%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET148+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 : n018.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 14:20:55 EDT 2024 % Result : Theorem 0.57s 0.62s % Output : CNFRefutation 0.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET148+3 : TPTP v8.2.0. Released v2.2.0. % 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n018.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 12:10:24 EDT 2024 % 0.12/0.34 % CPUTime : % 0.21/0.58 start to proof:theBenchmark % 0.21/0.61 %------------------------------------------- % 0.21/0.61 % File :CSE---1.7 % 0.21/0.61 % Problem :theBenchmark % 0.21/0.61 % Transform :cnf % 0.21/0.61 % Format :tptp:raw % 0.21/0.61 % Command :java -jar mcs_scs.jar %d %s % 0.21/0.61 % 0.21/0.61 % Result :Theorem 0.000000s % 0.21/0.61 % Output :CNFRefutation 0.000000s % 0.21/0.61 %------------------------------------------- % 0.57/0.62 %-------------------------------------------------------------------------- % 0.57/0.62 % File : SET148+3 : TPTP v8.2.0. Released v2.2.0. % 0.57/0.62 % Domain : Set Theory % 0.57/0.62 % Problem : Idempotency of intersection % 0.57/0.62 % Version : [Try90] axioms : Reduced > Incomplete. % 0.57/0.62 % English : % 0.57/0.62 % 0.57/0.62 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.57/0.62 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.57/0.62 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.57/0.62 % Source : [ILF] % 0.57/0.62 % Names : BOOLE (63) [TS89] % 0.57/0.62 % 0.57/0.62 % Status : Theorem % 0.57/0.62 % 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, 0.04 v5.3.0, 0.11 v5.2.0, 0.00 v5.0.0, 0.04 v4.0.1, 0.09 v4.0.0, 0.08 v3.7.0, 0.05 v3.3.0, 0.07 v3.2.0, 0.09 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1 % 0.57/0.62 % Syntax : Number of formulae : 8 ( 3 unt; 0 def) % 0.57/0.62 % Number of atoms : 17 ( 5 equ) % 0.57/0.62 % Maximal formula atoms : 3 ( 2 avg) % 0.57/0.62 % Number of connectives : 9 ( 0 ~; 0 |; 2 &) % 0.57/0.62 % ( 5 <=>; 2 =>; 0 <=; 0 <~>) % 0.57/0.62 % Maximal formula depth : 6 ( 4 avg) % 0.57/0.62 % Maximal term depth : 2 ( 1 avg) % 0.57/0.62 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty) % 0.57/0.62 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty) % 0.57/0.62 % Number of variables : 17 ( 17 !; 0 ?) % 0.57/0.62 % SPC : FOF_THM_RFO_SEQ % 0.57/0.62 % 0.57/0.62 % Comments : % 0.57/0.62 %-------------------------------------------------------------------------- % 0.57/0.62 %---- line(boole - th(42),1833351) % 0.57/0.62 fof(subset_intersection,axiom, % 0.57/0.62 ! [B,C] : % 0.57/0.62 ( subset(B,C) % 0.57/0.62 => intersection(B,C) = B ) ). % 0.57/0.62 % 0.57/0.62 %---- line(boole - df(3),1833060) % 0.57/0.62 fof(intersection_defn,axiom, % 0.57/0.62 ! [B,C,D] : % 0.57/0.62 ( member(D,intersection(B,C)) % 0.57/0.62 <=> ( member(D,B) % 0.57/0.62 & member(D,C) ) ) ). % 0.57/0.62 % 0.57/0.62 %---- line(boole - df(8),1833103) % 0.57/0.62 fof(equal_defn,axiom, % 0.57/0.62 ! [B,C] : % 0.57/0.62 ( B = C % 0.57/0.62 <=> ( subset(B,C) % 0.57/0.62 & subset(C,B) ) ) ). % 0.57/0.62 % 0.57/0.62 %---- property(commutativity,op(intersection,2,function)) % 0.57/0.62 fof(commutativity_of_intersection,axiom, % 0.57/0.62 ! [B,C] : intersection(B,C) = intersection(C,B) ). % 0.57/0.62 % 0.57/0.62 %---- line(tarski - df(3),1832749) % 0.57/0.62 fof(subset_defn,axiom, % 0.57/0.62 ! [B,C] : % 0.57/0.62 ( subset(B,C) % 0.57/0.62 <=> ! [D] : % 0.57/0.62 ( member(D,B) % 0.57/0.62 => member(D,C) ) ) ). % 0.57/0.62 % 0.57/0.62 %---- property(reflexivity,op(subset,2,predicate)) % 0.57/0.62 fof(reflexivity_of_subset,axiom, % 0.57/0.62 ! [B] : subset(B,B) ). % 0.57/0.62 % 0.57/0.62 %---- line(hidden - axiom106,1832615) % 0.57/0.62 fof(equal_member_defn,axiom, % 0.57/0.62 ! [B,C] : % 0.57/0.62 ( B = C % 0.57/0.62 <=> ! [D] : % 0.57/0.62 ( member(D,B) % 0.57/0.62 <=> member(D,C) ) ) ). % 0.57/0.62 % 0.57/0.62 %---- line(boole - th(65),1833713) % 0.57/0.62 fof(prove_idempotency_of_intersection,conjecture, % 0.57/0.62 ! [B] : intersection(B,B) = B ). % 0.57/0.62 % 0.57/0.62 %-------------------------------------------------------------------------- % 0.57/0.62 %------------------------------------------- % 0.57/0.62 % Proof found % 0.57/0.62 % SZS status Theorem for theBenchmark % 0.57/0.62 % SZS output start Proof % 0.57/0.62 %ClaNum:28(EqnAxiom:13) % 0.57/0.62 %VarNum:70(SingletonVarNum:29) % 0.57/0.62 %MaxLitNum:3 % 0.57/0.62 %MaxfuncDepth:1 % 0.57/0.62 %SharedTerms:3 % 0.57/0.62 %goalClause: 16 % 0.57/0.62 %singleGoalClaCount:1 % 0.57/0.62 [16]~E(f1(a2,a2),a2) % 0.57/0.62 [14]P1(x141,x141) % 0.57/0.62 [15]E(f1(x151,x152),f1(x152,x151)) % 0.57/0.62 [18]~E(x181,x182)+P1(x181,x182) % 0.57/0.62 [19]~P1(x191,x192)+E(f1(x191,x192),x191) % 0.57/0.62 [21]P1(x211,x212)+P2(f3(x211,x212),x211) % 0.57/0.62 [25]P1(x251,x252)+~P2(f3(x251,x252),x252) % 0.57/0.62 [23]P2(x231,x232)+~P2(x231,f1(x233,x232)) % 0.57/0.62 [24]P2(x241,x242)+~P2(x241,f1(x242,x243)) % 0.57/0.62 [20]~P1(x202,x201)+~P1(x201,x202)+E(x201,x202) % 0.57/0.62 [26]E(x261,x262)+P2(f4(x261,x262),x262)+P2(f4(x261,x262),x261) % 0.57/0.62 [28]E(x281,x282)+~P2(f4(x281,x282),x282)+~P2(f4(x281,x282),x281) % 0.57/0.62 [22]~P2(x221,x223)+P2(x221,x222)+~P1(x223,x222) % 0.57/0.62 [27]~P2(x271,x273)+~P2(x271,x272)+P2(x271,f1(x272,x273)) % 0.57/0.62 %EqnAxiom % 0.57/0.62 [1]E(x11,x11) % 0.57/0.62 [2]E(x22,x21)+~E(x21,x22) % 0.57/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.57/0.62 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43)) % 0.57/0.62 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52)) % 0.57/0.62 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63)) % 0.57/0.62 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72)) % 0.57/0.62 [8]~E(x81,x82)+E(f3(x81,x83),f3(x82,x83)) % 0.57/0.62 [9]~E(x91,x92)+E(f3(x93,x91),f3(x93,x92)) % 0.57/0.62 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103) % 0.57/0.62 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111) % 0.57/0.62 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123) % 0.57/0.62 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131) % 0.57/0.62 % 0.57/0.62 %------------------------------------------- % 0.57/0.63 cnf(30,plain, % 0.57/0.63 ($false), % 0.57/0.63 inference(scs_inference,[],[14,16,19]), % 0.57/0.63 ['proof']). % 0.57/0.63 % SZS output end Proof % 0.57/0.63 % Total time :0.000000s %------------------------------------------------------------------------------