%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET874+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 : 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 14:22:51 EDT 2024 % Result : Theorem 5.73s 5.84s % Output : CNFRefutation 5.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.09 % Problem : SET874+1 : TPTP v8.2.0. Released v3.2.0. % 0.02/0.09 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.09/0.29 % Computer : n001.cluster.edu % 0.09/0.29 % Model : x86_64 x86_64 % 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.29 % Memory : 8042.1875MB % 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.29 % CPULimit : 300 % 0.09/0.29 % WCLimit : 300 % 0.09/0.29 % DateTime : Sun Jun 23 17:31:23 EDT 2024 % 0.09/0.29 % CPUTime : % 0.14/0.51 start to proof:theBenchmark % 5.73/5.83 %------------------------------------------- % 5.73/5.83 % File :CSE---1.7 % 5.73/5.83 % Problem :theBenchmark % 5.73/5.83 % Transform :cnf % 5.73/5.83 % Format :tptp:raw % 5.73/5.83 % Command :java -jar mcs_scs.jar %d %s % 5.73/5.83 % 5.73/5.83 % Result :Theorem 5.290000s % 5.73/5.83 % Output :CNFRefutation 5.290000s % 5.73/5.83 %------------------------------------------- % 5.73/5.84 %------------------------------------------------------------------------------ % 5.73/5.84 % File : SET874+1 : TPTP v8.2.0. Released v3.2.0. % 5.73/5.84 % Domain : Set theory % 5.73/5.84 % Problem : union(singleton(A),unordered_pair(A,B)) = unordered_pair(A,B) % 5.73/5.84 % Version : [Urb06] axioms : Especial. % 5.73/5.84 % English : % 5.73/5.84 % 5.73/5.84 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 5.73/5.84 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 5.73/5.84 % Source : [Urb06] % 5.73/5.84 % Names : zfmisc_1__t14_zfmisc_1 [Urb06] % 5.73/5.84 % 5.73/5.84 % Status : Theorem % 5.73/5.84 % Rating : 0.08 v7.5.0, 0.09 v7.4.0, 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, 0.13 v5.5.0, 0.11 v5.4.0, 0.18 v5.3.0, 0.26 v5.2.0, 0.05 v5.0.0, 0.21 v4.1.0, 0.22 v4.0.0, 0.21 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.21 v3.2.0 % 5.73/5.84 % Syntax : Number of formulae : 11 ( 6 unt; 0 def) % 5.73/5.84 % Number of atoms : 18 ( 8 equ) % 5.73/5.84 % Maximal formula atoms : 4 ( 1 avg) % 5.73/5.84 % Number of connectives : 13 ( 6 ~; 1 |; 0 &) % 5.73/5.84 % ( 2 <=>; 4 =>; 0 <=; 0 <~>) % 5.73/5.84 % Maximal formula depth : 8 ( 4 avg) % 5.73/5.84 % Maximal term depth : 3 ( 1 avg) % 5.73/5.84 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 5.73/5.84 % Number of functors : 3 ( 3 usr; 0 con; 1-2 aty) % 5.73/5.84 % Number of variables : 22 ( 20 !; 2 ?) % 5.73/5.84 % SPC : FOF_THM_RFO_SEQ % 5.73/5.84 % 5.73/5.84 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 5.73/5.84 % library, www.mizar.org % 5.73/5.84 %------------------------------------------------------------------------------ % 5.73/5.84 fof(antisymmetry_r2_hidden,axiom, % 5.73/5.84 ! [A,B] : % 5.73/5.84 ( in(A,B) % 5.73/5.84 => ~ in(B,A) ) ). % 5.73/5.84 % 5.73/5.84 fof(commutativity_k2_tarski,axiom, % 5.73/5.84 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 5.73/5.84 % 5.73/5.84 fof(commutativity_k2_xboole_0,axiom, % 5.73/5.84 ! [A,B] : set_union2(A,B) = set_union2(B,A) ). % 5.73/5.84 % 5.73/5.84 fof(d2_tarski,axiom, % 5.73/5.84 ! [A,B,C] : % 5.73/5.84 ( C = unordered_pair(A,B) % 5.73/5.84 <=> ! [D] : % 5.73/5.84 ( in(D,C) % 5.73/5.84 <=> ( D = A % 5.73/5.84 | D = B ) ) ) ). % 5.73/5.84 % 5.73/5.84 fof(fc2_xboole_0,axiom, % 5.73/5.84 ! [A,B] : % 5.73/5.84 ( ~ empty(A) % 5.73/5.84 => ~ empty(set_union2(A,B)) ) ). % 5.73/5.84 % 5.73/5.84 fof(fc3_xboole_0,axiom, % 5.73/5.84 ! [A,B] : % 5.73/5.84 ( ~ empty(A) % 5.73/5.84 => ~ empty(set_union2(B,A)) ) ). % 5.73/5.84 % 5.73/5.84 fof(idempotence_k2_xboole_0,axiom, % 5.73/5.84 ! [A,B] : set_union2(A,A) = A ). % 5.73/5.84 % 5.73/5.84 fof(l23_zfmisc_1,axiom, % 5.73/5.84 ! [A,B] : % 5.73/5.84 ( in(A,B) % 5.73/5.84 => set_union2(singleton(A),B) = B ) ). % 5.73/5.84 % 5.73/5.84 fof(rc1_xboole_0,axiom, % 5.73/5.84 ? [A] : empty(A) ). % 5.73/5.84 % 5.73/5.84 fof(rc2_xboole_0,axiom, % 5.73/5.84 ? [A] : ~ empty(A) ). % 5.73/5.84 % 5.73/5.84 fof(t14_zfmisc_1,conjecture, % 5.73/5.84 ! [A,B] : set_union2(singleton(A),unordered_pair(A,B)) = unordered_pair(A,B) ). % 5.73/5.84 % 5.73/5.84 %------------------------------------------------------------------------------ % 5.73/5.84 %------------------------------------------- % 5.73/5.84 % Proof found % 5.73/5.84 % SZS status Theorem for theBenchmark % 5.73/5.84 % SZS output start Proof % 5.73/5.84 %ClaNum:30(EqnAxiom:14) % 5.73/5.84 %VarNum:86(SingletonVarNum:34) % 5.73/5.84 %MaxLitNum:4 % 5.73/5.84 %MaxfuncDepth:2 % 5.73/5.84 %SharedTerms:10 % 5.73/5.84 %goalClause: 20 % 5.73/5.84 %singleGoalClaCount:1 % 5.73/5.84 [15]P1(a1) % 5.73/5.84 [19]~P1(a4) % 5.73/5.84 [20]~E(f3(f8(a5),f7(a5,a6)),f7(a5,a6)) % 5.73/5.84 [16]E(f3(x161,x161),x161) % 5.73/5.84 [17]E(f7(x171,x172),f7(x172,x171)) % 5.73/5.84 [18]E(f3(x181,x182),f3(x182,x181)) % 5.73/5.84 [24]~P2(x242,x241)+~P2(x241,x242) % 5.73/5.84 [26]P1(x261)+~P1(f3(x262,x261)) % 5.73/5.84 [27]P1(x271)+~P1(f3(x271,x272)) % 5.73/5.84 [23]~P2(x231,x232)+E(f3(f8(x231),x232),x232) % 5.73/5.84 [29]~E(f2(x292,x293,x291),x293)+~P2(f2(x292,x293,x291),x291)+E(x291,f7(x292,x293)) % 5.73/5.84 [30]~E(f2(x302,x303,x301),x302)+~P2(f2(x302,x303,x301),x301)+E(x301,f7(x302,x303)) % 5.73/5.84 [21]P2(x211,x212)+~E(x211,x213)+~E(x212,f7(x214,x213)) % 5.73/5.84 [22]P2(x221,x222)+~E(x221,x223)+~E(x222,f7(x223,x224)) % 5.73/5.84 [28]E(f2(x282,x283,x281),x283)+E(f2(x282,x283,x281),x282)+P2(f2(x282,x283,x281),x281)+E(x281,f7(x282,x283)) % 5.73/5.84 [25]~P2(x251,x254)+E(x251,x252)+E(x251,x253)+~E(x254,f7(x253,x252)) % 5.73/5.84 %EqnAxiom % 5.73/5.84 [1]E(x11,x11) % 5.73/5.84 [2]E(x22,x21)+~E(x21,x22) % 5.73/5.84 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 5.73/5.84 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43)) % 5.73/5.84 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52)) % 5.73/5.84 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63)) % 5.73/5.84 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72)) % 5.73/5.84 [8]~E(x81,x82)+E(f2(x81,x83,x84),f2(x82,x83,x84)) % 5.73/5.84 [9]~E(x91,x92)+E(f2(x93,x91,x94),f2(x93,x92,x94)) % 5.73/5.84 [10]~E(x101,x102)+E(f2(x103,x104,x101),f2(x103,x104,x102)) % 5.73/5.84 [11]~E(x111,x112)+E(f8(x111),f8(x112)) % 5.73/5.84 [12]~P1(x121)+P1(x122)+~E(x121,x122) % 5.73/5.84 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133) % 5.73/5.84 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141) % 5.73/5.84 % 5.73/5.84 %------------------------------------------- % 5.73/5.85 cnf(31,plain, % 5.73/5.85 (~P2(x311,f7(x312,x313))+E(x311,x313)+E(x311,x312)), % 5.73/5.85 inference(equality_inference,[],[25])). % 5.73/5.85 cnf(32,plain, % 5.73/5.85 (~P2(a5,f7(a5,a6))), % 5.73/5.85 inference(scs_inference,[],[20,23])). % 5.73/5.85 cnf(34,plain, % 5.73/5.85 (E(x341,f3(x341,x341))), % 5.73/5.85 inference(scs_inference,[],[20,16,23,2])). % 5.73/5.85 cnf(1558,plain, % 5.73/5.85 (E(f7(f3(x15581,x15582),x15583),f7(f3(x15582,x15581),x15583))), % 5.73/5.85 inference(scs_inference,[],[18,2,6])). % 5.73/5.85 cnf(1560,plain, % 5.73/5.85 (E(f7(f3(x15601,x15602),x15603),f7(f3(x15602,x15601),x15603))), % 5.73/5.85 inference(rename_variables,[],[1558])). % 5.73/5.85 cnf(1562,plain, % 5.73/5.85 (P2(f3(x15621,x15622),f7(f3(x15623,x15624),f3(x15622,x15621)))), % 5.73/5.85 inference(scs_inference,[],[18,1558,1560,22,21])). % 5.73/5.85 cnf(2507,plain, % 5.73/5.85 (P2(x25071,f7(f3(x25071,x25071),x25072))), % 5.73/5.85 inference(scs_inference,[],[34,1558,22])). % 5.73/5.85 cnf(2508,plain, % 5.73/5.85 (E(f7(f3(x25081,x25082),x25083),f7(f3(x25082,x25081),x25083))), % 5.73/5.85 inference(rename_variables,[],[1558])). % 5.73/5.85 cnf(2511,plain, % 5.73/5.85 (E(x25111,f3(x25111,x25111))), % 5.73/5.85 inference(rename_variables,[],[34])). % 5.73/5.85 cnf(2512,plain, % 5.73/5.85 (P2(x25121,f7(f3(x25122,x25123),f3(x25121,x25121)))), % 5.73/5.85 inference(scs_inference,[],[34,2511,1558,2508,1562,22,13,21])). % 5.73/5.85 cnf(2529,plain, % 5.73/5.85 (E(f7(x25291,x25292),f7(x25292,x25291))), % 5.73/5.85 inference(rename_variables,[],[17])). % 5.73/5.85 cnf(2535,plain, % 5.73/5.85 ($false), % 5.73/5.85 inference(scs_inference,[],[34,32,2512,2507,16,17,2529,24,14,22,21,31,6]), % 5.73/5.85 ['proof']). % 5.73/5.85 % SZS output end Proof % 5.73/5.85 % Total time :5.290000s %------------------------------------------------------------------------------