%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET979+1 : TPTP v8.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n017.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 0.16s 0.53s % Output : CNFRefutation 0.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.10 % Problem : SET979+1 : TPTP v8.2.0. Released v3.2.0. % 0.03/0.10 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.10/0.30 % Computer : n017.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 300 % 0.10/0.30 % DateTime : Sun Jun 23 12:00:23 EDT 2024 % 0.10/0.30 % CPUTime : % 0.16/0.50 start to proof:theBenchmark % 0.16/0.52 %------------------------------------------- % 0.16/0.52 % File :CSE---1.7 % 0.16/0.52 % Problem :theBenchmark % 0.16/0.52 % Transform :cnf % 0.16/0.52 % Format :tptp:raw % 0.16/0.52 % Command :java -jar mcs_scs.jar %d %s % 0.16/0.52 % 0.16/0.52 % Result :Theorem 0.000000s % 0.16/0.52 % Output :CNFRefutation 0.000000s % 0.16/0.52 %------------------------------------------- % 0.16/0.53 %------------------------------------------------------------------------------ % 0.16/0.53 % File : SET979+1 : TPTP v8.2.0. Released v3.2.0. % 0.16/0.53 % Domain : Set theory % 0.16/0.53 % Problem : Basic properties of sets, theorem 132 % 0.16/0.53 % Version : [Urb06] axioms : Especial. % 0.16/0.53 % English : % 0.16/0.53 % 0.16/0.53 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.16/0.53 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.16/0.53 % Source : [Urb06] % 0.16/0.53 % Names : zfmisc_1__t132_zfmisc_1 [Urb06] % 0.16/0.53 % 0.16/0.53 % Status : Theorem % 0.16/0.53 % Rating : 0.14 v8.1.0, 0.19 v7.5.0, 0.22 v7.4.0, 0.13 v7.3.0, 0.10 v7.1.0, 0.09 v7.0.0, 0.10 v6.4.0, 0.12 v6.2.0, 0.20 v6.0.0, 0.13 v5.5.0, 0.19 v5.4.0, 0.21 v5.3.0, 0.30 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.12 v4.1.0, 0.17 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.07 v3.2.0 % 0.16/0.53 % Syntax : Number of formulae : 10 ( 6 unt; 0 def) % 0.16/0.53 % Number of atoms : 14 ( 8 equ) % 0.16/0.53 % Maximal formula atoms : 2 ( 1 avg) % 0.16/0.53 % Number of connectives : 9 ( 5 ~; 0 |; 2 &) % 0.16/0.53 % ( 0 <=>; 2 =>; 0 <=; 0 <~>) % 0.16/0.53 % Maximal formula depth : 5 ( 4 avg) % 0.16/0.53 % Maximal term depth : 4 ( 2 avg) % 0.16/0.53 % Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty) % 0.16/0.53 % Number of functors : 4 ( 4 usr; 0 con; 1-2 aty) % 0.16/0.53 % Number of variables : 20 ( 18 !; 2 ?) % 0.16/0.53 % SPC : FOF_THM_RFO_SEQ % 0.16/0.53 % 0.16/0.53 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.16/0.53 % library, www.mizar.org % 0.16/0.53 %------------------------------------------------------------------------------ % 0.16/0.53 fof(commutativity_k2_tarski,axiom, % 0.16/0.53 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 0.16/0.53 % 0.16/0.53 fof(commutativity_k2_xboole_0,axiom, % 0.16/0.53 ! [A,B] : set_union2(A,B) = set_union2(B,A) ). % 0.16/0.53 % 0.16/0.53 fof(fc2_xboole_0,axiom, % 0.16/0.53 ! [A,B] : % 0.16/0.53 ( ~ empty(A) % 0.16/0.53 => ~ empty(set_union2(A,B)) ) ). % 0.16/0.53 % 0.16/0.53 fof(fc3_xboole_0,axiom, % 0.16/0.53 ! [A,B] : % 0.16/0.53 ( ~ empty(A) % 0.16/0.53 => ~ empty(set_union2(B,A)) ) ). % 0.16/0.53 % 0.16/0.53 fof(idempotence_k2_xboole_0,axiom, % 0.16/0.53 ! [A,B] : set_union2(A,A) = A ). % 0.16/0.53 % 0.16/0.53 fof(rc1_xboole_0,axiom, % 0.16/0.53 ? [A] : empty(A) ). % 0.16/0.53 % 0.16/0.53 fof(rc2_xboole_0,axiom, % 0.16/0.53 ? [A] : ~ empty(A) ). % 0.16/0.53 % 0.16/0.53 fof(t120_zfmisc_1,axiom, % 0.16/0.53 ! [A,B,C] : % 0.16/0.53 ( cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)) % 0.16/0.53 & cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B)) ) ). % 0.16/0.53 % 0.16/0.53 fof(t132_zfmisc_1,conjecture, % 0.16/0.53 ! [A,B,C] : % 0.16/0.53 ( cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)) % 0.16/0.53 & cartesian_product2(C,unordered_pair(A,B)) = set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B))) ) ). % 0.16/0.53 % 0.16/0.53 fof(t41_enumset1,axiom, % 0.16/0.53 ! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)) ). % 0.16/0.53 % 0.16/0.53 %------------------------------------------------------------------------------ % 0.16/0.53 %------------------------------------------- % 0.16/0.53 % Proof found % 0.16/0.53 % SZS status Theorem for theBenchmark % 0.16/0.53 % SZS output start Proof % 0.16/0.53 %ClaNum:19(EqnAxiom:9) % 0.16/0.53 %VarNum:27(SingletonVarNum:13) % 0.16/0.53 %MaxLitNum:2 % 0.16/0.53 %MaxfuncDepth:3 % 0.16/0.53 %SharedTerms:26 % 0.16/0.53 %goalClause: 19 % 0.16/0.53 [10]P1(a1) % 0.16/0.53 [16]~P1(a4) % 0.16/0.53 [11]E(f3(x111,x111),x111) % 0.16/0.53 [12]E(f3(x121,x122),f3(x122,x121)) % 0.16/0.53 [14]E(f3(f2(x141,x142),f2(x141,x143)),f2(x141,f3(x142,x143))) % 0.16/0.53 [15]E(f3(f2(x151,x152),f2(x153,x152)),f2(f3(x151,x153),x152)) % 0.16/0.53 [19]~E(f3(f2(a5,f11(a6)),f2(a5,f11(a10))),f2(a5,f3(f11(a6),f11(a10))))+~E(f3(f2(f11(a7),a8),f2(f11(a9),a8)),f2(f3(f11(a7),f11(a9)),a8)) % 0.16/0.53 [17]P1(x171)+~P1(f3(x172,x171)) % 0.16/0.53 [18]P1(x181)+~P1(f3(x181,x182)) % 0.16/0.53 %EqnAxiom % 0.16/0.53 [1]E(x11,x11) % 0.16/0.53 [2]E(x22,x21)+~E(x21,x22) % 0.16/0.53 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.16/0.53 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43)) % 0.16/0.53 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52)) % 0.16/0.53 [6]~E(x61,x62)+E(f2(x61,x63),f2(x62,x63)) % 0.16/0.53 [7]~E(x71,x72)+E(f2(x73,x71),f2(x73,x72)) % 0.16/0.53 [8]~E(x81,x82)+E(f11(x81),f11(x82)) % 0.16/0.53 [9]~P1(x91)+P1(x92)+~E(x91,x92) % 0.16/0.53 % 0.16/0.53 %------------------------------------------- % 0.16/0.53 cnf(20,plain, % 0.16/0.53 ($false), % 0.16/0.53 inference(scs_inference,[],[14,15,19]), % 0.16/0.53 ['proof']). % 0.16/0.53 % SZS output end Proof % 0.16/0.53 % Total time :0.000000s %------------------------------------------------------------------------------