%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET885+1 : TPTP v8.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n017.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 14:22:53 EDT 2024 % Result : Theorem 58.56s 58.66s % Output : CNFRefutation 58.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET885+1 : TPTP v8.2.0. Released v3.2.0. % 0.11/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n017.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 15:18:38 EDT 2024 % 0.12/0.33 % CPUTime : % 0.19/0.55 start to proof:theBenchmark % 58.56/58.65 %------------------------------------------- % 58.56/58.65 % File :CSE---1.7 % 58.56/58.65 % Problem :theBenchmark % 58.56/58.65 % Transform :cnf % 58.56/58.65 % Format :tptp:raw % 58.56/58.65 % Command :java -jar mcs_scs.jar %d %s % 58.56/58.65 % 58.56/58.65 % Result :Theorem 58.050000s % 58.56/58.65 % Output :CNFRefutation 58.050000s % 58.56/58.65 %------------------------------------------- % 58.56/58.66 %------------------------------------------------------------------------------ % 58.56/58.66 % File : SET885+1 : TPTP v8.2.0. Released v3.2.0. % 58.56/58.66 % Domain : Set theory % 58.56/58.66 % Problem : subset(unordered_pair(A,B),singleton(C)) => A = C % 58.56/58.66 % Version : [Urb06] axioms : Especial. % 58.56/58.66 % English : % 58.56/58.66 % 58.56/58.66 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 58.56/58.66 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 58.56/58.66 % Source : [Urb06] % 58.56/58.66 % Names : zfmisc_1__t26_zfmisc_1 [Urb06] % 58.56/58.66 % 58.56/58.66 % Status : Theorem % 58.56/58.66 % Rating : 0.17 v7.5.0, 0.19 v7.4.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.2.0, 0.24 v6.1.0, 0.30 v5.5.0, 0.19 v5.4.0, 0.14 v5.3.0, 0.19 v5.2.0, 0.00 v5.0.0, 0.12 v4.1.0, 0.13 v4.0.1, 0.17 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.14 v3.2.0 % 58.56/58.66 % Syntax : Number of formulae : 9 ( 4 unt; 0 def) % 58.56/58.66 % Number of atoms : 18 ( 7 equ) % 58.56/58.66 % Maximal formula atoms : 4 ( 2 avg) % 58.56/58.66 % Number of connectives : 11 ( 2 ~; 1 |; 0 &) % 58.56/58.66 % ( 5 <=>; 3 =>; 0 <=; 0 <~>) % 58.56/58.66 % Maximal formula depth : 8 ( 5 avg) % 58.56/58.66 % Maximal term depth : 2 ( 1 avg) % 58.56/58.66 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty) % 58.56/58.66 % Number of functors : 2 ( 2 usr; 0 con; 1-2 aty) % 58.56/58.66 % Number of variables : 21 ( 19 !; 2 ?) % 58.56/58.66 % SPC : FOF_THM_RFO_SEQ % 58.56/58.66 % 58.56/58.66 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 58.56/58.66 % library, www.mizar.org % 58.56/58.66 %------------------------------------------------------------------------------ % 58.56/58.66 fof(antisymmetry_r2_hidden,axiom, % 58.56/58.66 ! [A,B] : % 58.56/58.66 ( in(A,B) % 58.56/58.66 => ~ in(B,A) ) ). % 58.56/58.66 % 58.56/58.66 fof(commutativity_k2_tarski,axiom, % 58.56/58.66 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 58.56/58.66 % 58.56/58.66 fof(d1_tarski,axiom, % 58.56/58.66 ! [A,B] : % 58.56/58.66 ( B = singleton(A) % 58.56/58.66 <=> ! [C] : % 58.56/58.66 ( in(C,B) % 58.56/58.66 <=> C = A ) ) ). % 58.56/58.66 % 58.56/58.66 fof(d2_tarski,axiom, % 58.56/58.66 ! [A,B,C] : % 58.56/58.66 ( C = unordered_pair(A,B) % 58.56/58.66 <=> ! [D] : % 58.56/58.66 ( in(D,C) % 58.56/58.66 <=> ( D = A % 58.56/58.66 | D = B ) ) ) ). % 58.56/58.66 % 58.56/58.66 fof(d3_tarski,axiom, % 58.56/58.66 ! [A,B] : % 58.56/58.66 ( subset(A,B) % 58.56/58.66 <=> ! [C] : % 58.56/58.66 ( in(C,A) % 58.56/58.66 => in(C,B) ) ) ). % 58.56/58.66 % 58.56/58.66 fof(rc1_xboole_0,axiom, % 58.56/58.66 ? [A] : empty(A) ). % 58.56/58.66 % 58.56/58.66 fof(rc2_xboole_0,axiom, % 58.56/58.66 ? [A] : ~ empty(A) ). % 58.56/58.66 % 58.56/58.66 fof(reflexivity_r1_tarski,axiom, % 58.56/58.66 ! [A,B] : subset(A,A) ). % 58.56/58.66 % 58.56/58.66 fof(t26_zfmisc_1,conjecture, % 58.56/58.66 ! [A,B,C] : % 58.56/58.66 ( subset(unordered_pair(A,B),singleton(C)) % 58.56/58.66 => A = C ) ). % 58.56/58.66 % 58.56/58.66 %------------------------------------------------------------------------------ % 58.56/58.66 %------------------------------------------- % 58.56/58.66 % Proof found % 58.56/58.66 % SZS status Theorem for theBenchmark % 58.56/58.66 % SZS output start Proof % 58.56/58.67 %ClaNum:38(EqnAxiom:18) % 58.56/58.67 %VarNum:114(SingletonVarNum:43) % 58.56/58.67 %MaxLitNum:4 % 58.56/58.67 %MaxfuncDepth:1 % 58.56/58.67 %SharedTerms:11 % 58.56/58.67 %goalClause: 22 23 % 58.56/58.67 %singleGoalClaCount:2 % 58.56/58.67 [19]P1(a1) % 58.56/58.67 [23]~E(a9,a6) % 58.56/58.67 [24]~P1(a7) % 58.56/58.67 [22]P2(f5(a6,a8),f10(a9)) % 58.56/58.67 [20]P2(x201,x201) % 58.56/58.67 [21]E(f5(x211,x212),f5(x212,x211)) % 58.56/58.67 [29]~P3(x292,x291)+~P3(x291,x292) % 58.56/58.67 [31]P2(x311,x312)+P3(f2(x311,x312),x311) % 58.56/58.67 [34]P2(x341,x342)+~P3(f2(x341,x342),x342) % 58.56/58.67 [33]E(f3(x332,x331),x332)+P3(f3(x332,x331),x331)+E(x331,f10(x332)) % 58.56/58.67 [35]~E(f3(x352,x351),x352)+~P3(f3(x352,x351),x351)+E(x351,f10(x352)) % 58.56/58.67 [32]~P2(x323,x322)+P3(x321,x322)+~P3(x321,x323) % 58.56/58.67 [25]P3(x251,x252)+~E(x251,x253)+~E(x252,f10(x253)) % 58.56/58.67 [26]~P3(x261,x263)+E(x261,x262)+~E(x263,f10(x262)) % 58.56/58.67 [37]~E(f4(x372,x373,x371),x373)+~P3(f4(x372,x373,x371),x371)+E(x371,f5(x372,x373)) % 58.56/58.67 [38]~E(f4(x382,x383,x381),x382)+~P3(f4(x382,x383,x381),x381)+E(x381,f5(x382,x383)) % 58.56/58.67 [27]P3(x271,x272)+~E(x271,x273)+~E(x272,f5(x274,x273)) % 58.56/58.67 [28]P3(x281,x282)+~E(x281,x283)+~E(x282,f5(x283,x284)) % 58.56/58.67 [36]E(f4(x362,x363,x361),x363)+E(f4(x362,x363,x361),x362)+P3(f4(x362,x363,x361),x361)+E(x361,f5(x362,x363)) % 58.56/58.67 [30]~P3(x301,x304)+E(x301,x302)+E(x301,x303)+~E(x304,f5(x303,x302)) % 58.56/58.67 %EqnAxiom % 58.56/58.67 [1]E(x11,x11) % 58.56/58.67 [2]E(x22,x21)+~E(x21,x22) % 58.56/58.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 58.56/58.67 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43)) % 58.56/58.67 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52)) % 58.56/58.67 [6]~E(x61,x62)+E(f4(x61,x63,x64),f4(x62,x63,x64)) % 58.56/58.67 [7]~E(x71,x72)+E(f4(x73,x71,x74),f4(x73,x72,x74)) % 58.56/58.67 [8]~E(x81,x82)+E(f4(x83,x84,x81),f4(x83,x84,x82)) % 58.56/58.67 [9]~E(x91,x92)+E(f3(x91,x93),f3(x92,x93)) % 58.56/58.67 [10]~E(x101,x102)+E(f3(x103,x101),f3(x103,x102)) % 58.56/58.67 [11]~E(x111,x112)+E(f10(x111),f10(x112)) % 58.56/58.67 [12]~E(x121,x122)+E(f2(x121,x123),f2(x122,x123)) % 58.56/58.67 [13]~E(x131,x132)+E(f2(x133,x131),f2(x133,x132)) % 58.56/58.67 [14]~P1(x141)+P1(x142)+~E(x141,x142) % 58.56/58.67 [15]P2(x152,x153)+~E(x151,x152)+~P2(x151,x153) % 58.56/58.67 [16]P2(x163,x162)+~E(x161,x162)+~P2(x163,x161) % 58.56/58.67 [17]P3(x172,x173)+~E(x171,x172)+~P3(x171,x173) % 58.56/58.67 [18]P3(x183,x182)+~E(x181,x182)+~P3(x183,x181) % 58.56/58.67 % 58.56/58.67 %------------------------------------------- % 58.56/58.68 cnf(39,plain, % 58.56/58.68 (~P3(x391,f10(x392))+E(x391,x392)), % 58.56/58.68 inference(equality_inference,[],[26])). % 58.56/58.68 cnf(88,plain, % 58.56/58.68 (~E(a6,x881)+E(a9,a6)+~E(a9,x881)), % 58.56/58.68 inference(scs_inference,[],[23,3,2])). % 58.56/58.68 cnf(89,plain, % 58.56/58.68 (~E(a9,x891)+~E(a6,x891)), % 58.56/58.68 inference(scs_inference,[],[23,88])). % 58.56/58.68 cnf(98,plain, % 58.56/58.68 (~P3(a6,f10(x981))+~E(a9,x981)), % 58.56/58.68 inference(scs_inference,[],[89,39])). % 58.56/58.68 cnf(99,plain, % 58.56/58.68 (~P3(a6,f10(a9))), % 58.56/58.68 inference(equality_inference,[],[98])). % 58.56/58.68 cnf(3732,plain, % 58.56/58.68 (~P3(a6,f5(a6,a8))), % 58.56/58.68 inference(scs_inference,[],[22,99,32])). % 58.56/58.68 cnf(5415,plain, % 58.56/58.68 ($false), % 58.56/58.68 inference(scs_inference,[],[3732,21,27]), % 58.56/58.68 ['proof']). % 58.56/58.68 % SZS output end Proof % 58.56/58.68 % Total time :58.050000s %------------------------------------------------------------------------------