%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM395+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 : n019.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 12:24:06 EDT 2024 % Result : Theorem 0.56s 0.63s % Output : CNFRefutation 0.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : NUM395+1 : TPTP v8.2.0. Released v3.2.0. % 0.04/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n019.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 01:00:24 EDT 2024 % 0.12/0.33 % CPUTime : % 0.56/0.59 start to proof:theBenchmark % 0.56/0.62 %------------------------------------------- % 0.56/0.62 % File :CSE---1.7 % 0.56/0.62 % Problem :theBenchmark % 0.56/0.62 % Transform :cnf % 0.56/0.62 % Format :tptp:raw % 0.56/0.62 % Command :java -jar mcs_scs.jar %d %s % 0.56/0.62 % 0.56/0.62 % Result :Theorem 0.000000s % 0.56/0.62 % Output :CNFRefutation 0.000000s % 0.56/0.62 %------------------------------------------- % 0.56/0.62 %------------------------------------------------------------------------------ % 0.56/0.62 % File : NUM395+1 : TPTP v8.2.0. Released v3.2.0. % 0.56/0.62 % Domain : Number Theory (Ordinals) % 0.56/0.62 % Problem : Ordinal numbers, theorem 27 % 0.56/0.62 % Version : [Urb06] axioms : Especial. % 0.56/0.62 % English : % 0.56/0.62 % 0.56/0.62 % Refs : [Ban90] Bancerek (1990), The Ordinal Numbers % 0.56/0.62 % [Urb06] Urban (2006), Email to G. Sutcliffe % 0.56/0.62 % Source : [Urb06] % 0.56/0.62 % Names : ordinal1__t27_ordinal1 [Urb06] % 0.56/0.62 % 0.56/0.62 % Status : Theorem % 0.56/0.62 % Rating : 0.06 v8.1.0, 0.03 v7.4.0, 0.00 v6.3.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.00 v3.2.0 % 0.56/0.62 % Syntax : Number of formulae : 29 ( 5 unt; 0 def) % 0.56/0.62 % Number of atoms : 68 ( 2 equ) % 0.56/0.62 % Maximal formula atoms : 6 ( 2 avg) % 0.56/0.62 % Number of connectives : 45 ( 6 ~; 1 |; 28 &) % 0.56/0.62 % ( 1 <=>; 9 =>; 0 <=; 0 <~>) % 0.56/0.62 % Maximal formula depth : 7 ( 4 avg) % 0.56/0.62 % Maximal term depth : 1 ( 1 avg) % 0.56/0.62 % Number of predicates : 12 ( 11 usr; 0 prp; 1-2 aty) % 0.56/0.62 % Number of functors : 1 ( 1 usr; 1 con; 0-0 aty) % 0.56/0.62 % Number of variables : 30 ( 18 !; 12 ?) % 0.56/0.62 % SPC : FOF_THM_RFO_SEQ % 0.56/0.62 % 0.56/0.62 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.56/0.62 % library, www.mizar.org % 0.56/0.62 %------------------------------------------------------------------------------ % 0.56/0.62 fof(existence_m1_subset_1,axiom, % 0.56/0.62 ! [A] : % 0.56/0.62 ? [B] : element(B,A) ). % 0.56/0.62 % 0.56/0.62 fof(t2_subset,axiom, % 0.56/0.62 ! [A,B] : % 0.56/0.62 ( element(A,B) % 0.56/0.62 => ( empty(B) % 0.56/0.62 | in(A,B) ) ) ). % 0.56/0.62 % 0.56/0.62 fof(antisymmetry_r2_hidden,axiom, % 0.56/0.62 ! [A,B] : % 0.56/0.62 ( in(A,B) % 0.56/0.62 => ~ in(B,A) ) ). % 0.56/0.62 % 0.56/0.62 fof(t1_subset,axiom, % 0.56/0.62 ! [A,B] : % 0.56/0.62 ( in(A,B) % 0.56/0.63 => element(A,B) ) ). % 0.56/0.63 % 0.56/0.63 fof(cc1_funct_1,axiom, % 0.56/0.63 ! [A] : % 0.56/0.63 ( empty(A) % 0.56/0.63 => function(A) ) ). % 0.56/0.63 % 0.56/0.63 fof(cc2_funct_1,axiom, % 0.56/0.63 ! [A] : % 0.56/0.63 ( ( relation(A) % 0.56/0.63 & empty(A) % 0.56/0.63 & function(A) ) % 0.56/0.63 => ( relation(A) % 0.56/0.63 & function(A) % 0.56/0.63 & one_to_one(A) ) ) ). % 0.56/0.63 % 0.56/0.63 fof(cc1_relat_1,axiom, % 0.56/0.63 ! [A] : % 0.56/0.63 ( empty(A) % 0.56/0.63 => relation(A) ) ). % 0.56/0.63 % 0.56/0.63 fof(t7_boole,axiom, % 0.56/0.63 ! [A,B] : % 0.56/0.63 ~ ( in(A,B) % 0.56/0.63 & empty(B) ) ). % 0.56/0.63 % 0.56/0.63 fof(t8_boole,axiom, % 0.56/0.63 ! [A,B] : % 0.56/0.63 ~ ( empty(A) % 0.56/0.63 & A != B % 0.56/0.63 & empty(B) ) ). % 0.56/0.63 % 0.56/0.63 fof(cc1_ordinal1,axiom, % 0.56/0.63 ! [A] : % 0.56/0.63 ( ordinal(A) % 0.56/0.63 => ( epsilon_transitive(A) % 0.56/0.63 & epsilon_connected(A) ) ) ). % 0.56/0.63 % 0.56/0.63 fof(cc2_ordinal1,axiom, % 0.56/0.63 ! [A] : % 0.56/0.63 ( ( epsilon_transitive(A) % 0.56/0.63 & epsilon_connected(A) ) % 0.56/0.63 => ordinal(A) ) ). % 0.56/0.63 % 0.56/0.63 fof(rc1_ordinal1,axiom, % 0.56/0.63 ? [A] : % 0.56/0.63 ( epsilon_transitive(A) % 0.56/0.63 & epsilon_connected(A) % 0.56/0.63 & ordinal(A) ) ). % 0.56/0.63 % 0.56/0.63 fof(rc1_funct_1,axiom, % 0.56/0.63 ? [A] : % 0.56/0.63 ( relation(A) % 0.56/0.63 & function(A) ) ). % 0.56/0.63 % 0.56/0.63 fof(rc2_funct_1,axiom, % 0.56/0.63 ? [A] : % 0.56/0.63 ( relation(A) % 0.56/0.63 & empty(A) % 0.56/0.63 & function(A) ) ). % 0.56/0.63 % 0.56/0.63 fof(rc3_funct_1,axiom, % 0.56/0.63 ? [A] : % 0.56/0.63 ( relation(A) % 0.56/0.63 & function(A) % 0.56/0.63 & one_to_one(A) ) ). % 0.56/0.63 % 0.56/0.63 fof(rc4_funct_1,axiom, % 0.56/0.63 ? [A] : % 0.56/0.63 ( relation(A) % 0.56/0.63 & relation_empty_yielding(A) % 0.56/0.63 & function(A) ) ). % 0.56/0.63 % 0.56/0.63 fof(rc5_funct_1,axiom, % 0.56/0.63 ? [A] : % 0.56/0.63 ( relation(A) % 0.56/0.63 & relation_non_empty(A) % 0.56/0.63 & function(A) ) ). % 0.56/0.63 % 0.56/0.63 fof(fc4_relat_1,axiom, % 0.56/0.63 ( empty(empty_set) % 0.56/0.63 & relation(empty_set) ) ). % 0.56/0.63 % 0.56/0.63 fof(fc12_relat_1,axiom, % 0.56/0.63 ( empty(empty_set) % 0.56/0.63 & relation(empty_set) % 0.56/0.63 & relation_empty_yielding(empty_set) ) ). % 0.56/0.63 % 0.56/0.63 fof(rc1_relat_1,axiom, % 0.56/0.63 ? [A] : % 0.56/0.63 ( empty(A) % 0.56/0.63 & relation(A) ) ). % 0.56/0.63 % 0.56/0.63 fof(rc2_relat_1,axiom, % 0.56/0.63 ? [A] : % 0.56/0.63 ( ~ empty(A) % 0.56/0.63 & relation(A) ) ). % 0.56/0.63 % 0.56/0.63 fof(rc3_relat_1,axiom, % 0.56/0.63 ? [A] : % 0.56/0.63 ( relation(A) % 0.56/0.63 & relation_empty_yielding(A) ) ). % 0.56/0.63 % 0.56/0.63 fof(fc1_xboole_0,axiom, % 0.56/0.63 empty(empty_set) ). % 0.56/0.63 % 0.56/0.63 fof(rc1_xboole_0,axiom, % 0.56/0.63 ? [A] : empty(A) ). % 0.56/0.63 % 0.56/0.63 fof(rc2_xboole_0,axiom, % 0.56/0.63 ? [A] : ~ empty(A) ). % 0.56/0.63 % 0.56/0.63 fof(t6_boole,axiom, % 0.56/0.63 ! [A] : % 0.56/0.63 ( empty(A) % 0.56/0.63 => A = empty_set ) ). % 0.56/0.63 % 0.56/0.63 fof(t27_ordinal1,conjecture, % 0.56/0.63 ordinal(empty_set) ). % 0.56/0.63 % 0.56/0.63 fof(d4_ordinal1,axiom, % 0.56/0.63 ! [A] : % 0.56/0.63 ( ordinal(A) % 0.56/0.63 <=> ( epsilon_transitive(A) % 0.56/0.63 & epsilon_connected(A) ) ) ). % 0.56/0.63 % 0.56/0.63 fof(l18_ordinal1,axiom, % 0.56/0.63 ( epsilon_transitive(empty_set) % 0.56/0.63 & epsilon_connected(empty_set) ) ). % 0.56/0.63 % 0.56/0.63 %------------------------------------------------------------------------------ % 0.56/0.63 %------------------------------------------- % 0.56/0.63 % Proof found % 0.56/0.63 % SZS status Theorem for theBenchmark % 0.56/0.63 % SZS output start Proof % 0.56/0.63 %ClaNum:67(EqnAxiom:17) % 0.56/0.63 %VarNum:39(SingletonVarNum:18) % 0.56/0.63 %MaxLitNum:4 % 0.56/0.63 %MaxfuncDepth:1 % 0.56/0.63 %SharedTerms:43 % 0.56/0.63 %goalClause: 52 % 0.56/0.63 %singleGoalClaCount:1 % 0.56/0.63 [20]P1(a1) % 0.56/0.63 [21]P1(a2) % 0.56/0.63 [22]P1(a9) % 0.56/0.63 [23]P1(a3) % 0.56/0.63 [24]P3(a5) % 0.56/0.63 [25]P3(a2) % 0.62/0.63 [26]P3(a10) % 0.62/0.63 [27]P3(a11) % 0.62/0.63 [28]P3(a12) % 0.62/0.63 [30]P6(a1) % 0.62/0.63 [31]P6(a5) % 0.62/0.63 [32]P6(a2) % 0.62/0.63 [33]P6(a10) % 0.62/0.63 [34]P6(a11) % 0.62/0.63 [35]P6(a12) % 0.62/0.63 [36]P6(a9) % 0.62/0.63 [37]P6(a13) % 0.62/0.63 [38]P6(a4) % 0.62/0.63 [39]P7(a10) % 0.62/0.63 [40]P9(a6) % 0.62/0.63 [41]P4(a1) % 0.62/0.63 [42]P4(a6) % 0.62/0.63 [43]P5(a1) % 0.62/0.63 [44]P5(a6) % 0.62/0.63 [45]P10(a1) % 0.62/0.63 [46]P10(a11) % 0.62/0.63 [47]P10(a4) % 0.62/0.63 [48]P11(a12) % 0.62/0.63 [50]~P1(a13) % 0.62/0.63 [51]~P1(a8) % 0.62/0.63 [52]~P9(a1) % 0.62/0.63 [49]P2(f7(x491),x491) % 0.62/0.63 [53]~P1(x531)+E(x531,a1) % 0.62/0.63 [54]~P1(x541)+P3(x541) % 0.62/0.63 [55]~P1(x551)+P6(x551) % 0.62/0.63 [57]~P9(x571)+P4(x571) % 0.62/0.63 [59]~P9(x591)+P5(x591) % 0.62/0.63 [64]~P1(x641)+~P8(x642,x641) % 0.62/0.63 [65]~P8(x651,x652)+P2(x651,x652) % 0.62/0.63 [67]~P8(x672,x671)+~P8(x671,x672) % 0.62/0.63 [62]~P4(x621)+~P5(x621)+P9(x621) % 0.62/0.63 [60]~P1(x602)+~P1(x601)+E(x601,x602) % 0.62/0.63 [66]~P2(x662,x661)+P1(x661)+P8(x662,x661) % 0.62/0.63 [63]~P1(x631)+~P3(x631)+~P6(x631)+P7(x631) % 0.62/0.63 %EqnAxiom % 0.62/0.63 [1]E(x11,x11) % 0.62/0.63 [2]E(x22,x21)+~E(x21,x22) % 0.62/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.62/0.63 [4]~E(x41,x42)+E(f7(x41),f7(x42)) % 0.62/0.63 [5]~P1(x51)+P1(x52)+~E(x51,x52) % 0.62/0.63 [6]P8(x62,x63)+~E(x61,x62)+~P8(x61,x63) % 0.62/0.63 [7]P8(x73,x72)+~E(x71,x72)+~P8(x73,x71) % 0.62/0.63 [8]~P9(x81)+P9(x82)+~E(x81,x82) % 0.62/0.63 [9]P2(x92,x93)+~E(x91,x92)+~P2(x91,x93) % 0.62/0.63 [10]P2(x103,x102)+~E(x101,x102)+~P2(x103,x101) % 0.62/0.63 [11]~P5(x111)+P5(x112)+~E(x111,x112) % 0.62/0.63 [12]~P4(x121)+P4(x122)+~E(x121,x122) % 0.62/0.63 [13]~P3(x131)+P3(x132)+~E(x131,x132) % 0.62/0.63 [14]~P11(x141)+P11(x142)+~E(x141,x142) % 0.62/0.63 [15]~P10(x151)+P10(x152)+~E(x151,x152) % 0.62/0.63 [16]~P6(x161)+P6(x162)+~E(x161,x162) % 0.62/0.63 [17]~P7(x171)+P7(x172)+~E(x171,x172) % 0.62/0.63 % 0.62/0.63 %------------------------------------------- % 0.62/0.63 cnf(68,plain, % 0.62/0.63 ($false), % 0.62/0.63 inference(scs_inference,[],[41,43,52,62]), % 0.62/0.63 ['proof']). % 0.62/0.63 % SZS output end Proof % 0.62/0.63 % Total time :0.000000s %------------------------------------------------------------------------------