%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET881+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 : n028.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 0.45s 0.62s % Output : CNFRefutation 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET881+1 : TPTP v8.2.0. Released v3.2.0. % 0.06/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n028.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 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sun Jun 23 14:24:39 EDT 2024 % 0.12/0.33 % CPUTime : % 0.45/0.57 start to proof:theBenchmark % 0.45/0.62 %------------------------------------------- % 0.45/0.62 % File :CSE---1.7 % 0.45/0.62 % Problem :theBenchmark % 0.45/0.62 % Transform :cnf % 0.45/0.62 % Format :tptp:raw % 0.45/0.62 % Command :java -jar mcs_scs.jar %d %s % 0.45/0.62 % 0.45/0.62 % Result :Theorem 0.000000s % 0.45/0.62 % Output :CNFRefutation 0.000000s % 0.45/0.62 %------------------------------------------- % 0.45/0.62 %------------------------------------------------------------------------------ % 0.45/0.62 % File : SET881+1 : TPTP v8.2.0. Released v3.2.0. % 0.45/0.62 % Domain : Set theory % 0.45/0.62 % Problem : difference(singleton(A),unordered_pair(A,B)) = empty_set % 0.45/0.62 % Version : [Urb06] axioms : Especial. % 0.45/0.62 % English : % 0.45/0.62 % 0.45/0.62 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.45/0.62 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.45/0.62 % Source : [Urb06] % 0.45/0.62 % Names : zfmisc_1__t22_zfmisc_1 [Urb06] % 0.45/0.62 % 0.45/0.62 % Status : Theorem % 0.45/0.62 % Rating : 0.06 v8.1.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.2.0, 0.20 v6.1.0, 0.23 v6.0.0, 0.17 v5.5.0, 0.11 v5.4.0, 0.18 v5.3.0, 0.19 v5.2.0, 0.00 v5.0.0, 0.17 v4.0.1, 0.22 v4.0.0, 0.21 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.14 v3.2.0 % 0.45/0.62 % Syntax : Number of formulae : 8 ( 5 unt; 0 def) % 0.45/0.62 % Number of atoms : 13 ( 6 equ) % 0.45/0.62 % Maximal formula atoms : 4 ( 1 avg) % 0.45/0.62 % Number of connectives : 7 ( 2 ~; 1 |; 0 &) % 0.45/0.62 % ( 3 <=>; 1 =>; 0 <=; 0 <~>) % 0.45/0.62 % Maximal formula depth : 8 ( 4 avg) % 0.45/0.62 % Maximal term depth : 3 ( 1 avg) % 0.45/0.62 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 0.45/0.62 % Number of functors : 4 ( 4 usr; 1 con; 0-2 aty) % 0.45/0.62 % Number of variables : 14 ( 12 !; 2 ?) % 0.45/0.62 % SPC : FOF_THM_RFO_SEQ % 0.45/0.62 % 0.45/0.62 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.45/0.62 % library, www.mizar.org % 0.45/0.62 %------------------------------------------------------------------------------ % 0.45/0.62 fof(antisymmetry_r2_hidden,axiom, % 0.45/0.62 ! [A,B] : % 0.45/0.62 ( in(A,B) % 0.45/0.62 => ~ in(B,A) ) ). % 0.45/0.62 % 0.45/0.62 fof(commutativity_k2_tarski,axiom, % 0.45/0.62 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 0.45/0.62 % 0.45/0.62 fof(d2_tarski,axiom, % 0.45/0.62 ! [A,B,C] : % 0.45/0.62 ( C = unordered_pair(A,B) % 0.45/0.62 <=> ! [D] : % 0.45/0.62 ( in(D,C) % 0.45/0.62 <=> ( D = A % 0.45/0.62 | D = B ) ) ) ). % 0.45/0.62 % 0.45/0.62 fof(fc1_xboole_0,axiom, % 0.45/0.62 empty(empty_set) ). % 0.45/0.62 % 0.45/0.62 fof(l36_zfmisc_1,axiom, % 0.45/0.62 ! [A,B] : % 0.45/0.62 ( set_difference(singleton(A),B) = empty_set % 0.45/0.62 <=> in(A,B) ) ). % 0.45/0.62 % 0.45/0.62 fof(rc1_xboole_0,axiom, % 0.45/0.62 ? [A] : empty(A) ). % 0.45/0.62 % 0.45/0.62 fof(rc2_xboole_0,axiom, % 0.45/0.62 ? [A] : ~ empty(A) ). % 0.45/0.62 % 0.45/0.62 fof(t22_zfmisc_1,conjecture, % 0.45/0.62 ! [A,B] : set_difference(singleton(A),unordered_pair(A,B)) = empty_set ). % 0.45/0.62 % 0.45/0.62 %------------------------------------------------------------------------------ % 0.45/0.62 %------------------------------------------- % 0.45/0.62 % Proof found % 0.45/0.62 % SZS status Theorem for theBenchmark % 0.45/0.62 % SZS output start Proof % 0.45/0.62 %ClaNum:28(EqnAxiom:14) % 0.45/0.62 %VarNum:76(SingletonVarNum:29) % 0.45/0.62 %MaxLitNum:4 % 0.45/0.62 %MaxfuncDepth:2 % 0.45/0.62 %SharedTerms:12 % 0.45/0.62 %goalClause: 19 % 0.45/0.62 %singleGoalClaCount:1 % 0.45/0.62 [15]P1(a1) % 0.45/0.62 [16]P1(a2) % 0.45/0.62 [18]~P1(a5) % 0.45/0.62 [19]~E(f9(f7(a6),f4(a6,a8)),a1) % 0.45/0.62 [17]E(f4(x171,x172),f4(x172,x171)) % 0.45/0.62 [23]~P2(x232,x231)+~P2(x231,x232) % 0.45/0.62 [22]~P2(x221,x222)+E(f9(f7(x221),x222),a1) % 0.45/0.62 [24]P2(x241,x242)+~E(f9(f7(x241),x242),a1) % 0.45/0.62 [27]~E(f3(x272,x273,x271),x273)+~P2(f3(x272,x273,x271),x271)+E(x271,f4(x272,x273)) % 0.45/0.62 [28]~E(f3(x282,x283,x281),x282)+~P2(f3(x282,x283,x281),x281)+E(x281,f4(x282,x283)) % 0.45/0.62 [20]P2(x201,x202)+~E(x201,x203)+~E(x202,f4(x204,x203)) % 0.45/0.62 [21]P2(x211,x212)+~E(x211,x213)+~E(x212,f4(x213,x214)) % 0.45/0.62 [26]E(f3(x262,x263,x261),x263)+E(f3(x262,x263,x261),x262)+P2(f3(x262,x263,x261),x261)+E(x261,f4(x262,x263)) % 0.45/0.62 [25]~P2(x251,x254)+E(x251,x252)+E(x251,x253)+~E(x254,f4(x253,x252)) % 0.45/0.62 %EqnAxiom % 0.45/0.62 [1]E(x11,x11) % 0.45/0.62 [2]E(x22,x21)+~E(x21,x22) % 0.45/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.45/0.62 [4]~E(x41,x42)+E(f4(x41,x43),f4(x42,x43)) % 0.45/0.62 [5]~E(x51,x52)+E(f4(x53,x51),f4(x53,x52)) % 0.45/0.62 [6]~E(x61,x62)+E(f3(x61,x63,x64),f3(x62,x63,x64)) % 0.45/0.62 [7]~E(x71,x72)+E(f3(x73,x71,x74),f3(x73,x72,x74)) % 0.45/0.62 [8]~E(x81,x82)+E(f3(x83,x84,x81),f3(x83,x84,x82)) % 0.45/0.62 [9]~E(x91,x92)+E(f7(x91),f7(x92)) % 0.45/0.62 [10]~E(x101,x102)+E(f9(x101,x103),f9(x102,x103)) % 0.45/0.62 [11]~E(x111,x112)+E(f9(x113,x111),f9(x113,x112)) % 0.45/0.62 [12]~P1(x121)+P1(x122)+~E(x121,x122) % 0.45/0.62 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133) % 0.45/0.62 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141) % 0.45/0.62 % 0.45/0.62 %------------------------------------------- % 0.45/0.63 cnf(30,plain, % 0.45/0.63 (~P2(a6,f4(a6,a8))), % 0.45/0.63 inference(scs_inference,[],[19,22])). % 0.45/0.63 cnf(47,plain, % 0.45/0.63 ($false), % 0.45/0.63 inference(scs_inference,[],[30,17,20]), % 0.45/0.63 ['proof']). % 0.45/0.63 % SZS output end Proof % 0.45/0.63 % Total time :0.000000s %------------------------------------------------------------------------------