%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET201+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 : n026.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 1.56s 1.67s % Output : CNFRefutation 1.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SET201+3 : TPTP v8.2.0. Released v2.2.0. % 0.08/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.35 % Computer : n026.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sun Jun 23 11:37:09 EDT 2024 % 0.13/0.35 % CPUTime : % 0.56/0.60 start to proof:theBenchmark % 1.56/1.67 %------------------------------------------- % 1.56/1.67 % File :CSE---1.7 % 1.56/1.67 % Problem :theBenchmark % 1.56/1.67 % Transform :cnf % 1.56/1.67 % Format :tptp:raw % 1.56/1.67 % Command :java -jar mcs_scs.jar %d %s % 1.56/1.67 % 1.56/1.67 % Result :Theorem 1.030000s % 1.56/1.67 % Output :CNFRefutation 1.030000s % 1.56/1.67 %------------------------------------------- % 1.56/1.67 %-------------------------------------------------------------------------- % 1.56/1.67 % File : SET201+3 : TPTP v8.2.0. Released v2.2.0. % 1.56/1.67 % Domain : Set Theory % 1.56/1.67 % Problem : Intersection is monotonic % 1.56/1.67 % Version : [Try90] axioms : Reduced > Incomplete. % 1.56/1.67 % English : If X is a subset of Y and Z is a subset of V, then the % 1.56/1.67 % intersection of X and Z is a subset of the intersection of Y % 1.56/1.67 % and V. % 1.56/1.67 % 1.56/1.67 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 1.56/1.67 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 1.56/1.67 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 1.56/1.67 % Source : [ILF] % 1.56/1.67 % Names : BOOLE (41) [TS89] % 1.56/1.67 % 1.56/1.67 % Status : Theorem % 1.56/1.67 % Rating : 0.11 v8.1.0, 0.06 v7.4.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.08 v6.2.0, 0.04 v6.1.0, 0.13 v6.0.0, 0.09 v5.5.0, 0.07 v5.4.0, 0.14 v5.3.0, 0.26 v5.2.0, 0.10 v5.1.0, 0.14 v5.0.0, 0.21 v4.1.0, 0.17 v4.0.0, 0.12 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.07 v3.2.0, 0.18 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1 % 1.56/1.67 % Syntax : Number of formulae : 6 ( 2 unt; 0 def) % 1.56/1.67 % Number of atoms : 14 ( 2 equ) % 1.56/1.67 % Maximal formula atoms : 3 ( 2 avg) % 1.56/1.67 % Number of connectives : 8 ( 0 ~; 0 |; 2 &) % 1.56/1.67 % ( 4 <=>; 2 =>; 0 <=; 0 <~>) % 1.56/1.67 % Maximal formula depth : 7 ( 5 avg) % 1.56/1.67 % Maximal term depth : 2 ( 1 avg) % 1.56/1.67 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty) % 1.56/1.67 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty) % 1.56/1.67 % Number of variables : 16 ( 16 !; 0 ?) % 1.56/1.67 % SPC : FOF_THM_RFO_SEQ % 1.56/1.67 % 1.56/1.67 % Comments : % 1.56/1.67 %-------------------------------------------------------------------------- % 1.56/1.67 %---- line(boole - df(3),1833060) % 1.56/1.67 fof(intersection_defn,axiom, % 1.56/1.67 ! [B,C,D] : % 1.56/1.67 ( member(D,intersection(B,C)) % 1.56/1.67 <=> ( member(D,B) % 1.56/1.67 & member(D,C) ) ) ). % 1.56/1.67 % 1.56/1.67 %---- line(tarski - df(3),1832749) % 1.56/1.67 fof(subset_defn,axiom, % 1.56/1.67 ! [B,C] : % 1.56/1.67 ( subset(B,C) % 1.56/1.67 <=> ! [D] : % 1.56/1.67 ( member(D,B) % 1.56/1.67 => member(D,C) ) ) ). % 1.56/1.67 % 1.56/1.67 %---- property(commutativity,op(intersection,2,function)) % 1.56/1.67 fof(commutativity_of_intersection,axiom, % 1.56/1.67 ! [B,C] : intersection(B,C) = intersection(C,B) ). % 1.56/1.67 % 1.56/1.67 %---- property(reflexivity,op(subset,2,predicate)) % 1.56/1.67 fof(reflexivity_of_subset,axiom, % 1.56/1.67 ! [B] : subset(B,B) ). % 1.56/1.67 % 1.56/1.67 %---- line(hidden - axiom53,1832615) % 1.56/1.67 fof(equal_member_defn,axiom, % 1.56/1.67 ! [B,C] : % 1.56/1.67 ( B = C % 1.56/1.67 <=> ! [D] : % 1.56/1.67 ( member(D,B) % 1.56/1.67 <=> member(D,C) ) ) ). % 1.56/1.67 % 1.56/1.67 %---- line(boole - th(41),1833336) % 1.56/1.67 fof(prove_th41,conjecture, % 1.56/1.67 ! [B,C,D,E] : % 1.56/1.67 ( ( subset(B,C) % 1.56/1.67 & subset(D,E) ) % 1.56/1.67 => subset(intersection(B,D),intersection(C,E)) ) ). % 1.56/1.67 % 1.56/1.67 %-------------------------------------------------------------------------- % 1.56/1.67 %------------------------------------------- % 1.56/1.67 % Proof found % 1.56/1.67 % SZS status Theorem for theBenchmark % 1.56/1.67 % SZS output start Proof % 1.56/1.67 %ClaNum:26(EqnAxiom:13) % 1.56/1.67 %VarNum:55(SingletonVarNum:23) % 1.56/1.67 %MaxLitNum:3 % 1.56/1.67 %MaxfuncDepth:1 % 1.56/1.67 %SharedTerms:9 % 1.56/1.67 %goalClause: 14 15 18 % 1.56/1.67 %singleGoalClaCount:3 % 1.56/1.67 [14]P1(a1,a4) % 1.56/1.67 [15]P1(a5,a6) % 1.56/1.67 [18]~P1(f7(a1,a5),f7(a4,a6)) % 1.56/1.67 [16]P1(x161,x161) % 1.56/1.67 [17]E(f7(x171,x172),f7(x172,x171)) % 1.56/1.67 [19]P1(x191,x192)+P2(f2(x191,x192),x191) % 1.56/1.67 [23]P1(x231,x232)+~P2(f2(x231,x232),x232) % 1.56/1.67 [21]P2(x211,x212)+~P2(x211,f7(x213,x212)) % 1.56/1.67 [22]P2(x221,x222)+~P2(x221,f7(x222,x223)) % 1.56/1.67 [24]E(x241,x242)+P2(f3(x241,x242),x242)+P2(f3(x241,x242),x241) % 1.56/1.67 [26]E(x261,x262)+~P2(f3(x261,x262),x262)+~P2(f3(x261,x262),x261) % 1.56/1.67 [20]~P1(x203,x202)+P2(x201,x202)+~P2(x201,x203) % 1.56/1.67 [25]~P2(x251,x253)+~P2(x251,x252)+P2(x251,f7(x252,x253)) % 1.56/1.67 %EqnAxiom % 1.56/1.67 [1]E(x11,x11) % 1.56/1.67 [2]E(x22,x21)+~E(x21,x22) % 1.56/1.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.56/1.67 [4]~E(x41,x42)+E(f7(x41,x43),f7(x42,x43)) % 1.56/1.67 [5]~E(x51,x52)+E(f7(x53,x51),f7(x53,x52)) % 1.56/1.67 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63)) % 1.56/1.67 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72)) % 1.56/1.67 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83)) % 1.56/1.67 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92)) % 1.56/1.67 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103) % 1.56/1.67 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111) % 1.56/1.67 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123) % 1.56/1.67 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131) % 1.56/1.67 % 1.56/1.67 %------------------------------------------- % 1.56/1.67 cnf(57,plain, % 1.56/1.67 (~P2(f2(f7(a1,a5),f7(a6,a4)),f7(a6,a4))), % 1.56/1.67 inference(scs_inference,[],[18,17,23,11])). % 1.56/1.67 cnf(421,plain, % 1.56/1.67 (P2(f2(f7(a1,a5),f7(a6,a4)),f7(a1,a5))), % 1.56/1.67 inference(scs_inference,[],[18,17,19,11])). % 1.56/1.67 cnf(422,plain, % 1.56/1.67 (P2(f2(f7(a1,a5),f7(a6,a4)),a5)), % 1.56/1.67 inference(scs_inference,[],[421,21])). % 1.56/1.67 cnf(424,plain, % 1.56/1.67 (P2(f2(f7(a1,a5),f7(a6,a4)),a1)), % 1.56/1.67 inference(scs_inference,[],[421,21,22])). % 1.56/1.67 cnf(449,plain, % 1.56/1.67 (~P2(f2(f7(a1,a5),f7(a6,a4)),a4)), % 1.56/1.68 inference(scs_inference,[],[15,57,422,20,25])). % 1.56/1.68 cnf(458,plain, % 1.56/1.68 ($false), % 1.56/1.68 inference(scs_inference,[],[14,424,449,20]), % 1.56/1.68 ['proof']). % 1.56/1.68 % SZS output end Proof % 1.56/1.68 % Total time :1.030000s %------------------------------------------------------------------------------