%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM387+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 : n021.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 12:24:05 EDT 2024 % Result : Theorem 6.59s 6.78s % Output : CNFRefutation 6.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.07 % Problem : NUM387+1 : TPTP v8.2.0. Released v3.2.0. % 0.02/0.07 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.06/0.26 % Computer : n021.cluster.edu % 0.06/0.26 % Model : x86_64 x86_64 % 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.06/0.26 % Memory : 8042.1875MB % 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.06/0.26 % CPULimit : 300 % 0.06/0.26 % WCLimit : 300 % 0.06/0.26 % DateTime : Sat Jun 22 20:11:54 EDT 2024 % 0.06/0.26 % CPUTime : % 0.11/0.41 start to proof:theBenchmark % 6.59/6.76 %------------------------------------------- % 6.59/6.76 % File :CSE---1.7 % 6.59/6.76 % Problem :theBenchmark % 6.59/6.76 % Transform :cnf % 6.59/6.76 % Format :tptp:raw % 6.59/6.76 % Command :java -jar mcs_scs.jar %d %s % 6.59/6.76 % 6.59/6.76 % Result :Theorem 6.310000s % 6.59/6.76 % Output :CNFRefutation 6.310000s % 6.59/6.76 %------------------------------------------- % 6.59/6.77 %------------------------------------------------------------------------------ % 6.59/6.77 % File : NUM387+1 : TPTP v8.2.0. Released v3.2.0. % 6.59/6.77 % Domain : Number Theory (Ordinals) % 6.59/6.77 % Problem : Ordinal numbers, theorem 14 % 6.59/6.77 % Version : [Urb06] axioms : Especial. % 6.59/6.77 % English : % 6.59/6.77 % 6.59/6.77 % Refs : [Ban90] Bancerek (1990), The Ordinal Numbers % 6.59/6.77 % [Urb06] Urban (2006), Email to G. Sutcliffe % 6.59/6.77 % Source : [Urb06] % 6.59/6.77 % Names : ordinal1__t14_ordinal1 [Urb06] % 6.59/6.77 % 6.59/6.77 % Status : Theorem % 6.59/6.77 % Rating : 0.11 v7.5.0, 0.12 v7.4.0, 0.03 v7.2.0, 0.07 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.2.0, 0.16 v6.1.0, 0.23 v6.0.0, 0.17 v5.5.0, 0.22 v5.4.0, 0.21 v5.3.0, 0.22 v5.2.0, 0.00 v5.0.0, 0.04 v4.0.1, 0.09 v4.0.0, 0.08 v3.7.0, 0.00 v3.4.0, 0.05 v3.3.0, 0.14 v3.2.0 % 6.59/6.77 % Syntax : Number of formulae : 33 ( 11 unt; 0 def) % 6.59/6.77 % Number of atoms : 67 ( 7 equ) % 6.59/6.77 % Maximal formula atoms : 6 ( 2 avg) % 6.59/6.77 % Number of connectives : 46 ( 12 ~; 1 |; 23 &) % 6.59/6.77 % ( 0 <=>; 10 =>; 0 <=; 0 <~>) % 6.59/6.77 % Maximal formula depth : 7 ( 4 avg) % 6.59/6.77 % Maximal term depth : 3 ( 1 avg) % 6.59/6.77 % Number of predicates : 9 ( 8 usr; 0 prp; 1-2 aty) % 6.59/6.77 % Number of functors : 4 ( 4 usr; 1 con; 0-2 aty) % 6.59/6.77 % Number of variables : 41 ( 30 !; 11 ?) % 6.59/6.77 % SPC : FOF_THM_RFO_SEQ % 6.59/6.77 % 6.59/6.77 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 6.59/6.77 % library, www.mizar.org % 6.59/6.77 %------------------------------------------------------------------------------ % 6.59/6.77 fof(antisymmetry_r2_hidden,axiom, % 6.59/6.77 ! [A,B] : % 6.59/6.77 ( in(A,B) % 6.59/6.77 => ~ in(B,A) ) ). % 6.59/6.77 % 6.59/6.77 fof(cc1_funct_1,axiom, % 6.59/6.77 ! [A] : % 6.59/6.77 ( empty(A) % 6.59/6.77 => function(A) ) ). % 6.59/6.77 % 6.59/6.77 fof(cc1_relat_1,axiom, % 6.59/6.77 ! [A] : % 6.59/6.77 ( empty(A) % 6.59/6.77 => relation(A) ) ). % 6.59/6.77 % 6.59/6.77 fof(cc2_funct_1,axiom, % 6.59/6.77 ! [A] : % 6.59/6.77 ( ( relation(A) % 6.59/6.77 & empty(A) % 6.59/6.77 & function(A) ) % 6.59/6.77 => ( relation(A) % 6.59/6.77 & function(A) % 6.59/6.77 & one_to_one(A) ) ) ). % 6.59/6.77 % 6.59/6.77 fof(commutativity_k2_xboole_0,axiom, % 6.59/6.77 ! [A,B] : set_union2(A,B) = set_union2(B,A) ). % 6.59/6.77 % 6.59/6.77 fof(d1_ordinal1,axiom, % 6.59/6.77 ! [A] : succ(A) = set_union2(A,singleton(A)) ). % 6.59/6.77 % 6.59/6.77 fof(existence_m1_subset_1,axiom, % 6.59/6.77 ! [A] : % 6.59/6.77 ? [B] : element(B,A) ). % 6.59/6.77 % 6.59/6.77 fof(fc12_relat_1,axiom, % 6.59/6.77 ( empty(empty_set) % 6.59/6.77 & relation(empty_set) % 6.59/6.77 & relation_empty_yielding(empty_set) ) ). % 6.59/6.77 % 6.59/6.77 fof(fc1_ordinal1,axiom, % 6.59/6.77 ! [A] : ~ empty(succ(A)) ). % 6.59/6.77 % 6.59/6.77 fof(fc1_xboole_0,axiom, % 6.59/6.77 empty(empty_set) ). % 6.59/6.77 % 6.59/6.77 fof(fc2_relat_1,axiom, % 6.59/6.77 ! [A,B] : % 6.59/6.77 ( ( relation(A) % 6.59/6.77 & relation(B) ) % 6.59/6.77 => relation(set_union2(A,B)) ) ). % 6.59/6.77 % 6.59/6.77 fof(fc2_xboole_0,axiom, % 6.59/6.77 ! [A,B] : % 6.59/6.77 ( ~ empty(A) % 6.59/6.77 => ~ empty(set_union2(A,B)) ) ). % 6.59/6.77 % 6.59/6.77 fof(fc3_xboole_0,axiom, % 6.59/6.77 ! [A,B] : % 6.59/6.77 ( ~ empty(A) % 6.59/6.77 => ~ empty(set_union2(B,A)) ) ). % 6.59/6.77 % 6.59/6.77 fof(fc4_relat_1,axiom, % 6.59/6.77 ( empty(empty_set) % 6.59/6.77 & relation(empty_set) ) ). % 6.59/6.77 % 6.59/6.77 fof(idempotence_k2_xboole_0,axiom, % 6.59/6.77 ! [A,B] : set_union2(A,A) = A ). % 6.59/6.77 % 6.59/6.77 fof(rc1_funct_1,axiom, % 6.59/6.77 ? [A] : % 6.59/6.77 ( relation(A) % 6.59/6.77 & function(A) ) ). % 6.59/6.77 % 6.59/6.77 fof(rc1_relat_1,axiom, % 6.59/6.77 ? [A] : % 6.59/6.77 ( empty(A) % 6.59/6.77 & relation(A) ) ). % 6.59/6.77 % 6.59/6.77 fof(rc1_xboole_0,axiom, % 6.59/6.77 ? [A] : empty(A) ). % 6.59/6.77 % 6.59/6.77 fof(rc2_funct_1,axiom, % 6.59/6.77 ? [A] : % 6.59/6.77 ( relation(A) % 6.59/6.77 & empty(A) % 6.59/6.77 & function(A) ) ). % 6.59/6.77 % 6.59/6.77 fof(rc2_relat_1,axiom, % 6.59/6.77 ? [A] : % 6.59/6.77 ( ~ empty(A) % 6.59/6.77 & relation(A) ) ). % 6.59/6.77 % 6.59/6.77 fof(rc2_xboole_0,axiom, % 6.59/6.77 ? [A] : ~ empty(A) ). % 6.59/6.77 % 6.59/6.77 fof(rc3_funct_1,axiom, % 6.59/6.77 ? [A] : % 6.59/6.77 ( relation(A) % 6.59/6.77 & function(A) % 6.59/6.77 & one_to_one(A) ) ). % 6.59/6.77 % 6.59/6.77 fof(rc3_relat_1,axiom, % 6.59/6.77 ? [A] : % 6.59/6.77 ( relation(A) % 6.59/6.77 & relation_empty_yielding(A) ) ). % 6.59/6.77 % 6.59/6.77 fof(rc4_funct_1,axiom, % 6.59/6.77 ? [A] : % 6.59/6.77 ( relation(A) % 6.59/6.77 & relation_empty_yielding(A) % 6.59/6.77 & function(A) ) ). % 6.59/6.77 % 6.59/6.77 fof(rc5_funct_1,axiom, % 6.59/6.77 ? [A] : % 6.59/6.77 ( relation(A) % 6.59/6.77 & relation_non_empty(A) % 6.59/6.77 & function(A) ) ). % 6.59/6.77 % 6.59/6.77 fof(t10_ordinal1,axiom, % 6.59/6.77 ! [A] : in(A,succ(A)) ). % 6.59/6.77 % 6.59/6.78 fof(t14_ordinal1,conjecture, % 6.59/6.78 ! [A] : A != succ(A) ). % 6.59/6.78 % 6.59/6.78 fof(t1_boole,axiom, % 6.59/6.78 ! [A] : set_union2(A,empty_set) = A ). % 6.59/6.78 % 6.59/6.78 fof(t1_subset,axiom, % 6.59/6.78 ! [A,B] : % 6.59/6.78 ( in(A,B) % 6.59/6.78 => element(A,B) ) ). % 6.59/6.78 % 6.59/6.78 fof(t2_subset,axiom, % 6.59/6.78 ! [A,B] : % 6.59/6.78 ( element(A,B) % 6.59/6.78 => ( empty(B) % 6.59/6.78 | in(A,B) ) ) ). % 6.59/6.78 % 6.59/6.78 fof(t6_boole,axiom, % 6.59/6.78 ! [A] : % 6.59/6.78 ( empty(A) % 6.59/6.78 => A = empty_set ) ). % 6.59/6.78 % 6.59/6.78 fof(t7_boole,axiom, % 6.59/6.78 ! [A,B] : % 6.59/6.78 ~ ( in(A,B) % 6.59/6.78 & empty(B) ) ). % 6.59/6.78 % 6.59/6.78 fof(t8_boole,axiom, % 6.59/6.78 ! [A,B] : % 6.59/6.78 ~ ( empty(A) % 6.59/6.78 & A != B % 6.59/6.78 & empty(B) ) ). % 6.59/6.78 % 6.59/6.78 %------------------------------------------------------------------------------ % 6.59/6.78 %------------------------------------------- % 6.59/6.78 % Proof found % 6.59/6.78 % SZS status Theorem for theBenchmark % 6.59/6.78 % SZS output start Proof % 6.59/6.78 %ClaNum:64(EqnAxiom:17) % 6.59/6.78 %VarNum:56(SingletonVarNum:27) % 6.59/6.78 %MaxLitNum:4 % 6.59/6.78 %MaxfuncDepth:2 % 6.59/6.78 %SharedTerms:40 % 6.59/6.78 %goalClause: 46 % 6.59/6.78 %singleGoalClaCount:1 % 6.59/6.78 [20]P1(a1) % 6.59/6.78 [21]P1(a2) % 6.59/6.78 [22]P1(a8) % 6.59/6.78 [23]P1(a9) % 6.59/6.78 [24]P3(a3) % 6.59/6.78 [25]P3(a9) % 6.59/6.78 [26]P3(a10) % 6.59/6.78 [27]P3(a4) % 6.59/6.78 [28]P3(a5) % 6.59/6.78 [30]P4(a1) % 6.59/6.78 [31]P4(a3) % 6.59/6.78 [32]P4(a2) % 6.59/6.78 [33]P4(a9) % 6.59/6.78 [34]P4(a11) % 6.59/6.78 [35]P4(a10) % 6.59/6.78 [36]P4(a13) % 6.59/6.78 [37]P4(a4) % 6.59/6.78 [38]P4(a5) % 6.59/6.78 [39]P5(a10) % 6.59/6.78 [40]P7(a1) % 6.59/6.78 [41]P7(a13) % 6.59/6.78 [42]P7(a4) % 6.59/6.78 [43]P8(a5) % 6.59/6.78 [50]~P1(a11) % 6.59/6.78 [51]~P1(a12) % 6.59/6.78 [46]E(f14(a6,f15(a6)),a6) % 6.59/6.78 [44]E(f14(x441,a1),x441) % 6.59/6.78 [45]E(f14(x451,x451),x451) % 6.59/6.78 [47]P2(f7(x471),x471) % 6.59/6.78 [49]P6(x491,f14(x491,f15(x491))) % 6.59/6.78 [52]~P1(f14(x521,f15(x521))) % 6.59/6.78 [48]E(f14(x481,x482),f14(x482,x481)) % 6.59/6.78 [53]~P1(x531)+E(x531,a1) % 6.59/6.78 [54]~P1(x541)+P3(x541) % 6.59/6.78 [55]~P1(x551)+P4(x551) % 6.59/6.78 [58]~P1(x581)+~P6(x582,x581) % 6.59/6.78 [59]~P6(x591,x592)+P2(x591,x592) % 6.59/6.78 [62]~P6(x622,x621)+~P6(x621,x622) % 6.59/6.78 [63]P1(x631)+~P1(f14(x632,x631)) % 6.59/6.78 [64]P1(x641)+~P1(f14(x641,x642)) % 6.59/6.78 [56]~P1(x562)+~P1(x561)+E(x561,x562) % 6.59/6.78 [60]~P2(x602,x601)+P1(x601)+P6(x602,x601) % 6.59/6.78 [61]~P4(x612)+~P4(x611)+P4(f14(x611,x612)) % 6.59/6.78 [57]~P1(x571)+~P3(x571)+~P4(x571)+P5(x571) % 6.59/6.78 %EqnAxiom % 6.59/6.78 [1]E(x11,x11) % 6.59/6.78 [2]E(x22,x21)+~E(x21,x22) % 6.59/6.78 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 6.59/6.78 [4]~E(x41,x42)+E(f14(x41,x43),f14(x42,x43)) % 6.59/6.78 [5]~E(x51,x52)+E(f14(x53,x51),f14(x53,x52)) % 6.59/6.78 [6]~E(x61,x62)+E(f15(x61),f15(x62)) % 6.59/6.78 [7]~E(x71,x72)+E(f7(x71),f7(x72)) % 6.59/6.78 [8]~P1(x81)+P1(x82)+~E(x81,x82) % 6.59/6.78 [9]P6(x92,x93)+~E(x91,x92)+~P6(x91,x93) % 6.59/6.78 [10]P6(x103,x102)+~E(x101,x102)+~P6(x103,x101) % 6.59/6.78 [11]~P5(x111)+P5(x112)+~E(x111,x112) % 6.59/6.78 [12]~P4(x121)+P4(x122)+~E(x121,x122) % 6.59/6.78 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133) % 6.59/6.78 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141) % 6.59/6.78 [15]~P3(x151)+P3(x152)+~E(x151,x152) % 6.59/6.78 [16]~P7(x161)+P7(x162)+~E(x161,x162) % 6.59/6.78 [17]~P8(x171)+P8(x172)+~E(x171,x172) % 6.59/6.78 % 6.59/6.78 %------------------------------------------- % 6.59/6.78 cnf(65,plain, % 6.59/6.78 (E(a6,f14(a6,f15(a6)))), % 6.59/6.78 inference(scs_inference,[],[46,2])). % 6.59/6.78 cnf(68,plain, % 6.59/6.78 (~P6(f14(x681,f15(x681)),x681)), % 6.59/6.78 inference(scs_inference,[],[46,20,49,2,58,62])). % 6.59/6.78 cnf(70,plain, % 6.59/6.78 (E(f14(f14(x701,a1),f14(x701,a1)),x701)), % 6.59/6.78 inference(scs_inference,[],[46,45,44,20,49,2,58,62,3])). % 6.59/6.78 cnf(96,plain, % 6.59/6.78 (~P1(a6)), % 6.59/6.78 inference(scs_inference,[],[65,70,68,21,30,51,52,58,2,60,12,8])). % 6.59/6.78 cnf(112,plain, % 6.59/6.78 (~P2(f14(a6,f15(a6)),a6)), % 6.59/6.78 inference(scs_inference,[],[96,22,68,45,58,2,60])). % 6.59/6.78 cnf(1184,plain, % 6.59/6.78 (P2(f14(a6,f15(a6)),f14(a6,f15(a6)))), % 6.59/6.78 inference(scs_inference,[],[49,65,9,59])). % 6.59/6.78 cnf(1186,plain, % 6.59/6.78 ($false), % 6.59/6.78 inference(scs_inference,[],[46,1184,112,13,14]), % 6.59/6.78 ['proof']). % 6.59/6.78 % SZS output end Proof % 6.59/6.78 % Total time :6.310000s %------------------------------------------------------------------------------