%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET879+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 : n024.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 107.97s 108.17s % Output : CNFRefutation 107.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET879+1 : TPTP v8.2.0. Released v3.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.13/0.33 % Computer : n024.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Sun Jun 23 15:19:39 EDT 2024 % 0.13/0.33 % CPUTime : % 0.46/0.59 start to proof:theBenchmark % 107.97/108.16 %------------------------------------------- % 107.97/108.16 % File :CSE---1.7 % 107.97/108.16 % Problem :theBenchmark % 107.97/108.16 % Transform :cnf % 107.97/108.16 % Format :tptp:raw % 107.97/108.16 % Command :java -jar mcs_scs.jar %d %s % 107.97/108.16 % 107.97/108.16 % Result :Theorem 107.330000s % 107.97/108.16 % Output :CNFRefutation 107.330000s % 107.97/108.16 %------------------------------------------- % 107.97/108.16 %------------------------------------------------------------------------------ % 107.97/108.16 % File : SET879+1 : TPTP v8.2.0. Released v3.2.0. % 107.97/108.17 % Domain : Set theory % 107.97/108.17 % Problem : difference(singleton(A),singleton(B)) = singleton(A) <=> A != B % 107.97/108.17 % Version : [Urb06] axioms : Especial. % 107.97/108.17 % English : % 107.97/108.17 % 107.97/108.17 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 107.97/108.17 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 107.97/108.17 % Source : [Urb06] % 107.97/108.17 % Names : zfmisc_1__t20_zfmisc_1 [Urb06] % 107.97/108.17 % 107.97/108.17 % Status : Theorem % 107.97/108.17 % Rating : 0.11 v8.1.0, 0.14 v7.5.0, 0.12 v7.4.0, 0.03 v7.2.0, 0.00 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.3.0, 0.04 v6.2.0, 0.12 v6.1.0, 0.17 v5.5.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.00 v5.0.0, 0.12 v4.1.0, 0.17 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.21 v3.2.0 % 107.97/108.17 % Syntax : Number of formulae : 6 ( 2 unt; 0 def) % 107.97/108.17 % Number of atoms : 11 ( 5 equ) % 107.97/108.17 % Maximal formula atoms : 3 ( 1 avg) % 107.97/108.17 % Number of connectives : 9 ( 4 ~; 0 |; 0 &) % 107.97/108.17 % ( 4 <=>; 1 =>; 0 <=; 0 <~>) % 107.97/108.17 % Maximal formula depth : 6 ( 4 avg) % 107.97/108.17 % Maximal term depth : 3 ( 1 avg) % 107.97/108.17 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 107.97/108.17 % Number of functors : 2 ( 2 usr; 0 con; 1-2 aty) % 107.97/108.17 % Number of variables : 11 ( 9 !; 2 ?) % 107.97/108.17 % SPC : FOF_THM_RFO_SEQ % 107.97/108.17 % 107.97/108.17 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 107.97/108.17 % library, www.mizar.org % 107.97/108.17 %------------------------------------------------------------------------------ % 107.97/108.17 fof(antisymmetry_r2_hidden,axiom, % 107.97/108.17 ! [A,B] : % 107.97/108.17 ( in(A,B) % 107.97/108.17 => ~ in(B,A) ) ). % 107.97/108.17 % 107.97/108.17 fof(d1_tarski,axiom, % 107.97/108.17 ! [A,B] : % 107.97/108.17 ( B = singleton(A) % 107.97/108.17 <=> ! [C] : % 107.97/108.17 ( in(C,B) % 107.97/108.17 <=> C = A ) ) ). % 107.97/108.17 % 107.97/108.17 fof(l34_zfmisc_1,axiom, % 107.97/108.17 ! [A,B] : % 107.97/108.17 ( set_difference(singleton(A),B) = singleton(A) % 107.97/108.17 <=> ~ in(A,B) ) ). % 107.97/108.17 % 107.97/108.17 fof(rc1_xboole_0,axiom, % 107.97/108.17 ? [A] : empty(A) ). % 107.97/108.17 % 107.97/108.17 fof(rc2_xboole_0,axiom, % 107.97/108.17 ? [A] : ~ empty(A) ). % 107.97/108.17 % 107.97/108.17 fof(t20_zfmisc_1,conjecture, % 107.97/108.17 ! [A,B] : % 107.97/108.17 ( set_difference(singleton(A),singleton(B)) = singleton(A) % 107.97/108.17 <=> A != B ) ). % 107.97/108.17 % 107.97/108.17 %------------------------------------------------------------------------------ % 107.97/108.17 %------------------------------------------- % 107.97/108.17 % Proof found % 107.97/108.17 % SZS status Theorem for theBenchmark % 107.97/108.17 % SZS output start Proof % 107.97/108.17 %ClaNum:22(EqnAxiom:11) % 107.97/108.17 %VarNum:42(SingletonVarNum:16) % 107.97/108.17 %MaxLitNum:3 % 107.97/108.17 %MaxfuncDepth:2 % 107.97/108.17 %SharedTerms:13 % 107.97/108.17 %goalClause: 14 17 % 107.97/108.17 [12]P1(a1) % 107.97/108.17 [13]~P1(a3) % 107.97/108.17 [14]~E(a4,a6)+E(f7(f5(a4),f5(a6)),f5(a4)) % 107.97/108.17 [17]E(a4,a6)+~E(f7(f5(a4),f5(a6)),f5(a4)) % 107.97/108.17 [19]~P2(x192,x191)+~P2(x191,x192) % 107.97/108.17 [18]P2(x181,x182)+E(f7(f5(x181),x182),f5(x181)) % 107.97/108.17 [21]~P2(x211,x212)+~E(f7(f5(x211),x212),f5(x211)) % 107.97/108.17 [20]E(f2(x202,x201),x202)+P2(f2(x202,x201),x201)+E(x201,f5(x202)) % 107.97/108.17 [22]~E(f2(x222,x221),x222)+~P2(f2(x222,x221),x221)+E(x221,f5(x222)) % 107.97/108.17 [15]P2(x151,x152)+~E(x151,x153)+~E(x152,f5(x153)) % 107.97/108.17 [16]~P2(x161,x163)+E(x161,x162)+~E(x163,f5(x162)) % 107.97/108.17 %EqnAxiom % 107.97/108.17 [1]E(x11,x11) % 107.97/108.17 [2]E(x22,x21)+~E(x21,x22) % 107.97/108.17 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 107.97/108.17 [4]~E(x41,x42)+E(f5(x41),f5(x42)) % 107.97/108.17 [5]~E(x51,x52)+E(f2(x51,x53),f2(x52,x53)) % 107.97/108.17 [6]~E(x61,x62)+E(f2(x63,x61),f2(x63,x62)) % 107.97/108.17 [7]~E(x71,x72)+E(f7(x71,x73),f7(x72,x73)) % 107.97/108.17 [8]~E(x81,x82)+E(f7(x83,x81),f7(x83,x82)) % 107.97/108.17 [9]~P1(x91)+P1(x92)+~E(x91,x92) % 107.97/108.17 [10]P2(x102,x103)+~E(x101,x102)+~P2(x101,x103) % 107.97/108.17 [11]P2(x113,x112)+~E(x111,x112)+~P2(x113,x111) % 107.97/108.17 % 107.97/108.17 %------------------------------------------- % 107.97/108.18 cnf(23,plain, % 107.97/108.18 (~P2(x231,f5(x232))+E(x231,x232)), % 107.97/108.18 inference(equality_inference,[],[16])). % 107.97/108.18 cnf(24,plain, % 107.97/108.18 (E(f5(x241),f5(x242))+~E(x242,x241)), % 107.97/108.18 inference(scs_inference,[],[2,4])). % 107.97/108.18 cnf(40,plain, % 107.97/108.18 (E(x401,f5(a4))+~E(x401,f7(f5(a4),f5(a6)))+~E(a4,a6)), % 107.97/108.18 inference(scs_inference,[],[3,14])). % 107.97/108.18 cnf(102,plain, % 107.97/108.18 (~E(f7(f5(a4),f5(a6)),x1021)+E(x1021,f5(a4))+~E(a4,a6)), % 107.97/108.18 inference(scs_inference,[],[40,2])). % 107.97/108.18 cnf(103,plain, % 107.97/108.18 (~E(f5(a4),x1031)+E(f7(x1031,f5(a6)),f5(a4))+~E(a4,a6)), % 107.97/108.18 inference(scs_inference,[],[102,7])). % 107.97/108.18 cnf(104,plain, % 107.97/108.18 (~E(a4,x1041)+E(f7(f5(x1041),f5(a6)),f5(a4))+~E(a4,a6)), % 107.97/108.18 inference(scs_inference,[],[103,4])). % 107.97/108.18 cnf(251,plain, % 107.97/108.18 (E(f5(a4),x2511)+~E(x2511,f7(f5(a4),f5(a6)))+~E(a4,a6)), % 107.97/108.18 inference(scs_inference,[],[2,40])). % 107.97/108.18 cnf(252,plain, % 107.97/108.18 (~E(x2521,f5(a4))+E(f5(a4),f7(x2521,f5(a6)))+~E(a4,a6)), % 107.97/108.18 inference(scs_inference,[],[251,7])). % 107.97/108.18 cnf(282,plain, % 107.97/108.18 (E(f5(a4),f7(f5(x2821),f5(a6)))+~E(a4,x2821)+~E(a4,a6)), % 107.97/108.18 inference(scs_inference,[],[2,104])). % 107.97/108.18 cnf(308,plain, % 107.97/108.18 (E(f7(x3081,f5(a6)),f5(a4))+~E(x3081,f5(a4))+~E(a4,a6)), % 107.97/108.18 inference(scs_inference,[],[2,252])). % 107.97/108.18 cnf(322,plain, % 107.97/108.18 (~E(a6,a4)+~E(x3221,f5(a4))+E(f7(x3221,f5(a6)),f5(a4))), % 107.97/108.18 inference(scs_inference,[],[2,308])). % 107.97/108.18 cnf(1951,plain, % 107.97/108.18 (~E(f5(a6),x19511)+~E(a4,a6)+E(f7(f5(a4),x19511),f5(a4))), % 107.97/108.18 inference(scs_inference,[],[8,102])). % 107.97/108.18 cnf(1952,plain, % 107.97/108.18 (~E(f5(a6),x19521)+E(f7(f5(a4),x19521),f5(a4))+~E(f7(f5(a4),f5(a6)),f5(a4))), % 107.97/108.18 inference(scs_inference,[],[1951,17])). % 107.97/108.18 cnf(1956,plain, % 107.97/108.18 (~E(x19561,f5(a6))+~E(a4,a6)+E(f5(a4),f7(f5(a4),x19561))), % 107.97/108.18 inference(scs_inference,[],[8,251])). % 107.97/108.18 cnf(2076,plain, % 107.97/108.18 (~P2(a4,f5(a6))+~E(a6,a4)), % 107.97/108.18 inference(scs_inference,[],[21,322])). % 107.97/108.18 cnf(2077,plain, % 107.97/108.18 (~E(a4,a6)+~P2(a4,f5(a6))), % 107.97/108.18 inference(scs_inference,[],[2076,2])). % 107.97/108.18 cnf(2078,plain, % 107.97/108.18 (~P2(a4,f5(a6))), % 107.97/108.18 inference(scs_inference,[],[2077,23])). % 107.97/108.18 cnf(2079,plain, % 107.97/108.18 (E(f7(f5(a4),f5(a6)),f5(a4))), % 107.97/108.18 inference(scs_inference,[],[2078,18])). % 107.97/108.18 cnf(2087,plain, % 107.97/108.18 (E(a4,a6)), % 107.97/108.18 inference(scs_inference,[],[2079,17])). % 107.97/108.18 cnf(2088,plain, % 107.97/108.18 (~E(f5(a6),x20881)+E(f7(f5(a4),x20881),f5(a4))), % 107.97/108.18 inference(scs_inference,[],[2079,1952])). % 107.97/108.18 cnf(2102,plain, % 107.97/108.18 (E(f7(f5(x21021),f5(a6)),f5(a4))+~E(a4,x21021)), % 107.97/108.18 inference(scs_inference,[],[2087,104])). % 107.97/108.18 cnf(2114,plain, % 107.97/108.18 (E(f5(a4),f7(f5(x21141),f5(a6)))+~E(a4,x21141)), % 107.97/108.18 inference(scs_inference,[],[2087,282])). % 107.97/108.18 cnf(2242,plain, % 107.97/108.18 (~E(x22421,f5(a6))+E(f5(a4),f7(f5(a4),x22421))), % 107.97/108.18 inference(scs_inference,[],[2087,1956])). % 107.97/108.18 cnf(2258,plain, % 107.97/108.18 (E(f2(a4,x22581),f2(a6,x22581))), % 107.97/108.18 inference(scs_inference,[],[2087,5])). % 107.97/108.18 cnf(2267,plain, % 107.97/108.18 (E(f5(a6),f5(a4))), % 107.97/108.18 inference(scs_inference,[],[2087,2078,5,6,2102,2114,15,7,8,24])). % 107.97/108.18 cnf(2268,plain, % 107.97/108.18 (E(f5(a4),f5(a6))), % 107.97/108.18 inference(scs_inference,[],[2087,2078,5,6,2102,2114,15,7,8,24,4])). % 107.97/108.18 cnf(2385,plain, % 107.97/108.18 (~P2(a4,f5(a4))), % 107.97/108.18 inference(scs_inference,[],[2267,2268,2258,2078,2087,2088,2242,2,15,11])). % 107.97/108.18 cnf(2391,plain, % 107.97/108.18 ($false), % 107.97/108.18 inference(scs_inference,[],[2385,2268,2087,15]), % 107.97/108.18 ['proof']). % 107.97/108.18 % SZS output end Proof % 107.97/108.18 % Total time :107.330000s %------------------------------------------------------------------------------