%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET942+1 : TPTP v8.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n024.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 14:23:04 EDT 2024 % Result : Theorem 116.44s 116.50s % Output : CNFRefutation 116.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET942+1 : TPTP v8.2.0. Released v3.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n024.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 15:47:24 EDT 2024 % 0.12/0.33 % CPUTime : % 0.46/0.57 start to proof:theBenchmark % 116.44/116.49 %------------------------------------------- % 116.44/116.49 % File :CSE---1.7 % 116.44/116.49 % Problem :theBenchmark % 116.44/116.49 % Transform :cnf % 116.44/116.49 % Format :tptp:raw % 116.44/116.49 % Command :java -jar mcs_scs.jar %d %s % 116.44/116.49 % 116.44/116.49 % Result :Theorem 115.870000s % 116.44/116.49 % Output :CNFRefutation 115.870000s % 116.44/116.49 %------------------------------------------- % 116.44/116.50 %------------------------------------------------------------------------------ % 116.44/116.50 % File : SET942+1 : TPTP v8.2.0. Released v3.2.0. % 116.44/116.50 % Domain : Set theory % 116.44/116.50 % Problem : subset(A,B) => subset(union(A),union(B)) % 116.44/116.50 % Version : [Urb06] axioms : Especial. % 116.44/116.50 % English : % 116.44/116.50 % 116.44/116.50 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 116.44/116.50 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 116.44/116.50 % Source : [Urb06] % 116.44/116.50 % Names : zfmisc_1__t95_zfmisc_1 [Urb06] % 116.44/116.50 % 116.44/116.50 % Status : Theorem % 116.44/116.50 % Rating : 0.25 v8.2.0, 0.28 v8.1.0, 0.25 v7.4.0, 0.13 v7.3.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.17 v6.4.0, 0.19 v6.3.0, 0.21 v6.2.0, 0.28 v6.1.0, 0.43 v6.0.0, 0.35 v5.5.0, 0.26 v5.4.0, 0.32 v5.3.0, 0.37 v5.2.0, 0.25 v5.1.0, 0.24 v5.0.0, 0.33 v4.1.0, 0.26 v4.0.0, 0.25 v3.7.0, 0.20 v3.5.0, 0.21 v3.4.0, 0.32 v3.3.0, 0.36 v3.2.0 % 116.44/116.50 % Syntax : Number of formulae : 7 ( 3 unt; 0 def) % 116.44/116.50 % Number of atoms : 14 ( 1 equ) % 116.44/116.50 % Maximal formula atoms : 4 ( 2 avg) % 116.44/116.50 % Number of connectives : 9 ( 2 ~; 0 |; 1 &) % 116.44/116.50 % ( 3 <=>; 3 =>; 0 <=; 0 <~>) % 116.44/116.50 % Maximal formula depth : 8 ( 4 avg) % 116.44/116.50 % Maximal term depth : 2 ( 1 avg) % 116.44/116.50 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty) % 116.44/116.50 % Number of functors : 1 ( 1 usr; 0 con; 1-1 aty) % 116.44/116.50 % Number of variables : 15 ( 12 !; 3 ?) % 116.44/116.50 % SPC : FOF_THM_RFO_SEQ % 116.44/116.50 % 116.44/116.50 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 116.44/116.50 % library, www.mizar.org % 116.44/116.50 %------------------------------------------------------------------------------ % 116.44/116.50 fof(antisymmetry_r2_hidden,axiom, % 116.44/116.50 ! [A,B] : % 116.44/116.50 ( in(A,B) % 116.44/116.50 => ~ in(B,A) ) ). % 116.44/116.50 % 116.44/116.50 fof(d3_tarski,axiom, % 116.44/116.50 ! [A,B] : % 116.44/116.50 ( subset(A,B) % 116.44/116.50 <=> ! [C] : % 116.44/116.50 ( in(C,A) % 116.44/116.50 => in(C,B) ) ) ). % 116.44/116.50 % 116.44/116.50 fof(d4_tarski,axiom, % 116.44/116.50 ! [A,B] : % 116.44/116.50 ( B = union(A) % 116.44/116.50 <=> ! [C] : % 116.44/116.50 ( in(C,B) % 116.44/116.50 <=> ? [D] : % 116.44/116.50 ( in(C,D) % 116.44/116.50 & in(D,A) ) ) ) ). % 116.44/116.50 % 116.44/116.50 fof(rc1_xboole_0,axiom, % 116.44/116.50 ? [A] : empty(A) ). % 116.44/116.50 % 116.44/116.50 fof(rc2_xboole_0,axiom, % 116.44/116.50 ? [A] : ~ empty(A) ). % 116.44/116.50 % 116.44/116.50 fof(reflexivity_r1_tarski,axiom, % 116.44/116.50 ! [A,B] : subset(A,A) ). % 116.44/116.50 % 116.44/116.50 fof(t95_zfmisc_1,conjecture, % 116.44/116.50 ! [A,B] : % 116.44/116.50 ( subset(A,B) % 116.44/116.50 => subset(union(A),union(B)) ) ). % 116.44/116.50 % 116.44/116.50 %------------------------------------------------------------------------------ % 116.44/116.50 %------------------------------------------- % 116.44/116.50 % Proof found % 116.44/116.50 % SZS status Theorem for theBenchmark % 116.44/116.50 % SZS output start Proof % 116.44/116.51 %ClaNum:33(EqnAxiom:18) % 116.44/116.51 %VarNum:73(SingletonVarNum:27) % 116.44/116.51 %MaxLitNum:4 % 116.44/116.51 %MaxfuncDepth:1 % 116.44/116.51 %SharedTerms:10 % 116.44/116.51 %goalClause: 20 23 % 116.44/116.51 %singleGoalClaCount:2 % 116.44/116.51 [19]P1(a1) % 116.44/116.51 [20]P2(a6,a8) % 116.44/116.51 [22]~P1(a7) % 116.44/116.51 [23]~P2(f9(a6),f9(a8)) % 116.44/116.51 [21]P2(x211,x211) % 116.44/116.51 [24]~P3(x242,x241)+~P3(x241,x242) % 116.44/116.51 [25]P2(x251,x252)+P3(f2(x251,x252),x251) % 116.44/116.51 [28]P2(x281,x282)+~P3(f2(x281,x282),x282) % 116.44/116.51 [29]P3(f3(x292,x291),x291)+P3(f5(x292,x291),x292)+E(x291,f9(x292)) % 116.44/116.51 [30]P3(f3(x302,x301),x301)+P3(f3(x302,x301),f5(x302,x301))+E(x301,f9(x302)) % 116.44/116.51 [26]~P2(x263,x262)+P3(x261,x262)+~P3(x261,x263) % 116.44/116.51 [31]~P3(x311,x313)+~E(x313,f9(x312))+P3(x311,f4(x312,x313,x311)) % 116.44/116.51 [32]~P3(x323,x322)+~E(x322,f9(x321))+P3(f4(x321,x322,x323),x321) % 116.44/116.51 [33]~P3(x333,x332)+~P3(f3(x332,x331),x333)+~P3(f3(x332,x331),x331)+E(x331,f9(x332)) % 116.44/116.51 [27]~P3(x271,x274)+P3(x271,x272)+~P3(x274,x273)+~E(x272,f9(x273)) % 116.44/116.51 %EqnAxiom % 116.44/116.51 [1]E(x11,x11) % 116.44/116.51 [2]E(x22,x21)+~E(x21,x22) % 116.44/116.51 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 116.44/116.51 [4]~E(x41,x42)+E(f9(x41),f9(x42)) % 116.44/116.51 [5]~E(x51,x52)+E(f3(x51,x53),f3(x52,x53)) % 116.44/116.51 [6]~E(x61,x62)+E(f3(x63,x61),f3(x63,x62)) % 116.44/116.51 [7]~E(x71,x72)+E(f2(x71,x73),f2(x72,x73)) % 116.44/116.51 [8]~E(x81,x82)+E(f2(x83,x81),f2(x83,x82)) % 116.44/116.51 [9]~E(x91,x92)+E(f5(x91,x93),f5(x92,x93)) % 116.44/116.51 [10]~E(x101,x102)+E(f5(x103,x101),f5(x103,x102)) % 116.44/116.51 [11]~E(x111,x112)+E(f4(x111,x113,x114),f4(x112,x113,x114)) % 116.44/116.51 [12]~E(x121,x122)+E(f4(x123,x121,x124),f4(x123,x122,x124)) % 116.44/116.51 [13]~E(x131,x132)+E(f4(x133,x134,x131),f4(x133,x134,x132)) % 116.44/116.51 [14]~P1(x141)+P1(x142)+~E(x141,x142) % 116.44/116.51 [15]P2(x152,x153)+~E(x151,x152)+~P2(x151,x153) % 116.44/116.51 [16]P2(x163,x162)+~E(x161,x162)+~P2(x163,x161) % 116.44/116.51 [17]P3(x172,x173)+~E(x171,x172)+~P3(x171,x173) % 116.44/116.51 [18]P3(x183,x182)+~E(x181,x182)+~P3(x183,x181) % 116.44/116.51 % 116.44/116.51 %------------------------------------------- % 116.44/116.51 cnf(34,plain, % 116.44/116.51 (~P3(x341,x342)+P3(x341,f9(x343))+~P3(x342,x343)), % 116.44/116.51 inference(equality_inference,[],[27])). % 116.44/116.51 cnf(35,plain, % 116.44/116.51 (~P3(x351,f9(x352))+P3(x351,f4(x352,f9(x352),x351))), % 116.44/116.51 inference(equality_inference,[],[31])). % 116.44/116.51 cnf(36,plain, % 116.44/116.51 (~P3(x361,f9(x362))+P3(f4(x362,f9(x362),x361),x362)), % 116.44/116.51 inference(equality_inference,[],[32])). % 116.44/116.51 cnf(100,plain, % 116.44/116.51 (~E(x1001,f9(a6))+~P3(f2(x1001,f9(a8)),f9(a8))), % 116.44/116.51 inference(scs_inference,[],[23,28,15])). % 116.44/116.51 cnf(101,plain, % 116.44/116.51 (~P3(f2(f9(a6),f9(a8)),f9(a8))), % 116.44/116.51 inference(equality_inference,[],[100])). % 116.44/116.51 cnf(216,plain, % 116.44/116.51 (~P3(f4(x2161,f9(x2161),x2162),x2162)+~P3(x2162,f9(x2161))), % 116.44/116.51 inference(scs_inference,[],[35,24])). % 116.44/116.52 cnf(232,plain, % 116.44/116.52 (~P3(x2321,f9(x2321))), % 116.44/116.52 inference(scs_inference,[],[36,216])). % 116.44/116.52 cnf(760,plain, % 116.44/116.52 (~E(x7601,a8)+P2(a6,x7601)), % 116.44/116.52 inference(scs_inference,[],[20,2,16])). % 116.44/116.52 cnf(794,plain, % 116.44/116.52 (~E(f9(a8),x7941)+~P3(f2(f9(a6),f9(a8)),x7941)), % 116.44/116.52 inference(scs_inference,[],[101,2,18])). % 116.44/116.52 cnf(862,plain, % 116.44/116.52 (~E(f9(x8621),f9(a8))+~P3(f2(f9(a6),f9(a8)),x8622)+~P3(x8622,x8621)), % 116.44/116.52 inference(scs_inference,[],[101,2,27])). % 116.44/116.52 cnf(863,plain, % 116.44/116.52 (~P3(x8631,a8)+~P3(f2(f9(a6),f9(a8)),x8631)), % 116.44/116.52 inference(equality_inference,[],[862])). % 116.44/116.52 cnf(4911,plain, % 116.44/116.52 (~P3(x49111,a6)+~E(f9(x49111),a8)), % 116.44/116.52 inference(scs_inference,[],[232,760,26])). % 116.44/116.52 cnf(7147,plain, % 116.44/116.52 (~P3(x71471,f9(x71472))+~E(x71471,x71472)), % 116.44/116.52 inference(scs_inference,[],[232,17])). % 116.44/116.52 cnf(10637,plain, % 116.44/116.52 (~P3(f2(f9(a6),f9(a8)),x106371)+~E(x106371,f9(a8))), % 116.44/116.52 inference(scs_inference,[],[101,18])). % 116.44/116.52 cnf(10652,plain, % 116.44/116.52 (~P3(x106521,x106522)+~E(x106522,f9(x106521))), % 116.44/116.52 inference(scs_inference,[],[232,18])). % 116.44/116.52 cnf(15090,plain, % 116.44/116.52 (~P3(x150901,f9(a6))+~E(f9(f4(a6,f9(a6),x150901)),a8)), % 116.44/116.52 inference(scs_inference,[],[4911,36])). % 116.44/116.52 cnf(16326,plain, % 116.44/116.52 (~E(f2(f9(a6),f9(a8)),a6)), % 116.44/116.52 inference(scs_inference,[],[23,7147,25])). % 116.44/116.52 cnf(16630,plain, % 116.44/116.52 (~P3(f4(a6,f9(a6),f2(f9(a6),f9(a8))),a8)), % 116.44/116.52 inference(scs_inference,[],[16326,23,232,2,25,35,34,10652,863])). % 116.44/116.52 cnf(16636,plain, % 116.44/116.52 (P3(f4(a6,f9(a6),f2(f9(a6),f9(a8))),a6)), % 116.44/116.52 inference(scs_inference,[],[16326,23,232,2,25,35,34,10652,863,794,10637,15090,36])). % 116.44/116.52 cnf(16683,plain, % 116.44/116.52 ($false), % 116.44/116.52 inference(scs_inference,[],[16630,16636,20,26]), % 116.44/116.52 ['proof']). % 116.44/116.52 % SZS output end Proof % 116.44/116.52 % Total time :115.870000s 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