%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET596+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 : n020.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 14:21:54 EDT 2024 % Result : Theorem 0.61s 0.72s % Output : CNFRefutation 0.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.15/0.15 % Problem : SET596+3 : TPTP v8.2.0. Released v2.2.0. % 0.15/0.15 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.15/0.37 % Computer : n020.cluster.edu % 0.15/0.37 % Model : x86_64 x86_64 % 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.37 % Memory : 8042.1875MB % 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.37 % CPULimit : 300 % 0.15/0.37 % WCLimit : 300 % 0.15/0.37 % DateTime : Sun Jun 23 15:36:09 EDT 2024 % 0.15/0.37 % CPUTime : % 0.57/0.66 start to proof:theBenchmark % 0.61/0.71 %------------------------------------------- % 0.61/0.71 % File :CSE---1.7 % 0.61/0.71 % Problem :theBenchmark % 0.61/0.71 % Transform :cnf % 0.61/0.71 % Format :tptp:raw % 0.61/0.71 % Command :java -jar mcs_scs.jar %d %s % 0.61/0.71 % 0.61/0.71 % Result :Theorem 0.000000s % 0.61/0.71 % Output :CNFRefutation 0.000000s % 0.61/0.71 %------------------------------------------- % 0.61/0.72 %-------------------------------------------------------------------------- % 0.61/0.72 % File : SET596+3 : TPTP v8.2.0. Released v2.2.0. % 0.61/0.72 % Domain : Set Theory % 0.61/0.72 % Problem : If X (= Y and Y ^ Z = the empty set, then X ^ Z = the empty set % 0.61/0.72 % Version : [Try90] axioms : Reduced > Incomplete. % 0.61/0.72 % English : If X is a subset of Y and the intersection of Y and Z is the % 0.61/0.72 % empty set, then the intersection of X and Z is the empty set. % 0.61/0.72 % 0.61/0.72 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.61/0.72 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.61/0.72 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.61/0.72 % Source : [ILF] % 0.61/0.72 % Names : BOOLE (55) [TS89] % 0.61/0.72 % 0.61/0.72 % Status : Theorem % 0.61/0.72 % Rating : 0.06 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.20 v6.0.0, 0.17 v5.5.0, 0.07 v5.3.0, 0.19 v5.2.0, 0.00 v5.0.0, 0.12 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.12 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.07 v3.2.0, 0.09 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1 % 0.61/0.72 % Syntax : Number of formulae : 11 ( 3 unt; 0 def) % 0.61/0.72 % Number of atoms : 24 ( 6 equ) % 0.61/0.72 % Maximal formula atoms : 3 ( 2 avg) % 0.61/0.72 % Number of connectives : 15 ( 2 ~; 0 |; 3 &) % 0.61/0.72 % ( 6 <=>; 4 =>; 0 <=; 0 <~>) % 0.61/0.72 % Maximal formula depth : 6 ( 5 avg) % 0.61/0.72 % Maximal term depth : 2 ( 1 avg) % 0.61/0.72 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty) % 0.61/0.72 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty) % 0.61/0.72 % Number of variables : 24 ( 24 !; 0 ?) % 0.61/0.72 % SPC : FOF_THM_RFO_SEQ % 0.61/0.72 % 0.61/0.72 % Comments : % 0.61/0.72 %-------------------------------------------------------------------------- % 0.61/0.72 %---- line(boole - th(30),1833179) % 0.61/0.72 fof(subset_of_empty_set_is_empty_set,axiom, % 0.61/0.72 ! [B] : % 0.61/0.72 ( subset(B,empty_set) % 0.61/0.72 => B = empty_set ) ). % 0.61/0.72 % 0.61/0.72 %---- line(boole - th(40),1833318) % 0.61/0.72 fof(intersection_of_subset,axiom, % 0.61/0.72 ! [B,C,D] : % 0.61/0.72 ( subset(B,C) % 0.61/0.72 => subset(intersection(B,D),intersection(C,D)) ) ). % 0.61/0.72 % 0.61/0.72 %---- line(hidden - axiom79,1832636) % 0.61/0.72 fof(empty_set_defn,axiom, % 0.61/0.72 ! [B] : ~ member(B,empty_set) ). % 0.61/0.72 % 0.61/0.72 %---- line(boole - df(3),1833060) % 0.61/0.72 fof(intersection_defn,axiom, % 0.61/0.72 ! [B,C,D] : % 0.61/0.72 ( member(D,intersection(B,C)) % 0.61/0.72 <=> ( member(D,B) % 0.61/0.72 & member(D,C) ) ) ). % 0.61/0.72 % 0.61/0.72 %---- line(tarski - df(3),1832749) % 0.61/0.72 fof(subset_defn,axiom, % 0.61/0.72 ! [B,C] : % 0.61/0.72 ( subset(B,C) % 0.61/0.72 <=> ! [D] : % 0.61/0.72 ( member(D,B) % 0.61/0.72 => member(D,C) ) ) ). % 0.61/0.72 % 0.61/0.72 %---- line(boole - df(8),1833103) % 0.61/0.72 fof(equal_defn,axiom, % 0.61/0.72 ! [B,C] : % 0.61/0.72 ( B = C % 0.61/0.72 <=> ( subset(B,C) % 0.61/0.72 & subset(C,B) ) ) ). % 0.61/0.72 % 0.61/0.72 %---- property(commutativity,op(intersection,2,function)) % 0.61/0.72 fof(commutativity_of_intersection,axiom, % 0.61/0.72 ! [B,C] : intersection(B,C) = intersection(C,B) ). % 0.61/0.72 % 0.61/0.72 %---- property(reflexivity,op(subset,2,predicate)) % 0.61/0.72 fof(reflexivity_of_subset,axiom, % 0.61/0.72 ! [B] : subset(B,B) ). % 0.61/0.72 % 0.61/0.72 %---- line(hidden - axiom81,1832628) % 0.61/0.72 fof(empty_defn,axiom, % 0.61/0.72 ! [B] : % 0.61/0.72 ( empty(B) % 0.61/0.72 <=> ! [C] : ~ member(C,B) ) ). % 0.61/0.72 % 0.61/0.72 %---- line(hidden - axiom82,1832615) % 0.61/0.72 fof(equal_member_defn,axiom, % 0.61/0.72 ! [B,C] : % 0.61/0.72 ( B = C % 0.61/0.72 <=> ! [D] : % 0.61/0.72 ( member(D,B) % 0.61/0.72 <=> member(D,C) ) ) ). % 0.61/0.72 % 0.61/0.72 %---- line(boole - th(55),1833564) % 0.61/0.72 fof(prove_th55,conjecture, % 0.61/0.72 ! [B,C,D] : % 0.61/0.72 ( ( subset(B,C) % 0.61/0.72 & intersection(C,D) = empty_set ) % 0.61/0.72 => intersection(B,D) = empty_set ) ). % 0.61/0.72 % 0.61/0.72 %-------------------------------------------------------------------------- % 0.61/0.72 %------------------------------------------- % 0.61/0.72 % Proof found % 0.61/0.72 % SZS status Theorem for theBenchmark % 0.61/0.72 % SZS output start Proof % 0.61/0.72 %ClaNum:36(EqnAxiom:15) % 0.61/0.72 %VarNum:80(SingletonVarNum:35) % 0.61/0.72 %MaxLitNum:3 % 0.61/0.72 %MaxfuncDepth:1 % 0.61/0.72 %SharedTerms:9 % 0.61/0.72 %goalClause: 16 17 20 % 0.61/0.72 %singleGoalClaCount:3 % 0.61/0.72 [17]P1(a3,a1) % 0.61/0.72 [16]E(f8(a1,a7),a2) % 0.61/0.72 [20]~E(f8(a3,a7),a2) % 0.61/0.72 [18]P1(x181,x181) % 0.61/0.72 [21]~P2(x211,a2) % 0.61/0.72 [19]E(f8(x191,x192),f8(x192,x191)) % 0.61/0.72 [24]~P1(x241,a2)+E(x241,a2) % 0.61/0.72 [25]P3(x251)+P2(f4(x251),x251) % 0.61/0.72 [23]~E(x231,x232)+P1(x231,x232) % 0.61/0.72 [26]~P3(x261)+~P2(x262,x261) % 0.61/0.72 [28]P1(x281,x282)+P2(f5(x281,x282),x281) % 0.61/0.72 [32]P1(x321,x322)+~P2(f5(x321,x322),x322) % 0.61/0.72 [30]P2(x301,x302)+~P2(x301,f8(x303,x302)) % 0.61/0.72 [31]P2(x311,x312)+~P2(x311,f8(x312,x313)) % 0.61/0.72 [35]~P1(x351,x353)+P1(f8(x351,x352),f8(x353,x352)) % 0.61/0.72 [27]~P1(x272,x271)+~P1(x271,x272)+E(x271,x272) % 0.61/0.72 [33]E(x331,x332)+P2(f6(x331,x332),x332)+P2(f6(x331,x332),x331) % 0.61/0.72 [36]E(x361,x362)+~P2(f6(x361,x362),x362)+~P2(f6(x361,x362),x361) % 0.61/0.72 [29]~P2(x291,x293)+P2(x291,x292)+~P1(x293,x292) % 0.61/0.72 [34]~P2(x341,x343)+~P2(x341,x342)+P2(x341,f8(x342,x343)) % 0.61/0.72 %EqnAxiom % 0.61/0.72 [1]E(x11,x11) % 0.61/0.72 [2]E(x22,x21)+~E(x21,x22) % 0.61/0.72 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.61/0.72 [4]~E(x41,x42)+E(f8(x41,x43),f8(x42,x43)) % 0.61/0.72 [5]~E(x51,x52)+E(f8(x53,x51),f8(x53,x52)) % 0.61/0.72 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63)) % 0.61/0.72 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72)) % 0.61/0.72 [8]~E(x81,x82)+E(f5(x81,x83),f5(x82,x83)) % 0.61/0.72 [9]~E(x91,x92)+E(f5(x93,x91),f5(x93,x92)) % 0.61/0.72 [10]~E(x101,x102)+E(f4(x101),f4(x102)) % 0.61/0.72 [11]P1(x112,x113)+~E(x111,x112)+~P1(x111,x113) % 0.61/0.72 [12]P1(x123,x122)+~E(x121,x122)+~P1(x123,x121) % 0.61/0.72 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133) % 0.61/0.72 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141) % 0.61/0.72 [15]~P3(x151)+P3(x152)+~E(x151,x152) % 0.61/0.72 % 0.61/0.72 %------------------------------------------- % 0.61/0.73 cnf(39,plain, % 0.61/0.73 (~P1(f8(a3,a7),a2)), % 0.61/0.73 inference(scs_inference,[],[16,20,2,24])). % 0.61/0.73 cnf(42,plain, % 0.61/0.73 (~P2(x421,a2)), % 0.61/0.73 inference(rename_variables,[],[21])). % 0.61/0.73 cnf(47,plain, % 0.61/0.73 (~E(f8(a3,a7),f8(a1,a7))), % 0.61/0.73 inference(scs_inference,[],[16,20,21,42,2,24,25,28,3])). % 0.61/0.73 cnf(50,plain, % 0.61/0.73 (P3(f8(a1,a7))), % 0.61/0.73 inference(scs_inference,[],[16,20,18,21,42,2,24,25,28,3,11,15])). % 0.61/0.73 cnf(52,plain, % 0.61/0.73 (~P2(x521,f8(a1,a7))), % 0.61/0.73 inference(scs_inference,[],[16,20,18,21,42,2,24,25,28,3,11,15,4,26])). % 0.61/0.73 cnf(55,plain, % 0.61/0.73 (~P1(a1,a3)), % 0.61/0.73 inference(scs_inference,[],[16,17,20,18,21,42,2,24,25,28,3,11,15,4,26,12,27])). % 0.61/0.73 cnf(68,plain, % 0.61/0.73 (P1(f8(a1,a7),x681)), % 0.61/0.73 inference(scs_inference,[],[52,55,23,28])). % 0.61/0.73 cnf(72,plain, % 0.61/0.73 (E(f8(x721,x722),f8(x722,x721))), % 0.61/0.73 inference(rename_variables,[],[19])). % 0.61/0.73 cnf(75,plain, % 0.61/0.73 (~E(f8(a1,a7),f8(a3,a7))), % 0.61/0.73 inference(scs_inference,[],[47,52,39,19,72,50,55,23,28,15,3,11])). % 0.61/0.73 cnf(76,plain, % 0.61/0.73 (~P2(x761,f8(a7,a1))), % 0.61/0.73 inference(scs_inference,[],[47,52,39,19,72,50,55,23,28,15,3,11,26])). % 0.61/0.73 cnf(87,plain, % 0.61/0.73 (~P2(x871,f8(a7,a1))), % 0.61/0.73 inference(rename_variables,[],[76])). % 0.61/0.73 cnf(97,plain, % 0.61/0.73 ($false), % 0.61/0.73 inference(scs_inference,[],[17,75,21,76,87,68,39,28,27,33,11,35]), % 0.61/0.73 ['proof']). % 0.61/0.73 % SZS output end Proof % 0.61/0.73 % Total time :0.000000s %------------------------------------------------------------------------------