%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET867+1 : TPTP v8.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/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 14:22:50 EDT 2024 % Result : Theorem 0.57s 0.60s % Output : CNFRefutation 0.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET867+1 : TPTP v8.2.0. Released v3.2.0. % 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.11/0.33 % Computer : n020.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Sun Jun 23 16:47:09 EDT 2024 % 0.19/0.33 % CPUTime : % 0.20/0.56 start to proof:theBenchmark % 0.53/0.60 %------------------------------------------- % 0.53/0.60 % File :CSE---1.7 % 0.53/0.60 % Problem :theBenchmark % 0.53/0.60 % Transform :cnf % 0.53/0.60 % Format :tptp:raw % 0.53/0.60 % Command :java -jar mcs_scs.jar %d %s % 0.53/0.60 % 0.53/0.60 % Result :Theorem 0.000000s % 0.53/0.60 % Output :CNFRefutation 0.000000s % 0.53/0.60 %------------------------------------------- % 0.53/0.60 %------------------------------------------------------------------------------ % 0.53/0.60 % File : SET867+1 : TPTP v8.2.0. Released v3.2.0. % 0.53/0.60 % Domain : Set theory % 0.53/0.60 % Problem : union(empty_set) = empty_set % 0.53/0.60 % Version : [Urb06] axioms : Especial. % 0.53/0.60 % English : % 0.53/0.60 % 0.53/0.60 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.53/0.60 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.53/0.60 % Source : [Urb06] % 0.53/0.60 % Names : zfmisc_1__t2_zfmisc_1 [Urb06] % 0.53/0.60 % 0.53/0.60 % Status : Theorem % 0.53/0.60 % Rating : 0.14 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.12 v6.1.0, 0.13 v5.5.0, 0.07 v5.4.0, 0.04 v5.3.0, 0.11 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 % 0.53/0.60 % Syntax : Number of formulae : 7 ( 4 unt; 0 def) % 0.53/0.60 % Number of atoms : 12 ( 3 equ) % 0.53/0.60 % Maximal formula atoms : 4 ( 1 avg) % 0.53/0.60 % Number of connectives : 8 ( 3 ~; 0 |; 1 &) % 0.53/0.60 % ( 3 <=>; 1 =>; 0 <=; 0 <~>) % 0.53/0.60 % Maximal formula depth : 8 ( 4 avg) % 0.53/0.60 % Maximal term depth : 2 ( 1 avg) % 0.53/0.60 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 0.53/0.60 % Number of functors : 2 ( 2 usr; 1 con; 0-1 aty) % 0.53/0.60 % Number of variables : 10 ( 7 !; 3 ?) % 0.53/0.60 % SPC : FOF_THM_RFO_SEQ % 0.53/0.60 % 0.53/0.60 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.53/0.60 % library, www.mizar.org % 0.53/0.60 %------------------------------------------------------------------------------ % 0.53/0.60 fof(antisymmetry_r2_hidden,axiom, % 0.53/0.60 ! [A,B] : % 0.53/0.60 ( in(A,B) % 0.53/0.60 => ~ in(B,A) ) ). % 0.53/0.60 % 0.53/0.60 fof(d1_xboole_0,axiom, % 0.53/0.60 ! [A] : % 0.53/0.60 ( A = empty_set % 0.53/0.60 <=> ! [B] : ~ in(B,A) ) ). % 0.53/0.60 % 0.53/0.60 fof(d4_tarski,axiom, % 0.53/0.60 ! [A,B] : % 0.53/0.60 ( B = union(A) % 0.53/0.60 <=> ! [C] : % 0.53/0.60 ( in(C,B) % 0.53/0.60 <=> ? [D] : % 0.53/0.60 ( in(C,D) % 0.53/0.60 & in(D,A) ) ) ) ). % 0.53/0.60 % 0.53/0.60 fof(fc1_xboole_0,axiom, % 0.57/0.60 empty(empty_set) ). % 0.57/0.60 % 0.57/0.60 fof(rc1_xboole_0,axiom, % 0.57/0.60 ? [A] : empty(A) ). % 0.57/0.60 % 0.57/0.60 fof(rc2_xboole_0,axiom, % 0.57/0.60 ? [A] : ~ empty(A) ). % 0.57/0.60 % 0.57/0.60 fof(t2_zfmisc_1,conjecture, % 0.57/0.60 union(empty_set) = empty_set ). % 0.57/0.60 % 0.57/0.60 %------------------------------------------------------------------------------ % 0.57/0.60 %------------------------------------------- % 0.57/0.60 % Proof found % 0.57/0.60 % SZS status Theorem for theBenchmark % 0.57/0.60 % SZS output start Proof % 0.57/0.61 %ClaNum:28(EqnAxiom:15) % 0.57/0.61 %VarNum:61(SingletonVarNum:22) % 0.57/0.61 %MaxLitNum:4 % 0.57/0.61 %MaxfuncDepth:1 % 0.57/0.61 %SharedTerms:8 % 0.57/0.61 %goalClause: 18 % 0.57/0.61 %singleGoalClaCount:1 % 0.57/0.61 [16]P1(a1) % 0.57/0.61 [17]P1(a2) % 0.57/0.61 [19]~P1(a8) % 0.57/0.61 [18]~E(f7(a1),a1) % 0.57/0.61 [20]P2(f3(x201),x201)+E(x201,a1) % 0.57/0.61 [21]~P2(x212,x211)+~E(x211,a1) % 0.57/0.61 [22]~P2(x222,x221)+~P2(x221,x222) % 0.57/0.61 [24]P2(f4(x242,x241),x241)+P2(f6(x242,x241),x242)+E(x241,f7(x242)) % 0.57/0.61 [25]P2(f4(x252,x251),x251)+P2(f4(x252,x251),f6(x252,x251))+E(x251,f7(x252)) % 0.57/0.61 [26]~P2(x261,x263)+~E(x263,f7(x262))+P2(x261,f5(x262,x263,x261)) % 0.57/0.61 [27]~P2(x273,x272)+~E(x272,f7(x271))+P2(f5(x271,x272,x273),x271) % 0.57/0.61 [28]~P2(x283,x282)+~P2(f4(x282,x281),x283)+~P2(f4(x282,x281),x281)+E(x281,f7(x282)) % 0.57/0.61 [23]~P2(x231,x234)+P2(x231,x232)+~P2(x234,x233)+~E(x232,f7(x233)) % 0.57/0.61 %EqnAxiom % 0.57/0.61 [1]E(x11,x11) % 0.57/0.61 [2]E(x22,x21)+~E(x21,x22) % 0.57/0.61 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.57/0.61 [4]~E(x41,x42)+E(f7(x41),f7(x42)) % 0.57/0.61 [5]~E(x51,x52)+E(f3(x51),f3(x52)) % 0.57/0.61 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63)) % 0.57/0.61 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72)) % 0.57/0.61 [8]~E(x81,x82)+E(f5(x81,x83,x84),f5(x82,x83,x84)) % 0.57/0.61 [9]~E(x91,x92)+E(f5(x93,x91,x94),f5(x93,x92,x94)) % 0.57/0.61 [10]~E(x101,x102)+E(f5(x103,x104,x101),f5(x103,x104,x102)) % 0.57/0.61 [11]~E(x111,x112)+E(f6(x111,x113),f6(x112,x113)) % 0.57/0.61 [12]~E(x121,x122)+E(f6(x123,x121),f6(x123,x122)) % 0.57/0.61 [13]~P1(x131)+P1(x132)+~E(x131,x132) % 0.57/0.61 [14]P2(x142,x143)+~E(x141,x142)+~P2(x141,x143) % 0.57/0.61 [15]P2(x153,x152)+~E(x151,x152)+~P2(x153,x151) % 0.57/0.61 % 0.57/0.61 %------------------------------------------- % 0.57/0.61 cnf(29,plain, % 0.57/0.61 (~P2(x291,a1)), % 0.57/0.61 inference(equality_inference,[],[21])). % 0.57/0.61 cnf(32,plain, % 0.57/0.61 (~P2(x321,f7(x322))+P2(f5(x322,f7(x322),x321),x322)), % 0.57/0.61 inference(equality_inference,[],[27])). % 0.57/0.61 cnf(37,plain, % 0.57/0.61 ($false), % 0.57/0.61 inference(scs_inference,[],[18,29,20,22,32]), % 0.57/0.61 ['proof']). % 0.57/0.61 % SZS output end Proof % 0.57/0.61 % Total time :0.000000s %------------------------------------------------------------------------------