%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET586+3 : TPTP v8.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/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 14:21:50 EDT 2024 % Result : Theorem 1.02s 1.10s % Output : CNFRefutation 1.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET586+3 : TPTP v8.2.0. Released v2.2.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n023.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 17:38:24 EDT 2024 % 0.12/0.33 % CPUTime : % 0.50/0.58 start to proof:theBenchmark % 1.02/1.10 %------------------------------------------- % 1.02/1.10 % File :CSE---1.7 % 1.02/1.10 % Problem :theBenchmark % 1.02/1.10 % Transform :cnf % 1.02/1.10 % Format :tptp:raw % 1.02/1.10 % Command :java -jar mcs_scs.jar %d %s % 1.02/1.10 % 1.02/1.10 % Result :Theorem 0.490000s % 1.02/1.10 % Output :CNFRefutation 0.490000s % 1.02/1.10 %------------------------------------------- % 1.02/1.10 %-------------------------------------------------------------------------- % 1.02/1.10 % File : SET586+3 : TPTP v8.2.0. Released v2.2.0. % 1.02/1.10 % Domain : Set Theory % 1.02/1.10 % Problem : If X (= Y, then X ^ Z (= Y ^ Z % 1.02/1.10 % Version : [Try90] axioms : Reduced > Incomplete. % 1.02/1.10 % English : If X is a subset of Y, then the intersection of X and Z is a % 1.02/1.10 % subset of the intersection of Y and Z. % 1.02/1.10 % 1.02/1.10 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 1.02/1.10 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 1.02/1.10 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 1.02/1.10 % Source : [ILF] % 1.02/1.10 % Names : BOOLE (40) [TS89] % 1.02/1.10 % 1.02/1.10 % Status : Theorem % 1.02/1.10 % Rating : 0.11 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.00 v7.0.0, 0.03 v6.4.0, 0.08 v6.3.0, 0.04 v6.2.0, 0.00 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.07 v5.4.0, 0.14 v5.3.0, 0.26 v5.2.0, 0.10 v5.1.0, 0.14 v5.0.0, 0.17 v4.1.0, 0.13 v4.0.0, 0.12 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 % 1.02/1.10 % Syntax : Number of formulae : 6 ( 2 unt; 0 def) % 1.02/1.10 % Number of atoms : 13 ( 2 equ) % 1.02/1.10 % Maximal formula atoms : 3 ( 2 avg) % 1.02/1.10 % Number of connectives : 7 ( 0 ~; 0 |; 1 &) % 1.02/1.10 % ( 4 <=>; 2 =>; 0 <=; 0 <~>) % 1.02/1.10 % Maximal formula depth : 6 ( 5 avg) % 1.02/1.10 % Maximal term depth : 2 ( 1 avg) % 1.02/1.10 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty) % 1.02/1.10 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty) % 1.02/1.10 % Number of variables : 15 ( 15 !; 0 ?) % 1.02/1.10 % SPC : FOF_THM_RFO_SEQ % 1.02/1.10 % 1.02/1.10 % Comments : % 1.02/1.10 %-------------------------------------------------------------------------- % 1.02/1.10 %---- line(boole - df(3),1833060) % 1.02/1.10 fof(intersection_defn,axiom, % 1.02/1.10 ! [B,C,D] : % 1.02/1.10 ( member(D,intersection(B,C)) % 1.02/1.10 <=> ( member(D,B) % 1.02/1.10 & member(D,C) ) ) ). % 1.02/1.10 % 1.02/1.10 %---- line(tarski - df(3),1832749) % 1.02/1.10 fof(subset_defn,axiom, % 1.02/1.10 ! [B,C] : % 1.02/1.10 ( subset(B,C) % 1.02/1.10 <=> ! [D] : % 1.02/1.10 ( member(D,B) % 1.02/1.10 => member(D,C) ) ) ). % 1.02/1.10 % 1.02/1.10 %---- property(commutativity,op(intersection,2,function)) % 1.02/1.10 fof(commutativity_of_intersection,axiom, % 1.02/1.10 ! [B,C] : intersection(B,C) = intersection(C,B) ). % 1.02/1.10 % 1.02/1.10 %---- property(reflexivity,op(subset,2,predicate)) % 1.02/1.10 fof(reflexivity_of_subset,axiom, % 1.02/1.10 ! [B] : subset(B,B) ). % 1.02/1.10 % 1.02/1.10 %---- line(hidden - axiom51,1832615) % 1.02/1.10 fof(equal_member_defn,axiom, % 1.02/1.10 ! [B,C] : % 1.02/1.10 ( B = C % 1.02/1.10 <=> ! [D] : % 1.02/1.10 ( member(D,B) % 1.02/1.10 <=> member(D,C) ) ) ). % 1.02/1.10 % 1.02/1.10 %---- line(boole - th(40),1833318) Looks like Quaife's LA3.2, but not mine % 1.02/1.10 fof(prove_intersection_of_subset,conjecture, % 1.02/1.10 ! [B,C,D] : % 1.02/1.10 ( subset(B,C) % 1.02/1.10 => subset(intersection(B,D),intersection(C,D)) ) ). % 1.02/1.10 % 1.02/1.10 %-------------------------------------------------------------------------- % 1.02/1.10 %------------------------------------------- % 1.02/1.10 % Proof found % 1.02/1.10 % SZS status Theorem for theBenchmark % 1.02/1.10 % SZS output start Proof % 1.02/1.10 %ClaNum:25(EqnAxiom:13) % 1.02/1.10 %VarNum:55(SingletonVarNum:23) % 1.02/1.10 %MaxLitNum:3 % 1.02/1.10 %MaxfuncDepth:1 % 1.02/1.10 %SharedTerms:7 % 1.02/1.10 %goalClause: 14 17 % 1.02/1.10 %singleGoalClaCount:2 % 1.02/1.10 [14]P1(a1,a4) % 1.02/1.10 [17]~P1(f5(a1,a6),f5(a4,a6)) % 1.02/1.10 [15]P1(x151,x151) % 1.02/1.10 [16]E(f5(x161,x162),f5(x162,x161)) % 1.02/1.10 [18]P1(x181,x182)+P2(f2(x181,x182),x181) % 1.02/1.10 [22]P1(x221,x222)+~P2(f2(x221,x222),x222) % 1.02/1.10 [20]P2(x201,x202)+~P2(x201,f5(x203,x202)) % 1.02/1.10 [21]P2(x211,x212)+~P2(x211,f5(x212,x213)) % 1.02/1.10 [23]E(x231,x232)+P2(f3(x231,x232),x232)+P2(f3(x231,x232),x231) % 1.02/1.10 [25]E(x251,x252)+~P2(f3(x251,x252),x252)+~P2(f3(x251,x252),x251) % 1.02/1.10 [19]~P1(x193,x192)+P2(x191,x192)+~P2(x191,x193) % 1.02/1.10 [24]~P2(x241,x243)+~P2(x241,x242)+P2(x241,f5(x242,x243)) % 1.02/1.10 %EqnAxiom % 1.02/1.10 [1]E(x11,x11) % 1.02/1.10 [2]E(x22,x21)+~E(x21,x22) % 1.02/1.10 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.02/1.10 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43)) % 1.02/1.10 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52)) % 1.02/1.10 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63)) % 1.02/1.10 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72)) % 1.02/1.10 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83)) % 1.02/1.10 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92)) % 1.02/1.10 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103) % 1.02/1.10 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111) % 1.02/1.10 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123) % 1.02/1.10 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131) % 1.02/1.10 % 1.02/1.10 %------------------------------------------- % 1.02/1.10 cnf(50,plain, % 1.02/1.10 (~P2(f2(f5(a1,a6),f5(a6,a4)),f5(a6,a4))), % 1.02/1.10 inference(scs_inference,[],[17,16,22,11])). % 1.02/1.10 cnf(51,plain, % 1.02/1.10 (~P2(f2(f5(a1,a6),f5(a6,a4)),a4)+~P2(f2(f5(a1,a6),f5(a6,a4)),a6)), % 1.02/1.10 inference(scs_inference,[],[50,24])). % 1.02/1.10 cnf(144,plain, % 1.02/1.10 (~P2(f2(f5(a1,a6),f5(a6,a4)),a4)+~P2(f2(f5(a1,a6),f5(a6,a4)),f5(x1441,a6))), % 1.02/1.10 inference(scs_inference,[],[51,20])). % 1.02/1.10 cnf(145,plain, % 1.02/1.10 (~P2(f2(f5(a1,a6),f5(a6,a4)),f5(x1451,a6))+~P2(f2(f5(a1,a6),f5(a6,a4)),f5(x1452,a4))), % 1.02/1.10 inference(scs_inference,[],[144,20])). % 1.02/1.10 cnf(146,plain, % 1.02/1.10 (P1(f5(a1,a6),f5(a6,a4))+~P2(f2(f5(a1,a6),f5(a6,a4)),f5(x1461,a4))), % 1.02/1.10 inference(scs_inference,[],[145,18])). % 1.02/1.10 cnf(147,plain, % 1.02/1.10 (~P2(f2(f5(a1,a6),f5(a6,a4)),f5(x1471,a4))), % 1.02/1.11 inference(scs_inference,[],[17,16,146,11])). % 1.02/1.11 cnf(148,plain, % 1.02/1.11 (~P2(f2(f5(a1,a6),f5(a6,a4)),a4)+~P2(f2(f5(a1,a6),f5(a6,a4)),x1481)), % 1.02/1.11 inference(scs_inference,[],[147,24])). % 1.02/1.11 cnf(150,plain, % 1.02/1.11 (~P2(f2(f5(a1,a6),f5(a6,a4)),a4)), % 1.02/1.11 inference(factoring_inference,[],[148])). % 1.02/1.11 cnf(283,plain, % 1.02/1.11 (P2(f2(f5(a1,a6),f5(a6,a4)),f5(a1,a6))), % 1.02/1.11 inference(scs_inference,[],[17,16,18,11])). % 1.02/1.11 cnf(284,plain, % 1.02/1.11 (P2(f2(f5(a1,a6),f5(a6,a4)),a1)), % 1.02/1.11 inference(scs_inference,[],[283,21])). % 1.02/1.11 cnf(311,plain, % 1.02/1.11 ($false), % 1.02/1.11 inference(scs_inference,[],[284,14,150,19]), % 1.02/1.11 ['proof']). % 1.02/1.11 % SZS output end Proof % 1.02/1.11 % Total time :0.490000s %------------------------------------------------------------------------------