%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET199+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 : n017.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 29.17s 29.25s % Output : CNFRefutation 29.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET199+3 : TPTP v8.2.0. Released v2.2.0. % 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n017.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 12:47:54 EDT 2024 % 0.12/0.33 % CPUTime : % 0.59/0.66 start to proof:theBenchmark % 29.17/29.25 %------------------------------------------- % 29.17/29.25 % File :CSE---1.7 % 29.17/29.25 % Problem :theBenchmark % 29.17/29.25 % Transform :cnf % 29.17/29.25 % Format :tptp:raw % 29.17/29.25 % Command :java -jar mcs_scs.jar %d %s % 29.17/29.25 % 29.17/29.25 % Result :Theorem 28.500000s % 29.17/29.25 % Output :CNFRefutation 28.500000s % 29.17/29.25 %------------------------------------------- % 29.17/29.25 %-------------------------------------------------------------------------- % 29.17/29.25 % File : SET199+3 : TPTP v8.2.0. Released v2.2.0. % 29.17/29.25 % Domain : Set Theory % 29.17/29.25 % Problem : If Z (= X and Z (= Y, then Z (= X ^ Y % 29.17/29.25 % Version : [Try90] axioms : Reduced > Incomplete. % 29.17/29.25 % English : If Z is a subset of X and Z is a subset of Y, then Z is a % 29.17/29.25 % subset of the intersection of X and Y. % 29.17/29.25 % 29.17/29.25 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 29.17/29.25 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 29.17/29.25 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 29.17/29.25 % Source : [ILF] % 29.17/29.25 % Names : BOOLE (39) [TS89] % 29.17/29.25 % 29.17/29.25 % Status : Theorem % 29.17/29.25 % Rating : 0.11 v8.1.0, 0.06 v7.4.0, 0.07 v7.2.0, 0.03 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, 0.10 v6.0.0, 0.09 v5.5.0, 0.11 v5.4.0, 0.18 v5.3.0, 0.22 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, 0.18 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1 % 29.17/29.25 % Syntax : Number of formulae : 6 ( 2 unt; 0 def) % 29.17/29.25 % Number of atoms : 14 ( 2 equ) % 29.17/29.25 % Maximal formula atoms : 3 ( 2 avg) % 29.17/29.25 % Number of connectives : 8 ( 0 ~; 0 |; 2 &) % 29.17/29.25 % ( 4 <=>; 2 =>; 0 <=; 0 <~>) % 29.17/29.25 % Maximal formula depth : 6 ( 5 avg) % 29.17/29.25 % Maximal term depth : 2 ( 1 avg) % 29.17/29.25 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty) % 29.17/29.25 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty) % 29.17/29.25 % Number of variables : 15 ( 15 !; 0 ?) % 29.17/29.25 % SPC : FOF_THM_RFO_SEQ % 29.17/29.25 % 29.17/29.25 % Comments : % 29.17/29.25 %-------------------------------------------------------------------------- % 29.17/29.25 %---- line(boole - df(3),1833060) % 29.17/29.25 fof(intersection_defn,axiom, % 29.17/29.25 ! [B,C,D] : % 29.17/29.25 ( member(D,intersection(B,C)) % 29.17/29.25 <=> ( member(D,B) % 29.17/29.25 & member(D,C) ) ) ). % 29.17/29.25 % 29.17/29.25 %---- line(tarski - df(3),1832749) % 29.17/29.25 fof(subset_defn,axiom, % 29.17/29.25 ! [B,C] : % 29.17/29.25 ( subset(B,C) % 29.17/29.25 <=> ! [D] : % 29.17/29.25 ( member(D,B) % 29.17/29.25 => member(D,C) ) ) ). % 29.17/29.25 % 29.17/29.25 %---- property(commutativity,op(intersection,2,function)) % 29.17/29.25 fof(commutativity_of_intersection,axiom, % 29.17/29.25 ! [B,C] : intersection(B,C) = intersection(C,B) ). % 29.17/29.25 % 29.17/29.25 %---- property(reflexivity,op(subset,2,predicate)) % 29.17/29.25 fof(reflexivity_of_subset,axiom, % 29.17/29.25 ! [B] : subset(B,B) ). % 29.17/29.25 % 29.17/29.25 %---- line(hidden - axiom49,1832615) % 29.17/29.25 fof(equal_member_defn,axiom, % 29.17/29.25 ! [B,C] : % 29.17/29.25 ( B = C % 29.17/29.25 <=> ! [D] : % 29.17/29.25 ( member(D,B) % 29.17/29.25 <=> member(D,C) ) ) ). % 29.17/29.25 % 29.17/29.25 %---- line(boole - th(39),1833302) % 29.17/29.25 fof(prove_intersection_of_subsets,conjecture, % 29.17/29.25 ! [B,C,D] : % 29.17/29.25 ( ( subset(B,C) % 29.17/29.25 & subset(B,D) ) % 29.17/29.25 => subset(B,intersection(C,D)) ) ). % 29.17/29.25 % 29.17/29.25 %-------------------------------------------------------------------------- % 29.17/29.25 %------------------------------------------- % 29.17/29.25 % Proof found % 29.17/29.25 % SZS status Theorem for theBenchmark % 29.17/29.25 % SZS output start Proof % 29.17/29.26 %ClaNum:26(EqnAxiom:13) % 29.17/29.26 %VarNum:55(SingletonVarNum:23) % 29.17/29.26 %MaxLitNum:3 % 29.17/29.26 %MaxfuncDepth:1 % 29.17/29.26 %SharedTerms:7 % 29.17/29.26 %goalClause: 14 15 18 % 29.17/29.26 %singleGoalClaCount:3 % 29.17/29.26 [14]P1(a1,a4) % 29.17/29.26 [15]P1(a1,a5) % 29.17/29.26 [18]~P1(a1,f6(a4,a5)) % 29.17/29.26 [16]P1(x161,x161) % 29.17/29.26 [17]E(f6(x171,x172),f6(x172,x171)) % 29.17/29.26 [19]P1(x191,x192)+P2(f2(x191,x192),x191) % 29.17/29.26 [23]P1(x231,x232)+~P2(f2(x231,x232),x232) % 29.17/29.26 [21]P2(x211,x212)+~P2(x211,f6(x213,x212)) % 29.17/29.26 [22]P2(x221,x222)+~P2(x221,f6(x222,x223)) % 29.17/29.26 [24]E(x241,x242)+P2(f3(x241,x242),x242)+P2(f3(x241,x242),x241) % 29.17/29.26 [26]E(x261,x262)+~P2(f3(x261,x262),x262)+~P2(f3(x261,x262),x261) % 29.17/29.26 [20]~P1(x203,x202)+P2(x201,x202)+~P2(x201,x203) % 29.17/29.26 [25]~P2(x251,x253)+~P2(x251,x252)+P2(x251,f6(x252,x253)) % 29.17/29.26 %EqnAxiom % 29.17/29.26 [1]E(x11,x11) % 29.17/29.26 [2]E(x22,x21)+~E(x21,x22) % 29.17/29.26 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 29.17/29.26 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43)) % 29.17/29.26 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52)) % 29.17/29.26 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63)) % 29.17/29.26 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72)) % 29.17/29.26 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83)) % 29.17/29.26 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92)) % 29.17/29.26 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103) % 29.17/29.26 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111) % 29.17/29.26 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123) % 29.17/29.26 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131) % 29.17/29.26 % 29.17/29.26 %------------------------------------------- % 29.17/29.26 cnf(40,plain, % 29.17/29.26 (P2(f2(a1,f6(a5,a4)),a1)), % 29.17/29.26 inference(scs_inference,[],[18,17,19,11])). % 29.17/29.26 cnf(41,plain, % 29.17/29.26 (P2(f2(a1,f6(a5,a4)),a4)), % 29.17/29.26 inference(scs_inference,[],[14,40,20])). % 29.17/29.26 cnf(103,plain, % 29.17/29.26 (P2(f2(a1,f6(a5,a4)),x1031)+~E(a5,x1031)), % 29.17/29.26 inference(scs_inference,[],[15,40,20,13])). % 29.17/29.26 cnf(202,plain, % 29.17/29.26 (P1(f6(x2021,x2022),f6(x2022,x2021))), % 29.17/29.26 inference(scs_inference,[],[17,16,2,10])). % 29.17/29.26 cnf(1394,plain, % 29.17/29.26 (~E(a5,x13941)+P2(f2(a1,f6(a5,a4)),f6(x13941,a4))), % 29.17/29.26 inference(scs_inference,[],[41,103,25])). % 29.17/29.26 cnf(1395,plain, % 29.17/29.26 (P2(f2(a1,f6(a5,a4)),f6(a5,a4))), % 29.17/29.26 inference(equality_inference,[],[1394])). % 29.17/29.26 cnf(1401,plain, % 29.17/29.26 ($false), % 29.17/29.26 inference(scs_inference,[],[18,202,17,1395,23,20,11]), % 29.17/29.26 ['proof']). % 29.17/29.27 % SZS output end Proof % 29.17/29.27 % Total time :28.500000s %------------------------------------------------------------------------------