%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET063+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 : 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 14:20:25 EDT 2024 % Result : Theorem 0.53s 0.60s % Output : CNFRefutation 0.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET063+3 : TPTP v8.2.0. Released v2.2.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.11/0.33 % Computer : n001.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Sun Jun 23 16:01:38 EDT 2024 % 0.11/0.33 % CPUTime : % 0.53/0.56 start to proof:theBenchmark % 0.53/0.59 %------------------------------------------- % 0.53/0.59 % File :CSE---1.7 % 0.53/0.59 % Problem :theBenchmark % 0.53/0.59 % Transform :cnf % 0.53/0.59 % Format :tptp:raw % 0.53/0.59 % Command :java -jar mcs_scs.jar %d %s % 0.53/0.59 % 0.53/0.59 % Result :Theorem 0.000000s % 0.53/0.59 % Output :CNFRefutation 0.000000s % 0.53/0.59 %------------------------------------------- % 0.53/0.60 %-------------------------------------------------------------------------- % 0.53/0.60 % File : SET063+3 : TPTP v8.2.0. Released v2.2.0. % 0.53/0.60 % Domain : Set Theory % 0.53/0.60 % Problem : If X is a subset of the empty set, then X is the empty set % 0.53/0.60 % Version : [Try90] axioms : Reduced > Incomplete. % 0.53/0.60 % English : % 0.53/0.60 % 0.53/0.60 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.53/0.60 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.53/0.60 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.53/0.60 % Source : [ILF] % 0.53/0.60 % Names : BOOLE (30) [TS89] % 0.53/0.60 % 0.53/0.60 % Status : Theorem % 0.53/0.60 % Rating : 0.00 v6.1.0, 0.03 v6.0.0, 0.00 v5.3.0, 0.07 v5.2.0, 0.00 v2.5.0, 0.33 v2.4.0, 0.33 v2.2.1 % 0.53/0.60 % Syntax : Number of formulae : 7 ( 3 unt; 0 def) % 0.53/0.60 % Number of atoms : 13 ( 2 equ) % 0.53/0.60 % Maximal formula atoms : 3 ( 1 avg) % 0.53/0.60 % Number of connectives : 8 ( 2 ~; 0 |; 1 &) % 0.53/0.60 % ( 3 <=>; 2 =>; 0 <=; 0 <~>) % 0.53/0.60 % Maximal formula depth : 6 ( 4 avg) % 0.53/0.60 % Maximal term depth : 1 ( 1 avg) % 0.53/0.60 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty) % 0.53/0.60 % Number of functors : 1 ( 1 usr; 1 con; 0-0 aty) % 0.53/0.60 % Number of variables : 11 ( 11 !; 0 ?) % 0.53/0.60 % SPC : FOF_THM_RFO_SEQ % 0.53/0.60 % 0.53/0.60 % Comments : % 0.53/0.60 %-------------------------------------------------------------------------- % 0.53/0.60 %---- line(boole - th(27),1833153) % 0.53/0.60 fof(empty_set_subset,axiom, % 0.53/0.60 ! [B] : subset(empty_set,B) ). % 0.53/0.60 % 0.53/0.60 %---- line(hidden - axiom31,1832636) % 0.53/0.60 fof(empty_set_defn,axiom, % 0.53/0.60 ! [B] : ~ member(B,empty_set) ). % 0.53/0.60 % 0.53/0.60 %---- line(tarski - df(3),1832749) % 0.53/0.60 fof(subset_defn,axiom, % 0.53/0.60 ! [B,C] : % 0.53/0.60 ( subset(B,C) % 0.53/0.60 <=> ! [D] : % 0.53/0.60 ( member(D,B) % 0.53/0.60 => member(D,C) ) ) ). % 0.53/0.60 % 0.53/0.60 %---- line(boole - df(8),1833103) % 0.53/0.60 fof(equal_defn,axiom, % 0.53/0.60 ! [B,C] : % 0.53/0.60 ( B = C % 0.53/0.60 <=> ( subset(B,C) % 0.53/0.60 & subset(C,B) ) ) ). % 0.53/0.60 % 0.53/0.60 %---- property(reflexivity,op(subset,2,predicate)) % 0.53/0.60 fof(reflexivity_of_subset,axiom, % 0.53/0.60 ! [B] : subset(B,B) ). % 0.53/0.60 % 0.53/0.60 %---- line(hidden - axiom33,1832628) % 0.53/0.60 fof(empty_defn,axiom, % 0.53/0.60 ! [B] : % 0.53/0.60 ( empty(B) % 0.53/0.60 <=> ! [C] : ~ member(C,B) ) ). % 0.53/0.60 % 0.53/0.60 %---- line(boole - th(30),1833179) % 0.53/0.60 fof(prove_subset_of_empty_set_is_empty_set,conjecture, % 0.53/0.60 ! [B] : % 0.53/0.60 ( subset(B,empty_set) % 0.53/0.60 => B = empty_set ) ). % 0.53/0.60 % 0.53/0.60 %-------------------------------------------------------------------------- % 0.53/0.60 %------------------------------------------- % 0.53/0.60 % Proof found % 0.53/0.60 % SZS status Theorem for theBenchmark % 0.53/0.60 % SZS output start Proof % 0.53/0.60 %ClaNum:24(EqnAxiom:11) % 0.53/0.60 %VarNum:36(SingletonVarNum:17) % 0.53/0.60 %MaxLitNum:3 % 0.53/0.60 %MaxfuncDepth:1 % 0.53/0.60 %SharedTerms:4 % 0.53/0.60 %goalClause: 12 15 % 0.53/0.60 %singleGoalClaCount:2 % 0.53/0.60 [12]P1(a1,a2) % 0.53/0.60 [15]~E(a1,a2) % 0.53/0.60 [13]P1(a2,x131) % 0.53/0.60 [14]P1(x141,x141) % 0.53/0.60 [16]~P2(x161,a2) % 0.53/0.60 [19]P3(x191)+P2(f3(x191),x191) % 0.53/0.60 [18]~E(x181,x182)+P1(x181,x182) % 0.53/0.60 [20]~P3(x201)+~P2(x202,x201) % 0.53/0.60 [22]P1(x221,x222)+P2(f4(x221,x222),x221) % 0.53/0.60 [24]P1(x241,x242)+~P2(f4(x241,x242),x242) % 0.53/0.60 [21]~P1(x212,x211)+~P1(x211,x212)+E(x211,x212) % 0.53/0.60 [23]~P2(x231,x233)+P2(x231,x232)+~P1(x233,x232) % 0.53/0.60 %EqnAxiom % 0.53/0.60 [1]E(x11,x11) % 0.53/0.60 [2]E(x22,x21)+~E(x21,x22) % 0.53/0.60 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.53/0.60 [4]~E(x41,x42)+E(f3(x41),f3(x42)) % 0.53/0.60 [5]~E(x51,x52)+E(f4(x51,x53),f4(x52,x53)) % 0.53/0.60 [6]~E(x61,x62)+E(f4(x63,x61),f4(x63,x62)) % 0.53/0.60 [7]P1(x72,x73)+~E(x71,x72)+~P1(x71,x73) % 0.53/0.60 [8]P1(x83,x82)+~E(x81,x82)+~P1(x83,x81) % 0.53/0.60 [9]P2(x92,x93)+~E(x91,x92)+~P2(x91,x93) % 0.53/0.60 [10]P2(x103,x102)+~E(x101,x102)+~P2(x103,x101) % 0.53/0.60 [11]~P3(x111)+P3(x112)+~E(x111,x112) % 0.53/0.60 % 0.53/0.60 %------------------------------------------- % 0.53/0.60 cnf(29,plain, % 0.53/0.60 ($false), % 0.53/0.60 inference(scs_inference,[],[12,15,13,16,19,21]), % 0.53/0.60 ['proof']). % 0.53/0.60 % SZS output end Proof % 0.53/0.60 % Total time :0.000000s %------------------------------------------------------------------------------