%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL656+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 : n028.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 11:19:30 AM UTC 2026 % Result : Theorem 0.23s 0.53s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL656+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 % 0.08/0.35 % Computer : n028.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Sat Sep 5 02:17:59 UTC 2026 % 0.08/0.36 % CPUTime : % 0.23/0.52 start to proof:theBenchmark % 0.23/0.52 %------------------------------------------- % 0.23/0.52 % File :CSE---1.7 % 0.23/0.52 % Problem :theBenchmark % 0.23/0.52 % Transform :cnf % 0.23/0.52 % Format :tptp:raw % 0.23/0.52 % Command :java -jar mcs_scs.jar %d %s % 0.23/0.52 % 0.23/0.52 % Result :Theorem 0.007130s % 0.23/0.52 % Output :CNFRefutation 0.007130s % 0.23/0.52 %------------------------------------------- % 0.23/0.52 %------------------------------------------------------------------------------ % 0.23/0.52 % File : LCL656+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.23/0.52 % Domain : Logic Calculi (Modal Logic) % 0.23/0.52 % Problem : In KT, the branching formula made provable, size 1 % 0.23/0.52 % Version : Especial. % 0.23/0.52 % English : The branching formula plus a negation symbol in front and an % 0.23/0.52 % additional subformula to make the formula provable. % 0.23/0.52 % 0.23/0.52 % Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro % 0.23/0.52 % : [Kam08] Kaminski (2008), Email to G. Sutcliffe % 0.23/0.52 % Source : [Kam08] % 0.23/0.52 % Names : kt_branch_p [BHS00] % 0.23/0.52 % 0.23/0.52 % Status : Theorem % 0.23/0.52 % 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, 0.08 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 % 0.23/0.52 % Syntax : Number of formulae : 2 ( 1 unt; 0 def) % 0.23/0.52 % Number of atoms : 38 ( 0 equ) % 0.23/0.52 % Maximal formula atoms : 37 ( 19 avg) % 0.23/0.52 % Number of connectives : 70 ( 34 ~; 22 |; 14 &) % 0.23/0.52 % ( 0 <=>; 0 =>; 0 <=; 0 <~>) % 0.23/0.52 % Maximal formula depth : 19 ( 11 avg) % 0.23/0.53 % Maximal term depth : 1 ( 1 avg) % 0.23/0.53 % Number of predicates : 6 ( 6 usr; 0 prp; 1-2 aty) % 0.23/0.53 % Number of functors : 0 ( 0 usr; 0 con; --- aty) % 0.23/0.53 % Number of variables : 10 ( 9 !; 1 ?) % 0.23/0.53 % SPC : FOF_THM_RFO_NEQ % 0.23/0.53 % 0.23/0.53 % Comments : A naive relational encoding of the modal logic problem into % 0.23/0.53 % first-order logic. % 0.23/0.53 %------------------------------------------------------------------------------ % 0.23/0.53 fof(reflexivity,axiom, % 0.23/0.53 ! [X] : r1(X,X) ). % 0.23/0.53 % 0.23/0.53 fof(main,conjecture, % 0.23/0.53 ~ ? [X] : % 0.23/0.53 ~ ( ~ ! [Y] : % 0.23/0.53 ( ~ r1(X,Y) % 0.23/0.53 | p2(Y) ) % 0.23/0.53 | ~ ( ! [Y] : % 0.23/0.53 ( ~ r1(X,Y) % 0.23/0.53 | ( ( ( ~ ! [X] : % 0.23/0.53 ( ~ r1(Y,X) % 0.23/0.53 | ~ ( ~ p2(X) % 0.23/0.53 & ~ p102(X) % 0.23/0.53 & p101(X) ) ) % 0.23/0.53 & ~ ! [X] : % 0.23/0.53 ( ~ r1(Y,X) % 0.23/0.53 | ~ ( p2(X) % 0.23/0.53 & ~ p102(X) % 0.23/0.53 & p101(X) ) ) ) % 0.23/0.53 | ~ ( ~ p101(Y) % 0.23/0.53 & p100(Y) ) ) % 0.23/0.53 & ( ( ( ! [X] : % 0.23/0.53 ( ~ r1(Y,X) % 0.23/0.53 | ~ p2(X) % 0.23/0.53 | ~ p101(X) ) % 0.23/0.53 | p2(Y) ) % 0.23/0.53 & ( ! [X] : % 0.23/0.53 ( ~ r1(Y,X) % 0.23/0.53 | p2(X) % 0.23/0.53 | ~ p101(X) ) % 0.23/0.53 | ~ p2(Y) ) ) % 0.23/0.53 | ~ p101(Y) ) % 0.23/0.53 & ( ( ( ! [X] : % 0.23/0.53 ( ~ r1(Y,X) % 0.23/0.53 | ~ p1(X) % 0.23/0.53 | ~ p100(X) ) % 0.23/0.53 | p1(Y) ) % 0.23/0.53 & ( ! [X] : % 0.23/0.53 ( ~ r1(Y,X) % 0.23/0.53 | p1(X) % 0.23/0.53 | ~ p100(X) ) % 0.23/0.53 | ~ p1(Y) ) ) % 0.23/0.53 | ~ p100(Y) ) % 0.23/0.53 & ( p101(Y) % 0.23/0.53 | ~ p102(Y) ) % 0.23/0.53 & ( p100(Y) % 0.23/0.53 | ~ p101(Y) ) ) ) % 0.23/0.53 & ~ p101(X) % 0.23/0.53 & p100(X) ) ) ). % 0.23/0.53 % 0.23/0.53 %------------------------------------------------------------------------------ % 0.23/0.53 %------------------------------------------- % 0.23/0.53 % Proof found % 0.23/0.53 % SZS status Theorem for theBenchmark % 0.23/0.53 % SZS output start Proof % 0.23/0.53 %ClaNum:18(EqnAxiom:0) % 0.23/0.53 %VarNum:65(SingletonVarNum:18) % 0.23/0.53 %MaxLitNum:6 % 0.23/0.53 %MaxfuncDepth:1 % 0.23/0.53 %SharedTerms:3 % 0.23/0.53 %goalClause: 1 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 % 0.23/0.53 %singleGoalClaCount:2 % 0.23/0.53 [1]P1(a1) % 0.23/0.53 [3]~P4(a1) % 0.23/0.53 [2]P3(x21,x21) % 0.23/0.53 [4]P5(x41)+~P3(a1,x41) % 0.23/0.53 [5]~P6(x51)+P4(x51)+~P3(a1,x51) % 0.23/0.53 [6]~P4(x61)+P1(x61)+~P3(a1,x61) % 0.23/0.53 [7]~P1(x71)+P4(x71)+~P3(a1,x71)+P5(f2(x71)) % 0.23/0.53 [8]~P1(x81)+P4(x81)+~P3(a1,x81)+P4(f3(x81)) % 0.23/0.53 [9]~P1(x91)+P4(x91)+~P3(a1,x91)+P4(f2(x91)) % 0.23/0.53 [10]~P1(x101)+P4(x101)+~P3(a1,x101)+~P5(f3(x101)) % 0.23/0.53 [11]~P1(x111)+P4(x111)+~P3(a1,x111)+~P6(f3(x111)) % 0.23/0.53 [12]~P1(x121)+P4(x121)+~P3(a1,x121)+~P6(f2(x121)) % 0.23/0.53 [13]~P1(x131)+P4(x131)+P3(x131,f3(x131))+~P3(a1,x131) % 0.23/0.53 [14]~P1(x141)+P4(x141)+P3(x141,f2(x141))+~P3(a1,x141) % 0.23/0.53 [15]~P4(x151)+~P4(x152)+~P3(x152,x151)+P5(x151)+~P5(x152)+~P3(a1,x152) % 0.23/0.53 [17]~P1(x171)+~P2(x172)+~P3(x172,x171)+P2(x171)+~P1(x172)+~P3(a1,x172) % 0.23/0.53 [18]~P1(x181)+~P2(x182)+~P3(x181,x182)+P2(x181)+~P1(x182)+~P3(a1,x181) % 0.23/0.53 %EqnAxiom % 0.23/0.53 % 0.23/0.53 %------------------------------------------- % 0.23/0.53 cnf(29,plain, % 0.23/0.53 (~P3(a1,f3(a1))), % 0.23/0.53 inference(scs_inference,[],[2,3,1,4,10])). % 0.23/0.53 cnf(30,plain, % 0.23/0.53 ($false), % 0.23/0.53 inference(scs_inference,[],[2,3,1,29,13]), % 0.23/0.53 ['proof']). % 0.23/0.53 % SZS output end Proof % 0.23/0.53 % Total time :0.007130s %------------------------------------------------------------------------------