%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET196+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 14:21:04 EDT 2024 % Result : Theorem 0.54s 0.64s % Output : CNFRefutation 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : SET196+3 : TPTP v8.2.0. Released v2.2.0. % 0.04/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.13/0.35 % Computer : n023.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sun Jun 23 17:14:39 EDT 2024 % 0.13/0.35 % CPUTime : % 0.47/0.59 start to proof:theBenchmark % 0.47/0.63 %------------------------------------------- % 0.47/0.63 % File :CSE---1.7 % 0.47/0.63 % Problem :theBenchmark % 0.47/0.63 % Transform :cnf % 0.47/0.63 % Format :tptp:raw % 0.47/0.63 % Command :java -jar mcs_scs.jar %d %s % 0.47/0.63 % 0.47/0.63 % Result :Theorem 0.010000s % 0.47/0.63 % Output :CNFRefutation 0.010000s % 0.47/0.63 %------------------------------------------- % 0.47/0.63 %-------------------------------------------------------------------------- % 0.47/0.63 % File : SET196+3 : TPTP v8.2.0. Released v2.2.0. % 0.47/0.63 % Domain : Set Theory % 0.47/0.63 % Problem : The intersection of X and Y is a subset of X % 0.47/0.63 % Version : [Try90] axioms : Reduced > Incomplete. % 0.47/0.63 % English : % 0.47/0.63 % 0.47/0.63 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.47/0.63 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.47/0.63 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.47/0.63 % Source : [ILF] % 0.47/0.63 % Names : BOOLE (37) [TS89] % 0.47/0.63 % 0.47/0.63 % Status : Theorem % 0.47/0.63 % Rating : 0.08 v7.5.0, 0.09 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.00 v7.0.0, 0.03 v6.4.0, 0.08 v6.3.0, 0.04 v6.2.0, 0.00 v6.1.0, 0.07 v6.0.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.15 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, 0.18 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1 % 0.47/0.63 % Syntax : Number of formulae : 6 ( 3 unt; 0 def) % 0.47/0.63 % Number of atoms : 12 ( 2 equ) % 0.47/0.63 % Maximal formula atoms : 3 ( 2 avg) % 0.47/0.63 % Number of connectives : 6 ( 0 ~; 0 |; 1 &) % 0.47/0.63 % ( 4 <=>; 1 =>; 0 <=; 0 <~>) % 0.47/0.63 % Maximal formula depth : 6 ( 4 avg) % 0.47/0.63 % Maximal term depth : 2 ( 1 avg) % 0.47/0.63 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty) % 0.47/0.64 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty) % 0.47/0.64 % Number of variables : 14 ( 14 !; 0 ?) % 0.47/0.64 % SPC : FOF_THM_RFO_SEQ % 0.47/0.64 % 0.47/0.64 % Comments : % 0.47/0.64 %-------------------------------------------------------------------------- % 0.47/0.64 %---- line(boole - df(3),1833060) % 0.47/0.64 fof(intersection_defn,axiom, % 0.54/0.64 ! [B,C,D] : % 0.54/0.64 ( member(D,intersection(B,C)) % 0.54/0.64 <=> ( member(D,B) % 0.54/0.64 & member(D,C) ) ) ). % 0.54/0.64 % 0.54/0.64 %---- line(tarski - df(3),1832749) % 0.54/0.64 fof(subset_defn,axiom, % 0.54/0.64 ! [B,C] : % 0.54/0.64 ( subset(B,C) % 0.54/0.64 <=> ! [D] : % 0.54/0.64 ( member(D,B) % 0.54/0.64 => member(D,C) ) ) ). % 0.54/0.64 % 0.54/0.64 %---- property(commutativity,op(intersection,2,function)) % 0.54/0.64 fof(commutativity_of_intersection,axiom, % 0.54/0.64 ! [B,C] : intersection(B,C) = intersection(C,B) ). % 0.54/0.64 % 0.54/0.64 %---- property(reflexivity,op(subset,2,predicate)) % 0.54/0.64 fof(reflexivity_of_subset,axiom, % 0.54/0.64 ! [B] : subset(B,B) ). % 0.54/0.64 % 0.54/0.64 %---- line(hidden - axiom45,1832615) % 0.54/0.64 fof(equal_member_defn,axiom, % 0.54/0.64 ! [B,C] : % 0.54/0.64 ( B = C % 0.54/0.64 <=> ! [D] : % 0.54/0.64 ( member(D,B) % 0.54/0.64 <=> member(D,C) ) ) ). % 0.54/0.64 % 0.54/0.64 %---- line(boole - th(37),1833277) % 0.54/0.64 fof(prove_intersection_is_subset,conjecture, % 0.54/0.64 ! [B,C] : subset(intersection(B,C),B) ). % 0.54/0.64 % 0.54/0.64 %-------------------------------------------------------------------------- % 0.54/0.64 %------------------------------------------- % 0.54/0.64 % Proof found % 0.54/0.64 % SZS status Theorem for theBenchmark % 0.54/0.64 % SZS output start Proof % 0.54/0.64 %ClaNum:24(EqnAxiom:13) % 0.54/0.64 %VarNum:55(SingletonVarNum:23) % 0.54/0.64 %MaxLitNum:3 % 0.54/0.64 %MaxfuncDepth:1 % 0.54/0.64 %SharedTerms:4 % 0.54/0.64 %goalClause: 16 % 0.54/0.64 %singleGoalClaCount:1 % 0.54/0.64 [16]~P1(f1(a2,a5),a2) % 0.54/0.64 [14]P1(x141,x141) % 0.54/0.64 [15]E(f1(x151,x152),f1(x152,x151)) % 0.54/0.64 [17]P1(x171,x172)+P2(f3(x171,x172),x171) % 0.54/0.64 [21]P1(x211,x212)+~P2(f3(x211,x212),x212) % 0.54/0.64 [19]P2(x191,x192)+~P2(x191,f1(x193,x192)) % 0.54/0.64 [20]P2(x201,x202)+~P2(x201,f1(x202,x203)) % 0.54/0.64 [22]E(x221,x222)+P2(f4(x221,x222),x222)+P2(f4(x221,x222),x221) % 0.54/0.64 [24]E(x241,x242)+~P2(f4(x241,x242),x242)+~P2(f4(x241,x242),x241) % 0.54/0.64 [18]~P1(x183,x182)+P2(x181,x182)+~P2(x181,x183) % 0.54/0.64 [23]~P2(x231,x233)+~P2(x231,x232)+P2(x231,f1(x232,x233)) % 0.54/0.64 %EqnAxiom % 0.54/0.64 [1]E(x11,x11) % 0.54/0.64 [2]E(x22,x21)+~E(x21,x22) % 0.54/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.54/0.64 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43)) % 0.54/0.64 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52)) % 0.54/0.64 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63)) % 0.54/0.64 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72)) % 0.54/0.64 [8]~E(x81,x82)+E(f3(x81,x83),f3(x82,x83)) % 0.54/0.64 [9]~E(x91,x92)+E(f3(x93,x91),f3(x93,x92)) % 0.54/0.64 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103) % 0.54/0.64 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111) % 0.54/0.64 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123) % 0.54/0.64 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131) % 0.54/0.64 % 0.54/0.64 %------------------------------------------- % 0.54/0.64 cnf(32,plain, % 0.54/0.64 (P2(f3(f1(a5,a2),a2),f1(a5,a2))), % 0.54/0.64 inference(scs_inference,[],[16,15,17,10])). % 0.54/0.64 cnf(39,plain, % 0.54/0.64 (P1(f1(a5,a2),a2)), % 0.54/0.64 inference(scs_inference,[],[15,32,19,20,13,21])). % 0.54/0.64 cnf(47,plain, % 0.54/0.64 ($false), % 0.54/0.64 inference(scs_inference,[],[15,16,39,10]), % 0.54/0.64 ['proof']). % 0.54/0.64 % SZS output end Proof % 0.54/0.64 % Total time :0.010000s %------------------------------------------------------------------------------