%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET577+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 14:21:48 EDT 2024 % Result : Theorem 2.21s 2.25s % Output : CNFRefutation 2.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET577+3 : TPTP v8.2.0. Released v2.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n029.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 12:47:09 EDT 2024 % 0.12/0.34 % CPUTime : % 0.48/0.60 start to proof:theBenchmark % 2.21/2.25 %------------------------------------------- % 2.21/2.25 % File :CSE---1.7 % 2.21/2.25 % Problem :theBenchmark % 2.21/2.25 % Transform :cnf % 2.21/2.25 % Format :tptp:raw % 2.21/2.25 % Command :java -jar mcs_scs.jar %d %s % 2.21/2.25 % 2.21/2.25 % Result :Theorem 1.610000s % 2.21/2.25 % Output :CNFRefutation 1.610000s % 2.21/2.25 %------------------------------------------- % 2.21/2.25 %-------------------------------------------------------------------------- % 2.21/2.25 % File : SET577+3 : TPTP v8.2.0. Released v2.2.0. % 2.21/2.25 % Domain : Set Theory % 2.21/2.25 % Problem : Trybulec's 18th Boolean property of sets % 2.21/2.25 % Version : [Try90] axioms : Reduced > Incomplete. % 2.21/2.25 % English : % 2.21/2.25 % 2.21/2.25 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 2.21/2.25 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 2.21/2.25 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 2.21/2.25 % Source : [ILF] % 2.21/2.25 % Names : BOOLE (18) [TS89] % 2.21/2.25 % 2.21/2.25 % Status : Theorem % 2.21/2.25 % Rating : 0.14 v8.1.0, 0.11 v7.5.0, 0.09 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.10 v6.4.0, 0.12 v6.1.0, 0.27 v6.0.0, 0.22 v5.5.0, 0.26 v5.4.0, 0.36 v5.3.0, 0.30 v5.2.0, 0.10 v5.1.0, 0.14 v5.0.0, 0.21 v4.1.0, 0.26 v4.0.0, 0.25 v3.7.0, 0.30 v3.5.0, 0.32 v3.4.0, 0.37 v3.3.0, 0.29 v3.2.0, 0.45 v3.1.0, 0.44 v2.7.0, 0.17 v2.6.0, 0.14 v2.5.0, 0.25 v2.4.0, 0.25 v2.3.0, 0.00 v2.2.1 % 2.21/2.25 % Syntax : Number of formulae : 7 ( 2 unt; 0 def) % 2.21/2.25 % Number of atoms : 18 ( 4 equ) % 2.21/2.25 % Maximal formula atoms : 4 ( 2 avg) % 2.21/2.25 % Number of connectives : 11 ( 0 ~; 2 |; 1 &) % 2.21/2.25 % ( 6 <=>; 2 =>; 0 <=; 0 <~>) % 2.21/2.25 % Maximal formula depth : 8 ( 5 avg) % 2.21/2.25 % Maximal term depth : 2 ( 1 avg) % 2.21/2.25 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty) % 2.21/2.25 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty) % 2.21/2.25 % Number of variables : 18 ( 18 !; 0 ?) % 2.21/2.25 % SPC : FOF_THM_RFO_SEQ % 2.21/2.25 % 2.21/2.25 % Comments : % 2.21/2.25 %-------------------------------------------------------------------------- % 2.21/2.25 %---- line(boole - df(2),1833042) % 2.21/2.25 fof(union_defn,axiom, % 2.21/2.25 ! [B,C,D] : % 2.21/2.25 ( member(D,union(B,C)) % 2.21/2.25 <=> ( member(D,B) % 2.21/2.25 | member(D,C) ) ) ). % 2.21/2.25 % 2.21/2.25 %---- line(boole - df(8),1833103) % 2.21/2.25 fof(equal_defn,axiom, % 2.21/2.25 ! [B,C] : % 2.21/2.25 ( B = C % 2.21/2.25 <=> ( subset(B,C) % 2.21/2.25 & subset(C,B) ) ) ). % 2.21/2.25 % 2.21/2.25 %---- property(commutativity,op(union,2,function)) % 2.21/2.25 fof(commutativity_of_union,axiom, % 2.21/2.25 ! [B,C] : union(B,C) = union(C,B) ). % 2.21/2.25 % 2.21/2.25 %---- line(tarski - df(3),1832749) % 2.21/2.25 fof(subset_defn,axiom, % 2.21/2.25 ! [B,C] : % 2.21/2.25 ( subset(B,C) % 2.21/2.25 <=> ! [D] : % 2.21/2.25 ( member(D,B) % 2.21/2.25 => member(D,C) ) ) ). % 2.21/2.25 % 2.21/2.25 %---- property(reflexivity,op(subset,2,predicate)) % 2.21/2.25 fof(reflexivity_of_subset,axiom, % 2.21/2.25 ! [B] : subset(B,B) ). % 2.21/2.25 % 2.21/2.25 %---- line(hidden - axiom13,1832615) % 2.21/2.25 fof(equal_member_defn,axiom, % 2.21/2.25 ! [B,C] : % 2.21/2.25 ( B = C % 2.21/2.25 <=> ! [D] : % 2.21/2.25 ( member(D,B) % 2.21/2.25 <=> member(D,C) ) ) ). % 2.21/2.25 % 2.21/2.25 %---- line(boole - th(18),1833113) % 2.21/2.25 fof(prove_th18,conjecture, % 2.21/2.25 ! [B,C,D] : % 2.21/2.25 ( ! [E] : % 2.21/2.25 ( member(E,B) % 2.21/2.25 <=> ( member(E,C) % 2.21/2.25 | member(E,D) ) ) % 2.21/2.25 => B = union(C,D) ) ). % 2.21/2.25 % 2.21/2.25 %-------------------------------------------------------------------------- % 2.21/2.25 %------------------------------------------- % 2.21/2.25 % Proof found % 2.21/2.25 % SZS status Theorem for theBenchmark % 2.21/2.25 % SZS output start Proof % 2.21/2.25 %ClaNum:30(EqnAxiom:13) % 2.21/2.25 %VarNum:72(SingletonVarNum:30) % 2.21/2.25 %MaxLitNum:3 % 2.21/2.25 %MaxfuncDepth:1 % 2.21/2.25 %SharedTerms:5 % 2.21/2.25 %goalClause: 16 19 20 21 % 2.21/2.25 %singleGoalClaCount:1 % 2.21/2.25 [16]~E(f1(a2,a6),a3) % 2.21/2.25 [14]P1(x141,x141) % 2.21/2.25 [15]E(f1(x151,x152),f1(x152,x151)) % 2.21/2.25 [19]~P2(x191,a2)+P2(x191,a3) % 2.21/2.25 [20]~P2(x201,a6)+P2(x201,a3) % 2.21/2.25 [18]~E(x181,x182)+P1(x181,x182) % 2.21/2.25 [23]P1(x231,x232)+P2(f4(x231,x232),x231) % 2.21/2.25 [27]P1(x271,x272)+~P2(f4(x271,x272),x272) % 2.21/2.25 [25]~P2(x251,x253)+P2(x251,f1(x252,x253)) % 2.21/2.25 [26]~P2(x261,x262)+P2(x261,f1(x262,x263)) % 2.21/2.25 [21]P2(x211,a6)+~P2(x211,a3)+P2(x211,a2) % 2.21/2.25 [22]~P1(x222,x221)+~P1(x221,x222)+E(x221,x222) % 2.21/2.25 [28]E(x281,x282)+P2(f5(x281,x282),x282)+P2(f5(x281,x282),x281) % 2.21/2.25 [30]E(x301,x302)+~P2(f5(x301,x302),x302)+~P2(f5(x301,x302),x301) % 2.21/2.25 [24]~P1(x243,x242)+P2(x241,x242)+~P2(x241,x243) % 2.21/2.25 [29]P2(x291,x292)+P2(x291,x293)+~P2(x291,f1(x293,x292)) % 2.21/2.25 %EqnAxiom % 2.21/2.25 [1]E(x11,x11) % 2.21/2.25 [2]E(x22,x21)+~E(x21,x22) % 2.21/2.25 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 2.21/2.25 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43)) % 2.21/2.25 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52)) % 2.21/2.25 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63)) % 2.21/2.25 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72)) % 2.21/2.25 [8]~E(x81,x82)+E(f4(x81,x83),f4(x82,x83)) % 2.21/2.26 [9]~E(x91,x92)+E(f4(x93,x91),f4(x93,x92)) % 2.21/2.26 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103) % 2.21/2.26 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111) % 2.21/2.26 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123) % 2.21/2.26 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131) % 2.21/2.26 % 2.21/2.26 %------------------------------------------- % 2.21/2.26 cnf(60,plain, % 2.21/2.26 (~E(a3,f1(a6,a2))), % 2.21/2.26 inference(scs_inference,[],[16,15,3,2])). % 2.21/2.26 cnf(61,plain, % 2.21/2.26 (~E(a3,f1(a2,a6))), % 2.21/2.26 inference(scs_inference,[],[15,60,3])). % 2.21/2.26 cnf(93,plain, % 2.21/2.26 (P2(f5(a3,f1(a2,a6)),f1(a2,a6))+P2(f5(a3,f1(a2,a6)),a3)), % 2.21/2.26 inference(scs_inference,[],[16,2,28])). % 2.21/2.26 cnf(140,plain, % 2.21/2.26 (~P2(f5(a3,f1(a2,a6)),f1(a2,a6))+~P2(f5(a3,f1(a2,a6)),a2)), % 2.21/2.26 inference(scs_inference,[],[61,19,30])). % 2.21/2.26 cnf(141,plain, % 2.21/2.26 (~P2(f5(a3,f1(a2,a6)),a2)), % 2.21/2.26 inference(scs_inference,[],[140,26])). % 2.21/2.26 cnf(194,plain, % 2.21/2.26 (~P2(f5(a3,f1(a2,a6)),f1(a2,a6))+~P2(f5(a3,f1(a2,a6)),a6)), % 2.21/2.26 inference(scs_inference,[],[61,20,30])). % 2.21/2.26 cnf(195,plain, % 2.21/2.26 (~P2(f5(a3,f1(a2,a6)),a6)), % 2.21/2.26 inference(scs_inference,[],[194,25])). % 2.21/2.26 cnf(212,plain, % 2.21/2.26 (P2(f5(a3,f1(a2,a6)),a3)+~P2(f5(a3,f1(a2,a6)),f1(a6,a6))), % 2.21/2.26 inference(scs_inference,[],[195,20,29])). % 2.21/2.26 cnf(213,plain, % 2.21/2.26 (~P2(f5(a3,f1(a2,a6)),f1(a6,a6))), % 2.21/2.26 inference(scs_inference,[],[141,195,212,21])). % 2.21/2.26 cnf(421,plain, % 2.21/2.26 (~P2(f5(a3,f1(a2,a6)),a3)), % 2.21/2.26 inference(scs_inference,[],[213,141,25,21])). % 2.21/2.26 cnf(422,plain, % 2.21/2.26 (P2(f5(a3,f1(a2,a6)),f1(a2,a6))), % 2.21/2.26 inference(scs_inference,[],[421,93])). % 2.21/2.26 cnf(428,plain, % 2.21/2.26 ($false), % 2.21/2.26 inference(scs_inference,[],[422,195,141,29]), % 2.21/2.26 ['proof']). % 2.21/2.26 % SZS output end Proof % 2.21/2.26 % Total time :1.610000s %------------------------------------------------------------------------------