%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SEU147+3 : TPTP v8.2.0. Bugfixed v4.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/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 15:01:19 EDT 2024 % Result : Theorem 1.79s 1.90s % Output : CNFRefutation 1.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.10 % Problem : SEU147+3 : TPTP v8.2.0. Bugfixed v4.0.0. % 0.06/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.10/0.31 % Computer : n029.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 : Fri Jun 21 11:19:23 EDT 2024 % 0.10/0.31 % CPUTime : % 0.47/0.56 start to proof:theBenchmark % 1.79/1.89 %------------------------------------------- % 1.79/1.89 % File :CSE---1.7 % 1.79/1.89 % Problem :theBenchmark % 1.79/1.89 % Transform :cnf % 1.79/1.89 % Format :tptp:raw % 1.79/1.89 % Command :java -jar mcs_scs.jar %d %s % 1.79/1.89 % 1.79/1.89 % Result :Theorem 1.290000s % 1.79/1.89 % Output :CNFRefutation 1.290000s % 1.79/1.89 %------------------------------------------- % 1.79/1.90 %------------------------------------------------------------------------------ % 1.79/1.90 % File : SEU147+3 : TPTP v8.2.0. Bugfixed v4.0.0. % 1.79/1.90 % Domain : Set theory % 1.79/1.90 % Problem : Basic properties of sets, theorem 1 % 1.79/1.90 % Version : [Urb06] axioms : Especial. % 1.79/1.90 % English : % 1.79/1.90 % 1.79/1.90 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 1.79/1.90 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 1.79/1.90 % Source : [Urb06] % 1.79/1.90 % Names : zfmisc_1__t1_zfmisc_1 [Urb06] % 1.79/1.90 % 1.79/1.90 % Status : Theorem % 1.79/1.90 % Rating : 0.19 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.13 v7.0.0, 0.10 v6.4.0, 0.12 v6.2.0, 0.16 v6.1.0, 0.13 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.00 v5.0.0, 0.08 v4.1.0, 0.13 v4.0.1, 0.22 v4.0.0 % 1.79/1.90 % Syntax : Number of formulae : 10 ( 5 unt; 0 def) % 1.79/1.90 % Number of atoms : 18 ( 6 equ) % 1.79/1.90 % Maximal formula atoms : 3 ( 1 avg) % 1.79/1.90 % Number of connectives : 10 ( 2 ~; 0 |; 0 &) % 1.79/1.90 % ( 5 <=>; 3 =>; 0 <=; 0 <~>) % 1.79/1.90 % Maximal formula depth : 6 ( 4 avg) % 1.79/1.90 % Maximal term depth : 2 ( 1 avg) % 1.79/1.90 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty) % 1.79/1.90 % Number of functors : 3 ( 3 usr; 1 con; 0-1 aty) % 1.79/1.90 % Number of variables : 16 ( 14 !; 2 ?) % 1.79/1.90 % SPC : FOF_THM_RFO_SEQ % 1.79/1.90 % 1.79/1.90 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 1.79/1.90 % library, www.mizar.org % 1.79/1.90 % Bugfixes : v4.0.0 - Removed duplicate formula t2_tarski % 1.79/1.90 %------------------------------------------------------------------------------ % 1.79/1.90 fof(antisymmetry_r2_hidden,axiom, % 1.79/1.90 ! [A,B] : % 1.79/1.90 ( in(A,B) % 1.79/1.90 => ~ in(B,A) ) ). % 1.79/1.90 % 1.79/1.90 fof(d1_tarski,axiom, % 1.79/1.90 ! [A,B] : % 1.79/1.90 ( B = singleton(A) % 1.79/1.90 <=> ! [C] : % 1.79/1.90 ( in(C,B) % 1.79/1.90 <=> C = A ) ) ). % 1.79/1.90 % 1.79/1.90 fof(d1_zfmisc_1,axiom, % 1.79/1.90 ! [A,B] : % 1.79/1.90 ( B = powerset(A) % 1.79/1.90 <=> ! [C] : % 1.79/1.90 ( in(C,B) % 1.79/1.90 <=> subset(C,A) ) ) ). % 1.79/1.90 % 1.79/1.90 fof(fc1_xboole_0,axiom, % 1.79/1.90 empty(empty_set) ). % 1.79/1.90 % 1.79/1.90 fof(rc1_xboole_0,axiom, % 1.79/1.90 ? [A] : empty(A) ). % 1.79/1.90 % 1.79/1.90 fof(rc2_xboole_0,axiom, % 1.79/1.90 ? [A] : ~ empty(A) ). % 1.79/1.90 % 1.79/1.90 fof(reflexivity_r1_tarski,axiom, % 1.79/1.90 ! [A,B] : subset(A,A) ). % 1.79/1.90 % 1.79/1.90 fof(t1_zfmisc_1,conjecture, % 1.79/1.90 powerset(empty_set) = singleton(empty_set) ). % 1.79/1.90 % 1.79/1.90 fof(t2_tarski,axiom, % 1.79/1.90 ! [A,B] : % 1.79/1.90 ( ! [C] : % 1.79/1.90 ( in(C,A) % 1.79/1.90 <=> in(C,B) ) % 1.79/1.90 => A = B ) ). % 1.79/1.90 % 1.79/1.90 fof(t3_xboole_1,axiom, % 1.79/1.90 ! [A] : % 1.79/1.90 ( subset(A,empty_set) % 1.79/1.90 => A = empty_set ) ). % 1.79/1.90 % 1.79/1.90 %------------------------------------------------------------------------------ % 1.79/1.90 %------------------------------------------- % 1.79/1.90 % Proof found % 1.79/1.90 % SZS status Theorem for theBenchmark % 1.79/1.90 % SZS output start Proof % 1.79/1.90 %ClaNum:33(EqnAxiom:16) % 1.79/1.90 %VarNum:80(SingletonVarNum:28) % 1.79/1.90 %MaxLitNum:3 % 1.79/1.90 %MaxfuncDepth:1 % 1.79/1.90 %SharedTerms:9 % 1.79/1.90 %goalClause: 21 % 1.79/1.90 %singleGoalClaCount:1 % 1.79/1.90 [17]P1(a1) % 1.79/1.90 [18]P1(a2) % 1.79/1.90 [20]~P1(a5) % 1.79/1.90 [21]~E(f6(a1),f7(a1)) % 1.79/1.90 [19]P2(x191,x191) % 1.79/1.90 [22]~P2(x221,a1)+E(x221,a1) % 1.79/1.90 [25]~P3(x252,x251)+~P3(x251,x252) % 1.79/1.90 [28]E(f3(x282,x281),x282)+P3(f3(x282,x281),x281)+E(x281,f6(x282)) % 1.79/1.90 [29]E(x291,x292)+P3(f8(x291,x292),x292)+P3(f8(x291,x292),x291) % 1.79/1.90 [30]P3(f4(x302,x301),x301)+P2(f4(x302,x301),x302)+E(x301,f7(x302)) % 1.79/1.90 [31]~E(f3(x312,x311),x312)+~P3(f3(x312,x311),x311)+E(x311,f6(x312)) % 1.79/1.90 [32]E(x321,x322)+~P3(f8(x321,x322),x322)+~P3(f8(x321,x322),x321) % 1.79/1.90 [33]~P3(f4(x332,x331),x331)+~P2(f4(x332,x331),x332)+E(x331,f7(x332)) % 1.79/1.90 [23]P3(x231,x232)+~E(x231,x233)+~E(x232,f6(x233)) % 1.79/1.90 [24]~P3(x241,x243)+E(x241,x242)+~E(x243,f6(x242)) % 1.79/1.90 [26]~P2(x261,x263)+P3(x261,x262)+~E(x262,f7(x263)) % 1.79/1.90 [27]~P3(x271,x273)+P2(x271,x272)+~E(x273,f7(x272)) % 1.79/1.90 %EqnAxiom % 1.79/1.90 [1]E(x11,x11) % 1.79/1.90 [2]E(x22,x21)+~E(x21,x22) % 1.79/1.90 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.79/1.90 [4]~E(x41,x42)+E(f6(x41),f6(x42)) % 1.79/1.90 [5]~E(x51,x52)+E(f7(x51),f7(x52)) % 1.79/1.90 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63)) % 1.79/1.90 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72)) % 1.79/1.90 [8]~E(x81,x82)+E(f8(x81,x83),f8(x82,x83)) % 1.79/1.90 [9]~E(x91,x92)+E(f8(x93,x91),f8(x93,x92)) % 1.79/1.90 [10]~E(x101,x102)+E(f3(x101,x103),f3(x102,x103)) % 1.79/1.90 [11]~E(x111,x112)+E(f3(x113,x111),f3(x113,x112)) % 1.79/1.90 [12]~P1(x121)+P1(x122)+~E(x121,x122) % 1.79/1.90 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133) % 1.79/1.90 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141) % 1.79/1.90 [15]P3(x152,x153)+~E(x151,x152)+~P3(x151,x153) % 1.79/1.90 [16]P3(x163,x162)+~E(x161,x162)+~P3(x163,x161) % 1.79/1.90 % 1.79/1.90 %------------------------------------------- % 1.79/1.90 cnf(34,plain, % 1.79/1.90 (~P3(x341,f6(x342))+E(x341,x342)), % 1.79/1.90 inference(equality_inference,[],[24])). % 1.79/1.90 cnf(35,plain, % 1.79/1.90 (~P2(x351,x352)+P3(x351,f7(x352))), % 1.79/1.90 inference(equality_inference,[],[26])). % 1.79/1.90 cnf(36,plain, % 1.79/1.90 (~P3(x361,f7(x362))+P2(x361,x362)), % 1.79/1.90 inference(equality_inference,[],[27])). % 1.79/1.90 cnf(53,plain, % 1.79/1.90 (P2(x531,x532)+~E(x531,x532)), % 1.79/1.90 inference(scs_inference,[],[21,19,33,14])). % 1.79/1.90 cnf(299,plain, % 1.79/1.91 (E(f3(a1,f7(a1)),a1)+P3(f3(a1,f7(a1)),f7(a1))), % 1.79/1.91 inference(scs_inference,[],[21,2,28])). % 1.79/1.91 cnf(318,plain, % 1.79/1.91 (E(a1,f3(a1,f7(a1)))+P3(f3(a1,f7(a1)),f7(a1))), % 1.79/1.91 inference(scs_inference,[],[2,299])). % 1.79/1.91 cnf(324,plain, % 1.79/1.91 (~E(f3(a1,f7(a1)),a1)+~P3(f3(a1,f7(a1)),f7(a1))), % 1.79/1.91 inference(scs_inference,[],[21,2,31])). % 1.79/1.91 cnf(325,plain, % 1.79/1.91 (~P2(f3(a1,f7(a1)),a1)+~E(f3(a1,f7(a1)),a1)), % 1.79/1.91 inference(scs_inference,[],[324,35])). % 1.79/1.91 cnf(326,plain, % 1.79/1.91 (~E(f3(a1,f7(a1)),a1)), % 1.79/1.91 inference(scs_inference,[],[325,53])). % 1.79/1.91 cnf(337,plain, % 1.79/1.91 ($false), % 1.79/1.91 inference(scs_inference,[],[326,22,34,36,318,2]), % 1.79/1.91 ['proof']). % 1.79/1.91 % SZS output end Proof % 1.79/1.91 % Total time :1.290000s %------------------------------------------------------------------------------