%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET853-2 : 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 : n022.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 14:22:46 EDT 2024 % Result : Unsatisfiable 0.52s 0.61s % Output : CNFRefutation 0.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET853-2 : TPTP v8.2.0. Released v3.2.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n022.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 11:29:23 EDT 2024 % 0.12/0.34 % CPUTime : % 0.19/0.55 start to proof:theBenchmark % 0.52/0.60 %------------------------------------------- % 0.52/0.60 % File :CSE---1.7 % 0.52/0.60 % Problem :theBenchmark % 0.52/0.60 % Transform :cnf % 0.52/0.60 % Format :tptp:raw % 0.52/0.60 % Command :java -jar mcs_scs.jar %d %s % 0.52/0.60 % 0.52/0.60 % Result :Theorem 0.010000s % 0.52/0.60 % Output :CNFRefutation 0.010000s % 0.52/0.60 %------------------------------------------- % 0.52/0.60 %------------------------------------------------------------------------------ % 0.52/0.60 % File : SET853-2 : TPTP v8.2.0. Released v3.2.0. % 0.52/0.60 % Domain : Set Theory % 0.52/0.60 % Problem : Problem about Zorn's lemma % 0.52/0.60 % Version : [Pau06] axioms : Reduced > Especial. % 0.52/0.60 % English : % 0.52/0.60 % 0.52/0.60 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe % 0.52/0.60 % Source : [Pau06] % 0.52/0.60 % Names : % 0.52/0.60 % 0.52/0.60 % Status : Unsatisfiable % 0.52/0.60 % Rating : 0.10 v8.1.0, 0.00 v7.5.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.17 v7.1.0, 0.08 v7.0.0, 0.27 v6.4.0, 0.20 v6.3.0, 0.18 v6.2.0, 0.10 v6.1.0, 0.14 v6.0.0, 0.10 v5.4.0, 0.15 v5.3.0, 0.22 v5.2.0, 0.12 v5.1.0, 0.18 v5.0.0, 0.14 v4.1.0, 0.23 v4.0.1, 0.18 v4.0.0, 0.09 v3.7.0, 0.10 v3.5.0, 0.09 v3.4.0, 0.17 v3.3.0, 0.21 v3.2.0 % 0.52/0.60 % Syntax : Number of clauses : 13 ( 6 unt; 5 nHn; 11 RR) % 0.52/0.60 % Number of literals : 35 ( 4 equ; 17 neg) % 0.52/0.60 % Maximal clause size : 5 ( 2 avg) % 0.52/0.60 % Maximal term depth : 3 ( 2 avg) % 0.52/0.60 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty) % 0.52/0.60 % Number of functors : 8 ( 8 usr; 4 con; 0-3 aty) % 0.52/0.60 % Number of variables : 26 ( 2 sgn) % 0.52/0.60 % SPC : CNF_UNS_RFO_SEQ_NHN % 0.52/0.60 % 0.52/0.60 % Comments : The problems in the [Pau06] collection each have very many axioms, % 0.52/0.60 % of which only a small selection are required for the refutation. % 0.52/0.60 % The mission is to find those few axioms, after which a refutation % 0.52/0.60 % can be quite easily found. This version has only the necessary % 0.52/0.60 % axioms. % 0.52/0.60 %------------------------------------------------------------------------------ % 0.52/0.60 cnf(cls_conjecture_0,negated_conjecture, % 0.52/0.60 c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ). % 0.52/0.60 % 0.52/0.60 cnf(cls_conjecture_1,negated_conjecture, % 0.52/0.60 c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ). % 0.52/0.60 % 0.52/0.60 cnf(cls_conjecture_2,negated_conjecture, % 0.52/0.60 c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ). % 0.52/0.60 % 0.52/0.60 cnf(cls_conjecture_3,negated_conjecture, % 0.52/0.60 v_xa != c_Zorn_Osucc(v_S,v_x,t_a) ). % 0.52/0.60 % 0.52/0.60 cnf(cls_conjecture_4,negated_conjecture, % 0.52/0.60 ~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ). % 0.52/0.60 % 0.52/0.60 cnf(cls_conjecture_5,negated_conjecture, % 0.52/0.60 ( c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_x,tc_set(tc_set(t_a))) % 0.52/0.60 | V_U = v_x % 0.52/0.60 | ~ c_lessequals(V_U,v_x,tc_set(tc_set(t_a))) % 0.52/0.60 | ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ) ). % 0.52/0.60 % 0.52/0.60 cnf(cls_Set_Osubset__antisym_0,axiom, % 0.52/0.60 ( ~ c_lessequals(V_B,V_A,tc_set(T_a)) % 0.52/0.60 | ~ c_lessequals(V_A,V_B,tc_set(T_a)) % 0.52/0.60 | V_A = V_B ) ). % 0.52/0.60 % 0.52/0.60 cnf(cls_Set_Osubset__refl_0,axiom, % 0.52/0.60 c_lessequals(V_A,V_A,tc_set(T_a)) ). % 0.52/0.60 % 0.52/0.60 cnf(cls_Zorn_OTFin__linear__lemma1_0,axiom, % 0.52/0.60 ( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.52/0.60 | ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.52/0.60 | 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))) % 0.52/0.60 | c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) % 0.52/0.60 | c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ). % 0.52/0.60 % 0.52/0.60 cnf(cls_Zorn_OTFin__linear__lemma1_1,axiom, % 0.52/0.60 ( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.52/0.60 | ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.52/0.60 | c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) % 0.52/0.60 | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),V_m,tc_set(tc_set(T_a))) % 0.52/0.60 | c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ). % 0.52/0.60 % 0.52/0.60 cnf(cls_Zorn_OTFin__linear__lemma1_2,axiom, % 0.52/0.60 ( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.52/0.60 | ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.52/0.60 | c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a) != V_m % 0.52/0.60 | c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) % 0.52/0.60 | c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ). % 0.52/0.60 % 0.52/0.60 cnf(cls_Zorn_OTFin__linear__lemma1_3,axiom, % 0.52/0.60 ( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.52/0.61 | ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) % 0.52/0.61 | ~ 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))) % 0.52/0.61 | c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) % 0.52/0.61 | c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ). % 0.52/0.61 % 0.52/0.61 cnf(cls_Zorn_Osucc__trans_0,axiom, % 0.52/0.61 ( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a))) % 0.52/0.61 | c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) ) ). % 0.52/0.61 % 0.52/0.61 %------------------------------------------------------------------------------ % 0.52/0.61 %------------------------------------------- % 0.52/0.61 % Proof found % 0.52/0.61 % SZS status Theorem for theBenchmark % 0.52/0.61 % SZS output start Proof % 0.52/0.61 %ClaNum:31(EqnAxiom:18) % 0.52/0.61 %VarNum:109(SingletonVarNum:26) % 0.52/0.61 %MaxLitNum:5 % 0.52/0.61 %MaxfuncDepth:2 % 0.52/0.61 %SharedTerms:14 % 0.52/0.61 %goalClause: 20 21 22 23 24 27 % 0.52/0.61 %singleGoalClaCount:5 % 0.52/0.61 [23]~E(f4(a7,a6,a2),a8) % 0.52/0.61 [20]P2(a6,f3(a7,a2),f1(f1(a2))) % 0.52/0.61 [21]P2(a8,f3(a7,a2),f1(f1(a2))) % 0.52/0.61 [22]P1(a8,f4(a7,a6,a2),f1(f1(a2))) % 0.52/0.61 [24]~P1(f4(a7,a8,a2),f4(a7,a6,a2),f1(f1(a2))) % 0.52/0.61 [19]P1(x191,x191,f1(x192)) % 0.52/0.61 [26]~P1(x261,x263,f1(f1(x264)))+P1(x261,f4(x262,x263,x264),f1(f1(x264))) % 0.52/0.61 [25]E(x251,x252)+~P1(x252,x251,f1(x253))+~P1(x251,x252,f1(x253)) % 0.52/0.61 [27]E(x271,a6)+~P2(x271,f3(a7,a2),f1(f1(a2)))+~P1(x271,a6,f1(f1(a2)))+P1(f4(a7,x271,a2),a6,f1(f1(a2))) % 0.52/0.61 [28]~E(f5(x284,x282,x283),x282)+~P2(x281,f3(x284,x283),f1(f1(x283)))+~P2(x282,f3(x284,x283),f1(f1(x283)))+P1(f4(x284,x282,x283),x281,f1(f1(x283)))+P1(x281,x282,f1(f1(x283))) % 0.52/0.61 [29]P1(f5(x294,x292,x293),x292,f1(f1(x293)))+~P2(x291,f3(x294,x293),f1(f1(x293)))+~P2(x292,f3(x294,x293),f1(f1(x293)))+P1(f4(x294,x292,x293),x291,f1(f1(x293)))+P1(x291,x292,f1(f1(x293))) % 0.52/0.61 [30]P2(f5(x304,x302,x303),f3(x304,x303),f1(f1(x303)))+~P2(x301,f3(x304,x303),f1(f1(x303)))+~P2(x302,f3(x304,x303),f1(f1(x303)))+P1(f4(x304,x302,x303),x301,f1(f1(x303)))+P1(x301,x302,f1(f1(x303))) % 0.52/0.61 [31]~P1(f4(x314,f5(x314,x312,x313),x313),x312,f1(f1(x313)))+~P2(x311,f3(x314,x313),f1(f1(x313)))+~P2(x312,f3(x314,x313),f1(f1(x313)))+P1(f4(x314,x312,x313),x311,f1(f1(x313)))+P1(x311,x312,f1(f1(x313))) % 0.52/0.61 %EqnAxiom % 0.52/0.61 [1]E(x11,x11) % 0.52/0.61 [2]E(x22,x21)+~E(x21,x22) % 0.52/0.61 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.52/0.61 [4]~E(x41,x42)+E(f1(x41),f1(x42)) % 0.52/0.61 [5]~E(x51,x52)+E(f3(x51,x53),f3(x52,x53)) % 0.52/0.61 [6]~E(x61,x62)+E(f3(x63,x61),f3(x63,x62)) % 0.52/0.61 [7]~E(x71,x72)+E(f4(x71,x73,x74),f4(x72,x73,x74)) % 0.52/0.61 [8]~E(x81,x82)+E(f4(x83,x81,x84),f4(x83,x82,x84)) % 0.52/0.61 [9]~E(x91,x92)+E(f4(x93,x94,x91),f4(x93,x94,x92)) % 0.52/0.61 [10]~E(x101,x102)+E(f5(x101,x103,x104),f5(x102,x103,x104)) % 0.52/0.61 [11]~E(x111,x112)+E(f5(x113,x111,x114),f5(x113,x112,x114)) % 0.52/0.61 [12]~E(x121,x122)+E(f5(x123,x124,x121),f5(x123,x124,x122)) % 0.52/0.61 [13]P1(x132,x133,x134)+~E(x131,x132)+~P1(x131,x133,x134) % 0.52/0.61 [14]P1(x143,x142,x144)+~E(x141,x142)+~P1(x143,x141,x144) % 0.52/0.61 [15]P1(x153,x154,x152)+~E(x151,x152)+~P1(x153,x154,x151) % 0.52/0.61 [16]P2(x162,x163,x164)+~E(x161,x162)+~P2(x161,x163,x164) % 0.52/0.61 [17]P2(x173,x172,x174)+~E(x171,x172)+~P2(x173,x171,x174) % 0.52/0.61 [18]P2(x183,x184,x182)+~E(x181,x182)+~P2(x183,x184,x181) % 0.52/0.61 % 0.52/0.61 %------------------------------------------- % 0.52/0.61 cnf(41,plain, % 0.52/0.61 (~P1(a8,a6,f1(f1(a2)))), % 0.52/0.61 inference(scs_inference,[],[20,24,22,21,23,19,26,25,13,14,8,16,27])). % 0.52/0.61 cnf(43,plain, % 0.52/0.61 (~E(f5(a7,a6,a2),a6)), % 0.52/0.61 inference(scs_inference,[],[20,24,22,21,23,19,26,25,13,14,8,16,27,28])). % 0.52/0.61 cnf(45,plain, % 0.52/0.61 (P1(f5(a7,a6,a2),a6,f1(f1(a2)))), % 0.52/0.61 inference(scs_inference,[],[20,24,22,21,23,19,26,25,13,14,8,16,27,28,29])). % 0.52/0.61 cnf(47,plain, % 0.52/0.61 (P2(f5(a7,a6,a2),f3(a7,a2),f1(f1(a2)))), % 0.52/0.61 inference(scs_inference,[],[20,24,22,21,23,19,26,25,13,14,8,16,27,28,29,30])). % 0.52/0.61 cnf(49,plain, % 0.52/0.61 (~P1(f4(a7,f5(a7,a6,a2),a2),a6,f1(f1(a2)))), % 0.52/0.61 inference(scs_inference,[],[20,24,22,21,23,19,26,25,13,14,8,16,27,28,29,30,31])). % 0.52/0.61 cnf(60,plain, % 0.52/0.61 ($false), % 0.52/0.61 inference(scs_inference,[],[43,41,22,47,45,49,13,14,27]), % 0.52/0.61 ['proof']). % 0.52/0.61 % SZS output end Proof % 0.52/0.61 % Total time :0.010000s %------------------------------------------------------------------------------