%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET585+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 14:21:50 EDT 2024 % Result : Theorem 0.55s 0.61s % Output : CNFRefutation 0.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET585+3 : TPTP v8.2.0. Released v2.2.0. % 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n029.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sun Jun 23 14:44:09 EDT 2024 % 0.13/0.34 % CPUTime : % 0.20/0.56 start to proof:theBenchmark % 0.55/0.60 %------------------------------------------- % 0.55/0.60 % File :CSE---1.7 % 0.55/0.60 % Problem :theBenchmark % 0.55/0.60 % Transform :cnf % 0.55/0.60 % Format :tptp:raw % 0.55/0.60 % Command :java -jar mcs_scs.jar %d %s % 0.55/0.60 % 0.55/0.60 % Result :Theorem 0.000000s % 0.55/0.60 % Output :CNFRefutation 0.000000s % 0.55/0.60 %------------------------------------------- % 0.55/0.61 %-------------------------------------------------------------------------- % 0.55/0.61 % File : SET585+3 : TPTP v8.2.0. Released v2.2.0. % 0.55/0.61 % Domain : Set Theory % 0.55/0.61 % Problem : The intersection of X and Y is a subset of the union of X and Z % 0.55/0.61 % Version : [Try90] axioms : Reduced > Incomplete. % 0.55/0.61 % English : % 0.55/0.61 % 0.55/0.61 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.55/0.61 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.55/0.61 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.55/0.61 % Source : [ILF] % 0.55/0.61 % Names : BOOLE (38) [TS89] % 0.55/0.61 % 0.55/0.61 % Status : Theorem % 0.55/0.61 % Rating : 0.03 v8.1.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.00 v6.1.0, 0.07 v6.0.0, 0.13 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.00 v5.0.0, 0.08 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 v3.4.0, 0.05 v3.3.0, 0.14 v3.2.0, 0.09 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1 % 0.55/0.61 % Syntax : Number of formulae : 11 ( 6 unt; 0 def) % 0.55/0.61 % Number of atoms : 21 ( 3 equ) % 0.55/0.61 % Maximal formula atoms : 3 ( 1 avg) % 0.55/0.61 % Number of connectives : 10 ( 0 ~; 1 |; 2 &) % 0.55/0.61 % ( 5 <=>; 2 =>; 0 <=; 0 <~>) % 0.55/0.61 % Maximal formula depth : 6 ( 4 avg) % 0.55/0.61 % Maximal term depth : 2 ( 1 avg) % 0.55/0.61 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty) % 0.55/0.61 % Number of functors : 2 ( 2 usr; 0 con; 2-2 aty) % 0.55/0.61 % Number of variables : 27 ( 27 !; 0 ?) % 0.55/0.61 % SPC : FOF_THM_RFO_SEQ % 0.55/0.61 % 0.55/0.61 % Comments : % 0.55/0.61 %-------------------------------------------------------------------------- % 0.55/0.61 %---- line(boole - th(29),1833172) % 0.55/0.61 fof(transitivity_of_subset,axiom, % 0.55/0.61 ! [B,C,D] : % 0.55/0.61 ( ( subset(B,C) % 0.55/0.61 & subset(C,D) ) % 0.55/0.61 => subset(B,D) ) ). % 0.55/0.61 % 0.55/0.61 %---- line(boole - th(31),1833190) % 0.55/0.61 fof(subset_of_union,axiom, % 0.55/0.61 ! [B,C] : subset(B,union(B,C)) ). % 0.55/0.61 % 0.55/0.61 %---- line(boole - th(37),1833277) % 0.55/0.61 fof(intersection_is_subset,axiom, % 0.55/0.61 ! [B,C] : subset(intersection(B,C),B) ). % 0.55/0.61 % 0.55/0.61 %---- line(boole - df(2),1833042) % 0.55/0.61 fof(union_defn,axiom, % 0.55/0.61 ! [B,C,D] : % 0.55/0.61 ( member(D,union(B,C)) % 0.55/0.61 <=> ( member(D,B) % 0.55/0.61 | member(D,C) ) ) ). % 0.55/0.61 % 0.55/0.61 %---- line(boole - df(3),1833060) % 0.55/0.61 fof(intersection_defn,axiom, % 0.55/0.61 ! [B,C,D] : % 0.55/0.61 ( member(D,intersection(B,C)) % 0.55/0.61 <=> ( member(D,B) % 0.55/0.61 & member(D,C) ) ) ). % 0.55/0.61 % 0.55/0.61 %---- line(tarski - df(3),1832749) % 0.55/0.61 fof(subset_defn,axiom, % 0.55/0.61 ! [B,C] : % 0.55/0.61 ( subset(B,C) % 0.55/0.61 <=> ! [D] : % 0.55/0.61 ( member(D,B) % 0.55/0.61 => member(D,C) ) ) ). % 0.55/0.61 % 0.55/0.61 %---- property(commutativity,op(union,2,function)) % 0.55/0.61 fof(commutativity_of_union,axiom, % 0.55/0.61 ! [B,C] : union(B,C) = union(C,B) ). % 0.55/0.61 % 0.55/0.61 %---- property(commutativity,op(intersection,2,function)) % 0.55/0.61 fof(commutativity_of_intersection,axiom, % 0.55/0.61 ! [B,C] : intersection(B,C) = intersection(C,B) ). % 0.55/0.61 % 0.55/0.61 %---- property(reflexivity,op(subset,2,predicate)) % 0.55/0.61 fof(reflexivity_of_subset,axiom, % 0.55/0.61 ! [B] : subset(B,B) ). % 0.55/0.61 % 0.55/0.61 %---- line(hidden - axiom47,1832615) % 0.55/0.61 fof(equal_member_defn,axiom, % 0.55/0.61 ! [B,C] : % 0.55/0.61 ( B = C % 0.55/0.61 <=> ! [D] : % 0.55/0.61 ( member(D,B) % 0.55/0.61 <=> member(D,C) ) ) ). % 0.55/0.61 % 0.55/0.61 %---- line(boole - th(38),1833287) % 0.55/0.61 fof(prove_intersection_subset_of_union,conjecture, % 0.55/0.61 ! [B,C,D] : subset(intersection(B,C),union(B,D)) ). % 0.55/0.61 % 0.55/0.61 %-------------------------------------------------------------------------- % 0.55/0.61 %------------------------------------------- % 0.55/0.61 % Proof found % 0.55/0.61 % SZS status Theorem for theBenchmark % 0.55/0.61 % SZS output start Proof % 0.55/0.61 %ClaNum:33(EqnAxiom:15) % 0.55/0.61 %VarNum:88(SingletonVarNum:41) % 0.55/0.61 %MaxLitNum:3 % 0.55/0.61 %MaxfuncDepth:1 % 0.55/0.61 %SharedTerms:6 % 0.55/0.61 %goalClause: 21 % 0.55/0.61 %singleGoalClaCount:1 % 0.55/0.61 [21]~P1(f2(a3,a6),f1(a3,a7)) % 0.55/0.61 [16]P1(x161,x161) % 0.55/0.61 [17]E(f1(x171,x172),f1(x172,x171)) % 0.55/0.61 [18]E(f2(x181,x182),f2(x182,x181)) % 0.55/0.61 [19]P1(x191,f1(x191,x192)) % 0.55/0.61 [20]P1(f2(x201,x202),x201) % 0.55/0.61 [22]P1(x221,x222)+P2(f4(x221,x222),x221) % 0.55/0.61 [29]P1(x291,x292)+~P2(f4(x291,x292),x292) % 0.55/0.61 [25]~P2(x251,x253)+P2(x251,f1(x252,x253)) % 0.55/0.61 [26]~P2(x261,x262)+P2(x261,f1(x262,x263)) % 0.55/0.61 [27]P2(x271,x272)+~P2(x271,f2(x273,x272)) % 0.55/0.61 [28]P2(x281,x282)+~P2(x281,f2(x282,x283)) % 0.55/0.61 [30]E(x301,x302)+P2(f5(x301,x302),x302)+P2(f5(x301,x302),x301) % 0.55/0.61 [33]E(x331,x332)+~P2(f5(x331,x332),x332)+~P2(f5(x331,x332),x331) % 0.55/0.61 [23]~P1(x231,x233)+P1(x231,x232)+~P1(x233,x232) % 0.55/0.61 [24]~P2(x241,x243)+P2(x241,x242)+~P1(x243,x242) % 0.55/0.61 [31]~P2(x311,x313)+~P2(x311,x312)+P2(x311,f2(x312,x313)) % 0.55/0.61 [32]P2(x321,x322)+P2(x321,x323)+~P2(x321,f1(x323,x322)) % 0.55/0.61 %EqnAxiom % 0.55/0.61 [1]E(x11,x11) % 0.55/0.61 [2]E(x22,x21)+~E(x21,x22) % 0.55/0.61 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.55/0.61 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43)) % 0.55/0.61 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52)) % 0.55/0.61 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63)) % 0.55/0.61 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72)) % 0.55/0.61 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83)) % 0.55/0.61 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92)) % 0.55/0.61 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103)) % 0.55/0.61 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112)) % 0.55/0.61 [12]P1(x122,x123)+~E(x121,x122)+~P1(x121,x123) % 0.55/0.61 [13]P1(x133,x132)+~E(x131,x132)+~P1(x133,x131) % 0.55/0.61 [14]P2(x142,x143)+~E(x141,x142)+~P2(x141,x143) % 0.55/0.61 [15]P2(x153,x152)+~E(x151,x152)+~P2(x153,x151) % 0.55/0.61 % 0.55/0.61 %------------------------------------------- % 0.55/0.61 cnf(43,plain, % 0.55/0.61 ($false), % 0.55/0.61 inference(scs_inference,[],[21,19,20,23]), % 0.55/0.61 ['proof']). % 0.55/0.61 % SZS output end Proof % 0.55/0.61 % Total time :0.000000s %------------------------------------------------------------------------------