%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET909+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 : n029.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 14:22:57 EDT 2024 % Result : Theorem 0.55s 0.65s % Output : CNFRefutation 0.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SET909+1 : TPTP v8.2.0. Released v3.2.0. % 0.04/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n029.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 15:11:24 EDT 2024 % 0.13/0.35 % CPUTime : % 0.50/0.59 start to proof:theBenchmark % 0.50/0.64 %------------------------------------------- % 0.50/0.64 % File :CSE---1.7 % 0.50/0.64 % Problem :theBenchmark % 0.50/0.64 % Transform :cnf % 0.50/0.64 % Format :tptp:raw % 0.50/0.64 % Command :java -jar mcs_scs.jar %d %s % 0.50/0.64 % 0.50/0.64 % Result :Theorem 0.010000s % 0.50/0.64 % Output :CNFRefutation 0.010000s % 0.50/0.64 %------------------------------------------- % 0.50/0.64 %------------------------------------------------------------------------------ % 0.50/0.64 % File : SET909+1 : TPTP v8.2.0. Released v3.2.0. % 0.50/0.64 % Domain : Set theory % 0.50/0.64 % Problem : union(unordered_pair(A,B),C) != empty_set % 0.50/0.64 % Version : [Urb06] axioms : Especial. % 0.50/0.64 % English : % 0.50/0.64 % 0.50/0.64 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.50/0.64 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.50/0.64 % Source : [Urb06] % 0.50/0.64 % Names : zfmisc_1__t50_zfmisc_1 [Urb06] % 0.50/0.64 % 0.50/0.64 % Status : Theorem % 0.50/0.64 % Rating : 0.19 v7.5.0, 0.22 v7.4.0, 0.10 v7.3.0, 0.14 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.21 v6.2.0, 0.36 v6.1.0, 0.33 v6.0.0, 0.26 v5.5.0, 0.22 v5.4.0, 0.25 v5.3.0, 0.30 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.21 v4.1.0, 0.22 v4.0.1, 0.26 v4.0.0, 0.25 v3.7.0, 0.20 v3.5.0, 0.21 v3.2.0 % 0.50/0.64 % Syntax : Number of formulae : 13 ( 7 unt; 0 def) % 0.50/0.64 % Number of atoms : 23 ( 9 equ) % 0.50/0.64 % Maximal formula atoms : 4 ( 1 avg) % 0.50/0.64 % Number of connectives : 18 ( 8 ~; 2 |; 0 &) % 0.50/0.64 % ( 5 <=>; 3 =>; 0 <=; 0 <~>) % 0.50/0.64 % Maximal formula depth : 8 ( 4 avg) % 0.50/0.64 % Maximal term depth : 3 ( 1 avg) % 0.50/0.64 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 0.50/0.64 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty) % 0.50/0.64 % Number of variables : 27 ( 25 !; 2 ?) % 0.50/0.64 % SPC : FOF_THM_RFO_SEQ % 0.50/0.64 % 0.50/0.64 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.55/0.64 % library, www.mizar.org % 0.55/0.64 %------------------------------------------------------------------------------ % 0.55/0.64 fof(antisymmetry_r2_hidden,axiom, % 0.55/0.64 ! [A,B] : % 0.55/0.64 ( in(A,B) % 0.55/0.64 => ~ in(B,A) ) ). % 0.55/0.64 % 0.55/0.64 fof(commutativity_k2_tarski,axiom, % 0.55/0.64 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 0.55/0.64 % 0.55/0.64 fof(commutativity_k2_xboole_0,axiom, % 0.55/0.65 ! [A,B] : set_union2(A,B) = set_union2(B,A) ). % 0.55/0.65 % 0.55/0.65 fof(d1_xboole_0,axiom, % 0.55/0.65 ! [A] : % 0.55/0.65 ( A = empty_set % 0.55/0.65 <=> ! [B] : ~ in(B,A) ) ). % 0.55/0.65 % 0.55/0.65 fof(d2_tarski,axiom, % 0.55/0.65 ! [A,B,C] : % 0.55/0.65 ( C = unordered_pair(A,B) % 0.55/0.65 <=> ! [D] : % 0.55/0.65 ( in(D,C) % 0.55/0.65 <=> ( D = A % 0.55/0.65 | D = B ) ) ) ). % 0.55/0.65 % 0.55/0.65 fof(d2_xboole_0,axiom, % 0.55/0.65 ! [A,B,C] : % 0.55/0.65 ( C = set_union2(A,B) % 0.55/0.65 <=> ! [D] : % 0.55/0.65 ( in(D,C) % 0.55/0.65 <=> ( in(D,A) % 0.55/0.65 | in(D,B) ) ) ) ). % 0.55/0.65 % 0.55/0.65 fof(fc1_xboole_0,axiom, % 0.55/0.65 empty(empty_set) ). % 0.55/0.65 % 0.55/0.65 fof(fc2_xboole_0,axiom, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( ~ empty(A) % 0.55/0.65 => ~ empty(set_union2(A,B)) ) ). % 0.55/0.65 % 0.55/0.65 fof(fc3_xboole_0,axiom, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( ~ empty(A) % 0.55/0.65 => ~ empty(set_union2(B,A)) ) ). % 0.55/0.65 % 0.55/0.65 fof(idempotence_k2_xboole_0,axiom, % 0.55/0.65 ! [A,B] : set_union2(A,A) = A ). % 0.55/0.65 % 0.55/0.65 fof(rc1_xboole_0,axiom, % 0.55/0.65 ? [A] : empty(A) ). % 0.55/0.65 % 0.55/0.65 fof(rc2_xboole_0,axiom, % 0.55/0.65 ? [A] : ~ empty(A) ). % 0.55/0.65 % 0.55/0.65 fof(t50_zfmisc_1,conjecture, % 0.55/0.65 ! [A,B,C] : set_union2(unordered_pair(A,B),C) != empty_set ). % 0.55/0.65 % 0.55/0.65 %------------------------------------------------------------------------------ % 0.55/0.65 %------------------------------------------- % 0.55/0.65 % Proof found % 0.55/0.65 % SZS status Theorem for theBenchmark % 0.55/0.65 % SZS output start Proof % 0.55/0.65 %ClaNum:41(EqnAxiom:17) % 0.55/0.65 %VarNum:147(SingletonVarNum:56) % 0.55/0.65 %MaxLitNum:4 % 0.55/0.65 %MaxfuncDepth:2 % 0.55/0.65 %SharedTerms:12 % 0.55/0.65 %goalClause: 23 % 0.55/0.65 %singleGoalClaCount:1 % 0.55/0.65 [18]P1(a1) % 0.55/0.65 [19]P1(a2) % 0.55/0.65 [24]~P1(a8) % 0.55/0.65 [23]E(f6(f11(a7,a9),a10),a1) % 0.55/0.65 [20]E(f6(x201,x201),x201) % 0.55/0.65 [21]E(f11(x211,x212),f11(x212,x211)) % 0.55/0.65 [22]E(f6(x221,x222),f6(x222,x221)) % 0.55/0.65 [25]P2(f3(x251),x251)+E(x251,a1) % 0.55/0.65 [26]~P2(x262,x261)+~E(x261,a1) % 0.55/0.65 [29]~P2(x292,x291)+~P2(x291,x292) % 0.55/0.65 [31]P1(x311)+~P1(f6(x312,x311)) % 0.55/0.65 [32]P1(x321)+~P1(f6(x321,x322)) % 0.55/0.65 [37]~E(f4(x372,x373,x371),x373)+~P2(f4(x372,x373,x371),x371)+E(x371,f11(x372,x373)) % 0.55/0.65 [38]~E(f4(x382,x383,x381),x382)+~P2(f4(x382,x383,x381),x381)+E(x381,f11(x382,x383)) % 0.55/0.65 [40]~P2(f5(x402,x403,x401),x401)+~P2(f5(x402,x403,x401),x403)+E(x401,f6(x402,x403)) % 0.55/0.65 [41]~P2(f5(x412,x413,x411),x411)+~P2(f5(x412,x413,x411),x412)+E(x411,f6(x412,x413)) % 0.55/0.65 [27]P2(x271,x272)+~E(x271,x273)+~E(x272,f11(x274,x273)) % 0.55/0.65 [28]P2(x281,x282)+~E(x281,x283)+~E(x282,f11(x283,x284)) % 0.55/0.65 [33]~P2(x331,x334)+P2(x331,x332)+~E(x332,f6(x333,x334)) % 0.55/0.65 [34]~P2(x341,x343)+P2(x341,x342)+~E(x342,f6(x343,x344)) % 0.55/0.65 [36]E(f4(x362,x363,x361),x363)+E(f4(x362,x363,x361),x362)+P2(f4(x362,x363,x361),x361)+E(x361,f11(x362,x363)) % 0.55/0.65 [39]P2(f5(x392,x393,x391),x391)+P2(f5(x392,x393,x391),x393)+P2(f5(x392,x393,x391),x392)+E(x391,f6(x392,x393)) % 0.55/0.65 [30]~P2(x301,x304)+E(x301,x302)+E(x301,x303)+~E(x304,f11(x303,x302)) % 0.55/0.65 [35]~P2(x351,x354)+P2(x351,x352)+P2(x351,x353)+~E(x354,f6(x353,x352)) % 0.55/0.65 %EqnAxiom % 0.55/0.65 [1]E(x11,x11) % 0.55/0.65 [2]E(x22,x21)+~E(x21,x22) % 0.55/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.55/0.65 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43)) % 0.55/0.65 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52)) % 0.55/0.65 [6]~E(x61,x62)+E(f11(x61,x63),f11(x62,x63)) % 0.55/0.65 [7]~E(x71,x72)+E(f11(x73,x71),f11(x73,x72)) % 0.55/0.65 [8]~E(x81,x82)+E(f4(x81,x83,x84),f4(x82,x83,x84)) % 0.55/0.65 [9]~E(x91,x92)+E(f4(x93,x91,x94),f4(x93,x92,x94)) % 0.55/0.65 [10]~E(x101,x102)+E(f4(x103,x104,x101),f4(x103,x104,x102)) % 0.55/0.65 [11]~E(x111,x112)+E(f5(x111,x113,x114),f5(x112,x113,x114)) % 0.55/0.65 [12]~E(x121,x122)+E(f5(x123,x121,x124),f5(x123,x122,x124)) % 0.55/0.65 [13]~E(x131,x132)+E(f5(x133,x134,x131),f5(x133,x134,x132)) % 0.55/0.65 [14]~E(x141,x142)+E(f3(x141),f3(x142)) % 0.55/0.65 [15]~P1(x151)+P1(x152)+~E(x151,x152) % 0.55/0.65 [16]P2(x162,x163)+~E(x161,x162)+~P2(x161,x163) % 0.55/0.65 [17]P2(x173,x172)+~E(x171,x172)+~P2(x173,x171) % 0.55/0.65 % 0.55/0.65 %------------------------------------------- % 0.55/0.65 cnf(42,plain, % 0.55/0.65 (~P2(x421,a1)), % 0.55/0.65 inference(equality_inference,[],[26])). % 0.55/0.65 cnf(51,plain, % 0.55/0.65 (E(f6(x511,x511),x511)), % 0.55/0.65 inference(rename_variables,[],[20])). % 0.55/0.65 cnf(54,plain, % 0.55/0.65 (E(f6(x541,x541),x541)), % 0.55/0.65 inference(rename_variables,[],[20])). % 0.55/0.65 cnf(60,plain, % 0.55/0.65 (~P2(x601,f11(a7,a9))), % 0.55/0.65 inference(scs_inference,[],[23,42,20,51,54,24,26,2,27,28,15,33,34])). % 0.55/0.65 cnf(77,plain, % 0.55/0.65 ($false), % 0.55/0.65 inference(scs_inference,[],[60,20,21,2,28]), % 0.55/0.65 ['proof']). % 0.55/0.65 % SZS output end Proof % 0.55/0.65 % Total time :0.010000s %------------------------------------------------------------------------------