%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET578+3 : TPTP v8.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/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 14:21:48 EDT 2024 % Result : Theorem 6.74s 6.83s % Output : CNFRefutation 6.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET578+3 : TPTP v8.2.0. Released v2.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n018.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sun Jun 23 13:19:24 EDT 2024 % 0.12/0.33 % CPUTime : % 0.43/0.60 start to proof:theBenchmark % 6.74/6.83 %------------------------------------------- % 6.74/6.83 % File :CSE---1.7 % 6.74/6.83 % Problem :theBenchmark % 6.74/6.83 % Transform :cnf % 6.74/6.83 % Format :tptp:raw % 6.74/6.83 % Command :java -jar mcs_scs.jar %d %s % 6.74/6.83 % 6.74/6.83 % Result :Theorem 6.160000s % 6.74/6.83 % Output :CNFRefutation 6.160000s % 6.74/6.83 %------------------------------------------- % 6.74/6.83 %-------------------------------------------------------------------------- % 6.74/6.83 % File : SET578+3 : TPTP v8.2.0. Released v2.2.0. % 6.74/6.83 % Domain : Set Theory % 6.74/6.83 % Problem : Trybulec's 19th Boolean property of sets % 6.74/6.83 % Version : [Try90] axioms : Reduced > Incomplete. % 6.74/6.83 % English : % 6.74/6.83 % 6.74/6.83 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 6.74/6.83 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 6.74/6.83 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 6.74/6.83 % Source : [ILF] % 6.74/6.83 % Names : BOOLE (19) [TS89] % 6.74/6.83 % 6.74/6.83 % Status : Theorem % 6.74/6.83 % Rating : 0.17 v8.2.0, 0.19 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.04 v6.3.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.20 v6.0.0, 0.26 v5.5.0, 0.15 v5.4.0, 0.21 v5.3.0, 0.30 v5.2.0, 0.05 v5.0.0, 0.17 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.14 v3.2.0, 0.18 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1 % 6.74/6.83 % Syntax : Number of formulae : 7 ( 2 unt; 0 def) % 6.74/6.83 % Number of atoms : 18 ( 4 equ) % 6.74/6.83 % Maximal formula atoms : 4 ( 2 avg) % 6.74/6.83 % Number of connectives : 11 ( 0 ~; 0 |; 3 &) % 6.74/6.83 % ( 6 <=>; 2 =>; 0 <=; 0 <~>) % 6.74/6.83 % Maximal formula depth : 8 ( 5 avg) % 6.74/6.83 % Maximal term depth : 2 ( 1 avg) % 6.74/6.83 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty) % 6.74/6.83 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty) % 6.74/6.83 % Number of variables : 18 ( 18 !; 0 ?) % 6.74/6.83 % SPC : FOF_THM_RFO_SEQ % 6.74/6.83 % 6.74/6.83 % Comments : % 6.74/6.83 %-------------------------------------------------------------------------- % 6.74/6.83 %---- line(boole - df(3),1833060) % 6.74/6.83 fof(intersection_defn,axiom, % 6.74/6.83 ! [B,C,D] : % 6.74/6.83 ( member(D,intersection(B,C)) % 6.74/6.83 <=> ( member(D,B) % 6.74/6.83 & member(D,C) ) ) ). % 6.74/6.83 % 6.74/6.83 %---- line(boole - df(8),1833103) % 6.74/6.83 fof(equal_defn,axiom, % 6.74/6.83 ! [B,C] : % 6.74/6.83 ( B = C % 6.74/6.83 <=> ( subset(B,C) % 6.74/6.83 & subset(C,B) ) ) ). % 6.74/6.83 % 6.74/6.83 %---- property(commutativity,op(intersection,2,function)) % 6.74/6.83 fof(commutativity_of_intersection,axiom, % 6.74/6.83 ! [B,C] : intersection(B,C) = intersection(C,B) ). % 6.74/6.83 % 6.74/6.83 %---- line(tarski - df(3),1832749) % 6.74/6.83 fof(subset_defn,axiom, % 6.74/6.83 ! [B,C] : % 6.74/6.83 ( subset(B,C) % 6.74/6.83 <=> ! [D] : % 6.74/6.83 ( member(D,B) % 6.74/6.83 => member(D,C) ) ) ). % 6.74/6.83 % 6.74/6.83 %---- property(reflexivity,op(subset,2,predicate)) % 6.74/6.83 fof(reflexivity_of_subset,axiom, % 6.74/6.83 ! [B] : subset(B,B) ). % 6.74/6.83 % 6.74/6.83 %---- line(hidden - axiom15,1832615) % 6.74/6.83 fof(equal_member_defn,axiom, % 6.74/6.83 ! [B,C] : % 6.74/6.83 ( B = C % 6.74/6.83 <=> ! [D] : % 6.74/6.83 ( member(D,B) % 6.74/6.83 <=> member(D,C) ) ) ). % 6.74/6.83 % 6.74/6.83 %---- line(boole - th(19),1833114) % 6.74/6.83 fof(prove_th19,conjecture, % 6.74/6.83 ! [B,C,D] : % 6.74/6.83 ( ! [E] : % 6.74/6.83 ( member(E,B) % 6.74/6.83 <=> ( member(E,C) % 6.74/6.83 & member(E,D) ) ) % 6.74/6.83 => B = intersection(C,D) ) ). % 6.74/6.83 % 6.74/6.83 %-------------------------------------------------------------------------- % 6.74/6.83 %------------------------------------------- % 6.74/6.83 % Proof found % 6.74/6.83 % SZS status Theorem for theBenchmark % 6.74/6.83 % SZS output start Proof % 6.74/6.83 %ClaNum:30(EqnAxiom:13) % 6.74/6.83 %VarNum:72(SingletonVarNum:30) % 6.74/6.83 %MaxLitNum:3 % 6.74/6.83 %MaxfuncDepth:1 % 6.74/6.83 %SharedTerms:5 % 6.74/6.83 %goalClause: 16 19 20 22 % 6.74/6.83 %singleGoalClaCount:1 % 6.74/6.83 [16]~E(f1(a2,a6),a3) % 6.74/6.83 [14]P1(x141,x141) % 6.74/6.83 [15]E(f1(x151,x152),f1(x152,x151)) % 6.74/6.83 [19]~P2(x191,a3)+P2(x191,a2) % 6.74/6.83 [20]~P2(x201,a3)+P2(x201,a6) % 6.74/6.83 [18]~E(x181,x182)+P1(x181,x182) % 6.74/6.83 [23]P1(x231,x232)+P2(f4(x231,x232),x231) % 6.74/6.83 [27]P1(x271,x272)+~P2(f4(x271,x272),x272) % 6.74/6.83 [25]P2(x251,x252)+~P2(x251,f1(x253,x252)) % 6.74/6.83 [26]P2(x261,x262)+~P2(x261,f1(x262,x263)) % 6.74/6.83 [22]~P2(x221,a2)+~P2(x221,a6)+P2(x221,a3) % 6.74/6.83 [21]~P1(x212,x211)+~P1(x211,x212)+E(x211,x212) % 6.74/6.83 [28]E(x281,x282)+P2(f5(x281,x282),x282)+P2(f5(x281,x282),x281) % 6.74/6.83 [30]E(x301,x302)+~P2(f5(x301,x302),x302)+~P2(f5(x301,x302),x301) % 6.74/6.83 [24]~P1(x243,x242)+P2(x241,x242)+~P2(x241,x243) % 6.74/6.84 [29]~P2(x291,x293)+~P2(x291,x292)+P2(x291,f1(x292,x293)) % 6.74/6.84 %EqnAxiom % 6.74/6.84 [1]E(x11,x11) % 6.74/6.84 [2]E(x22,x21)+~E(x21,x22) % 6.74/6.84 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 6.74/6.84 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43)) % 6.74/6.84 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52)) % 6.74/6.84 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63)) % 6.74/6.84 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72)) % 6.74/6.84 [8]~E(x81,x82)+E(f4(x81,x83),f4(x82,x83)) % 6.74/6.84 [9]~E(x91,x92)+E(f4(x93,x91),f4(x93,x92)) % 6.74/6.84 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103) % 6.74/6.84 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111) % 6.74/6.84 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123) % 6.74/6.84 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131) % 6.74/6.84 % 6.74/6.84 %------------------------------------------- % 6.74/6.84 cnf(32,plain, % 6.74/6.84 (P1(f1(x321,x322),f1(x322,x321))), % 6.74/6.84 inference(scs_inference,[],[14,15,10])). % 6.74/6.84 cnf(53,plain, % 6.74/6.84 (~E(a3,f1(a6,a2))), % 6.74/6.84 inference(scs_inference,[],[16,15,3,2])). % 6.74/6.84 cnf(54,plain, % 6.74/6.84 (~E(a3,f1(a2,a6))), % 6.74/6.84 inference(scs_inference,[],[53,15,3])). % 6.74/6.84 cnf(63,plain, % 6.74/6.84 (~P1(a3,f1(a2,a6))+P2(f4(f1(a2,a6),a3),f1(a2,a6))), % 6.74/6.84 inference(scs_inference,[],[16,21,23])). % 6.74/6.84 cnf(64,plain, % 6.74/6.84 (P2(f4(f1(a2,a6),a3),a6)+~P1(a3,f1(a2,a6))), % 6.74/6.84 inference(scs_inference,[],[63,25])). % 6.74/6.84 cnf(130,plain, % 6.74/6.84 (~P2(x1301,x1302)+P2(x1301,f1(x1302,a2))+~P2(x1301,a3)), % 6.74/6.84 inference(scs_inference,[],[19,29])). % 6.74/6.84 cnf(439,plain, % 6.74/6.84 (P2(x4391,f1(a6,a2))+~P2(x4391,a3)), % 6.74/6.84 inference(scs_inference,[],[20,130])). % 6.74/6.84 cnf(440,plain, % 6.74/6.84 (P1(x4401,f1(a6,a2))+~P2(f4(x4401,f1(a6,a2)),a3)), % 6.74/6.84 inference(scs_inference,[],[439,27])). % 6.74/6.84 cnf(1185,plain, % 6.74/6.84 (P1(a3,f1(a6,a2))), % 6.74/6.84 inference(scs_inference,[],[23,440])). % 6.74/6.84 cnf(1207,plain, % 6.74/6.84 (~P1(f1(a2,a6),a3)), % 6.74/6.84 inference(scs_inference,[],[54,15,32,1185,11,63,64,26,24,21])). % 6.74/6.84 cnf(1209,plain, % 6.74/6.84 (P2(f4(f1(a2,a6),a3),a3)), % 6.74/6.84 inference(scs_inference,[],[54,15,32,1185,11,63,64,26,24,21,22])). % 6.74/6.84 cnf(1239,plain, % 6.74/6.84 ($false), % 6.74/6.84 inference(scs_inference,[],[1207,1209,27]), % 6.74/6.84 ['proof']). % 6.74/6.84 % SZS output end Proof % 6.74/6.84 % Total time :6.160000s %------------------------------------------------------------------------------