%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET987+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 : n018.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 14:23:09 EDT 2024 % Result : Theorem 0.55s 0.89s % Output : CNFRefutation 0.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET987+1 : TPTP v8.2.0. Released v3.2.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n018.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 14:25:24 EDT 2024 % 0.12/0.33 % CPUTime : % 0.50/0.58 start to proof:theBenchmark % 0.55/0.88 %------------------------------------------- % 0.55/0.88 % File :CSE---1.7 % 0.55/0.88 % Problem :theBenchmark % 0.55/0.88 % Transform :cnf % 0.55/0.88 % Format :tptp:raw % 0.55/0.88 % Command :java -jar mcs_scs.jar %d %s % 0.55/0.88 % 0.55/0.88 % Result :Theorem 0.260000s % 0.55/0.88 % Output :CNFRefutation 0.260000s % 0.55/0.88 %------------------------------------------- % 0.55/0.89 %------------------------------------------------------------------------------ % 0.55/0.89 % File : SET987+1 : TPTP v8.2.0. Released v3.2.0. % 0.55/0.89 % Domain : Set theory % 0.55/0.89 % Problem : ~ in(A,B) => difference(union(B,singleton(A)),singleton(A)) = B % 0.55/0.89 % Version : [Urb06] axioms : Especial. % 0.55/0.89 % English : % 0.55/0.89 % 0.55/0.89 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.55/0.89 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.55/0.89 % Source : [Urb06] % 0.55/0.89 % Names : zfmisc_1__t141_zfmisc_1 [Urb06] % 0.55/0.89 % 0.55/0.89 % Status : Theorem % 0.55/0.89 % Rating : 0.08 v8.1.0, 0.06 v7.4.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.00 v7.0.0, 0.03 v6.4.0, 0.08 v6.1.0, 0.07 v6.0.0, 0.09 v5.5.0, 0.11 v5.3.0, 0.19 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.12 v3.7.0, 0.05 v3.3.0, 0.14 v3.2.0 % 0.55/0.89 % Syntax : Number of formulae : 10 ( 5 unt; 0 def) % 0.55/0.89 % Number of atoms : 15 ( 5 equ) % 0.55/0.89 % Maximal formula atoms : 2 ( 1 avg) % 0.55/0.89 % Number of connectives : 13 ( 8 ~; 0 |; 0 &) % 0.55/0.89 % ( 1 <=>; 4 =>; 0 <=; 0 <~>) % 0.55/0.89 % Maximal formula depth : 5 ( 4 avg) % 0.55/0.89 % Maximal term depth : 4 ( 1 avg) % 0.55/0.89 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 0.55/0.89 % Number of functors : 3 ( 3 usr; 0 con; 1-2 aty) % 0.55/0.89 % Number of variables : 18 ( 16 !; 2 ?) % 0.55/0.89 % SPC : FOF_THM_RFO_SEQ % 0.55/0.89 % 0.55/0.89 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.55/0.89 % library, www.mizar.org % 0.55/0.89 %------------------------------------------------------------------------------ % 0.55/0.89 fof(antisymmetry_r2_hidden,axiom, % 0.55/0.89 ! [A,B] : % 0.55/0.89 ( in(A,B) % 0.55/0.89 => ~ in(B,A) ) ). % 0.55/0.89 % 0.55/0.89 fof(commutativity_k2_xboole_0,axiom, % 0.55/0.89 ! [A,B] : set_union2(A,B) = set_union2(B,A) ). % 0.55/0.89 % 0.55/0.89 fof(fc2_xboole_0,axiom, % 0.55/0.89 ! [A,B] : % 0.55/0.89 ( ~ empty(A) % 0.55/0.89 => ~ empty(set_union2(A,B)) ) ). % 0.55/0.89 % 0.55/0.89 fof(fc3_xboole_0,axiom, % 0.55/0.89 ! [A,B] : % 0.55/0.89 ( ~ empty(A) % 0.55/0.89 => ~ empty(set_union2(B,A)) ) ). % 0.55/0.89 % 0.55/0.89 fof(idempotence_k2_xboole_0,axiom, % 0.55/0.89 ! [A,B] : set_union2(A,A) = A ). % 0.55/0.89 % 0.55/0.89 fof(rc1_xboole_0,axiom, % 0.55/0.89 ? [A] : empty(A) ). % 0.55/0.89 % 0.55/0.89 fof(rc2_xboole_0,axiom, % 0.55/0.89 ? [A] : ~ empty(A) ). % 0.55/0.89 % 0.55/0.89 fof(t141_zfmisc_1,conjecture, % 0.55/0.89 ! [A,B] : % 0.55/0.89 ( ~ in(A,B) % 0.55/0.89 => set_difference(set_union2(B,singleton(A)),singleton(A)) = B ) ). % 0.55/0.89 % 0.55/0.89 fof(t40_xboole_1,axiom, % 0.55/0.89 ! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B) ). % 0.55/0.89 % 0.55/0.89 fof(t65_zfmisc_1,axiom, % 0.55/0.89 ! [A,B] : % 0.55/0.89 ( set_difference(A,singleton(B)) = A % 0.55/0.89 <=> ~ in(B,A) ) ). % 0.55/0.89 % 0.55/0.89 %------------------------------------------------------------------------------ % 0.55/0.89 %------------------------------------------- % 0.55/0.89 % Proof found % 0.55/0.89 % SZS status Theorem for theBenchmark % 0.55/0.89 % SZS output start Proof % 0.55/0.89 %ClaNum:23(EqnAxiom:11) % 0.55/0.89 %VarNum:32(SingletonVarNum:15) % 0.55/0.89 %MaxLitNum:2 % 0.55/0.89 %MaxfuncDepth:2 % 0.55/0.89 %SharedTerms:11 % 0.55/0.89 %goalClause: 17 18 % 0.55/0.89 %singleGoalClaCount:2 % 0.55/0.89 [12]P1(a1) % 0.55/0.89 [16]~P1(a4) % 0.55/0.89 [17]~P2(a5,a6) % 0.55/0.89 [18]~E(f3(f2(a6,f7(a5)),f7(a5)),a6) % 0.55/0.89 [13]E(f2(x131,x131),x131) % 0.55/0.89 [14]E(f2(x141,x142),f2(x142,x141)) % 0.55/0.89 [15]E(f3(f2(x151,x152),x152),f3(x151,x152)) % 0.55/0.89 [20]~P2(x202,x201)+~P2(x201,x202) % 0.55/0.89 [21]P1(x211)+~P1(f2(x212,x211)) % 0.55/0.89 [22]P1(x221)+~P1(f2(x221,x222)) % 0.55/0.89 [19]P2(x192,x191)+E(f3(x191,f7(x192)),x191) % 0.55/0.89 [23]~P2(x232,x231)+~E(f3(x231,f7(x232)),x231) % 0.55/0.89 %EqnAxiom % 0.55/0.89 [1]E(x11,x11) % 0.55/0.89 [2]E(x22,x21)+~E(x21,x22) % 0.55/0.89 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.55/0.89 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.55/0.89 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.55/0.89 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63)) % 0.55/0.89 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72)) % 0.55/0.89 [8]~E(x81,x82)+E(f7(x81),f7(x82)) % 0.55/0.89 [9]~P1(x91)+P1(x92)+~E(x91,x92) % 0.55/0.89 [10]P2(x102,x103)+~E(x101,x102)+~P2(x101,x103) % 0.55/0.89 [11]P2(x113,x112)+~E(x111,x112)+~P2(x113,x111) % 0.55/0.89 % 0.55/0.89 %------------------------------------------- % 0.55/0.89 cnf(103,plain, % 0.55/0.89 (E(a6,f3(a6,f7(a5)))), % 0.55/0.89 inference(scs_inference,[],[17,2,19])). % 0.55/0.89 cnf(105,plain, % 0.55/0.89 ($false), % 0.55/0.89 inference(scs_inference,[],[18,103,15,2,3]), % 0.55/0.89 ['proof']). % 0.55/0.89 % SZS output end Proof % 0.55/0.89 % Total time :0.260000s %------------------------------------------------------------------------------