%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET877+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 : n026.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 14:22:52 EDT 2024 % Result : Theorem 2.71s 2.81s % Output : CNFRefutation 2.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET877+1 : TPTP v8.2.0. Released v3.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.11/0.33 % Computer : n026.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 15:42:53 EDT 2024 % 0.11/0.33 % CPUTime : % 0.52/0.55 start to proof:theBenchmark % 2.71/2.80 %------------------------------------------- % 2.71/2.80 % File :CSE---1.7 % 2.71/2.80 % Problem :theBenchmark % 2.71/2.80 % Transform :cnf % 2.71/2.80 % Format :tptp:raw % 2.71/2.80 % Command :java -jar mcs_scs.jar %d %s % 2.71/2.80 % 2.71/2.80 % Result :Theorem 2.210000s % 2.71/2.80 % Output :CNFRefutation 2.210000s % 2.71/2.80 %------------------------------------------- % 2.71/2.80 %------------------------------------------------------------------------------ % 2.71/2.80 % File : SET877+1 : TPTP v8.2.0. Released v3.2.0. % 2.71/2.80 % Domain : Set theory % 2.71/2.80 % Problem : intersection(singleton(A),singleton(B)) = singleton(A) => A = B % 2.71/2.80 % Version : [Urb06] axioms : Especial. % 2.71/2.80 % English : % 2.71/2.80 % 2.71/2.80 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 2.71/2.80 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 2.71/2.80 % Source : [Urb06] % 2.71/2.80 % Names : zfmisc_1__t18_zfmisc_1 [Urb06] % 2.71/2.80 % 2.71/2.80 % Status : Theorem % 2.71/2.80 % Rating : 0.11 v7.5.0, 0.12 v7.4.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.17 v5.5.0, 0.07 v5.4.0, 0.14 v5.3.0, 0.19 v5.2.0, 0.00 v5.0.0, 0.17 v4.0.1, 0.22 v4.0.0, 0.21 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.14 v3.2.0 % 2.71/2.80 % Syntax : Number of formulae : 8 ( 4 unt; 0 def) % 2.71/2.80 % Number of atoms : 13 ( 7 equ) % 2.71/2.80 % Maximal formula atoms : 3 ( 1 avg) % 2.71/2.80 % Number of connectives : 7 ( 2 ~; 0 |; 0 &) % 2.71/2.80 % ( 2 <=>; 3 =>; 0 <=; 0 <~>) % 2.71/2.80 % Maximal formula depth : 6 ( 4 avg) % 2.71/2.80 % Maximal term depth : 3 ( 1 avg) % 2.71/2.80 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 2.71/2.80 % Number of functors : 2 ( 2 usr; 0 con; 1-2 aty) % 2.71/2.80 % Number of variables : 15 ( 13 !; 2 ?) % 2.71/2.80 % SPC : FOF_THM_RFO_SEQ % 2.71/2.80 % 2.71/2.80 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 2.71/2.80 % library, www.mizar.org % 2.71/2.81 %------------------------------------------------------------------------------ % 2.71/2.81 fof(antisymmetry_r2_hidden,axiom, % 2.71/2.81 ! [A,B] : % 2.71/2.81 ( in(A,B) % 2.71/2.81 => ~ in(B,A) ) ). % 2.71/2.81 % 2.71/2.81 fof(commutativity_k3_xboole_0,axiom, % 2.71/2.81 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ). % 2.71/2.81 % 2.71/2.81 fof(d1_tarski,axiom, % 2.71/2.81 ! [A,B] : % 2.71/2.81 ( B = singleton(A) % 2.71/2.81 <=> ! [C] : % 2.71/2.81 ( in(C,B) % 2.71/2.81 <=> C = A ) ) ). % 2.71/2.81 % 2.71/2.81 fof(idempotence_k3_xboole_0,axiom, % 2.71/2.81 ! [A,B] : set_intersection2(A,A) = A ). % 2.71/2.81 % 2.71/2.81 fof(l30_zfmisc_1,axiom, % 2.71/2.81 ! [A,B] : % 2.71/2.81 ( set_intersection2(A,singleton(B)) = singleton(B) % 2.71/2.81 => in(B,A) ) ). % 2.71/2.81 % 2.71/2.81 fof(rc1_xboole_0,axiom, % 2.71/2.81 ? [A] : empty(A) ). % 2.71/2.81 % 2.71/2.81 fof(rc2_xboole_0,axiom, % 2.71/2.81 ? [A] : ~ empty(A) ). % 2.71/2.81 % 2.71/2.81 fof(t18_zfmisc_1,conjecture, % 2.71/2.81 ! [A,B] : % 2.71/2.81 ( set_intersection2(singleton(A),singleton(B)) = singleton(A) % 2.71/2.81 => A = B ) ). % 2.71/2.81 % 2.71/2.81 %------------------------------------------------------------------------------ % 2.71/2.81 %------------------------------------------- % 2.71/2.81 % Proof found % 2.71/2.81 % SZS status Theorem for theBenchmark % 2.71/2.81 % SZS output start Proof % 2.71/2.81 %ClaNum:23(EqnAxiom:11) % 2.71/2.81 %VarNum:44(SingletonVarNum:17) % 2.71/2.81 %MaxLitNum:3 % 2.71/2.81 %MaxfuncDepth:2 % 2.71/2.81 %SharedTerms:11 % 2.71/2.81 %goalClause: 14 16 % 2.71/2.81 %singleGoalClaCount:2 % 2.71/2.81 [12]P1(a1) % 2.71/2.81 [16]~E(a6,a4) % 2.71/2.81 [17]~P1(a5) % 2.71/2.81 [14]E(f3(f7(a4),f7(a6)),f7(a4)) % 2.71/2.81 [13]E(f3(x131,x131),x131) % 2.71/2.81 [15]E(f3(x151,x152),f3(x152,x151)) % 2.71/2.81 [20]~P2(x202,x201)+~P2(x201,x202) % 2.71/2.81 [21]P2(x211,x212)+~E(f3(x212,f7(x211)),f7(x211)) % 2.71/2.81 [22]E(f2(x222,x221),x222)+P2(f2(x222,x221),x221)+E(x221,f7(x222)) % 2.71/2.81 [23]~E(f2(x232,x231),x232)+~P2(f2(x232,x231),x231)+E(x231,f7(x232)) % 2.71/2.81 [18]P2(x181,x182)+~E(x181,x183)+~E(x182,f7(x183)) % 2.71/2.81 [19]~P2(x191,x193)+E(x191,x192)+~E(x193,f7(x192)) % 2.71/2.81 %EqnAxiom % 2.71/2.81 [1]E(x11,x11) % 2.71/2.81 [2]E(x22,x21)+~E(x21,x22) % 2.71/2.81 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 2.71/2.81 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43)) % 2.71/2.81 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52)) % 2.71/2.81 [6]~E(x61,x62)+E(f7(x61),f7(x62)) % 2.71/2.81 [7]~E(x71,x72)+E(f2(x71,x73),f2(x72,x73)) % 2.71/2.81 [8]~E(x81,x82)+E(f2(x83,x81),f2(x83,x82)) % 2.71/2.81 [9]~P1(x91)+P1(x92)+~E(x91,x92) % 2.71/2.81 [10]P2(x102,x103)+~E(x101,x102)+~P2(x101,x103) % 2.71/2.81 [11]P2(x113,x112)+~E(x111,x112)+~P2(x113,x111) % 2.71/2.81 % 2.71/2.81 %------------------------------------------- % 2.71/2.81 cnf(24,plain, % 2.71/2.81 (~P2(x241,f7(x242))+E(x241,x242)), % 2.71/2.81 inference(equality_inference,[],[19])). % 2.71/2.81 cnf(28,plain, % 2.71/2.81 (P2(x281,f7(x281))), % 2.71/2.81 inference(scs_inference,[],[14,16,13,24,2,21])). % 2.71/2.81 cnf(29,plain, % 2.71/2.81 (E(f3(x291,x291),x291)), % 2.71/2.81 inference(rename_variables,[],[13])). % 2.71/2.81 cnf(32,plain, % 2.71/2.81 (E(f3(x321,x321),x321)), % 2.71/2.81 inference(rename_variables,[],[13])). % 2.71/2.81 cnf(35,plain, % 2.71/2.81 (E(f3(x351,x351),x351)), % 2.71/2.81 inference(rename_variables,[],[13])). % 2.71/2.81 cnf(38,plain, % 2.71/2.81 (E(f3(x381,x381),x381)), % 2.71/2.81 inference(rename_variables,[],[13])). % 2.71/2.81 cnf(41,plain, % 2.71/2.81 (~E(a4,a6)), % 2.71/2.81 inference(scs_inference,[],[14,16,13,29,32,35,38,17,24,2,21,18,19,3,9,10])). % 2.71/2.81 cnf(57,plain, % 2.71/2.81 (~P2(a4,f7(a6))), % 2.71/2.81 inference(scs_inference,[],[28,41,20,24])). % 2.71/2.81 cnf(371,plain, % 2.71/2.81 (P2(f3(f7(a4),f7(a6)),f7(f7(a4)))), % 2.71/2.81 inference(scs_inference,[],[14,28,2,10])). % 2.71/2.81 cnf(494,plain, % 2.71/2.81 (~P2(f3(f7(a6),f7(a4)),f7(f7(a4)))), % 2.71/2.81 inference(scs_inference,[],[57,24,21])). % 2.71/2.81 cnf(560,plain, % 2.71/2.81 ($false), % 2.71/2.81 inference(scs_inference,[],[494,15,371,10]), % 2.71/2.81 ['proof']). % 2.71/2.81 % SZS output end Proof % 2.71/2.81 % Total time :2.210000s %------------------------------------------------------------------------------