%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET910+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 : n027.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 14:22:57 EDT 2024 % Result : Theorem 0.18s 0.56s % Output : CNFRefutation 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SET910+1 : TPTP v8.2.0. Released v3.2.0. % 0.00/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.10/0.32 % Computer : n027.cluster.edu % 0.10/0.32 % Model : x86_64 x86_64 % 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.32 % Memory : 8042.1875MB % 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.32 % CPULimit : 300 % 0.10/0.32 % WCLimit : 300 % 0.10/0.32 % DateTime : Sun Jun 23 16:43:23 EDT 2024 % 0.10/0.32 % CPUTime : % 0.18/0.53 start to proof:theBenchmark % 0.18/0.56 %------------------------------------------- % 0.18/0.56 % File :CSE---1.7 % 0.18/0.56 % Problem :theBenchmark % 0.18/0.56 % Transform :cnf % 0.18/0.56 % Format :tptp:raw % 0.18/0.56 % Command :java -jar mcs_scs.jar %d %s % 0.18/0.56 % 0.18/0.56 % Result :Theorem 0.000000s % 0.18/0.56 % Output :CNFRefutation 0.000000s % 0.18/0.56 %------------------------------------------- % 0.18/0.56 %------------------------------------------------------------------------------ % 0.18/0.56 % File : SET910+1 : TPTP v8.2.0. Released v3.2.0. % 0.18/0.56 % Domain : Set theory % 0.18/0.56 % Problem : intersection(A,singleton(B)) = singleton(B) => in(B,A) % 0.18/0.56 % Version : [Urb06] axioms : Especial. % 0.18/0.56 % English : % 0.18/0.56 % 0.18/0.56 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.18/0.56 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.18/0.56 % Source : [Urb06] % 0.18/0.56 % Names : zfmisc_1__t51_zfmisc_1 [Urb06] % 0.18/0.56 % 0.18/0.56 % Status : Theorem % 0.18/0.56 % Rating : 0.00 v6.4.0, 0.04 v6.2.0, 0.08 v6.1.0, 0.13 v5.5.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.05 v5.0.0, 0.04 v3.7.0, 0.05 v3.4.0, 0.11 v3.3.0, 0.07 v3.2.0 % 0.18/0.56 % Syntax : Number of formulae : 7 ( 4 unt; 0 def) % 0.18/0.56 % Number of atoms : 10 ( 4 equ) % 0.18/0.56 % Maximal formula atoms : 2 ( 1 avg) % 0.18/0.56 % Number of connectives : 5 ( 2 ~; 0 |; 0 &) % 0.18/0.56 % ( 0 <=>; 3 =>; 0 <=; 0 <~>) % 0.18/0.56 % Maximal formula depth : 5 ( 3 avg) % 0.18/0.56 % Maximal term depth : 3 ( 1 avg) % 0.18/0.56 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 0.18/0.56 % Number of functors : 2 ( 2 usr; 0 con; 1-2 aty) % 0.18/0.56 % Number of variables : 12 ( 10 !; 2 ?) % 0.18/0.56 % SPC : FOF_THM_RFO_SEQ % 0.18/0.56 % 0.18/0.56 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.18/0.56 % library, www.mizar.org % 0.18/0.56 %------------------------------------------------------------------------------ % 0.18/0.56 fof(commutativity_k3_xboole_0,axiom, % 0.18/0.56 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ). % 0.18/0.56 % 0.18/0.56 fof(idempotence_k3_xboole_0,axiom, % 0.18/0.56 ! [A,B] : set_intersection2(A,A) = A ). % 0.18/0.56 % 0.18/0.56 fof(antisymmetry_r2_hidden,axiom, % 0.18/0.56 ! [A,B] : % 0.18/0.56 ( in(A,B) % 0.18/0.56 => ~ in(B,A) ) ). % 0.18/0.56 % 0.18/0.56 fof(rc1_xboole_0,axiom, % 0.18/0.56 ? [A] : empty(A) ). % 0.18/0.56 % 0.18/0.56 fof(rc2_xboole_0,axiom, % 0.18/0.56 ? [A] : ~ empty(A) ). % 0.18/0.56 % 0.18/0.56 fof(t51_zfmisc_1,conjecture, % 0.18/0.56 ! [A,B] : % 0.18/0.56 ( set_intersection2(A,singleton(B)) = singleton(B) % 0.18/0.56 => in(B,A) ) ). % 0.18/0.56 % 0.18/0.56 fof(l30_zfmisc_1,axiom, % 0.18/0.56 ! [A,B] : % 0.18/0.56 ( set_intersection2(A,singleton(B)) = singleton(B) % 0.18/0.56 => in(B,A) ) ). % 0.18/0.56 % 0.18/0.56 %------------------------------------------------------------------------------ % 0.18/0.56 %------------------------------------------- % 0.18/0.56 % Proof found % 0.18/0.56 % SZS status Theorem for theBenchmark % 0.18/0.56 % SZS output start Proof % 0.18/0.56 %ClaNum:17(EqnAxiom:9) % 0.18/0.56 %VarNum:16(SingletonVarNum:7) % 0.18/0.56 %MaxLitNum:2 % 0.18/0.56 %MaxfuncDepth:2 % 0.18/0.56 %SharedTerms:10 % 0.18/0.56 %goalClause: 12 15 % 0.18/0.56 %singleGoalClaCount:2 % 0.18/0.56 [10]P1(a1) % 0.18/0.56 [14]~P1(a4) % 0.18/0.56 [15]~P2(a5,a3) % 0.18/0.56 [12]E(f2(a3,f6(a5)),f6(a5)) % 0.18/0.56 [11]E(f2(x111,x111),x111) % 0.18/0.56 [13]E(f2(x131,x132),f2(x132,x131)) % 0.18/0.56 [16]~P2(x162,x161)+~P2(x161,x162) % 0.18/0.56 [17]P2(x171,x172)+~E(f2(x172,f6(x171)),f6(x171)) % 0.18/0.56 %EqnAxiom % 0.18/0.56 [1]E(x11,x11) % 0.18/0.56 [2]E(x22,x21)+~E(x21,x22) % 0.18/0.56 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.18/0.56 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.18/0.56 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.18/0.56 [6]~E(x61,x62)+E(f6(x61),f6(x62)) % 0.18/0.56 [7]~P1(x71)+P1(x72)+~E(x71,x72) % 0.18/0.56 [8]P2(x82,x83)+~E(x81,x82)+~P2(x81,x83) % 0.18/0.56 [9]P2(x93,x92)+~E(x91,x92)+~P2(x93,x91) % 0.18/0.56 % 0.18/0.56 %------------------------------------------- % 0.18/0.56 cnf(18,plain, % 0.18/0.56 ($false), % 0.18/0.56 inference(scs_inference,[],[15,12,17]), % 0.18/0.56 ['proof']). % 0.18/0.56 % SZS output end Proof % 0.18/0.56 % Total time :0.000000s %------------------------------------------------------------------------------