%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET183+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 : n025.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 14:21:01 EDT 2024 % Result : Theorem 0.90s 0.95s % Output : CNFRefutation 0.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET183+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 : n025.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 16:04:09 EDT 2024 % 0.12/0.33 % CPUTime : % 0.20/0.56 start to proof:theBenchmark % 0.90/0.94 %------------------------------------------- % 0.90/0.94 % File :CSE---1.7 % 0.90/0.94 % Problem :theBenchmark % 0.90/0.94 % Transform :cnf % 0.90/0.94 % Format :tptp:raw % 0.90/0.94 % Command :java -jar mcs_scs.jar %d %s % 0.90/0.94 % 0.90/0.94 % Result :Theorem 0.340000s % 0.90/0.94 % Output :CNFRefutation 0.340000s % 0.90/0.94 %------------------------------------------- % 0.90/0.95 %-------------------------------------------------------------------------- % 0.90/0.95 % File : SET183+3 : TPTP v8.2.0. Released v2.2.0. % 0.90/0.95 % Domain : Set Theory % 0.90/0.95 % Problem : If X is a subset of Y, then the intersection of X and Y is X % 0.90/0.95 % Version : [Try90] axioms : Reduced > Incomplete. % 0.90/0.95 % English : % 0.90/0.95 % 0.90/0.95 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.90/0.95 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.90/0.95 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.90/0.95 % Source : [ILF] % 0.90/0.95 % Names : BOOLE (42) [TS89] % 0.90/0.95 % 0.90/0.95 % Status : Theorem % 0.90/0.95 % Rating : 0.08 v8.1.0, 0.06 v7.4.0, 0.03 v7.2.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.00 v6.2.0, 0.04 v6.1.0, 0.13 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.00 v5.0.0, 0.08 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.12 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.07 v3.2.0, 0.18 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1 % 0.90/0.95 % Syntax : Number of formulae : 8 ( 3 unt; 0 def) % 0.90/0.95 % Number of atoms : 17 ( 4 equ) % 0.90/0.95 % Maximal formula atoms : 3 ( 2 avg) % 0.90/0.95 % Number of connectives : 9 ( 0 ~; 0 |; 2 &) % 0.90/0.95 % ( 5 <=>; 2 =>; 0 <=; 0 <~>) % 0.90/0.95 % Maximal formula depth : 6 ( 4 avg) % 0.90/0.95 % Maximal term depth : 2 ( 1 avg) % 0.90/0.95 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty) % 0.90/0.95 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty) % 0.90/0.95 % Number of variables : 18 ( 18 !; 0 ?) % 0.90/0.95 % SPC : FOF_THM_RFO_SEQ % 0.90/0.95 % 0.90/0.95 % Comments : % 0.90/0.95 %-------------------------------------------------------------------------- % 0.90/0.95 %---- line(boole - df(3),1833060) % 0.90/0.95 fof(intersection_defn,axiom, % 0.90/0.95 ! [B,C,D] : % 0.90/0.95 ( member(D,intersection(B,C)) % 0.90/0.95 <=> ( member(D,B) % 0.90/0.95 & member(D,C) ) ) ). % 0.90/0.95 % 0.90/0.95 %---- line(boole - th(37),1833277) % 0.90/0.95 fof(intersection_is_subset,axiom, % 0.90/0.95 ! [B,C] : subset(intersection(B,C),B) ). % 0.90/0.95 % 0.90/0.95 %---- line(tarski - df(3),1832749) % 0.90/0.95 fof(subset_defn,axiom, % 0.90/0.95 ! [B,C] : % 0.90/0.95 ( subset(B,C) % 0.90/0.95 <=> ! [D] : % 0.90/0.95 ( member(D,B) % 0.90/0.95 => member(D,C) ) ) ). % 0.90/0.95 % 0.90/0.95 %---- line(boole - df(8),1833103) % 0.90/0.95 fof(equal_defn,axiom, % 0.90/0.95 ! [B,C] : % 0.90/0.95 ( B = C % 0.90/0.95 <=> ( subset(B,C) % 0.90/0.95 & subset(C,B) ) ) ). % 0.90/0.95 % 0.90/0.95 %---- property(commutativity,op(intersection,2,function)) % 0.90/0.95 fof(commutativity_of_intersection,axiom, % 0.90/0.95 ! [B,C] : intersection(B,C) = intersection(C,B) ). % 0.90/0.95 % 0.90/0.95 %---- property(reflexivity,op(subset,2,predicate)) % 0.90/0.95 fof(reflexivity_of_subset,axiom, % 0.90/0.95 ! [B] : subset(B,B) ). % 0.90/0.95 % 0.90/0.95 %---- line(hidden - axiom55,1832615) % 0.90/0.95 fof(equal_member_defn,axiom, % 0.90/0.95 ! [B,C] : % 0.90/0.95 ( B = C % 0.90/0.95 <=> ! [D] : % 0.90/0.95 ( member(D,B) % 0.90/0.95 <=> member(D,C) ) ) ). % 0.90/0.95 % 0.90/0.95 %---- line(boole - th(42),1833351) % 0.90/0.95 fof(prove_subset_intersection,conjecture, % 0.90/0.95 ! [B,C] : % 0.90/0.95 ( subset(B,C) % 0.90/0.95 => intersection(B,C) = B ) ). % 0.90/0.95 % 0.90/0.95 %-------------------------------------------------------------------------- % 0.90/0.95 %------------------------------------------- % 0.90/0.95 % Proof found % 0.90/0.95 % SZS status Theorem for theBenchmark % 0.90/0.95 % SZS output start Proof % 0.90/0.95 %ClaNum:29(EqnAxiom:13) % 0.90/0.95 %VarNum:68(SingletonVarNum:29) % 0.90/0.95 %MaxLitNum:3 % 0.90/0.95 %MaxfuncDepth:1 % 0.90/0.95 %SharedTerms:5 % 0.90/0.95 %goalClause: 14 18 % 0.90/0.95 %singleGoalClaCount:2 % 0.90/0.95 [14]P1(a1,a4) % 0.90/0.95 [18]~E(f5(a1,a4),a1) % 0.90/0.95 [15]P1(x151,x151) % 0.90/0.95 [16]E(f5(x161,x162),f5(x162,x161)) % 0.90/0.95 [17]P1(f5(x171,x172),x171) % 0.90/0.95 [20]~E(x201,x202)+P1(x201,x202) % 0.90/0.95 [22]P1(x221,x222)+P2(f2(x221,x222),x221) % 0.90/0.95 [26]P1(x261,x262)+~P2(f2(x261,x262),x262) % 0.90/0.95 [24]P2(x241,x242)+~P2(x241,f5(x243,x242)) % 0.90/0.95 [25]P2(x251,x252)+~P2(x251,f5(x252,x253)) % 0.90/0.95 [21]~P1(x212,x211)+~P1(x211,x212)+E(x211,x212) % 0.90/0.95 [27]E(x271,x272)+P2(f3(x271,x272),x272)+P2(f3(x271,x272),x271) % 0.90/0.95 [29]E(x291,x292)+~P2(f3(x291,x292),x292)+~P2(f3(x291,x292),x291) % 0.90/0.95 [23]~P1(x233,x232)+P2(x231,x232)+~P2(x231,x233) % 0.90/0.95 [28]~P2(x281,x283)+~P2(x281,x282)+P2(x281,f5(x282,x283)) % 0.90/0.95 %EqnAxiom % 0.90/0.95 [1]E(x11,x11) % 0.90/0.95 [2]E(x22,x21)+~E(x21,x22) % 0.90/0.95 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.90/0.95 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43)) % 0.90/0.95 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52)) % 0.90/0.95 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63)) % 0.90/0.95 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72)) % 0.90/0.95 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83)) % 0.90/0.95 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92)) % 0.90/0.95 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103) % 0.90/0.95 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111) % 0.90/0.95 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123) % 0.90/0.95 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131) % 0.90/0.95 % 0.90/0.95 %------------------------------------------- % 0.90/0.96 cnf(31,plain, % 0.90/0.96 (~P1(a1,f5(a1,a4))), % 0.90/0.96 inference(scs_inference,[],[18,17,21])). % 0.90/0.96 cnf(90,plain, % 0.90/0.96 (P2(x901,a1)+~E(f2(a1,f5(a1,a4)),x901)), % 0.90/0.96 inference(scs_inference,[],[31,12,22])). % 0.90/0.96 cnf(91,plain, % 0.90/0.96 (P2(f2(a1,f5(a1,a4)),a1)), % 0.90/0.96 inference(equality_inference,[],[90])). % 0.90/0.96 cnf(92,plain, % 0.90/0.96 (P2(f2(a1,f5(a1,a4)),a4)), % 0.90/0.96 inference(scs_inference,[],[14,91,23])). % 0.90/0.96 cnf(204,plain, % 0.90/0.96 (~P2(x2041,f5(x2042,x2043))+P2(x2041,f5(x2043,x2042))), % 0.90/0.96 inference(scs_inference,[],[16,2,13])). % 0.90/0.96 cnf(205,plain, % 0.90/0.96 (~P2(f2(a1,f5(a1,a4)),f5(a4,a1))), % 0.90/0.96 inference(scs_inference,[],[31,204,26])). % 0.90/0.96 cnf(207,plain, % 0.90/0.96 ($false), % 0.90/0.96 inference(scs_inference,[],[92,91,205,204,28]), % 0.90/0.96 ['proof']). % 0.90/0.96 % SZS output end Proof % 0.90/0.96 % Total time :0.340000s %------------------------------------------------------------------------------