%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL682+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 : n003.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 0.24s 0.54s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL682+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 % 0.10/0.36 % Computer : n003.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Fri Sep 4 16:08:04 UTC 2026 % 0.10/0.36 % CPUTime : % 0.24/0.53 start to proof:theBenchmark % 0.24/0.53 %------------------------------------------- % 0.24/0.53 % File :CSE---1.7 % 0.24/0.53 % Problem :theBenchmark % 0.24/0.53 % Transform :cnf % 0.24/0.53 % Format :tptp:raw % 0.24/0.53 % Command :java -jar mcs_scs.jar %d %s % 0.24/0.53 % 0.24/0.53 % Result :Theorem 0.003735s % 0.24/0.53 % Output :CNFRefutation 0.003735s % 0.24/0.54 %------------------------------------------- % 0.24/0.54 %------------------------------------------------------------------------------ % 0.24/0.54 % File : LCL682+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.24/0.54 % Domain : Logic Calculi (Modal Logic) % 0.24/0.54 % Problem : In S4, path through a labyrinth, size 1 % 0.24/0.54 % Version : Especial. % 0.24/0.54 % English : % 0.24/0.54 % 0.24/0.54 % Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro % 0.24/0.54 % : [Kam08] Kaminski (2008), Email to G. Sutcliffe % 0.24/0.54 % Source : [Kam08] % 0.24/0.54 % Names : s4_path_p [BHS00] % 0.24/0.54 % 0.24/0.54 % Status : Theorem % 0.24/0.54 % 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 % 0.24/0.54 % Syntax : Number of formulae : 3 ( 1 unt; 0 def) % 0.24/0.54 % Number of atoms : 25 ( 0 equ) % 0.24/0.54 % Maximal formula atoms : 21 ( 8 avg) % 0.24/0.54 % Number of connectives : 43 ( 21 ~; 20 |; 1 &) % 0.24/0.54 % ( 0 <=>; 1 =>; 0 <=; 0 <~>) % 0.24/0.54 % Maximal formula depth : 16 ( 8 avg) % 0.24/0.54 % Maximal term depth : 1 ( 1 avg) % 0.24/0.54 % Number of predicates : 7 ( 7 usr; 0 prp; 1-2 aty) % 0.24/0.54 % Number of functors : 0 ( 0 usr; 0 con; --- aty) % 0.24/0.54 % Number of variables : 18 ( 17 !; 1 ?) % 0.24/0.54 % SPC : FOF_THM_RFO_NEQ % 0.24/0.54 % 0.24/0.54 % Comments : A naive relational encoding of the modal logic problem into % 0.24/0.54 % first-order logic. % 0.24/0.54 %------------------------------------------------------------------------------ % 0.24/0.54 fof(reflexivity,axiom, % 0.24/0.54 ! [X] : r1(X,X) ). % 0.24/0.54 % 0.24/0.54 fof(transitivity,axiom, % 0.24/0.54 ! [X,Y,Z] : % 0.24/0.54 ( ( r1(X,Y) % 0.24/0.54 & r1(Y,Z) ) % 0.24/0.54 => r1(X,Z) ) ). % 0.24/0.54 % 0.24/0.54 fof(main,conjecture, % 0.24/0.54 ~ ? [X] : % 0.24/0.54 ~ ( ~ ! [Y] : % 0.24/0.54 ( ~ r1(X,Y) % 0.24/0.54 | ~ ( ~ ! [X] : % 0.24/0.54 ( ~ r1(Y,X) % 0.24/0.54 | p16(X) ) % 0.24/0.54 | ~ ! [X] : % 0.24/0.54 ( ~ r1(Y,X) % 0.24/0.54 | p12(X) ) % 0.24/0.54 | ~ ! [X] : % 0.24/0.54 ( ~ r1(Y,X) % 0.24/0.54 | p14(X) ) % 0.24/0.54 | ~ ! [X] : % 0.24/0.54 ( ~ r1(Y,X) % 0.24/0.54 | p12(X) ) ) ) % 0.24/0.54 | ! [Y] : % 0.24/0.54 ( ~ r1(X,Y) % 0.24/0.54 | ! [X] : % 0.24/0.54 ( ~ r1(Y,X) % 0.24/0.54 | p15(X) ) ) % 0.24/0.54 | ! [Y] : % 0.24/0.54 ( ~ r1(X,Y) % 0.24/0.54 | ! [X] : % 0.24/0.54 ( ~ r1(Y,X) % 0.24/0.54 | p13(X) ) ) % 0.24/0.54 | ! [Y] : % 0.24/0.54 ( ~ r1(X,Y) % 0.24/0.54 | ! [X] : % 0.24/0.54 ( ~ r1(Y,X) % 0.24/0.54 | p12(X) ) ) % 0.24/0.54 | ! [Y] : % 0.24/0.54 ( ~ r1(X,Y) % 0.24/0.54 | ! [X] : % 0.24/0.54 ( ~ r1(Y,X) % 0.24/0.54 | p11(X) ) ) ) ). % 0.24/0.54 % 0.24/0.54 %------------------------------------------------------------------------------ % 0.24/0.54 %------------------------------------------- % 0.24/0.54 % Proof found % 0.24/0.54 % SZS status Theorem for theBenchmark % 0.24/0.54 % SZS output start Proof % 0.24/0.54 %ClaNum:18(EqnAxiom:0) % 0.24/0.54 %VarNum:20(SingletonVarNum:10) % 0.24/0.54 %MaxLitNum:3 % 0.24/0.54 %MaxfuncDepth:0 % 0.24/0.54 %SharedTerms:21 % 0.24/0.54 %goalClause: 1 2 3 4 5 6 7 8 10 11 12 13 14 16 17 % 0.24/0.54 %singleGoalClaCount:12 % 0.24/0.54 [1]P1(a1,a2) % 0.24/0.54 [2]P1(a1,a3) % 0.24/0.54 [3]P1(a1,a5) % 0.24/0.54 [4]P1(a1,a7) % 0.24/0.54 [5]P1(a2,a4) % 0.24/0.54 [6]P1(a3,a6) % 0.24/0.54 [7]P1(a5,a8) % 0.24/0.54 [8]P1(a7,a9) % 0.24/0.54 [10]~P2(a8) % 0.24/0.54 [11]~P4(a4) % 0.24/0.54 [12]~P5(a6) % 0.24/0.54 [13]~P3(a9) % 0.24/0.54 [9]P1(x91,x91) % 0.24/0.54 [14]P7(x141)+~P1(x142,x141)+~P1(a1,x142) % 0.24/0.54 [16]P2(x161)+~P1(x162,x161)+~P1(a1,x162) % 0.24/0.54 [17]P6(x171)+~P1(x172,x171)+~P1(a1,x172) % 0.24/0.54 [18]~P1(x181,x183)+P1(x181,x182)+~P1(x183,x182) % 0.24/0.54 %EqnAxiom % 0.24/0.54 % 0.24/0.54 %------------------------------------------- % 0.24/0.54 cnf(19,plain, % 0.24/0.54 ($false), % 0.24/0.54 inference(scs_inference,[],[10,7,3,16]), % 0.24/0.54 ['proof']). % 0.24/0.54 % SZS output end Proof % 0.24/0.54 % Total time :0.003735s %------------------------------------------------------------------------------