%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET630+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 : 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 14:22:03 EDT 2024 % Result : Theorem 0.67s 0.71s % Output : CNFRefutation 0.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET630+3 : TPTP v8.2.0. Released v2.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.32 % Computer : n022.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Sun Jun 23 15:35:09 EDT 2024 % 0.12/0.32 % CPUTime : % 0.20/0.56 start to proof:theBenchmark % 0.20/0.71 %------------------------------------------- % 0.20/0.71 % File :CSE---1.7 % 0.20/0.71 % Problem :theBenchmark % 0.20/0.71 % Transform :cnf % 0.20/0.71 % Format :tptp:raw % 0.20/0.71 % Command :java -jar mcs_scs.jar %d %s % 0.20/0.71 % 0.20/0.71 % Result :Theorem 0.110000s % 0.20/0.71 % Output :CNFRefutation 0.110000s % 0.20/0.71 %------------------------------------------- % 0.67/0.71 %------------------------------------------------------------------------------ % 0.67/0.71 % File : SET630+3 : TPTP v8.2.0. Released v2.2.0. % 0.67/0.71 % Domain : Set Theory % 0.67/0.71 % Problem : X ^ Y is disjoint from X sym\ Y % 0.67/0.71 % Version : [Try90] axioms : Reduced > Incomplete. % 0.67/0.71 % English : The intersection of X and Y is disjoint from the symmetric % 0.67/0.71 % difference of X and Y. % 0.67/0.71 % 0.67/0.71 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.67/0.71 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.67/0.71 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.67/0.71 % Source : [ILF] % 0.67/0.71 % Names : BOOLE (112) [TS89] % 0.67/0.71 % 0.67/0.71 % Status : Theorem % 0.67/0.71 % Rating : 0.22 v8.2.0, 0.19 v8.1.0, 0.22 v7.5.0, 0.25 v7.4.0, 0.13 v7.3.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.13 v6.4.0, 0.15 v6.3.0, 0.08 v6.2.0, 0.16 v6.1.0, 0.27 v6.0.0, 0.22 v5.5.0, 0.26 v5.4.0, 0.29 v5.3.0, 0.30 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.21 v4.1.0, 0.22 v4.0.1, 0.26 v4.0.0, 0.25 v3.5.0, 0.26 v3.4.0, 0.32 v3.3.0, 0.29 v3.2.0, 0.36 v3.1.0, 0.44 v2.7.0, 0.33 v2.6.0, 0.43 v2.5.0, 0.38 v2.4.0, 0.50 v2.3.0, 0.33 v2.2.1 % 0.67/0.71 % Syntax : Number of formulae : 12 ( 6 unt; 0 def) % 0.67/0.71 % Number of atoms : 22 ( 5 equ) % 0.67/0.71 % Maximal formula atoms : 3 ( 1 avg) % 0.67/0.71 % Number of connectives : 11 ( 1 ~; 1 |; 2 &) % 0.67/0.71 % ( 6 <=>; 1 =>; 0 <=; 0 <~>) % 0.67/0.71 % Maximal formula depth : 6 ( 4 avg) % 0.67/0.71 % Maximal term depth : 3 ( 1 avg) % 0.67/0.71 % Number of predicates : 4 ( 3 usr; 0 prp; 2-2 aty) % 0.67/0.71 % Number of functors : 4 ( 4 usr; 0 con; 2-2 aty) % 0.67/0.71 % Number of variables : 28 ( 27 !; 1 ?) % 0.67/0.71 % SPC : FOF_THM_RFO_SEQ % 0.67/0.71 % 0.67/0.71 % Comments : % 0.67/0.71 %------------------------------------------------------------------------------ % 0.67/0.71 %---- line(boole - df(7),1833089) % 0.67/0.71 fof(symmetric_difference_defn,axiom, % 0.67/0.71 ! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) ). % 0.67/0.71 % 0.67/0.71 %---- line(boole - th(100),1834297) % 0.67/0.71 fof(intersect_with_union,axiom, % 0.67/0.71 ! [B,C,D] : % 0.67/0.71 ( intersect(B,union(C,D)) % 0.67/0.71 <=> ( intersect(B,C) % 0.67/0.71 | intersect(B,D) ) ) ). % 0.67/0.71 % 0.67/0.71 %---- line(boole - th(111),1834358) % 0.67/0.71 fof(intersection_and_union_disjoint,axiom, % 0.67/0.71 ! [B,C] : disjoint(intersection(B,C),difference(B,C)) ). % 0.67/0.71 % 0.67/0.71 %---- line(boole - df(3),1833060) % 0.67/0.71 fof(intersection_defn,axiom, % 0.67/0.71 ! [B,C,D] : % 0.67/0.71 ( member(D,intersection(B,C)) % 0.67/0.71 <=> ( member(D,B) % 0.67/0.71 & member(D,C) ) ) ). % 0.67/0.71 % 0.67/0.71 %---- line(boole - df(5),1833080) % 0.67/0.71 fof(intersect_defn,axiom, % 0.67/0.71 ! [B,C] : % 0.67/0.71 ( intersect(B,C) % 0.67/0.71 <=> ? [D] : % 0.67/0.71 ( member(D,B) % 0.67/0.71 & member(D,C) ) ) ). % 0.67/0.71 % 0.67/0.71 %---- line(boole - axiom202,1833083) % 0.67/0.71 fof(disjoint_defn,axiom, % 0.67/0.71 ! [B,C] : % 0.67/0.71 ( disjoint(B,C) % 0.67/0.71 <=> ~ intersect(B,C) ) ). % 0.67/0.71 % 0.67/0.71 %---- property(commutativity,op(union,2,function)) % 0.67/0.71 fof(commutativity_of_union,axiom, % 0.67/0.71 ! [B,C] : union(B,C) = union(C,B) ). % 0.67/0.71 % 0.67/0.71 %---- property(commutativity,op(intersection,2,function)) % 0.67/0.71 fof(commutativity_of_intersection,axiom, % 0.67/0.71 ! [B,C] : intersection(B,C) = intersection(C,B) ). % 0.67/0.71 % 0.67/0.71 %---- property(commutativity,op(symmetric_difference,2,function)) % 0.67/0.71 fof(commutativity_of_symmetric_difference,axiom, % 0.67/0.71 ! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B) ). % 0.67/0.71 % 0.67/0.71 %---- property(symmetry,op(intersect,2,predicate)) % 0.67/0.71 fof(symmetry_of_intersect,axiom, % 0.67/0.71 ! [B,C] : % 0.67/0.71 ( intersect(B,C) % 0.67/0.71 => intersect(C,B) ) ). % 0.67/0.71 % 0.67/0.71 %---- line(hidden - axiom203,1832615) % 0.67/0.71 fof(equal_member_defn,axiom, % 0.67/0.71 ! [B,C] : % 0.67/0.71 ( B = C % 0.67/0.71 <=> ! [D] : % 0.67/0.71 ( member(D,B) % 0.67/0.71 <=> member(D,C) ) ) ). % 0.67/0.71 % 0.67/0.71 %---- line(boole - th(112),1834367) % 0.67/0.71 fof(prove_intersection_and_symmetric_difference_disjoint,conjecture, % 0.67/0.71 ! [B,C] : disjoint(intersection(B,C),symmetric_difference(B,C)) ). % 0.67/0.71 % 0.67/0.71 %------------------------------------------------------------------------------ % 0.67/0.71 %------------------------------------------- % 0.67/0.71 % Proof found % 0.67/0.71 % SZS status Theorem for theBenchmark % 0.67/0.71 % SZS output start Proof % 0.67/0.71 %ClaNum:38(EqnAxiom:19) % 0.67/0.71 %VarNum:90(SingletonVarNum:41) % 0.67/0.71 %MaxLitNum:3 % 0.67/0.71 %MaxfuncDepth:2 % 0.67/0.71 %SharedTerms:7 % 0.67/0.71 %goalClause: 24 % 0.67/0.71 %singleGoalClaCount:1 % 0.67/0.71 [24]~P1(f2(a4,a7),f1(f3(a4,a7),f3(a7,a4))) % 0.67/0.71 [20]E(f1(x201,x202),f1(x202,x201)) % 0.67/0.71 [21]E(f2(x211,x212),f2(x212,x211)) % 0.67/0.71 [22]P1(f2(x221,x222),f3(x221,x222)) % 0.67/0.71 [25]P1(x251,x252)+P2(x251,x252) % 0.67/0.71 [26]~P2(x262,x261)+P2(x261,x262) % 0.67/0.71 [27]~P1(x271,x272)+~P2(x271,x272) % 0.67/0.71 [31]~P2(x311,x312)+P3(f5(x311,x312),x312) % 0.67/0.72 [32]~P2(x321,x322)+P3(f5(x321,x322),x321) % 0.67/0.72 [29]~P2(x291,x293)+P2(x291,f1(x292,x293)) % 0.67/0.72 [30]~P2(x301,x302)+P2(x301,f1(x302,x303)) % 0.67/0.72 [33]P3(x331,x332)+~P3(x331,f2(x333,x332)) % 0.67/0.72 [34]P3(x341,x342)+~P3(x341,f2(x342,x343)) % 0.67/0.72 [35]E(x351,x352)+P3(f6(x351,x352),x352)+P3(f6(x351,x352),x351) % 0.67/0.72 [38]E(x381,x382)+~P3(f6(x381,x382),x382)+~P3(f6(x381,x382),x381) % 0.67/0.72 [28]~P3(x283,x281)+P2(x281,x282)+~P3(x283,x282) % 0.67/0.72 [36]~P3(x361,x363)+~P3(x361,x362)+P3(x361,f2(x362,x363)) % 0.67/0.72 [37]P2(x371,x372)+P2(x371,x373)+~P2(x371,f1(x373,x372)) % 0.67/0.72 %EqnAxiom % 0.67/0.72 [1]E(x11,x11) % 0.67/0.72 [2]E(x22,x21)+~E(x21,x22) % 0.67/0.72 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.67/0.72 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43)) % 0.67/0.72 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52)) % 0.67/0.72 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63)) % 0.67/0.72 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72)) % 0.67/0.72 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83)) % 0.67/0.72 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92)) % 0.67/0.72 [10]~E(x101,x102)+E(f5(x101,x103),f5(x102,x103)) % 0.67/0.72 [11]~E(x111,x112)+E(f5(x113,x111),f5(x113,x112)) % 0.67/0.72 [12]~E(x121,x122)+E(f3(x121,x123),f3(x122,x123)) % 0.67/0.72 [13]~E(x131,x132)+E(f3(x133,x131),f3(x133,x132)) % 0.67/0.72 [14]P1(x142,x143)+~E(x141,x142)+~P1(x141,x143) % 0.67/0.72 [15]P1(x153,x152)+~E(x151,x152)+~P1(x153,x151) % 0.67/0.72 [16]P3(x162,x163)+~E(x161,x162)+~P3(x161,x163) % 0.67/0.72 [17]P3(x173,x172)+~E(x171,x172)+~P3(x173,x171) % 0.67/0.72 [18]P2(x182,x183)+~E(x181,x182)+~P2(x181,x183) % 0.67/0.72 [19]P2(x193,x192)+~E(x191,x192)+~P2(x193,x191) % 0.67/0.72 % 0.67/0.72 %------------------------------------------- % 0.67/0.72 cnf(39,plain, % 0.67/0.72 (P1(f2(x391,x392),f3(x392,x391))), % 0.67/0.72 inference(scs_inference,[],[21,22,14])). % 0.67/0.72 cnf(104,plain, % 0.67/0.72 (P2(f2(x1041,x1042),x1043)+~P2(f2(x1041,x1042),f1(x1043,f3(x1042,x1041)))), % 0.67/0.72 inference(scs_inference,[],[39,37,27])). % 0.67/0.72 cnf(157,plain, % 0.67/0.72 (P2(f2(a4,a7),f3(a4,a7))), % 0.67/0.72 inference(scs_inference,[],[24,104,25])). % 0.67/0.72 cnf(158,plain, % 0.67/0.72 ($false), % 0.67/0.72 inference(scs_inference,[],[22,157,27]), % 0.67/0.72 ['proof']). % 0.67/0.72 % SZS output end Proof % 0.67/0.72 % Total time :0.110000s %------------------------------------------------------------------------------