%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM394+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 : n029.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 17.93s 18.14s % Output : CNFRefutation 17.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : NUM394+1 : TPTP v8.2.0. Released v3.2.0. % 0.08/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.33 % Computer : n029.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Sun Jun 23 02:56:09 EDT 2024 % 0.13/0.34 % CPUTime : % 0.20/0.58 start to proof:theBenchmark % 17.93/18.12 %------------------------------------------- % 17.93/18.12 % File :CSE---1.7 % 17.93/18.12 % Problem :theBenchmark % 17.93/18.12 % Transform :cnf % 17.93/18.12 % Format :tptp:raw % 17.93/18.12 % Command :java -jar mcs_scs.jar %d %s % 17.93/18.12 % 17.93/18.12 % Result :Theorem 17.400000s % 17.93/18.12 % Output :CNFRefutation 17.400000s % 17.93/18.12 %------------------------------------------- % 17.93/18.13 %------------------------------------------------------------------------------ % 17.93/18.13 % File : NUM394+1 : TPTP v8.2.0. Released v3.2.0. % 17.93/18.13 % Domain : Number Theory (Ordinals) % 17.93/18.13 % Problem : Ordinal numbers, theorem 26 % 17.93/18.13 % Version : [Urb06] axioms : Especial. % 17.93/18.13 % English : % 17.93/18.13 % 17.93/18.13 % Refs : [Ban90] Bancerek (1990), The Ordinal Numbers % 17.93/18.13 % [Urb06] Urban (2006), Email to G. Sutcliffe % 17.93/18.13 % Source : [Urb06] % 17.93/18.13 % Names : ordinal1__t26_ordinal1 [Urb06] % 17.93/18.13 % 17.93/18.13 % Status : Theorem % 17.93/18.13 % Rating : 0.14 v8.1.0, 0.08 v7.5.0, 0.09 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, 0.13 v6.0.0, 0.09 v5.5.0, 0.11 v5.3.0, 0.19 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.09 v4.0.0, 0.08 v3.7.0, 0.05 v3.4.0, 0.11 v3.3.0, 0.07 v3.2.0 % 17.93/18.13 % Syntax : Number of formulae : 36 ( 5 unt; 0 def) % 17.93/18.13 % Number of atoms : 94 ( 3 equ) % 17.93/18.13 % Maximal formula atoms : 6 ( 2 avg) % 17.93/18.13 % Number of connectives : 69 ( 11 ~; 3 |; 34 &) % 17.93/18.13 % ( 3 <=>; 18 =>; 0 <=; 0 <~>) % 17.93/18.13 % Maximal formula depth : 9 ( 4 avg) % 17.93/18.13 % Maximal term depth : 2 ( 1 avg) % 17.93/18.13 % Number of predicates : 14 ( 13 usr; 0 prp; 1-2 aty) % 17.93/18.13 % Number of functors : 2 ( 2 usr; 1 con; 0-1 aty) % 17.93/18.13 % Number of variables : 51 ( 39 !; 12 ?) % 17.93/18.13 % SPC : FOF_THM_RFO_SEQ % 17.93/18.13 % 17.93/18.13 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 17.93/18.13 % library, www.mizar.org % 17.93/18.13 %------------------------------------------------------------------------------ % 17.93/18.13 fof(antisymmetry_r2_hidden,axiom, % 17.93/18.13 ! [A,B] : % 17.93/18.13 ( in(A,B) % 17.93/18.13 => ~ in(B,A) ) ). % 17.93/18.13 % 17.93/18.13 fof(cc1_funct_1,axiom, % 17.93/18.13 ! [A] : % 17.93/18.13 ( empty(A) % 17.93/18.13 => function(A) ) ). % 17.93/18.13 % 17.93/18.13 fof(cc1_ordinal1,axiom, % 17.93/18.13 ! [A] : % 17.93/18.13 ( ordinal(A) % 17.93/18.13 => ( epsilon_transitive(A) % 17.93/18.13 & epsilon_connected(A) ) ) ). % 17.93/18.13 % 17.93/18.13 fof(cc1_relat_1,axiom, % 17.93/18.13 ! [A] : % 17.93/18.13 ( empty(A) % 17.93/18.13 => relation(A) ) ). % 17.93/18.13 % 17.93/18.13 fof(cc2_funct_1,axiom, % 17.93/18.13 ! [A] : % 17.93/18.13 ( ( relation(A) % 17.93/18.13 & empty(A) % 17.93/18.13 & function(A) ) % 17.93/18.13 => ( relation(A) % 17.93/18.13 & function(A) % 17.93/18.13 & one_to_one(A) ) ) ). % 17.93/18.13 % 17.93/18.13 fof(cc2_ordinal1,axiom, % 17.93/18.13 ! [A] : % 17.93/18.13 ( ( epsilon_transitive(A) % 17.93/18.13 & epsilon_connected(A) ) % 17.93/18.13 => ordinal(A) ) ). % 17.93/18.13 % 17.93/18.13 fof(connectedness_r1_ordinal1,axiom, % 17.93/18.13 ! [A,B] : % 17.93/18.13 ( ( ordinal(A) % 17.93/18.13 & ordinal(B) ) % 17.93/18.13 => ( ordinal_subset(A,B) % 17.93/18.13 | ordinal_subset(B,A) ) ) ). % 17.93/18.13 % 17.93/18.13 fof(d2_ordinal1,axiom, % 17.93/18.13 ! [A] : % 17.93/18.13 ( epsilon_transitive(A) % 17.93/18.13 <=> ! [B] : % 17.93/18.13 ( in(B,A) % 17.93/18.13 => subset(B,A) ) ) ). % 17.93/18.13 % 17.93/18.13 fof(existence_m1_subset_1,axiom, % 17.93/18.13 ! [A] : % 17.93/18.13 ? [B] : element(B,A) ). % 17.93/18.13 % 17.93/18.13 fof(fc12_relat_1,axiom, % 17.93/18.13 ( empty(empty_set) % 17.93/18.13 & relation(empty_set) % 17.93/18.13 & relation_empty_yielding(empty_set) ) ). % 17.93/18.13 % 17.93/18.13 fof(fc1_xboole_0,axiom, % 17.93/18.13 empty(empty_set) ). % 17.93/18.13 % 17.93/18.13 fof(fc4_relat_1,axiom, % 17.93/18.13 ( empty(empty_set) % 17.93/18.13 & relation(empty_set) ) ). % 17.93/18.13 % 17.93/18.13 fof(rc1_funct_1,axiom, % 17.93/18.13 ? [A] : % 17.93/18.13 ( relation(A) % 17.93/18.13 & function(A) ) ). % 17.93/18.13 % 17.93/18.13 fof(rc1_ordinal1,axiom, % 17.93/18.13 ? [A] : % 17.93/18.13 ( epsilon_transitive(A) % 17.93/18.13 & epsilon_connected(A) % 17.93/18.13 & ordinal(A) ) ). % 17.93/18.13 % 17.93/18.13 fof(rc1_relat_1,axiom, % 17.93/18.13 ? [A] : % 17.93/18.13 ( empty(A) % 17.93/18.13 & relation(A) ) ). % 17.93/18.13 % 17.93/18.13 fof(rc1_xboole_0,axiom, % 17.93/18.13 ? [A] : empty(A) ). % 17.93/18.13 % 17.93/18.13 fof(rc2_funct_1,axiom, % 17.93/18.13 ? [A] : % 17.93/18.13 ( relation(A) % 17.93/18.13 & empty(A) % 17.93/18.13 & function(A) ) ). % 17.93/18.13 % 17.93/18.13 fof(rc2_relat_1,axiom, % 17.93/18.13 ? [A] : % 17.93/18.13 ( ~ empty(A) % 17.93/18.13 & relation(A) ) ). % 17.93/18.13 % 17.93/18.13 fof(rc2_xboole_0,axiom, % 17.93/18.13 ? [A] : ~ empty(A) ). % 17.93/18.13 % 17.93/18.13 fof(rc3_funct_1,axiom, % 17.93/18.13 ? [A] : % 17.93/18.13 ( relation(A) % 17.93/18.13 & function(A) % 17.93/18.13 & one_to_one(A) ) ). % 17.93/18.13 % 17.93/18.13 fof(rc3_relat_1,axiom, % 17.93/18.13 ? [A] : % 17.93/18.13 ( relation(A) % 17.93/18.13 & relation_empty_yielding(A) ) ). % 17.93/18.13 % 17.93/18.13 fof(rc4_funct_1,axiom, % 17.93/18.13 ? [A] : % 17.93/18.13 ( relation(A) % 17.93/18.13 & relation_empty_yielding(A) % 17.93/18.13 & function(A) ) ). % 17.93/18.13 % 17.93/18.13 fof(rc5_funct_1,axiom, % 17.93/18.13 ? [A] : % 17.93/18.13 ( relation(A) % 17.93/18.13 & relation_non_empty(A) % 17.93/18.13 & function(A) ) ). % 17.93/18.13 % 17.93/18.13 fof(redefinition_r1_ordinal1,axiom, % 17.93/18.13 ! [A,B] : % 17.93/18.13 ( ( ordinal(A) % 17.93/18.13 & ordinal(B) ) % 17.93/18.13 => ( ordinal_subset(A,B) % 17.93/18.13 <=> subset(A,B) ) ) ). % 17.93/18.13 % 17.93/18.13 fof(reflexivity_r1_ordinal1,axiom, % 17.93/18.13 ! [A,B] : % 17.93/18.13 ( ( ordinal(A) % 17.93/18.13 & ordinal(B) ) % 17.93/18.13 => ordinal_subset(A,A) ) ). % 17.93/18.13 % 17.93/18.13 fof(reflexivity_r1_tarski,axiom, % 17.93/18.13 ! [A,B] : subset(A,A) ). % 17.93/18.13 % 17.93/18.13 fof(t1_subset,axiom, % 17.93/18.13 ! [A,B] : % 17.93/18.13 ( in(A,B) % 17.93/18.13 => element(A,B) ) ). % 17.93/18.13 % 17.93/18.13 fof(t24_ordinal1,axiom, % 17.93/18.13 ! [A] : % 17.93/18.13 ( ordinal(A) % 17.93/18.13 => ! [B] : % 17.93/18.13 ( ordinal(B) % 17.93/18.14 => ~ ( ~ in(A,B) % 17.93/18.14 & A != B % 17.93/18.14 & ~ in(B,A) ) ) ) ). % 17.93/18.14 % 17.93/18.14 fof(t26_ordinal1,conjecture, % 17.93/18.14 ! [A] : % 17.93/18.14 ( ordinal(A) % 17.93/18.14 => ! [B] : % 17.93/18.14 ( ordinal(B) % 17.93/18.14 => ( ordinal_subset(A,B) % 17.93/18.14 | in(B,A) ) ) ) ). % 17.93/18.14 % 17.93/18.14 fof(t2_subset,axiom, % 17.93/18.14 ! [A,B] : % 17.93/18.14 ( element(A,B) % 17.93/18.14 => ( empty(B) % 17.93/18.14 | in(A,B) ) ) ). % 17.93/18.14 % 17.93/18.14 fof(t3_subset,axiom, % 17.93/18.14 ! [A,B] : % 17.93/18.14 ( element(A,powerset(B)) % 17.93/18.14 <=> subset(A,B) ) ). % 17.93/18.14 % 17.93/18.14 fof(t4_subset,axiom, % 17.93/18.14 ! [A,B,C] : % 17.93/18.14 ( ( in(A,B) % 17.93/18.14 & element(B,powerset(C)) ) % 17.93/18.14 => element(A,C) ) ). % 17.93/18.14 % 17.93/18.14 fof(t5_subset,axiom, % 17.93/18.14 ! [A,B,C] : % 17.93/18.14 ~ ( in(A,B) % 17.93/18.14 & element(B,powerset(C)) % 17.93/18.14 & empty(C) ) ). % 17.93/18.14 % 17.93/18.14 fof(t6_boole,axiom, % 17.93/18.14 ! [A] : % 17.93/18.14 ( empty(A) % 17.93/18.14 => A = empty_set ) ). % 17.93/18.14 % 17.93/18.14 fof(t7_boole,axiom, % 17.93/18.14 ! [A,B] : % 17.93/18.14 ~ ( in(A,B) % 17.93/18.14 & empty(B) ) ). % 17.93/18.14 % 17.93/18.14 fof(t8_boole,axiom, % 17.93/18.14 ! [A,B] : % 17.93/18.14 ~ ( empty(A) % 17.93/18.14 & A != B % 17.93/18.14 & empty(B) ) ). % 17.93/18.14 % 17.93/18.14 %------------------------------------------------------------------------------ % 17.93/18.14 %------------------------------------------- % 17.93/18.14 % Proof found % 17.93/18.14 % SZS status Theorem for theBenchmark % 17.93/18.14 % SZS output start Proof % 17.93/18.14 %ClaNum:84(EqnAxiom:23) % 17.93/18.14 %VarNum:101(SingletonVarNum:43) % 17.93/18.14 %MaxLitNum:5 % 17.93/18.14 %MaxfuncDepth:1 % 17.93/18.14 %SharedTerms:46 % 17.93/18.14 %goalClause: 36 37 59 60 % 17.93/18.14 %singleGoalClaCount:4 % 17.93/18.14 [26]P1(a1) % 17.93/18.14 [27]P1(a2) % 17.93/18.14 [28]P1(a13) % 17.93/18.14 [29]P1(a14) % 17.93/18.14 [30]P3(a3) % 17.93/18.14 [31]P3(a14) % 17.93/18.14 [32]P3(a4) % 17.93/18.14 [33]P3(a5) % 17.93/18.14 [34]P3(a7) % 17.93/18.14 [35]P6(a12) % 17.93/18.14 [36]P6(a8) % 17.93/18.14 [37]P6(a9) % 17.93/18.14 [38]P4(a12) % 17.93/18.14 [39]P5(a12) % 17.93/18.14 [41]P9(a1) % 17.93/18.14 [42]P9(a3) % 17.93/18.14 [43]P9(a2) % 17.93/18.14 [44]P9(a14) % 17.93/18.14 [45]P9(a15) % 17.93/18.14 [46]P9(a4) % 17.93/18.14 [47]P9(a6) % 17.93/18.14 [48]P9(a5) % 17.93/18.14 [49]P9(a7) % 17.93/18.14 [50]P7(a4) % 17.93/18.14 [51]P11(a1) % 17.93/18.14 [52]P11(a6) % 17.93/18.14 [53]P11(a5) % 17.93/18.14 [54]P12(a7) % 17.93/18.14 [57]~P1(a15) % 17.93/18.14 [58]~P1(a16) % 17.93/18.14 [59]~P8(a9,a8) % 17.93/18.14 [60]~P10(a8,a9) % 17.93/18.14 [55]P13(x551,x551) % 17.93/18.14 [56]P2(f10(x561),x561) % 17.93/18.14 [61]~P1(x611)+E(x611,a1) % 17.93/18.14 [62]~P1(x621)+P3(x621) % 17.93/18.14 [63]~P6(x631)+P4(x631) % 17.93/18.14 [64]~P6(x641)+P5(x641) % 17.93/18.14 [65]~P1(x651)+P9(x651) % 17.93/18.14 [68]P4(x681)+P8(f11(x681),x681) % 17.93/18.14 [72]P4(x721)+~P13(f11(x721),x721) % 17.93/18.14 [71]~P1(x711)+~P8(x712,x711) % 17.93/18.14 [73]~P8(x731,x732)+P2(x731,x732) % 17.93/18.14 [78]~P8(x782,x781)+~P8(x781,x782) % 17.93/18.14 [75]~P13(x751,x752)+P2(x751,f17(x752)) % 17.93/18.14 [80]P13(x801,x802)+~P2(x801,f17(x802)) % 17.93/18.14 [67]~P4(x671)+~P5(x671)+P6(x671) % 17.93/18.14 [66]~P1(x662)+~P1(x661)+E(x661,x662) % 17.93/18.14 [70]~P6(x701)+P10(x701,x701)+~P6(x702) % 17.93/18.14 [74]~P2(x742,x741)+P1(x741)+P8(x742,x741) % 17.93/18.14 [77]~P4(x772)+~P8(x771,x772)+P13(x771,x772) % 17.93/18.14 [83]~P1(x831)+~P8(x832,x833)+~P2(x833,f17(x831)) % 17.93/18.14 [84]P2(x841,x842)+~P8(x841,x843)+~P2(x843,f17(x842)) % 17.93/18.14 [69]~P1(x691)+~P3(x691)+~P9(x691)+P7(x691) % 17.93/18.14 [76]P10(x762,x761)+~P6(x761)+~P6(x762)+P10(x761,x762) % 17.93/18.14 [81]~P6(x812)+~P6(x811)+~P13(x811,x812)+P10(x811,x812) % 17.93/18.14 [82]~P6(x822)+~P6(x821)+~P10(x821,x822)+P13(x821,x822) % 17.93/18.14 [79]P8(x792,x791)+P8(x791,x792)+~P6(x792)+~P6(x791)+E(x791,x792) % 17.93/18.14 %EqnAxiom % 17.93/18.14 [1]E(x11,x11) % 17.93/18.14 [2]E(x22,x21)+~E(x21,x22) % 17.93/18.14 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 17.93/18.14 [4]~E(x41,x42)+E(f10(x41),f10(x42)) % 17.93/18.14 [5]~E(x51,x52)+E(f11(x51),f11(x52)) % 17.93/18.14 [6]~E(x61,x62)+E(f17(x61),f17(x62)) % 17.93/18.14 [7]~P1(x71)+P1(x72)+~E(x71,x72) % 17.93/18.14 [8]P2(x82,x83)+~E(x81,x82)+~P2(x81,x83) % 17.93/18.14 [9]P2(x93,x92)+~E(x91,x92)+~P2(x93,x91) % 17.93/18.14 [10]P8(x102,x103)+~E(x101,x102)+~P8(x101,x103) % 17.93/18.14 [11]P8(x113,x112)+~E(x111,x112)+~P8(x113,x111) % 17.93/18.14 [12]~P6(x121)+P6(x122)+~E(x121,x122) % 17.93/18.14 [13]P13(x132,x133)+~E(x131,x132)+~P13(x131,x133) % 17.93/18.14 [14]P13(x143,x142)+~E(x141,x142)+~P13(x143,x141) % 17.93/18.14 [15]~P4(x151)+P4(x152)+~E(x151,x152) % 17.93/18.14 [16]~P3(x161)+P3(x162)+~E(x161,x162) % 17.93/18.14 [17]P10(x172,x173)+~E(x171,x172)+~P10(x171,x173) % 17.93/18.14 [18]P10(x183,x182)+~E(x181,x182)+~P10(x183,x181) % 17.93/18.14 [19]~P7(x191)+P7(x192)+~E(x191,x192) % 17.93/18.14 [20]~P9(x201)+P9(x202)+~E(x201,x202) % 17.93/18.14 [21]~P12(x211)+P12(x212)+~E(x211,x212) % 17.93/18.14 [22]~P5(x221)+P5(x222)+~E(x221,x222) % 17.93/18.14 [23]~P11(x231)+P11(x232)+~E(x231,x232) % 17.93/18.14 % 17.93/18.14 %------------------------------------------- % 17.93/18.14 cnf(88,plain, % 17.93/18.14 (P2(f10(x881),x881)), % 17.93/18.14 inference(rename_variables,[],[56])). % 17.93/18.14 cnf(92,plain, % 17.93/18.14 (P8(f10(a15),a15)), % 17.93/18.14 inference(scs_inference,[],[56,88,26,57,71,80,68,74])). % 17.93/18.14 cnf(93,plain, % 17.93/18.14 (P2(f10(x931),x931)), % 17.93/18.14 inference(rename_variables,[],[56])). % 17.93/18.14 cnf(95,plain, % 17.93/18.14 (~P8(x951,f10(f17(a1)))), % 17.93/18.14 inference(scs_inference,[],[56,88,93,26,57,71,80,68,74,83])). % 17.93/18.14 cnf(119,plain, % 17.93/18.14 (P10(x1191,x1191)+~P6(x1191)), % 17.93/18.14 inference(scs_inference,[],[36,70])). % 17.93/18.14 cnf(127,plain, % 17.93/18.14 (P2(f10(x1271),x1271)), % 17.93/18.14 inference(rename_variables,[],[56])). % 17.93/18.14 cnf(137,plain, % 17.93/18.14 (P8(a8,a9)), % 17.93/18.14 inference(scs_inference,[],[36,37,59,60,35,95,27,58,56,127,119,71,68,74,83,17,11,76,79])). % 17.93/18.14 cnf(170,plain, % 17.93/18.14 (~P8(x1701,f10(f17(a14)))), % 17.93/18.14 inference(scs_inference,[],[29,56,71,68,83])). % 17.93/18.14 cnf(181,plain, % 17.93/18.14 (~E(a15,f10(f17(a14)))), % 17.93/18.14 inference(scs_inference,[],[92,170,11])). % 17.93/18.14 cnf(7107,plain, % 17.93/18.14 (P13(a8,a9)+~P4(a9)), % 17.93/18.14 inference(scs_inference,[],[181,137,2,77])). % 17.93/18.14 cnf(7280,plain, % 17.93/18.14 (~P4(a9)), % 17.93/18.14 inference(scs_inference,[],[60,37,36,7107,81])). % 17.93/18.14 cnf(7281,plain, % 17.93/18.14 ($false), % 17.93/18.14 inference(scs_inference,[],[37,7280,63]), % 17.93/18.14 ['proof']). % 17.93/18.15 % SZS output end Proof % 17.93/18.15 % Total time :17.400000s %------------------------------------------------------------------------------