%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET974+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 : n020.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 14:23:08 EDT 2024 % Result : Theorem 0.79s 0.89s % Output : CNFRefutation 0.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.11 % Problem : SET974+1 : TPTP v8.2.0. Released v3.2.0. % 0.09/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.10/0.31 % Computer : n020.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Sun Jun 23 14:55:24 EDT 2024 % 0.10/0.31 % CPUTime : % 0.16/0.54 start to proof:theBenchmark % 0.79/0.89 %------------------------------------------- % 0.79/0.89 % File :CSE---1.7 % 0.79/0.89 % Problem :theBenchmark % 0.79/0.89 % Transform :cnf % 0.79/0.89 % Format :tptp:raw % 0.79/0.89 % Command :java -jar mcs_scs.jar %d %s % 0.79/0.89 % 0.79/0.89 % Result :Theorem 0.290000s % 0.79/0.89 % Output :CNFRefutation 0.290000s % 0.79/0.89 %------------------------------------------- % 0.79/0.89 %------------------------------------------------------------------------------ % 0.79/0.89 % File : SET974+1 : TPTP v8.2.0. Released v3.2.0. % 0.79/0.89 % Domain : Set theory % 0.79/0.89 % Problem : Basic properties of sets, theorem 127 % 0.79/0.89 % Version : [Urb06] axioms : Especial. % 0.79/0.89 % English : % 0.79/0.89 % 0.79/0.89 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.79/0.89 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.79/0.89 % Source : [Urb06] % 0.79/0.89 % Names : zfmisc_1__t127_zfmisc_1 [Urb06] % 0.79/0.89 % 0.79/0.89 % Status : Theorem % 0.79/0.89 % Rating : 0.14 v8.2.0, 0.17 v8.1.0, 0.22 v7.4.0, 0.13 v7.3.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.17 v6.4.0, 0.23 v6.3.0, 0.21 v6.2.0, 0.20 v6.1.0, 0.23 v6.0.0, 0.17 v5.5.0, 0.22 v5.4.0, 0.25 v5.3.0, 0.30 v5.2.0, 0.20 v5.1.0, 0.19 v5.0.0, 0.21 v4.1.0, 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 % 0.79/0.89 % Syntax : Number of formulae : 12 ( 7 unt; 0 def) % 0.79/0.89 % Number of atoms : 22 ( 5 equ) % 0.79/0.89 % Maximal formula atoms : 4 ( 1 avg) % 0.79/0.89 % Number of connectives : 19 ( 9 ~; 1 |; 6 &) % 0.79/0.89 % ( 0 <=>; 3 =>; 0 <=; 0 <~>) % 0.79/0.89 % Maximal formula depth : 13 ( 5 avg) % 0.79/0.89 % Maximal term depth : 3 ( 1 avg) % 0.79/0.89 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty) % 0.79/0.89 % Number of functors : 5 ( 5 usr; 0 con; 1-2 aty) % 0.79/0.89 % Number of variables : 31 ( 28 !; 3 ?) % 0.79/0.89 % SPC : FOF_THM_RFO_SEQ % 0.79/0.89 % 0.79/0.89 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.79/0.89 % library, www.mizar.org % 0.79/0.89 %------------------------------------------------------------------------------ % 0.79/0.89 fof(antisymmetry_r2_hidden,axiom, % 0.79/0.89 ! [A,B] : % 0.79/0.89 ( in(A,B) % 0.79/0.89 => ~ in(B,A) ) ). % 0.79/0.89 % 0.79/0.89 fof(commutativity_k2_tarski,axiom, % 0.79/0.89 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 0.79/0.89 % 0.79/0.89 fof(commutativity_k3_xboole_0,axiom, % 0.79/0.89 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ). % 0.79/0.89 % 0.79/0.89 fof(d5_tarski,axiom, % 0.79/0.89 ! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) ). % 0.79/0.89 % 0.79/0.89 fof(fc1_zfmisc_1,axiom, % 0.79/0.89 ! [A,B] : ~ empty(ordered_pair(A,B)) ). % 0.79/0.89 % 0.79/0.89 fof(idempotence_k3_xboole_0,axiom, % 0.79/0.89 ! [A,B] : set_intersection2(A,A) = A ). % 0.79/0.89 % 0.79/0.89 fof(rc1_xboole_0,axiom, % 0.79/0.89 ? [A] : empty(A) ). % 0.79/0.89 % 0.79/0.89 fof(rc2_xboole_0,axiom, % 0.79/0.89 ? [A] : ~ empty(A) ). % 0.79/0.89 % 0.79/0.89 fof(symmetry_r1_xboole_0,axiom, % 0.79/0.89 ! [A,B] : % 0.79/0.89 ( disjoint(A,B) % 0.79/0.89 => disjoint(B,A) ) ). % 0.79/0.89 % 0.79/0.89 fof(t104_zfmisc_1,axiom, % 0.79/0.89 ! [A,B,C,D,E] : % 0.79/0.89 ~ ( in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) % 0.79/0.89 & ! [F,G] : % 0.79/0.89 ~ ( A = ordered_pair(F,G) % 0.79/0.89 & in(F,set_intersection2(B,D)) % 0.79/0.89 & in(G,set_intersection2(C,E)) ) ) ). % 0.79/0.89 % 0.79/0.89 fof(t127_zfmisc_1,conjecture, % 0.79/0.89 ! [A,B,C,D] : % 0.79/0.89 ( ( disjoint(A,B) % 0.79/0.89 | disjoint(C,D) ) % 0.79/0.89 => disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ) ). % 0.79/0.89 % 0.79/0.89 fof(t4_xboole_0,axiom, % 0.79/0.89 ! [A,B] : % 0.79/0.89 ( ~ ( ~ disjoint(A,B) % 0.79/0.89 & ! [C] : ~ in(C,set_intersection2(A,B)) ) % 0.79/0.89 & ~ ( ? [C] : in(C,set_intersection2(A,B)) % 0.79/0.89 & disjoint(A,B) ) ) ). % 0.79/0.89 % 0.79/0.89 %------------------------------------------------------------------------------ % 0.79/0.89 %------------------------------------------- % 0.79/0.89 % Proof found % 0.79/0.89 % SZS status Theorem for theBenchmark % 0.79/0.89 % SZS output start Proof % 0.79/0.90 %ClaNum:42(EqnAxiom:27) % 0.79/0.90 %VarNum:78(SingletonVarNum:31) % 0.79/0.90 %MaxLitNum:2 % 0.79/0.90 %MaxfuncDepth:3 % 0.79/0.90 %SharedTerms:13 % 0.79/0.90 %goalClause: 33 35 % 0.79/0.90 %singleGoalClaCount:1 % 0.79/0.90 [28]P1(a1) % 0.79/0.90 [32]~P1(a4) % 0.79/0.90 [33]~P2(f2(a5,a8),f2(a9,a10)) % 0.79/0.90 [29]E(f3(x291,x291),x291) % 0.79/0.90 [30]E(f12(x301,x302),f12(x302,x301)) % 0.79/0.90 [31]E(f3(x311,x312),f3(x312,x311)) % 0.79/0.90 [34]~P1(f12(f12(x341,x342),f13(x341))) % 0.79/0.90 [35]P2(a5,a9)+P2(a8,a10) % 0.79/0.90 [36]~P2(x362,x361)+P2(x361,x362) % 0.79/0.90 [37]~P3(x372,x371)+~P3(x371,x372) % 0.79/0.90 [38]P2(x381,x382)+P3(f11(x381,x382),f3(x381,x382)) % 0.79/0.90 [39]~P2(x391,x392)+~P3(x393,f3(x391,x392)) % 0.79/0.90 [40]P3(f6(x401,x402,x403,x404,x405),f3(x402,x404))+~P3(x401,f3(f2(x402,x403),f2(x404,x405))) % 0.79/0.90 [41]P3(f7(x411,x412,x413,x414,x415),f3(x413,x415))+~P3(x411,f3(f2(x412,x413),f2(x414,x415))) % 0.79/0.90 [42]~P3(x421,f3(f2(x422,x423),f2(x424,x425)))+E(f12(f12(f6(x421,x422,x423,x424,x425),f7(x421,x422,x423,x424,x425)),f13(f6(x421,x422,x423,x424,x425))),x421) % 0.79/0.90 %EqnAxiom % 0.79/0.90 [1]E(x11,x11) % 0.79/0.90 [2]E(x22,x21)+~E(x21,x22) % 0.79/0.90 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.79/0.90 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43)) % 0.79/0.90 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52)) % 0.79/0.90 [6]~E(x61,x62)+E(f12(x61,x63),f12(x62,x63)) % 0.79/0.90 [7]~E(x71,x72)+E(f12(x73,x71),f12(x73,x72)) % 0.79/0.90 [8]~E(x81,x82)+E(f6(x81,x83,x84,x85,x86),f6(x82,x83,x84,x85,x86)) % 0.79/0.90 [9]~E(x91,x92)+E(f6(x93,x91,x94,x95,x96),f6(x93,x92,x94,x95,x96)) % 0.79/0.90 [10]~E(x101,x102)+E(f6(x103,x104,x101,x105,x106),f6(x103,x104,x102,x105,x106)) % 0.79/0.90 [11]~E(x111,x112)+E(f6(x113,x114,x115,x111,x116),f6(x113,x114,x115,x112,x116)) % 0.79/0.90 [12]~E(x121,x122)+E(f6(x123,x124,x125,x126,x121),f6(x123,x124,x125,x126,x122)) % 0.79/0.90 [13]~E(x131,x132)+E(f2(x131,x133),f2(x132,x133)) % 0.79/0.90 [14]~E(x141,x142)+E(f2(x143,x141),f2(x143,x142)) % 0.79/0.90 [15]~E(x151,x152)+E(f7(x151,x153,x154,x155,x156),f7(x152,x153,x154,x155,x156)) % 0.79/0.90 [16]~E(x161,x162)+E(f7(x163,x161,x164,x165,x166),f7(x163,x162,x164,x165,x166)) % 0.79/0.90 [17]~E(x171,x172)+E(f7(x173,x174,x171,x175,x176),f7(x173,x174,x172,x175,x176)) % 0.79/0.90 [18]~E(x181,x182)+E(f7(x183,x184,x185,x181,x186),f7(x183,x184,x185,x182,x186)) % 0.79/0.90 [19]~E(x191,x192)+E(f7(x193,x194,x195,x196,x191),f7(x193,x194,x195,x196,x192)) % 0.79/0.90 [20]~E(x201,x202)+E(f13(x201),f13(x202)) % 0.79/0.90 [21]~E(x211,x212)+E(f11(x211,x213),f11(x212,x213)) % 0.79/0.90 [22]~E(x221,x222)+E(f11(x223,x221),f11(x223,x222)) % 0.79/0.90 [23]~P1(x231)+P1(x232)+~E(x231,x232) % 0.79/0.90 [24]P3(x242,x243)+~E(x241,x242)+~P3(x241,x243) % 0.79/0.90 [25]P3(x253,x252)+~E(x251,x252)+~P3(x253,x251) % 0.79/0.90 [26]P2(x262,x263)+~E(x261,x262)+~P2(x261,x263) % 0.79/0.90 [27]P2(x273,x272)+~E(x271,x272)+~P2(x273,x271) % 0.79/0.90 % 0.79/0.90 %------------------------------------------- % 0.79/0.90 cnf(43,plain, % 0.79/0.90 (~P2(f2(a9,a10),f2(a5,a8))), % 0.79/0.90 inference(scs_inference,[],[33,36])). % 0.79/0.90 cnf(73,plain, % 0.79/0.90 (P2(a9,a5)+P2(a8,a10)), % 0.79/0.90 inference(scs_inference,[],[35,36])). % 0.79/0.90 cnf(79,plain, % 0.79/0.90 (~P3(x791,f3(a9,a5))+P2(a8,a10)), % 0.79/0.90 inference(scs_inference,[],[73,39])). % 0.79/0.90 cnf(82,plain, % 0.79/0.90 (P2(a8,a10)+~P3(x821,f3(f2(a9,x822),f2(a5,x823)))), % 0.79/0.90 inference(scs_inference,[],[79,40])). % 0.79/0.90 cnf(101,plain, % 0.79/0.90 (P2(a8,a10)), % 0.79/0.90 inference(scs_inference,[],[43,82,38])). % 0.79/0.90 cnf(167,plain, % 0.79/0.90 (~P3(x1671,f3(f2(x1672,a8),f2(x1673,a10)))), % 0.79/0.90 inference(scs_inference,[],[101,41,39])). % 0.79/0.90 cnf(168,plain, % 0.79/0.90 ($false), % 0.79/0.90 inference(scs_inference,[],[33,167,38]), % 0.79/0.90 ['proof']). % 0.79/0.90 % SZS output end Proof % 0.79/0.90 % Total time :0.290000s %------------------------------------------------------------------------------