%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL429-2 : 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 : n011.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 0.52s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL429-2 : TPTP v9.3.1. Released v3.2.0. % 0.00/0.02 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.06/0.33 % Computer : n011.cluster.edu % 0.06/0.33 % Model : x86_64 x86_64 % 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.06/0.33 % Memory : 8046.5625MB % 0.06/0.33 % OS : Linux 6.8.0-71-generic % 0.06/0.33 % CPULimit : 300 % 0.06/0.33 % WCLimit : 300 % 0.06/0.33 % DateTime : Sat Sep 5 19:09:14 UTC 2026 % 0.06/0.33 % CPUTime : % 0.24/0.50 start to proof:theBenchmark % 0.24/0.51 %------------------------------------------- % 0.24/0.51 % File :CSE---1.7 % 0.24/0.51 % Problem :theBenchmark % 0.24/0.51 % Transform :cnf % 0.24/0.51 % Format :tptp:raw % 0.24/0.51 % Command :java -jar mcs_scs.jar %d %s % 0.24/0.51 % 0.24/0.51 % Result :Theorem 0.029593s % 0.24/0.51 % Output :CNFRefutation 0.029593s % 0.24/0.51 %------------------------------------------- % 0.24/0.51 %------------------------------------------------------------------------------ % 0.24/0.51 % File : LCL429-2 : TPTP v9.3.1. Released v3.2.0. % 0.24/0.51 % Domain : Logic Calculi (Propositional) % 0.24/0.51 % Problem : Problem about propositional logic % 0.24/0.51 % Version : [Pau06] axioms : Reduced > Especial. % 0.24/0.51 % English : % 0.24/0.51 % 0.24/0.51 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe % 0.24/0.51 % Source : [Pau06] % 0.24/0.51 % Names : % 0.24/0.51 % 0.24/0.51 % Status : Unsatisfiable % 0.24/0.51 % Rating : 0.25 v9.3.0, 0.06 v9.1.0, 0.00 v5.4.0, 0.06 v5.3.0, 0.15 v5.2.0, 0.08 v5.1.0, 0.06 v5.0.0, 0.00 v3.2.0 % 0.24/0.51 % Syntax : Number of clauses : 8 ( 5 unt; 0 nHn; 4 RR) % 0.24/0.51 % Number of literals : 14 ( 0 equ; 7 neg) % 0.24/0.51 % Maximal clause size : 3 ( 1 avg) % 0.24/0.51 % Maximal term depth : 5 ( 2 avg) % 0.24/0.51 % Number of predicates : 2 ( 2 usr; 0 prp; 3-3 aty) % 0.24/0.51 % Number of functors : 15 ( 15 usr; 7 con; 0-3 aty) % 0.24/0.51 % Number of variables : 27 ( 1 sgn) % 0.24/0.51 % SPC : CNF_UNS_RFO_NEQ_HRN % 0.24/0.51 % 0.24/0.51 % Comments : The problems in the [Pau06] collection each have very many axioms, % 0.24/0.51 % of which only a small selection are required for the refutation. % 0.24/0.51 % The mission is to find those few axioms, after which a refutation % 0.24/0.51 % can be quite easily found. This version has only the necessary % 0.24/0.51 % axioms. % 0.24/0.51 %------------------------------------------------------------------------------ % 0.24/0.51 cnf(cls_PropLog_ODiff__weaken__left_0,axiom, % 0.24/0.51 ( ~ c_in(V_p,c_PropLog_Othms(c_minus(V_A,V_B,tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) % 0.24/0.51 | ~ c_lessequals(V_A,V_C,tc_set(tc_PropLog_Opl(T_a))) % 0.24/0.51 | c_in(V_p,c_PropLog_Othms(c_minus(V_C,V_B,tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_PropLog_Ohyps__Diff_0,axiom, % 0.24/0.51 c_lessequals(c_PropLog_Ohyps(V_p,c_minus(V_t,c_insert(V_v,c_emptyset,T_a),tc_set(T_a)),T_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(V_v,T_a),c_PropLog_Opl_Ofalse,T_a),c_minus(c_PropLog_Ohyps(V_p,V_t,T_a),c_insert(c_PropLog_Opl_Ovar(V_v,T_a),c_emptyset,tc_PropLog_Opl(T_a)),tc_set(tc_PropLog_Opl(T_a))),tc_PropLog_Opl(T_a)),tc_set(tc_PropLog_Opl(T_a))) ). % 0.24/0.51 % 0.24/0.52 cnf(cls_PropLog_Oinsert__Diff__same_0,axiom, % 0.24/0.52 c_lessequals(c_minus(V_B,V_C,tc_set(T_a)),c_insert(V_a,c_minus(V_B,c_insert(V_a,V_C,T_a),tc_set(T_a)),T_a),tc_set(T_a)) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_PropLog_Oinsert__Diff__subset2_0,axiom, % 0.24/0.52 c_lessequals(c_minus(c_insert(V_a,c_minus(V_B,c_insert(V_c,c_emptyset,T_a),tc_set(T_a)),T_a),V_D,tc_set(T_a)),c_insert(V_a,c_minus(V_B,c_insert(V_c,V_D,T_a),tc_set(T_a)),T_a),tc_set(T_a)) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_PropLog_Othms__excluded__middle__rule_0,axiom, % 0.24/0.52 ( ~ c_in(V_q,c_PropLog_Othms(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) % 0.24/0.52 | ~ c_in(V_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,T_a),V_H,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) % 0.24/0.52 | c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_PropLog_Oweaken__left_0,axiom, % 0.24/0.52 ( ~ c_in(V_p,c_PropLog_Othms(V_G,T_a),tc_PropLog_Opl(T_a)) % 0.24/0.52 | ~ c_lessequals(V_G,V_H,tc_set(tc_PropLog_Opl(T_a))) % 0.24/0.52 | c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_conjecture_3,negated_conjecture, % 0.24/0.52 c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,V_U,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_conjecture_5,negated_conjecture, % 0.24/0.52 ~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) ). % 0.24/0.52 % 0.24/0.52 %------------------------------------------------------------------------------ % 0.24/0.52 %------------------------------------------- % 0.24/0.52 % Proof found % 0.24/0.52 % SZS status Theorem for theBenchmark % 0.24/0.52 % SZS output start Proof % 0.24/0.52 %ClaNum:8(EqnAxiom:0) % 0.24/0.52 %VarNum:89(SingletonVarNum:27) % 0.24/0.52 %MaxLitNum:3 % 0.24/0.52 %MaxfuncDepth:4 % 0.24/0.52 %SharedTerms:15 % 0.24/0.52 %goalClause: 1 5 % 0.24/0.52 %singleGoalClaCount:2 % 0.24/0.52 [5]~P1(a1,f5(f4(f3(a1,a14,a2),f9(f6(a15,a2),a11,f12(a2)),f13(f12(a2))),a2),f12(a2)) % 0.24/0.52 [1]P1(a1,f5(f4(f3(a1,x11,a2),a11,f13(f12(a2))),a2),f12(a2)) % 0.24/0.52 [2]P2(f4(x21,x22,f13(x23)),f9(x24,f4(x21,f9(x24,x22,x23),f13(x23)),x23),f13(x23)) % 0.24/0.52 [4]P2(f3(x41,f4(x42,f9(x43,a10,x44),f13(x44)),x44),f9(f8(f6(x43,x44),a7,x44),f4(f3(x41,x42,x44),f9(f6(x43,x44),a10,f12(x44)),f13(f12(x44))),f12(x44)),f13(f12(x44))) % 0.24/0.52 [3]P2(f4(f9(x31,f4(x32,f9(x33,a10,x34),f13(x34)),x34),x35,f13(x34)),f9(x31,f4(x32,f9(x33,x35,x34),f13(x34)),x34),f13(x34)) % 0.24/0.52 [6]~P1(x61,f5(x64,x63),f12(x63))+P1(x61,f5(x62,x63),f12(x63))+~P2(x64,x62,f13(f12(x63))) % 0.24/0.52 [8]P1(x81,f5(x82,x83),f12(x83))+~P1(x81,f5(f9(x84,x82,f12(x83)),x83),f12(x83))+~P1(x81,f5(f9(f8(x84,a7,x83),x82,f12(x83)),x83),f12(x83)) % 0.24/0.52 [7]~P2(x75,x72,f13(f12(x74)))+P1(x71,f5(f4(x72,x73,f13(f12(x74))),x74),f12(x74))+~P1(x71,f5(f4(x75,x73,f13(f12(x74))),x74),f12(x74)) % 0.24/0.52 %EqnAxiom % 0.24/0.52 % 0.24/0.52 %------------------------------------------- % 0.24/0.52 cnf(9,plain, % 0.24/0.52 (P1(a1,f5(f9(x91,f4(f3(a1,x92,a2),f9(x91,a11,f12(a2)),f13(f12(a2))),f12(a2)),a2),f12(a2))), % 0.24/0.52 inference(scs_inference,[],[1,2,6])). % 0.24/0.52 cnf(14,plain, % 0.24/0.52 (~P1(x141,f5(f4(f9(x142,f4(x143,f9(x144,a10,f12(x145)),f13(f12(x145))),f12(x145)),x146,f13(f12(x145))),x145),f12(x145))+P1(x141,f5(f9(x142,f4(x143,f9(x144,x146,f12(x145)),f13(f12(x145))),f12(x145)),x145),f12(x145))), % 0.24/0.52 inference(scs_inference,[],[3,6])). % 0.24/0.52 cnf(30,plain, % 0.24/0.52 (P1(a1,f5(f9(f8(f6(x301,a2),a7,a2),f4(f3(a1,x302,a2),f9(f6(x301,a2),a11,f12(a2)),f13(f12(a2))),f12(a2)),a2),f12(a2))), % 0.24/0.52 inference(scs_inference,[],[1,4,14,7])). % 0.24/0.52 cnf(31,plain, % 0.24/0.52 ($false), % 0.24/0.52 inference(scs_inference,[],[5,9,30,8]), % 0.24/0.52 ['proof']). % 0.24/0.52 % SZS output end Proof % 0.24/0.52 % Total time :0.029593s %------------------------------------------------------------------------------