%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET592+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 : n023.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 14:21:52 EDT 2024 % Result : Theorem 0.53s 0.63s % Output : CNFRefutation 0.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET592+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 : n023.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 14:05:39 EDT 2024 % 0.12/0.33 % CPUTime : % 0.51/0.57 start to proof:theBenchmark % 0.53/0.62 %------------------------------------------- % 0.53/0.62 % File :CSE---1.7 % 0.53/0.62 % Problem :theBenchmark % 0.53/0.62 % Transform :cnf % 0.53/0.62 % Format :tptp:raw % 0.53/0.62 % Command :java -jar mcs_scs.jar %d %s % 0.53/0.62 % 0.53/0.62 % Result :Theorem 0.010000s % 0.53/0.62 % Output :CNFRefutation 0.010000s % 0.53/0.62 %------------------------------------------- % 0.53/0.62 %-------------------------------------------------------------------------- % 0.53/0.62 % File : SET592+3 : TPTP v8.2.0. Released v2.2.0. % 0.53/0.62 % Domain : Set Theory % 0.53/0.62 % Problem : If X (= Y and X (= Z and Y ^ Z = empty set, then X = empty set % 0.53/0.62 % Version : [Try90] axioms : Reduced > Incomplete. % 0.53/0.62 % English : If X is a subset of Y and X is a subset of Z and the % 0.53/0.62 % intersection of Y and Z is the empty set, then X is the empty % 0.53/0.62 % set. % 0.53/0.62 % 0.53/0.62 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.53/0.62 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.53/0.62 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.53/0.62 % Source : [ILF] % 0.53/0.62 % Names : BOOLE (51) [TS89] % 0.53/0.62 % 0.53/0.62 % Status : Theorem % 0.53/0.62 % Rating : 0.06 v8.1.0, 0.03 v7.4.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.08 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.07 v5.3.0, 0.19 v5.2.0, 0.00 v5.0.0, 0.04 v4.0.1, 0.09 v4.0.0, 0.08 v3.7.0, 0.05 v3.3.0, 0.07 v3.2.0, 0.09 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1 % 0.53/0.62 % Syntax : Number of formulae : 11 ( 3 unt; 0 def) % 0.53/0.62 % Number of atoms : 26 ( 6 equ) % 0.53/0.62 % Maximal formula atoms : 4 ( 2 avg) % 0.53/0.62 % Number of connectives : 17 ( 2 ~; 0 |; 5 &) % 0.53/0.62 % ( 6 <=>; 4 =>; 0 <=; 0 <~>) % 0.53/0.62 % Maximal formula depth : 7 ( 5 avg) % 0.53/0.62 % Maximal term depth : 2 ( 1 avg) % 0.53/0.62 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty) % 0.53/0.62 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty) % 0.53/0.62 % Number of variables : 24 ( 24 !; 0 ?) % 0.53/0.62 % SPC : FOF_THM_RFO_SEQ % 0.53/0.62 % 0.53/0.62 % Comments : % 0.53/0.62 %-------------------------------------------------------------------------- % 0.53/0.62 %---- line(boole - th(30),1833179) % 0.53/0.62 fof(subset_of_empty_set_is_empty_set,axiom, % 0.53/0.62 ! [B] : % 0.53/0.62 ( subset(B,empty_set) % 0.53/0.62 => B = empty_set ) ). % 0.53/0.62 % 0.53/0.62 %---- line(boole - th(39),1833302) % 0.53/0.62 fof(intersection_of_subsets,axiom, % 0.53/0.62 ! [B,C,D] : % 0.53/0.62 ( ( subset(B,C) % 0.53/0.62 & subset(B,D) ) % 0.53/0.62 => subset(B,intersection(C,D)) ) ). % 0.53/0.62 % 0.53/0.62 %---- line(hidden - axiom69,1832636) % 0.53/0.62 fof(empty_set_defn,axiom, % 0.53/0.62 ! [B] : ~ member(B,empty_set) ). % 0.53/0.62 % 0.53/0.62 %---- line(boole - df(3),1833060) % 0.53/0.62 fof(intersection_defn,axiom, % 0.53/0.62 ! [B,C,D] : % 0.53/0.62 ( member(D,intersection(B,C)) % 0.53/0.62 <=> ( member(D,B) % 0.53/0.62 & member(D,C) ) ) ). % 0.53/0.62 % 0.53/0.62 %---- line(tarski - df(3),1832749) % 0.53/0.62 fof(subset_defn,axiom, % 0.53/0.62 ! [B,C] : % 0.53/0.62 ( subset(B,C) % 0.53/0.62 <=> ! [D] : % 0.53/0.62 ( member(D,B) % 0.53/0.62 => member(D,C) ) ) ). % 0.53/0.62 % 0.53/0.62 %---- line(boole - df(8),1833103) % 0.53/0.62 fof(equal_defn,axiom, % 0.53/0.62 ! [B,C] : % 0.53/0.62 ( B = C % 0.53/0.62 <=> ( subset(B,C) % 0.53/0.62 & subset(C,B) ) ) ). % 0.53/0.62 % 0.53/0.62 %---- property(commutativity,op(intersection,2,function)) % 0.53/0.62 fof(commutativity_of_intersection,axiom, % 0.53/0.62 ! [B,C] : intersection(B,C) = intersection(C,B) ). % 0.53/0.62 % 0.53/0.62 %---- property(reflexivity,op(subset,2,predicate)) % 0.53/0.62 fof(reflexivity_of_subset,axiom, % 0.53/0.62 ! [B] : subset(B,B) ). % 0.53/0.62 % 0.53/0.62 %---- line(hidden - axiom71,1832628) % 0.53/0.62 fof(empty_defn,axiom, % 0.53/0.62 ! [B] : % 0.53/0.63 ( empty(B) % 0.53/0.63 <=> ! [C] : ~ member(C,B) ) ). % 0.53/0.63 % 0.53/0.63 %---- line(hidden - axiom72,1832615) % 0.53/0.63 fof(equal_member_defn,axiom, % 0.53/0.63 ! [B,C] : % 0.53/0.63 ( B = C % 0.53/0.63 <=> ! [D] : % 0.53/0.63 ( member(D,B) % 0.53/0.63 <=> member(D,C) ) ) ). % 0.53/0.63 % 0.53/0.63 %---- line(boole - th(51),1833491) % 0.53/0.63 fof(prove_th51,conjecture, % 0.53/0.63 ! [B,C,D] : % 0.53/0.63 ( ( subset(B,C) % 0.53/0.63 & subset(B,D) % 0.53/0.63 & intersection(C,D) = empty_set ) % 0.53/0.63 => B = empty_set ) ). % 0.53/0.63 % 0.53/0.63 %-------------------------------------------------------------------------- % 0.53/0.63 %------------------------------------------- % 0.53/0.63 % Proof found % 0.53/0.63 % SZS status Theorem for theBenchmark % 0.53/0.63 % SZS output start Proof % 0.53/0.63 %ClaNum:37(EqnAxiom:15) % 0.53/0.63 %VarNum:81(SingletonVarNum:35) % 0.53/0.63 %MaxLitNum:3 % 0.53/0.63 %MaxfuncDepth:1 % 0.53/0.63 %SharedTerms:9 % 0.53/0.63 %goalClause: 16 17 18 21 % 0.53/0.63 %singleGoalClaCount:4 % 0.53/0.63 [17]P1(a3,a1) % 0.53/0.63 [18]P1(a3,a7) % 0.53/0.63 [21]~E(a3,a2) % 0.53/0.63 [16]E(f8(a1,a7),a2) % 0.53/0.63 [19]P1(x191,x191) % 0.53/0.63 [22]~P2(x221,a2) % 0.53/0.63 [20]E(f8(x201,x202),f8(x202,x201)) % 0.53/0.63 [25]~P1(x251,a2)+E(x251,a2) % 0.53/0.63 [26]P3(x261)+P2(f4(x261),x261) % 0.53/0.63 [24]~E(x241,x242)+P1(x241,x242) % 0.53/0.63 [27]~P3(x271)+~P2(x272,x271) % 0.53/0.63 [29]P1(x291,x292)+P2(f5(x291,x292),x291) % 0.53/0.63 [33]P1(x331,x332)+~P2(f5(x331,x332),x332) % 0.53/0.63 [31]P2(x311,x312)+~P2(x311,f8(x313,x312)) % 0.53/0.63 [32]P2(x321,x322)+~P2(x321,f8(x322,x323)) % 0.53/0.63 [28]~P1(x282,x281)+~P1(x281,x282)+E(x281,x282) % 0.53/0.63 [34]E(x341,x342)+P2(f6(x341,x342),x342)+P2(f6(x341,x342),x341) % 0.53/0.63 [37]E(x371,x372)+~P2(f6(x371,x372),x372)+~P2(f6(x371,x372),x371) % 0.53/0.63 [30]~P2(x301,x303)+P2(x301,x302)+~P1(x303,x302) % 0.53/0.63 [35]~P1(x351,x353)+~P1(x351,x352)+P1(x351,f8(x352,x353)) % 0.53/0.63 [36]~P2(x361,x363)+~P2(x361,x362)+P2(x361,f8(x362,x363)) % 0.53/0.63 %EqnAxiom % 0.53/0.63 [1]E(x11,x11) % 0.53/0.63 [2]E(x22,x21)+~E(x21,x22) % 0.53/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.53/0.63 [4]~E(x41,x42)+E(f8(x41,x43),f8(x42,x43)) % 0.53/0.63 [5]~E(x51,x52)+E(f8(x53,x51),f8(x53,x52)) % 0.53/0.63 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63)) % 0.53/0.63 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72)) % 0.53/0.63 [8]~E(x81,x82)+E(f5(x81,x83),f5(x82,x83)) % 0.53/0.63 [9]~E(x91,x92)+E(f5(x93,x91),f5(x93,x92)) % 0.53/0.63 [10]~E(x101,x102)+E(f4(x101),f4(x102)) % 0.53/0.63 [11]P1(x112,x113)+~E(x111,x112)+~P1(x111,x113) % 0.53/0.63 [12]P1(x123,x122)+~E(x121,x122)+~P1(x123,x121) % 0.53/0.63 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133) % 0.53/0.63 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141) % 0.53/0.63 [15]~P3(x151)+P3(x152)+~E(x151,x152) % 0.53/0.63 % 0.53/0.63 %------------------------------------------- % 0.53/0.63 cnf(40,plain, % 0.53/0.63 (~P1(a3,a2)), % 0.53/0.63 inference(scs_inference,[],[16,21,2,25])). % 0.53/0.63 cnf(43,plain, % 0.53/0.63 (~P2(x431,a2)), % 0.53/0.63 inference(rename_variables,[],[22])). % 0.53/0.63 cnf(48,plain, % 0.53/0.63 (~E(a3,f8(a1,a7))), % 0.53/0.63 inference(scs_inference,[],[16,21,22,43,2,25,26,29,3])). % 0.53/0.63 cnf(51,plain, % 0.53/0.63 (~E(a1,a2)), % 0.53/0.63 inference(scs_inference,[],[16,17,21,19,22,43,2,25,26,29,3,11,12])). % 0.53/0.63 cnf(52,plain, % 0.53/0.63 (P3(f8(a1,a7))), % 0.53/0.63 inference(scs_inference,[],[16,17,21,19,22,43,2,25,26,29,3,11,12,15])). % 0.53/0.63 cnf(53,plain, % 0.53/0.63 (~P2(x531,f8(a1,a7))), % 0.53/0.63 inference(scs_inference,[],[16,17,21,19,22,43,2,25,26,29,3,11,12,15,27])). % 0.53/0.63 cnf(61,plain, % 0.53/0.63 (P1(f8(a1,a7),x611)), % 0.53/0.63 inference(scs_inference,[],[53,29])). % 0.53/0.63 cnf(67,plain, % 0.53/0.63 (E(f8(x671,x672),f8(x672,x671))), % 0.53/0.63 inference(rename_variables,[],[20])). % 0.53/0.63 cnf(68,plain, % 0.53/0.63 (~E(f8(a1,a7),a3)), % 0.53/0.63 inference(scs_inference,[],[51,53,40,20,52,29,25,15,11])). % 0.53/0.63 cnf(71,plain, % 0.53/0.63 (~E(a7,a2)), % 0.53/0.63 inference(scs_inference,[],[18,48,51,53,40,20,67,52,29,25,15,11,3,12])). % 0.53/0.63 cnf(72,plain, % 0.53/0.63 (~P2(x721,f8(a7,a1))), % 0.53/0.63 inference(scs_inference,[],[18,48,51,53,40,20,67,52,29,25,15,11,3,12,27])). % 0.53/0.63 cnf(85,plain, % 0.53/0.63 (~P2(x851,f8(a7,a1))), % 0.53/0.63 inference(rename_variables,[],[72])). % 0.53/0.63 cnf(98,plain, % 0.53/0.63 ($false), % 0.53/0.63 inference(scs_inference,[],[17,18,68,71,22,40,72,85,61,29,25,34,28,11,2,35]), % 0.53/0.63 ['proof']). % 0.53/0.63 % SZS output end Proof % 0.53/0.63 % Total time :0.010000s %------------------------------------------------------------------------------