%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n005.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:19:09 AM UTC 2026 % Result : Unsatisfiable 0.24s 0.53s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0. % 0.00/0.03 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.08/0.34 % Computer : n005.cluster.edu % 0.08/0.34 % Model : x86_64 x86_64 % 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.34 % Memory : 8046.5625MB % 0.08/0.34 % OS : Linux 6.8.0-71-generic % 0.08/0.34 % CPULimit : 300 % 0.08/0.34 % WCLimit : 300 % 0.08/0.34 % DateTime : Fri Sep 4 17:23:05 UTC 2026 % 0.08/0.34 % CPUTime : % 0.24/0.51 start to proof:theBenchmark % 0.24/0.52 %------------------------------------------- % 0.24/0.52 % File :CSE---1.7 % 0.24/0.52 % Problem :theBenchmark % 0.24/0.52 % Transform :cnf % 0.24/0.52 % Format :tptp:raw % 0.24/0.52 % Command :java -jar mcs_scs.jar %d %s % 0.24/0.52 % 0.24/0.52 % Result :Theorem 0.032389s % 0.24/0.52 % Output :CNFRefutation 0.032389s % 0.24/0.52 %------------------------------------------- % 0.24/0.52 %------------------------------------------------------------------------------ % 0.24/0.52 % File : LCL431-2 : TPTP v9.3.1. Released v3.2.0. % 0.24/0.52 % Domain : Logic Calculi (Propositional) % 0.24/0.52 % Problem : Problem about propositional logic % 0.24/0.52 % Version : [Pau06] axioms : Reduced > Especial. % 0.24/0.52 % English : % 0.24/0.52 % 0.24/0.52 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe % 0.24/0.52 % Source : [Pau06] % 0.24/0.52 % Names : % 0.24/0.53 % 0.24/0.53 % Status : Unsatisfiable % 0.24/0.53 % Rating : 0.00 v5.5.0, 0.06 v5.4.0, 0.07 v5.3.0, 0.17 v5.2.0, 0.00 v4.1.0, 0.11 v4.0.1, 0.17 v3.3.0, 0.14 v3.2.0 % 0.24/0.53 % Syntax : Number of clauses : 4 ( 3 unt; 0 nHn; 2 RR) % 0.24/0.53 % Number of literals : 5 ( 1 equ; 2 neg) % 0.24/0.53 % Maximal clause size : 2 ( 1 avg) % 0.24/0.53 % Maximal term depth : 5 ( 2 avg) % 0.24/0.53 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty) % 0.24/0.53 % Number of functors : 8 ( 8 usr; 3 con; 0-3 aty) % 0.24/0.53 % Number of variables : 6 ( 3 sgn) % 0.24/0.53 % SPC : CNF_UNS_RFO_SEQ_HRN % 0.24/0.53 % 0.24/0.53 % Comments : The problems in the [Pau06] collection each have very many axioms, % 0.24/0.53 % of which only a small selection are required for the refutation. % 0.24/0.53 % The mission is to find those few axioms, after which a refutation % 0.24/0.53 % can be quite easily found. This version has only the necessary % 0.24/0.53 % axioms. % 0.24/0.53 %------------------------------------------------------------------------------ % 0.24/0.53 cnf(cls_conjecture_0,negated_conjecture, % 0.24/0.53 c_PropLog_Osat(c_emptyset,v_p,t_a) ). % 0.24/0.53 % 0.24/0.53 cnf(cls_conjecture_1,negated_conjecture, % 0.24/0.53 ~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)) ). % 0.24/0.53 % 0.24/0.53 cnf(cls_PropLog_Ocompleteness__0__lemma__dest_0,axiom, % 0.24/0.53 ( ~ c_PropLog_Osat(c_emptyset,V_p,T_a) % 0.24/0.53 | c_in(V_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p,V_U,T_a),c_PropLog_Ohyps(V_p,V_t0,T_a),tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) ) ). % 0.24/0.53 % 0.24/0.53 cnf(cls_Set_ODiff__cancel_0,axiom, % 0.24/0.53 c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset ). % 0.24/0.53 % 0.24/0.53 %------------------------------------------------------------------------------ % 0.24/0.53 %------------------------------------------- % 0.24/0.53 % Proof found % 0.24/0.53 % SZS status Theorem for theBenchmark % 0.24/0.53 % SZS output start Proof % 0.24/0.53 %ClaNum:23(EqnAxiom:19) % 0.24/0.53 %VarNum:15(SingletonVarNum:6) % 0.24/0.53 %MaxLitNum:2 % 0.24/0.53 %MaxfuncDepth:4 % 0.24/0.53 %SharedTerms:7 % 0.24/0.53 %goalClause: 20 22 % 0.24/0.53 %singleGoalClaCount:2 % 0.24/0.53 [20]P1(a1,a4,a5) % 0.24/0.53 [22]~P2(a4,f2(a1,a5),f8(a5)) % 0.24/0.53 [21]E(f6(x211,x211,f7(x212)),a1) % 0.24/0.53 [23]~P1(a1,x231,x233)+P2(x231,f2(f6(f3(x231,x232,x233),f3(x231,x234,x233),f7(f8(x233))),x233),f8(x233)) % 0.24/0.53 %EqnAxiom % 0.24/0.53 [1]E(x11,x11) % 0.24/0.53 [2]E(x22,x21)+~E(x21,x22) % 0.24/0.53 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.24/0.53 [4]~E(x41,x42)+E(f7(x41),f7(x42)) % 0.24/0.53 [5]~E(x51,x52)+E(f6(x51,x53,x54),f6(x52,x53,x54)) % 0.24/0.53 [6]~E(x61,x62)+E(f6(x63,x61,x64),f6(x63,x62,x64)) % 0.24/0.53 [7]~E(x71,x72)+E(f6(x73,x74,x71),f6(x73,x74,x72)) % 0.24/0.53 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83)) % 0.24/0.53 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92)) % 0.24/0.53 [10]~E(x101,x102)+E(f8(x101),f8(x102)) % 0.24/0.53 [11]~E(x111,x112)+E(f3(x111,x113,x114),f3(x112,x113,x114)) % 0.24/0.53 [12]~E(x121,x122)+E(f3(x123,x121,x124),f3(x123,x122,x124)) % 0.24/0.53 [13]~E(x131,x132)+E(f3(x133,x134,x131),f3(x133,x134,x132)) % 0.24/0.53 [14]P1(x142,x143,x144)+~E(x141,x142)+~P1(x141,x143,x144) % 0.24/0.53 [15]P1(x153,x152,x154)+~E(x151,x152)+~P1(x153,x151,x154) % 0.24/0.53 [16]P1(x163,x164,x162)+~E(x161,x162)+~P1(x163,x164,x161) % 0.24/0.53 [17]P2(x172,x173,x174)+~E(x171,x172)+~P2(x171,x173,x174) % 0.24/0.53 [18]P2(x183,x182,x184)+~E(x181,x182)+~P2(x183,x181,x184) % 0.24/0.53 [19]P2(x193,x194,x192)+~E(x191,x192)+~P2(x193,x194,x191) % 0.24/0.53 % 0.24/0.53 %------------------------------------------- % 0.24/0.53 cnf(24,plain, % 0.24/0.53 (E(a1,f6(x241,x241,f7(x242)))), % 0.24/0.53 inference(scs_inference,[],[21,2])). % 0.24/0.53 cnf(26,plain, % 0.24/0.53 (P1(a1,x261,a5)+~E(a4,x261)), % 0.24/0.53 inference(scs_inference,[],[20,21,2,14,15])). % 0.24/0.53 cnf(44,plain, % 0.24/0.53 (E(f3(f3(x441,f6(x442,x442,f7(x443)),x444),x445,x446),f3(f3(x441,a1,x444),x445,x446))), % 0.24/0.53 inference(scs_inference,[],[21,11,12])). % 0.24/0.53 cnf(45,plain, % 0.24/0.53 (E(f3(f3(x451,a1,x452),x453,x454),f3(f3(x451,f6(x455,x455,f7(x456)),x452),x453,x454))), % 0.24/0.53 inference(scs_inference,[],[44,2])). % 0.24/0.53 cnf(46,plain, % 0.24/0.53 (E(f3(x461,x462,f6(x463,x463,f7(x464))),f3(x461,x462,a1))), % 0.24/0.53 inference(scs_inference,[],[24,13,2])). % 0.24/0.53 cnf(48,plain, % 0.24/0.53 (E(f3(f3(x481,a1,x482),x483,a1),f3(f3(x481,f6(x484,x484,f7(x485)),x482),x483,f6(x486,x486,f7(x487))))), % 0.24/0.53 inference(scs_inference,[],[45,46,2,3])). % 0.24/0.53 cnf(50,plain, % 0.24/0.53 (~E(a4,x501)+P2(x501,f2(f6(f3(x501,x502,a5),f3(x501,x503,a5),f7(f8(a5))),a5),f8(a5))), % 0.24/0.53 inference(scs_inference,[],[23,26])). % 0.24/0.53 cnf(51,plain, % 0.24/0.53 (P2(a4,f2(f6(f3(a4,x511,a5),f3(a4,x512,a5),f7(f8(a5))),a5),f8(a5))), % 0.24/0.53 inference(equality_inference,[],[50])). % 0.24/0.53 cnf(54,plain, % 0.24/0.53 ($false), % 0.24/0.53 inference(scs_inference,[],[22,51,21,48,2,18,8]), % 0.24/0.53 ['proof']). % 0.24/0.53 % SZS output end Proof % 0.24/0.53 % Total time :0.032389s %------------------------------------------------------------------------------