%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET977+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 : n032.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 14:23:08 EDT 2024 % Result : Theorem 0.14s 0.54s % Output : CNFRefutation 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : SET977+1 : TPTP v8.2.0. Released v3.2.0. % 0.00/0.09 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.09/0.28 % Computer : n032.cluster.edu % 0.09/0.28 % Model : x86_64 x86_64 % 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.28 % Memory : 8042.1875MB % 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.28 % CPULimit : 300 % 0.09/0.28 % WCLimit : 300 % 0.09/0.28 % DateTime : Sun Jun 23 12:15:24 EDT 2024 % 0.09/0.28 % CPUTime : % 0.14/0.46 start to proof:theBenchmark % 0.14/0.54 %------------------------------------------- % 0.14/0.54 % File :CSE---1.7 % 0.14/0.54 % Problem :theBenchmark % 0.14/0.54 % Transform :cnf % 0.14/0.54 % Format :tptp:raw % 0.14/0.54 % Command :java -jar mcs_scs.jar %d %s % 0.14/0.54 % 0.14/0.54 % Result :Theorem 0.040000s % 0.14/0.54 % Output :CNFRefutation 0.040000s % 0.14/0.54 %------------------------------------------- % 0.14/0.54 %------------------------------------------------------------------------------ % 0.14/0.54 % File : SET977+1 : TPTP v8.2.0. Released v3.2.0. % 0.14/0.54 % Domain : Set theory % 0.14/0.54 % Problem : Basic properties of sets, theorem 130 % 0.14/0.54 % Version : [Urb06] axioms : Especial. % 0.14/0.54 % English : % 0.14/0.54 % 0.14/0.54 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.14/0.54 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.14/0.54 % Source : [Urb06] % 0.14/0.54 % Names : zfmisc_1__t130_zfmisc_1 [Urb06] % 0.14/0.54 % 0.14/0.54 % Status : Theorem % 0.14/0.54 % Rating : 0.33 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 0.34 v7.4.0, 0.30 v7.3.0, 0.34 v7.2.0, 0.31 v7.1.0, 0.30 v7.0.0, 0.23 v6.4.0, 0.27 v6.3.0, 0.25 v6.2.0, 0.32 v6.1.0, 0.30 v6.0.0, 0.26 v5.4.0, 0.25 v5.3.0, 0.26 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.25 v4.1.0, 0.17 v4.0.1, 0.13 v4.0.0, 0.12 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.21 v3.2.0 % 0.14/0.54 % Syntax : Number of formulae : 11 ( 6 unt; 0 def) % 0.14/0.54 % Number of atoms : 19 ( 8 equ) % 0.14/0.54 % Maximal formula atoms : 3 ( 1 avg) % 0.14/0.54 % Number of connectives : 15 ( 7 ~; 0 |; 3 &) % 0.14/0.54 % ( 3 <=>; 2 =>; 0 <=; 0 <~>) % 0.14/0.54 % Maximal formula depth : 7 ( 4 avg) % 0.14/0.54 % Maximal term depth : 3 ( 1 avg) % 0.14/0.54 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 0.14/0.54 % Number of functors : 5 ( 5 usr; 1 con; 0-2 aty) % 0.14/0.54 % Number of variables : 22 ( 20 !; 2 ?) % 0.14/0.54 % SPC : FOF_THM_RFO_SEQ % 0.14/0.54 % 0.14/0.54 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.14/0.54 % library, www.mizar.org % 0.14/0.54 %------------------------------------------------------------------------------ % 0.14/0.54 fof(antisymmetry_r2_hidden,axiom, % 0.14/0.54 ! [A,B] : % 0.14/0.54 ( in(A,B) % 0.14/0.54 => ~ in(B,A) ) ). % 0.14/0.54 % 0.14/0.54 fof(commutativity_k2_tarski,axiom, % 0.14/0.54 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 0.14/0.54 % 0.14/0.54 fof(d1_xboole_0,axiom, % 0.14/0.54 ! [A] : % 0.14/0.54 ( A = empty_set % 0.14/0.54 <=> ! [B] : ~ in(B,A) ) ). % 0.14/0.54 % 0.14/0.54 fof(d5_tarski,axiom, % 0.14/0.54 ! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) ). % 0.14/0.54 % 0.14/0.54 fof(fc1_xboole_0,axiom, % 0.14/0.54 empty(empty_set) ). % 0.14/0.54 % 0.14/0.54 fof(fc1_zfmisc_1,axiom, % 0.14/0.54 ! [A,B] : ~ empty(ordered_pair(A,B)) ). % 0.14/0.54 % 0.14/0.54 fof(rc1_xboole_0,axiom, % 0.14/0.54 ? [A] : empty(A) ). % 0.14/0.54 % 0.14/0.54 fof(rc2_xboole_0,axiom, % 0.14/0.54 ? [A] : ~ empty(A) ). % 0.14/0.54 % 0.14/0.54 fof(t128_zfmisc_1,axiom, % 0.14/0.54 ! [A,B,C,D] : % 0.14/0.54 ( in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) % 0.14/0.54 <=> ( A = C % 0.14/0.54 & in(B,D) ) ) ). % 0.14/0.54 % 0.14/0.54 fof(t129_zfmisc_1,axiom, % 0.14/0.54 ! [A,B,C,D] : % 0.14/0.54 ( in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) % 0.14/0.54 <=> ( in(A,C) % 0.14/0.54 & B = D ) ) ). % 0.14/0.54 % 0.14/0.54 fof(t130_zfmisc_1,conjecture, % 0.14/0.54 ! [A,B] : % 0.14/0.54 ( A != empty_set % 0.14/0.54 => ( cartesian_product2(singleton(B),A) != empty_set % 0.14/0.54 & cartesian_product2(A,singleton(B)) != empty_set ) ) ). % 0.14/0.54 % 0.14/0.54 %------------------------------------------------------------------------------ % 0.14/0.54 %------------------------------------------- % 0.14/0.54 % Proof found % 0.14/0.54 % SZS status Theorem for theBenchmark % 0.14/0.54 % SZS output start Proof % 0.14/0.55 %ClaNum:28(EqnAxiom:12) % 0.14/0.55 %VarNum:63(SingletonVarNum:33) % 0.14/0.55 %MaxLitNum:3 % 0.14/0.55 %MaxfuncDepth:2 % 0.14/0.55 %SharedTerms:16 % 0.14/0.55 %goalClause: 16 21 % 0.14/0.55 %singleGoalClaCount:1 % 0.14/0.55 [13]P1(a1) % 0.14/0.55 [14]P1(a3) % 0.14/0.55 [16]~E(a6,a1) % 0.14/0.55 [17]~P1(a7) % 0.14/0.55 [15]E(f5(x151,x152),f5(x152,x151)) % 0.14/0.55 [18]~P1(f5(f5(x181,x182),f8(x181))) % 0.14/0.55 [21]E(f2(a6,f8(a9)),a1)+E(f2(f8(a10),a6),a1) % 0.14/0.55 [19]P2(f4(x191),x191)+E(x191,a1) % 0.14/0.55 [20]~P2(x202,x201)+~E(x201,a1) % 0.14/0.55 [22]~P2(x222,x221)+~P2(x221,x222) % 0.14/0.55 [25]E(x251,x252)+~P2(f5(f5(x253,x251),f8(x253)),f2(x254,f8(x252))) % 0.14/0.55 [26]E(x261,x262)+~P2(f5(f5(x261,x263),f8(x261)),f2(f8(x262),x264)) % 0.14/0.55 [27]P2(x271,x272)+~P2(f5(f5(x271,x273),f8(x271)),f2(x272,f8(x274))) % 0.14/0.55 [28]P2(x281,x282)+~P2(f5(f5(x283,x281),f8(x283)),f2(f8(x284),x282)) % 0.14/0.55 [23]~E(x232,x234)+~P2(x231,x233)+P2(f5(f5(x231,x232),f8(x231)),f2(x233,f8(x234))) % 0.14/0.55 [24]~E(x241,x243)+~P2(x242,x244)+P2(f5(f5(x241,x242),f8(x241)),f2(f8(x243),x244)) % 0.14/0.55 %EqnAxiom % 0.14/0.55 [1]E(x11,x11) % 0.14/0.55 [2]E(x22,x21)+~E(x21,x22) % 0.14/0.55 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.14/0.55 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43)) % 0.14/0.55 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52)) % 0.14/0.55 [6]~E(x61,x62)+E(f2(x61,x63),f2(x62,x63)) % 0.14/0.55 [7]~E(x71,x72)+E(f2(x73,x71),f2(x73,x72)) % 0.14/0.55 [8]~E(x81,x82)+E(f8(x81),f8(x82)) % 0.14/0.55 [9]~E(x91,x92)+E(f4(x91),f4(x92)) % 0.14/0.55 [10]~P1(x101)+P1(x102)+~E(x101,x102) % 0.14/0.55 [11]P2(x112,x113)+~E(x111,x112)+~P2(x111,x113) % 0.14/0.55 [12]P2(x123,x122)+~E(x121,x122)+~P2(x123,x121) % 0.14/0.55 % 0.14/0.55 %------------------------------------------- % 0.14/0.55 cnf(29,plain, % 0.14/0.55 (~P2(x291,a1)), % 0.14/0.55 inference(equality_inference,[],[20])). % 0.14/0.55 cnf(30,plain, % 0.14/0.55 (~P2(x302,x303)+P2(f5(f5(x302,x301),f8(x302)),f2(x303,f8(x301)))), % 0.14/0.55 inference(equality_inference,[],[23])). % 0.14/0.55 cnf(31,plain, % 0.14/0.55 (~P2(x312,x313)+P2(f5(f5(x311,x312),f8(x311)),f2(f8(x311),x313))), % 0.14/0.55 inference(equality_inference,[],[24])). % 0.14/0.55 cnf(32,plain, % 0.14/0.55 (P2(f4(a6),a6)), % 0.14/0.55 inference(scs_inference,[],[16,19])). % 0.14/0.55 cnf(65,plain, % 0.14/0.55 (~E(f2(a6,f8(x651)),a1)), % 0.14/0.55 inference(scs_inference,[],[29,32,12,30])). % 0.14/0.55 cnf(66,plain, % 0.14/0.55 (E(f2(f8(a10),a6),a1)), % 0.14/0.55 inference(scs_inference,[],[65,21])). % 0.14/0.55 cnf(71,plain, % 0.14/0.55 ($false), % 0.14/0.55 inference(scs_inference,[],[32,66,20,2,31]), % 0.14/0.55 ['proof']). % 0.14/0.55 % SZS output end Proof % 0.14/0.55 % Total time :0.040000s %------------------------------------------------------------------------------