%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET027+3 : TPTP v8.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n020.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Jun 24 14:20:10 EDT 2024 % Result : Theorem 0.50s 0.61s % Output : CNFRefutation 0.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET027+3 : TPTP v8.2.0. Released v2.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n020.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sun Jun 23 13:14:09 EDT 2024 % 0.12/0.33 % CPUTime : % 0.50/0.56 start to proof:theBenchmark % 0.50/0.60 %------------------------------------------- % 0.50/0.60 % File :CSE---1.7 % 0.50/0.60 % Problem :theBenchmark % 0.50/0.60 % Transform :cnf % 0.50/0.60 % Format :tptp:raw % 0.50/0.60 % Command :java -jar mcs_scs.jar %d %s % 0.50/0.60 % 0.50/0.60 % Result :Theorem 0.000000s % 0.50/0.60 % Output :CNFRefutation 0.000000s % 0.50/0.60 %------------------------------------------- % 0.50/0.61 %-------------------------------------------------------------------------- % 0.50/0.61 % File : SET027+3 : TPTP v8.2.0. Released v2.2.0. % 0.50/0.61 % Domain : Set Theory % 0.50/0.61 % Problem : Transitivity of subset % 0.50/0.61 % Version : [Try90] axioms : Reduced > Incomplete. % 0.50/0.61 % English : If X is a subset of Y and Y is a subset of Z, then X is a % 0.50/0.61 % subset of Z. % 0.50/0.61 % 0.50/0.61 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.50/0.61 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.50/0.61 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.50/0.61 % Source : [ILF] % 0.50/0.61 % Names : BOOLE (29) [TS89] % 0.50/0.61 % 0.50/0.61 % Status : Theorem % 0.50/0.61 % Rating : 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, 0.04 v5.3.0, 0.13 v5.2.0, 0.00 v3.2.0, 0.11 v3.1.0, 0.00 v2.2.1 % 0.50/0.61 % Syntax : Number of formulae : 3 ( 1 unt; 0 def) % 0.50/0.61 % Number of atoms : 7 ( 0 equ) % 0.50/0.61 % Maximal formula atoms : 3 ( 2 avg) % 0.50/0.61 % Number of connectives : 4 ( 0 ~; 0 |; 1 &) % 0.50/0.61 % ( 1 <=>; 2 =>; 0 <=; 0 <~>) % 0.50/0.61 % Maximal formula depth : 6 ( 5 avg) % 0.50/0.61 % Maximal term depth : 1 ( 1 avg) % 0.50/0.61 % Number of predicates : 2 ( 2 usr; 0 prp; 2-2 aty) % 0.50/0.61 % Number of functors : 0 ( 0 usr; 0 con; --- aty) % 0.50/0.61 % Number of variables : 7 ( 7 !; 0 ?) % 0.50/0.61 % SPC : FOF_THM_RFO_NEQ % 0.50/0.61 % 0.50/0.61 % Comments : % 0.50/0.61 %-------------------------------------------------------------------------- % 0.50/0.61 %---- line(tarski - df(3),1832749) % 0.50/0.61 fof(subset_defn,axiom, % 0.50/0.61 ! [B,C] : % 0.50/0.61 ( subset(B,C) % 0.50/0.61 <=> ! [D] : % 0.50/0.61 ( member(D,B) % 0.50/0.61 => member(D,C) ) ) ). % 0.50/0.61 % 0.50/0.61 %---- property(reflexivity,op(subset,2,predicate)) % 0.50/0.61 fof(reflexivity_of_subset,axiom, % 0.50/0.61 ! [B] : subset(B,B) ). % 0.50/0.61 % 0.50/0.61 %---- line(boole - th(29),1833172) % 0.50/0.61 fof(prove_transitivity_of_subset,conjecture, % 0.50/0.61 ! [B,C,D] : % 0.50/0.61 ( ( subset(B,C) % 0.50/0.61 & subset(C,D) ) % 0.50/0.61 => subset(B,D) ) ). % 0.50/0.61 % 0.50/0.61 %-------------------------------------------------------------------------- % 0.50/0.61 %------------------------------------------- % 0.50/0.61 % Proof found % 0.50/0.61 % SZS status Theorem for theBenchmark % 0.50/0.61 % SZS output start Proof % 0.50/0.61 %ClaNum:7(EqnAxiom:0) % 0.50/0.61 %VarNum:18(SingletonVarNum:8) % 0.50/0.61 %MaxLitNum:3 % 0.50/0.61 %MaxfuncDepth:1 % 0.50/0.61 %SharedTerms:6 % 0.50/0.61 %goalClause: 1 2 4 % 0.50/0.61 %singleGoalClaCount:3 % 0.50/0.61 [1]P1(a1,a3) % 0.50/0.61 [2]P1(a3,a4) % 0.50/0.61 [4]~P1(a1,a4) % 0.50/0.61 [3]P1(x31,x31) % 0.50/0.61 [5]P1(x51,x52)+P2(f2(x51,x52),x51) % 0.50/0.61 [7]P1(x71,x72)+~P2(f2(x71,x72),x72) % 0.50/0.61 [6]~P2(x61,x63)+P2(x61,x62)+~P1(x63,x62) % 0.50/0.61 %EqnAxiom % 0.50/0.61 % 0.50/0.61 %------------------------------------------- % 0.50/0.61 cnf(8,plain, % 0.50/0.61 (~P2(x81,a1)+P2(x81,a3)), % 0.50/0.61 inference(scs_inference,[],[1,6])). % 0.50/0.61 cnf(11,plain, % 0.50/0.61 (~P2(x111,a3)+P2(x111,a4)), % 0.50/0.61 inference(scs_inference,[],[2,6])). % 0.50/0.61 cnf(21,plain, % 0.50/0.61 (~P2(f2(a1,a4),a3)), % 0.50/0.62 inference(scs_inference,[],[4,11,7])). % 0.50/0.62 cnf(24,plain, % 0.50/0.62 ($false), % 0.50/0.62 inference(scs_inference,[],[4,21,8,5]), % 0.50/0.62 ['proof']). % 0.50/0.62 % SZS output end Proof % 0.50/0.62 % Total time :0.000000s %------------------------------------------------------------------------------