%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET200+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 : n028.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 14:21:05 EDT 2024 % Result : Theorem 1.52s 1.65s % Output : CNFRefutation 1.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : SET200+3 : TPTP v8.2.0. Released v2.2.0. % 0.08/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.14/0.35 % Computer : n028.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sun Jun 23 16:13:23 EDT 2024 % 0.14/0.36 % CPUTime : % 0.21/0.61 start to proof:theBenchmark % 1.52/1.64 %------------------------------------------- % 1.52/1.64 % File :CSE---1.7 % 1.52/1.64 % Problem :theBenchmark % 1.52/1.64 % Transform :cnf % 1.52/1.64 % Format :tptp:raw % 1.52/1.64 % Command :java -jar mcs_scs.jar %d %s % 1.52/1.64 % 1.52/1.64 % Result :Theorem 1.000000s % 1.52/1.64 % Output :CNFRefutation 1.000000s % 1.52/1.64 %------------------------------------------- % 1.52/1.65 %-------------------------------------------------------------------------- % 1.52/1.65 % File : SET200+3 : TPTP v8.2.0. Released v2.2.0. % 1.52/1.65 % Domain : Set Theory % 1.52/1.65 % Problem : Union is monotonic % 1.52/1.65 % Version : [Try90] axioms : Reduced > Incomplete. % 1.52/1.65 % English : If X is a subset of Y and Z is a subset of V, then the union of % 1.52/1.65 % X and Z is a subset of the union of Y and V. % 1.52/1.65 % 1.52/1.65 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 1.52/1.65 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 1.52/1.65 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 1.52/1.65 % Source : [ILF] % 1.52/1.65 % Names : BOOLE (34) [TS89] % 1.52/1.65 % 1.52/1.65 % Status : Theorem % 1.52/1.65 % Rating : 0.14 v8.1.0, 0.08 v7.5.0, 0.12 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, 0.04 v6.1.0, 0.17 v6.0.0, 0.13 v5.5.0, 0.33 v5.4.0, 0.39 v5.3.0, 0.41 v5.2.0, 0.30 v5.1.0, 0.33 v5.0.0, 0.38 v4.1.0, 0.35 v4.0.0, 0.29 v3.7.0, 0.30 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, 0.17 v2.6.0, 0.29 v2.5.0, 0.25 v2.4.0, 0.25 v2.3.0, 0.00 v2.2.1 % 1.52/1.65 % Syntax : Number of formulae : 6 ( 2 unt; 0 def) % 1.52/1.65 % Number of atoms : 14 ( 2 equ) % 1.52/1.65 % Maximal formula atoms : 3 ( 2 avg) % 1.52/1.65 % Number of connectives : 8 ( 0 ~; 1 |; 1 &) % 1.52/1.65 % ( 4 <=>; 2 =>; 0 <=; 0 <~>) % 1.52/1.65 % Maximal formula depth : 7 ( 5 avg) % 1.52/1.65 % Maximal term depth : 2 ( 1 avg) % 1.52/1.65 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty) % 1.52/1.65 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty) % 1.52/1.65 % Number of variables : 16 ( 16 !; 0 ?) % 1.52/1.65 % SPC : FOF_THM_RFO_SEQ % 1.52/1.65 % 1.52/1.65 % Comments : % 1.52/1.65 %-------------------------------------------------------------------------- % 1.52/1.65 %---- line(boole - df(2),1833042) % 1.52/1.65 fof(union_defn,axiom, % 1.52/1.65 ! [B,C,D] : % 1.52/1.65 ( member(D,union(B,C)) % 1.52/1.65 <=> ( member(D,B) % 1.52/1.65 | member(D,C) ) ) ). % 1.52/1.65 % 1.52/1.65 %---- line(tarski - df(3),1832749) % 1.52/1.65 fof(subset_defn,axiom, % 1.52/1.65 ! [B,C] : % 1.52/1.65 ( subset(B,C) % 1.52/1.65 <=> ! [D] : % 1.52/1.65 ( member(D,B) % 1.52/1.65 => member(D,C) ) ) ). % 1.52/1.65 % 1.52/1.65 %---- property(commutativity,op(union,2,function)) % 1.52/1.65 fof(commutativity_of_union,axiom, % 1.52/1.65 ! [B,C] : union(B,C) = union(C,B) ). % 1.52/1.65 % 1.52/1.65 %---- property(reflexivity,op(subset,2,predicate)) % 1.52/1.65 fof(reflexivity_of_subset,axiom, % 1.52/1.65 ! [B] : subset(B,B) ). % 1.52/1.65 % 1.52/1.65 %---- line(hidden - axiom41,1832615) % 1.52/1.65 fof(equal_member_defn,axiom, % 1.52/1.65 ! [B,C] : % 1.52/1.65 ( B = C % 1.52/1.65 <=> ! [D] : % 1.52/1.65 ( member(D,B) % 1.52/1.65 <=> member(D,C) ) ) ). % 1.52/1.65 % 1.52/1.65 %---- line(boole - th(34),1833242) % 1.52/1.65 fof(prove_th34,conjecture, % 1.52/1.65 ! [B,C,D,E] : % 1.52/1.65 ( ( subset(B,C) % 1.52/1.65 & subset(D,E) ) % 1.52/1.65 => subset(union(B,D),union(C,E)) ) ). % 1.52/1.65 % 1.52/1.65 %-------------------------------------------------------------------------- % 1.52/1.65 %------------------------------------------- % 1.52/1.65 % Proof found % 1.52/1.65 % SZS status Theorem for theBenchmark % 1.52/1.65 % SZS output start Proof % 1.52/1.66 %ClaNum:26(EqnAxiom:13) % 1.52/1.66 %VarNum:55(SingletonVarNum:23) % 1.52/1.66 %MaxLitNum:3 % 1.52/1.66 %MaxfuncDepth:1 % 1.52/1.66 %SharedTerms:9 % 1.52/1.66 %goalClause: 14 15 18 % 1.52/1.66 %singleGoalClaCount:3 % 1.52/1.66 [14]P1(a1,a4) % 1.52/1.66 [15]P1(a5,a6) % 1.52/1.66 [18]~P1(f7(a1,a5),f7(a4,a6)) % 1.52/1.66 [16]P1(x161,x161) % 1.52/1.66 [17]E(f7(x171,x172),f7(x172,x171)) % 1.52/1.66 [19]P1(x191,x192)+P2(f2(x191,x192),x191) % 1.52/1.66 [23]P1(x231,x232)+~P2(f2(x231,x232),x232) % 1.52/1.66 [21]~P2(x211,x213)+P2(x211,f7(x212,x213)) % 1.52/1.66 [22]~P2(x221,x222)+P2(x221,f7(x222,x223)) % 1.52/1.66 [24]E(x241,x242)+P2(f3(x241,x242),x242)+P2(f3(x241,x242),x241) % 1.52/1.66 [26]E(x261,x262)+~P2(f3(x261,x262),x262)+~P2(f3(x261,x262),x261) % 1.52/1.66 [20]~P1(x203,x202)+P2(x201,x202)+~P2(x201,x203) % 1.52/1.66 [25]P2(x251,x252)+P2(x251,x253)+~P2(x251,f7(x253,x252)) % 1.52/1.66 %EqnAxiom % 1.52/1.66 [1]E(x11,x11) % 1.52/1.66 [2]E(x22,x21)+~E(x21,x22) % 1.52/1.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.52/1.66 [4]~E(x41,x42)+E(f7(x41,x43),f7(x42,x43)) % 1.52/1.66 [5]~E(x51,x52)+E(f7(x53,x51),f7(x53,x52)) % 1.52/1.66 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63)) % 1.52/1.66 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72)) % 1.52/1.66 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83)) % 1.52/1.66 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92)) % 1.52/1.66 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103) % 1.52/1.66 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111) % 1.52/1.66 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123) % 1.52/1.66 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131) % 1.52/1.66 % 1.52/1.66 %------------------------------------------- % 1.52/1.67 cnf(33,plain, % 1.52/1.67 (P1(a1,x331)+~E(a4,x331)), % 1.52/1.67 inference(scs_inference,[],[14,11])). % 1.52/1.67 cnf(63,plain, % 1.52/1.67 (~P2(f2(f7(a1,a5),f7(a6,a4)),f7(a6,a4))), % 1.52/1.67 inference(scs_inference,[],[18,17,23,11])). % 1.52/1.67 cnf(64,plain, % 1.52/1.67 (~P2(f2(f7(a1,a5),f7(a6,a4)),a4)), % 1.52/1.67 inference(scs_inference,[],[63,21])). % 1.52/1.67 cnf(66,plain, % 1.52/1.67 (~P2(f2(f7(a1,a5),f7(a6,a4)),a6)), % 1.52/1.67 inference(scs_inference,[],[63,21,22])). % 1.52/1.67 cnf(127,plain, % 1.52/1.67 (P1(f7(x1271,x1272),f7(x1272,x1271))), % 1.52/1.67 inference(scs_inference,[],[17,16,2,10])). % 1.52/1.67 cnf(143,plain, % 1.52/1.67 (~P2(f2(f7(a1,a5),f7(a6,a4)),a1)), % 1.52/1.67 inference(scs_inference,[],[64,33,20])). % 1.52/1.67 cnf(294,plain, % 1.52/1.67 (P2(f2(f7(a1,a5),f7(a6,a4)),f7(a1,a5))), % 1.52/1.67 inference(scs_inference,[],[18,17,19,11])). % 1.52/1.67 cnf(298,plain, % 1.52/1.67 (P2(f2(f7(a1,a5),f7(a6,a4)),a5)), % 1.52/1.67 inference(scs_inference,[],[127,143,294,20,25])). % 1.52/1.67 cnf(312,plain, % 1.52/1.67 ($false), % 1.52/1.67 inference(scs_inference,[],[15,66,298,20]), % 1.52/1.67 ['proof']). % 1.52/1.67 % SZS output end Proof % 1.52/1.67 % Total time :1.000000s %------------------------------------------------------------------------------