%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL674+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n002.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 11:19:35 AM UTC 2026 % Result : Theorem 0.24s 0.51s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL674+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.03 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.08/0.34 % Computer : n002.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 02:07:50 UTC 2026 % 0.08/0.34 % CPUTime : % 0.24/0.51 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 0.008668s % 0.24/0.51 % Output :CNFRefutation 0.008668s % 0.24/0.51 %------------------------------------------- % 0.24/0.51 %------------------------------------------------------------------------------ % 0.24/0.51 % File : LCL674+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.24/0.51 % Domain : Logic Calculi (Modal Logic) % 0.24/0.51 % Problem : In S4, the branching formula made provable, size 1 % 0.24/0.51 % Version : Especial. % 0.24/0.51 % English : The branching formula plus a negation symbol in front and an % 0.24/0.51 % additional subformula to make the formula provable. % 0.24/0.51 % 0.24/0.51 % Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro % 0.24/0.51 % : [Kam08] Kaminski (2008), Email to G. Sutcliffe % 0.24/0.51 % Source : [Kam08] % 0.24/0.51 % Names : s4_branch_p [BHS00] % 0.24/0.51 % 0.24/0.51 % Status : Theorem % 0.24/0.51 % Rating : 0.00 v9.1.0, 0.07 v9.0.0, 0.00 v6.1.0, 0.04 v6.0.0, 0.25 v5.5.0, 0.08 v5.4.0, 0.09 v5.3.0, 0.17 v5.2.0, 0.07 v5.0.0, 0.05 v4.1.0, 0.06 v4.0.1, 0.05 v4.0.0 % 0.24/0.51 % Syntax : Number of formulae : 3 ( 1 unt; 0 def) % 0.24/0.51 % Number of atoms : 41 ( 0 equ) % 0.24/0.51 % Maximal formula atoms : 37 ( 13 avg) % 0.24/0.51 % Number of connectives : 72 ( 34 ~; 22 |; 15 &) % 0.24/0.51 % ( 0 <=>; 1 =>; 0 <=; 0 <~>) % 0.24/0.51 % Maximal formula depth : 19 ( 9 avg) % 0.24/0.51 % Maximal term depth : 1 ( 1 avg) % 0.24/0.51 % Number of predicates : 6 ( 6 usr; 0 prp; 1-2 aty) % 0.24/0.51 % Number of functors : 0 ( 0 usr; 0 con; --- aty) % 0.24/0.51 % Number of variables : 13 ( 12 !; 1 ?) % 0.24/0.51 % SPC : FOF_THM_RFO_NEQ % 0.24/0.51 % 0.24/0.51 % Comments : A naive relational encoding of the modal logic problem into % 0.24/0.51 % first-order logic. % 0.24/0.51 %------------------------------------------------------------------------------ % 0.24/0.51 fof(reflexivity,axiom, % 0.24/0.51 ! [X] : r1(X,X) ). % 0.24/0.51 % 0.24/0.51 fof(transitivity,axiom, % 0.24/0.51 ! [X,Y,Z] : % 0.24/0.51 ( ( r1(X,Y) % 0.24/0.51 & r1(Y,Z) ) % 0.24/0.51 => r1(X,Z) ) ). % 0.24/0.51 % 0.24/0.51 fof(main,conjecture, % 0.24/0.51 ~ ? [X] : % 0.24/0.51 ~ ( ~ ! [Y] : % 0.24/0.51 ( ~ r1(X,Y) % 0.24/0.51 | p2(Y) ) % 0.24/0.51 | ~ ( ! [Y] : % 0.24/0.51 ( ~ r1(X,Y) % 0.24/0.51 | ( ( ( ~ ! [X] : % 0.24/0.51 ( ~ r1(Y,X) % 0.24/0.51 | ~ ( ~ p2(X) % 0.24/0.51 & ~ p102(X) % 0.24/0.51 & p101(X) ) ) % 0.24/0.51 & ~ ! [X] : % 0.24/0.51 ( ~ r1(Y,X) % 0.24/0.51 | ~ ( p2(X) % 0.24/0.51 & ~ p102(X) % 0.24/0.51 & p101(X) ) ) ) % 0.24/0.51 | ~ ( ~ p101(Y) % 0.24/0.51 & p100(Y) ) ) % 0.24/0.51 & ( ( ( ! [X] : % 0.24/0.51 ( ~ r1(Y,X) % 0.24/0.51 | ~ p2(X) % 0.24/0.51 | ~ p101(X) ) % 0.24/0.51 | p2(Y) ) % 0.24/0.51 & ( ! [X] : % 0.24/0.51 ( ~ r1(Y,X) % 0.24/0.51 | p2(X) % 0.24/0.51 | ~ p101(X) ) % 0.24/0.51 | ~ p2(Y) ) ) % 0.24/0.51 | ~ p101(Y) ) % 0.24/0.51 & ( ( ( ! [X] : % 0.24/0.51 ( ~ r1(Y,X) % 0.24/0.51 | ~ p1(X) % 0.24/0.51 | ~ p100(X) ) % 0.24/0.51 | p1(Y) ) % 0.24/0.51 & ( ! [X] : % 0.24/0.51 ( ~ r1(Y,X) % 0.24/0.51 | p1(X) % 0.24/0.51 | ~ p100(X) ) % 0.24/0.51 | ~ p1(Y) ) ) % 0.24/0.51 | ~ p100(Y) ) % 0.24/0.51 & ( p101(Y) % 0.24/0.51 | ~ p102(Y) ) % 0.24/0.51 & ( p100(Y) % 0.24/0.51 | ~ p101(Y) ) ) ) % 0.24/0.51 & ~ p101(X) % 0.24/0.51 & p100(X) ) ) ). % 0.24/0.51 % 0.24/0.51 %------------------------------------------------------------------------------ % 0.24/0.51 %------------------------------------------- % 0.24/0.51 % Proof found % 0.24/0.51 % SZS status Theorem for theBenchmark % 0.24/0.51 % SZS output start Proof % 0.24/0.51 %ClaNum:19(EqnAxiom:0) % 0.24/0.51 %VarNum:71(SingletonVarNum:21) % 0.24/0.51 %MaxLitNum:6 % 0.24/0.51 %MaxfuncDepth:1 % 0.24/0.51 %SharedTerms:3 % 0.24/0.51 %goalClause: 1 3 4 5 6 7 8 9 10 11 12 13 14 16 18 19 % 0.24/0.51 %singleGoalClaCount:2 % 0.24/0.51 [1]P1(a1) % 0.24/0.51 [3]~P4(a1) % 0.24/0.51 [2]P3(x21,x21) % 0.24/0.51 [4]P5(x41)+~P3(a1,x41) % 0.24/0.51 [5]~P6(x51)+P4(x51)+~P3(a1,x51) % 0.24/0.51 [6]~P4(x61)+P1(x61)+~P3(a1,x61) % 0.24/0.51 [15]~P3(x151,x153)+P3(x151,x152)+~P3(x153,x152) % 0.24/0.51 [7]~P1(x71)+P4(x71)+~P3(a1,x71)+P5(f2(x71)) % 0.24/0.51 [8]~P1(x81)+P4(x81)+~P3(a1,x81)+P4(f3(x81)) % 0.24/0.51 [9]~P1(x91)+P4(x91)+~P3(a1,x91)+P4(f2(x91)) % 0.24/0.51 [10]~P1(x101)+P4(x101)+~P3(a1,x101)+~P5(f3(x101)) % 0.24/0.51 [11]~P1(x111)+P4(x111)+~P3(a1,x111)+~P6(f3(x111)) % 0.24/0.51 [12]~P1(x121)+P4(x121)+~P3(a1,x121)+~P6(f2(x121)) % 0.24/0.51 [13]~P1(x131)+P4(x131)+P3(x131,f3(x131))+~P3(a1,x131) % 0.24/0.51 [14]~P1(x141)+P4(x141)+P3(x141,f2(x141))+~P3(a1,x141) % 0.24/0.51 [16]~P4(x161)+~P4(x162)+~P3(x162,x161)+P5(x161)+~P5(x162)+~P3(a1,x162) % 0.24/0.51 [18]~P1(x181)+~P2(x182)+~P3(x182,x181)+P2(x181)+~P1(x182)+~P3(a1,x182) % 0.24/0.51 [19]~P1(x191)+~P2(x192)+~P3(x191,x192)+P2(x191)+~P1(x192)+~P3(a1,x191) % 0.24/0.51 %EqnAxiom % 0.24/0.51 % 0.24/0.51 %------------------------------------------- % 0.24/0.51 cnf(30,plain, % 0.24/0.51 (~P3(a1,f3(a1))), % 0.24/0.51 inference(scs_inference,[],[2,3,1,4,10])). % 0.24/0.51 cnf(31,plain, % 0.24/0.51 ($false), % 0.24/0.51 inference(scs_inference,[],[3,1,30,2,13]), % 0.24/0.51 ['proof']). % 0.24/0.51 % SZS output end Proof % 0.24/0.51 % Total time :0.008668s %------------------------------------------------------------------------------