%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET858-2 : 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 : n026.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 14:22:48 EDT 2024 % Result : Unsatisfiable 0.18s 0.58s % Output : CNFRefutation 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : SET858-2 : TPTP v8.2.0. Released v3.2.0. % 0.10/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.10/0.32 % Computer : n026.cluster.edu % 0.10/0.32 % Model : x86_64 x86_64 % 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.32 % Memory : 8042.1875MB % 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.32 % CPULimit : 300 % 0.10/0.32 % WCLimit : 300 % 0.10/0.32 % DateTime : Sun Jun 23 16:33:24 EDT 2024 % 0.10/0.32 % CPUTime : % 0.18/0.54 start to proof:theBenchmark % 0.18/0.57 %------------------------------------------- % 0.18/0.57 % File :CSE---1.7 % 0.18/0.57 % Problem :theBenchmark % 0.18/0.57 % Transform :cnf % 0.18/0.57 % Format :tptp:raw % 0.18/0.57 % Command :java -jar mcs_scs.jar %d %s % 0.18/0.57 % 0.18/0.57 % Result :Theorem 0.000000s % 0.18/0.57 % Output :CNFRefutation 0.000000s % 0.18/0.57 %------------------------------------------- % 0.18/0.58 %------------------------------------------------------------------------------ % 0.18/0.58 % File : SET858-2 : TPTP v8.2.0. Released v3.2.0. % 0.18/0.58 % Domain : Set Theory % 0.18/0.58 % Problem : Problem about Zorn's lemma % 0.18/0.58 % Version : [Pau06] axioms : Reduced > Especial. % 0.18/0.58 % English : % 0.18/0.58 % 0.18/0.58 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe % 0.18/0.58 % Source : [Pau06] % 0.18/0.58 % Names : % 0.18/0.58 % 0.18/0.58 % Status : Unsatisfiable % 0.18/0.58 % Rating : 0.05 v8.1.0, 0.00 v7.3.0, 0.08 v7.0.0, 0.20 v6.4.0, 0.13 v6.3.0, 0.18 v6.2.0, 0.10 v6.1.0, 0.07 v6.0.0, 0.10 v5.5.0, 0.05 v5.4.0, 0.10 v5.3.0, 0.17 v5.2.0, 0.12 v5.1.0, 0.18 v5.0.0, 0.14 v4.1.0, 0.23 v4.0.1, 0.27 v4.0.0, 0.18 v3.7.0, 0.10 v3.5.0, 0.09 v3.4.0, 0.17 v3.3.0, 0.21 v3.2.0 % 0.18/0.58 % Syntax : Number of clauses : 11 ( 5 unt; 5 nHn; 10 RR) % 0.18/0.58 % Number of literals : 33 ( 2 equ; 17 neg) % 0.18/0.58 % Maximal clause size : 5 ( 3 avg) % 0.18/0.58 % Maximal term depth : 3 ( 2 avg) % 0.18/0.58 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty) % 0.18/0.58 % Number of functors : 8 ( 8 usr; 4 con; 0-3 aty) % 0.18/0.58 % Number of variables : 27 ( 1 sgn) % 0.18/0.58 % SPC : CNF_UNS_RFO_SEQ_NHN % 0.18/0.58 % 0.18/0.58 % Comments : The problems in the [Pau06] collection each have very many axioms, % 0.18/0.58 % of which only a small selection are required for the refutation. % 0.18/0.58 % The mission is to find those few axioms, after which a refutation % 0.18/0.58 % can be quite easily found. This version has only the necessary % 0.18/0.58 % axioms. % 0.18/0.58 %------------------------------------------------------------------------------ % 0.18/0.58 cnf(cls_conjecture_0,negated_conjecture, % 0.18/0.58 c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ). % 0.18/0.58 % 0.18/0.58 cnf(cls_conjecture_1,negated_conjecture, % 0.18/0.58 c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ). % 0.18/0.58 % 0.18/0.58 cnf(cls_conjecture_2,negated_conjecture, % 0.18/0.58 ~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ). % 0.18/0.58 % 0.18/0.58 cnf(cls_conjecture_3,negated_conjecture, % 0.18/0.58 ~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ). % 0.18/0.58 % 0.18/0.58 cnf(cls_Set_Osubset__trans_0,axiom, % 0.18/0.58 ( ~ c_lessequals(V_B,V_C,tc_set(T_a)) % 0.18/0.58 | ~ c_lessequals(V_A,V_B,tc_set(T_a)) % 0.18/0.58 | c_lessequals(V_A,V_C,tc_set(T_a)) ) ). % 0.18/0.58 % 0.18/0.58 cnf(cls_Zorn_OAbrial__axiom1_0,axiom, % 0.18/0.58 c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))) ). % 0.18/0.58 % 0.18/0.58 cnf(cls_Zorn_OTFin__linear__lemma1_0,axiom, % 0.18/0.58 ( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.18/0.58 | ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.18/0.58 | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.18/0.58 | c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) % 0.18/0.58 | c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ). % 0.18/0.58 % 0.18/0.58 cnf(cls_Zorn_OTFin__linear__lemma1_1,axiom, % 0.18/0.58 ( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.18/0.58 | ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.18/0.58 | c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) % 0.18/0.58 | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),V_m,tc_set(tc_set(T_a))) % 0.18/0.58 | c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ). % 0.18/0.58 % 0.18/0.58 cnf(cls_Zorn_OTFin__linear__lemma1_2,axiom, % 0.18/0.58 ( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.18/0.58 | ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.18/0.58 | c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a) != V_m % 0.18/0.58 | c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) % 0.18/0.58 | c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ). % 0.18/0.58 % 0.18/0.58 cnf(cls_Zorn_OTFin__linear__lemma1_3,axiom, % 0.18/0.58 ( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.18/0.58 | ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.18/0.58 | ~ c_lessequals(c_Zorn_Osucc(V_S,c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),T_a),V_m,tc_set(tc_set(T_a))) % 0.18/0.58 | c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) % 0.18/0.58 | c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ). % 0.18/0.58 % 0.18/0.58 cnf(cls_Zorn_OTFin__linear__lemma2_0,axiom, % 0.18/0.58 ( ~ c_in(V_U,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.18/0.58 | ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.18/0.58 | ~ c_lessequals(V_U,V_m,tc_set(tc_set(T_a))) % 0.18/0.58 | c_lessequals(c_Zorn_Osucc(V_S,V_U,T_a),V_m,tc_set(tc_set(T_a))) % 0.18/0.58 | V_U = V_m ) ). % 0.18/0.58 % 0.18/0.58 %------------------------------------------------------------------------------ % 0.18/0.58 %------------------------------------------- % 0.18/0.58 % Proof found % 0.18/0.58 % SZS status Theorem for theBenchmark % 0.18/0.58 % SZS output start Proof % 0.18/0.58 %ClaNum:29(EqnAxiom:18) % 0.18/0.58 %VarNum:118(SingletonVarNum:27) % 0.18/0.58 %MaxLitNum:5 % 0.18/0.58 %MaxfuncDepth:2 % 0.18/0.58 %SharedTerms:11 % 0.18/0.58 %goalClause: 19 20 22 23 % 0.18/0.58 %singleGoalClaCount:4 % 0.18/0.58 [19]P1(a1,f4(a2,a3),f7(f7(a3))) % 0.18/0.58 [20]P1(a8,f4(a2,a3),f7(f7(a3))) % 0.18/0.58 [22]~P2(a1,a8,f7(f7(a3))) % 0.18/0.58 [23]~P2(a8,a1,f7(f7(a3))) % 0.18/0.58 [21]P2(x211,f5(x212,x211,x213),f7(f7(x213))) % 0.18/0.58 [24]P2(x241,x242,f7(x243))+~P2(x244,x242,f7(x243))+~P2(x241,x244,f7(x243)) % 0.18/0.58 [25]E(x251,x252)+~P2(x251,x252,f7(f7(x254)))+~P1(x252,f4(x253,x254),f7(f7(x254)))+~P1(x251,f4(x253,x254),f7(f7(x254)))+P2(f5(x253,x251,x254),x252,f7(f7(x254))) % 0.18/0.58 [26]~E(f6(x264,x262,x263),x262)+~P1(x261,f4(x264,x263),f7(f7(x263)))+~P1(x262,f4(x264,x263),f7(f7(x263)))+P2(f5(x264,x262,x263),x261,f7(f7(x263)))+P2(x261,x262,f7(f7(x263))) % 0.18/0.58 [27]P2(f6(x274,x272,x273),x272,f7(f7(x273)))+~P1(x271,f4(x274,x273),f7(f7(x273)))+~P1(x272,f4(x274,x273),f7(f7(x273)))+P2(f5(x274,x272,x273),x271,f7(f7(x273)))+P2(x271,x272,f7(f7(x273))) % 0.18/0.58 [28]P1(f6(x284,x282,x283),f4(x284,x283),f7(f7(x283)))+~P1(x281,f4(x284,x283),f7(f7(x283)))+~P1(x282,f4(x284,x283),f7(f7(x283)))+P2(f5(x284,x282,x283),x281,f7(f7(x283)))+P2(x281,x282,f7(f7(x283))) % 0.18/0.58 [29]~P2(f5(x294,f6(x294,x292,x293),x293),x292,f7(f7(x293)))+~P1(x291,f4(x294,x293),f7(f7(x293)))+~P1(x292,f4(x294,x293),f7(f7(x293)))+P2(f5(x294,x292,x293),x291,f7(f7(x293)))+P2(x291,x292,f7(f7(x293))) % 0.18/0.58 %EqnAxiom % 0.18/0.58 [1]E(x11,x11) % 0.18/0.58 [2]E(x22,x21)+~E(x21,x22) % 0.18/0.58 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.18/0.58 [4]~E(x41,x42)+E(f4(x41,x43),f4(x42,x43)) % 0.18/0.58 [5]~E(x51,x52)+E(f4(x53,x51),f4(x53,x52)) % 0.18/0.58 [6]~E(x61,x62)+E(f7(x61),f7(x62)) % 0.18/0.58 [7]~E(x71,x72)+E(f5(x71,x73,x74),f5(x72,x73,x74)) % 0.18/0.58 [8]~E(x81,x82)+E(f5(x83,x81,x84),f5(x83,x82,x84)) % 0.18/0.58 [9]~E(x91,x92)+E(f5(x93,x94,x91),f5(x93,x94,x92)) % 0.18/0.58 [10]~E(x101,x102)+E(f6(x101,x103,x104),f6(x102,x103,x104)) % 0.18/0.58 [11]~E(x111,x112)+E(f6(x113,x111,x114),f6(x113,x112,x114)) % 0.18/0.58 [12]~E(x121,x122)+E(f6(x123,x124,x121),f6(x123,x124,x122)) % 0.18/0.58 [13]P1(x132,x133,x134)+~E(x131,x132)+~P1(x131,x133,x134) % 0.18/0.58 [14]P1(x143,x142,x144)+~E(x141,x142)+~P1(x143,x141,x144) % 0.18/0.58 [15]P1(x153,x154,x152)+~E(x151,x152)+~P1(x153,x154,x151) % 0.18/0.58 [16]P2(x162,x163,x164)+~E(x161,x162)+~P2(x161,x163,x164) % 0.18/0.58 [17]P2(x173,x172,x174)+~E(x171,x172)+~P2(x173,x171,x174) % 0.18/0.58 [18]P2(x183,x184,x182)+~E(x181,x182)+~P2(x183,x184,x181) % 0.18/0.58 % 0.18/0.58 %------------------------------------------- % 0.18/0.58 cnf(31,plain, % 0.18/0.58 (P2(x311,f5(x312,x311,x313),f7(f7(x313)))), % 0.18/0.58 inference(rename_variables,[],[21])). % 0.18/0.58 cnf(35,plain, % 0.18/0.58 (~E(f6(a2,a1,a3),a1)), % 0.18/0.58 inference(scs_inference,[],[19,20,22,23,21,31,24,17,26])). % 0.18/0.58 cnf(37,plain, % 0.18/0.58 (P2(f6(a2,a1,a3),a1,f7(f7(a3)))), % 0.18/0.58 inference(scs_inference,[],[19,20,22,23,21,31,24,17,26,27])). % 0.18/0.58 cnf(39,plain, % 0.18/0.58 (P1(f6(a2,a1,a3),f4(a2,a3),f7(f7(a3)))), % 0.18/0.58 inference(scs_inference,[],[19,20,22,23,21,31,24,17,26,27,28])). % 0.18/0.58 cnf(41,plain, % 0.18/0.58 (~P2(f5(a2,f6(a2,a1,a3),a3),a1,f7(f7(a3)))), % 0.18/0.58 inference(scs_inference,[],[19,20,22,23,21,31,24,17,26,27,28,29])). % 0.18/0.58 cnf(62,plain, % 0.18/0.58 ($false), % 0.18/0.58 inference(scs_inference,[],[19,22,20,23,39,37,41,35,21,24,26,29,27,25]), % 0.18/0.58 ['proof']). % 0.18/0.58 % SZS output end Proof % 0.18/0.58 % Total time :0.000000s %------------------------------------------------------------------------------