%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n015.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 11:19:39 AM UTC 2026 % Result : Theorem 0.72s 0.95s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.03 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.08/0.34 % Computer : n015.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 : Sat Sep 5 09:53:42 UTC 2026 % 0.08/0.35 % CPUTime : % 0.23/0.51 start to proof:theBenchmark % 0.72/0.94 %------------------------------------------- % 0.72/0.94 % File :CSE---1.7 % 0.72/0.94 % Problem :theBenchmark % 0.72/0.94 % Transform :cnf % 0.72/0.94 % Format :tptp:raw % 0.72/0.94 % Command :java -jar mcs_scs.jar %d %s % 0.72/0.94 % 0.72/0.94 % Result :Theorem 0.443803s % 0.72/0.94 % Output :CNFRefutation 0.443803s % 0.72/0.94 %------------------------------------------- % 0.72/0.94 %------------------------------------------------------------------------------ % 0.72/0.94 % File : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.72/0.95 % Domain : Logic Calculi (Modal Logic) % 0.72/0.95 % Problem : In S4, formula provable in S5 embedding, size 1 % 0.72/0.95 % Version : Especial. % 0.72/0.95 % English : % 0.72/0.95 % 0.72/0.95 % Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro % 0.72/0.95 % : [Kam08] Kaminski (2008), Email to G. Sutcliffe % 0.72/0.95 % Source : [Kam08] % 0.72/0.95 % Names : s4_s5_p [BHS00] % 0.72/0.95 % 0.72/0.95 % Status : Theorem % 0.72/0.95 % Rating : 0.00 v9.1.0, 0.07 v9.0.0, 0.00 v6.3.0, 0.08 v6.2.0, 0.00 v6.1.0, 0.04 v6.0.0, 0.25 v5.5.0, 0.17 v5.4.0, 0.13 v5.3.0, 0.17 v5.2.0, 0.07 v5.0.0, 0.05 v4.1.0, 0.06 v4.0.1, 0.11 v4.0.0 % 0.72/0.95 % Syntax : Number of formulae : 3 ( 1 unt; 0 def) % 0.72/0.95 % Number of atoms : 24 ( 0 equ) % 0.72/0.95 % Maximal formula atoms : 20 ( 8 avg) % 0.72/0.95 % Number of connectives : 41 ( 20 ~; 15 |; 5 &) % 0.72/0.95 % ( 0 <=>; 1 =>; 0 <=; 0 <~>) % 0.72/0.95 % Maximal formula depth : 20 ( 9 avg) % 0.72/0.95 % Maximal term depth : 1 ( 1 avg) % 0.72/0.95 % Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty) % 0.72/0.95 % Number of functors : 0 ( 0 usr; 0 con; --- aty) % 0.72/0.95 % Number of variables : 13 ( 12 !; 1 ?) % 0.72/0.95 % SPC : FOF_THM_RFO_NEQ % 0.72/0.95 % 0.72/0.95 % Comments : A naive relational encoding of the modal logic problem into % 0.72/0.95 % first-order logic. % 0.72/0.95 %------------------------------------------------------------------------------ % 0.72/0.95 fof(reflexivity,axiom, % 0.72/0.95 ! [X] : r1(X,X) ). % 0.72/0.95 % 0.72/0.95 fof(transitivity,axiom, % 0.72/0.95 ! [X,Y,Z] : % 0.72/0.95 ( ( r1(X,Y) % 0.72/0.95 & r1(Y,Z) ) % 0.72/0.95 => r1(X,Z) ) ). % 0.72/0.95 % 0.72/0.95 fof(main,conjecture, % 0.72/0.95 ~ ? [X] : % 0.72/0.95 ~ ( ! [Y] : % 0.72/0.95 ( ~ r1(X,Y) % 0.72/0.95 | ~ p3(Y) % 0.72/0.95 | ! [X] : % 0.72/0.95 ( ~ r1(Y,X) % 0.72/0.95 | ~ p1(X) ) ) % 0.72/0.95 | ! [Y] : % 0.72/0.95 ( ~ r1(X,Y) % 0.72/0.95 | ~ ! [X] : % 0.72/0.95 ( ~ r1(Y,X) % 0.72/0.95 | ~ ( ! [Y] : % 0.72/0.95 ( ~ r1(X,Y) % 0.72/0.95 | $false ) % 0.72/0.95 | ~ ! [Y] : % 0.72/0.95 ( ~ r1(X,Y) % 0.72/0.95 | ~ ( ( p2(Y) % 0.72/0.95 & ~ p1(Y) ) % 0.72/0.95 | ( ~ p2(Y) % 0.72/0.95 & p1(Y) ) ) ) % 0.72/0.95 | ! [Y] : % 0.72/0.95 ( ~ r1(X,Y) % 0.72/0.95 | p3(Y) ) % 0.72/0.95 | ! [Y] : % 0.72/0.95 ( ~ r1(X,Y) % 0.72/0.95 | ( ~ p1(Y) % 0.72/0.95 & ~ p2(Y) ) % 0.72/0.95 | ( p2(Y) % 0.72/0.95 & p1(Y) ) ) ) ) ) ) ). % 0.72/0.95 % 0.72/0.95 %------------------------------------------------------------------------------ % 0.72/0.95 %------------------------------------------- % 0.72/0.95 % Proof found % 0.72/0.95 % SZS status Theorem for theBenchmark % 0.72/0.95 % SZS output start Proof % 0.72/0.95 %ClaNum:15(EqnAxiom:0) % 0.72/0.95 %VarNum:35(SingletonVarNum:14) % 0.72/0.95 %MaxLitNum:4 % 0.72/0.95 %MaxfuncDepth:1 % 0.72/0.95 %SharedTerms:9 % 0.72/0.95 %goalClause: 1 2 3 4 5 7 8 9 10 11 12 13 14 % 0.72/0.95 %singleGoalClaCount:5 % 0.72/0.95 [1]P1(a1) % 0.72/0.95 [2]P2(a3) % 0.72/0.95 [3]P4(a2,a1) % 0.72/0.95 [4]P4(a2,a4) % 0.72/0.95 [5]P4(a1,a3) % 0.72/0.95 [6]P4(x61,x61) % 0.72/0.95 [7]~P4(a4,x71)+~P1(f5(x71)) % 0.72/0.95 [8]~P4(a4,x81)+P4(x81,f6(x81)) % 0.72/0.95 [9]~P4(a4,x91)+P4(x91,f5(x91)) % 0.72/0.95 [10]~P4(a4,x101)+P4(x101,f7(x101)) % 0.72/0.95 [11]~P4(a4,x111)+P2(f7(x111))+P3(f7(x111)) % 0.72/0.95 [12]~P4(a4,x121)+~P2(f7(x121))+~P3(f7(x121)) % 0.72/0.95 [15]~P4(x151,x153)+P4(x151,x152)+~P4(x153,x152) % 0.72/0.95 [13]~P3(x131)+P2(x131)+~P4(x132,x131)+~P4(a4,x132) % 0.72/0.95 [14]~P2(x141)+P3(x141)+~P4(x142,x141)+~P4(a4,x142) % 0.72/0.95 %EqnAxiom % 0.72/0.95 % 0.72/0.95 %------------------------------------------- % 0.72/0.95 cnf(33,plain, % 0.72/0.95 (P4(f6(a4),f7(f6(a4)))), % 0.72/0.95 inference(scs_inference,[],[6,8,10])). % 0.72/0.95 cnf(36,plain, % 0.72/0.95 (P4(a4,f7(f6(a4)))), % 0.72/0.95 inference(scs_inference,[],[6,33,8,15])). % 0.72/0.95 cnf(39,plain, % 0.72/0.95 (P2(f7(f6(a4)))+~P3(f7(f6(a4)))), % 0.72/0.95 inference(scs_inference,[],[4,36,6,15,13])). % 0.72/0.95 cnf(134,plain, % 0.72/0.95 (P2(f7(f6(a4)))+P3(f7(f6(a4)))), % 0.72/0.95 inference(scs_inference,[],[6,11,8])). % 0.72/0.95 cnf(135,plain, % 0.72/0.95 (P3(f7(f6(a4)))), % 0.72/0.95 inference(scs_inference,[],[36,6,134,14])). % 0.72/0.95 cnf(136,plain, % 0.72/0.95 (P2(f7(f6(a4)))), % 0.72/0.95 inference(scs_inference,[],[135,39])). % 0.72/0.95 cnf(141,plain, % 0.72/0.95 ($false), % 0.72/0.95 inference(scs_inference,[],[135,136,6,12,8]), % 0.72/0.95 ['proof']). % 0.72/0.95 % SZS output end Proof % 0.72/0.95 % Total time :0.443803s %------------------------------------------------------------------------------