%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL678+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 : n012.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 11:19:37 AM UTC 2026 % Result : Theorem 0.09s 0.40s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.01 % Problem : LCL678+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.01 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.04/0.30 % Computer : n012.cluster.edu % 0.04/0.30 % Model : x86_64 x86_64 % 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.04/0.30 % Memory : 8046.5625MB % 0.04/0.30 % OS : Linux 6.8.0-71-generic % 0.04/0.30 % CPULimit : 300 % 0.04/0.30 % WCLimit : 300 % 0.04/0.30 % DateTime : Sat Sep 5 23:56:42 UTC 2026 % 0.04/0.30 % CPUTime : % 0.09/0.39 start to proof:theBenchmark % 0.09/0.39 %------------------------------------------- % 0.09/0.39 % File :CSE---1.7 % 0.09/0.39 % Problem :theBenchmark % 0.09/0.39 % Transform :cnf % 0.09/0.39 % Format :tptp:raw % 0.09/0.39 % Command :java -jar mcs_scs.jar %d %s % 0.09/0.39 % 0.09/0.39 % Result :Theorem 0.010007s % 0.09/0.39 % Output :CNFRefutation 0.010007s % 0.09/0.39 %------------------------------------------- % 0.09/0.39 %------------------------------------------------------------------------------ % 0.09/0.39 % File : LCL678+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.09/0.39 % Domain : Logic Calculi (Modal Logic) % 0.09/0.39 % Problem : In S4, formula provable in intuitionistic logic, size 1 % 0.09/0.39 % Version : Especial. % 0.09/0.39 % English : % 0.09/0.40 % 0.09/0.40 % Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro % 0.09/0.40 % : [Kam08] Kaminski (2008), Email to G. Sutcliffe % 0.09/0.40 % Source : [Kam08] % 0.09/0.40 % Names : s4_ipc_p [BHS00] % 0.09/0.40 % 0.09/0.40 % Status : Theorem % 0.09/0.40 % 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, 0.13 v5.3.0, 0.22 v5.2.0, 0.07 v5.0.0, 0.05 v4.1.0, 0.06 v4.0.1, 0.11 v4.0.0 % 0.09/0.40 % Syntax : Number of formulae : 3 ( 1 unt; 0 def) % 0.09/0.40 % Number of atoms : 12 ( 0 equ) % 0.09/0.40 % Maximal formula atoms : 8 ( 4 avg) % 0.09/0.40 % Number of connectives : 18 ( 9 ~; 7 |; 1 &) % 0.09/0.40 % ( 0 <=>; 1 =>; 0 <=; 0 <~>) % 0.09/0.40 % Maximal formula depth : 17 ( 8 avg) % 0.09/0.40 % Maximal term depth : 1 ( 1 avg) % 0.09/0.40 % Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty) % 0.09/0.40 % Number of functors : 0 ( 0 usr; 0 con; --- aty) % 0.09/0.40 % Number of variables : 9 ( 8 !; 1 ?) % 0.09/0.40 % SPC : FOF_THM_RFO_NEQ % 0.09/0.40 % 0.09/0.40 % Comments : A naive relational encoding of the modal logic problem into % 0.09/0.40 % first-order logic. % 0.09/0.40 %------------------------------------------------------------------------------ % 0.09/0.40 fof(reflexivity,axiom, % 0.09/0.40 ! [X] : r1(X,X) ). % 0.09/0.40 % 0.09/0.40 fof(transitivity,axiom, % 0.09/0.40 ! [X,Y,Z] : % 0.09/0.40 ( ( r1(X,Y) % 0.09/0.40 & r1(Y,Z) ) % 0.09/0.40 => r1(X,Z) ) ). % 0.09/0.40 % 0.09/0.40 fof(main,conjecture, % 0.09/0.40 ~ ? [X] : % 0.09/0.40 ~ ( $false % 0.09/0.40 | ~ ! [Y] : % 0.09/0.40 ( ~ r1(X,Y) % 0.09/0.40 | $false % 0.09/0.40 | ~ ! [X] : % 0.09/0.40 ( ~ r1(Y,X) % 0.09/0.40 | ! [Y] : % 0.09/0.40 ( ~ r1(X,Y) % 0.09/0.40 | p1(Y) ) % 0.09/0.40 | ~ ! [Y] : % 0.09/0.40 ( ~ r1(X,Y) % 0.09/0.40 | p1(Y) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 %------------------------------------------------------------------------------ % 0.09/0.40 %------------------------------------------- % 0.09/0.40 % Proof found % 0.09/0.40 % SZS status Theorem for theBenchmark % 0.09/0.40 % SZS output start Proof % 0.09/0.40 %ClaNum:6(EqnAxiom:0) % 0.09/0.40 %VarNum:20(SingletonVarNum:9) % 0.09/0.40 %MaxLitNum:3 % 0.09/0.40 %MaxfuncDepth:1 % 0.09/0.40 %SharedTerms:1 % 0.09/0.40 %goalClause: 2 3 4 5 % 0.09/0.40 [1]P1(x11,x11) % 0.09/0.40 [2]~P1(a2,x21)+~P2(f1(x21)) % 0.09/0.40 [3]~P1(a2,x31)+P1(x31,f3(x31)) % 0.09/0.40 [4]~P1(a2,x41)+P1(f3(x41),f1(x41)) % 0.09/0.40 [5]P2(x51)+~P1(f3(x52),x51)+~P1(a2,x52) % 0.09/0.40 [6]~P1(x61,x63)+P1(x61,x62)+~P1(x63,x62) % 0.09/0.40 %EqnAxiom % 0.09/0.40 % 0.09/0.40 %------------------------------------------- % 0.09/0.40 cnf(7,plain, % 0.09/0.40 (P2(x71)+~P1(f3(a2),x71)), % 0.09/0.40 inference(scs_inference,[],[1,5])). % 0.09/0.40 cnf(106,plain, % 0.09/0.40 (P2(f1(a2))), % 0.09/0.40 inference(scs_inference,[],[1,4,7])). % 0.09/0.40 cnf(107,plain, % 0.09/0.40 ($false), % 0.09/0.40 inference(scs_inference,[],[1,106,2]), % 0.09/0.40 ['proof']). % 0.09/0.40 % SZS output end Proof % 0.09/0.40 % Total time :0.010007s %------------------------------------------------------------------------------