%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET864-2 : 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 : n032.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 0.12s 0.51s % Output : CNFRefutation 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.08 % Problem : SET864-2 : TPTP v8.2.0. Released v3.2.0. % 0.00/0.08 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.07/0.26 % Computer : n032.cluster.edu % 0.07/0.26 % Model : x86_64 x86_64 % 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.26 % Memory : 8042.1875MB % 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.26 % CPULimit : 300 % 0.07/0.26 % WCLimit : 300 % 0.07/0.26 % DateTime : Sun Jun 23 16:47:08 EDT 2024 % 0.07/0.27 % CPUTime : % 0.12/0.45 start to proof:theBenchmark % 0.12/0.51 %------------------------------------------- % 0.12/0.51 % File :CSE---1.7 % 0.12/0.51 % Problem :theBenchmark % 0.12/0.51 % Transform :cnf % 0.12/0.51 % Format :tptp:raw % 0.12/0.51 % Command :java -jar mcs_scs.jar %d %s % 0.12/0.51 % 0.12/0.51 % Result :Theorem 0.030000s % 0.12/0.51 % Output :CNFRefutation 0.030000s % 0.12/0.51 %------------------------------------------- % 0.12/0.51 %------------------------------------------------------------------------------ % 0.12/0.51 % File : SET864-2 : TPTP v8.2.0. Released v3.2.0. % 0.12/0.51 % Domain : Set Theory % 0.12/0.51 % Problem : Problem about Zorn's lemma % 0.12/0.51 % Version : [Pau06] axioms : Reduced > Especial. % 0.12/0.51 % English : % 0.12/0.51 % 0.12/0.51 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe % 0.12/0.51 % Source : [Pau06] % 0.12/0.51 % Names : % 0.12/0.51 % 0.12/0.51 % Status : Unsatisfiable % 0.12/0.51 % Rating : 0.00 v5.3.0, 0.08 v5.2.0, 0.00 v4.1.0, 0.11 v4.0.1, 0.17 v3.3.0, 0.14 v3.2.0 % 0.12/0.51 % Syntax : Number of clauses : 6 ( 2 unt; 0 nHn; 6 RR) % 0.12/0.51 % Number of literals : 12 ( 2 equ; 7 neg) % 0.12/0.51 % Maximal clause size : 4 ( 2 avg) % 0.12/0.51 % Maximal term depth : 3 ( 1 avg) % 0.12/0.51 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty) % 0.12/0.51 % Number of functors : 7 ( 7 usr; 3 con; 0-2 aty) % 0.12/0.51 % Number of variables : 7 ( 0 sgn) % 0.12/0.51 % SPC : CNF_UNS_RFO_SEQ_HRN % 0.12/0.51 % 0.12/0.51 % Comments : The problems in the [Pau06] collection each have very many axioms, % 0.12/0.51 % of which only a small selection are required for the refutation. % 0.12/0.51 % The mission is to find those few axioms, after which a refutation % 0.12/0.51 % can be quite easily found. This version has only the necessary % 0.12/0.51 % axioms. % 0.12/0.51 %------------------------------------------------------------------------------ % 0.12/0.51 cnf(cls_Zorn_Omaxchain__Zorn_0,axiom, % 0.12/0.51 ( ~ c_in(V_u,V_S,tc_set(T_a)) % 0.12/0.51 | ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a))) % 0.12/0.51 | ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a)) % 0.12/0.51 | c_Union(V_c,T_a) = V_u ) ). % 0.12/0.51 % 0.12/0.51 cnf(cls_conjecture_0,negated_conjecture, % 0.12/0.51 c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ). % 0.12/0.51 % 0.12/0.51 cnf(cls_conjecture_2,negated_conjecture, % 0.12/0.51 c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)) ). % 0.12/0.51 % 0.12/0.51 cnf(cls_conjecture_3,negated_conjecture, % 0.12/0.51 ( c_in(v_x(V_U),v_S,tc_set(t_a)) % 0.12/0.51 | ~ c_in(V_U,v_S,tc_set(t_a)) ) ). % 0.12/0.51 % 0.12/0.51 cnf(cls_conjecture_4,negated_conjecture, % 0.12/0.51 ( c_lessequals(V_U,v_x(V_U),tc_set(t_a)) % 0.12/0.51 | ~ c_in(V_U,v_S,tc_set(t_a)) ) ). % 0.12/0.51 % 0.12/0.51 cnf(cls_conjecture_5,negated_conjecture, % 0.12/0.51 ( V_U != v_x(V_U) % 0.12/0.51 | ~ c_in(V_U,v_S,tc_set(t_a)) ) ). % 0.12/0.51 % 0.12/0.51 %------------------------------------------------------------------------------ % 0.12/0.51 %------------------------------------------- % 0.12/0.51 % Proof found % 0.12/0.51 % SZS status Theorem for theBenchmark % 0.12/0.51 % SZS output start Proof % 0.12/0.51 %ClaNum:21(EqnAxiom:15) % 0.12/0.51 %VarNum:22(SingletonVarNum:7) % 0.12/0.51 %MaxLitNum:4 % 0.12/0.51 %MaxfuncDepth:2 % 0.12/0.51 %SharedTerms:9 % 0.12/0.51 %goalClause: 16 17 18 19 20 % 0.12/0.51 %singleGoalClaCount:2 % 0.12/0.51 [16]P1(f3(a1,a2),a5,f6(a2)) % 0.12/0.51 [17]P1(a1,f4(a5,a2),f6(f6(a2))) % 0.12/0.51 [18]~E(f7(x181),x181)+~P1(x181,a5,f6(a2)) % 0.12/0.51 [19]~P1(x191,a5,f6(a2))+P1(f7(x191),a5,f6(a2)) % 0.12/0.51 [20]P2(x201,f7(x201),f6(a2))+~P1(x201,a5,f6(a2)) % 0.12/0.51 [21]~P2(f3(x211,x212),x213,f6(x212))+~P1(x213,x214,f6(x212))+E(f3(x211,x212),x213)+~P1(x211,f4(x214,x212),f6(f6(x212))) % 0.12/0.51 %EqnAxiom % 0.12/0.51 [1]E(x11,x11) % 0.12/0.51 [2]E(x22,x21)+~E(x21,x22) % 0.12/0.51 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.12/0.51 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43)) % 0.12/0.51 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52)) % 0.12/0.51 [6]~E(x61,x62)+E(f6(x61),f6(x62)) % 0.12/0.51 [7]~E(x71,x72)+E(f4(x71,x73),f4(x72,x73)) % 0.12/0.51 [8]~E(x81,x82)+E(f4(x83,x81),f4(x83,x82)) % 0.12/0.51 [9]~E(x91,x92)+E(f7(x91),f7(x92)) % 0.12/0.51 [10]P1(x102,x103,x104)+~E(x101,x102)+~P1(x101,x103,x104) % 0.12/0.51 [11]P1(x113,x112,x114)+~E(x111,x112)+~P1(x113,x111,x114) % 0.12/0.51 [12]P1(x123,x124,x122)+~E(x121,x122)+~P1(x123,x124,x121) % 0.12/0.51 [13]P2(x132,x133,x134)+~E(x131,x132)+~P2(x131,x133,x134) % 0.12/0.51 [14]P2(x143,x142,x144)+~E(x141,x142)+~P2(x143,x141,x144) % 0.12/0.52 [15]P2(x153,x154,x152)+~E(x151,x152)+~P2(x153,x154,x151) % 0.12/0.52 % 0.12/0.52 %------------------------------------------- % 0.12/0.52 cnf(22,plain, % 0.12/0.52 (~E(f7(f3(a1,a2)),f3(a1,a2))), % 0.12/0.52 inference(scs_inference,[],[16,18])). % 0.12/0.52 cnf(24,plain, % 0.12/0.52 (P2(f3(a1,a2),f7(f3(a1,a2)),f6(a2))), % 0.12/0.52 inference(scs_inference,[],[16,18,20])). % 0.12/0.52 cnf(45,plain, % 0.12/0.52 (~E(f6(f6(a2)),x451)+~P1(f7(f3(a1,a2)),a5,f6(a2))+E(f3(a1,a2),f7(f3(a1,a2)))), % 0.12/0.52 inference(scs_inference,[],[16,17,24,12,21])). % 0.12/0.52 cnf(47,plain, % 0.12/0.52 (E(f3(a1,a2),f7(f3(a1,a2)))+~P1(f7(f3(a1,a2)),a5,f6(a2))), % 0.12/0.52 inference(equality_inference,[],[45])). % 0.12/0.52 cnf(60,plain, % 0.12/0.52 (~P1(f7(f3(a1,a2)),a5,f6(a2))), % 0.12/0.52 inference(scs_inference,[],[22,2,47])). % 0.12/0.52 cnf(61,plain, % 0.12/0.52 ($false), % 0.12/0.52 inference(scs_inference,[],[16,60,19]), % 0.12/0.52 ['proof']). % 0.12/0.52 % SZS output end Proof % 0.12/0.52 % Total time :0.030000s %------------------------------------------------------------------------------