%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET604+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 : n025.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 14:21:56 EDT 2024 % Result : Theorem 0.54s 0.61s % Output : CNFRefutation 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET604+3 : TPTP v8.2.0. Released v2.2.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n025.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 14:46:39 EDT 2024 % 0.12/0.33 % CPUTime : % 0.53/0.57 start to proof:theBenchmark % 0.54/0.60 %------------------------------------------- % 0.54/0.60 % File :CSE---1.7 % 0.54/0.60 % Problem :theBenchmark % 0.54/0.60 % Transform :cnf % 0.54/0.60 % Format :tptp:raw % 0.54/0.60 % Command :java -jar mcs_scs.jar %d %s % 0.54/0.60 % 0.54/0.60 % Result :Theorem 0.000000s % 0.54/0.60 % Output :CNFRefutation 0.000000s % 0.54/0.60 %------------------------------------------- % 0.54/0.60 %-------------------------------------------------------------------------- % 0.54/0.60 % File : SET604+3 : TPTP v8.2.0. Released v2.2.0. % 0.54/0.60 % Domain : Set Theory % 0.54/0.60 % Problem : The difference of the empty set and X is the empty set % 0.54/0.60 % Version : [Try90] axioms : Reduced > Incomplete. % 0.54/0.60 % English : % 0.54/0.60 % 0.54/0.60 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.54/0.60 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.54/0.60 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.54/0.60 % Source : [ILF] % 0.54/0.60 % Names : BOOLE (75) [TS89] % 0.54/0.60 % 0.54/0.61 % Status : Theorem % 0.54/0.61 % Rating : 0.00 v6.4.0, 0.04 v6.3.0, 0.00 v6.2.0, 0.04 v6.1.0, 0.00 v5.3.0, 0.07 v5.2.0, 0.00 v4.0.1, 0.04 v3.7.0, 0.00 v2.3.0, 0.33 v2.2.1 % 0.54/0.61 % Syntax : Number of formulae : 9 ( 4 unt; 0 def) % 0.54/0.61 % Number of atoms : 17 ( 3 equ) % 0.54/0.61 % Maximal formula atoms : 3 ( 1 avg) % 0.54/0.61 % Number of connectives : 11 ( 3 ~; 0 |; 2 &) % 0.54/0.61 % ( 5 <=>; 1 =>; 0 <=; 0 <~>) % 0.54/0.61 % Maximal formula depth : 7 ( 4 avg) % 0.54/0.61 % Maximal term depth : 2 ( 1 avg) % 0.54/0.61 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty) % 0.54/0.61 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty) % 0.54/0.61 % Number of variables : 16 ( 16 !; 0 ?) % 0.54/0.61 % SPC : FOF_THM_RFO_SEQ % 0.54/0.61 % 0.54/0.61 % Comments : % 0.54/0.61 %-------------------------------------------------------------------------- % 0.54/0.61 %---- line(boole - th(27),1833153) % 0.54/0.61 fof(empty_set_subset,axiom, % 0.54/0.61 ! [B] : subset(empty_set,B) ). % 0.54/0.61 % 0.54/0.61 %---- line(boole - th(45),1833405) % 0.54/0.61 fof(difference_empty_set,axiom, % 0.54/0.61 ! [B,C] : % 0.54/0.61 ( difference(B,C) = empty_set % 0.54/0.61 <=> subset(B,C) ) ). % 0.54/0.61 % 0.54/0.61 %---- line(hidden - axiom126,1832636) % 0.54/0.61 fof(empty_set_defn,axiom, % 0.54/0.61 ! [B] : ~ member(B,empty_set) ). % 0.54/0.61 % 0.54/0.61 %---- line(boole - df(4),1833078) % 0.54/0.61 fof(difference_defn,axiom, % 0.54/0.61 ! [B,C,D] : % 0.54/0.61 ( member(D,difference(B,C)) % 0.54/0.61 <=> ( member(D,B) % 0.54/0.61 & ~ member(D,C) ) ) ). % 0.54/0.61 % 0.54/0.61 %---- line(boole - df(8),1833103) % 0.54/0.61 fof(equal_defn,axiom, % 0.54/0.61 ! [B,C] : % 0.54/0.61 ( B = C % 0.54/0.61 <=> ( subset(B,C) % 0.54/0.61 & subset(C,B) ) ) ). % 0.54/0.61 % 0.54/0.61 %---- line(tarski - df(3),1832749) % 0.54/0.61 fof(subset_defn,axiom, % 0.54/0.61 ! [B,C] : % 0.54/0.61 ( subset(B,C) % 0.54/0.61 <=> ! [D] : % 0.54/0.61 ( member(D,B) % 0.54/0.61 => member(D,C) ) ) ). % 0.54/0.61 % 0.54/0.61 %---- property(reflexivity,op(subset,2,predicate)) % 0.54/0.61 fof(reflexivity_of_subset,axiom, % 0.54/0.61 ! [B] : subset(B,B) ). % 0.54/0.61 % 0.54/0.61 %---- line(hidden - axiom128,1832628) % 0.54/0.61 fof(empty_defn,axiom, % 0.54/0.61 ! [B] : % 0.54/0.61 ( empty(B) % 0.54/0.61 <=> ! [C] : ~ member(C,B) ) ). % 0.54/0.61 % 0.54/0.61 %---- line(boole - th(75),1833864) % 0.54/0.61 fof(prove_no_difference_with_empty_set,conjecture, % 0.54/0.61 ! [B] : difference(empty_set,B) = empty_set ). % 0.54/0.61 % 0.54/0.61 %-------------------------------------------------------------------------- % 0.54/0.61 %------------------------------------------- % 0.54/0.61 % Proof found % 0.54/0.61 % SZS status Theorem for theBenchmark % 0.54/0.61 % SZS output start Proof % 0.54/0.61 %ClaNum:30(EqnAxiom:13) % 0.54/0.61 %VarNum:61(SingletonVarNum:30) % 0.54/0.61 %MaxLitNum:3 % 0.54/0.61 %MaxfuncDepth:1 % 0.54/0.61 %SharedTerms:4 % 0.54/0.61 %goalClause: 16 % 0.54/0.61 %singleGoalClaCount:1 % 0.54/0.61 [16]~E(f2(a1,a3),a1) % 0.54/0.61 [14]P1(a1,x141) % 0.54/0.61 [15]P1(x151,x151) % 0.54/0.61 [17]~P2(x171,a1) % 0.54/0.61 [20]P3(x201)+P2(f4(x201),x201) % 0.54/0.61 [19]~E(x191,x192)+P1(x191,x192) % 0.54/0.61 [21]~P3(x211)+~P2(x212,x211) % 0.54/0.61 [22]~P1(x221,x222)+E(f2(x221,x222),a1) % 0.54/0.61 [23]P1(x231,x232)+~E(f2(x231,x232),a1) % 0.54/0.61 [25]P1(x251,x252)+P2(f5(x251,x252),x251) % 0.54/0.61 [29]P1(x291,x292)+~P2(f5(x291,x292),x292) % 0.54/0.61 [28]P2(x281,x282)+~P2(x281,f2(x282,x283)) % 0.54/0.61 [30]~P2(x301,x302)+~P2(x301,f2(x303,x302)) % 0.54/0.61 [24]~P1(x242,x241)+~P1(x241,x242)+E(x241,x242) % 0.54/0.61 [26]~P2(x261,x263)+P2(x261,x262)+~P1(x263,x262) % 0.54/0.61 [27]~P2(x271,x273)+P2(x271,x272)+P2(x271,f2(x273,x272)) % 0.54/0.61 %EqnAxiom % 0.54/0.61 [1]E(x11,x11) % 0.54/0.61 [2]E(x22,x21)+~E(x21,x22) % 0.54/0.61 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.54/0.61 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.54/0.61 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.54/0.61 [6]~E(x61,x62)+E(f4(x61),f4(x62)) % 0.54/0.61 [7]~E(x71,x72)+E(f5(x71,x73),f5(x72,x73)) % 0.54/0.61 [8]~E(x81,x82)+E(f5(x83,x81),f5(x83,x82)) % 0.54/0.61 [9]P1(x92,x93)+~E(x91,x92)+~P1(x91,x93) % 0.54/0.61 [10]P1(x103,x102)+~E(x101,x102)+~P1(x103,x101) % 0.54/0.61 [11]P2(x112,x113)+~E(x111,x112)+~P2(x111,x113) % 0.54/0.61 [12]P2(x123,x122)+~E(x121,x122)+~P2(x123,x121) % 0.54/0.61 [13]~P3(x131)+P3(x132)+~E(x131,x132) % 0.54/0.61 % 0.54/0.61 %------------------------------------------- % 0.54/0.61 cnf(32,plain, % 0.54/0.61 ($false), % 0.54/0.61 inference(scs_inference,[],[14,16,22]), % 0.54/0.61 ['proof']). % 0.54/0.61 % SZS output end Proof % 0.54/0.61 % Total time :0.000000s %------------------------------------------------------------------------------