%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET886+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 : n001.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 14:22:53 EDT 2024 % Result : Theorem 0.56s 0.68s % Output : CNFRefutation 0.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET886+1 : TPTP v8.2.0. Released v3.2.0. % 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n001.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sun Jun 23 17:50:09 EDT 2024 % 0.12/0.34 % CPUTime : % 0.53/0.59 start to proof:theBenchmark % 0.56/0.67 %------------------------------------------- % 0.56/0.67 % File :CSE---1.7 % 0.56/0.67 % Problem :theBenchmark % 0.56/0.67 % Transform :cnf % 0.56/0.67 % Format :tptp:raw % 0.56/0.67 % Command :java -jar mcs_scs.jar %d %s % 0.56/0.67 % 0.56/0.67 % Result :Theorem 0.050000s % 0.56/0.67 % Output :CNFRefutation 0.050000s % 0.56/0.67 %------------------------------------------- % 0.56/0.68 %------------------------------------------------------------------------------ % 0.56/0.68 % File : SET886+1 : TPTP v8.2.0. Released v3.2.0. % 0.56/0.68 % Domain : Set theory % 0.56/0.68 % Problem : subset(uno_pair(A,B),singleton(C)) => uno_pair(A,B) = singleton(C) % 0.56/0.68 % Version : [Urb06] axioms : Especial. % 0.56/0.68 % English : % 0.56/0.68 % 0.56/0.68 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.56/0.68 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.56/0.68 % Source : [Urb06] % 0.56/0.68 % Names : zfmisc_1__t27_zfmisc_1 [Urb06] % 0.56/0.68 % 0.56/0.68 % Status : Theorem % 0.56/0.68 % Rating : 0.06 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 v6.1.0, 0.13 v6.0.0, 0.09 v5.5.0, 0.04 v5.3.0, 0.15 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.09 v4.0.0, 0.08 v3.7.0, 0.05 v3.4.0, 0.11 v3.3.0, 0.07 v3.2.0 % 0.56/0.68 % Syntax : Number of formulae : 7 ( 5 unt; 0 def) % 0.56/0.68 % Number of atoms : 9 ( 4 equ) % 0.56/0.68 % Maximal formula atoms : 2 ( 1 avg) % 0.56/0.68 % Number of connectives : 3 ( 1 ~; 0 |; 0 &) % 0.56/0.68 % ( 0 <=>; 2 =>; 0 <=; 0 <~>) % 0.56/0.68 % Maximal formula depth : 5 ( 3 avg) % 0.56/0.68 % Maximal term depth : 2 ( 1 avg) % 0.56/0.68 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 0.56/0.68 % Number of functors : 2 ( 2 usr; 0 con; 1-2 aty) % 0.56/0.68 % Number of variables : 13 ( 11 !; 2 ?) % 0.56/0.68 % SPC : FOF_THM_RFO_SEQ % 0.56/0.68 % 0.56/0.68 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.56/0.68 % library, www.mizar.org % 0.56/0.68 %------------------------------------------------------------------------------ % 0.56/0.68 fof(commutativity_k2_tarski,axiom, % 0.56/0.68 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 0.56/0.68 % 0.56/0.68 fof(rc1_xboole_0,axiom, % 0.56/0.68 ? [A] : empty(A) ). % 0.56/0.68 % 0.56/0.68 fof(rc2_xboole_0,axiom, % 0.56/0.68 ? [A] : ~ empty(A) ). % 0.56/0.68 % 0.56/0.68 fof(reflexivity_r1_tarski,axiom, % 0.56/0.68 ! [A,B] : subset(A,A) ). % 0.56/0.68 % 0.56/0.68 fof(t26_zfmisc_1,axiom, % 0.56/0.68 ! [A,B,C] : % 0.56/0.68 ( subset(unordered_pair(A,B),singleton(C)) % 0.56/0.68 => A = C ) ). % 0.56/0.68 % 0.56/0.68 fof(t27_zfmisc_1,conjecture, % 0.56/0.68 ! [A,B,C] : % 0.56/0.68 ( subset(unordered_pair(A,B),singleton(C)) % 0.56/0.68 => unordered_pair(A,B) = singleton(C) ) ). % 0.56/0.68 % 0.56/0.68 fof(t69_enumset1,axiom, % 0.56/0.68 ! [A] : unordered_pair(A,A) = singleton(A) ). % 0.56/0.68 % 0.56/0.68 %------------------------------------------------------------------------------ % 0.56/0.68 %------------------------------------------- % 0.56/0.68 % Proof found % 0.56/0.68 % SZS status Theorem for theBenchmark % 0.56/0.68 % SZS output start Proof % 0.56/0.68 %ClaNum:15(EqnAxiom:8) % 0.56/0.68 %VarNum:12(SingletonVarNum:6) % 0.56/0.68 %MaxLitNum:2 % 0.56/0.68 %MaxfuncDepth:1 % 0.56/0.68 %SharedTerms:11 % 0.56/0.68 %goalClause: 12 14 % 0.56/0.68 %singleGoalClaCount:2 % 0.56/0.68 [9]P1(a1) % 0.56/0.68 [13]~P1(a4) % 0.56/0.68 [12]P2(f2(a3,a5),f2(a6,a6)) % 0.56/0.68 [14]~E(f2(a6,a6),f2(a3,a5)) % 0.56/0.68 [10]P2(x101,x101) % 0.56/0.68 [11]E(f2(x111,x112),f2(x112,x111)) % 0.56/0.68 [15]E(x151,x152)+~P2(f2(x151,x153),f2(x152,x152)) % 0.56/0.68 %EqnAxiom % 0.56/0.68 [1]E(x11,x11) % 0.56/0.68 [2]E(x22,x21)+~E(x21,x22) % 0.56/0.68 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.56/0.68 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.56/0.68 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.56/0.68 [6]~P1(x61)+P1(x62)+~E(x61,x62) % 0.56/0.68 [7]P2(x72,x73)+~E(x71,x72)+~P2(x71,x73) % 0.56/0.68 [8]P2(x83,x82)+~E(x81,x82)+~P2(x83,x81) % 0.56/0.68 % 0.56/0.68 %------------------------------------------- % 0.56/0.68 cnf(18,plain, % 0.56/0.68 (E(a6,a3)), % 0.56/0.68 inference(scs_inference,[],[12,15,2])). % 0.56/0.68 cnf(19,plain, % 0.56/0.68 (~E(f2(a6,a6),f2(a5,a3))), % 0.56/0.68 inference(scs_inference,[],[12,14,11,15,2,3])). % 0.56/0.68 cnf(20,plain, % 0.56/0.68 (E(f2(x201,x202),f2(x202,x201))), % 0.56/0.68 inference(rename_variables,[],[11])). % 0.56/0.68 cnf(21,plain, % 0.56/0.68 (P2(f2(a5,a3),f2(a6,a6))), % 0.56/0.68 inference(scs_inference,[],[12,14,11,20,15,2,3,7])). % 0.56/0.68 cnf(22,plain, % 0.56/0.68 (E(f2(x221,x222),f2(x222,x221))), % 0.56/0.68 inference(rename_variables,[],[11])). % 0.56/0.68 cnf(23,plain, % 0.56/0.68 (P2(f2(x231,x232),f2(x232,x231))), % 0.56/0.68 inference(scs_inference,[],[12,14,10,11,20,22,15,2,3,7,8])). % 0.56/0.68 cnf(26,plain, % 0.56/0.68 (E(a5,a6)), % 0.56/0.68 inference(scs_inference,[],[21,15])). % 0.56/0.68 cnf(50,plain, % 0.56/0.68 (E(f2(a6,x501),f2(a5,x501))), % 0.56/0.68 inference(scs_inference,[],[26,4,2])). % 0.56/0.68 cnf(53,plain, % 0.56/0.69 (E(f2(a6,x531),f2(a5,x531))), % 0.56/0.69 inference(rename_variables,[],[50])). % 0.56/0.69 cnf(58,plain, % 0.56/0.69 ($false), % 0.56/0.69 inference(scs_inference,[],[19,12,18,23,50,53,2,3,7,8,5]), % 0.56/0.69 ['proof']). % 0.56/0.69 % SZS output end Proof % 0.56/0.69 % Total time :0.050000s %------------------------------------------------------------------------------