%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET162+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 : n027.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 14:20:57 EDT 2024 % Result : Theorem 1.24s 1.30s % Output : CNFRefutation 1.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET162+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 % 0.12/0.33 % Computer : n027.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 16:50:39 EDT 2024 % 0.12/0.33 % CPUTime : % 0.47/0.59 start to proof:theBenchmark % 1.24/1.30 %------------------------------------------- % 1.24/1.30 % File :CSE---1.7 % 1.24/1.30 % Problem :theBenchmark % 1.24/1.30 % Transform :cnf % 1.24/1.30 % Format :tptp:raw % 1.24/1.30 % Command :java -jar mcs_scs.jar %d %s % 1.24/1.30 % 1.24/1.30 % Result :Theorem 0.670000s % 1.24/1.30 % Output :CNFRefutation 0.670000s % 1.24/1.30 %------------------------------------------- % 1.24/1.30 %-------------------------------------------------------------------------- % 1.24/1.30 % File : SET162+3 : TPTP v8.2.0. Released v2.2.0. % 1.24/1.30 % Domain : Set Theory % 1.24/1.30 % Problem : The union of X and the empty set is X % 1.24/1.30 % Version : [Try90] axioms : Reduced > Incomplete. % 1.24/1.30 % English : % 1.24/1.30 % 1.24/1.30 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 1.24/1.30 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 1.24/1.30 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 1.24/1.30 % Source : [ILF] % 1.24/1.30 % Names : BOOLE (60) [TS89] % 1.24/1.30 % 1.24/1.30 % Status : Theorem % 1.24/1.30 % Rating : 0.11 v8.2.0, 0.08 v8.1.0, 0.03 v7.2.0, 0.00 v7.1.0, 0.04 v7.0.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.12 v6.1.0, 0.17 v5.5.0, 0.15 v5.4.0, 0.18 v5.3.0, 0.26 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.13 v4.0.1, 0.17 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 % 1.24/1.30 % Syntax : Number of formulae : 9 ( 4 unt; 0 def) % 1.24/1.30 % Number of atoms : 18 ( 4 equ) % 1.24/1.30 % Maximal formula atoms : 3 ( 2 avg) % 1.24/1.30 % Number of connectives : 11 ( 2 ~; 1 |; 1 &) % 1.24/1.30 % ( 6 <=>; 1 =>; 0 <=; 0 <~>) % 1.24/1.30 % Maximal formula depth : 6 ( 4 avg) % 1.24/1.30 % Maximal term depth : 2 ( 1 avg) % 1.24/1.30 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty) % 1.24/1.30 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty) % 1.24/1.30 % Number of variables : 18 ( 18 !; 0 ?) % 1.24/1.30 % SPC : FOF_THM_RFO_SEQ % 1.24/1.30 % 1.24/1.30 % Comments : % 1.24/1.30 %-------------------------------------------------------------------------- % 1.24/1.30 %---- line(boole - df(2),1833042) % 1.24/1.30 fof(union_defn,axiom, % 1.24/1.30 ! [B,C,D] : % 1.24/1.30 ( member(D,union(B,C)) % 1.24/1.30 <=> ( member(D,B) % 1.24/1.30 | member(D,C) ) ) ). % 1.24/1.30 % 1.24/1.30 %---- line(hidden - axiom93,1832636) % 1.24/1.30 fof(empty_set_defn,axiom, % 1.24/1.30 ! [B] : ~ member(B,empty_set) ). % 1.24/1.30 % 1.24/1.30 %---- line(boole - df(8),1833103) % 1.24/1.30 fof(equal_defn,axiom, % 1.24/1.30 ! [B,C] : % 1.24/1.30 ( B = C % 1.24/1.30 <=> ( subset(B,C) % 1.24/1.30 & subset(C,B) ) ) ). % 1.24/1.30 % 1.24/1.30 %---- property(commutativity,op(union,2,function)) % 1.24/1.30 fof(commutativity_of_union,axiom, % 1.24/1.30 ! [B,C] : union(B,C) = union(C,B) ). % 1.24/1.30 % 1.24/1.30 %---- line(tarski - df(3),1832749) % 1.24/1.30 fof(subset_defn,axiom, % 1.24/1.30 ! [B,C] : % 1.24/1.30 ( subset(B,C) % 1.24/1.30 <=> ! [D] : % 1.24/1.30 ( member(D,B) % 1.24/1.30 => member(D,C) ) ) ). % 1.24/1.30 % 1.24/1.30 %---- property(reflexivity,op(subset,2,predicate)) % 1.24/1.30 fof(reflexivity_of_subset,axiom, % 1.24/1.30 ! [B] : subset(B,B) ). % 1.24/1.30 % 1.24/1.30 %---- line(hidden - axiom95,1832628) % 1.24/1.30 fof(empty_defn,axiom, % 1.24/1.30 ! [B] : % 1.24/1.30 ( empty(B) % 1.24/1.30 <=> ! [C] : ~ member(C,B) ) ). % 1.24/1.30 % 1.24/1.30 %---- line(hidden - axiom96,1832615) % 1.24/1.30 fof(equal_member_defn,axiom, % 1.24/1.30 ! [B,C] : % 1.24/1.30 ( B = C % 1.24/1.30 <=> ! [D] : % 1.24/1.30 ( member(D,B) % 1.24/1.30 <=> member(D,C) ) ) ). % 1.24/1.30 % 1.24/1.30 %---- line(boole - th(60),1833665) % 1.24/1.30 fof(prove_union_empty_set,conjecture, % 1.24/1.30 ! [B] : union(B,empty_set) = B ). % 1.24/1.30 % 1.24/1.30 %-------------------------------------------------------------------------- % 1.24/1.30 %------------------------------------------- % 1.24/1.30 % Proof found % 1.24/1.30 % SZS status Theorem for theBenchmark % 1.24/1.30 % SZS output start Proof % 1.24/1.30 %ClaNum:32(EqnAxiom:15) % 1.24/1.30 %VarNum:72(SingletonVarNum:31) % 1.24/1.30 %MaxLitNum:3 % 1.24/1.30 %MaxfuncDepth:1 % 1.24/1.30 %SharedTerms:4 % 1.24/1.30 %goalClause: 18 % 1.24/1.30 %singleGoalClaCount:1 % 1.24/1.30 [18]~E(f1(a2,a3),a2) % 1.24/1.30 [16]P1(x161,x161) % 1.24/1.30 [19]~P2(x191,a3) % 1.24/1.30 [17]E(f1(x171,x172),f1(x172,x171)) % 1.24/1.30 [22]P3(x221)+P2(f4(x221),x221) % 1.24/1.30 [21]~E(x211,x212)+P1(x211,x212) % 1.24/1.30 [23]~P3(x231)+~P2(x232,x231) % 1.24/1.30 [25]P1(x251,x252)+P2(f5(x251,x252),x251) % 1.24/1.30 [29]P1(x291,x292)+~P2(f5(x291,x292),x292) % 1.24/1.30 [27]~P2(x271,x273)+P2(x271,f1(x272,x273)) % 1.24/1.30 [28]~P2(x281,x282)+P2(x281,f1(x282,x283)) % 1.24/1.30 [24]~P1(x242,x241)+~P1(x241,x242)+E(x241,x242) % 1.24/1.30 [30]E(x301,x302)+P2(f6(x301,x302),x302)+P2(f6(x301,x302),x301) % 1.24/1.30 [32]E(x321,x322)+~P2(f6(x321,x322),x322)+~P2(f6(x321,x322),x321) % 1.24/1.30 [26]~P1(x263,x262)+P2(x261,x262)+~P2(x261,x263) % 1.24/1.30 [31]P2(x311,x312)+P2(x311,x313)+~P2(x311,f1(x313,x312)) % 1.24/1.30 %EqnAxiom % 1.24/1.30 [1]E(x11,x11) % 1.24/1.30 [2]E(x22,x21)+~E(x21,x22) % 1.24/1.30 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.24/1.30 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43)) % 1.24/1.30 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52)) % 1.24/1.30 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63)) % 1.24/1.30 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72)) % 1.24/1.30 [8]~E(x81,x82)+E(f5(x81,x83),f5(x82,x83)) % 1.24/1.30 [9]~E(x91,x92)+E(f5(x93,x91),f5(x93,x92)) % 1.24/1.30 [10]~E(x101,x102)+E(f4(x101),f4(x102)) % 1.24/1.30 [11]P1(x112,x113)+~E(x111,x112)+~P1(x111,x113) % 1.24/1.31 [12]P1(x123,x122)+~E(x121,x122)+~P1(x123,x121) % 1.24/1.31 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133) % 1.24/1.31 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141) % 1.24/1.31 [15]~P3(x151)+P3(x152)+~E(x151,x152) % 1.24/1.31 % 1.24/1.31 %------------------------------------------- % 1.24/1.31 cnf(100,plain, % 1.24/1.31 (~P2(f6(a2,f1(a2,a3)),f1(a2,a3))+~P2(f6(a2,f1(a2,a3)),a2)), % 1.24/1.31 inference(scs_inference,[],[18,32,2])). % 1.24/1.31 cnf(101,plain, % 1.24/1.31 (~P2(f6(a2,f1(a2,a3)),a2)), % 1.24/1.31 inference(scs_inference,[],[100,28])). % 1.24/1.31 cnf(344,plain, % 1.24/1.31 (P2(f6(a2,f1(a2,a3)),f1(a2,a3))), % 1.24/1.31 inference(scs_inference,[],[18,101,2,30])). % 1.24/1.31 cnf(345,plain, % 1.24/1.31 ($false), % 1.24/1.31 inference(scs_inference,[],[344,19,101,31]), % 1.24/1.31 ['proof']). % 1.24/1.31 % SZS output end Proof % 1.24/1.31 % Total time :0.670000s %------------------------------------------------------------------------------