%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET873+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 : n025.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 14:22:51 EDT 2024 % Result : Theorem 0.64s 0.77s % Output : CNFRefutation 0.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SET873+1 : TPTP v8.2.0. Released v3.2.0. % 0.00/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.10/0.30 % Computer : n025.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 300 % 0.10/0.30 % DateTime : Sun Jun 23 11:50:39 EDT 2024 % 0.10/0.30 % CPUTime : % 0.16/0.51 start to proof:theBenchmark % 0.64/0.77 %------------------------------------------- % 0.64/0.77 % File :CSE---1.7 % 0.64/0.77 % Problem :theBenchmark % 0.64/0.77 % Transform :cnf % 0.64/0.77 % Format :tptp:raw % 0.64/0.77 % Command :java -jar mcs_scs.jar %d %s % 0.64/0.77 % 0.64/0.77 % Result :Theorem 0.230000s % 0.64/0.77 % Output :CNFRefutation 0.230000s % 0.64/0.77 %------------------------------------------- % 0.64/0.77 %------------------------------------------------------------------------------ % 0.64/0.77 % File : SET873+1 : TPTP v8.2.0. Released v3.2.0. % 0.64/0.77 % Domain : Set theory % 0.64/0.77 % Problem : union(singleton(A),singleton(B)) = singleton(A) => A = B % 0.64/0.77 % Version : [Urb06] axioms : Especial. % 0.64/0.77 % English : % 0.64/0.77 % 0.64/0.77 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.64/0.77 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.64/0.77 % Source : [Urb06] % 0.64/0.77 % Names : zfmisc_1__t13_zfmisc_1 [Urb06] % 0.64/0.77 % 0.64/0.77 % Status : Theorem % 0.64/0.77 % Rating : 0.11 v7.5.0, 0.12 v7.4.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.17 v5.5.0, 0.11 v5.4.0, 0.14 v5.3.0, 0.22 v5.2.0, 0.00 v5.0.0, 0.12 v4.1.0, 0.17 v4.0.1, 0.22 v4.0.0, 0.21 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.14 v3.2.0 % 0.64/0.77 % Syntax : Number of formulae : 11 ( 5 unt; 0 def) % 0.64/0.77 % Number of atoms : 18 ( 6 equ) % 0.64/0.77 % Maximal formula atoms : 3 ( 1 avg) % 0.64/0.77 % Number of connectives : 13 ( 6 ~; 0 |; 0 &) % 0.64/0.77 % ( 2 <=>; 5 =>; 0 <=; 0 <~>) % 0.64/0.77 % Maximal formula depth : 6 ( 4 avg) % 0.64/0.77 % Maximal term depth : 3 ( 1 avg) % 0.64/0.77 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty) % 0.64/0.77 % Number of functors : 2 ( 2 usr; 0 con; 1-2 aty) % 0.64/0.77 % Number of variables : 21 ( 19 !; 2 ?) % 0.64/0.77 % SPC : FOF_THM_RFO_SEQ % 0.64/0.77 % 0.64/0.77 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.64/0.77 % library, www.mizar.org % 0.64/0.77 %------------------------------------------------------------------------------ % 0.64/0.77 fof(antisymmetry_r2_hidden,axiom, % 0.64/0.77 ! [A,B] : % 0.64/0.77 ( in(A,B) % 0.64/0.77 => ~ in(B,A) ) ). % 0.64/0.77 % 0.64/0.77 fof(commutativity_k2_xboole_0,axiom, % 0.64/0.77 ! [A,B] : set_union2(A,B) = set_union2(B,A) ). % 0.64/0.77 % 0.64/0.77 fof(d1_tarski,axiom, % 0.64/0.77 ! [A,B] : % 0.64/0.77 ( B = singleton(A) % 0.64/0.77 <=> ! [C] : % 0.64/0.77 ( in(C,B) % 0.64/0.77 <=> C = A ) ) ). % 0.64/0.77 % 0.64/0.77 fof(fc2_xboole_0,axiom, % 0.64/0.77 ! [A,B] : % 0.64/0.77 ( ~ empty(A) % 0.64/0.77 => ~ empty(set_union2(A,B)) ) ). % 0.64/0.77 % 0.64/0.77 fof(fc3_xboole_0,axiom, % 0.64/0.77 ! [A,B] : % 0.64/0.77 ( ~ empty(A) % 0.64/0.77 => ~ empty(set_union2(B,A)) ) ). % 0.64/0.77 % 0.64/0.77 fof(idempotence_k2_xboole_0,axiom, % 0.64/0.77 ! [A,B] : set_union2(A,A) = A ). % 0.64/0.77 % 0.64/0.77 fof(l21_zfmisc_1,axiom, % 0.64/0.77 ! [A,B] : % 0.64/0.77 ( subset(set_union2(singleton(A),B),B) % 0.64/0.77 => in(A,B) ) ). % 0.64/0.77 % 0.64/0.77 fof(rc1_xboole_0,axiom, % 0.64/0.77 ? [A] : empty(A) ). % 0.64/0.77 % 0.64/0.77 fof(rc2_xboole_0,axiom, % 0.64/0.77 ? [A] : ~ empty(A) ). % 0.64/0.77 % 0.64/0.77 fof(reflexivity_r1_tarski,axiom, % 0.64/0.77 ! [A,B] : subset(A,A) ). % 0.64/0.77 % 0.64/0.77 fof(t13_zfmisc_1,conjecture, % 0.64/0.77 ! [A,B] : % 0.64/0.77 ( set_union2(singleton(A),singleton(B)) = singleton(A) % 0.64/0.77 => A = B ) ). % 0.64/0.77 % 0.64/0.77 %------------------------------------------------------------------------------ % 0.64/0.77 %------------------------------------------- % 0.64/0.77 % Proof found % 0.64/0.77 % SZS status Theorem for theBenchmark % 0.64/0.77 % SZS output start Proof % 0.64/0.78 %ClaNum:28(EqnAxiom:13) % 0.64/0.78 %VarNum:52(SingletonVarNum:22) % 0.64/0.78 %MaxLitNum:3 % 0.64/0.78 %MaxfuncDepth:2 % 0.64/0.78 %SharedTerms:11 % 0.64/0.78 %goalClause: 17 19 % 0.64/0.78 %singleGoalClaCount:2 % 0.64/0.78 [14]P1(a1) % 0.64/0.78 [19]~E(a6,a4) % 0.64/0.78 [20]~P1(a5) % 0.64/0.78 [17]E(f3(f7(a4),f7(a6)),f7(a4)) % 0.64/0.78 [15]P2(x151,x151) % 0.64/0.78 [16]E(f3(x161,x161),x161) % 0.64/0.78 [18]E(f3(x181,x182),f3(x182,x181)) % 0.64/0.78 [23]~P3(x232,x231)+~P3(x231,x232) % 0.64/0.78 [24]P1(x241)+~P1(f3(x242,x241)) % 0.64/0.78 [25]P1(x251)+~P1(f3(x251,x252)) % 0.64/0.78 [28]P3(x281,x282)+~P2(f3(f7(x281),x282),x282) % 0.64/0.78 [26]E(f2(x262,x261),x262)+P3(f2(x262,x261),x261)+E(x261,f7(x262)) % 0.64/0.78 [27]~E(f2(x272,x271),x272)+~P3(f2(x272,x271),x271)+E(x271,f7(x272)) % 0.64/0.78 [21]P3(x211,x212)+~E(x211,x213)+~E(x212,f7(x213)) % 0.64/0.78 [22]~P3(x221,x223)+E(x221,x222)+~E(x223,f7(x222)) % 0.64/0.78 %EqnAxiom % 0.64/0.78 [1]E(x11,x11) % 0.64/0.78 [2]E(x22,x21)+~E(x21,x22) % 0.64/0.78 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.64/0.78 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43)) % 0.64/0.78 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52)) % 0.64/0.78 [6]~E(x61,x62)+E(f7(x61),f7(x62)) % 0.64/0.78 [7]~E(x71,x72)+E(f2(x71,x73),f2(x72,x73)) % 0.64/0.78 [8]~E(x81,x82)+E(f2(x83,x81),f2(x83,x82)) % 0.64/0.78 [9]~P1(x91)+P1(x92)+~E(x91,x92) % 0.64/0.78 [10]P2(x102,x103)+~E(x101,x102)+~P2(x101,x103) % 0.64/0.78 [11]P2(x113,x112)+~E(x111,x112)+~P2(x113,x111) % 0.64/0.78 [12]P3(x122,x123)+~E(x121,x122)+~P3(x121,x123) % 0.64/0.78 [13]P3(x133,x132)+~E(x131,x132)+~P3(x133,x131) % 0.64/0.78 % 0.64/0.78 %------------------------------------------- % 0.72/0.78 cnf(29,plain, % 0.72/0.78 (~P3(x291,f7(x292))+E(x291,x292)), % 0.72/0.78 inference(equality_inference,[],[22])). % 0.72/0.78 cnf(30,plain, % 0.72/0.78 (~P3(a6,f7(a4))), % 0.72/0.78 inference(scs_inference,[],[19,29])). % 0.72/0.78 cnf(34,plain, % 0.72/0.78 (E(f3(x341,x341),x341)), % 0.72/0.78 inference(rename_variables,[],[16])). % 0.72/0.78 cnf(37,plain, % 0.72/0.78 (E(f3(x371,x371),x371)), % 0.72/0.78 inference(rename_variables,[],[16])). % 0.72/0.78 cnf(40,plain, % 0.72/0.78 (E(f3(x401,x401),x401)), % 0.72/0.78 inference(rename_variables,[],[16])). % 0.72/0.78 cnf(43,plain, % 0.72/0.78 (P2(f7(a4),f3(f7(a4),f7(a6)))), % 0.72/0.78 inference(scs_inference,[],[17,19,15,16,34,37,40,20,29,2,21,22,3,9,10])). % 0.72/0.78 cnf(44,plain, % 0.72/0.78 (P2(x441,x441)), % 0.72/0.78 inference(rename_variables,[],[15])). % 0.72/0.78 cnf(45,plain, % 0.72/0.78 (P2(f3(f7(a4),f7(a6)),f7(a4))), % 0.72/0.78 inference(scs_inference,[],[17,19,15,44,16,34,37,40,20,29,2,21,22,3,9,10,11])). % 0.72/0.78 cnf(239,plain, % 0.72/0.78 (E(f3(x2391,x2392),f3(x2392,x2391))), % 0.72/0.78 inference(rename_variables,[],[18])). % 0.72/0.78 cnf(242,plain, % 0.72/0.78 ($false), % 0.72/0.78 inference(scs_inference,[],[18,239,45,43,30,10,11,28]), % 0.72/0.78 ['proof']). % 0.72/0.78 % SZS output end Proof % 0.72/0.78 % Total time :0.230000s %------------------------------------------------------------------------------