%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET846-2 : 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 : n029.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 14:22:43 EDT 2024 % Result : Unsatisfiable 0.52s 0.58s % Output : CNFRefutation 0.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET846-2 : TPTP v8.2.0. Released v3.2.0. % 0.06/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.11/0.33 % Computer : n029.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Sun Jun 23 17:05:09 EDT 2024 % 0.11/0.33 % CPUTime : % 0.50/0.54 start to proof:theBenchmark % 0.52/0.58 %------------------------------------------- % 0.52/0.58 % File :CSE---1.7 % 0.52/0.58 % Problem :theBenchmark % 0.52/0.58 % Transform :cnf % 0.52/0.58 % Format :tptp:raw % 0.52/0.58 % Command :java -jar mcs_scs.jar %d %s % 0.52/0.58 % 0.52/0.58 % Result :Theorem 0.000000s % 0.52/0.58 % Output :CNFRefutation 0.000000s % 0.52/0.58 %------------------------------------------- % 0.52/0.58 %------------------------------------------------------------------------------ % 0.52/0.58 % File : SET846-2 : TPTP v8.2.0. Released v3.2.0. % 0.52/0.58 % Domain : Set Theory % 0.52/0.58 % Problem : Problem about Zorn's lemma % 0.52/0.58 % Version : [Pau06] axioms : Reduced > Especial. % 0.52/0.58 % English : % 0.52/0.58 % 0.52/0.58 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe % 0.52/0.58 % Source : [Pau06] % 0.52/0.58 % Names : % 0.52/0.58 % 0.52/0.58 % Status : Unsatisfiable % 0.52/0.58 % Rating : 0.00 v5.3.0, 0.05 v5.2.0, 0.00 v3.2.0 % 0.52/0.58 % Syntax : Number of clauses : 5 ( 2 unt; 0 nHn; 4 RR) % 0.52/0.58 % Number of literals : 8 ( 0 equ; 4 neg) % 0.52/0.58 % Maximal clause size : 2 ( 1 avg) % 0.52/0.58 % Maximal term depth : 4 ( 2 avg) % 0.52/0.58 % Number of predicates : 2 ( 2 usr; 0 prp; 3-3 aty) % 0.52/0.58 % Number of functors : 6 ( 6 usr; 2 con; 0-3 aty) % 0.52/0.58 % Number of variables : 11 ( 1 sgn) % 0.52/0.58 % SPC : CNF_UNS_RFO_NEQ_HRN % 0.52/0.58 % 0.52/0.58 % Comments : The problems in the [Pau06] collection each have very many axioms, % 0.52/0.58 % of which only a small selection are required for the refutation. % 0.52/0.58 % The mission is to find those few axioms, after which a refutation % 0.52/0.58 % can be quite easily found. This version has only the necessary % 0.52/0.58 % axioms. % 0.52/0.58 %------------------------------------------------------------------------------ % 0.52/0.58 cnf(cls_Set_OUnion__upper_0,axiom, % 0.52/0.58 ( ~ c_in(V_B,V_A,tc_set(T_a)) % 0.52/0.58 | c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a)) ) ). % 0.52/0.58 % 0.52/0.58 cnf(cls_Set_Osubset__refl_0,axiom, % 0.52/0.58 c_lessequals(V_A,V_A,tc_set(T_a)) ). % 0.52/0.58 % 0.52/0.58 cnf(cls_Zorn_OTFin_OsuccI_0,axiom, % 0.52/0.58 ( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.52/0.58 | c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ). % 0.52/0.58 % 0.52/0.58 cnf(cls_Zorn_OTFin__UnionI_0,axiom, % 0.52/0.58 ( ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a)))) % 0.52/0.58 | c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ). % 0.52/0.58 % 0.52/0.58 cnf(cls_conjecture_1,negated_conjecture, % 0.52/0.58 ~ c_lessequals(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))) ). % 0.52/0.58 % 0.52/0.58 %------------------------------------------------------------------------------ % 0.52/0.58 %------------------------------------------- % 0.52/0.58 % Proof found % 0.52/0.58 % SZS status Theorem for theBenchmark % 0.52/0.58 % SZS output start Proof % 0.52/0.58 %ClaNum:5(EqnAxiom:0) % 0.52/0.58 %VarNum:29(SingletonVarNum:11) % 0.52/0.58 %MaxLitNum:2 % 0.52/0.58 %MaxfuncDepth:3 % 0.52/0.58 %SharedTerms:8 % 0.52/0.58 %goalClause: 2 % 0.52/0.58 %singleGoalClaCount:1 % 0.52/0.58 [2]~P1(f5(a6,f4(f3(a6,a2),f1(a2)),a2),f4(f3(a6,a2),f1(a2)),f1(f1(a2))) % 0.52/0.58 [1]P1(x11,x11,f1(x12)) % 0.52/0.58 [3]~P2(x31,x32,f1(x33))+P1(x31,f4(x32,x33),f1(x33)) % 0.52/0.58 [5]~P2(x52,f3(x51,x53),f1(f1(x53)))+P2(f5(x51,x52,x53),f3(x51,x53),f1(f1(x53))) % 0.52/0.58 [4]P2(f4(x41,f1(x42)),f3(x43,x42),f1(f1(x42)))+~P1(x41,f3(x43,x42),f1(f1(f1(x42)))) % 0.52/0.58 %EqnAxiom % 0.52/0.58 % 0.52/0.58 %------------------------------------------- % 0.52/0.58 cnf(10,plain, % 0.52/0.58 ($false), % 0.52/0.58 inference(scs_inference,[],[2,1,3,5,4]), % 0.52/0.58 ['proof']). % 0.52/0.58 % SZS output end Proof % 0.52/0.58 % Total time :0.000000s %------------------------------------------------------------------------------