%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET639+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 : n022.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 14:22:06 EDT 2024 % Result : Theorem 0.54s 0.66s % Output : CNFRefutation 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SET639+3 : TPTP v8.2.0. Released v2.2.0. % 0.03/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n022.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sun Jun 23 12:00:24 EDT 2024 % 0.13/0.35 % CPUTime : % 0.50/0.58 start to proof:theBenchmark % 0.54/0.65 %------------------------------------------- % 0.54/0.65 % File :CSE---1.7 % 0.54/0.65 % Problem :theBenchmark % 0.54/0.65 % Transform :cnf % 0.54/0.65 % Format :tptp:raw % 0.54/0.65 % Command :java -jar mcs_scs.jar %d %s % 0.54/0.65 % 0.54/0.65 % Result :Theorem 0.000000s % 0.54/0.65 % Output :CNFRefutation 0.000000s % 0.54/0.65 %------------------------------------------- % 0.54/0.66 %-------------------------------------------------------------------------- % 0.54/0.66 % File : SET639+3 : TPTP v8.2.0. Released v2.2.0. % 0.54/0.66 % Domain : Set Theory % 0.54/0.66 % Problem : Trybulec's 121th Boolean property of sets % 0.54/0.66 % Version : [Try89] axioms : Reduced > Incomplete. % 0.54/0.66 % English : % 0.54/0.66 % 0.54/0.66 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.54/0.66 % : [Try89] Trybulec (1989), Tarski Grothendieck Set Theory % 0.54/0.66 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.54/0.66 % Source : [ILF] % 0.54/0.66 % Names : BOOLE (121) [TS89] % 0.54/0.66 % 0.54/0.66 % Status : Theorem % 0.54/0.66 % Rating : 0.03 v8.1.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.08 v6.2.0, 0.04 v6.1.0, 0.07 v6.0.0, 0.09 v5.5.0, 0.04 v5.3.0, 0.15 v5.2.0, 0.00 v5.0.0, 0.08 v4.1.0, 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 % 0.54/0.66 % Syntax : Number of formulae : 10 ( 3 unt; 0 def) % 0.54/0.66 % Number of atoms : 22 ( 6 equ) % 0.54/0.66 % Maximal formula atoms : 3 ( 2 avg) % 0.54/0.66 % Number of connectives : 14 ( 2 ~; 0 |; 3 &) % 0.54/0.66 % ( 6 <=>; 3 =>; 0 <=; 0 <~>) % 0.54/0.66 % Maximal formula depth : 6 ( 5 avg) % 0.54/0.66 % Maximal term depth : 2 ( 1 avg) % 0.54/0.66 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty) % 0.54/0.66 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty) % 0.54/0.66 % Number of variables : 21 ( 21 !; 0 ?) % 0.54/0.66 % SPC : FOF_THM_RFO_SEQ % 0.54/0.66 % 0.54/0.66 % Comments : % 0.54/0.66 %-------------------------------------------------------------------------- % 0.54/0.66 %---- line(boole - th(42),1833351) % 0.54/0.66 fof(subset_intersection,axiom, % 0.54/0.66 ! [B,C] : % 0.54/0.66 ( subset(B,C) % 0.54/0.66 => intersection(B,C) = B ) ). % 0.54/0.66 % 0.54/0.66 %---- line(hidden - axiom232,1832636) % 0.54/0.66 fof(empty_set_defn,axiom, % 0.54/0.66 ! [B] : ~ member(B,empty_set) ). % 0.54/0.66 % 0.54/0.66 %---- line(boole - df(3),1833060) % 0.54/0.66 fof(intersection_defn,axiom, % 0.54/0.66 ! [B,C,D] : % 0.54/0.66 ( member(D,intersection(B,C)) % 0.54/0.66 <=> ( member(D,B) % 0.54/0.66 & member(D,C) ) ) ). % 0.54/0.66 % 0.54/0.66 %---- line(tarski - df(3),1832749) % 0.54/0.66 fof(subset_defn,axiom, % 0.54/0.66 ! [B,C] : % 0.54/0.66 ( subset(B,C) % 0.54/0.66 <=> ! [D] : % 0.54/0.66 ( member(D,B) % 0.54/0.66 => member(D,C) ) ) ). % 0.54/0.66 % 0.54/0.66 %---- line(boole - df(8),1833103) % 0.54/0.66 fof(equal_defn,axiom, % 0.54/0.66 ! [B,C] : % 0.54/0.66 ( B = C % 0.54/0.66 <=> ( subset(B,C) % 0.54/0.66 & subset(C,B) ) ) ). % 0.54/0.66 % 0.54/0.66 %---- property(commutativity,op(intersection,2,function)) % 0.54/0.66 fof(commutativity_of_intersection,axiom, % 0.54/0.66 ! [B,C] : intersection(B,C) = intersection(C,B) ). % 0.54/0.66 % 0.54/0.66 %---- property(reflexivity,op(subset,2,predicate)) % 0.54/0.66 fof(reflexivity_of_subset,axiom, % 0.54/0.66 ! [B] : subset(B,B) ). % 0.54/0.66 % 0.54/0.66 %---- line(hidden - axiom234,1832628) % 0.54/0.66 fof(empty_defn,axiom, % 0.54/0.66 ! [B] : % 0.54/0.66 ( empty(B) % 0.54/0.66 <=> ! [C] : ~ member(C,B) ) ). % 0.54/0.66 % 0.54/0.66 %---- line(hidden - axiom235,1832615) % 0.54/0.66 fof(equal_member_defn,axiom, % 0.54/0.66 ! [B,C] : % 0.54/0.66 ( B = C % 0.54/0.66 <=> ! [D] : % 0.54/0.66 ( member(D,B) % 0.54/0.66 <=> member(D,C) ) ) ). % 0.54/0.66 % 0.54/0.66 %---- line(boole - th(121),1834507) % 0.54/0.66 fof(prove_th121,conjecture, % 0.54/0.66 ! [B,C] : % 0.54/0.66 ( ( subset(B,C) % 0.54/0.66 & intersection(C,B) = empty_set ) % 0.54/0.66 => B = empty_set ) ). % 0.54/0.66 % 0.54/0.66 %-------------------------------------------------------------------------- % 0.54/0.66 %------------------------------------------- % 0.54/0.66 % Proof found % 0.54/0.66 % SZS status Theorem for theBenchmark % 0.54/0.66 % SZS output start Proof % 0.54/0.66 %ClaNum:35(EqnAxiom:15) % 0.54/0.66 %VarNum:77(SingletonVarNum:33) % 0.54/0.66 %MaxLitNum:3 % 0.54/0.66 %MaxfuncDepth:1 % 0.54/0.66 %SharedTerms:7 % 0.54/0.66 %goalClause: 16 17 20 % 0.54/0.66 %singleGoalClaCount:3 % 0.54/0.66 [17]P1(a2,a1) % 0.54/0.66 [20]~E(a3,a2) % 0.54/0.66 [16]E(f7(a1,a2),a3) % 0.54/0.66 [18]P1(x181,x181) % 0.54/0.66 [21]~P2(x211,a3) % 0.54/0.66 [19]E(f7(x191,x192),f7(x192,x191)) % 0.54/0.66 [24]P3(x241)+P2(f4(x241),x241) % 0.54/0.66 [23]~E(x231,x232)+P1(x231,x232) % 0.54/0.66 [25]~P3(x251)+~P2(x252,x251) % 0.54/0.66 [26]~P1(x261,x262)+E(f7(x261,x262),x261) % 0.54/0.66 [28]P1(x281,x282)+P2(f5(x281,x282),x281) % 0.54/0.66 [32]P1(x321,x322)+~P2(f5(x321,x322),x322) % 0.54/0.66 [30]P2(x301,x302)+~P2(x301,f7(x303,x302)) % 0.54/0.66 [31]P2(x311,x312)+~P2(x311,f7(x312,x313)) % 0.54/0.66 [27]~P1(x272,x271)+~P1(x271,x272)+E(x271,x272) % 0.54/0.66 [33]E(x331,x332)+P2(f6(x331,x332),x332)+P2(f6(x331,x332),x331) % 0.54/0.66 [35]E(x351,x352)+~P2(f6(x351,x352),x352)+~P2(f6(x351,x352),x351) % 0.54/0.66 [29]~P2(x291,x293)+P2(x291,x292)+~P1(x293,x292) % 0.54/0.66 [34]~P2(x341,x343)+~P2(x341,x342)+P2(x341,f7(x342,x343)) % 0.54/0.66 %EqnAxiom % 0.54/0.66 [1]E(x11,x11) % 0.54/0.66 [2]E(x22,x21)+~E(x21,x22) % 0.54/0.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.54/0.66 [4]~E(x41,x42)+E(f7(x41,x43),f7(x42,x43)) % 0.54/0.66 [5]~E(x51,x52)+E(f7(x53,x51),f7(x53,x52)) % 0.54/0.66 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63)) % 0.54/0.66 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72)) % 0.54/0.66 [8]~E(x81,x82)+E(f5(x81,x83),f5(x82,x83)) % 0.54/0.66 [9]~E(x91,x92)+E(f5(x93,x91),f5(x93,x92)) % 0.54/0.66 [10]~E(x101,x102)+E(f4(x101),f4(x102)) % 0.54/0.66 [11]P1(x112,x113)+~E(x111,x112)+~P1(x111,x113) % 0.54/0.66 [12]P1(x123,x122)+~E(x121,x122)+~P1(x123,x121) % 0.54/0.66 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133) % 0.54/0.66 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141) % 0.54/0.66 [15]~P3(x151)+P3(x152)+~E(x151,x152) % 0.54/0.66 % 0.54/0.66 %------------------------------------------- % 0.54/0.67 cnf(39,plain, % 0.54/0.67 (~P2(x391,a3)), % 0.54/0.67 inference(rename_variables,[],[21])). % 0.54/0.67 cnf(44,plain, % 0.54/0.67 (E(f7(a2,a1),a3)), % 0.54/0.67 inference(scs_inference,[],[16,21,39,19,2,24,28,3])). % 0.54/0.67 cnf(46,plain, % 0.54/0.67 (P1(f7(a1,a2),x461)), % 0.54/0.67 inference(scs_inference,[],[16,21,39,19,2,24,28,3,11])). % 0.54/0.67 cnf(47,plain, % 0.54/0.67 (~P1(a2,a3)), % 0.54/0.67 inference(scs_inference,[],[16,20,21,39,19,2,24,28,3,11,27])). % 0.54/0.67 cnf(49,plain, % 0.54/0.67 (P3(f7(a1,a2))), % 0.54/0.67 inference(scs_inference,[],[16,20,21,39,19,2,24,28,3,11,27,15])). % 0.54/0.67 cnf(50,plain, % 0.54/0.67 (~E(a2,a3)), % 0.54/0.67 inference(scs_inference,[],[16,20,21,39,19,2,24,28,3,11,27,15,23])). % 0.54/0.67 cnf(67,plain, % 0.54/0.67 (P1(f7(a2,a1),x671)), % 0.54/0.67 inference(scs_inference,[],[16,50,46,44,49,47,19,2,3,11,15,25,28])). % 0.54/0.67 cnf(80,plain, % 0.54/0.67 ($false), % 0.54/0.67 inference(scs_inference,[],[17,50,44,47,67,3,11,26]), % 0.54/0.67 ['proof']). % 0.54/0.67 % SZS output end Proof % 0.54/0.67 % Total time :0.000000s %------------------------------------------------------------------------------