%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET983+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 : n022.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 14:23:09 EDT 2024 % Result : Theorem 0.15s 0.58s % Output : CNFRefutation 0.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : SET983+1 : TPTP v8.2.0. Released v3.2.0. % 0.00/0.09 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.09/0.30 % Computer : n022.cluster.edu % 0.09/0.30 % Model : x86_64 x86_64 % 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.30 % Memory : 8042.1875MB % 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.30 % CPULimit : 300 % 0.09/0.30 % WCLimit : 300 % 0.09/0.30 % DateTime : Sun Jun 23 14:57:08 EDT 2024 % 0.09/0.30 % CPUTime : % 0.15/0.54 start to proof:theBenchmark % 0.15/0.57 %------------------------------------------- % 0.15/0.57 % File :CSE---1.7 % 0.15/0.57 % Problem :theBenchmark % 0.15/0.57 % Transform :cnf % 0.15/0.57 % Format :tptp:raw % 0.15/0.57 % Command :java -jar mcs_scs.jar %d %s % 0.15/0.57 % 0.15/0.58 % Result :Theorem 0.010000s % 0.15/0.58 % Output :CNFRefutation 0.010000s % 0.15/0.58 %------------------------------------------- % 0.15/0.58 %------------------------------------------------------------------------------ % 0.15/0.58 % File : SET983+1 : TPTP v8.2.0. Released v3.2.0. % 0.15/0.58 % Domain : Set theory % 0.15/0.58 % Problem : Basic properties of sets, theorem 137 % 0.15/0.58 % Version : [Urb06] axioms : Especial. % 0.15/0.58 % English : % 0.15/0.58 % 0.15/0.58 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.15/0.58 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.15/0.58 % Source : [Urb06] % 0.15/0.58 % Names : zfmisc_1__t137_zfmisc_1 [Urb06] % 0.15/0.58 % 0.15/0.58 % Status : Theorem % 0.15/0.58 % Rating : 0.14 v7.5.0, 0.16 v7.4.0, 0.03 v7.3.0, 0.07 v7.2.0, 0.10 v7.1.0, 0.13 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.17 v6.2.0, 0.28 v6.1.0, 0.30 v6.0.0, 0.26 v5.5.0, 0.22 v5.4.0, 0.21 v5.3.0, 0.30 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.25 v4.1.0, 0.26 v4.0.0, 0.25 v3.7.0, 0.20 v3.5.0, 0.21 v3.4.0, 0.16 v3.3.0, 0.21 v3.2.0 % 0.15/0.58 % Syntax : Number of formulae : 8 ( 5 unt; 0 def) % 0.15/0.58 % Number of atoms : 14 ( 4 equ) % 0.15/0.58 % Maximal formula atoms : 4 ( 1 avg) % 0.15/0.58 % Number of connectives : 8 ( 2 ~; 0 |; 2 &) % 0.15/0.58 % ( 2 <=>; 2 =>; 0 <=; 0 <~>) % 0.15/0.58 % Maximal formula depth : 8 ( 5 avg) % 0.15/0.58 % Maximal term depth : 3 ( 1 avg) % 0.15/0.58 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 0.15/0.58 % Number of functors : 2 ( 2 usr; 0 con; 2-2 aty) % 0.15/0.58 % Number of variables : 21 ( 19 !; 2 ?) % 0.15/0.58 % SPC : FOF_THM_RFO_SEQ % 0.15/0.58 % 0.15/0.58 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.15/0.58 % library, www.mizar.org % 0.15/0.58 %------------------------------------------------------------------------------ % 0.15/0.58 fof(antisymmetry_r2_hidden,axiom, % 0.15/0.58 ! [A,B] : % 0.15/0.58 ( in(A,B) % 0.15/0.58 => ~ in(B,A) ) ). % 0.15/0.58 % 0.15/0.58 fof(commutativity_k3_xboole_0,axiom, % 0.15/0.58 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ). % 0.15/0.58 % 0.15/0.58 fof(d3_xboole_0,axiom, % 0.15/0.58 ! [A,B,C] : % 0.15/0.58 ( C = set_intersection2(A,B) % 0.15/0.58 <=> ! [D] : % 0.15/0.58 ( in(D,C) % 0.15/0.58 <=> ( in(D,A) % 0.15/0.58 & in(D,B) ) ) ) ). % 0.15/0.58 % 0.15/0.58 fof(idempotence_k3_xboole_0,axiom, % 0.15/0.58 ! [A,B] : set_intersection2(A,A) = A ). % 0.15/0.58 % 0.15/0.58 fof(rc1_xboole_0,axiom, % 0.15/0.58 ? [A] : empty(A) ). % 0.15/0.58 % 0.15/0.58 fof(rc2_xboole_0,axiom, % 0.15/0.58 ? [A] : ~ empty(A) ). % 0.15/0.58 % 0.15/0.58 fof(t123_zfmisc_1,axiom, % 0.15/0.58 ! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)) ). % 0.15/0.58 % 0.15/0.58 fof(t137_zfmisc_1,conjecture, % 0.15/0.58 ! [A,B,C,D,E] : % 0.15/0.58 ( ( in(A,cartesian_product2(B,C)) % 0.15/0.58 & in(A,cartesian_product2(D,E)) ) % 0.15/0.58 => in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ) ). % 0.15/0.58 % 0.15/0.58 %------------------------------------------------------------------------------ % 0.15/0.58 %------------------------------------------- % 0.15/0.58 % Proof found % 0.15/0.58 % SZS status Theorem for theBenchmark % 0.15/0.58 % SZS output start Proof % 0.15/0.58 %ClaNum:28(EqnAxiom:13) % 0.15/0.58 %VarNum:79(SingletonVarNum:30) % 0.15/0.58 %MaxLitNum:4 % 0.15/0.58 %MaxfuncDepth:2 % 0.15/0.58 %SharedTerms:17 % 0.15/0.58 %goalClause: 17 18 21 % 0.15/0.58 %singleGoalClaCount:3 % 0.15/0.58 [14]P1(a1) % 0.15/0.58 [20]~P1(a6) % 0.15/0.58 [17]P2(a5,f2(a7,a8)) % 0.15/0.58 [18]P2(a5,f2(a9,a10)) % 0.15/0.58 [21]~P2(a5,f2(f4(a7,a9),f4(a8,a10))) % 0.15/0.58 [15]E(f4(x151,x151),x151) % 0.15/0.58 [16]E(f4(x161,x162),f4(x162,x161)) % 0.15/0.58 [19]E(f2(f4(x191,x192),f4(x193,x194)),f4(f2(x191,x193),f2(x192,x194))) % 0.15/0.58 [22]~P2(x222,x221)+~P2(x221,x222) % 0.15/0.58 [26]P2(f3(x262,x263,x261),x261)+P2(f3(x262,x263,x261),x263)+E(x261,f4(x262,x263)) % 0.15/0.58 [27]P2(f3(x272,x273,x271),x271)+P2(f3(x272,x273,x271),x272)+E(x271,f4(x272,x273)) % 0.15/0.58 [23]~P2(x231,x233)+P2(x231,x232)+~E(x233,f4(x234,x232)) % 0.15/0.58 [24]~P2(x241,x243)+P2(x241,x242)+~E(x243,f4(x242,x244)) % 0.15/0.58 [28]~P2(f3(x282,x283,x281),x281)+~P2(f3(x282,x283,x281),x283)+~P2(f3(x282,x283,x281),x282)+E(x281,f4(x282,x283)) % 0.15/0.58 [25]~P2(x251,x254)+~P2(x251,x253)+P2(x251,x252)+~E(x252,f4(x253,x254)) % 0.15/0.58 %EqnAxiom % 0.15/0.58 [1]E(x11,x11) % 0.15/0.58 [2]E(x22,x21)+~E(x21,x22) % 0.15/0.58 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.15/0.58 [4]~E(x41,x42)+E(f4(x41,x43),f4(x42,x43)) % 0.15/0.58 [5]~E(x51,x52)+E(f4(x53,x51),f4(x53,x52)) % 0.15/0.58 [6]~E(x61,x62)+E(f3(x61,x63,x64),f3(x62,x63,x64)) % 0.15/0.58 [7]~E(x71,x72)+E(f3(x73,x71,x74),f3(x73,x72,x74)) % 0.15/0.58 [8]~E(x81,x82)+E(f3(x83,x84,x81),f3(x83,x84,x82)) % 0.15/0.58 [9]~E(x91,x92)+E(f2(x91,x93),f2(x92,x93)) % 0.15/0.58 [10]~E(x101,x102)+E(f2(x103,x101),f2(x103,x102)) % 0.15/0.58 [11]~P1(x111)+P1(x112)+~E(x111,x112) % 0.15/0.58 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123) % 0.15/0.58 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131) % 0.15/0.58 % 0.15/0.58 %------------------------------------------- % 0.15/0.58 cnf(29,plain, % 0.15/0.58 (~P2(x291,f4(x292,x293))+P2(x291,x293)), % 0.15/0.58 inference(equality_inference,[],[23])). % 0.15/0.58 cnf(30,plain, % 0.15/0.58 (~P2(x301,f4(x302,x303))+P2(x301,x302)), % 0.15/0.58 inference(equality_inference,[],[24])). % 0.15/0.58 cnf(32,plain, % 0.15/0.58 (~P2(f2(a7,a8),a5)), % 0.15/0.58 inference(scs_inference,[],[17,22])). % 0.15/0.58 cnf(38,plain, % 0.15/0.58 (E(x381,f4(x381,x381))), % 0.15/0.58 inference(scs_inference,[],[17,21,15,22,29,30,2])). % 0.15/0.58 cnf(40,plain, % 0.15/0.58 (~E(f2(a7,a8),f2(f4(a7,a9),f4(a8,a10)))), % 0.15/0.58 inference(scs_inference,[],[17,21,15,22,29,30,2,12,13])). % 0.15/0.58 cnf(55,plain, % 0.15/0.58 (E(f4(x551,x551),x551)), % 0.15/0.58 inference(rename_variables,[],[15])). % 0.15/0.58 cnf(62,plain, % 0.15/0.58 (E(x621,f4(x621,x621))), % 0.15/0.59 inference(rename_variables,[],[38])). % 0.15/0.59 cnf(66,plain, % 0.15/0.59 ($false), % 0.15/0.59 inference(scs_inference,[],[17,32,18,21,40,38,62,15,55,19,14,29,22,30,2,23,24,13,12,11,3,25]), % 0.15/0.59 ['proof']). % 0.15/0.59 % SZS output end Proof % 0.15/0.59 % Total time :0.010000s %------------------------------------------------------------------------------