%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET062+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 : n001.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 14:20:24 EDT 2024 % Result : Theorem 0.54s 0.59s % Output : CNFRefutation 0.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET062+3 : TPTP v8.2.0. Released v2.2.0. % 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n001.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 14:28:09 EDT 2024 % 0.18/0.34 % CPUTime : % 0.21/0.56 start to proof:theBenchmark % 0.54/0.59 %------------------------------------------- % 0.54/0.59 % File :CSE---1.7 % 0.54/0.59 % Problem :theBenchmark % 0.54/0.59 % Transform :cnf % 0.54/0.59 % Format :tptp:raw % 0.54/0.59 % Command :java -jar mcs_scs.jar %d %s % 0.54/0.59 % 0.54/0.59 % Result :Theorem 0.000000s % 0.54/0.59 % Output :CNFRefutation 0.000000s % 0.54/0.59 %------------------------------------------- % 0.54/0.59 %-------------------------------------------------------------------------- % 0.54/0.59 % File : SET062+3 : TPTP v8.2.0. Released v2.2.0. % 0.54/0.59 % Domain : Set Theory % 0.54/0.59 % Problem : The empty set is a subset of X % 0.54/0.59 % Version : [Try90] axioms : Reduced > Incomplete. % 0.54/0.59 % English : % 0.54/0.59 % 0.54/0.59 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.54/0.59 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.54/0.59 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.54/0.59 % Source : [ILF] % 0.54/0.59 % Names : BOOLE (27) [TS89] % 0.54/0.59 % 0.54/0.59 % Status : Theorem % 0.54/0.59 % 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, 0.17 v5.2.0, 0.00 v3.2.0, 0.11 v3.1.0, 0.00 v2.2.1 % 0.54/0.59 % Syntax : Number of formulae : 5 ( 3 unt; 0 def) % 0.54/0.59 % Number of atoms : 8 ( 0 equ) % 0.54/0.59 % Maximal formula atoms : 3 ( 1 avg) % 0.54/0.59 % Number of connectives : 5 ( 2 ~; 0 |; 0 &) % 0.54/0.59 % ( 2 <=>; 1 =>; 0 <=; 0 <~>) % 0.54/0.59 % Maximal formula depth : 6 ( 4 avg) % 0.54/0.59 % Maximal term depth : 1 ( 1 avg) % 0.54/0.59 % Number of predicates : 3 ( 3 usr; 0 prp; 1-2 aty) % 0.54/0.59 % Number of functors : 1 ( 1 usr; 1 con; 0-0 aty) % 0.54/0.59 % Number of variables : 8 ( 8 !; 0 ?) % 0.54/0.59 % SPC : FOF_THM_RFO_NEQ % 0.54/0.59 % 0.54/0.59 % Comments : % 0.54/0.59 %-------------------------------------------------------------------------- % 0.54/0.59 %---- line(hidden - axiom26,1832636) % 0.54/0.59 fof(empty_set_defn,axiom, % 0.54/0.59 ! [B] : ~ member(B,empty_set) ). % 0.54/0.59 % 0.54/0.59 %---- line(tarski - df(3),1832749) % 0.54/0.59 fof(subset_defn,axiom, % 0.54/0.59 ! [B,C] : % 0.54/0.59 ( subset(B,C) % 0.54/0.59 <=> ! [D] : % 0.54/0.59 ( member(D,B) % 0.54/0.59 => member(D,C) ) ) ). % 0.54/0.59 % 0.54/0.59 %---- property(reflexivity,op(subset,2,predicate)) % 0.54/0.59 fof(reflexivity_of_subset,axiom, % 0.54/0.59 ! [B] : subset(B,B) ). % 0.54/0.59 % 0.54/0.59 %---- line(hidden - axiom28,1832628) % 0.54/0.59 fof(empty_defn,axiom, % 0.54/0.59 ! [B] : % 0.54/0.59 ( empty(B) % 0.54/0.59 <=> ! [C] : ~ member(C,B) ) ). % 0.54/0.59 % 0.54/0.59 %---- line(boole - th(27),1833153) % 0.54/0.59 fof(prove_empty_set_subset,conjecture, % 0.54/0.59 ! [B] : subset(empty_set,B) ). % 0.54/0.59 % 0.54/0.59 %-------------------------------------------------------------------------- % 0.54/0.59 %------------------------------------------- % 0.54/0.59 % Proof found % 0.54/0.59 % SZS status Theorem for theBenchmark % 0.57/0.59 % SZS output start Proof % 0.57/0.60 %ClaNum:8(EqnAxiom:0) % 0.57/0.60 %VarNum:25(SingletonVarNum:12) % 0.57/0.60 %MaxLitNum:3 % 0.57/0.60 %MaxfuncDepth:1 % 0.57/0.60 %SharedTerms:3 % 0.57/0.60 %goalClause: 2 % 0.57/0.60 %singleGoalClaCount:1 % 0.57/0.60 [2]~P1(a1,a2) % 0.57/0.60 [1]P1(x11,x11) % 0.57/0.60 [3]~P2(x31,a1) % 0.57/0.60 [4]P3(x41)+P2(f3(x41),x41) % 0.57/0.60 [5]~P3(x51)+~P2(x52,x51) % 0.57/0.60 [6]P1(x61,x62)+P2(f4(x61,x62),x61) % 0.57/0.60 [8]P1(x81,x82)+~P2(f4(x81,x82),x82) % 0.57/0.60 [7]~P1(x73,x72)+P2(x71,x72)+~P2(x71,x73) % 0.57/0.60 %EqnAxiom % 0.57/0.60 % 0.57/0.60 %------------------------------------------- % 0.57/0.60 cnf(9,plain, % 0.57/0.60 ($false), % 0.57/0.60 inference(scs_inference,[],[2,3,6]), % 0.57/0.60 ['proof']). % 0.57/0.60 % SZS output end Proof % 0.57/0.60 % Total time :0.000000s %------------------------------------------------------------------------------