%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET925+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 : n017.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 0.16s 0.51s % Output : CNFRefutation 0.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SET925+1 : TPTP v8.2.0. Released v3.2.0. % 0.06/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.11/0.30 % Computer : n017.cluster.edu % 0.11/0.30 % Model : x86_64 x86_64 % 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.30 % Memory : 8042.1875MB % 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.31 % CPULimit : 300 % 0.11/0.31 % WCLimit : 300 % 0.11/0.31 % DateTime : Sun Jun 23 17:05:24 EDT 2024 % 0.11/0.31 % CPUTime : % 0.16/0.46 start to proof:theBenchmark % 0.16/0.50 %------------------------------------------- % 0.16/0.50 % File :CSE---1.7 % 0.16/0.50 % Problem :theBenchmark % 0.16/0.50 % Transform :cnf % 0.16/0.50 % Format :tptp:raw % 0.16/0.50 % Command :java -jar mcs_scs.jar %d %s % 0.16/0.50 % 0.16/0.50 % Result :Theorem 0.000000s % 0.16/0.50 % Output :CNFRefutation 0.000000s % 0.16/0.50 %------------------------------------------- % 0.16/0.50 %------------------------------------------------------------------------------ % 0.16/0.50 % File : SET925+1 : TPTP v8.2.0. Released v3.2.0. % 0.16/0.50 % Domain : Set theory % 0.16/0.50 % Problem : difference(singleton(A),B) = empty_set <=> in(A,B) % 0.16/0.50 % Version : [Urb06] axioms : Especial. % 0.16/0.50 % English : % 0.16/0.50 % 0.16/0.50 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.16/0.50 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.16/0.50 % Source : [Urb06] % 0.16/0.50 % Names : zfmisc_1__t68_zfmisc_1 [Urb06] % 0.16/0.50 % 0.16/0.50 % Status : Theorem % 0.16/0.50 % Rating : 0.03 v7.2.0, 0.00 v6.4.0, 0.04 v6.1.0, 0.07 v6.0.0, 0.04 v5.5.0, 0.00 v5.4.0, 0.04 v5.3.0, 0.11 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 % 0.16/0.50 % Syntax : Number of formulae : 6 ( 3 unt; 0 def) % 0.16/0.50 % Number of atoms : 9 ( 2 equ) % 0.16/0.50 % Maximal formula atoms : 2 ( 1 avg) % 0.16/0.50 % Number of connectives : 5 ( 2 ~; 0 |; 0 &) % 0.16/0.50 % ( 2 <=>; 1 =>; 0 <=; 0 <~>) % 0.16/0.50 % Maximal formula depth : 5 ( 3 avg) % 0.16/0.50 % Maximal term depth : 3 ( 1 avg) % 0.16/0.50 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 0.16/0.50 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty) % 0.16/0.50 % Number of variables : 8 ( 6 !; 2 ?) % 0.16/0.50 % SPC : FOF_THM_RFO_SEQ % 0.16/0.50 % 0.16/0.50 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.16/0.50 % library, www.mizar.org % 0.16/0.50 %------------------------------------------------------------------------------ % 0.16/0.50 fof(antisymmetry_r2_hidden,axiom, % 0.16/0.50 ! [A,B] : % 0.16/0.50 ( in(A,B) % 0.16/0.50 => ~ in(B,A) ) ). % 0.16/0.50 % 0.16/0.50 fof(fc1_xboole_0,axiom, % 0.16/0.50 empty(empty_set) ). % 0.16/0.50 % 0.16/0.50 fof(rc1_xboole_0,axiom, % 0.16/0.50 ? [A] : empty(A) ). % 0.16/0.50 % 0.16/0.50 fof(rc2_xboole_0,axiom, % 0.16/0.50 ? [A] : ~ empty(A) ). % 0.16/0.50 % 0.16/0.50 fof(t68_zfmisc_1,conjecture, % 0.16/0.50 ! [A,B] : % 0.16/0.51 ( set_difference(singleton(A),B) = empty_set % 0.16/0.51 <=> in(A,B) ) ). % 0.16/0.51 % 0.16/0.51 fof(l36_zfmisc_1,axiom, % 0.16/0.51 ! [A,B] : % 0.16/0.51 ( set_difference(singleton(A),B) = empty_set % 0.16/0.51 <=> in(A,B) ) ). % 0.16/0.51 % 0.16/0.51 %------------------------------------------------------------------------------ % 0.16/0.51 %------------------------------------------- % 0.16/0.51 % Proof found % 0.16/0.51 % SZS status Theorem for theBenchmark % 0.16/0.51 % SZS output start Proof % 0.16/0.51 %ClaNum:17(EqnAxiom:9) % 0.16/0.51 %VarNum:12(SingletonVarNum:6) % 0.16/0.51 %MaxLitNum:2 % 0.16/0.51 %MaxfuncDepth:2 % 0.16/0.51 %SharedTerms:14 % 0.16/0.51 %goalClause: 13 14 % 0.16/0.51 [10]P1(a1) % 0.16/0.51 [11]P1(a2) % 0.16/0.51 [12]~P1(a3) % 0.16/0.51 [13]P2(a4,a6)+E(f7(f5(a4),a6),a1) % 0.16/0.51 [14]~P2(a4,a6)+~E(f7(f5(a4),a6),a1) % 0.16/0.51 [16]~P2(x162,x161)+~P2(x161,x162) % 0.16/0.51 [15]~P2(x151,x152)+E(f7(f5(x151),x152),a1) % 0.16/0.51 [17]P2(x171,x172)+~E(f7(f5(x171),x172),a1) % 0.16/0.51 %EqnAxiom % 0.16/0.51 [1]E(x11,x11) % 0.16/0.51 [2]E(x22,x21)+~E(x21,x22) % 0.16/0.51 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.16/0.51 [4]~E(x41,x42)+E(f5(x41),f5(x42)) % 0.16/0.51 [5]~E(x51,x52)+E(f7(x51,x53),f7(x52,x53)) % 0.16/0.51 [6]~E(x61,x62)+E(f7(x63,x61),f7(x63,x62)) % 0.16/0.51 [7]~P1(x71)+P1(x72)+~E(x71,x72) % 0.16/0.51 [8]P2(x82,x83)+~E(x81,x82)+~P2(x81,x83) % 0.16/0.51 [9]P2(x93,x92)+~E(x91,x92)+~P2(x93,x91) % 0.16/0.51 % 0.16/0.51 %------------------------------------------- % 0.16/0.51 cnf(21,plain, % 0.16/0.51 (~E(f7(f5(a4),a6),a1)), % 0.16/0.51 inference(scs_inference,[],[14,17])). % 0.16/0.51 cnf(22,plain, % 0.16/0.51 (P2(a4,a6)), % 0.16/0.51 inference(scs_inference,[],[21,13])). % 0.16/0.51 cnf(24,plain, % 0.16/0.51 (~P2(a4,a6)), % 0.16/0.51 inference(scs_inference,[],[21,15])). % 0.16/0.51 cnf(26,plain, % 0.16/0.51 ($false), % 0.16/0.51 inference(scs_inference,[],[22,24]), % 0.16/0.51 ['proof']). % 0.16/0.51 % SZS output end Proof % 0.16/0.51 % Total time :0.000000s %------------------------------------------------------------------------------