%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET985+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 : 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 14:23:09 EDT 2024 % Result : Theorem 3.03s 3.11s % Output : CNFRefutation 3.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET985+1 : TPTP v8.2.0. Released v3.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox/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 17:26:54 EDT 2024 % 0.12/0.33 % CPUTime : % 0.44/0.57 start to proof:theBenchmark % 3.03/3.11 %------------------------------------------- % 3.03/3.11 % File :CSE---1.7 % 3.03/3.11 % Problem :theBenchmark % 3.03/3.11 % Transform :cnf % 3.03/3.11 % Format :tptp:raw % 3.03/3.11 % Command :java -jar mcs_scs.jar %d %s % 3.03/3.11 % 3.03/3.11 % Result :Theorem 2.500000s % 3.03/3.11 % Output :CNFRefutation 2.500000s % 3.03/3.11 %------------------------------------------- % 3.03/3.11 %------------------------------------------------------------------------------ % 3.03/3.11 % File : SET985+1 : TPTP v8.2.0. Released v3.2.0. % 3.03/3.11 % Domain : Set theory % 3.03/3.11 % Problem : Basic properties of sets, theorem 139 % 3.03/3.11 % Version : [Urb06] axioms : Especial. % 3.03/3.11 % English : % 3.03/3.11 % 3.03/3.11 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 3.03/3.11 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 3.03/3.11 % Source : [Urb06] % 3.03/3.11 % Names : zfmisc_1__t139_zfmisc_1 [Urb06] % 3.03/3.11 % 3.03/3.11 % Status : Theorem % 3.03/3.11 % Rating : 0.11 v8.1.0, 0.14 v7.5.0, 0.16 v7.4.0, 0.07 v7.3.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.03 v6.4.0, 0.08 v6.2.0, 0.16 v6.1.0, 0.20 v6.0.0, 0.13 v5.5.0, 0.07 v5.4.0, 0.14 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, 0.10 v3.5.0, 0.11 v3.3.0, 0.07 v3.2.0 % 3.03/3.11 % Syntax : Number of formulae : 8 ( 5 unt; 0 def) % 3.03/3.11 % Number of atoms : 16 ( 4 equ) % 3.03/3.11 % Maximal formula atoms : 4 ( 2 avg) % 3.03/3.11 % Number of connectives : 10 ( 2 ~; 3 |; 1 &) % 3.03/3.11 % ( 1 <=>; 3 =>; 0 <=; 0 <~>) % 3.03/3.11 % Maximal formula depth : 8 ( 4 avg) % 3.03/3.11 % Maximal term depth : 2 ( 1 avg) % 3.03/3.11 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty) % 3.03/3.11 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty) % 3.03/3.11 % Number of variables : 15 ( 13 !; 2 ?) % 3.03/3.11 % SPC : FOF_THM_RFO_SEQ % 3.03/3.11 % 3.03/3.11 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 3.03/3.11 % library, www.mizar.org % 3.03/3.11 %------------------------------------------------------------------------------ % 3.03/3.11 fof(fc1_xboole_0,axiom, % 3.03/3.11 empty(empty_set) ). % 3.03/3.11 % 3.03/3.11 fof(rc1_xboole_0,axiom, % 3.03/3.11 ? [A] : empty(A) ). % 3.03/3.11 % 3.03/3.11 fof(rc2_xboole_0,axiom, % 3.03/3.11 ? [A] : ~ empty(A) ). % 3.03/3.11 % 3.03/3.11 fof(reflexivity_r1_tarski,axiom, % 3.03/3.11 ! [A,B] : subset(A,A) ). % 3.03/3.11 % 3.03/3.11 fof(t113_zfmisc_1,axiom, % 3.03/3.11 ! [A,B] : % 3.03/3.11 ( cartesian_product2(A,B) = empty_set % 3.03/3.11 <=> ( A = empty_set % 3.03/3.11 | B = empty_set ) ) ). % 3.03/3.11 % 3.03/3.11 fof(t138_zfmisc_1,axiom, % 3.03/3.11 ! [A,B,C,D] : % 3.03/3.11 ( subset(cartesian_product2(A,B),cartesian_product2(C,D)) % 3.03/3.11 => ( cartesian_product2(A,B) = empty_set % 3.03/3.11 | ( subset(A,C) % 3.03/3.11 & subset(B,D) ) ) ) ). % 3.03/3.11 % 3.03/3.11 fof(t139_zfmisc_1,conjecture, % 3.03/3.11 ! [A] : % 3.03/3.11 ( ~ empty(A) % 3.03/3.11 => ! [B,C,D] : % 3.03/3.11 ( ( subset(cartesian_product2(A,B),cartesian_product2(C,D)) % 3.03/3.11 | subset(cartesian_product2(B,A),cartesian_product2(D,C)) ) % 3.03/3.11 => subset(B,D) ) ) ). % 3.03/3.11 % 3.03/3.11 fof(t2_xboole_1,axiom, % 3.03/3.11 ! [A] : subset(empty_set,A) ). % 3.03/3.11 % 3.03/3.11 %------------------------------------------------------------------------------ % 3.03/3.11 %------------------------------------------- % 3.03/3.11 % Proof found % 3.03/3.11 % SZS status Theorem for theBenchmark % 3.03/3.11 % SZS output start Proof % 3.03/3.11 %ClaNum:21(EqnAxiom:8) % 3.03/3.11 %VarNum:29(SingletonVarNum:16) % 3.03/3.11 %MaxLitNum:3 % 3.03/3.11 %MaxfuncDepth:1 % 3.03/3.11 %SharedTerms:18 % 3.03/3.11 %goalClause: 14 15 19 % 3.03/3.11 %singleGoalClaCount:2 % 3.03/3.11 [9]P1(a1) % 3.03/3.11 [10]P1(a3) % 3.03/3.11 [13]~P1(a4) % 3.03/3.11 [14]~P1(a5) % 3.03/3.11 [15]~P2(a6,a7) % 3.03/3.11 [11]P2(a1,x111) % 3.03/3.11 [12]P2(x121,x121) % 3.03/3.11 [19]P2(f2(a5,a6),f2(a8,a7))+P2(f2(a6,a5),f2(a7,a8)) % 3.03/3.11 [16]~E(x162,a1)+E(f2(x161,x162),a1) % 3.03/3.11 [17]~E(x171,a1)+E(f2(x171,x172),a1) % 3.03/3.11 [18]E(x181,a1)+E(x182,a1)+~E(f2(x182,x181),a1) % 3.03/3.11 [20]P2(x202,x203)+~P2(f2(x201,x202),f2(x204,x203))+E(f2(x201,x202),a1) % 3.03/3.11 [21]P2(x211,x213)+~P2(f2(x211,x212),f2(x213,x214))+E(f2(x211,x212),a1) % 3.03/3.11 %EqnAxiom % 3.03/3.11 [1]E(x11,x11) % 3.03/3.11 [2]E(x22,x21)+~E(x21,x22) % 3.03/3.11 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 3.03/3.11 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 3.03/3.11 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 3.03/3.11 [6]~P1(x61)+P1(x62)+~E(x61,x62) % 3.03/3.11 [7]P2(x72,x73)+~E(x71,x72)+~P2(x71,x73) % 3.03/3.11 [8]P2(x83,x82)+~E(x81,x82)+~P2(x83,x81) % 3.03/3.11 % 3.03/3.11 %------------------------------------------- % 3.03/3.12 cnf(22,plain, % 3.03/3.12 (E(f2(x221,a1),a1)), % 3.03/3.12 inference(equality_inference,[],[16])). % 3.03/3.12 cnf(23,plain, % 3.03/3.12 (E(f2(a1,x231),a1)), % 3.03/3.12 inference(equality_inference,[],[17])). % 3.03/3.12 cnf(24,plain, % 3.03/3.12 (E(a1,f2(x241,a1))), % 3.03/3.12 inference(scs_inference,[],[22,2])). % 3.03/3.12 cnf(33,plain, % 3.03/3.12 (~E(a1,a6)), % 3.03/3.12 inference(scs_inference,[],[15,11,23,24,9,2,3,6,7])). % 3.03/3.12 cnf(40,plain, % 3.03/3.12 (P2(f2(a6,a5),f2(a7,a8))+E(f2(a5,a6),a1)), % 3.03/3.12 inference(scs_inference,[],[15,19,20])). % 3.03/3.12 cnf(384,plain, % 3.03/3.12 (E(f2(a5,a6),a1)+E(f2(a6,a5),a1)), % 3.03/3.12 inference(scs_inference,[],[15,40,21])). % 3.03/3.12 cnf(385,plain, % 3.03/3.12 (E(a5,a1)+E(a6,a1)+E(f2(a5,a6),a1)), % 3.03/3.12 inference(scs_inference,[],[384,18])). % 3.03/3.12 cnf(386,plain, % 3.03/3.12 (E(a6,a1)+E(a5,a1)), % 3.03/3.12 inference(scs_inference,[],[385,18])). % 3.03/3.12 cnf(387,plain, % 3.03/3.12 (E(a5,a1)), % 3.03/3.12 inference(scs_inference,[],[33,386,2])). % 3.03/3.12 cnf(389,plain, % 3.03/3.12 ($false), % 3.03/3.12 inference(scs_inference,[],[14,387,9,2,6]), % 3.03/3.12 ['proof']). % 3.03/3.12 % SZS output end Proof % 3.03/3.12 % Total time :2.500000s %------------------------------------------------------------------------------