%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL636+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 : n008.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 11:19:23 AM UTC 2026 % Result : Theorem 0.24s 0.53s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL636+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 % 0.07/0.34 % Computer : n008.cluster.edu % 0.07/0.34 % Model : x86_64 x86_64 % 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.34 % Memory : 8046.5625MB % 0.07/0.34 % OS : Linux 6.8.0-71-generic % 0.07/0.35 % CPULimit : 300 % 0.07/0.35 % WCLimit : 300 % 0.07/0.35 % DateTime : Sat Sep 5 13:22:53 UTC 2026 % 0.07/0.35 % CPUTime : % 0.24/0.52 start to proof:theBenchmark % 0.24/0.52 %------------------------------------------- % 0.24/0.52 % File :CSE---1.7 % 0.24/0.52 % Problem :theBenchmark % 0.24/0.52 % Transform :cnf % 0.24/0.52 % Format :tptp:raw % 0.24/0.52 % Command :java -jar mcs_scs.jar %d %s % 0.24/0.52 % 0.24/0.52 % Result :Theorem 0.005684s % 0.24/0.52 % Output :CNFRefutation 0.005684s % 0.24/0.52 %------------------------------------------- % 0.24/0.52 %------------------------------------------------------------------------------ % 0.24/0.52 % File : LCL636+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.24/0.52 % Domain : Logic Calculi (Modal Logic) % 0.24/0.52 % Problem : In K, the branching formula made provable, size 1 % 0.24/0.52 % Version : Especial. % 0.24/0.52 % English : The branching formula plus a negation symbol in front and an % 0.24/0.52 % additional subformula to make the formula provable. % 0.24/0.52 % 0.24/0.52 % Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro % 0.24/0.52 % : [Kam08] Kaminski (2008), Email to G. Sutcliffe % 0.24/0.52 % Source : [Kam08] % 0.24/0.52 % Names : k_branch_p [BHS00] % 0.24/0.52 % 0.24/0.52 % Status : Theorem % 0.24/0.52 % 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, 0.12 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 % 0.24/0.52 % Syntax : Number of formulae : 1 ( 0 unt; 0 def) % 0.24/0.52 % Number of atoms : 69 ( 0 equ) % 0.24/0.52 % Maximal formula atoms : 69 ( 69 avg) % 0.24/0.52 % Number of connectives : 129 ( 61 ~; 41 |; 27 &) % 0.24/0.52 % ( 0 <=>; 0 =>; 0 <=; 0 <~>) % 0.24/0.52 % Maximal formula depth : 19 ( 19 avg) % 0.24/0.52 % Maximal term depth : 1 ( 1 avg) % 0.24/0.52 % Number of predicates : 6 ( 6 usr; 0 prp; 1-2 aty) % 0.24/0.52 % Number of functors : 0 ( 0 usr; 0 con; --- aty) % 0.24/0.52 % Number of variables : 15 ( 14 !; 1 ?) % 0.24/0.52 % SPC : FOF_THM_RFO_NEQ % 0.24/0.52 % 0.24/0.52 % Comments : A naive relational encoding of the modal logic problem into % 0.24/0.52 % first-order logic. % 0.24/0.52 %------------------------------------------------------------------------------ % 0.24/0.52 fof(main,conjecture, % 0.24/0.52 ~ ? [X] : % 0.24/0.52 ~ ( ~ ! [Y] : % 0.24/0.52 ( ~ r1(X,Y) % 0.24/0.52 | p2(Y) ) % 0.24/0.52 | ~ ( ! [Y] : % 0.24/0.52 ( ~ r1(X,Y) % 0.24/0.52 | ( ( ( ~ ! [X] : % 0.24/0.52 ( ~ r1(Y,X) % 0.24/0.52 | ~ ( ~ p2(X) % 0.24/0.52 & ~ p102(X) % 0.24/0.52 & p101(X) ) ) % 0.24/0.52 & ~ ! [X] : % 0.24/0.52 ( ~ r1(Y,X) % 0.24/0.52 | ~ ( p2(X) % 0.24/0.52 & ~ p102(X) % 0.24/0.52 & p101(X) ) ) ) % 0.24/0.52 | ~ ( ~ p101(Y) % 0.24/0.52 & p100(Y) ) ) % 0.24/0.52 & ( ( ( ! [X] : % 0.24/0.52 ( ~ r1(Y,X) % 0.24/0.52 | ~ p2(X) % 0.24/0.52 | ~ p101(X) ) % 0.24/0.52 | p2(Y) ) % 0.24/0.52 & ( ! [X] : % 0.24/0.53 ( ~ r1(Y,X) % 0.24/0.53 | p2(X) % 0.24/0.53 | ~ p101(X) ) % 0.24/0.53 | ~ p2(Y) ) ) % 0.24/0.53 | ~ p101(Y) ) % 0.24/0.53 & ( ( ( ! [X] : % 0.24/0.53 ( ~ r1(Y,X) % 0.24/0.53 | ~ p1(X) % 0.24/0.53 | ~ p100(X) ) % 0.24/0.53 | p1(Y) ) % 0.24/0.53 & ( ! [X] : % 0.24/0.53 ( ~ r1(Y,X) % 0.24/0.53 | p1(X) % 0.24/0.53 | ~ p100(X) ) % 0.24/0.53 | ~ p1(Y) ) ) % 0.24/0.53 | ~ p100(Y) ) % 0.24/0.53 & ( p101(Y) % 0.24/0.53 | ~ p102(Y) ) % 0.24/0.53 & ( p100(Y) % 0.24/0.53 | ~ p101(Y) ) ) ) % 0.24/0.53 & ( ( ~ ! [Y] : % 0.24/0.53 ( ~ r1(X,Y) % 0.24/0.53 | ~ ( ~ p2(Y) % 0.24/0.53 & ~ p102(Y) % 0.24/0.53 & p101(Y) ) ) % 0.24/0.53 & ~ ! [Y] : % 0.24/0.53 ( ~ r1(X,Y) % 0.24/0.53 | ~ ( p2(Y) % 0.24/0.53 & ~ p102(Y) % 0.24/0.53 & p101(Y) ) ) ) % 0.24/0.53 | ~ ( ~ p101(X) % 0.24/0.53 & p100(X) ) ) % 0.24/0.53 & ( ( ( ! [Y] : % 0.24/0.53 ( ~ r1(X,Y) % 0.24/0.53 | ~ p2(Y) % 0.24/0.53 | ~ p101(Y) ) % 0.24/0.53 | p2(X) ) % 0.24/0.53 & ( ! [Y] : % 0.24/0.53 ( ~ r1(X,Y) % 0.24/0.53 | p2(Y) % 0.24/0.53 | ~ p101(Y) ) % 0.24/0.53 | ~ p2(X) ) ) % 0.24/0.53 | ~ p101(X) ) % 0.24/0.53 & ( ( ( ! [Y] : % 0.24/0.53 ( ~ r1(X,Y) % 0.24/0.53 | ~ p1(Y) % 0.24/0.53 | ~ p100(Y) ) % 0.24/0.53 | p1(X) ) % 0.24/0.53 & ( ! [Y] : % 0.24/0.53 ( ~ r1(X,Y) % 0.24/0.53 | p1(Y) % 0.24/0.53 | ~ p100(Y) ) % 0.24/0.53 | ~ p1(X) ) ) % 0.24/0.53 | ~ p100(X) ) % 0.24/0.53 & ( p101(X) % 0.24/0.53 | ~ p102(X) ) % 0.24/0.53 & ( p100(X) % 0.24/0.53 | ~ p101(X) ) % 0.24/0.53 & ~ p101(X) % 0.24/0.53 & p100(X) ) ) ). % 0.24/0.53 % 0.24/0.53 %------------------------------------------------------------------------------ % 0.24/0.53 %------------------------------------------- % 0.24/0.53 % Proof found % 0.24/0.53 % SZS status Theorem for theBenchmark % 0.24/0.53 % SZS output start Proof % 0.24/0.53 %ClaNum:31(EqnAxiom:0) % 0.24/0.53 %VarNum:69(SingletonVarNum:19) % 0.24/0.53 %MaxLitNum:6 % 0.24/0.53 %MaxfuncDepth:1 % 0.24/0.53 %SharedTerms:20 % 0.24/0.53 %goalClause: 1 2 3 5 6 7 8 9 10 11 12 13 14 15 17 19 20 21 22 23 24 25 26 27 28 30 31 % 0.24/0.53 %singleGoalClaCount:2 % 0.24/0.53 [1]P1(a1) % 0.24/0.53 [2]~P3(a1) % 0.24/0.53 [3]P3(a1)+~P4(a1) % 0.24/0.53 [13]P5(x131)+~P6(a1,x131) % 0.24/0.53 [5]P5(a2)+P3(a1)+~P1(a1) % 0.24/0.53 [6]P3(a1)+P3(a3)+~P1(a1) % 0.24/0.53 [7]P3(a1)+P3(a2)+~P1(a1) % 0.24/0.53 [8]P3(a1)+~P5(a3)+~P1(a1) % 0.24/0.53 [9]P3(a1)+~P4(a3)+~P1(a1) % 0.24/0.53 [10]P3(a1)+~P4(a2)+~P1(a1) % 0.24/0.53 [11]P3(a1)+P6(a1,a3)+~P1(a1) % 0.24/0.53 [12]P3(a1)+P6(a1,a2)+~P1(a1) % 0.24/0.53 [14]~P4(x141)+P3(x141)+~P6(a1,x141) % 0.24/0.53 [15]~P3(x151)+P1(x151)+~P6(a1,x151) % 0.24/0.53 [20]~P1(x201)+P3(x201)+~P6(a1,x201)+P5(f4(x201)) % 0.24/0.53 [21]~P1(x211)+P3(x211)+~P6(a1,x211)+P3(f5(x211)) % 0.24/0.53 [22]~P1(x221)+P3(x221)+~P6(a1,x221)+P3(f4(x221)) % 0.24/0.53 [23]~P1(x231)+P3(x231)+~P6(a1,x231)+~P5(f5(x231)) % 0.24/0.53 [24]~P1(x241)+P3(x241)+~P6(a1,x241)+~P4(f5(x241)) % 0.24/0.53 [25]~P1(x251)+P3(x251)+~P6(a1,x251)+~P4(f4(x251)) % 0.24/0.53 [26]~P1(x261)+P3(x261)+P6(x261,f5(x261))+~P6(a1,x261) % 0.24/0.53 [27]~P1(x271)+P3(x271)+P6(x271,f4(x271))+~P6(a1,x271) % 0.24/0.53 [17]~P1(x171)+P2(x171)+~P6(a1,x171)+~P1(a1)+~P2(a1) % 0.24/0.53 [19]~P2(x191)+~P1(x191)+~P6(a1,x191)+P2(a1)+~P1(a1) % 0.24/0.53 [28]~P3(x281)+~P3(x282)+~P6(x282,x281)+P5(x281)+~P5(x282)+~P6(a1,x282) % 0.24/0.53 [30]~P1(x301)+~P2(x302)+~P6(x302,x301)+P2(x301)+~P1(x302)+~P6(a1,x302) % 0.24/0.53 [31]~P1(x311)+~P2(x312)+~P6(x311,x312)+P2(x311)+~P1(x312)+~P6(a1,x311) % 0.24/0.53 %EqnAxiom % 0.24/0.53 % 0.24/0.53 %------------------------------------------- % 0.24/0.53 cnf(39,plain, % 0.24/0.53 ($false), % 0.24/0.53 inference(scs_inference,[],[1,2,6,7,8,11,12,15,13]), % 0.24/0.53 ['proof']). % 0.24/0.53 % SZS output end Proof % 0.24/0.53 % Total time :0.005684s %------------------------------------------------------------------------------