%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM390+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 : 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 12:24:05 EDT 2024 % Result : Theorem 0.60s 0.82s % Output : CNFRefutation 0.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : NUM390+1 : TPTP v8.2.0. Released v3.2.0. % 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n026.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Jun 22 22:39:24 EDT 2024 % 0.12/0.34 % CPUTime : % 0.44/0.62 start to proof:theBenchmark % 0.60/0.81 %------------------------------------------- % 0.60/0.81 % File :CSE---1.7 % 0.60/0.81 % Problem :theBenchmark % 0.60/0.81 % Transform :cnf % 0.60/0.81 % Format :tptp:raw % 0.60/0.81 % Command :java -jar mcs_scs.jar %d %s % 0.60/0.81 % 0.60/0.81 % Result :Theorem 0.150000s % 0.60/0.81 % Output :CNFRefutation 0.150000s % 0.60/0.81 %------------------------------------------- % 0.60/0.81 %------------------------------------------------------------------------------ % 0.60/0.81 % File : NUM390+1 : TPTP v8.2.0. Released v3.2.0. % 0.60/0.81 % Domain : Number Theory (Ordinals) % 0.60/0.81 % Problem : Ordinal numbers, theorem 22 % 0.60/0.81 % Version : [Urb06] axioms : Especial. % 0.60/0.81 % English : % 0.60/0.81 % 0.60/0.81 % Refs : [Ban90] Bancerek (1990), The Ordinal Numbers % 0.60/0.81 % [Urb06] Urban (2006), Email to G. Sutcliffe % 0.60/0.81 % Source : [Urb06] % 0.60/0.81 % Names : ordinal1__t22_ordinal1 [Urb06] % 0.60/0.81 % 0.60/0.81 % Status : Theorem % 0.60/0.81 % Rating : 0.17 v8.1.0, 0.14 v7.5.0, 0.16 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.17 v6.0.0, 0.09 v5.5.0, 0.19 v5.4.0, 0.14 v5.3.0, 0.22 v5.2.0, 0.05 v5.1.0, 0.10 v5.0.0, 0.12 v4.1.0, 0.13 v4.0.0, 0.12 v3.7.0, 0.05 v3.4.0, 0.11 v3.3.0, 0.07 v3.2.0 % 0.60/0.81 % Syntax : Number of formulae : 38 ( 6 unt; 0 def) % 0.60/0.81 % Number of atoms : 95 ( 3 equ) % 0.60/0.81 % Maximal formula atoms : 6 ( 2 avg) % 0.60/0.81 % Number of connectives : 68 ( 11 ~; 1 |; 33 &) % 0.60/0.81 % ( 3 <=>; 20 =>; 0 <=; 0 <~>) % 0.60/0.81 % Maximal formula depth : 9 ( 4 avg) % 0.60/0.81 % Maximal term depth : 2 ( 1 avg) % 0.60/0.81 % Number of predicates : 14 ( 13 usr; 0 prp; 1-2 aty) % 0.60/0.81 % Number of functors : 2 ( 2 usr; 1 con; 0-1 aty) % 0.60/0.81 % Number of variables : 57 ( 45 !; 12 ?) % 0.60/0.81 % SPC : FOF_THM_RFO_SEQ % 0.60/0.81 % 0.60/0.81 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.60/0.81 % library, www.mizar.org % 0.60/0.81 %------------------------------------------------------------------------------ % 0.60/0.81 fof(antisymmetry_r2_hidden,axiom, % 0.60/0.81 ! [A,B] : % 0.60/0.81 ( in(A,B) % 0.60/0.81 => ~ in(B,A) ) ). % 0.60/0.81 % 0.60/0.81 fof(antisymmetry_r2_xboole_0,axiom, % 0.60/0.81 ! [A,B] : % 0.60/0.81 ( proper_subset(A,B) % 0.60/0.81 => ~ proper_subset(B,A) ) ). % 0.60/0.81 % 0.60/0.81 fof(cc1_funct_1,axiom, % 0.60/0.81 ! [A] : % 0.60/0.81 ( empty(A) % 0.60/0.81 => function(A) ) ). % 0.60/0.81 % 0.60/0.81 fof(cc1_ordinal1,axiom, % 0.60/0.81 ! [A] : % 0.60/0.81 ( ordinal(A) % 0.60/0.81 => ( epsilon_transitive(A) % 0.60/0.81 & epsilon_connected(A) ) ) ). % 0.60/0.81 % 0.60/0.81 fof(cc1_relat_1,axiom, % 0.60/0.81 ! [A] : % 0.60/0.81 ( empty(A) % 0.60/0.81 => relation(A) ) ). % 0.60/0.81 % 0.60/0.81 fof(cc2_funct_1,axiom, % 0.60/0.81 ! [A] : % 0.60/0.81 ( ( relation(A) % 0.60/0.81 & empty(A) % 0.60/0.81 & function(A) ) % 0.60/0.81 => ( relation(A) % 0.60/0.81 & function(A) % 0.60/0.81 & one_to_one(A) ) ) ). % 0.60/0.81 % 0.60/0.81 fof(cc2_ordinal1,axiom, % 0.60/0.81 ! [A] : % 0.60/0.81 ( ( epsilon_transitive(A) % 0.60/0.81 & epsilon_connected(A) ) % 0.60/0.81 => ordinal(A) ) ). % 0.60/0.81 % 0.60/0.81 fof(d2_ordinal1,axiom, % 0.60/0.81 ! [A] : % 0.60/0.81 ( epsilon_transitive(A) % 0.60/0.81 <=> ! [B] : % 0.60/0.82 ( in(B,A) % 0.60/0.82 => subset(B,A) ) ) ). % 0.60/0.82 % 0.60/0.82 fof(d8_xboole_0,axiom, % 0.60/0.82 ! [A,B] : % 0.60/0.82 ( proper_subset(A,B) % 0.60/0.82 <=> ( subset(A,B) % 0.60/0.82 & A != B ) ) ). % 0.60/0.82 % 0.60/0.82 fof(existence_m1_subset_1,axiom, % 0.60/0.82 ! [A] : % 0.60/0.82 ? [B] : element(B,A) ). % 0.60/0.82 % 0.60/0.82 fof(fc12_relat_1,axiom, % 0.60/0.82 ( empty(empty_set) % 0.60/0.82 & relation(empty_set) % 0.60/0.82 & relation_empty_yielding(empty_set) ) ). % 0.60/0.82 % 0.60/0.82 fof(fc1_xboole_0,axiom, % 0.60/0.82 empty(empty_set) ). % 0.60/0.82 % 0.60/0.82 fof(fc4_relat_1,axiom, % 0.60/0.82 ( empty(empty_set) % 0.60/0.82 & relation(empty_set) ) ). % 0.60/0.82 % 0.60/0.82 fof(irreflexivity_r2_xboole_0,axiom, % 0.60/0.82 ! [A,B] : ~ proper_subset(A,A) ). % 0.60/0.82 % 0.60/0.82 fof(rc1_funct_1,axiom, % 0.60/0.82 ? [A] : % 0.60/0.82 ( relation(A) % 0.60/0.82 & function(A) ) ). % 0.60/0.82 % 0.60/0.82 fof(rc1_ordinal1,axiom, % 0.60/0.82 ? [A] : % 0.60/0.82 ( epsilon_transitive(A) % 0.60/0.82 & epsilon_connected(A) % 0.60/0.82 & ordinal(A) ) ). % 0.60/0.82 % 0.60/0.82 fof(rc1_relat_1,axiom, % 0.60/0.82 ? [A] : % 0.60/0.82 ( empty(A) % 0.60/0.82 & relation(A) ) ). % 0.60/0.82 % 0.60/0.82 fof(rc1_xboole_0,axiom, % 0.60/0.82 ? [A] : empty(A) ). % 0.60/0.82 % 0.60/0.82 fof(rc2_funct_1,axiom, % 0.60/0.82 ? [A] : % 0.60/0.82 ( relation(A) % 0.60/0.82 & empty(A) % 0.60/0.82 & function(A) ) ). % 0.60/0.82 % 0.60/0.82 fof(rc2_relat_1,axiom, % 0.60/0.82 ? [A] : % 0.60/0.82 ( ~ empty(A) % 0.60/0.82 & relation(A) ) ). % 0.60/0.82 % 0.60/0.82 fof(rc2_xboole_0,axiom, % 0.60/0.82 ? [A] : ~ empty(A) ). % 0.60/0.82 % 0.60/0.82 fof(rc3_funct_1,axiom, % 0.60/0.82 ? [A] : % 0.60/0.82 ( relation(A) % 0.60/0.82 & function(A) % 0.60/0.82 & one_to_one(A) ) ). % 0.60/0.82 % 0.60/0.82 fof(rc3_relat_1,axiom, % 0.60/0.82 ? [A] : % 0.60/0.82 ( relation(A) % 0.60/0.82 & relation_empty_yielding(A) ) ). % 0.60/0.82 % 0.60/0.82 fof(rc4_funct_1,axiom, % 0.60/0.82 ? [A] : % 0.60/0.82 ( relation(A) % 0.60/0.82 & relation_empty_yielding(A) % 0.60/0.82 & function(A) ) ). % 0.60/0.82 % 0.60/0.82 fof(rc5_funct_1,axiom, % 0.60/0.82 ? [A] : % 0.60/0.82 ( relation(A) % 0.60/0.82 & relation_non_empty(A) % 0.60/0.82 & function(A) ) ). % 0.60/0.82 % 0.60/0.82 fof(reflexivity_r1_tarski,axiom, % 0.60/0.82 ! [A,B] : subset(A,A) ). % 0.60/0.82 % 0.60/0.82 fof(t1_subset,axiom, % 0.60/0.82 ! [A,B] : % 0.60/0.82 ( in(A,B) % 0.60/0.82 => element(A,B) ) ). % 0.60/0.82 % 0.60/0.82 fof(t1_xboole_1,axiom, % 0.60/0.82 ! [A,B,C] : % 0.60/0.82 ( ( subset(A,B) % 0.60/0.82 & subset(B,C) ) % 0.60/0.82 => subset(A,C) ) ). % 0.60/0.82 % 0.60/0.82 fof(t21_ordinal1,axiom, % 0.60/0.82 ! [A] : % 0.60/0.82 ( epsilon_transitive(A) % 0.60/0.82 => ! [B] : % 0.60/0.82 ( ordinal(B) % 0.60/0.82 => ( proper_subset(A,B) % 0.60/0.82 => in(A,B) ) ) ) ). % 0.60/0.82 % 0.60/0.82 fof(t22_ordinal1,conjecture, % 0.60/0.82 ! [A] : % 0.60/0.82 ( epsilon_transitive(A) % 0.60/0.82 => ! [B] : % 0.60/0.82 ( ordinal(B) % 0.60/0.82 => ! [C] : % 0.60/0.82 ( ordinal(C) % 0.60/0.82 => ( ( subset(A,B) % 0.60/0.82 & in(B,C) ) % 0.60/0.82 => in(A,C) ) ) ) ) ). % 0.60/0.82 % 0.60/0.82 fof(t2_subset,axiom, % 0.60/0.82 ! [A,B] : % 0.60/0.82 ( element(A,B) % 0.60/0.82 => ( empty(B) % 0.60/0.82 | in(A,B) ) ) ). % 0.60/0.82 % 0.60/0.82 fof(t3_subset,axiom, % 0.60/0.82 ! [A,B] : % 0.60/0.82 ( element(A,powerset(B)) % 0.60/0.82 <=> subset(A,B) ) ). % 0.60/0.82 % 0.60/0.82 fof(t4_subset,axiom, % 0.60/0.82 ! [A,B,C] : % 0.60/0.82 ( ( in(A,B) % 0.60/0.82 & element(B,powerset(C)) ) % 0.60/0.82 => element(A,C) ) ). % 0.60/0.82 % 0.60/0.82 fof(t5_subset,axiom, % 0.60/0.82 ! [A,B,C] : % 0.60/0.82 ~ ( in(A,B) % 0.60/0.82 & element(B,powerset(C)) % 0.60/0.82 & empty(C) ) ). % 0.60/0.82 % 0.60/0.82 fof(t6_boole,axiom, % 0.60/0.82 ! [A] : % 0.60/0.82 ( empty(A) % 0.60/0.82 => A = empty_set ) ). % 0.60/0.82 % 0.60/0.82 fof(t7_boole,axiom, % 0.60/0.82 ! [A,B] : % 0.60/0.82 ~ ( in(A,B) % 0.60/0.82 & empty(B) ) ). % 0.60/0.82 % 0.60/0.82 fof(t7_ordinal1,axiom, % 0.60/0.82 ! [A,B] : % 0.60/0.82 ~ ( in(A,B) % 0.60/0.82 & subset(B,A) ) ). % 0.60/0.82 % 0.60/0.82 fof(t8_boole,axiom, % 0.60/0.82 ! [A,B] : % 0.60/0.82 ~ ( empty(A) % 0.60/0.82 & A != B % 0.60/0.82 & empty(B) ) ). % 0.60/0.82 % 0.60/0.82 %------------------------------------------------------------------------------ % 0.60/0.82 %------------------------------------------- % 0.60/0.82 % Proof found % 0.60/0.82 % SZS status Theorem for theBenchmark % 0.60/0.82 % SZS output start Proof % 0.60/0.82 %ClaNum:89(EqnAxiom:23) % 0.60/0.82 %VarNum:107(SingletonVarNum:49) % 0.60/0.82 %MaxLitNum:4 % 0.60/0.82 %MaxfuncDepth:1 % 0.60/0.82 %SharedTerms:49 % 0.60/0.82 %goalClause: 36 37 39 56 57 62 % 0.60/0.82 %singleGoalClaCount:6 % 0.60/0.82 [26]P1(a1) % 0.60/0.82 [27]P1(a2) % 0.60/0.82 [28]P1(a14) % 0.60/0.82 [29]P1(a15) % 0.60/0.82 [30]P3(a3) % 0.60/0.82 [31]P3(a15) % 0.60/0.82 [32]P3(a4) % 0.60/0.82 [33]P3(a5) % 0.60/0.82 [34]P3(a7) % 0.60/0.82 [35]P6(a13) % 0.60/0.82 [36]P6(a8) % 0.60/0.82 [37]P6(a10) % 0.60/0.82 [38]P4(a13) % 0.60/0.82 [39]P4(a9) % 0.60/0.82 [40]P5(a13) % 0.60/0.82 [42]P9(a1) % 0.60/0.82 [43]P9(a3) % 0.60/0.82 [44]P9(a2) % 0.60/0.82 [45]P9(a15) % 0.60/0.82 [46]P9(a16) % 0.60/0.82 [47]P9(a4) % 0.60/0.82 [48]P9(a6) % 0.60/0.82 [49]P9(a5) % 0.60/0.82 [50]P9(a7) % 0.60/0.82 [51]P7(a4) % 0.60/0.82 [52]P11(a1) % 0.60/0.82 [53]P11(a6) % 0.60/0.82 [54]P11(a5) % 0.60/0.82 [55]P12(a7) % 0.60/0.82 [56]P8(a8,a10) % 0.60/0.82 [57]P13(a9,a8) % 0.60/0.82 [60]~P1(a16) % 0.60/0.82 [61]~P1(a17) % 0.60/0.82 [62]~P8(a9,a10) % 0.60/0.82 [58]P13(x581,x581) % 0.60/0.82 [63]~P10(x631,x631) % 0.60/0.82 [59]P2(f11(x591),x591) % 0.60/0.82 [64]~P1(x641)+E(x641,a1) % 0.60/0.82 [65]~P1(x651)+P3(x651) % 0.60/0.82 [66]~P6(x661)+P4(x661) % 0.60/0.82 [67]~P6(x671)+P5(x671) % 0.60/0.82 [68]~P1(x681)+P9(x681) % 0.60/0.82 [71]P4(x711)+P8(f12(x711),x711) % 0.60/0.82 [75]P4(x751)+~P13(f12(x751),x751) % 0.60/0.82 [73]~P10(x731,x732)+~E(x731,x732) % 0.60/0.82 [74]~P1(x741)+~P8(x742,x741) % 0.60/0.82 [76]~P10(x761,x762)+P13(x761,x762) % 0.60/0.82 [77]~P8(x771,x772)+P2(x771,x772) % 0.60/0.82 [82]~P8(x822,x821)+~P8(x821,x822) % 0.60/0.82 [83]~P13(x832,x831)+~P8(x831,x832) % 0.60/0.82 [84]~P10(x842,x841)+~P10(x841,x842) % 0.60/0.82 [80]~P13(x801,x802)+P2(x801,f18(x802)) % 0.60/0.82 [85]P13(x851,x852)+~P2(x851,f18(x852)) % 0.60/0.82 [70]~P4(x701)+~P5(x701)+P6(x701) % 0.60/0.82 [69]~P1(x692)+~P1(x691)+E(x691,x692) % 0.60/0.82 [78]P10(x781,x782)+~P13(x781,x782)+E(x781,x782) % 0.60/0.82 [79]~P2(x792,x791)+P1(x791)+P8(x792,x791) % 0.60/0.82 [81]~P4(x812)+~P8(x811,x812)+P13(x811,x812) % 0.60/0.82 [87]~P13(x871,x873)+P13(x871,x872)+~P13(x873,x872) % 0.60/0.82 [88]~P1(x881)+~P8(x882,x883)+~P2(x883,f18(x881)) % 0.60/0.82 [89]P2(x891,x892)+~P8(x891,x893)+~P2(x893,f18(x892)) % 0.60/0.82 [72]~P1(x721)+~P3(x721)+~P9(x721)+P7(x721) % 0.60/0.82 [86]~P6(x862)+~P4(x861)+~P10(x861,x862)+P8(x861,x862) % 0.60/0.82 %EqnAxiom % 0.60/0.82 [1]E(x11,x11) % 0.60/0.82 [2]E(x22,x21)+~E(x21,x22) % 0.60/0.82 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.60/0.82 [4]~E(x41,x42)+E(f11(x41),f11(x42)) % 0.60/0.82 [5]~E(x51,x52)+E(f12(x51),f12(x52)) % 0.60/0.82 [6]~E(x61,x62)+E(f18(x61),f18(x62)) % 0.60/0.82 [7]~P1(x71)+P1(x72)+~E(x71,x72) % 0.60/0.82 [8]P2(x82,x83)+~E(x81,x82)+~P2(x81,x83) % 0.60/0.82 [9]P2(x93,x92)+~E(x91,x92)+~P2(x93,x91) % 0.60/0.82 [10]P8(x102,x103)+~E(x101,x102)+~P8(x101,x103) % 0.60/0.82 [11]P8(x113,x112)+~E(x111,x112)+~P8(x113,x111) % 0.60/0.82 [12]P10(x122,x123)+~E(x121,x122)+~P10(x121,x123) % 0.60/0.82 [13]P10(x133,x132)+~E(x131,x132)+~P10(x133,x131) % 0.60/0.82 [14]P13(x142,x143)+~E(x141,x142)+~P13(x141,x143) % 0.60/0.82 [15]P13(x153,x152)+~E(x151,x152)+~P13(x153,x151) % 0.60/0.82 [16]~P3(x161)+P3(x162)+~E(x161,x162) % 0.60/0.82 [17]~P9(x171)+P9(x172)+~E(x171,x172) % 0.60/0.82 [18]~P6(x181)+P6(x182)+~E(x181,x182) % 0.60/0.82 [19]~P5(x191)+P5(x192)+~E(x191,x192) % 0.60/0.82 [20]~P11(x201)+P11(x202)+~E(x201,x202) % 0.60/0.82 [21]~P4(x211)+P4(x212)+~E(x211,x212) % 0.60/0.82 [22]~P7(x221)+P7(x222)+~E(x221,x222) % 0.60/0.82 [23]~P12(x231)+P12(x232)+~E(x231,x232) % 0.60/0.82 % 0.60/0.82 %------------------------------------------- % 0.60/0.82 cnf(101,plain, % 0.60/0.82 (P13(f11(f18(x1011)),x1011)), % 0.60/0.82 inference(scs_inference,[],[56,59,26,74,82,83,71,76,85])). % 0.60/0.82 cnf(102,plain, % 0.60/0.82 (P2(f11(x1021),x1021)), % 0.60/0.82 inference(rename_variables,[],[59])). % 0.60/0.82 cnf(105,plain, % 0.60/0.83 (P2(f11(x1051),x1051)), % 0.60/0.83 inference(rename_variables,[],[59])). % 0.60/0.83 cnf(112,plain, % 0.60/0.83 (~E(a9,a10)), % 0.60/0.83 inference(scs_inference,[],[56,57,62,59,102,105,26,60,74,82,83,71,76,85,79,88,10,11,14])). % 0.60/0.83 cnf(280,plain, % 0.60/0.83 (P13(a8,a10)), % 0.60/0.83 inference(scs_inference,[],[37,56,66,81])). % 0.60/0.83 cnf(281,plain, % 0.60/0.83 (P13(a9,a10)), % 0.60/0.83 inference(scs_inference,[],[57,280,87])). % 0.60/0.83 cnf(297,plain, % 0.60/0.83 ($false), % 0.60/0.83 inference(scs_inference,[],[37,39,62,112,281,101,87,78,86]), % 0.60/0.83 ['proof']). % 0.60/0.83 % SZS output end Proof % 0.60/0.83 % Total time :0.150000s %------------------------------------------------------------------------------