%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET891+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 : n022.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 14:22:54 EDT 2024 % Result : Theorem 0.19s 0.59s % Output : CNFRefutation 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET891+1 : TPTP v8.2.0. Released v3.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n022.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 15:05:09 EDT 2024 % 0.12/0.33 % CPUTime : % 0.19/0.56 start to proof:theBenchmark % 0.19/0.59 %------------------------------------------- % 0.19/0.59 % File :CSE---1.7 % 0.19/0.59 % Problem :theBenchmark % 0.19/0.59 % Transform :cnf % 0.19/0.59 % Format :tptp:raw % 0.19/0.59 % Command :java -jar mcs_scs.jar %d %s % 0.19/0.59 % 0.19/0.59 % Result :Theorem 0.000000s % 0.19/0.59 % Output :CNFRefutation 0.000000s % 0.19/0.59 %------------------------------------------- % 0.19/0.59 %------------------------------------------------------------------------------ % 0.19/0.59 % File : SET891+1 : TPTP v8.2.0. Released v3.2.0. % 0.19/0.59 % Domain : Set theory % 0.19/0.59 % Problem : union(uno_pair(singleton(A),singleton(B))) = uno_pair(A,B) % 0.19/0.59 % Version : [Urb06] axioms : Especial. % 0.19/0.59 % English : % 0.19/0.59 % 0.19/0.59 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.19/0.59 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.19/0.59 % Source : [Urb06] % 0.19/0.59 % Names : zfmisc_1__t32_zfmisc_1 [Urb06] % 0.19/0.59 % 0.19/0.59 % Status : Theorem % 0.19/0.59 % Rating : 0.06 v8.1.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.1.0, 0.20 v6.0.0, 0.13 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.19 v5.2.0, 0.05 v5.0.0, 0.12 v4.1.0, 0.17 v4.0.1, 0.22 v4.0.0, 0.21 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.07 v3.2.0 % 0.19/0.59 % Syntax : Number of formulae : 10 ( 8 unt; 0 def) % 0.19/0.59 % Number of atoms : 12 ( 6 equ) % 0.19/0.59 % Maximal formula atoms : 2 ( 1 avg) % 0.19/0.59 % Number of connectives : 7 ( 5 ~; 0 |; 0 &) % 0.19/0.59 % ( 0 <=>; 2 =>; 0 <=; 0 <~>) % 0.19/0.59 % Maximal formula depth : 5 ( 3 avg) % 0.19/0.59 % Maximal term depth : 4 ( 1 avg) % 0.19/0.59 % Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty) % 0.19/0.59 % Number of functors : 4 ( 4 usr; 0 con; 1-2 aty) % 0.19/0.59 % Number of variables : 18 ( 16 !; 2 ?) % 0.19/0.59 % SPC : FOF_THM_RFO_SEQ % 0.19/0.59 % 0.19/0.59 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.19/0.59 % library, www.mizar.org % 0.19/0.59 %------------------------------------------------------------------------------ % 0.19/0.59 fof(commutativity_k2_tarski,axiom, % 0.19/0.59 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 0.19/0.59 % 0.19/0.59 fof(commutativity_k2_xboole_0,axiom, % 0.19/0.59 ! [A,B] : set_union2(A,B) = set_union2(B,A) ). % 0.19/0.59 % 0.19/0.59 fof(fc2_xboole_0,axiom, % 0.19/0.59 ! [A,B] : % 0.19/0.59 ( ~ empty(A) % 0.19/0.59 => ~ empty(set_union2(A,B)) ) ). % 0.19/0.59 % 0.19/0.59 fof(fc3_xboole_0,axiom, % 0.19/0.59 ! [A,B] : % 0.19/0.59 ( ~ empty(A) % 0.19/0.59 => ~ empty(set_union2(B,A)) ) ). % 0.19/0.59 % 0.19/0.59 fof(idempotence_k2_xboole_0,axiom, % 0.19/0.59 ! [A,B] : set_union2(A,A) = A ). % 0.19/0.59 % 0.19/0.59 fof(l52_zfmisc_1,axiom, % 0.19/0.59 ! [A,B] : union(unordered_pair(A,B)) = set_union2(A,B) ). % 0.19/0.59 % 0.19/0.59 fof(rc1_xboole_0,axiom, % 0.19/0.59 ? [A] : empty(A) ). % 0.19/0.59 % 0.19/0.59 fof(rc2_xboole_0,axiom, % 0.19/0.59 ? [A] : ~ empty(A) ). % 0.19/0.59 % 0.19/0.59 fof(t32_zfmisc_1,conjecture, % 0.19/0.59 ! [A,B] : union(unordered_pair(singleton(A),singleton(B))) = unordered_pair(A,B) ). % 0.19/0.59 % 0.19/0.59 fof(t41_enumset1,axiom, % 0.19/0.59 ! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)) ). % 0.19/0.59 % 0.19/0.59 %------------------------------------------------------------------------------ % 0.19/0.59 %------------------------------------------- % 0.19/0.59 % Proof found % 0.19/0.59 % SZS status Theorem for theBenchmark % 0.19/0.59 % SZS output start Proof % 0.19/0.59 %ClaNum:17(EqnAxiom:8) % 0.19/0.59 %VarNum:21(SingletonVarNum:11) % 0.19/0.59 %MaxLitNum:2 % 0.19/0.59 %MaxfuncDepth:3 % 0.19/0.59 %SharedTerms:12 % 0.19/0.59 %goalClause: 15 % 0.19/0.59 %singleGoalClaCount:1 % 0.19/0.59 [9]P1(a1) % 0.19/0.59 [14]~P1(a5) % 0.19/0.59 [15]~E(f3(f2(f4(a6),f4(a7))),f2(a6,a7)) % 0.19/0.59 [11]E(f3(f2(x111,x111)),x111) % 0.19/0.59 [10]E(f2(x101,x102),f2(x102,x101)) % 0.19/0.59 [12]E(f3(f2(x121,x122)),f3(f2(x122,x121))) % 0.19/0.59 [13]E(f3(f2(f4(x131),f4(x132))),f2(x131,x132)) % 0.19/0.59 [16]P1(x161)+~P1(f3(f2(x162,x161))) % 0.19/0.59 [17]P1(x171)+~P1(f3(f2(x171,x172))) % 0.19/0.59 %EqnAxiom % 0.19/0.59 [1]E(x11,x11) % 0.19/0.59 [2]E(x22,x21)+~E(x21,x22) % 0.19/0.59 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.19/0.59 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.19/0.59 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.19/0.59 [6]~E(x61,x62)+E(f3(x61),f3(x62)) % 0.19/0.59 [7]~E(x71,x72)+E(f4(x71),f4(x72)) % 0.19/0.59 [8]~P1(x81)+P1(x82)+~E(x81,x82) % 0.19/0.59 % 0.19/0.59 %------------------------------------------- % 0.19/0.60 cnf(18,plain, % 0.19/0.60 ($false), % 0.19/0.60 inference(scs_inference,[],[15,13]), % 0.19/0.60 ['proof']). % 0.19/0.60 % SZS output end Proof % 0.19/0.60 % Total time :0.000000s %------------------------------------------------------------------------------