%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET904+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 : 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 14:22:56 EDT 2024 % Result : Theorem 0.20s 0.59s % Output : CNFRefutation 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET904+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 : n017.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 13:42:54 EDT 2024 % 0.12/0.33 % CPUTime : % 0.20/0.55 start to proof:theBenchmark % 0.20/0.58 %------------------------------------------- % 0.20/0.58 % File :CSE---1.7 % 0.20/0.58 % Problem :theBenchmark % 0.20/0.58 % Transform :cnf % 0.20/0.58 % Format :tptp:raw % 0.20/0.58 % Command :java -jar mcs_scs.jar %d %s % 0.20/0.58 % 0.20/0.58 % Result :Theorem 0.000000s % 0.20/0.58 % Output :CNFRefutation 0.000000s % 0.20/0.58 %------------------------------------------- % 0.20/0.58 %------------------------------------------------------------------------------ % 0.20/0.58 % File : SET904+1 : TPTP v8.2.0. Released v3.2.0. % 0.20/0.58 % Domain : Set theory % 0.20/0.58 % Problem : subset(set_union2(singleton(A),B),B) => in(A,B) % 0.20/0.58 % Version : [Urb06] axioms : Especial. % 0.20/0.58 % English : % 0.20/0.58 % 0.20/0.58 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.20/0.58 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.20/0.58 % Source : [Urb06] % 0.20/0.58 % Names : zfmisc_1__t45_zfmisc_1 [Urb06] % 0.20/0.58 % 0.20/0.58 % Status : Theorem % 0.20/0.58 % Rating : 0.00 v6.4.0, 0.04 v6.2.0, 0.08 v6.1.0, 0.13 v5.5.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.05 v5.0.0, 0.04 v4.0.1, 0.09 v4.0.0, 0.08 v3.7.0, 0.05 v3.3.0, 0.00 v3.2.0 % 0.20/0.58 % Syntax : Number of formulae : 10 ( 5 unt; 0 def) % 0.20/0.58 % Number of atoms : 15 ( 2 equ) % 0.20/0.58 % Maximal formula atoms : 2 ( 1 avg) % 0.20/0.58 % Number of connectives : 11 ( 6 ~; 0 |; 0 &) % 0.20/0.58 % ( 0 <=>; 5 =>; 0 <=; 0 <~>) % 0.20/0.58 % Maximal formula depth : 5 ( 4 avg) % 0.20/0.58 % Maximal term depth : 3 ( 1 avg) % 0.20/0.58 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty) % 0.20/0.58 % Number of functors : 2 ( 2 usr; 0 con; 1-2 aty) % 0.20/0.58 % Number of variables : 18 ( 16 !; 2 ?) % 0.20/0.58 % SPC : FOF_THM_RFO_SEQ % 0.20/0.58 % 0.20/0.58 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.20/0.58 % library, www.mizar.org % 0.20/0.58 %------------------------------------------------------------------------------ % 0.20/0.58 fof(fc2_xboole_0,axiom, % 0.20/0.58 ! [A,B] : % 0.20/0.58 ( ~ empty(A) % 0.20/0.58 => ~ empty(set_union2(A,B)) ) ). % 0.20/0.58 % 0.20/0.58 fof(fc3_xboole_0,axiom, % 0.20/0.58 ! [A,B] : % 0.20/0.58 ( ~ empty(A) % 0.20/0.58 => ~ empty(set_union2(B,A)) ) ). % 0.20/0.59 % 0.20/0.59 fof(commutativity_k2_xboole_0,axiom, % 0.20/0.59 ! [A,B] : set_union2(A,B) = set_union2(B,A) ). % 0.20/0.59 % 0.20/0.59 fof(idempotence_k2_xboole_0,axiom, % 0.20/0.59 ! [A,B] : set_union2(A,A) = A ). % 0.20/0.59 % 0.20/0.59 fof(reflexivity_r1_tarski,axiom, % 0.20/0.59 ! [A,B] : subset(A,A) ). % 0.20/0.59 % 0.20/0.59 fof(antisymmetry_r2_hidden,axiom, % 0.20/0.59 ! [A,B] : % 0.20/0.59 ( in(A,B) % 0.20/0.59 => ~ in(B,A) ) ). % 0.20/0.59 % 0.20/0.59 fof(rc1_xboole_0,axiom, % 0.20/0.59 ? [A] : empty(A) ). % 0.20/0.59 % 0.20/0.59 fof(rc2_xboole_0,axiom, % 0.20/0.59 ? [A] : ~ empty(A) ). % 0.20/0.59 % 0.20/0.59 fof(t45_zfmisc_1,conjecture, % 0.20/0.59 ! [A,B] : % 0.20/0.59 ( subset(set_union2(singleton(A),B),B) % 0.20/0.59 => in(A,B) ) ). % 0.20/0.59 % 0.20/0.59 fof(l21_zfmisc_1,axiom, % 0.20/0.59 ! [A,B] : % 0.20/0.59 ( subset(set_union2(singleton(A),B),B) % 0.20/0.59 => in(A,B) ) ). % 0.20/0.59 % 0.20/0.59 %------------------------------------------------------------------------------ % 0.20/0.59 %------------------------------------------- % 0.20/0.59 % Proof found % 0.20/0.59 % SZS status Theorem for theBenchmark % 0.20/0.59 % SZS output start Proof % 0.54/0.59 %ClaNum:22(EqnAxiom:11) % 0.54/0.59 %VarNum:24(SingletonVarNum:12) % 0.54/0.59 %MaxLitNum:2 % 0.54/0.59 %MaxfuncDepth:2 % 0.54/0.59 %SharedTerms:10 % 0.54/0.59 %goalClause: 16 18 % 0.54/0.59 %singleGoalClaCount:2 % 0.54/0.59 [12]P1(a1) % 0.54/0.59 [17]~P1(a4) % 0.54/0.59 [18]~P3(a3,a5) % 0.54/0.59 [16]P2(f2(f6(a3),a5),a5) % 0.54/0.59 [13]P2(x131,x131) % 0.54/0.59 [14]E(f2(x141,x141),x141) % 0.54/0.59 [15]E(f2(x151,x152),f2(x152,x151)) % 0.54/0.59 [19]~P3(x192,x191)+~P3(x191,x192) % 0.54/0.59 [20]P1(x201)+~P1(f2(x202,x201)) % 0.54/0.59 [21]P1(x211)+~P1(f2(x211,x212)) % 0.54/0.59 [22]P3(x221,x222)+~P2(f2(f6(x221),x222),x222) % 0.54/0.59 %EqnAxiom % 0.54/0.59 [1]E(x11,x11) % 0.54/0.59 [2]E(x22,x21)+~E(x21,x22) % 0.54/0.59 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.54/0.59 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.54/0.59 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.54/0.59 [6]~E(x61,x62)+E(f6(x61),f6(x62)) % 0.54/0.59 [7]~P1(x71)+P1(x72)+~E(x71,x72) % 0.54/0.59 [8]P2(x82,x83)+~E(x81,x82)+~P2(x81,x83) % 0.54/0.59 [9]P2(x93,x92)+~E(x91,x92)+~P2(x93,x91) % 0.54/0.59 [10]P3(x102,x103)+~E(x101,x102)+~P3(x101,x103) % 0.54/0.59 [11]P3(x113,x112)+~E(x111,x112)+~P3(x113,x111) % 0.54/0.59 % 0.54/0.59 %------------------------------------------- % 0.54/0.59 cnf(23,plain, % 0.54/0.59 ($false), % 0.54/0.59 inference(scs_inference,[],[18,16,22]), % 0.54/0.59 ['proof']). % 0.54/0.59 % SZS output end Proof % 0.54/0.59 % Total time :0.000000s %------------------------------------------------------------------------------