%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET594+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 : n029.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 14:21:53 EDT 2024 % Result : Theorem 0.54s 1.01s % Output : CNFRefutation 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET594+3 : TPTP v8.2.0. Released v2.2.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n029.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 12:01:54 EDT 2024 % 0.12/0.34 % CPUTime : % 0.47/0.57 start to proof:theBenchmark % 0.54/1.00 %------------------------------------------- % 0.54/1.00 % File :CSE---1.7 % 0.54/1.00 % Problem :theBenchmark % 0.54/1.00 % Transform :cnf % 0.54/1.00 % Format :tptp:raw % 0.54/1.00 % Command :java -jar mcs_scs.jar %d %s % 0.54/1.00 % 0.54/1.00 % Result :Theorem 0.390000s % 0.54/1.00 % Output :CNFRefutation 0.390000s % 0.54/1.00 %------------------------------------------- % 0.54/1.01 %-------------------------------------------------------------------------- % 0.54/1.01 % File : SET594+3 : TPTP v8.2.0. Released v2.2.0. % 0.54/1.01 % Domain : Set Theory % 0.54/1.01 % Problem : If X ^ Y U X ^ Z = X, then X (= Y U Z % 0.54/1.01 % Version : [Try90] axioms : Reduced > Incomplete. % 0.54/1.01 % English : If the intersection of X and the union of Y and the % 0.54/1.01 % intersection of X and Z is X, then X is a subset of the union % 0.54/1.01 % of Y and Z. % 0.54/1.01 % 0.54/1.01 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.54/1.01 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.54/1.01 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.54/1.01 % Source : [ILF] % 0.54/1.01 % Names : BOOLE (53) [TS89] % 0.54/1.01 % 0.54/1.01 % Status : Theorem % 0.54/1.01 % Rating : 0.22 v8.2.0, 0.19 v8.1.0, 0.28 v7.4.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.17 v7.0.0, 0.23 v6.3.0, 0.12 v6.1.0, 0.30 v6.0.0, 0.26 v5.5.0, 0.37 v5.4.0, 0.43 v5.3.0, 0.44 v5.2.0, 0.30 v5.1.0, 0.29 v5.0.0, 0.33 v4.1.0, 0.35 v4.0.0, 0.33 v3.7.0, 0.35 v3.5.0, 0.32 v3.4.0, 0.37 v3.3.0, 0.43 v3.2.0, 0.55 v3.1.0, 0.56 v2.7.0, 0.33 v2.6.0, 0.14 v2.5.0, 0.12 v2.4.0, 0.25 v2.3.0, 0.00 v2.2.1 % 0.54/1.01 % Syntax : Number of formulae : 9 ( 3 unt; 0 def) % 0.54/1.01 % Number of atoms : 20 ( 5 equ) % 0.54/1.01 % Maximal formula atoms : 3 ( 2 avg) % 0.54/1.01 % Number of connectives : 11 ( 0 ~; 1 |; 2 &) % 0.54/1.01 % ( 6 <=>; 2 =>; 0 <=; 0 <~>) % 0.54/1.01 % Maximal formula depth : 6 ( 5 avg) % 0.54/1.01 % Maximal term depth : 3 ( 1 avg) % 0.54/1.01 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty) % 0.54/1.01 % Number of functors : 2 ( 2 usr; 0 con; 2-2 aty) % 0.54/1.01 % Number of variables : 22 ( 22 !; 0 ?) % 0.54/1.01 % SPC : FOF_THM_RFO_SEQ % 0.54/1.01 % 0.54/1.01 % Comments : % 0.54/1.01 %-------------------------------------------------------------------------- % 0.54/1.01 %---- line(tarski - df(3),1832749) % 0.54/1.01 fof(subset_defn,axiom, % 0.54/1.01 ! [B,C] : % 0.54/1.01 ( subset(B,C) % 0.54/1.01 <=> ! [D] : % 0.54/1.01 ( member(D,B) % 0.54/1.01 => member(D,C) ) ) ). % 0.54/1.01 % 0.54/1.01 %---- line(boole - df(2),1833042) % 0.54/1.01 fof(union_defn,axiom, % 0.54/1.01 ! [B,C,D] : % 0.54/1.01 ( member(D,union(B,C)) % 0.54/1.01 <=> ( member(D,B) % 0.54/1.01 | member(D,C) ) ) ). % 0.54/1.01 % 0.54/1.01 %---- line(boole - df(3),1833060) % 0.54/1.01 fof(intersection_defn,axiom, % 0.54/1.01 ! [B,C,D] : % 0.54/1.01 ( member(D,intersection(B,C)) % 0.54/1.01 <=> ( member(D,B) % 0.54/1.01 & member(D,C) ) ) ). % 0.54/1.01 % 0.54/1.01 %---- line(boole - df(8),1833103) % 0.54/1.01 fof(equal_defn,axiom, % 0.54/1.01 ! [B,C] : % 0.54/1.01 ( B = C % 0.54/1.01 <=> ( subset(B,C) % 0.54/1.01 & subset(C,B) ) ) ). % 0.54/1.01 % 0.54/1.01 %---- property(commutativity,op(union,2,function)) % 0.54/1.01 fof(commutativity_of_union,axiom, % 0.54/1.01 ! [B,C] : union(B,C) = union(C,B) ). % 0.54/1.01 % 0.54/1.01 %---- property(commutativity,op(intersection,2,function)) % 0.54/1.01 fof(commutativity_of_intersection,axiom, % 0.54/1.01 ! [B,C] : intersection(B,C) = intersection(C,B) ). % 0.54/1.01 % 0.54/1.01 %---- property(reflexivity,op(subset,2,predicate)) % 0.54/1.01 fof(reflexivity_of_subset,axiom, % 0.54/1.01 ! [B] : subset(B,B) ). % 0.54/1.01 % 0.54/1.01 %---- line(hidden - axiom76,1832615) % 0.54/1.01 fof(equal_member_defn,axiom, % 0.54/1.01 ! [B,C] : % 0.54/1.01 ( B = C % 0.54/1.01 <=> ! [D] : % 0.54/1.01 ( member(D,B) % 0.54/1.01 <=> member(D,C) ) ) ). % 0.54/1.01 % 0.54/1.01 %---- line(boole - th(53),1833539) % 0.54/1.01 fof(prove_th53,conjecture, % 0.54/1.01 ! [B,C,D] : % 0.54/1.01 ( union(intersection(B,C),intersection(B,D)) = B % 0.54/1.01 => subset(B,union(C,D)) ) ). % 0.54/1.01 % 0.54/1.01 %-------------------------------------------------------------------------- % 0.54/1.01 %------------------------------------------- % 0.54/1.01 % Proof found % 0.54/1.01 % SZS status Theorem for theBenchmark % 0.54/1.01 % SZS output start Proof % 0.54/1.01 %ClaNum:34(EqnAxiom:15) % 0.54/1.01 %VarNum:86(SingletonVarNum:38) % 0.54/1.01 %MaxLitNum:3 % 0.54/1.01 %MaxfuncDepth:2 % 0.54/1.01 %SharedTerms:9 % 0.54/1.01 %goalClause: 19 20 % 0.54/1.01 %singleGoalClaCount:2 % 0.54/1.01 [20]~P1(a3,f1(a6,a7)) % 0.54/1.01 [19]E(f1(f2(a3,a6),f2(a3,a7)),a3) % 0.54/1.01 [16]P1(x161,x161) % 0.54/1.01 [17]E(f1(x171,x172),f1(x172,x171)) % 0.54/1.01 [18]E(f2(x181,x182),f2(x182,x181)) % 0.54/1.01 [22]~E(x221,x222)+P1(x221,x222) % 0.54/1.01 [24]P1(x241,x242)+P2(f4(x241,x242),x241) % 0.54/1.01 [30]P1(x301,x302)+~P2(f4(x301,x302),x302) % 0.54/1.01 [26]~P2(x261,x263)+P2(x261,f1(x262,x263)) % 0.54/1.01 [27]~P2(x271,x272)+P2(x271,f1(x272,x273)) % 0.54/1.01 [28]P2(x281,x282)+~P2(x281,f2(x283,x282)) % 0.54/1.01 [29]P2(x291,x292)+~P2(x291,f2(x292,x293)) % 0.54/1.01 [23]~P1(x232,x231)+~P1(x231,x232)+E(x231,x232) % 0.54/1.01 [31]E(x311,x312)+P2(f5(x311,x312),x312)+P2(f5(x311,x312),x311) % 0.54/1.01 [34]E(x341,x342)+~P2(f5(x341,x342),x342)+~P2(f5(x341,x342),x341) % 0.54/1.01 [25]~P2(x251,x253)+P2(x251,x252)+~P1(x253,x252) % 0.54/1.01 [32]~P2(x321,x323)+~P2(x321,x322)+P2(x321,f2(x322,x323)) % 0.54/1.01 [33]P2(x331,x332)+P2(x331,x333)+~P2(x331,f1(x333,x332)) % 0.54/1.01 %EqnAxiom % 0.54/1.01 [1]E(x11,x11) % 0.54/1.01 [2]E(x22,x21)+~E(x21,x22) % 0.54/1.01 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.54/1.01 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43)) % 0.54/1.01 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52)) % 0.54/1.01 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63)) % 0.54/1.01 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72)) % 0.54/1.01 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83)) % 0.54/1.01 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92)) % 0.54/1.01 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103)) % 0.54/1.01 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112)) % 0.54/1.01 [12]P1(x122,x123)+~E(x121,x122)+~P1(x121,x123) % 0.54/1.01 [13]P1(x133,x132)+~E(x131,x132)+~P1(x133,x131) % 0.54/1.01 [14]P2(x142,x143)+~E(x141,x142)+~P2(x141,x143) % 0.54/1.01 [15]P2(x153,x152)+~E(x151,x152)+~P2(x153,x151) % 0.54/1.01 % 0.54/1.01 %------------------------------------------- % 0.54/1.02 cnf(38,plain, % 0.54/1.02 (E(a3,f1(f2(a3,a6),f2(a3,a7)))), % 0.54/1.02 inference(scs_inference,[],[19,20,22,2])). % 0.54/1.02 cnf(39,plain, % 0.54/1.02 (E(f1(f2(a3,a7),f2(a3,a6)),a3)), % 0.54/1.02 inference(scs_inference,[],[19,20,17,22,2,3])). % 0.54/1.02 cnf(46,plain, % 0.54/1.02 (E(a3,f1(f2(a3,a7),f2(a3,a6)))), % 0.54/1.02 inference(scs_inference,[],[39,2])). % 0.54/1.02 cnf(51,plain, % 0.54/1.02 (P2(f4(a3,f1(a6,a7)),f1(x511,a3))), % 0.54/1.02 inference(scs_inference,[],[20,26,24])). % 0.54/1.02 cnf(52,plain, % 0.54/1.02 (P2(f4(a3,f1(a6,a7)),f1(a3,x521))), % 0.54/1.02 inference(scs_inference,[],[51,17,15])). % 0.54/1.02 cnf(64,plain, % 0.54/1.02 (P2(f4(a3,f1(a6,a7)),a3)), % 0.54/1.02 inference(scs_inference,[],[19,51,33,15])). % 0.54/1.02 cnf(67,plain, % 0.54/1.02 (~P2(f4(a3,f1(a6,a7)),f2(x671,f1(a6,a7)))), % 0.54/1.02 inference(scs_inference,[],[20,28,30])). % 0.54/1.02 cnf(69,plain, % 0.54/1.02 (~P2(f4(a3,f1(a6,a7)),f2(x691,f1(a6,a7)))), % 0.54/1.02 inference(rename_variables,[],[67])). % 0.54/1.02 cnf(74,plain, % 0.54/1.02 (~P2(f4(a3,f1(a6,a7)),a7)), % 0.54/1.02 inference(scs_inference,[],[18,52,67,69,32,15,3,26])). % 0.54/1.02 cnf(76,plain, % 0.54/1.02 (~P2(f4(a3,f1(a6,a7)),a6)), % 0.54/1.02 inference(scs_inference,[],[18,52,67,69,32,15,3,26,27])). % 0.54/1.02 cnf(179,plain, % 0.54/1.02 (P1(f1(f2(a3,a6),f2(a3,a7)),a3)), % 0.54/1.02 inference(scs_inference,[],[38,2,22])). % 0.54/1.02 cnf(190,plain, % 0.54/1.02 (P1(a3,f1(f2(a3,a7),f2(a3,a6)))), % 0.54/1.02 inference(scs_inference,[],[19,179,46,13,12])). % 0.54/1.02 cnf(205,plain, % 0.54/1.02 (P2(f4(a3,f1(a6,a7)),f2(a3,a6))+P2(f4(a3,f1(a6,a7)),f2(a3,a7))), % 0.54/1.02 inference(scs_inference,[],[20,190,64,25,13,33])). % 0.54/1.02 cnf(217,plain, % 0.54/1.02 (P2(f4(a3,f1(a6,a7)),f2(a3,a6))), % 0.54/1.02 inference(scs_inference,[],[74,205,28])). % 0.54/1.02 cnf(218,plain, % 0.54/1.02 ($false), % 0.54/1.02 inference(scs_inference,[],[217,76,28]), % 0.54/1.02 ['proof']). % 0.54/1.02 % SZS output end Proof % 0.54/1.02 % Total time :0.390000s %------------------------------------------------------------------------------