%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET581+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 14:21:49 EDT 2024 % Result : Theorem 0.54s 0.81s % Output : CNFRefutation 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET581+3 : TPTP v8.2.0. Released v2.2.0. % 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n027.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sun Jun 23 11:22:09 EDT 2024 % 0.13/0.34 % CPUTime : % 0.47/0.57 start to proof:theBenchmark % 0.54/0.81 %------------------------------------------- % 0.54/0.81 % File :CSE---1.7 % 0.54/0.81 % Problem :theBenchmark % 0.54/0.81 % Transform :cnf % 0.54/0.81 % Format :tptp:raw % 0.54/0.81 % Command :java -jar mcs_scs.jar %d %s % 0.54/0.81 % 0.54/0.81 % Result :Theorem 0.200000s % 0.54/0.81 % Output :CNFRefutation 0.200000s % 0.54/0.81 %------------------------------------------- % 0.54/0.81 %-------------------------------------------------------------------------- % 0.54/0.81 % File : SET581+3 : TPTP v8.2.0. Released v2.2.0. % 0.54/0.81 % Domain : Set Theory % 0.54/0.81 % Problem : Trybulec's 24th Boolean property of sets % 0.54/0.81 % Version : [Try90] axioms : Reduced > Incomplete. % 0.54/0.81 % English : % 0.54/0.81 % 0.54/0.81 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.54/0.81 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.54/0.81 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.54/0.81 % Source : [ILF] % 0.54/0.81 % Names : BOOLE (24) [TS89] % 0.54/0.81 % 0.54/0.81 % Status : Theorem % 0.54/0.81 % Rating : 0.11 v7.5.0, 0.12 v7.4.0, 0.03 v7.2.0, 0.00 v6.4.0, 0.04 v6.2.0, 0.08 v6.1.0, 0.17 v5.5.0, 0.15 v5.4.0, 0.14 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, 0.05 v3.3.0, 0.07 v3.2.0, 0.09 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1 % 0.54/0.81 % Syntax : Number of formulae : 7 ( 2 unt; 0 def) % 0.54/0.81 % Number of atoms : 15 ( 3 equ) % 0.54/0.81 % Maximal formula atoms : 3 ( 2 avg) % 0.54/0.81 % Number of connectives : 11 ( 3 ~; 0 |; 2 &) % 0.54/0.81 % ( 5 <=>; 1 =>; 0 <=; 0 <~>) % 0.54/0.81 % Maximal formula depth : 6 ( 5 avg) % 0.54/0.81 % Maximal term depth : 2 ( 1 avg) % 0.54/0.81 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty) % 0.54/0.81 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty) % 0.54/0.81 % Number of variables : 16 ( 16 !; 0 ?) % 0.54/0.81 % SPC : FOF_THM_RFO_SEQ % 0.54/0.81 % 0.54/0.81 % Comments : % 0.54/0.81 %-------------------------------------------------------------------------- % 0.54/0.81 %---- line(boole - df(3),1833060) % 0.54/0.81 fof(intersection_defn,axiom, % 0.54/0.81 ! [B,C,D] : % 0.54/0.81 ( member(D,intersection(B,C)) % 0.54/0.81 <=> ( member(D,B) % 0.54/0.81 & member(D,C) ) ) ). % 0.54/0.81 % 0.54/0.81 %---- line(hidden - axiom19,1832636) % 0.54/0.81 fof(empty_set_defn,axiom, % 0.54/0.81 ! [B] : ~ member(B,empty_set) ). % 0.54/0.81 % 0.54/0.81 %---- line(hidden - axiom20,1832615) % 0.54/0.81 fof(equal_member_defn,axiom, % 0.54/0.81 ! [B,C] : % 0.54/0.81 ( B = C % 0.54/0.81 <=> ! [D] : % 0.54/0.81 ( member(D,B) % 0.54/0.81 <=> member(D,C) ) ) ). % 0.54/0.81 % 0.54/0.81 %---- line(hidden - axiom21,1832619) % 0.54/0.81 fof(not_equal_defn,axiom, % 0.54/0.81 ! [B,C] : % 0.54/0.81 ( not_equal(B,C) % 0.54/0.81 <=> B != C ) ). % 0.54/0.81 % 0.54/0.81 %---- property(commutativity,op(intersection,2,function)) % 0.54/0.81 fof(commutativity_of_intersection,axiom, % 0.54/0.81 ! [B,C] : intersection(B,C) = intersection(C,B) ). % 0.54/0.81 % 0.54/0.81 %---- line(hidden - axiom23,1832628) % 0.54/0.81 fof(empty_defn,axiom, % 0.54/0.81 ! [B] : % 0.54/0.81 ( empty(B) % 0.54/0.81 <=> ! [C] : ~ member(C,B) ) ). % 0.54/0.81 % 0.54/0.81 %---- line(boole - th(24),1833127) % 0.54/0.81 fof(prove_th24,conjecture, % 0.54/0.81 ! [B,C,D] : % 0.54/0.81 ( ( member(B,C) % 0.54/0.81 & member(B,D) ) % 0.54/0.81 => not_equal(intersection(C,D),empty_set) ) ). % 0.54/0.81 % 0.54/0.81 %-------------------------------------------------------------------------- % 0.54/0.81 %------------------------------------------- % 0.54/0.81 % Proof found % 0.54/0.81 % SZS status Theorem for theBenchmark % 0.54/0.82 % SZS output start Proof % 0.54/0.82 %ClaNum:27(EqnAxiom:13) % 0.54/0.82 %VarNum:52(SingletonVarNum:23) % 0.54/0.82 %MaxLitNum:3 % 0.54/0.82 %MaxfuncDepth:1 % 0.54/0.82 %SharedTerms:8 % 0.54/0.82 %goalClause: 14 15 18 % 0.54/0.82 %singleGoalClaCount:3 % 0.54/0.82 [14]P1(a1,a5) % 0.54/0.82 [15]P1(a1,a6) % 0.54/0.82 [18]~P3(f7(a5,a6),a2) % 0.54/0.82 [17]~P1(x171,a2) % 0.54/0.82 [16]E(f7(x161,x162),f7(x162,x161)) % 0.54/0.82 [20]P2(x201)+P1(f3(x201),x201) % 0.54/0.82 [19]P3(x191,x192)+E(x191,x192) % 0.54/0.82 [21]~P3(x211,x212)+~E(x211,x212) % 0.54/0.82 [22]~P2(x221)+~P1(x222,x221) % 0.54/0.82 [23]P1(x231,x232)+~P1(x231,f7(x233,x232)) % 0.54/0.82 [24]P1(x241,x242)+~P1(x241,f7(x242,x243)) % 0.54/0.82 [25]E(x251,x252)+P1(f4(x251,x252),x252)+P1(f4(x251,x252),x251) % 0.54/0.82 [27]E(x271,x272)+~P1(f4(x271,x272),x272)+~P1(f4(x271,x272),x271) % 0.54/0.82 [26]~P1(x261,x263)+~P1(x261,x262)+P1(x261,f7(x262,x263)) % 0.54/0.82 %EqnAxiom % 0.54/0.82 [1]E(x11,x11) % 0.54/0.82 [2]E(x22,x21)+~E(x21,x22) % 0.54/0.82 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.54/0.82 [4]~E(x41,x42)+E(f7(x41,x43),f7(x42,x43)) % 0.54/0.82 [5]~E(x51,x52)+E(f7(x53,x51),f7(x53,x52)) % 0.54/0.82 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63)) % 0.54/0.82 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72)) % 0.54/0.82 [8]~E(x81,x82)+E(f3(x81),f3(x82)) % 0.54/0.82 [9]P1(x92,x93)+~E(x91,x92)+~P1(x91,x93) % 0.54/0.82 [10]P1(x103,x102)+~E(x101,x102)+~P1(x103,x101) % 0.54/0.82 [11]~P2(x111)+P2(x112)+~E(x111,x112) % 0.54/0.82 [12]P3(x122,x123)+~E(x121,x122)+~P3(x121,x123) % 0.54/0.82 [13]P3(x133,x132)+~E(x131,x132)+~P3(x133,x131) % 0.54/0.82 % 0.54/0.82 %------------------------------------------- % 0.54/0.82 cnf(28,plain, % 0.54/0.82 (~P3(x281,x281)), % 0.54/0.82 inference(equality_inference,[],[21])). % 0.54/0.82 cnf(29,plain, % 0.54/0.82 (P2(a2)), % 0.54/0.82 inference(scs_inference,[],[17,20])). % 0.54/0.82 cnf(30,plain, % 0.54/0.82 (~P1(x301,a2)), % 0.54/0.82 inference(rename_variables,[],[17])). % 0.54/0.82 cnf(32,plain, % 0.54/0.82 (~P3(f7(x321,x322),f7(x322,x321))), % 0.54/0.82 inference(scs_inference,[],[17,16,20,21])). % 0.54/0.82 cnf(43,plain, % 0.54/0.82 (E(f7(x431,x432),f7(x432,x431))), % 0.54/0.82 inference(rename_variables,[],[16])). % 0.54/0.82 cnf(44,plain, % 0.54/0.82 (~P2(f7(x441,x442))+P2(f7(x442,x441))), % 0.54/0.82 inference(scs_inference,[],[14,18,28,17,30,16,43,20,21,10,19,9,12,13,3,11])). % 0.54/0.82 cnf(90,plain, % 0.54/0.82 (~P1(x901,f7(x902,f7(a2,x903)))), % 0.54/0.82 inference(scs_inference,[],[17,23,24])). % 0.54/0.82 cnf(91,plain, % 0.54/0.82 (~P1(a1,f7(a2,x911))), % 0.54/0.82 inference(scs_inference,[],[14,90,26])). % 0.54/0.82 cnf(94,plain, % 0.54/0.82 (~P2(f7(x941,x942))+~P1(x943,f7(x942,x941))), % 0.54/0.82 inference(scs_inference,[],[44,22])). % 0.54/0.82 cnf(98,plain, % 0.54/0.82 (~E(a5,f7(x981,a2))), % 0.54/0.82 inference(scs_inference,[],[14,91,32,10,19,12])). % 0.54/0.82 cnf(102,plain, % 0.54/0.82 (~P1(x1021,f7(f7(a2,x1022),x1023))), % 0.54/0.82 inference(scs_inference,[],[90,94,20])). % 0.54/0.82 cnf(105,plain, % 0.54/0.82 (E(f7(f7(a2,x1051),x1052),a2)), % 0.54/0.82 inference(scs_inference,[],[102,17,98,19,25])). % 0.54/0.82 cnf(107,plain, % 0.54/0.82 (~P1(x1071,f7(f7(a2,x1072),x1073))), % 0.54/0.82 inference(rename_variables,[],[102])). % 0.54/0.82 cnf(109,plain, % 0.54/0.82 (~E(a5,f7(f7(a2,x1091),x1092))), % 0.54/0.82 inference(scs_inference,[],[14,102,107,17,98,19,25,10])). % 0.54/0.82 cnf(114,plain, % 0.54/0.82 (E(a2,f7(f7(a2,x1141),x1142))), % 0.54/0.82 inference(scs_inference,[],[105,2])). % 0.54/0.82 cnf(119,plain, % 0.54/0.82 (P2(f7(f7(a2,x1191),x1192))), % 0.54/0.82 inference(scs_inference,[],[109,29,105,2,21,19,11])). % 0.54/0.82 cnf(122,plain, % 0.54/0.82 (~E(a6,f7(f7(a2,x1221),x1222))), % 0.54/0.82 inference(scs_inference,[],[16,15,109,102,29,105,2,21,19,11,3,10])). % 0.54/0.82 cnf(132,plain, % 0.54/0.82 (E(f7(x1321,x1322),f7(x1322,x1321))), % 0.54/0.82 inference(rename_variables,[],[16])). % 0.54/0.82 cnf(133,plain, % 0.54/0.82 (~E(a6,f7(x1331,f7(a2,x1332)))), % 0.54/0.82 inference(scs_inference,[],[16,132,122,119,114,21,19,11,3])). % 0.54/0.82 cnf(135,plain, % 0.54/0.82 (~E(f7(f7(a2,x1351),x1352),a6)), % 0.54/0.82 inference(scs_inference,[],[16,132,122,119,114,28,21,19,11,3,13])). % 0.54/0.82 cnf(144,plain, % 0.54/0.82 (~P1(x1441,f7(x1442,a2))), % 0.54/0.82 inference(scs_inference,[],[29,22,23])). % 0.54/0.82 cnf(146,plain, % 0.54/0.82 (~P1(x1461,f7(x1462,a2))), % 0.54/0.82 inference(rename_variables,[],[144])). % 0.54/0.82 cnf(150,plain, % 0.54/0.82 (E(f7(f7(a2,x1501),x1502),f7(x1503,a2))), % 0.54/0.82 inference(scs_inference,[],[102,144,146,133,20,19,25])). % 0.54/0.82 cnf(156,plain, % 0.54/0.82 (~P1(x1561,f7(a2,x1562))), % 0.54/0.82 inference(scs_inference,[],[102,144,146,133,28,20,19,25,13,94])). % 0.54/0.82 cnf(160,plain, % 0.54/0.82 (~P1(x1601,f7(a2,x1602))), % 0.54/0.82 inference(rename_variables,[],[156])). % 0.54/0.82 cnf(162,plain, % 0.54/0.82 (E(f7(x1621,a2),f7(f7(a2,x1622),x1623))), % 0.54/0.82 inference(scs_inference,[],[156,150,20,2])). % 0.54/0.82 cnf(167,plain, % 0.54/0.82 (E(f7(a2,x1671),a2)), % 0.54/0.82 inference(scs_inference,[],[156,160,17,150,135,20,2,21,19,25])). % 0.54/0.82 cnf(169,plain, % 0.54/0.82 (~P1(x1691,f7(a2,x1692))), % 0.54/0.82 inference(rename_variables,[],[156])). % 0.54/0.82 cnf(171,plain, % 0.54/0.82 (~E(a6,f7(a2,x1711))), % 0.54/0.82 inference(scs_inference,[],[15,156,160,169,17,150,135,20,2,21,19,25,10])). % 0.54/0.82 cnf(184,plain, % 0.54/0.82 (~E(a6,f7(x1841,a2))), % 0.54/0.82 inference(scs_inference,[],[16,102,171,156,162,167,2,21,19,25,3])). % 0.54/0.82 cnf(186,plain, % 0.54/0.82 (~E(f7(a2,x1861),a6)), % 0.54/0.82 inference(scs_inference,[],[16,102,171,156,162,167,28,2,21,19,25,3,13])). % 0.54/0.82 cnf(212,plain, % 0.54/0.82 (~E(f7(x2121,a2),a6)), % 0.54/0.82 inference(scs_inference,[],[184,28,19,13])). % 0.54/0.82 cnf(222,plain, % 0.54/0.82 (E(f7(x2221,a2),f7(a2,x2222))), % 0.54/0.82 inference(scs_inference,[],[156,144,186,19,25,2])). % 0.54/0.82 cnf(225,plain, % 0.54/0.82 (E(a2,f7(a5,a6))), % 0.54/0.82 inference(scs_inference,[],[18,19,2])). % 0.54/0.82 cnf(238,plain, % 0.54/0.82 ($false), % 0.54/0.82 inference(scs_inference,[],[14,15,29,222,225,212,2,21,19,11,22,94,20,26]), % 0.54/0.82 ['proof']). % 0.54/0.82 % SZS output end Proof % 0.54/0.82 % Total time :0.200000s %------------------------------------------------------------------------------