%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET878+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 : n032.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 14:22:52 EDT 2024 % Result : Theorem 13.28s 13.41s % Output : CNFRefutation 13.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.09 % Problem : SET878+1 : TPTP v8.2.0. Released v3.2.0. % 0.05/0.09 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.08/0.28 % Computer : n032.cluster.edu % 0.08/0.28 % Model : x86_64 x86_64 % 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.28 % Memory : 8042.1875MB % 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.28 % CPULimit : 300 % 0.08/0.28 % WCLimit : 300 % 0.08/0.28 % DateTime : Sun Jun 23 12:25:08 EDT 2024 % 0.08/0.29 % CPUTime : % 0.13/0.46 start to proof:theBenchmark % 13.28/13.40 %------------------------------------------- % 13.28/13.40 % File :CSE---1.7 % 13.28/13.40 % Problem :theBenchmark % 13.28/13.40 % Transform :cnf % 13.28/13.40 % Format :tptp:raw % 13.28/13.40 % Command :java -jar mcs_scs.jar %d %s % 13.28/13.40 % 13.28/13.40 % Result :Theorem 12.910000s % 13.28/13.40 % Output :CNFRefutation 12.910000s % 13.28/13.40 %------------------------------------------- % 13.28/13.40 %------------------------------------------------------------------------------ % 13.28/13.40 % File : SET878+1 : TPTP v8.2.0. Released v3.2.0. % 13.28/13.40 % Domain : Set theory % 13.28/13.40 % Problem : intersection(singleton(A),unordered_pair(A,B)) = singleton(A) % 13.28/13.40 % Version : [Urb06] axioms : Especial. % 13.28/13.40 % English : % 13.28/13.40 % 13.28/13.40 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 13.28/13.40 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 13.28/13.40 % Source : [Urb06] % 13.28/13.40 % Names : zfmisc_1__t19_zfmisc_1 [Urb06] % 13.28/13.40 % 13.28/13.40 % Status : Theorem % 13.28/13.40 % Rating : 0.14 v7.5.0, 0.16 v7.4.0, 0.03 v7.3.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.10 v6.4.0, 0.15 v6.3.0, 0.17 v6.2.0, 0.28 v6.1.0, 0.30 v6.0.0, 0.22 v5.5.0, 0.19 v5.4.0, 0.21 v5.3.0, 0.26 v5.2.0, 0.10 v5.0.0, 0.21 v4.1.0, 0.22 v4.0.1, 0.26 v4.0.0, 0.25 v3.7.0, 0.15 v3.5.0, 0.16 v3.3.0, 0.21 v3.2.0 % 13.28/13.40 % Syntax : Number of formulae : 9 ( 6 unt; 0 def) % 13.28/13.40 % Number of atoms : 14 ( 8 equ) % 13.28/13.40 % Maximal formula atoms : 4 ( 1 avg) % 13.28/13.40 % Number of connectives : 7 ( 2 ~; 1 |; 0 &) % 13.28/13.40 % ( 2 <=>; 2 =>; 0 <=; 0 <~>) % 13.28/13.40 % Maximal formula depth : 8 ( 4 avg) % 13.28/13.40 % Maximal term depth : 3 ( 1 avg) % 13.28/13.40 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 13.28/13.40 % Number of functors : 3 ( 3 usr; 0 con; 1-2 aty) % 13.28/13.40 % Number of variables : 18 ( 16 !; 2 ?) % 13.28/13.40 % SPC : FOF_THM_RFO_SEQ % 13.28/13.40 % 13.28/13.40 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 13.28/13.40 % library, www.mizar.org % 13.28/13.40 %------------------------------------------------------------------------------ % 13.28/13.40 fof(antisymmetry_r2_hidden,axiom, % 13.28/13.40 ! [A,B] : % 13.28/13.40 ( in(A,B) % 13.28/13.40 => ~ in(B,A) ) ). % 13.28/13.40 % 13.28/13.40 fof(commutativity_k2_tarski,axiom, % 13.28/13.40 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 13.28/13.40 % 13.28/13.40 fof(commutativity_k3_xboole_0,axiom, % 13.28/13.40 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ). % 13.28/13.40 % 13.28/13.40 fof(d2_tarski,axiom, % 13.28/13.40 ! [A,B,C] : % 13.28/13.40 ( C = unordered_pair(A,B) % 13.28/13.40 <=> ! [D] : % 13.28/13.40 ( in(D,C) % 13.28/13.40 <=> ( D = A % 13.28/13.40 | D = B ) ) ) ). % 13.28/13.40 % 13.28/13.40 fof(idempotence_k3_xboole_0,axiom, % 13.28/13.40 ! [A,B] : set_intersection2(A,A) = A ). % 13.28/13.40 % 13.28/13.40 fof(l32_zfmisc_1,axiom, % 13.28/13.40 ! [A,B] : % 13.28/13.40 ( in(A,B) % 13.28/13.41 => set_intersection2(B,singleton(A)) = singleton(A) ) ). % 13.28/13.41 % 13.28/13.41 fof(rc1_xboole_0,axiom, % 13.28/13.41 ? [A] : empty(A) ). % 13.28/13.41 % 13.28/13.41 fof(rc2_xboole_0,axiom, % 13.28/13.41 ? [A] : ~ empty(A) ). % 13.28/13.41 % 13.28/13.41 fof(t19_zfmisc_1,conjecture, % 13.28/13.41 ! [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) = singleton(A) ). % 13.28/13.41 % 13.28/13.41 %------------------------------------------------------------------------------ % 13.28/13.41 %------------------------------------------- % 13.28/13.41 % Proof found % 13.28/13.41 % SZS status Theorem for theBenchmark % 13.28/13.41 % SZS output start Proof % 13.28/13.41 %ClaNum:28(EqnAxiom:14) % 13.28/13.41 %VarNum:80(SingletonVarNum:30) % 13.28/13.41 %MaxLitNum:4 % 13.28/13.41 %MaxfuncDepth:2 % 13.28/13.41 %SharedTerms:10 % 13.28/13.41 %goalClause: 20 % 13.28/13.41 %singleGoalClaCount:1 % 13.28/13.41 [15]P1(a1) % 13.28/13.41 [19]~P1(a4) % 13.28/13.41 [20]~E(f3(f8(a5),f7(a5,a6)),f8(a5)) % 13.28/13.41 [16]E(f3(x161,x161),x161) % 13.28/13.41 [17]E(f7(x171,x172),f7(x172,x171)) % 13.28/13.41 [18]E(f3(x181,x182),f3(x182,x181)) % 13.28/13.41 [23]~P2(x232,x231)+~P2(x231,x232) % 13.28/13.41 [24]~P2(x242,x241)+E(f3(x241,f8(x242)),f8(x242)) % 13.28/13.41 [27]~E(f2(x272,x273,x271),x273)+~P2(f2(x272,x273,x271),x271)+E(x271,f7(x272,x273)) % 13.28/13.41 [28]~E(f2(x282,x283,x281),x282)+~P2(f2(x282,x283,x281),x281)+E(x281,f7(x282,x283)) % 13.28/13.41 [21]P2(x211,x212)+~E(x211,x213)+~E(x212,f7(x214,x213)) % 13.28/13.41 [22]P2(x221,x222)+~E(x221,x223)+~E(x222,f7(x223,x224)) % 13.28/13.41 [26]E(f2(x262,x263,x261),x263)+E(f2(x262,x263,x261),x262)+P2(f2(x262,x263,x261),x261)+E(x261,f7(x262,x263)) % 13.28/13.41 [25]~P2(x251,x254)+E(x251,x252)+E(x251,x253)+~E(x254,f7(x253,x252)) % 13.28/13.41 %EqnAxiom % 13.28/13.41 [1]E(x11,x11) % 13.28/13.41 [2]E(x22,x21)+~E(x21,x22) % 13.28/13.41 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 13.28/13.41 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43)) % 13.28/13.41 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52)) % 13.28/13.41 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63)) % 13.28/13.41 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72)) % 13.28/13.41 [8]~E(x81,x82)+E(f2(x81,x83,x84),f2(x82,x83,x84)) % 13.28/13.41 [9]~E(x91,x92)+E(f2(x93,x91,x94),f2(x93,x92,x94)) % 13.28/13.41 [10]~E(x101,x102)+E(f2(x103,x104,x101),f2(x103,x104,x102)) % 13.28/13.41 [11]~E(x111,x112)+E(f8(x111),f8(x112)) % 13.28/13.41 [12]~P1(x121)+P1(x122)+~E(x121,x122) % 13.28/13.41 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133) % 13.28/13.41 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141) % 13.28/13.41 % 13.28/13.41 %------------------------------------------- % 13.28/13.41 cnf(61,plain, % 13.28/13.41 (E(f3(f7(x611,x612),x613),f3(f7(x612,x611),x613))), % 13.28/13.41 inference(scs_inference,[],[17,4,2])). % 13.28/13.41 cnf(830,plain, % 13.28/13.41 (~E(f8(a5),f3(f7(a5,a6),f8(a5)))), % 13.28/13.41 inference(scs_inference,[],[20,18,2,3])). % 13.28/13.41 cnf(927,plain, % 13.28/13.41 (~E(f8(a5),f3(f7(a6,a5),f8(a5)))), % 13.28/13.41 inference(scs_inference,[],[830,61,3])). % 13.28/13.41 cnf(951,plain, % 13.28/13.41 (~P2(a5,f7(a6,a5))), % 13.28/13.41 inference(scs_inference,[],[927,2,24])). % 13.28/13.41 cnf(3911,plain, % 13.28/13.41 ($false), % 13.28/13.41 inference(scs_inference,[],[16,17,951,22,23,13]), % 13.28/13.41 ['proof']). % 13.28/13.41 % SZS output end Proof % 13.28/13.41 % Total time :12.910000s %------------------------------------------------------------------------------