%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET903+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 : n026.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 14:22:55 EDT 2024 % Result : Theorem 0.57s 0.62s % Output : CNFRefutation 0.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET903+1 : TPTP v8.2.0. Released v3.2.0. % 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.13/0.35 % Computer : n026.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sun Jun 23 11:26:24 EDT 2024 % 0.13/0.35 % CPUTime : % 0.21/0.58 start to proof:theBenchmark % 0.57/0.62 %------------------------------------------- % 0.57/0.62 % File :CSE---1.7 % 0.57/0.62 % Problem :theBenchmark % 0.57/0.62 % Transform :cnf % 0.57/0.62 % Format :tptp:raw % 0.57/0.62 % Command :java -jar mcs_scs.jar %d %s % 0.57/0.62 % 0.57/0.62 % Result :Theorem 0.010000s % 0.57/0.62 % Output :CNFRefutation 0.010000s % 0.57/0.62 %------------------------------------------- % 0.57/0.62 %------------------------------------------------------------------------------ % 0.57/0.62 % File : SET903+1 : TPTP v8.2.0. Released v3.2.0. % 0.57/0.62 % Domain : Set theory % 0.57/0.62 % Problem : ~ ( sgtn(A) = union(B,C) & B != C & B != empty & C != empty ) % 0.57/0.62 % Version : [Urb06] axioms : Especial. % 0.57/0.62 % English : % 0.57/0.62 % 0.57/0.62 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.57/0.62 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.57/0.62 % Source : [Urb06] % 0.57/0.62 % Names : zfmisc_1__t44_zfmisc_1 [Urb06] % 0.57/0.62 % 0.57/0.62 % Status : Theorem % 0.57/0.62 % Rating : 0.11 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.04 v6.2.0, 0.12 v6.1.0, 0.13 v6.0.0, 0.04 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.19 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.13 v4.0.1, 0.17 v3.7.0, 0.05 v3.4.0, 0.11 v3.3.0, 0.14 v3.2.0 % 0.57/0.62 % Syntax : Number of formulae : 9 ( 5 unt; 0 def) % 0.57/0.62 % Number of atoms : 20 ( 13 equ) % 0.57/0.62 % Maximal formula atoms : 7 ( 2 avg) % 0.57/0.62 % Number of connectives : 24 ( 13 ~; 0 |; 9 &) % 0.57/0.62 % ( 0 <=>; 2 =>; 0 <=; 0 <~>) % 0.57/0.62 % Maximal formula depth : 10 ( 5 avg) % 0.57/0.62 % Maximal term depth : 2 ( 1 avg) % 0.57/0.62 % Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty) % 0.57/0.62 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty) % 0.57/0.62 % Number of variables : 16 ( 14 !; 2 ?) % 0.57/0.62 % SPC : FOF_THM_RFO_SEQ % 0.57/0.62 % 0.57/0.62 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.57/0.62 % library, www.mizar.org % 0.57/0.62 %------------------------------------------------------------------------------ % 0.57/0.62 fof(commutativity_k2_xboole_0,axiom, % 0.57/0.62 ! [A,B] : set_union2(A,B) = set_union2(B,A) ). % 0.57/0.62 % 0.57/0.62 fof(fc1_xboole_0,axiom, % 0.57/0.62 empty(empty_set) ). % 0.57/0.62 % 0.57/0.62 fof(fc2_xboole_0,axiom, % 0.57/0.62 ! [A,B] : % 0.57/0.62 ( ~ empty(A) % 0.57/0.62 => ~ empty(set_union2(A,B)) ) ). % 0.57/0.62 % 0.57/0.62 fof(fc3_xboole_0,axiom, % 0.57/0.62 ! [A,B] : % 0.57/0.62 ( ~ empty(A) % 0.57/0.62 => ~ empty(set_union2(B,A)) ) ). % 0.57/0.62 % 0.57/0.62 fof(idempotence_k2_xboole_0,axiom, % 0.57/0.62 ! [A,B] : set_union2(A,A) = A ). % 0.57/0.62 % 0.57/0.62 fof(rc1_xboole_0,axiom, % 0.57/0.62 ? [A] : empty(A) ). % 0.57/0.62 % 0.57/0.62 fof(rc2_xboole_0,axiom, % 0.57/0.62 ? [A] : ~ empty(A) ). % 0.57/0.62 % 0.57/0.62 fof(t43_zfmisc_1,axiom, % 0.57/0.62 ! [A,B,C] : % 0.57/0.62 ~ ( singleton(A) = set_union2(B,C) % 0.57/0.62 & ~ ( B = singleton(A) % 0.57/0.62 & C = singleton(A) ) % 0.57/0.62 & ~ ( B = empty_set % 0.57/0.62 & C = singleton(A) ) % 0.57/0.62 & ~ ( B = singleton(A) % 0.57/0.62 & C = empty_set ) ) ). % 0.57/0.62 % 0.57/0.62 fof(t44_zfmisc_1,conjecture, % 0.57/0.62 ! [A,B,C] : % 0.57/0.62 ~ ( singleton(A) = set_union2(B,C) % 0.57/0.62 & B != C % 0.57/0.62 & B != empty_set % 0.57/0.62 & C != empty_set ) ). % 0.57/0.62 % 0.57/0.62 %------------------------------------------------------------------------------ % 0.57/0.62 %------------------------------------------- % 0.57/0.62 % Proof found % 0.57/0.62 % SZS status Theorem for theBenchmark % 0.57/0.62 % SZS output start Proof % 0.57/0.63 %ClaNum:26(EqnAxiom:7) % 0.57/0.63 %VarNum:32(SingletonVarNum:16) % 0.57/0.63 %MaxLitNum:3 % 0.57/0.63 %MaxfuncDepth:1 % 0.57/0.63 %SharedTerms:15 % 0.57/0.63 %goalClause: 10 13 14 15 % 0.57/0.63 %singleGoalClaCount:4 % 0.57/0.63 [8]P1(a1) % 0.57/0.63 [9]P1(a2) % 0.57/0.63 [13]~E(a3,a1) % 0.57/0.63 [14]~E(a6,a1) % 0.57/0.63 [15]~E(a6,a3) % 0.57/0.63 [16]~P1(a5) % 0.57/0.63 [10]E(f7(a3,a6),f8(a4)) % 0.57/0.63 [11]E(f7(x111,x111),x111) % 0.57/0.63 [12]E(f7(x121,x122),f7(x122,x121)) % 0.57/0.63 [25]P1(x251)+~P1(f7(x252,x251)) % 0.57/0.63 [26]P1(x261)+~P1(f7(x261,x262)) % 0.57/0.63 [17]E(x171,a1)+E(x171,f8(x172))+~E(f8(x172),f7(x173,x171)) % 0.57/0.63 [18]E(x181,a1)+E(x181,f8(x182))+~E(f8(x182),f7(x181,x183)) % 0.57/0.63 [22]~E(f8(x222),f7(x223,x221))+E(x221,f8(x222))+E(x223,f8(x222)) % 0.57/0.63 %EqnAxiom % 0.57/0.63 [1]E(x11,x11) % 0.57/0.63 [2]E(x22,x21)+~E(x21,x22) % 0.57/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.57/0.63 [4]~E(x41,x42)+E(f7(x41,x43),f7(x42,x43)) % 0.57/0.63 [5]~E(x51,x52)+E(f7(x53,x51),f7(x53,x52)) % 0.57/0.63 [6]~E(x61,x62)+E(f8(x61),f8(x62)) % 0.57/0.63 [7]~P1(x71)+P1(x72)+~E(x71,x72) % 0.57/0.63 % 0.57/0.63 %------------------------------------------- % 0.59/0.63 cnf(29,plain, % 0.59/0.63 (E(f7(x291,x291),x291)), % 0.59/0.63 inference(rename_variables,[],[11])). % 0.59/0.63 cnf(32,plain, % 0.59/0.63 (E(a6,f8(a4))), % 0.59/0.63 inference(scs_inference,[],[10,14,11,29,16,2,3,7,17])). % 0.59/0.63 cnf(34,plain, % 0.59/0.63 (E(a3,f8(a4))), % 0.59/0.63 inference(scs_inference,[],[10,13,14,11,29,16,2,3,7,17,18])). % 0.59/0.63 cnf(65,plain, % 0.59/0.63 ($false), % 0.59/0.63 inference(scs_inference,[],[15,34,32,2,3]), % 0.59/0.63 ['proof']). % 0.59/0.63 % SZS output end Proof % 0.59/0.63 % Total time :0.010000s %------------------------------------------------------------------------------