%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET882+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 12.52s 12.61s % Output : CNFRefutation 12.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SET882+1 : TPTP v8.2.0. Released v3.2.0. % 0.08/0.12 % 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 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sun Jun 23 17:52:09 EDT 2024 % 0.12/0.34 % CPUTime : % 0.52/0.56 start to proof:theBenchmark % 12.52/12.60 %------------------------------------------- % 12.52/12.60 % File :CSE---1.7 % 12.52/12.60 % Problem :theBenchmark % 12.52/12.60 % Transform :cnf % 12.52/12.60 % Format :tptp:raw % 12.52/12.60 % Command :java -jar mcs_scs.jar %d %s % 12.52/12.60 % 12.52/12.60 % Result :Theorem 12.010000s % 12.52/12.60 % Output :CNFRefutation 12.010000s % 12.52/12.60 %------------------------------------------- % 12.52/12.61 %------------------------------------------------------------------------------ % 12.52/12.61 % File : SET882+1 : TPTP v8.2.0. Released v3.2.0. % 12.52/12.61 % Domain : Set theory % 12.52/12.61 % Problem : A != B => diff(unordered_pair(A,B),singleton(B)) = singleton(A) % 12.52/12.61 % Version : [Urb06] axioms : Especial. % 12.52/12.61 % English : % 12.52/12.61 % 12.52/12.61 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 12.52/12.61 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 12.52/12.61 % Source : [Urb06] % 12.52/12.61 % Names : zfmisc_1__t23_zfmisc_1 [Urb06] % 12.52/12.61 % 12.52/12.61 % Status : Theorem % 12.52/12.61 % Rating : 0.14 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.2.0, 0.28 v6.1.0, 0.27 v6.0.0, 0.22 v5.5.0, 0.11 v5.4.0, 0.14 v5.3.0, 0.26 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 v3.4.0, 0.16 v3.3.0, 0.21 v3.2.0 % 12.52/12.61 % Syntax : Number of formulae : 7 ( 3 unt; 0 def) % 12.52/12.61 % Number of atoms : 14 ( 7 equ) % 12.52/12.61 % Maximal formula atoms : 4 ( 2 avg) % 12.52/12.61 % Number of connectives : 11 ( 4 ~; 1 |; 1 &) % 12.52/12.61 % ( 3 <=>; 2 =>; 0 <=; 0 <~>) % 12.52/12.61 % Maximal formula depth : 7 ( 4 avg) % 12.52/12.61 % Maximal term depth : 3 ( 1 avg) % 12.52/12.61 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 12.52/12.61 % Number of functors : 3 ( 3 usr; 0 con; 1-2 aty) % 12.52/12.61 % Number of variables : 14 ( 12 !; 2 ?) % 12.52/12.61 % SPC : FOF_THM_RFO_SEQ % 12.52/12.61 % 12.52/12.61 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 12.52/12.61 % library, www.mizar.org % 12.52/12.61 %------------------------------------------------------------------------------ % 12.52/12.61 fof(antisymmetry_r2_hidden,axiom, % 12.52/12.61 ! [A,B] : % 12.52/12.61 ( in(A,B) % 12.52/12.61 => ~ in(B,A) ) ). % 12.52/12.61 % 12.52/12.61 fof(commutativity_k2_tarski,axiom, % 12.52/12.61 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 12.52/12.61 % 12.52/12.61 fof(d1_tarski,axiom, % 12.52/12.61 ! [A,B] : % 12.52/12.61 ( B = singleton(A) % 12.52/12.61 <=> ! [C] : % 12.52/12.61 ( in(C,B) % 12.52/12.61 <=> C = A ) ) ). % 12.52/12.61 % 12.52/12.61 fof(l39_zfmisc_1,axiom, % 12.52/12.61 ! [A,B,C] : % 12.52/12.61 ( set_difference(unordered_pair(A,B),C) = singleton(A) % 12.52/12.61 <=> ( ~ in(A,C) % 12.52/12.61 & ( in(B,C) % 12.52/12.61 | A = B ) ) ) ). % 12.52/12.61 % 12.52/12.61 fof(rc1_xboole_0,axiom, % 12.52/12.61 ? [A] : empty(A) ). % 12.52/12.61 % 12.52/12.61 fof(rc2_xboole_0,axiom, % 12.52/12.61 ? [A] : ~ empty(A) ). % 12.52/12.61 % 12.52/12.61 fof(t23_zfmisc_1,conjecture, % 12.52/12.61 ! [A,B] : % 12.52/12.61 ( A != B % 12.52/12.61 => set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ) ). % 12.52/12.61 % 12.52/12.61 %------------------------------------------------------------------------------ % 12.52/12.61 %------------------------------------------- % 12.52/12.61 % Proof found % 12.52/12.61 % SZS status Theorem for theBenchmark % 12.52/12.61 % SZS output start Proof % 12.52/12.61 %ClaNum:27(EqnAxiom:13) % 12.52/12.61 %VarNum:66(SingletonVarNum:26) % 12.52/12.61 %MaxLitNum:3 % 12.52/12.61 %MaxfuncDepth:2 % 12.52/12.61 %SharedTerms:12 % 12.52/12.61 %goalClause: 16 18 % 12.52/12.61 %singleGoalClaCount:2 % 12.52/12.61 [14]P1(a1) % 12.52/12.61 [16]~E(a4,a6) % 12.52/12.61 [17]~P1(a5) % 12.52/12.61 [18]~E(f8(f3(a4,a6),f7(a6)),f7(a4)) % 12.52/12.61 [15]E(f3(x151,x152),f3(x152,x151)) % 12.52/12.61 [21]~P2(x212,x211)+~P2(x211,x212) % 12.52/12.61 [26]~P2(x261,x263)+~E(f8(f3(x261,x262),x263),f7(x261)) % 12.52/12.61 [22]E(f2(x222,x221),x222)+P2(f2(x222,x221),x221)+E(x221,f7(x222)) % 12.52/12.61 [27]~E(f2(x272,x271),x272)+~P2(f2(x272,x271),x271)+E(x271,f7(x272)) % 12.52/12.61 [19]P2(x191,x192)+~E(x191,x193)+~E(x192,f7(x193)) % 12.52/12.61 [20]~P2(x201,x203)+E(x201,x202)+~E(x203,f7(x202)) % 12.52/12.61 [23]P2(x231,x233)+~E(x231,x232)+E(f8(f3(x231,x232),x233),f7(x231)) % 12.52/12.61 [24]P2(x241,x243)+~P2(x242,x243)+E(f8(f3(x241,x242),x243),f7(x241)) % 12.52/12.61 [25]E(x251,x252)+P2(x251,x253)+~E(f8(f3(x252,x251),x253),f7(x252)) % 12.52/12.61 %EqnAxiom % 12.52/12.61 [1]E(x11,x11) % 12.52/12.61 [2]E(x22,x21)+~E(x21,x22) % 12.52/12.61 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 12.52/12.61 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43)) % 12.52/12.61 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52)) % 12.52/12.61 [6]~E(x61,x62)+E(f2(x61,x63),f2(x62,x63)) % 12.52/12.61 [7]~E(x71,x72)+E(f2(x73,x71),f2(x73,x72)) % 12.52/12.61 [8]~E(x81,x82)+E(f7(x81),f7(x82)) % 12.52/12.61 [9]~E(x91,x92)+E(f8(x91,x93),f8(x92,x93)) % 12.52/12.61 [10]~E(x101,x102)+E(f8(x103,x101),f8(x103,x102)) % 12.52/12.61 [11]~P1(x111)+P1(x112)+~E(x111,x112) % 12.52/12.61 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123) % 12.52/12.61 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131) % 12.52/12.61 % 12.52/12.61 %------------------------------------------- % 12.52/12.61 cnf(28,plain, % 12.52/12.61 (~P2(x281,f7(x282))+E(x281,x282)), % 12.52/12.61 inference(equality_inference,[],[20])). % 12.52/12.61 cnf(29,plain, % 12.52/12.61 (P2(x291,x292)+E(f8(f3(x291,x291),x292),f7(x291))), % 12.52/12.61 inference(equality_inference,[],[23])). % 12.52/12.61 cnf(32,plain, % 12.52/12.61 (~P2(a6,f7(a6))), % 12.52/12.61 inference(scs_inference,[],[16,18,28,24])). % 12.52/12.61 cnf(58,plain, % 12.52/12.61 (E(f8(f3(x581,x581),f7(a6)),f7(x581))+~E(x581,a6)), % 12.52/12.61 inference(scs_inference,[],[32,12,29])). % 12.52/12.61 cnf(59,plain, % 12.52/12.61 (E(f8(f3(a6,a6),f7(a6)),f7(a6))), % 12.52/12.61 inference(equality_inference,[],[58])). % 12.52/12.61 cnf(761,plain, % 12.52/12.61 (~P2(a6,f8(f3(a6,a6),f7(a6)))), % 12.52/12.61 inference(scs_inference,[],[59,26,13])). % 12.52/12.61 cnf(795,plain, % 12.52/12.61 ($false), % 12.52/12.61 inference(scs_inference,[],[761,59,19]), % 12.52/12.61 ['proof']). % 12.52/12.61 % SZS output end Proof % 12.52/12.61 % Total time :12.010000s %------------------------------------------------------------------------------