CNFRefutation 0.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SET845-2 : TPTP v8.2.0. Released v3.2.0. % 0.12/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n023.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 17:47:09 EDT 2024 % 0.12/0.33 % CPUTime : % 0.19/0.56 start to proof:theBenchmark % 0.54/0.61 %------------------------------------------- % 0.54/0.61 % File :CSE---1.7 % 0.54/0.61 % Problem :theBenchmark % 0.54/0.61 % Transform :cnf % 0.54/0.61 % Format :tptp:raw % 0.54/0.61 % Command :java -jar mcs_scs.jar %d %s % 0.54/0.61 % 0.54/0.61 % Result :Theorem 0.000000s % 0.54/0.61 % Output :CNFRefutation 0.000000s % 0.54/0.61 %------------------------------------------- % 0.55/0.61 %------------------------------------------------------------------------------ % 0.55/0.61 % File : SET845-2 : TPTP v8.2.0. Released v3.2.0. % 0.55/0.61 % Domain : Set Theory % 0.55/0.61 % Problem : Problem about Zorn's lemma % 0.55/0.61 % Version : [Pau06] axioms : Reduced > Especial. % 0.55/0.61 % English : % 0.55/0.61 % 0.55/0.61 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe % 0.55/0.61 % Source : [Pau06] % 0.55/0.61 % Names : % 0.55/0.61 % 0.55/0.61 % Status : Unsatisfiable % 0.55/0.61 % Rating : 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 % 0.55/0.61 % Syntax : Number of clauses : 7 ( 4 unt; 0 nHn; 6 RR) % 0.55/0.61 % Number of literals : 11 ( 3 equ; 5 neg) % 0.55/0.61 % Maximal clause size : 3 ( 1 avg) % 0.55/0.61 % Maximal term depth : 3 ( 1 avg) % 0.55/0.61 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty) % 0.55/0.61 % Number of functors : 7 ( 7 usr; 3 con; 0-3 aty) % 0.55/0.61 % Number of variables : 12 ( 1 sgn) % 0.55/0.61 % SPC : CNF_UNS_RFO_SEQ_HRN % 0.55/0.61 % 0.55/0.61 % Comments : The problems in the [Pau06] collection each have very many axioms, % 0.55/0.61 % of which only a small selection are required for the refutation. % 0.55/0.61 % The mission is to find those few axioms, after which a refutation % 0.55/0.61 % can be quite easily found. This version has only the necessary % 0.55/0.61 % axioms. % 0.55/0.61 %------------------------------------------------------------------------------ % 0.55/0.61 cnf(cls_Set_OUnion__upper_0,axiom, % 0.55/0.61 ( ~ c_in(V_B,V_A,tc_set(T_a)) % 0.55/0.61 | c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a)) ) ). % 0.55/0.61 % 0.55/0.61 cnf(cls_Set_Osubset__antisym_0,axiom, % 0.55/0.61 ( ~ c_lessequals(V_B,V_A,tc_set(T_a)) % 0.55/0.61 | ~ c_lessequals(V_A,V_B,tc_set(T_a)) % 0.55/0.61 | V_A = V_B ) ). % 0.55/0.61 % 0.55/0.61 cnf(cls_Zorn_OAbrial__axiom1_0,axiom, % 0.55/0.61 c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))) ). % 0.55/0.61 % 0.55/0.61 cnf(cls_Zorn_OTFin_OsuccI_0,axiom, % 0.55/0.61 ( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.55/0.61 | c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ). % 0.55/0.61 % 0.55/0.61 cnf(cls_conjecture_0,negated_conjecture, % 0.55/0.61 c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ). % 0.55/0.61 % 0.55/0.61 cnf(cls_conjecture_1,negated_conjecture, % 0.55/0.61 v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ). % 0.55/0.61 % 0.55/0.61 cnf(cls_conjecture_2,negated_conjecture, % 0.55/0.61 v_m != c_Zorn_Osucc(v_S,v_m,t_a) ). % 0.55/0.61 % 0.55/0.61 %------------------------------------------------------------------------------ % 0.55/0.61 %------------------------------------------- % 0.55/0.61 % Proof found % 0.55/0.61 % SZS status Theorem for theBenchmark % 0.55/0.61 % SZS output start Proof % 0.55/0.61 %ClaNum:24(EqnAxiom:17) % 0.55/0.61 %VarNum:30(SingletonVarNum:12) % 0.55/0.61 %MaxLitNum:3 % 0.55/0.61 %MaxfuncDepth:2 % 0.55/0.61 %SharedTerms:11 % 0.55/0.61 %goalClause: 18 19 21 % 0.55/0.61 %singleGoalClaCount:3 % 0.55/0.61 [21]~E(f5(a1,a7,a2),a7) % 0.55/0.61 [18]E(f4(f3(a1,a2),f6(a2)),a7) % 0.55/0.61 [19]P1(a7,f3(a1,a2),f6(f6(a2))) % 0.55/0.61 [20]P2(x201,f5(x202,x201,x203),f6(f6(x203))) % 0.55/0.61 [22]~P1(x221,x222,f6(x223))+P2(x221,f4(x222,x223),f6(x223)) % 0.55/0.61 [24]~P1(x242,f3(x241,x243),f6(f6(x243)))+P1(f5(x241,x242,x243),f3(x241,x243),f6(f6(x243))) % 0.55/0.61 [23]E(x231,x232)+~P2(x232,x231,f6(x233))+~P2(x231,x232,f6(x233)) % 0.55/0.61 %EqnAxiom % 0.55/0.61 [1]E(x11,x11) % 0.55/0.61 [2]E(x22,x21)+~E(x21,x22) % 0.55/0.61 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.55/0.61 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43)) % 0.55/0.61 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52)) % 0.55/0.61 [6]~E(x61,x62)+E(f6(x61),f6(x62)) % 0.55/0.61 [7]~E(x71,x72)+E(f4(x71,x73),f4(x72,x73)) % 0.55/0.61 [8]~E(x81,x82)+E(f4(x83,x81),f4(x83,x82)) % 0.55/0.61 [9]~E(x91,x92)+E(f5(x91,x93,x94),f5(x92,x93,x94)) % 0.55/0.61 [10]~E(x101,x102)+E(f5(x103,x101,x104),f5(x103,x102,x104)) % 0.55/0.61 [11]~E(x111,x112)+E(f5(x113,x114,x111),f5(x113,x114,x112)) % 0.55/0.61 [12]P1(x122,x123,x124)+~E(x121,x122)+~P1(x121,x123,x124) % 0.55/0.61 [13]P1(x133,x132,x134)+~E(x131,x132)+~P1(x133,x131,x134) % 0.55/0.61 [14]P1(x143,x144,x142)+~E(x141,x142)+~P1(x143,x144,x141) % 0.55/0.61 [15]P2(x152,x153,x154)+~E(x151,x152)+~P2(x151,x153,x154) % 0.55/0.61 [16]P2(x163,x162,x164)+~E(x161,x162)+~P2(x163,x161,x164) % 0.55/0.61 [17]P2(x173,x174,x172)+~E(x171,x172)+~P2(x173,x174,x171) % 0.55/0.61 % 0.55/0.61 %------------------------------------------- % 0.55/0.62 cnf(25,plain, % 0.55/0.62 (E(a7,f4(f3(a1,a2),f6(a2)))), % 0.55/0.62 inference(scs_inference,[],[18,2])). % 0.55/0.62 cnf(26,plain, % 0.55/0.62 (~E(f5(a1,a7,a2),f4(f3(a1,a2),f6(a2)))), % 0.55/0.62 inference(scs_inference,[],[18,21,2,3])). % 0.55/0.62 cnf(50,plain, % 0.55/0.62 ($false), % 0.55/0.62 inference(scs_inference,[],[19,25,26,20,15,23,22,24]), % 0.55/0.62 ['proof']). % 0.55/0.62 % SZS output end Proof % 0.55/0.62 % Total time :0.000000s %------------------------------------------------------------------------------