%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET880+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 : n021.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 0.64s 0.72s % Output : CNFRefutation 0.64s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : SET880+1 : TPTP v8.2.0. Released v3.2.0. % 0.08/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.14/0.36 % Computer : n021.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Sun Jun 23 13:05:54 EDT 2024 % 0.14/0.37 % CPUTime : % 0.23/0.61 start to proof:theBenchmark % 0.23/0.71 %------------------------------------------- % 0.23/0.71 % File :CSE---1.7 % 0.23/0.71 % Problem :theBenchmark % 0.23/0.71 % Transform :cnf % 0.23/0.71 % Format :tptp:raw % 0.23/0.71 % Command :java -jar mcs_scs.jar %d %s % 0.23/0.71 % 0.23/0.71 % Result :Theorem 0.070000s % 0.23/0.71 % Output :CNFRefutation 0.070000s % 0.23/0.71 %------------------------------------------- % 0.23/0.71 %------------------------------------------------------------------------------ % 0.23/0.71 % File : SET880+1 : TPTP v8.2.0. Released v3.2.0. % 0.23/0.71 % Domain : Set theory % 0.23/0.72 % Problem : difference(singleton(A),singleton(B)) = empty_set => A = B % 0.23/0.72 % Version : [Urb06] axioms : Especial. % 0.23/0.72 % English : % 0.23/0.72 % 0.23/0.72 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.23/0.72 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.23/0.72 % Source : [Urb06] % 0.23/0.72 % Names : zfmisc_1__t21_zfmisc_1 [Urb06] % 0.23/0.72 % 0.23/0.72 % Status : Theorem % 0.23/0.72 % Rating : 0.06 v7.4.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.10 v6.0.0, 0.13 v5.5.0, 0.07 v5.3.0, 0.11 v5.2.0, 0.00 v5.0.0, 0.12 v4.1.0, 0.13 v4.0.0, 0.12 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.14 v3.2.0 % 0.23/0.72 % Syntax : Number of formulae : 7 ( 3 unt; 0 def) % 0.23/0.72 % Number of atoms : 12 ( 5 equ) % 0.23/0.72 % Maximal formula atoms : 3 ( 1 avg) % 0.23/0.72 % Number of connectives : 7 ( 2 ~; 0 |; 0 &) % 0.23/0.72 % ( 3 <=>; 2 =>; 0 <=; 0 <~>) % 0.23/0.72 % Maximal formula depth : 6 ( 4 avg) % 0.23/0.72 % Maximal term depth : 3 ( 1 avg) % 0.23/0.72 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 0.23/0.72 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty) % 0.23/0.72 % Number of variables : 11 ( 9 !; 2 ?) % 0.23/0.72 % SPC : FOF_THM_RFO_SEQ % 0.23/0.72 % 0.23/0.72 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.23/0.72 % library, www.mizar.org % 0.23/0.72 %------------------------------------------------------------------------------ % 0.23/0.72 fof(antisymmetry_r2_hidden,axiom, % 0.23/0.72 ! [A,B] : % 0.23/0.72 ( in(A,B) % 0.23/0.72 => ~ in(B,A) ) ). % 0.23/0.72 % 0.23/0.72 fof(d1_tarski,axiom, % 0.23/0.72 ! [A,B] : % 0.23/0.72 ( B = singleton(A) % 0.23/0.72 <=> ! [C] : % 0.23/0.72 ( in(C,B) % 0.23/0.72 <=> C = A ) ) ). % 0.23/0.72 % 0.23/0.72 fof(fc1_xboole_0,axiom, % 0.23/0.72 empty(empty_set) ). % 0.23/0.72 % 0.23/0.72 fof(l36_zfmisc_1,axiom, % 0.23/0.72 ! [A,B] : % 0.23/0.72 ( set_difference(singleton(A),B) = empty_set % 0.23/0.72 <=> in(A,B) ) ). % 0.23/0.72 % 0.23/0.72 fof(rc1_xboole_0,axiom, % 0.23/0.72 ? [A] : empty(A) ). % 0.23/0.72 % 0.23/0.72 fof(rc2_xboole_0,axiom, % 0.23/0.72 ? [A] : ~ empty(A) ). % 0.23/0.72 % 0.23/0.72 fof(t21_zfmisc_1,conjecture, % 0.23/0.72 ! [A,B] : % 0.23/0.72 ( set_difference(singleton(A),singleton(B)) = empty_set % 0.64/0.72 => A = B ) ). % 0.64/0.72 % 0.64/0.72 %------------------------------------------------------------------------------ % 0.64/0.72 %------------------------------------------- % 0.64/0.72 % Proof found % 0.64/0.72 % SZS status Theorem for theBenchmark % 0.64/0.72 % SZS output start Proof % 0.64/0.72 %ClaNum:23(EqnAxiom:11) % 0.64/0.72 %VarNum:40(SingletonVarNum:16) % 0.64/0.72 %MaxLitNum:3 % 0.64/0.72 %MaxfuncDepth:2 % 0.64/0.72 %SharedTerms:13 % 0.64/0.72 %goalClause: 14 15 % 0.64/0.72 %singleGoalClaCount:2 % 0.64/0.72 [12]P1(a1) % 0.64/0.72 [13]P1(a2) % 0.64/0.72 [15]~E(a7,a4) % 0.64/0.72 [16]~P1(a5) % 0.64/0.72 [14]E(f8(f6(a4),f6(a7)),a1) % 0.64/0.72 [20]~P2(x202,x201)+~P2(x201,x202) % 0.64/0.72 [19]~P2(x191,x192)+E(f8(f6(x191),x192),a1) % 0.64/0.72 [21]P2(x211,x212)+~E(f8(f6(x211),x212),a1) % 0.64/0.72 [22]E(f3(x222,x221),x222)+P2(f3(x222,x221),x221)+E(x221,f6(x222)) % 0.64/0.72 [23]~E(f3(x232,x231),x232)+~P2(f3(x232,x231),x231)+E(x231,f6(x232)) % 0.64/0.72 [17]P2(x171,x172)+~E(x171,x173)+~E(x172,f6(x173)) % 0.64/0.72 [18]~P2(x181,x183)+E(x181,x182)+~E(x183,f6(x182)) % 0.64/0.72 %EqnAxiom % 0.64/0.72 [1]E(x11,x11) % 0.64/0.72 [2]E(x22,x21)+~E(x21,x22) % 0.64/0.72 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.64/0.72 [4]~E(x41,x42)+E(f6(x41),f6(x42)) % 0.64/0.72 [5]~E(x51,x52)+E(f3(x51,x53),f3(x52,x53)) % 0.64/0.72 [6]~E(x61,x62)+E(f3(x63,x61),f3(x63,x62)) % 0.64/0.72 [7]~E(x71,x72)+E(f8(x71,x73),f8(x72,x73)) % 0.64/0.72 [8]~E(x81,x82)+E(f8(x83,x81),f8(x83,x82)) % 0.64/0.72 [9]~P1(x91)+P1(x92)+~E(x91,x92) % 0.64/0.72 [10]P2(x102,x103)+~E(x101,x102)+~P2(x101,x103) % 0.64/0.72 [11]P2(x113,x112)+~E(x111,x112)+~P2(x113,x111) % 0.64/0.72 % 0.64/0.72 %------------------------------------------- % 0.64/0.72 cnf(24,plain, % 0.64/0.72 (~P2(x241,f6(x242))+E(x241,x242)), % 0.64/0.72 inference(equality_inference,[],[18])). % 0.64/0.72 cnf(25,plain, % 0.64/0.72 (P2(a4,f6(a7))), % 0.64/0.72 inference(scs_inference,[],[14,21])). % 0.64/0.72 cnf(34,plain, % 0.64/0.72 (~E(f6(a7),f6(a4))+~E(a4,a7)), % 0.64/0.72 inference(scs_inference,[],[14,15,12,21,24,2,20,9,10,11])). % 0.64/0.72 cnf(43,plain, % 0.64/0.72 (~E(f6(a7),f6(a4))), % 0.64/0.72 inference(scs_inference,[],[25,34,24])). % 0.64/0.72 cnf(70,plain, % 0.64/0.72 (~E(a4,a7)), % 0.64/0.72 inference(scs_inference,[],[43,2,4])). % 0.64/0.72 cnf(71,plain, % 0.64/0.72 ($false), % 0.64/0.72 inference(scs_inference,[],[25,70,24]), % 0.64/0.72 ['proof']). % 0.64/0.72 % SZS output end Proof % 0.64/0.72 % Total time :0.070000s %------------------------------------------------------------------------------