%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET930+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 14:23:02 EDT 2024 % Result : Theorem 0.71s 0.85s % Output : CNFRefutation 0.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : SET930+1 : TPTP v8.2.0. Released v3.2.0. % 0.10/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.11/0.32 % Computer : n028.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Sun Jun 23 12:02:09 EDT 2024 % 0.11/0.32 % CPUTime : % 0.17/0.57 start to proof:theBenchmark % 0.71/0.84 %------------------------------------------- % 0.71/0.84 % File :CSE---1.7 % 0.71/0.84 % Problem :theBenchmark % 0.71/0.84 % Transform :cnf % 0.71/0.84 % Format :tptp:raw % 0.71/0.84 % Command :java -jar mcs_scs.jar %d %s % 0.71/0.84 % 0.71/0.84 % Result :Theorem 0.220000s % 0.71/0.84 % Output :CNFRefutation 0.220000s % 0.71/0.84 %------------------------------------------- % 0.71/0.85 %------------------------------------------------------------------------------ % 0.71/0.85 % File : SET930+1 : TPTP v8.2.0. Released v3.2.0. % 0.71/0.85 % Domain : Set theory % 0.71/0.85 % Problem : Basic properties of sets, theorem 74 % 0.71/0.85 % Version : [Urb06] axioms : Especial. % 0.71/0.85 % English : ~ ( difference(unordered_pair(A,B),C) != empty_set % 0.71/0.85 % & difference(unordered_pair(A,B),C) != singleton(A) % 0.71/0.85 % & difference(unordered_pair(A,B),C) != singleton(B) % 0.71/0.85 % & difference(unordered_pair(A,B),C) != unordered_pair(A,B) ) % 0.71/0.85 % 0.71/0.85 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.71/0.85 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.71/0.85 % Source : [Urb06] % 0.71/0.85 % Names : zfmisc_1__t74_zfmisc_1 [Urb06] % 0.71/0.85 % 0.71/0.85 % Status : Theorem % 0.71/0.85 % Rating : 0.17 v8.2.0, 0.14 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.10 v7.3.0, 0.14 v7.2.0, 0.10 v7.1.0, 0.13 v7.0.0, 0.10 v6.4.0, 0.15 v6.3.0, 0.12 v6.2.0, 0.16 v6.1.0, 0.17 v6.0.0, 0.09 v5.5.0, 0.15 v5.4.0, 0.18 v5.3.0, 0.26 v5.2.0, 0.10 v5.0.0, 0.17 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.14 v3.2.0 % 0.71/0.85 % Syntax : Number of formulae : 9 ( 4 unt; 0 def) % 0.71/0.85 % Number of atoms : 20 ( 9 equ) % 0.71/0.85 % Maximal formula atoms : 4 ( 2 avg) % 0.71/0.85 % Number of connectives : 21 ( 10 ~; 1 |; 6 &) % 0.71/0.85 % ( 3 <=>; 1 =>; 0 <=; 0 <~>) % 0.71/0.85 % Maximal formula depth : 9 ( 5 avg) % 0.71/0.85 % Maximal term depth : 3 ( 1 avg) % 0.71/0.85 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 0.71/0.85 % Number of functors : 4 ( 4 usr; 1 con; 0-2 aty) % 0.71/0.85 % Number of variables : 18 ( 16 !; 2 ?) % 0.71/0.85 % SPC : FOF_THM_RFO_SEQ % 0.71/0.85 % 0.71/0.85 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.71/0.85 % library, www.mizar.org % 0.71/0.85 %------------------------------------------------------------------------------ % 0.71/0.85 fof(antisymmetry_r2_hidden,axiom, % 0.71/0.85 ! [A,B] : % 0.71/0.85 ( in(A,B) % 0.71/0.85 => ~ in(B,A) ) ). % 0.71/0.85 % 0.71/0.85 fof(commutativity_k2_tarski,axiom, % 0.71/0.85 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 0.71/0.85 % 0.71/0.85 fof(fc1_xboole_0,axiom, % 0.71/0.85 empty(empty_set) ). % 0.71/0.85 % 0.71/0.85 fof(l39_zfmisc_1,axiom, % 0.71/0.85 ! [A,B,C] : % 0.71/0.85 ( set_difference(unordered_pair(A,B),C) = singleton(A) % 0.71/0.85 <=> ( ~ in(A,C) % 0.71/0.85 & ( in(B,C) % 0.71/0.85 | A = B ) ) ) ). % 0.71/0.85 % 0.71/0.85 fof(rc1_xboole_0,axiom, % 0.71/0.85 ? [A] : empty(A) ). % 0.71/0.85 % 0.71/0.85 fof(rc2_xboole_0,axiom, % 0.71/0.85 ? [A] : ~ empty(A) ). % 0.71/0.85 % 0.71/0.85 fof(t72_zfmisc_1,axiom, % 0.71/0.85 ! [A,B,C] : % 0.71/0.85 ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) % 0.71/0.85 <=> ( ~ in(A,C) % 0.71/0.85 & ~ in(B,C) ) ) ). % 0.71/0.85 % 0.71/0.85 fof(t73_zfmisc_1,axiom, % 0.71/0.85 ! [A,B,C] : % 0.71/0.85 ( set_difference(unordered_pair(A,B),C) = empty_set % 0.71/0.85 <=> ( in(A,C) % 0.71/0.85 & in(B,C) ) ) ). % 0.71/0.85 % 0.71/0.85 fof(t74_zfmisc_1,conjecture, % 0.71/0.85 ! [A,B,C] : % 0.71/0.85 ~ ( set_difference(unordered_pair(A,B),C) != empty_set % 0.71/0.85 & set_difference(unordered_pair(A,B),C) != singleton(A) % 0.71/0.85 & set_difference(unordered_pair(A,B),C) != singleton(B) % 0.71/0.85 & set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ) ). % 0.71/0.85 % 0.71/0.85 %------------------------------------------------------------------------------ % 0.71/0.85 %------------------------------------------- % 0.71/0.85 % Proof found % 0.71/0.85 % SZS status Theorem for theBenchmark % 0.71/0.85 % SZS output start Proof % 0.71/0.85 %ClaNum:30(EqnAxiom:11) % 0.71/0.85 %VarNum:78(SingletonVarNum:34) % 0.71/0.85 %MaxLitNum:3 % 0.71/0.85 %MaxfuncDepth:2 % 0.78/0.85 %SharedTerms:17 % 0.78/0.85 %goalClause: 16 17 18 19 % 0.78/0.85 %singleGoalClaCount:4 % 0.78/0.85 [12]P1(a1) % 0.78/0.85 [13]P1(a2) % 0.78/0.85 [15]~P1(a4) % 0.78/0.85 [16]~E(f8(f3(a5,a6),a7),a1) % 0.78/0.85 [17]~E(f8(f3(a5,a6),a7),f9(a5)) % 0.78/0.85 [18]~E(f8(f3(a5,a6),a7),f9(a6)) % 0.78/0.85 [19]~E(f8(f3(a5,a6),a7),f3(a5,a6)) % 0.78/0.85 [14]E(f3(x141,x142),f3(x142,x141)) % 0.78/0.85 [20]~P2(x202,x201)+~P2(x201,x202) % 0.78/0.85 [22]P2(x221,x222)+~E(f8(f3(x223,x221),x222),a1) % 0.78/0.85 [23]P2(x231,x232)+~E(f8(f3(x231,x233),x232),a1) % 0.78/0.85 [28]~P2(x281,x283)+~E(f8(f3(x281,x282),x283),f9(x281)) % 0.78/0.85 [29]~P2(x292,x293)+~E(f8(f3(x291,x292),x293),f3(x291,x292)) % 0.78/0.85 [30]~P2(x301,x303)+~E(f8(f3(x301,x302),x303),f3(x301,x302)) % 0.78/0.85 [21]P2(x211,x213)+~E(x211,x212)+E(f8(f3(x211,x212),x213),f9(x211)) % 0.78/0.85 [24]P2(x241,x243)+~P2(x242,x243)+E(f8(f3(x241,x242),x243),f9(x241)) % 0.78/0.85 [25]P2(x252,x253)+P2(x251,x253)+E(f8(f3(x251,x252),x253),f3(x251,x252)) % 0.78/0.85 [26]~P2(x262,x263)+~P2(x261,x263)+E(f8(f3(x261,x262),x263),a1) % 0.78/0.85 [27]E(x271,x272)+P2(x271,x273)+~E(f8(f3(x272,x271),x273),f9(x272)) % 0.78/0.85 %EqnAxiom % 0.78/0.85 [1]E(x11,x11) % 0.78/0.85 [2]E(x22,x21)+~E(x21,x22) % 0.78/0.85 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.78/0.85 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43)) % 0.78/0.85 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52)) % 0.78/0.85 [6]~E(x61,x62)+E(f8(x61,x63),f8(x62,x63)) % 0.78/0.85 [7]~E(x71,x72)+E(f8(x73,x71),f8(x73,x72)) % 0.78/0.85 [8]~E(x81,x82)+E(f9(x81),f9(x82)) % 0.78/0.85 [9]~P1(x91)+P1(x92)+~E(x91,x92) % 0.78/0.85 [10]P2(x102,x103)+~E(x101,x102)+~P2(x101,x103) % 0.78/0.85 [11]P2(x113,x112)+~E(x111,x112)+~P2(x113,x111) % 0.78/0.85 % 0.78/0.85 %------------------------------------------- % 0.78/0.86 cnf(34,plain, % 0.78/0.86 (~P2(a6,a7)+~P2(a5,a7)), % 0.78/0.86 inference(scs_inference,[],[16,19,14,3,26])). % 0.78/0.86 cnf(43,plain, % 0.78/0.86 (P2(a5,a7)), % 0.78/0.86 inference(scs_inference,[],[19,17,25,24])). % 0.78/0.86 cnf(46,plain, % 0.78/0.86 (~P2(a6,a7)), % 0.78/0.86 inference(scs_inference,[],[43,34])). % 0.78/0.86 cnf(98,plain, % 0.78/0.86 (E(f9(a6),f8(f3(a6,a5),a7))), % 0.78/0.86 inference(scs_inference,[],[46,43,2,24])). % 0.78/0.86 cnf(99,plain, % 0.78/0.86 (E(f8(f3(a6,a5),a7),f9(a6))), % 0.78/0.86 inference(scs_inference,[],[98,2])). % 0.78/0.86 cnf(108,plain, % 0.78/0.86 ($false), % 0.78/0.86 inference(scs_inference,[],[18,99,14,3,6]), % 0.78/0.86 ['proof']). % 0.78/0.86 % SZS output end Proof % 0.78/0.86 % Total time :0.220000s %------------------------------------------------------------------------------