%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET185+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 : n023.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 14:21:02 EDT 2024 % Result : Theorem 0.58s 0.69s % Output : CNFRefutation 0.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET185+3 : TPTP v8.2.0. Released v2.2.0. % 0.11/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.32 % Computer : n023.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Sun Jun 23 14:13:24 EDT 2024 % 0.12/0.33 % CPUTime : % 0.18/0.55 start to proof:theBenchmark % 0.58/0.69 %------------------------------------------- % 0.58/0.69 % File :CSE---1.7 % 0.58/0.69 % Problem :theBenchmark % 0.58/0.69 % Transform :cnf % 0.58/0.69 % Format :tptp:raw % 0.58/0.69 % Command :java -jar mcs_scs.jar %d %s % 0.58/0.69 % 0.58/0.69 % Result :Theorem 0.100000s % 0.58/0.69 % Output :CNFRefutation 0.100000s % 0.58/0.69 %------------------------------------------- % 0.58/0.69 %-------------------------------------------------------------------------- % 0.58/0.69 % File : SET185+3 : TPTP v8.2.0. Released v2.2.0. % 0.58/0.69 % Domain : Set Theory % 0.58/0.69 % Problem : If X is a subset of Y, then the union of X and Y is Y % 0.58/0.69 % Version : [Try90] axioms : Reduced > Incomplete. % 0.58/0.69 % English : % 0.58/0.69 % 0.58/0.69 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.58/0.69 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.58/0.69 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.58/0.69 % Source : [ILF] % 0.58/0.69 % Names : BOOLE (35) [TS89] % 0.58/0.69 % 0.58/0.69 % Status : Theorem % 0.58/0.69 % Rating : 0.11 v8.1.0, 0.06 v7.4.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.08 v6.3.0, 0.12 v6.2.0, 0.08 v6.1.0, 0.10 v6.0.0, 0.26 v5.5.0, 0.11 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0, 0.00 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 % 0.58/0.69 % Syntax : Number of formulae : 7 ( 2 unt; 0 def) % 0.58/0.69 % Number of atoms : 16 ( 4 equ) % 0.58/0.69 % Maximal formula atoms : 3 ( 2 avg) % 0.58/0.69 % Number of connectives : 9 ( 0 ~; 1 |; 1 &) % 0.58/0.69 % ( 5 <=>; 2 =>; 0 <=; 0 <~>) % 0.58/0.69 % Maximal formula depth : 6 ( 5 avg) % 0.58/0.69 % Maximal term depth : 2 ( 1 avg) % 0.58/0.69 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty) % 0.58/0.69 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty) % 0.58/0.69 % Number of variables : 16 ( 16 !; 0 ?) % 0.58/0.69 % SPC : FOF_THM_RFO_SEQ % 0.58/0.69 % 0.58/0.69 % Comments : % 0.58/0.69 %-------------------------------------------------------------------------- % 0.58/0.69 %---- line(boole - df(2),1833042) % 0.58/0.69 fof(union_defn,axiom, % 0.58/0.69 ! [B,C,D] : % 0.58/0.69 ( member(D,union(B,C)) % 0.58/0.69 <=> ( member(D,B) % 0.58/0.69 | member(D,C) ) ) ). % 0.58/0.69 % 0.58/0.69 %---- line(tarski - df(3),1832749) % 0.58/0.69 fof(subset_defn,axiom, % 0.58/0.69 ! [B,C] : % 0.58/0.69 ( subset(B,C) % 0.58/0.69 <=> ! [D] : % 0.58/0.69 ( member(D,B) % 0.58/0.69 => member(D,C) ) ) ). % 0.58/0.69 % 0.58/0.69 %---- line(boole - df(8),1833103) % 0.58/0.69 fof(equal_defn,axiom, % 0.58/0.69 ! [B,C] : % 0.58/0.69 ( B = C % 0.58/0.69 <=> ( subset(B,C) % 0.58/0.69 & subset(C,B) ) ) ). % 0.58/0.69 % 0.58/0.69 %---- property(commutativity,op(union,2,function)) % 0.58/0.69 fof(commutativity_of_union,axiom, % 0.58/0.69 ! [B,C] : union(B,C) = union(C,B) ). % 0.58/0.69 % 0.58/0.69 %---- property(reflexivity,op(subset,2,predicate)) % 0.58/0.69 fof(reflexivity_of_subset,axiom, % 0.58/0.69 ! [B] : subset(B,B) ). % 0.58/0.69 % 0.58/0.69 %---- line(hidden - axiom43,1832615) % 0.58/0.69 fof(equal_member_defn,axiom, % 0.58/0.69 ! [B,C] : % 0.58/0.69 ( B = C % 0.58/0.69 <=> ! [D] : % 0.58/0.69 ( member(D,B) % 0.58/0.69 <=> member(D,C) ) ) ). % 0.58/0.69 % 0.58/0.69 %---- line(boole - th(35),1833266) % 0.58/0.69 fof(prove_subset_union,conjecture, % 0.58/0.69 ! [B,C] : % 0.58/0.69 ( subset(B,C) % 0.58/0.69 => union(B,C) = C ) ). % 0.58/0.69 % 0.58/0.69 %-------------------------------------------------------------------------- % 0.58/0.69 %------------------------------------------- % 0.58/0.69 % Proof found % 0.58/0.69 % SZS status Theorem for theBenchmark % 0.58/0.69 % SZS output start Proof % 0.58/0.69 %ClaNum:28(EqnAxiom:13) % 0.58/0.69 %VarNum:65(SingletonVarNum:27) % 0.58/0.69 %MaxLitNum:3 % 0.58/0.69 %MaxfuncDepth:1 % 0.58/0.69 %SharedTerms:5 % 0.58/0.69 %goalClause: 14 17 % 0.58/0.69 %singleGoalClaCount:2 % 0.58/0.69 [14]P1(a1,a4) % 0.58/0.69 [17]~E(f5(a1,a4),a4) % 0.58/0.69 [15]P1(x151,x151) % 0.58/0.69 [16]E(f5(x161,x162),f5(x162,x161)) % 0.58/0.69 [19]~E(x191,x192)+P1(x191,x192) % 0.58/0.69 [21]P1(x211,x212)+P2(f2(x211,x212),x211) % 0.58/0.69 [25]P1(x251,x252)+~P2(f2(x251,x252),x252) % 0.58/0.69 [23]~P2(x231,x233)+P2(x231,f5(x232,x233)) % 0.58/0.69 [24]~P2(x241,x242)+P2(x241,f5(x242,x243)) % 0.58/0.69 [20]~P1(x202,x201)+~P1(x201,x202)+E(x201,x202) % 0.58/0.69 [26]E(x261,x262)+P2(f3(x261,x262),x262)+P2(f3(x261,x262),x261) % 0.58/0.69 [28]E(x281,x282)+~P2(f3(x281,x282),x282)+~P2(f3(x281,x282),x281) % 0.58/0.69 [22]~P1(x223,x222)+P2(x221,x222)+~P2(x221,x223) % 0.58/0.69 [27]P2(x271,x272)+P2(x271,x273)+~P2(x271,f5(x273,x272)) % 0.58/0.69 %EqnAxiom % 0.58/0.69 [1]E(x11,x11) % 0.58/0.69 [2]E(x22,x21)+~E(x21,x22) % 0.58/0.69 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.58/0.69 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43)) % 0.58/0.69 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52)) % 0.58/0.69 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63)) % 0.58/0.69 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72)) % 0.58/0.69 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83)) % 0.58/0.69 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92)) % 0.58/0.69 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103) % 0.58/0.69 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111) % 0.58/0.69 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123) % 0.58/0.69 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131) % 0.58/0.69 % 0.58/0.69 %------------------------------------------- % 0.58/0.70 cnf(30,plain, % 0.58/0.70 (P1(f5(x301,x302),f5(x302,x301))), % 0.58/0.70 inference(scs_inference,[],[15,16,10])). % 0.58/0.70 cnf(73,plain, % 0.58/0.70 (P2(f3(a4,f5(a1,a4)),f5(a1,a4))+P2(f3(a4,f5(a1,a4)),a4)), % 0.58/0.70 inference(scs_inference,[],[17,26,2])). % 0.58/0.70 cnf(75,plain, % 0.58/0.70 (~P2(f3(a4,f5(a1,a4)),f5(a1,a4))+~P2(f3(a4,f5(a1,a4)),a4)), % 0.58/0.70 inference(scs_inference,[],[17,28,2])). % 0.58/0.70 cnf(76,plain, % 0.58/0.70 (~P2(f3(a4,f5(a1,a4)),a4)), % 0.58/0.70 inference(scs_inference,[],[75,23])). % 0.58/0.70 cnf(77,plain, % 0.58/0.70 (P2(f3(a4,f5(a1,a4)),f5(a1,a4))), % 0.58/0.70 inference(scs_inference,[],[76,73])). % 0.58/0.70 cnf(83,plain, % 0.58/0.70 (P2(f3(a4,f5(a1,a4)),a1)), % 0.58/0.70 inference(scs_inference,[],[76,30,77,22,27])). % 0.58/0.70 cnf(91,plain, % 0.58/0.70 ($false), % 0.58/0.70 inference(scs_inference,[],[76,14,83,22]), % 0.58/0.70 ['proof']). % 0.58/0.70 % SZS output end Proof % 0.58/0.70 % Total time :0.100000s %------------------------------------------------------------------------------