%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET924+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 : 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 14:23:00 EDT 2024 % Result : Theorem 0.13s 0.52s % Output : CNFRefutation 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.09 % Problem : SET924+1 : TPTP v8.2.0. Released v3.2.0. % 0.04/0.09 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.09/0.27 % Computer : n024.cluster.edu % 0.09/0.27 % Model : x86_64 x86_64 % 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.27 % Memory : 8042.1875MB % 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.27 % CPULimit : 300 % 0.09/0.27 % WCLimit : 300 % 0.09/0.27 % DateTime : Sun Jun 23 15:00:38 EDT 2024 % 0.09/0.27 % CPUTime : % 0.13/0.43 start to proof:theBenchmark % 0.13/0.52 %------------------------------------------- % 0.13/0.52 % File :CSE---1.7 % 0.13/0.52 % Problem :theBenchmark % 0.13/0.52 % Transform :cnf % 0.13/0.52 % Format :tptp:raw % 0.13/0.52 % Command :java -jar mcs_scs.jar %d %s % 0.13/0.52 % 0.13/0.52 % Result :Theorem 0.060000s % 0.13/0.52 % Output :CNFRefutation 0.060000s % 0.13/0.52 %------------------------------------------- % 0.13/0.52 %------------------------------------------------------------------------------ % 0.13/0.52 % File : SET924+1 : TPTP v8.2.0. Released v3.2.0. % 0.13/0.52 % Domain : Set theory % 0.13/0.52 % Problem : difference(singleton(A),B) = singleton(A) <=> ~ in(A,B) % 0.13/0.52 % Version : [Urb06] axioms : Especial. % 0.13/0.52 % English : % 0.13/0.52 % 0.13/0.52 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.13/0.52 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.13/0.52 % Source : [Urb06] % 0.13/0.52 % Names : zfmisc_1__t67_zfmisc_1 [Urb06] % 0.13/0.52 % 0.13/0.52 % Status : Theorem % 0.13/0.52 % Rating : 0.03 v7.2.0, 0.00 v6.4.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.00 v4.1.0, 0.04 v4.0.1, 0.09 v4.0.0, 0.08 v3.7.0, 0.00 v3.4.0, 0.05 v3.3.0, 0.07 v3.2.0 % 0.13/0.52 % Syntax : Number of formulae : 5 ( 2 unt; 0 def) % 0.13/0.52 % Number of atoms : 8 ( 2 equ) % 0.13/0.52 % Maximal formula atoms : 2 ( 1 avg) % 0.13/0.52 % Number of connectives : 7 ( 4 ~; 0 |; 0 &) % 0.13/0.52 % ( 2 <=>; 1 =>; 0 <=; 0 <~>) % 0.13/0.52 % Maximal formula depth : 5 ( 4 avg) % 0.13/0.52 % Maximal term depth : 3 ( 1 avg) % 0.13/0.52 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 0.13/0.52 % Number of functors : 2 ( 2 usr; 0 con; 1-2 aty) % 0.13/0.52 % Number of variables : 8 ( 6 !; 2 ?) % 0.13/0.52 % SPC : FOF_THM_RFO_SEQ % 0.13/0.52 % 0.13/0.52 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.13/0.52 % library, www.mizar.org % 0.13/0.52 %------------------------------------------------------------------------------ % 0.13/0.52 fof(antisymmetry_r2_hidden,axiom, % 0.13/0.52 ! [A,B] : % 0.13/0.52 ( in(A,B) % 0.13/0.52 => ~ in(B,A) ) ). % 0.13/0.52 % 0.13/0.52 fof(rc1_xboole_0,axiom, % 0.13/0.52 ? [A] : empty(A) ). % 0.13/0.52 % 0.13/0.52 fof(rc2_xboole_0,axiom, % 0.13/0.52 ? [A] : ~ empty(A) ). % 0.13/0.52 % 0.13/0.52 fof(t67_zfmisc_1,conjecture, % 0.13/0.52 ! [A,B] : % 0.13/0.52 ( set_difference(singleton(A),B) = singleton(A) % 0.13/0.52 <=> ~ in(A,B) ) ). % 0.13/0.52 % 0.13/0.52 fof(l34_zfmisc_1,axiom, % 0.13/0.52 ! [A,B] : % 0.13/0.52 ( set_difference(singleton(A),B) = singleton(A) % 0.13/0.52 <=> ~ in(A,B) ) ). % 0.13/0.52 % 0.13/0.52 %------------------------------------------------------------------------------ % 0.13/0.52 %------------------------------------------- % 0.13/0.52 % Proof found % 0.13/0.52 % SZS status Theorem for theBenchmark % 0.13/0.52 % SZS output start Proof % 0.13/0.52 %ClaNum:16(EqnAxiom:9) % 0.13/0.52 %VarNum:14(SingletonVarNum:6) % 0.13/0.52 %MaxLitNum:2 % 0.13/0.52 %MaxfuncDepth:2 % 0.13/0.52 %SharedTerms:12 % 0.13/0.52 %goalClause: 12 14 % 0.13/0.52 [10]P1(a1) % 0.13/0.52 [11]~P1(a2) % 0.13/0.52 [12]~P2(a3,a5)+E(f6(f4(a3),a5),f4(a3)) % 0.13/0.52 [14]P2(a3,a5)+~E(f6(f4(a3),a5),f4(a3)) % 0.13/0.52 [15]~P2(x152,x151)+~P2(x151,x152) % 0.13/0.52 [13]P2(x131,x132)+E(f6(f4(x131),x132),f4(x131)) % 0.13/0.52 [16]~P2(x161,x162)+~E(f6(f4(x161),x162),f4(x161)) % 0.13/0.52 %EqnAxiom % 0.13/0.52 [1]E(x11,x11) % 0.13/0.52 [2]E(x22,x21)+~E(x21,x22) % 0.13/0.52 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.13/0.52 [4]~E(x41,x42)+E(f4(x41),f4(x42)) % 0.13/0.52 [5]~E(x51,x52)+E(f6(x51,x53),f6(x52,x53)) % 0.13/0.52 [6]~E(x61,x62)+E(f6(x63,x61),f6(x63,x62)) % 0.13/0.52 [7]~P1(x71)+P1(x72)+~E(x71,x72) % 0.13/0.52 [8]P2(x82,x83)+~E(x81,x82)+~P2(x81,x83) % 0.13/0.52 [9]P2(x93,x92)+~E(x91,x92)+~P2(x93,x91) % 0.13/0.52 % 0.13/0.53 %------------------------------------------- % 0.13/0.53 cnf(30,plain, % 0.13/0.53 (P2(a3,x301)+~E(a5,x301)+~E(f6(f4(a3),a5),f4(a3))), % 0.13/0.53 inference(scs_inference,[],[9,14])). % 0.13/0.53 cnf(54,plain, % 0.13/0.53 (E(f4(x541),f6(f4(x541),x542))+P2(x541,x542)), % 0.13/0.53 inference(scs_inference,[],[2,13])). % 0.13/0.53 cnf(57,plain, % 0.13/0.53 (~E(f4(a3),f6(f4(a3),a5))+~E(a5,x571)+P2(a3,x571)), % 0.13/0.53 inference(scs_inference,[],[2,30])). % 0.13/0.53 cnf(58,plain, % 0.13/0.53 (P2(a3,a5)+P2(a3,x581)+~E(a5,x581)), % 0.13/0.53 inference(scs_inference,[],[57,54])). % 0.13/0.53 cnf(59,plain, % 0.13/0.53 (P2(a3,a5)+P2(a3,a5)), % 0.13/0.53 inference(equality_inference,[],[58])). % 0.13/0.53 cnf(60,plain, % 0.13/0.53 (P2(a3,a5)), % 0.13/0.53 inference(factoring_inference,[],[59])). % 0.13/0.53 cnf(61,plain, % 0.13/0.53 (E(f6(f4(a3),a5),f4(a3))), % 0.13/0.53 inference(scs_inference,[],[60,12])). % 0.13/0.53 cnf(81,plain, % 0.13/0.53 ($false), % 0.13/0.53 inference(scs_inference,[],[61,60,16]), % 0.13/0.53 ['proof']). % 0.13/0.53 % SZS output end Proof % 0.13/0.53 % Total time :0.060000s %------------------------------------------------------------------------------