%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL684+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 : n018.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 11:19:38 AM UTC 2026 % Result : Theorem 0.25s 0.52s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL684+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.02 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.09/0.35 % Computer : n018.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sat Sep 5 16:35:19 UTC 2026 % 0.09/0.35 % CPUTime : % 0.25/0.52 start to proof:theBenchmark % 0.25/0.52 %------------------------------------------- % 0.25/0.52 % File :CSE---1.7 % 0.25/0.52 % Problem :theBenchmark % 0.25/0.52 % Transform :cnf % 0.25/0.52 % Format :tptp:raw % 0.25/0.52 % Command :java -jar mcs_scs.jar %d %s % 0.25/0.52 % 0.25/0.52 % Result :Theorem 0.002003s % 0.25/0.52 % Output :CNFRefutation 0.002003s % 0.25/0.52 %------------------------------------------- % 0.25/0.52 %------------------------------------------------------------------------------ % 0.25/0.52 % File : LCL684+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.25/0.52 % Domain : Logic Calculi (Modal Logic) % 0.25/0.52 % Problem : In S4, pigeonhole formulae, size 1 % 0.25/0.52 % Version : Especial. % 0.25/0.52 % English : % 0.25/0.52 % 0.25/0.52 % Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro % 0.25/0.52 % : [Kam08] Kaminski (2008), Email to G. Sutcliffe % 0.25/0.52 % Source : [Kam08] % 0.25/0.52 % Names : s4_ph_p [BHS00] % 0.25/0.52 % 0.25/0.52 % Status : Theorem % 0.25/0.52 % Rating : 0.00 v5.3.0, 0.09 v5.2.0, 0.00 v4.1.0, 0.06 v4.0.1, 0.05 v4.0.0 % 0.25/0.52 % Syntax : Number of formulae : 3 ( 1 unt; 0 def) % 0.25/0.52 % Number of atoms : 10 ( 0 equ) % 0.25/0.52 % Maximal formula atoms : 6 ( 3 avg) % 0.25/0.52 % Number of connectives : 14 ( 7 ~; 3 |; 3 &) % 0.25/0.52 % ( 0 <=>; 1 =>; 0 <=; 0 <~>) % 0.25/0.52 % Maximal formula depth : 12 ( 7 avg) % 0.25/0.52 % Maximal term depth : 1 ( 1 avg) % 0.25/0.52 % Number of predicates : 3 ( 3 usr; 0 prp; 1-2 aty) % 0.25/0.52 % Number of functors : 0 ( 0 usr; 0 con; --- aty) % 0.25/0.52 % Number of variables : 7 ( 6 !; 1 ?) % 0.25/0.52 % SPC : FOF_THM_RFO_NEQ % 0.25/0.52 % 0.25/0.52 % Comments : A naive relational encoding of the modal logic problem into % 0.25/0.52 % first-order logic. % 0.25/0.52 %------------------------------------------------------------------------------ % 0.25/0.52 fof(reflexivity,axiom, % 0.25/0.52 ! [X] : r1(X,X) ). % 0.25/0.52 % 0.25/0.52 fof(transitivity,axiom, % 0.25/0.52 ! [X,Y,Z] : % 0.25/0.52 ( ( r1(X,Y) % 0.25/0.52 & r1(Y,Z) ) % 0.25/0.52 => r1(X,Z) ) ). % 0.25/0.52 % 0.25/0.52 fof(main,conjecture, % 0.25/0.52 ~ ? [X] : % 0.25/0.52 ~ ( ~ ! [Y] : % 0.25/0.52 ( ~ r1(X,Y) % 0.25/0.52 | ! [X] : % 0.25/0.52 ( ~ r1(Y,X) % 0.25/0.52 | ~ ( p201(X) % 0.25/0.52 & p101(X) ) ) ) % 0.25/0.52 | ~ ( p201(X) % 0.25/0.52 & p101(X) ) ) ). % 0.25/0.52 % 0.25/0.52 %------------------------------------------------------------------------------ % 0.25/0.52 %------------------------------------------- % 0.25/0.52 % Proof found % 0.25/0.52 % SZS status Theorem for theBenchmark % 0.25/0.52 % SZS output start Proof % 0.25/0.52 %ClaNum:5(EqnAxiom:0) % 0.25/0.52 %VarNum:13(SingletonVarNum:6) % 0.25/0.52 %MaxLitNum:4 % 0.25/0.52 %MaxfuncDepth:0 % 0.25/0.52 %SharedTerms:3 % 0.25/0.52 %goalClause: 1 2 4 % 0.25/0.52 %singleGoalClaCount:2 % 0.25/0.52 [1]P1(a1) % 0.25/0.52 [2]P2(a1) % 0.25/0.52 [3]P3(x31,x31) % 0.25/0.52 [5]~P3(x51,x53)+P3(x51,x52)+~P3(x53,x52) % 0.25/0.52 [4]~P2(x41)+~P1(x41)+~P3(x42,x41)+~P3(a1,x42) % 0.25/0.52 %EqnAxiom % 0.25/0.52 % 0.25/0.52 %------------------------------------------- % 0.25/0.52 cnf(6,plain, % 0.25/0.52 ($false), % 0.25/0.52 inference(scs_inference,[],[2,1,3,4]), % 0.25/0.52 ['proof']). % 0.25/0.52 % SZS output end Proof % 0.25/0.52 % Total time :0.002003s %------------------------------------------------------------------------------