%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET629+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 : n027.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 0.14s 0.54s % Output : CNFRefutation 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : SET629+3 : TPTP v8.2.0. Released v2.2.0. % 0.00/0.09 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.09/0.29 % Computer : n027.cluster.edu % 0.09/0.29 % Model : x86_64 x86_64 % 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.29 % Memory : 8042.1875MB % 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.29 % CPULimit : 300 % 0.09/0.29 % WCLimit : 300 % 0.09/0.29 % DateTime : Sun Jun 23 14:06:24 EDT 2024 % 0.09/0.29 % CPUTime : % 0.14/0.50 start to proof:theBenchmark % 0.14/0.53 %------------------------------------------- % 0.14/0.53 % File :CSE---1.7 % 0.14/0.53 % Problem :theBenchmark % 0.14/0.53 % Transform :cnf % 0.14/0.53 % Format :tptp:raw % 0.14/0.54 % Command :java -jar mcs_scs.jar %d %s % 0.14/0.54 % 0.14/0.54 % Result :Theorem 0.000000s % 0.14/0.54 % Output :CNFRefutation 0.000000s % 0.14/0.54 %------------------------------------------- % 0.14/0.54 %-------------------------------------------------------------------------- % 0.14/0.54 % File : SET629+3 : TPTP v8.2.0. Released v2.2.0. % 0.14/0.54 % Domain : Set Theory % 0.14/0.54 % Problem : X ^ Y is disjoint from X \ Y % 0.14/0.54 % Version : [Try90] axioms : Reduced > Incomplete. % 0.14/0.54 % English : The intersection of X and Y is disjoint from the difference of % 0.14/0.54 % X and Y. % 0.14/0.54 % 0.14/0.54 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.14/0.54 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.14/0.54 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.14/0.54 % Source : [ILF] % 0.14/0.54 % Names : BOOLE (111) [TS89] % 0.14/0.54 % 0.14/0.54 % Status : Theorem % 0.14/0.54 % Rating : 0.17 v7.5.0, 0.19 v7.4.0, 0.13 v7.3.0, 0.14 v7.2.0, 0.10 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.1.0, 0.20 v6.0.0, 0.17 v5.5.0, 0.19 v5.4.0, 0.21 v5.3.0, 0.26 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.17 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 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 % 0.14/0.54 % Syntax : Number of formulae : 8 ( 2 unt; 0 def) % 0.14/0.54 % Number of atoms : 18 ( 2 equ) % 0.14/0.54 % Maximal formula atoms : 3 ( 2 avg) % 0.14/0.54 % Number of connectives : 12 ( 2 ~; 0 |; 3 &) % 0.14/0.54 % ( 6 <=>; 1 =>; 0 <=; 0 <~>) % 0.14/0.54 % Maximal formula depth : 7 ( 5 avg) % 0.14/0.54 % Maximal term depth : 2 ( 1 avg) % 0.14/0.54 % Number of predicates : 4 ( 3 usr; 0 prp; 2-2 aty) % 0.14/0.54 % Number of functors : 2 ( 2 usr; 0 con; 2-2 aty) % 0.14/0.54 % Number of variables : 20 ( 19 !; 1 ?) % 0.14/0.54 % SPC : FOF_THM_RFO_SEQ % 0.14/0.54 % 0.14/0.54 % Comments : % 0.14/0.54 %-------------------------------------------------------------------------- % 0.14/0.54 %---- line(boole - df(3),1833060) % 0.14/0.54 fof(intersection_defn,axiom, % 0.14/0.54 ! [B,C,D] : % 0.14/0.54 ( member(D,intersection(B,C)) % 0.14/0.54 <=> ( member(D,B) % 0.14/0.54 & member(D,C) ) ) ). % 0.14/0.54 % 0.14/0.54 %---- line(boole - df(4),1833078) % 0.14/0.54 fof(difference_defn,axiom, % 0.14/0.54 ! [B,C,D] : % 0.14/0.54 ( member(D,difference(B,C)) % 0.14/0.54 <=> ( member(D,B) % 0.14/0.54 & ~ member(D,C) ) ) ). % 0.14/0.54 % 0.14/0.54 %---- line(boole - df(5),1833080) % 0.14/0.54 fof(intersect_defn,axiom, % 0.14/0.54 ! [B,C] : % 0.14/0.54 ( intersect(B,C) % 0.14/0.54 <=> ? [D] : % 0.14/0.54 ( member(D,B) % 0.14/0.54 & member(D,C) ) ) ). % 0.14/0.54 % 0.14/0.54 %---- line(boole - axiom199,1833083) % 0.14/0.54 fof(disjoint_defn,axiom, % 0.14/0.54 ! [B,C] : % 0.14/0.54 ( disjoint(B,C) % 0.14/0.54 <=> ~ intersect(B,C) ) ). % 0.14/0.54 % 0.14/0.54 %---- property(commutativity,op(intersection,2,function)) % 0.14/0.54 fof(commutativity_of_intersection,axiom, % 0.14/0.54 ! [B,C] : intersection(B,C) = intersection(C,B) ). % 0.14/0.54 % 0.14/0.54 %---- property(symmetry,op(intersect,2,predicate)) % 0.14/0.54 fof(symmetry_of_intersect,axiom, % 0.14/0.54 ! [B,C] : % 0.14/0.54 ( intersect(B,C) % 0.14/0.54 => intersect(C,B) ) ). % 0.14/0.54 % 0.14/0.54 %---- line(hidden - axiom201,1832615) % 0.14/0.54 fof(equal_member_defn,axiom, % 0.14/0.54 ! [B,C] : % 0.14/0.54 ( B = C % 0.14/0.54 <=> ! [D] : % 0.14/0.54 ( member(D,B) % 0.14/0.54 <=> member(D,C) ) ) ). % 0.14/0.54 % 0.14/0.54 %---- line(boole - th(111),1834358) % 0.14/0.54 fof(prove_intersection_and_difference_disjoint,conjecture, % 0.14/0.54 ! [B,C] : disjoint(intersection(B,C),difference(B,C)) ). % 0.14/0.54 % 0.14/0.54 %-------------------------------------------------------------------------- % 0.14/0.54 %------------------------------------------- % 0.14/0.54 % Proof found % 0.14/0.54 % SZS status Theorem for theBenchmark % 0.14/0.54 % SZS output start Proof % 0.14/0.54 %ClaNum:33(EqnAxiom:17) % 0.14/0.54 %VarNum:82(SingletonVarNum:37) % 0.14/0.54 %MaxLitNum:3 % 0.14/0.54 %MaxfuncDepth:1 % 0.14/0.54 %SharedTerms:5 % 0.14/0.54 %goalClause: 19 % 0.14/0.54 %singleGoalClaCount:1 % 0.14/0.54 [19]~P1(f1(a2,a6),f3(a2,a6)) % 0.14/0.54 [18]E(f1(x181,x182),f1(x182,x181)) % 0.14/0.54 [20]P1(x201,x202)+P2(x201,x202) % 0.14/0.54 [21]~P2(x212,x211)+P2(x211,x212) % 0.14/0.54 [22]~P1(x221,x222)+~P2(x221,x222) % 0.14/0.54 [24]~P2(x241,x242)+P3(f4(x241,x242),x242) % 0.14/0.54 [25]~P2(x251,x252)+P3(f4(x251,x252),x251) % 0.14/0.54 [27]P3(x271,x272)+~P3(x271,f1(x273,x272)) % 0.14/0.54 [28]P3(x281,x282)+~P3(x281,f1(x282,x283)) % 0.14/0.54 [29]P3(x291,x292)+~P3(x291,f3(x292,x293)) % 0.14/0.54 [32]~P3(x321,x322)+~P3(x321,f3(x323,x322)) % 0.14/0.54 [30]E(x301,x302)+P3(f5(x301,x302),x302)+P3(f5(x301,x302),x301) % 0.14/0.54 [33]E(x331,x332)+~P3(f5(x331,x332),x332)+~P3(f5(x331,x332),x331) % 0.14/0.54 [23]~P3(x233,x231)+P2(x231,x232)+~P3(x233,x232) % 0.14/0.54 [26]~P3(x261,x263)+P3(x261,x262)+P3(x261,f3(x263,x262)) % 0.14/0.54 [31]~P3(x311,x313)+~P3(x311,x312)+P3(x311,f1(x312,x313)) % 0.14/0.54 %EqnAxiom % 0.14/0.54 [1]E(x11,x11) % 0.14/0.54 [2]E(x22,x21)+~E(x21,x22) % 0.14/0.54 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.14/0.54 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43)) % 0.14/0.54 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52)) % 0.14/0.54 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63)) % 0.14/0.54 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72)) % 0.14/0.54 [8]~E(x81,x82)+E(f3(x81,x83),f3(x82,x83)) % 0.14/0.54 [9]~E(x91,x92)+E(f3(x93,x91),f3(x93,x92)) % 0.14/0.54 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103)) % 0.14/0.54 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112)) % 0.14/0.54 [12]P1(x122,x123)+~E(x121,x122)+~P1(x121,x123) % 0.14/0.54 [13]P1(x133,x132)+~E(x131,x132)+~P1(x133,x131) % 0.14/0.54 [14]P2(x142,x143)+~E(x141,x142)+~P2(x141,x143) % 0.14/0.54 [15]P2(x153,x152)+~E(x151,x152)+~P2(x153,x151) % 0.14/0.54 [16]P3(x162,x163)+~E(x161,x162)+~P3(x161,x163) % 0.14/0.54 [17]P3(x173,x172)+~E(x171,x172)+~P3(x173,x171) % 0.14/0.54 % 0.14/0.54 %------------------------------------------- % 0.14/0.54 cnf(35,plain, % 0.14/0.54 (P2(f3(a2,a6),f1(a2,a6))), % 0.14/0.54 inference(scs_inference,[],[19,20,21])). % 0.14/0.54 cnf(42,plain, % 0.14/0.54 (P3(f4(f1(a2,a6),f3(a2,a6)),f3(a2,a6))), % 0.14/0.54 inference(scs_inference,[],[19,24,20])). % 0.14/0.54 cnf(45,plain, % 0.14/0.54 (~P3(f4(f1(a2,a6),f3(a2,a6)),a6)), % 0.14/0.54 inference(scs_inference,[],[42,29,32])). % 0.14/0.54 cnf(58,plain, % 0.14/0.54 (P3(f4(f1(a2,a6),f3(a2,a6)),f1(a2,a6))), % 0.14/0.54 inference(scs_inference,[],[35,25,21])). % 0.14/0.54 cnf(59,plain, % 0.14/0.54 ($false), % 0.14/0.54 inference(scs_inference,[],[58,45,27]), % 0.14/0.54 ['proof']). % 0.14/0.54 % SZS output end Proof % 0.14/0.54 % Total time :0.000000s %------------------------------------------------------------------------------