%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET175+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 14:21:00 EDT 2024 % Result : Theorem 117.61s 117.76s % Output : CNFRefutation 117.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SET175+3 : TPTP v8.2.0. Released v2.2.0. % 0.12/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n020.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sun Jun 23 14:16:39 EDT 2024 % 0.12/0.34 % CPUTime : % 0.54/0.58 start to proof:theBenchmark % 117.61/117.74 %------------------------------------------- % 117.61/117.74 % File :CSE---1.7 % 117.61/117.74 % Problem :theBenchmark % 117.61/117.74 % Transform :cnf % 117.61/117.74 % Format :tptp:raw % 117.61/117.74 % Command :java -jar mcs_scs.jar %d %s % 117.61/117.74 % 117.61/117.74 % Result :Theorem 117.020000s % 117.61/117.74 % Output :CNFRefutation 117.020000s % 117.61/117.74 %------------------------------------------- % 117.61/117.75 %-------------------------------------------------------------------------- % 117.61/117.75 % File : SET175+3 : TPTP v8.2.0. Released v2.2.0. % 117.61/117.75 % Domain : Set Theory % 117.61/117.75 % Problem : Absorbtion for union % 117.61/117.75 % Version : [Try90] axioms : Reduced > Incomplete. % 117.61/117.75 % English : The union of X and the intersection of X and Y is X. % 117.61/117.75 % 117.61/117.75 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 117.61/117.75 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 117.61/117.75 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 117.61/117.75 % Source : [ILF] % 117.61/117.75 % Names : BOOLE (69) [TS89] % 117.61/117.75 % 117.61/117.75 % Status : Theorem % 117.61/117.75 % Rating : 0.19 v8.2.0, 0.22 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.13 v7.3.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.17 v7.0.0, 0.20 v6.4.0, 0.19 v6.3.0, 0.25 v6.2.0, 0.24 v6.1.0, 0.33 v6.0.0, 0.35 v5.5.0, 0.41 v5.4.0, 0.46 v5.3.0, 0.52 v5.2.0, 0.35 v5.1.0, 0.33 v4.1.0, 0.22 v4.0.1, 0.26 v4.0.0, 0.25 v3.7.0, 0.20 v3.5.0, 0.21 v3.2.0, 0.18 v3.1.0, 0.22 v2.7.0, 0.00 v2.6.0, 0.14 v2.5.0, 0.12 v2.4.0, 0.00 v2.2.1 % 117.61/117.75 % Syntax : Number of formulae : 9 ( 4 unt; 0 def) % 117.61/117.75 % Number of atoms : 19 ( 5 equ) % 117.61/117.76 % Maximal formula atoms : 3 ( 2 avg) % 117.61/117.76 % Number of connectives : 10 ( 0 ~; 1 |; 2 &) % 117.61/117.76 % ( 6 <=>; 1 =>; 0 <=; 0 <~>) % 117.61/117.76 % Maximal formula depth : 6 ( 4 avg) % 117.61/117.76 % Maximal term depth : 3 ( 1 avg) % 117.61/117.76 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty) % 117.61/117.76 % Number of functors : 2 ( 2 usr; 0 con; 2-2 aty) % 117.61/117.76 % Number of variables : 21 ( 21 !; 0 ?) % 117.61/117.76 % SPC : FOF_THM_RFO_SEQ % 117.61/117.76 % 117.61/117.76 % Comments : % 117.61/117.76 %-------------------------------------------------------------------------- % 117.61/117.76 %---- line(boole - df(2),1833042) % 117.61/117.76 fof(union_defn,axiom, % 117.61/117.76 ! [B,C,D] : % 117.61/117.76 ( member(D,union(B,C)) % 117.61/117.76 <=> ( member(D,B) % 117.61/117.76 | member(D,C) ) ) ). % 117.61/117.76 % 117.61/117.76 %---- line(boole - df(3),1833060) % 117.61/117.76 fof(intersection_defn,axiom, % 117.61/117.76 ! [B,C,D] : % 117.61/117.76 ( member(D,intersection(B,C)) % 117.61/117.76 <=> ( member(D,B) % 117.61/117.76 & member(D,C) ) ) ). % 117.61/117.76 % 117.61/117.76 %---- line(boole - df(8),1833103) % 117.61/117.76 fof(equal_defn,axiom, % 117.61/117.76 ! [B,C] : % 117.61/117.76 ( B = C % 117.61/117.76 <=> ( subset(B,C) % 117.61/117.76 & subset(C,B) ) ) ). % 117.61/117.76 % 117.61/117.76 %---- property(commutativity,op(union,2,function)) % 117.61/117.76 fof(commutativity_of_union,axiom, % 117.61/117.76 ! [B,C] : union(B,C) = union(C,B) ). % 117.61/117.76 % 117.61/117.76 %---- property(commutativity,op(intersection,2,function)) % 117.61/117.76 fof(commutativity_of_intersection,axiom, % 117.61/117.76 ! [B,C] : intersection(B,C) = intersection(C,B) ). % 117.61/117.76 % 117.61/117.76 %---- line(tarski - df(3),1832749) % 117.61/117.76 fof(subset_defn,axiom, % 117.61/117.76 ! [B,C] : % 117.61/117.76 ( subset(B,C) % 117.61/117.76 <=> ! [D] : % 117.61/117.76 ( member(D,B) % 117.61/117.76 => member(D,C) ) ) ). % 117.61/117.76 % 117.61/117.76 %---- property(reflexivity,op(subset,2,predicate)) % 117.61/117.76 fof(reflexivity_of_subset,axiom, % 117.61/117.76 ! [B] : subset(B,B) ). % 117.61/117.76 % 117.61/117.76 %---- line(hidden - axiom112,1832615) % 117.61/117.76 fof(equal_member_defn,axiom, % 117.61/117.76 ! [B,C] : % 117.61/117.76 ( B = C % 117.61/117.76 <=> ! [D] : % 117.61/117.76 ( member(D,B) % 117.61/117.76 <=> member(D,C) ) ) ). % 117.61/117.76 % 117.61/117.76 %---- line(boole - th(69),1833784) % 117.61/117.76 fof(prove_absorbtion_for_union,conjecture, % 117.61/117.76 ! [B,C] : union(B,intersection(B,C)) = B ). % 117.61/117.76 % 117.61/117.76 %-------------------------------------------------------------------------- % 117.61/117.76 %------------------------------------------- % 117.61/117.76 % Proof found % 117.61/117.76 % SZS status Theorem for theBenchmark % 117.61/117.76 % SZS output start Proof % 117.61/117.77 %ClaNum:33(EqnAxiom:15) % 117.61/117.77 %VarNum:86(SingletonVarNum:38) % 117.61/117.77 %MaxLitNum:3 % 117.61/117.77 %MaxfuncDepth:2 % 117.61/117.77 %SharedTerms:5 % 117.61/117.77 %goalClause: 19 % 117.61/117.77 %singleGoalClaCount:1 % 117.61/117.77 [19]~E(f1(a3,f2(a3,a6)),a3) % 117.61/117.77 [16]P1(x161,x161) % 117.61/117.77 [17]E(f1(x171,x172),f1(x172,x171)) % 117.61/117.77 [18]E(f2(x181,x182),f2(x182,x181)) % 117.61/117.77 [21]~E(x211,x212)+P1(x211,x212) % 117.61/117.77 [23]P1(x231,x232)+P2(f4(x231,x232),x231) % 117.61/117.77 [29]P1(x291,x292)+~P2(f4(x291,x292),x292) % 117.61/117.77 [25]~P2(x251,x253)+P2(x251,f1(x252,x253)) % 117.61/117.77 [26]~P2(x261,x262)+P2(x261,f1(x262,x263)) % 117.61/117.77 [27]P2(x271,x272)+~P2(x271,f2(x273,x272)) % 117.61/117.77 [28]P2(x281,x282)+~P2(x281,f2(x282,x283)) % 117.61/117.77 [22]~P1(x222,x221)+~P1(x221,x222)+E(x221,x222) % 117.61/117.77 [30]E(x301,x302)+P2(f5(x301,x302),x302)+P2(f5(x301,x302),x301) % 117.61/117.77 [33]E(x331,x332)+~P2(f5(x331,x332),x332)+~P2(f5(x331,x332),x331) % 117.61/117.77 [24]~P1(x243,x242)+P2(x241,x242)+~P2(x241,x243) % 117.61/117.77 [31]~P2(x311,x313)+~P2(x311,x312)+P2(x311,f2(x312,x313)) % 117.61/117.77 [32]P2(x321,x322)+P2(x321,x323)+~P2(x321,f1(x323,x322)) % 117.61/117.77 %EqnAxiom % 117.61/117.77 [1]E(x11,x11) % 117.61/117.77 [2]E(x22,x21)+~E(x21,x22) % 117.61/117.77 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 117.61/117.77 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43)) % 117.61/117.77 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52)) % 117.61/117.77 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63)) % 117.61/117.77 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72)) % 117.61/117.77 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83)) % 117.61/117.77 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92)) % 117.61/117.77 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103)) % 117.61/117.77 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112)) % 117.61/117.77 [12]P1(x122,x123)+~E(x121,x122)+~P1(x121,x123) % 117.61/117.77 [13]P1(x133,x132)+~E(x131,x132)+~P1(x133,x131) % 117.61/117.77 [14]P2(x142,x143)+~E(x141,x142)+~P2(x141,x143) % 117.61/117.77 [15]P2(x153,x152)+~E(x151,x152)+~P2(x153,x151) % 117.61/117.77 % 117.61/117.77 %------------------------------------------- % 117.61/117.79 cnf(35,plain, % 117.61/117.79 (P1(f1(x351,x352),f1(x352,x351))), % 117.61/117.79 inference(scs_inference,[],[16,17,12])). % 117.61/117.79 cnf(39,plain, % 117.61/117.79 (E(f1(f1(x391,x392),x393),f1(f1(x392,x391),x393))), % 117.61/117.79 inference(scs_inference,[],[17,2,4])). % 117.61/117.79 cnf(42,plain, % 117.61/117.79 (P1(f1(f1(x421,x422),x423),f1(x423,f1(x422,x421)))), % 117.61/117.79 inference(scs_inference,[],[16,39,35,13,12])). % 117.61/117.79 cnf(45,plain, % 117.61/117.79 (P1(f1(f1(x451,x452),f1(x453,x454)),f1(f1(x454,x453),f1(x452,x451)))), % 117.61/117.79 inference(scs_inference,[],[39,42,13])). % 117.61/117.79 cnf(51,plain, % 117.61/117.79 (P1(f1(x511,f1(x512,x513)),f1(f1(x513,x512),x511))), % 117.61/117.79 inference(scs_inference,[],[39,35,13])). % 117.61/117.79 cnf(54,plain, % 117.61/117.79 (P1(f1(x541,x542),x543)+~P2(f4(f1(x542,x541),x543),x543)), % 117.61/117.79 inference(scs_inference,[],[17,29,12])). % 117.61/117.79 cnf(56,plain, % 117.61/117.79 (E(f1(x561,x562),f1(x562,x561))), % 117.61/117.79 inference(rename_variables,[],[17])). % 117.61/117.79 cnf(57,plain, % 117.61/117.79 (P1(f1(x571,f1(x572,x573)),f1(x571,f1(x573,x572)))), % 117.61/117.79 inference(scs_inference,[],[17,56,45,51,12,13])). % 117.61/117.79 cnf(69,plain, % 117.61/117.79 (~E(a3,f1(f2(a3,a6),a3))), % 117.61/117.79 inference(scs_inference,[],[19,17,3,2])). % 117.61/117.79 cnf(96,plain, % 117.61/117.79 (E(f1(f2(x961,x962),x963),f1(f2(x962,x961),x963))), % 117.61/117.79 inference(scs_inference,[],[18,2,4])). % 117.61/117.79 cnf(97,plain, % 117.61/117.79 (~E(a3,f1(f2(a6,a3),a3))), % 117.61/117.79 inference(scs_inference,[],[96,69,3])). % 117.61/117.79 cnf(98,plain, % 117.61/117.79 (E(f1(f2(x981,x982),x983),f1(f2(x982,x981),x983))), % 117.61/117.79 inference(rename_variables,[],[96])). % 117.61/117.79 cnf(101,plain, % 117.61/117.79 (E(f1(f2(x1011,x1012),x1013),f1(f2(x1012,x1011),x1013))), % 117.61/117.79 inference(rename_variables,[],[96])). % 117.61/117.79 cnf(102,plain, % 117.61/117.79 (P1(f1(x1021,f2(x1022,x1023)),f1(f2(x1023,x1022),x1021))), % 117.61/117.79 inference(scs_inference,[],[96,98,101,69,57,35,3,12,13])). % 117.61/117.79 cnf(107,plain, % 117.61/117.79 (E(f1(f2(x1071,x1072),x1073),f1(f2(x1072,x1071),x1073))), % 117.61/117.79 inference(rename_variables,[],[96])). % 117.61/117.79 cnf(108,plain, % 117.61/117.79 (P1(f1(f1(x1081,x1082),f2(x1083,x1084)),f1(f2(x1084,x1083),f1(x1082,x1081)))), % 117.61/117.79 inference(scs_inference,[],[96,107,102,42,12,13])). % 117.61/117.79 cnf(143,plain, % 117.61/117.79 (E(f1(f2(x1431,x1432),x1433),f1(f2(x1432,x1431),x1433))), % 117.61/117.79 inference(rename_variables,[],[96])). % 117.61/117.79 cnf(148,plain, % 117.61/117.79 (E(f1(f2(x1481,x1482),f1(x1483,x1484)),f1(f1(x1484,x1483),f2(x1481,x1482)))), % 117.61/117.79 inference(scs_inference,[],[96,143,108,51,16,12,13,22,3])). % 117.61/117.79 cnf(152,plain, % 117.61/117.79 (E(f1(f1(x1521,x1522),f2(x1523,x1524)),f1(f2(x1523,x1524),f1(x1522,x1521)))), % 117.61/117.79 inference(scs_inference,[],[148,2])). % 117.61/117.79 cnf(213,plain, % 117.61/117.79 (E(f5(f1(f2(x2131,x2132),f1(x2133,x2134)),x2135),f5(f1(f1(x2134,x2133),f2(x2131,x2132)),x2135))), % 117.61/117.79 inference(scs_inference,[],[152,2,6])). % 117.61/117.79 cnf(1068,plain, % 117.61/117.79 (P1(f1(x10681,x10682),x10683)+P2(f4(f1(x10681,x10682),x10683),x10682)+P2(f4(f1(x10681,x10682),x10683),x10681)), % 117.61/117.79 inference(scs_inference,[],[23,32])). % 117.61/117.79 cnf(1501,plain, % 117.61/117.79 (~P2(f4(x15011,f1(x15012,x15013)),x15013)+P1(x15011,f1(x15012,x15013))), % 117.61/117.79 inference(scs_inference,[],[25,29])). % 117.61/117.79 cnf(1502,plain, % 117.61/117.79 (P1(x15021,f1(x15022,x15021))), % 117.61/117.79 inference(scs_inference,[],[1501,23])). % 117.61/117.79 cnf(1575,plain, % 117.61/117.79 (~P1(f1(f2(a6,a3),a3),a3)), % 117.61/117.79 inference(scs_inference,[],[97,1502,22])). % 117.61/117.79 cnf(1721,plain, % 117.61/117.79 (P2(f4(f1(f2(a6,a3),a3),a3),a3)), % 117.61/117.79 inference(scs_inference,[],[1575,27,1068])). % 117.61/117.79 cnf(1857,plain, % 117.61/117.79 (~P1(f1(a3,f2(a6,a3)),a3)), % 117.61/117.79 inference(scs_inference,[],[17,1575,12])). % 117.61/117.79 cnf(2256,plain, % 117.61/117.79 ($false), % 117.61/117.79 inference(scs_inference,[],[1857,1721,213,2,54]), % 117.61/117.79 ['proof']). % 117.61/117.79 % SZS output end Proof % 117.61/117.79 % Total time :117.020000s %------------------------------------------------------------------------------