%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET014+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 : n032.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 14:20:01 EDT 2024 % Result : Theorem 0.12s 0.52s % Output : CNFRefutation 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.08 % Problem : SET014+3 : TPTP v8.2.0. Released v2.2.0. % 0.00/0.08 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.07/0.27 % Computer : n032.cluster.edu % 0.07/0.27 % Model : x86_64 x86_64 % 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.27 % Memory : 8042.1875MB % 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.27 % CPULimit : 300 % 0.07/0.27 % WCLimit : 300 % 0.07/0.27 % DateTime : Sun Jun 23 14:38:24 EDT 2024 % 0.07/0.27 % CPUTime : % 0.12/0.46 start to proof:theBenchmark % 0.12/0.52 %------------------------------------------- % 0.12/0.52 % File :CSE---1.7 % 0.12/0.52 % Problem :theBenchmark % 0.12/0.52 % Transform :cnf % 0.12/0.52 % Format :tptp:raw % 0.12/0.52 % Command :java -jar mcs_scs.jar %d %s % 0.12/0.52 % 0.12/0.52 % Result :Theorem 0.020000s % 0.12/0.52 % Output :CNFRefutation 0.020000s % 0.12/0.52 %------------------------------------------- % 0.12/0.52 %------------------------------------------------------------------------------ % 0.12/0.52 % File : SET014+3 : TPTP v8.2.0. Released v2.2.0. % 0.12/0.52 % Domain : Set Theory % 0.12/0.52 % Problem : If X (= Z and Y (= Z, then X U Y (= Z % 0.12/0.52 % Version : [Try90] axioms : Reduced > Incomplete. % 0.12/0.52 % English : If X is a subset of Z and Y is a subset of Z, then the union of % 0.12/0.52 % X and Y is a subset of Z. % 0.12/0.52 % 0.12/0.52 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.12/0.52 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.12/0.52 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.12/0.52 % Source : [ILF] % 0.12/0.52 % Names : BOOLE (32) [TS89] % 0.12/0.52 % 0.12/0.52 % Status : Theorem % 0.12/0.52 % Rating : 0.11 v8.1.0, 0.06 v7.4.0, 0.10 v7.3.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.00 v6.4.0, 0.04 v6.2.0, 0.00 v6.1.0, 0.13 v5.5.0, 0.19 v5.4.0, 0.25 v5.3.0, 0.30 v5.2.0, 0.05 v5.1.0, 0.10 v5.0.0, 0.12 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.12 v3.7.0, 0.15 v3.5.0, 0.11 v3.4.0, 0.26 v3.3.0, 0.21 v3.2.0, 0.36 v3.1.0, 0.33 v2.7.0, 0.17 v2.6.0, 0.14 v2.5.0, 0.12 v2.4.0, 0.25 v2.3.0, 0.00 v2.2.1 % 0.12/0.52 % Syntax : Number of formulae : 6 ( 2 unt; 0 def) % 0.12/0.52 % Number of atoms : 14 ( 2 equ) % 0.12/0.52 % Maximal formula atoms : 3 ( 2 avg) % 0.12/0.52 % Number of connectives : 8 ( 0 ~; 1 |; 1 &) % 0.12/0.52 % ( 4 <=>; 2 =>; 0 <=; 0 <~>) % 0.12/0.52 % Maximal formula depth : 6 ( 5 avg) % 0.12/0.52 % Maximal term depth : 2 ( 1 avg) % 0.12/0.52 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty) % 0.12/0.52 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty) % 0.12/0.52 % Number of variables : 15 ( 15 !; 0 ?) % 0.12/0.52 % SPC : FOF_THM_RFO_SEQ % 0.12/0.52 % 0.12/0.52 % Comments : % 0.12/0.52 %------------------------------------------------------------------------------ % 0.12/0.52 %---- line(boole - df(2),1833042) % 0.12/0.52 fof(union_defn,axiom, % 0.12/0.52 ! [B,C,D] : % 0.12/0.52 ( member(D,union(B,C)) % 0.12/0.52 <=> ( member(D,B) % 0.12/0.52 | member(D,C) ) ) ). % 0.12/0.52 % 0.12/0.52 %---- line(tarski - df(3),1832749) % 0.12/0.52 fof(subset_defn,axiom, % 0.12/0.52 ! [B,C] : % 0.12/0.52 ( subset(B,C) % 0.12/0.52 <=> ! [D] : % 0.12/0.52 ( member(D,B) % 0.12/0.52 => member(D,C) ) ) ). % 0.12/0.52 % 0.12/0.52 %---- property(commutativity,op(union,2,function)) % 0.12/0.52 fof(commutativity_of_union,axiom, % 0.12/0.52 ! [B,C] : union(B,C) = union(C,B) ). % 0.12/0.52 % 0.12/0.52 %---- property(reflexivity,op(subset,2,predicate)) % 0.12/0.52 fof(reflexivity_of_subset,axiom, % 0.12/0.52 ! [B] : subset(B,B) ). % 0.12/0.52 % 0.12/0.52 %---- line(hidden - axiom37,1832615) % 0.12/0.52 fof(equal_member_defn,axiom, % 0.12/0.52 ! [B,C] : % 0.12/0.52 ( B = C % 0.12/0.52 <=> ! [D] : % 0.12/0.52 ( member(D,B) % 0.12/0.52 <=> member(D,C) ) ) ). % 0.12/0.52 % 0.12/0.52 %---- line(boole - th(32),1833206) % 0.12/0.52 fof(prove_union_subset,conjecture, % 0.12/0.52 ! [B,C,D] : % 0.12/0.52 ( ( subset(B,C) % 0.12/0.52 & subset(D,C) ) % 0.12/0.52 => subset(union(B,D),C) ) ). % 0.12/0.52 % 0.12/0.52 %------------------------------------------------------------------------------ % 0.12/0.52 %------------------------------------------- % 0.12/0.52 % Proof found % 0.12/0.52 % SZS status Theorem for theBenchmark % 0.12/0.52 % SZS output start Proof % 0.12/0.52 %ClaNum:26(EqnAxiom:13) % 0.12/0.52 %VarNum:55(SingletonVarNum:23) % 0.12/0.52 %MaxLitNum:3 % 0.12/0.52 %MaxfuncDepth:1 % 0.12/0.52 %SharedTerms:7 % 0.12/0.52 %goalClause: 14 15 18 % 0.12/0.52 %singleGoalClaCount:3 % 0.12/0.52 [14]P1(a1,a4) % 0.12/0.52 [15]P1(a5,a4) % 0.12/0.52 [18]~P1(f6(a1,a5),a4) % 0.12/0.52 [16]P1(x161,x161) % 0.12/0.52 [17]E(f6(x171,x172),f6(x172,x171)) % 0.12/0.52 [19]P1(x191,x192)+P2(f2(x191,x192),x191) % 0.12/0.52 [23]P1(x231,x232)+~P2(f2(x231,x232),x232) % 0.12/0.52 [21]~P2(x211,x213)+P2(x211,f6(x212,x213)) % 0.12/0.52 [22]~P2(x221,x222)+P2(x221,f6(x222,x223)) % 0.12/0.52 [24]E(x241,x242)+P2(f3(x241,x242),x242)+P2(f3(x241,x242),x241) % 0.12/0.52 [26]E(x261,x262)+~P2(f3(x261,x262),x262)+~P2(f3(x261,x262),x261) % 0.12/0.52 [20]~P1(x203,x202)+P2(x201,x202)+~P2(x201,x203) % 0.12/0.52 [25]P2(x251,x252)+P2(x251,x253)+~P2(x251,f6(x253,x252)) % 0.12/0.52 %EqnAxiom % 0.12/0.52 [1]E(x11,x11) % 0.12/0.52 [2]E(x22,x21)+~E(x21,x22) % 0.12/0.52 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.12/0.52 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43)) % 0.12/0.52 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52)) % 0.12/0.52 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63)) % 0.12/0.52 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72)) % 0.12/0.52 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83)) % 0.12/0.52 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92)) % 0.12/0.52 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103) % 0.12/0.52 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111) % 0.12/0.52 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123) % 0.12/0.52 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131) % 0.12/0.52 % 0.12/0.52 %------------------------------------------- % 0.12/0.52 cnf(40,plain, % 0.12/0.52 (P2(f2(f6(a5,a1),a4),f6(a5,a1))), % 0.12/0.52 inference(scs_inference,[],[18,17,19,10])). % 0.12/0.52 cnf(45,plain, % 0.12/0.52 (P2(f2(f6(a5,a1),a4),a4)+P2(f2(f6(a5,a1),a4),a5)), % 0.12/0.52 inference(scs_inference,[],[14,17,40,13,25,20])). % 0.12/0.52 cnf(64,plain, % 0.12/0.52 (~P2(f2(f6(a5,a1),a4),a4)), % 0.12/0.52 inference(scs_inference,[],[18,17,23,10])). % 0.12/0.52 cnf(65,plain, % 0.12/0.52 (P2(f2(f6(a5,a1),a4),a5)), % 0.12/0.52 inference(scs_inference,[],[64,45])). % 0.12/0.52 cnf(79,plain, % 0.12/0.52 ($false), % 0.12/0.52 inference(scs_inference,[],[15,65,64,20]), % 0.12/0.52 ['proof']). % 0.12/0.52 % SZS output end Proof % 0.12/0.52 % Total time :0.020000s %------------------------------------------------------------------------------