%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET602+3 : TPTP v8.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n021.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 14:21:55 EDT 2024 % Result : Theorem 0.17s 0.57s % Output : CNFRefutation 0.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : SET602+3 : TPTP v8.2.0. Released v2.2.0. % 0.10/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.10/0.32 % Computer : n021.cluster.edu % 0.10/0.32 % Model : x86_64 x86_64 % 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.32 % Memory : 8042.1875MB % 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.32 % CPULimit : 300 % 0.10/0.32 % WCLimit : 300 % 0.10/0.32 % DateTime : Sun Jun 23 12:23:09 EDT 2024 % 0.10/0.32 % CPUTime : % 0.17/0.53 start to proof:theBenchmark % 0.17/0.56 %------------------------------------------- % 0.17/0.56 % File :CSE---1.7 % 0.17/0.56 % Problem :theBenchmark % 0.17/0.56 % Transform :cnf % 0.17/0.56 % Format :tptp:raw % 0.17/0.56 % Command :java -jar mcs_scs.jar %d %s % 0.17/0.56 % 0.17/0.56 % Result :Theorem 0.000000s % 0.17/0.56 % Output :CNFRefutation 0.000000s % 0.17/0.56 %------------------------------------------- % 0.17/0.57 %-------------------------------------------------------------------------- % 0.17/0.57 % File : SET602+3 : TPTP v8.2.0. Released v2.2.0. % 0.17/0.57 % Domain : Set Theory % 0.17/0.57 % Problem : The difference of X and X is the empty set % 0.17/0.57 % Version : [Try90] axioms : Reduced > Incomplete. % 0.17/0.57 % English : % 0.17/0.57 % 0.17/0.57 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.17/0.57 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.17/0.57 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.17/0.57 % Source : [ILF] % 0.17/0.57 % Names : BOOLE (73) [TS89] % 0.17/0.57 % 0.17/0.57 % Status : Theorem % 0.17/0.57 % Rating : 0.00 v6.4.0, 0.04 v6.3.0, 0.00 v5.3.0, 0.04 v5.2.0, 0.00 v2.3.0, 0.33 v2.2.1 % 0.17/0.57 % Syntax : Number of formulae : 8 ( 3 unt; 0 def) % 0.17/0.57 % Number of atoms : 16 ( 3 equ) % 0.17/0.57 % Maximal formula atoms : 3 ( 2 avg) % 0.17/0.57 % Number of connectives : 11 ( 3 ~; 0 |; 2 &) % 0.17/0.57 % ( 5 <=>; 1 =>; 0 <=; 0 <~>) % 0.17/0.57 % Maximal formula depth : 7 ( 4 avg) % 0.17/0.57 % Maximal term depth : 2 ( 1 avg) % 0.17/0.57 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty) % 0.17/0.57 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty) % 0.17/0.57 % Number of variables : 15 ( 15 !; 0 ?) % 0.17/0.57 % SPC : FOF_THM_RFO_SEQ % 0.17/0.57 % 0.17/0.57 % Comments : % 0.17/0.57 %-------------------------------------------------------------------------- % 0.17/0.57 %---- line(boole - th(45),1833405) % 0.17/0.57 fof(difference_empty_set,axiom, % 0.17/0.57 ! [B,C] : % 0.17/0.57 ( difference(B,C) = empty_set % 0.17/0.57 <=> subset(B,C) ) ). % 0.17/0.57 % 0.17/0.57 %---- line(hidden - axiom119,1832636) % 0.17/0.57 fof(empty_set_defn,axiom, % 0.17/0.57 ! [B] : ~ member(B,empty_set) ). % 0.17/0.57 % 0.17/0.57 %---- line(boole - df(4),1833078) % 0.17/0.57 fof(difference_defn,axiom, % 0.17/0.57 ! [B,C,D] : % 0.17/0.57 ( member(D,difference(B,C)) % 0.17/0.57 <=> ( member(D,B) % 0.17/0.57 & ~ member(D,C) ) ) ). % 0.17/0.57 % 0.17/0.57 %---- line(boole - df(8),1833103) % 0.17/0.57 fof(equal_defn,axiom, % 0.17/0.57 ! [B,C] : % 0.17/0.57 ( B = C % 0.17/0.57 <=> ( subset(B,C) % 0.17/0.57 & subset(C,B) ) ) ). % 0.17/0.57 % 0.17/0.57 %---- line(tarski - df(3),1832749) % 0.17/0.57 fof(subset_defn,axiom, % 0.17/0.57 ! [B,C] : % 0.17/0.57 ( subset(B,C) % 0.17/0.57 <=> ! [D] : % 0.17/0.57 ( member(D,B) % 0.17/0.57 => member(D,C) ) ) ). % 0.17/0.57 % 0.17/0.57 %---- property(reflexivity,op(subset,2,predicate)) % 0.17/0.57 fof(reflexivity_of_subset,axiom, % 0.17/0.57 ! [B] : subset(B,B) ). % 0.17/0.57 % 0.17/0.57 %---- line(hidden - axiom121,1832628) % 0.17/0.57 fof(empty_defn,axiom, % 0.17/0.57 ! [B] : % 0.17/0.57 ( empty(B) % 0.17/0.57 <=> ! [C] : ~ member(C,B) ) ). % 0.17/0.57 % 0.17/0.57 %---- line(boole - th(73),1833852) % 0.17/0.57 fof(prove_self_difference_is_empty_set,conjecture, % 0.17/0.57 ! [B] : difference(B,B) = empty_set ). % 0.17/0.57 % 0.17/0.57 %-------------------------------------------------------------------------- % 0.17/0.57 %------------------------------------------- % 0.17/0.57 % Proof found % 0.17/0.57 % SZS status Theorem for theBenchmark % 0.17/0.57 % SZS output start Proof % 0.17/0.57 %ClaNum:29(EqnAxiom:13) % 0.17/0.57 %VarNum:60(SingletonVarNum:29) % 0.17/0.57 %MaxLitNum:3 % 0.17/0.57 %MaxfuncDepth:1 % 0.17/0.57 %SharedTerms:4 % 0.17/0.57 %goalClause: 15 % 0.17/0.57 %singleGoalClaCount:1 % 0.17/0.57 [15]~E(f2(a1,a1),a3) % 0.17/0.57 [14]P1(x141,x141) % 0.17/0.57 [16]~P2(x161,a3) % 0.17/0.57 [19]P3(x191)+P2(f4(x191),x191) % 0.17/0.57 [18]~E(x181,x182)+P1(x181,x182) % 0.17/0.57 [20]~P3(x201)+~P2(x202,x201) % 0.17/0.57 [21]~P1(x211,x212)+E(f2(x211,x212),a3) % 0.17/0.57 [22]P1(x221,x222)+~E(f2(x221,x222),a3) % 0.17/0.57 [24]P1(x241,x242)+P2(f5(x241,x242),x241) % 0.17/0.57 [28]P1(x281,x282)+~P2(f5(x281,x282),x282) % 0.17/0.57 [27]P2(x271,x272)+~P2(x271,f2(x272,x273)) % 0.17/0.57 [29]~P2(x291,x292)+~P2(x291,f2(x293,x292)) % 0.17/0.57 [23]~P1(x232,x231)+~P1(x231,x232)+E(x231,x232) % 0.17/0.57 [25]~P2(x251,x253)+P2(x251,x252)+~P1(x253,x252) % 0.17/0.57 [26]~P2(x261,x263)+P2(x261,x262)+P2(x261,f2(x263,x262)) % 0.17/0.57 %EqnAxiom % 0.17/0.57 [1]E(x11,x11) % 0.17/0.57 [2]E(x22,x21)+~E(x21,x22) % 0.17/0.57 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.17/0.57 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.17/0.57 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.17/0.57 [6]~E(x61,x62)+E(f4(x61),f4(x62)) % 0.17/0.57 [7]~E(x71,x72)+E(f5(x71,x73),f5(x72,x73)) % 0.17/0.57 [8]~E(x81,x82)+E(f5(x83,x81),f5(x83,x82)) % 0.17/0.57 [9]P1(x92,x93)+~E(x91,x92)+~P1(x91,x93) % 0.17/0.57 [10]P1(x103,x102)+~E(x101,x102)+~P1(x103,x101) % 0.17/0.57 [11]P2(x112,x113)+~E(x111,x112)+~P2(x111,x113) % 0.17/0.57 [12]P2(x123,x122)+~E(x121,x122)+~P2(x123,x121) % 0.17/0.57 [13]~P3(x131)+P3(x132)+~E(x131,x132) % 0.17/0.57 % 0.17/0.57 %------------------------------------------- % 0.17/0.58 cnf(31,plain, % 0.17/0.58 ($false), % 0.17/0.58 inference(scs_inference,[],[14,15,21]), % 0.17/0.58 ['proof']). % 0.17/0.58 % SZS output end Proof % 0.17/0.58 % Total time :0.000000s %------------------------------------------------------------------------------