TSTP Solution File: NUM393+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM393+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n006.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 : Thu Aug 31 10:21:55 EDT 2023
% Result : Theorem 0.81s 0.87s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM393+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 10:49:52 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.59 start to proof:theBenchmark
% 0.81/0.86 %-------------------------------------------
% 0.81/0.86 % File :CSE---1.6
% 0.81/0.86 % Problem :theBenchmark
% 0.81/0.86 % Transform :cnf
% 0.81/0.86 % Format :tptp:raw
% 0.81/0.86 % Command :java -jar mcs_scs.jar %d %s
% 0.81/0.86
% 0.81/0.86 % Result :Theorem 0.210000s
% 0.81/0.86 % Output :CNFRefutation 0.210000s
% 0.81/0.86 %-------------------------------------------
% 0.81/0.87 %------------------------------------------------------------------------------
% 0.81/0.87 % File : NUM393+1 : TPTP v8.1.2. Released v3.2.0.
% 0.81/0.87 % Domain : Number Theory (Ordinals)
% 0.81/0.87 % Problem : Ordinal numbers, theorem 25
% 0.81/0.87 % Version : [Urb06] axioms : Especial.
% 0.81/0.87 % English :
% 0.81/0.87
% 0.81/0.87 % Refs : [Ban90] Bancerek (1990), The Ordinal Numbers
% 0.81/0.87 % [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.81/0.87 % Source : [Urb06]
% 0.81/0.87 % Names : ordinal1__t25_ordinal1 [Urb06]
% 0.81/0.87
% 0.81/0.87 % Status : Theorem
% 0.81/0.87 % Rating : 0.11 v8.1.0, 0.06 v7.4.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.04 v6.3.0, 0.08 v6.1.0, 0.07 v6.0.0, 0.04 v5.5.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.05 v5.0.0, 0.04 v3.7.0, 0.05 v3.4.0, 0.11 v3.3.0, 0.07 v3.2.0
% 0.81/0.87 % Syntax : Number of formulae : 37 ( 6 unt; 0 def)
% 0.81/0.87 % Number of atoms : 91 ( 2 equ)
% 0.81/0.87 % Maximal formula atoms : 6 ( 2 avg)
% 0.81/0.87 % Number of connectives : 61 ( 7 ~; 3 |; 32 &)
% 0.81/0.87 % ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% 0.81/0.87 % Maximal formula depth : 7 ( 4 avg)
% 0.81/0.87 % Maximal term depth : 2 ( 1 avg)
% 0.81/0.87 % Number of predicates : 15 ( 14 usr; 0 prp; 1-2 aty)
% 0.81/0.87 % Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% 0.81/0.87 % Number of variables : 53 ( 41 !; 12 ?)
% 0.81/0.87 % SPC : FOF_THM_RFO_SEQ
% 0.81/0.87
% 0.81/0.87 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.81/0.87 % library, www.mizar.org
% 0.81/0.87 %------------------------------------------------------------------------------
% 0.81/0.87 fof(antisymmetry_r2_hidden,axiom,
% 0.81/0.87 ! [A,B] :
% 0.81/0.87 ( in(A,B)
% 0.81/0.87 => ~ in(B,A) ) ).
% 0.81/0.87
% 0.81/0.87 fof(cc1_funct_1,axiom,
% 0.81/0.87 ! [A] :
% 0.81/0.87 ( empty(A)
% 0.81/0.87 => function(A) ) ).
% 0.81/0.87
% 0.81/0.87 fof(cc1_ordinal1,axiom,
% 0.81/0.87 ! [A] :
% 0.81/0.87 ( ordinal(A)
% 0.81/0.87 => ( epsilon_transitive(A)
% 0.81/0.87 & epsilon_connected(A) ) ) ).
% 0.81/0.87
% 0.81/0.87 fof(cc1_relat_1,axiom,
% 0.81/0.87 ! [A] :
% 0.81/0.87 ( empty(A)
% 0.81/0.87 => relation(A) ) ).
% 0.81/0.87
% 0.81/0.87 fof(cc2_funct_1,axiom,
% 0.81/0.87 ! [A] :
% 0.81/0.87 ( ( relation(A)
% 0.81/0.87 & empty(A)
% 0.81/0.87 & function(A) )
% 0.81/0.87 => ( relation(A)
% 0.81/0.87 & function(A)
% 0.81/0.87 & one_to_one(A) ) ) ).
% 0.81/0.87
% 0.81/0.87 fof(cc2_ordinal1,axiom,
% 0.81/0.87 ! [A] :
% 0.81/0.87 ( ( epsilon_transitive(A)
% 0.81/0.87 & epsilon_connected(A) )
% 0.81/0.87 => ordinal(A) ) ).
% 0.81/0.87
% 0.81/0.87 fof(connectedness_r1_ordinal1,axiom,
% 0.81/0.87 ! [A,B] :
% 0.81/0.87 ( ( ordinal(A)
% 0.81/0.87 & ordinal(B) )
% 0.81/0.87 => ( ordinal_subset(A,B)
% 0.81/0.87 | ordinal_subset(B,A) ) ) ).
% 0.81/0.87
% 0.81/0.87 fof(d9_xboole_0,axiom,
% 0.81/0.87 ! [A,B] :
% 0.81/0.87 ( inclusion_comparable(A,B)
% 0.81/0.87 <=> ( subset(A,B)
% 0.81/0.87 | subset(B,A) ) ) ).
% 0.81/0.87
% 0.81/0.87 fof(existence_m1_subset_1,axiom,
% 0.81/0.87 ! [A] :
% 0.81/0.87 ? [B] : element(B,A) ).
% 0.81/0.87
% 0.81/0.87 fof(fc12_relat_1,axiom,
% 0.81/0.87 ( empty(empty_set)
% 0.81/0.87 & relation(empty_set)
% 0.81/0.87 & relation_empty_yielding(empty_set) ) ).
% 0.81/0.87
% 0.81/0.87 fof(fc1_xboole_0,axiom,
% 0.81/0.87 empty(empty_set) ).
% 0.81/0.87
% 0.81/0.87 fof(fc4_relat_1,axiom,
% 0.81/0.87 ( empty(empty_set)
% 0.81/0.87 & relation(empty_set) ) ).
% 0.81/0.87
% 0.81/0.87 fof(rc1_funct_1,axiom,
% 0.81/0.87 ? [A] :
% 0.81/0.87 ( relation(A)
% 0.81/0.87 & function(A) ) ).
% 0.81/0.87
% 0.81/0.87 fof(rc1_ordinal1,axiom,
% 0.81/0.87 ? [A] :
% 0.81/0.87 ( epsilon_transitive(A)
% 0.81/0.87 & epsilon_connected(A)
% 0.81/0.87 & ordinal(A) ) ).
% 0.81/0.87
% 0.81/0.87 fof(rc1_relat_1,axiom,
% 0.81/0.87 ? [A] :
% 0.81/0.87 ( empty(A)
% 0.81/0.87 & relation(A) ) ).
% 0.81/0.87
% 0.81/0.87 fof(rc1_xboole_0,axiom,
% 0.81/0.87 ? [A] : empty(A) ).
% 0.81/0.87
% 0.81/0.87 fof(rc2_funct_1,axiom,
% 0.81/0.87 ? [A] :
% 0.81/0.87 ( relation(A)
% 0.81/0.87 & empty(A)
% 0.81/0.87 & function(A) ) ).
% 0.81/0.87
% 0.81/0.87 fof(rc2_relat_1,axiom,
% 0.81/0.87 ? [A] :
% 0.81/0.87 ( ~ empty(A)
% 0.81/0.87 & relation(A) ) ).
% 0.81/0.87
% 0.81/0.87 fof(rc2_xboole_0,axiom,
% 0.81/0.87 ? [A] : ~ empty(A) ).
% 0.81/0.87
% 0.81/0.87 fof(rc3_funct_1,axiom,
% 0.81/0.87 ? [A] :
% 0.81/0.87 ( relation(A)
% 0.81/0.87 & function(A)
% 0.81/0.87 & one_to_one(A) ) ).
% 0.81/0.87
% 0.81/0.87 fof(rc3_relat_1,axiom,
% 0.81/0.87 ? [A] :
% 0.81/0.87 ( relation(A)
% 0.81/0.87 & relation_empty_yielding(A) ) ).
% 0.81/0.87
% 0.81/0.87 fof(rc4_funct_1,axiom,
% 0.81/0.87 ? [A] :
% 0.81/0.87 ( relation(A)
% 0.81/0.87 & relation_empty_yielding(A)
% 0.81/0.87 & function(A) ) ).
% 0.81/0.87
% 0.81/0.87 fof(rc5_funct_1,axiom,
% 0.81/0.87 ? [A] :
% 0.81/0.87 ( relation(A)
% 0.81/0.87 & relation_non_empty(A)
% 0.81/0.87 & function(A) ) ).
% 0.81/0.87
% 0.81/0.87 fof(redefinition_r1_ordinal1,axiom,
% 0.81/0.87 ! [A,B] :
% 0.81/0.87 ( ( ordinal(A)
% 0.81/0.87 & ordinal(B) )
% 0.81/0.87 => ( ordinal_subset(A,B)
% 0.81/0.87 <=> subset(A,B) ) ) ).
% 0.81/0.87
% 0.81/0.87 fof(reflexivity_r1_ordinal1,axiom,
% 0.81/0.87 ! [A,B] :
% 0.81/0.87 ( ( ordinal(A)
% 0.81/0.87 & ordinal(B) )
% 0.81/0.87 => ordinal_subset(A,A) ) ).
% 0.81/0.87
% 0.81/0.87 fof(reflexivity_r1_tarski,axiom,
% 0.81/0.87 ! [A,B] : subset(A,A) ).
% 0.81/0.87
% 0.81/0.87 fof(reflexivity_r3_xboole_0,axiom,
% 0.81/0.87 ! [A,B] : inclusion_comparable(A,A) ).
% 0.81/0.87
% 0.81/0.87 fof(symmetry_r3_xboole_0,axiom,
% 0.81/0.87 ! [A,B] :
% 0.81/0.87 ( inclusion_comparable(A,B)
% 0.81/0.87 => inclusion_comparable(B,A) ) ).
% 0.81/0.87
% 0.81/0.87 fof(t1_subset,axiom,
% 0.81/0.87 ! [A,B] :
% 0.81/0.87 ( in(A,B)
% 0.81/0.87 => element(A,B) ) ).
% 0.81/0.87
% 0.81/0.87 fof(t25_ordinal1,conjecture,
% 0.81/0.87 ! [A] :
% 0.81/0.87 ( ordinal(A)
% 0.81/0.87 => ! [B] :
% 0.81/0.87 ( ordinal(B)
% 0.81/0.87 => inclusion_comparable(A,B) ) ) ).
% 0.81/0.87
% 0.81/0.87 fof(t2_subset,axiom,
% 0.81/0.87 ! [A,B] :
% 0.81/0.87 ( element(A,B)
% 0.81/0.87 => ( empty(B)
% 0.81/0.87 | in(A,B) ) ) ).
% 0.81/0.87
% 0.81/0.87 fof(t3_subset,axiom,
% 0.81/0.87 ! [A,B] :
% 0.81/0.87 ( element(A,powerset(B))
% 0.81/0.87 <=> subset(A,B) ) ).
% 0.81/0.87
% 0.81/0.87 fof(t4_subset,axiom,
% 0.81/0.87 ! [A,B,C] :
% 0.81/0.87 ( ( in(A,B)
% 0.81/0.87 & element(B,powerset(C)) )
% 0.81/0.87 => element(A,C) ) ).
% 0.81/0.87
% 0.81/0.87 fof(t5_subset,axiom,
% 0.81/0.87 ! [A,B,C] :
% 0.81/0.87 ~ ( in(A,B)
% 0.81/0.87 & element(B,powerset(C))
% 0.81/0.87 & empty(C) ) ).
% 0.81/0.87
% 0.81/0.87 fof(t6_boole,axiom,
% 0.81/0.87 ! [A] :
% 0.81/0.87 ( empty(A)
% 0.81/0.87 => A = empty_set ) ).
% 0.81/0.87
% 0.81/0.87 fof(t7_boole,axiom,
% 0.81/0.87 ! [A,B] :
% 0.81/0.87 ~ ( in(A,B)
% 0.81/0.87 & empty(B) ) ).
% 0.81/0.87
% 0.81/0.87 fof(t8_boole,axiom,
% 0.81/0.87 ! [A,B] :
% 0.81/0.87 ~ ( empty(A)
% 0.81/0.87 & A != B
% 0.81/0.87 & empty(B) ) ).
% 0.81/0.87
% 0.81/0.87 %------------------------------------------------------------------------------
% 0.81/0.87 %-------------------------------------------
% 0.81/0.87 % Proof found
% 0.81/0.87 % SZS status Theorem for theBenchmark
% 0.81/0.88 % SZS output start Proof
% 0.81/0.88 %ClaNum:85(EqnAxiom:24)
% 0.81/0.88 %VarNum:102(SingletonVarNum:46)
% 0.81/0.88 %MaxLitNum:4
% 0.81/0.88 %MaxfuncDepth:1
% 0.81/0.88 %SharedTerms:45
% 0.81/0.88 %goalClause: 37 38 61
% 0.81/0.88 %singleGoalClaCount:3
% 0.81/0.88 [27]P1(a1)
% 0.81/0.88 [28]P1(a2)
% 0.81/0.88 [29]P1(a11)
% 0.81/0.88 [30]P1(a12)
% 0.81/0.88 [31]P3(a3)
% 0.81/0.88 [32]P3(a12)
% 0.81/0.88 [33]P3(a13)
% 0.81/0.88 [34]P3(a4)
% 0.81/0.88 [35]P3(a6)
% 0.81/0.88 [36]P6(a10)
% 0.81/0.88 [37]P6(a7)
% 0.81/0.88 [38]P6(a8)
% 0.81/0.88 [39]P4(a10)
% 0.81/0.88 [40]P5(a10)
% 0.81/0.88 [42]P10(a1)
% 0.81/0.88 [43]P10(a3)
% 0.81/0.88 [44]P10(a2)
% 0.81/0.88 [45]P10(a12)
% 0.81/0.88 [46]P10(a14)
% 0.81/0.88 [47]P10(a13)
% 0.81/0.88 [48]P10(a5)
% 0.81/0.88 [49]P10(a4)
% 0.81/0.88 [50]P10(a6)
% 0.81/0.88 [51]P7(a13)
% 0.81/0.88 [52]P12(a1)
% 0.81/0.88 [53]P12(a5)
% 0.81/0.88 [54]P12(a4)
% 0.81/0.88 [55]P13(a6)
% 0.81/0.88 [59]~P1(a14)
% 0.81/0.88 [60]~P1(a15)
% 0.81/0.88 [61]~P8(a7,a8)
% 0.81/0.88 [56]P8(x561,x561)
% 0.81/0.88 [57]P14(x571,x571)
% 0.81/0.88 [58]P2(f9(x581),x581)
% 0.81/0.88 [62]~P1(x621)+E(x621,a1)
% 0.81/0.88 [63]~P1(x631)+P3(x631)
% 0.81/0.88 [64]~P6(x641)+P4(x641)
% 0.81/0.88 [65]~P6(x651)+P5(x651)
% 0.81/0.88 [66]~P1(x661)+P10(x661)
% 0.81/0.88 [71]~P1(x711)+~P9(x712,x711)
% 0.81/0.88 [72]~P8(x722,x721)+P8(x721,x722)
% 0.81/0.88 [73]~P14(x732,x731)+P8(x731,x732)
% 0.81/0.88 [74]~P14(x741,x742)+P8(x741,x742)
% 0.81/0.88 [75]~P9(x751,x752)+P2(x751,x752)
% 0.81/0.88 [79]~P9(x792,x791)+~P9(x791,x792)
% 0.81/0.88 [77]~P14(x771,x772)+P2(x771,f16(x772))
% 0.81/0.88 [80]P14(x801,x802)+~P2(x801,f16(x802))
% 0.81/0.88 [68]~P4(x681)+~P5(x681)+P6(x681)
% 0.81/0.88 [67]~P1(x672)+~P1(x671)+E(x671,x672)
% 0.81/0.88 [70]~P6(x701)+P11(x701,x701)+~P6(x702)
% 0.81/0.88 [76]~P2(x762,x761)+P1(x761)+P9(x762,x761)
% 0.81/0.88 [83]P14(x832,x831)+~P8(x832,x831)+P14(x831,x832)
% 0.81/0.88 [84]~P1(x841)+~P9(x842,x843)+~P2(x843,f16(x841))
% 0.81/0.88 [85]P2(x851,x852)+~P9(x851,x853)+~P2(x853,f16(x852))
% 0.81/0.88 [69]~P1(x691)+~P3(x691)+~P10(x691)+P7(x691)
% 0.81/0.88 [78]P11(x782,x781)+~P6(x781)+~P6(x782)+P11(x781,x782)
% 0.81/0.88 [81]~P6(x812)+~P6(x811)+~P14(x811,x812)+P11(x811,x812)
% 0.81/0.88 [82]~P6(x822)+~P6(x821)+~P11(x821,x822)+P14(x821,x822)
% 0.81/0.88 %EqnAxiom
% 0.81/0.88 [1]E(x11,x11)
% 0.81/0.88 [2]E(x22,x21)+~E(x21,x22)
% 0.81/0.88 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.81/0.88 [4]~E(x41,x42)+E(f9(x41),f9(x42))
% 0.81/0.88 [5]~E(x51,x52)+E(f16(x51),f16(x52))
% 0.81/0.88 [6]~P1(x61)+P1(x62)+~E(x61,x62)
% 0.81/0.88 [7]P2(x72,x73)+~E(x71,x72)+~P2(x71,x73)
% 0.81/0.88 [8]P2(x83,x82)+~E(x81,x82)+~P2(x83,x81)
% 0.81/0.88 [9]P9(x92,x93)+~E(x91,x92)+~P9(x91,x93)
% 0.81/0.88 [10]P9(x103,x102)+~E(x101,x102)+~P9(x103,x101)
% 0.81/0.88 [11]P11(x112,x113)+~E(x111,x112)+~P11(x111,x113)
% 0.81/0.88 [12]P11(x123,x122)+~E(x121,x122)+~P11(x123,x121)
% 0.81/0.88 [13]P14(x132,x133)+~E(x131,x132)+~P14(x131,x133)
% 0.81/0.88 [14]P14(x143,x142)+~E(x141,x142)+~P14(x143,x141)
% 0.81/0.88 [15]~P6(x151)+P6(x152)+~E(x151,x152)
% 0.81/0.88 [16]~P3(x161)+P3(x162)+~E(x161,x162)
% 0.81/0.88 [17]~P10(x171)+P10(x172)+~E(x171,x172)
% 0.81/0.88 [18]~P5(x181)+P5(x182)+~E(x181,x182)
% 0.81/0.88 [19]P8(x192,x193)+~E(x191,x192)+~P8(x191,x193)
% 0.81/0.88 [20]P8(x203,x202)+~E(x201,x202)+~P8(x203,x201)
% 0.81/0.88 [21]~P4(x211)+P4(x212)+~E(x211,x212)
% 0.81/0.88 [22]~P12(x221)+P12(x222)+~E(x221,x222)
% 0.81/0.88 [23]~P7(x231)+P7(x232)+~E(x231,x232)
% 0.81/0.88 [24]~P13(x241)+P13(x242)+~E(x241,x242)
% 0.81/0.88
% 0.81/0.88 %-------------------------------------------
% 0.81/0.88 cnf(86,plain,
% 0.81/0.88 (~P14(a7,a8)),
% 0.81/0.88 inference(scs_inference,[],[61,74])).
% 0.81/0.88 cnf(87,plain,
% 0.81/0.88 (~P14(a8,a7)),
% 0.81/0.88 inference(scs_inference,[],[61,74,73])).
% 0.81/0.88 cnf(93,plain,
% 0.81/0.88 (P2(f9(x931),x931)),
% 0.81/0.88 inference(rename_variables,[],[58])).
% 0.81/0.88 cnf(113,plain,
% 0.81/0.88 (P3(a1)),
% 0.81/0.88 inference(scs_inference,[],[37,56,57,38,61,27,29,30,32,45,59,58,93,74,73,72,71,80,20,13,76,81,78,69,79,66,65,64,63])).
% 0.81/0.88 cnf(126,plain,
% 0.81/0.88 (~P2(a14,f16(a1))),
% 0.81/0.88 inference(scs_inference,[],[37,56,57,38,61,27,28,29,30,32,36,45,55,59,58,93,74,73,72,71,80,20,13,76,81,78,69,79,66,65,64,63,62,77,5,4,24,10,6,70,84])).
% 0.81/0.88 cnf(128,plain,
% 0.81/0.88 (~P11(a7,a8)),
% 0.81/0.88 inference(scs_inference,[],[37,56,57,38,61,27,28,29,30,32,36,45,55,59,58,93,74,73,72,71,80,20,13,76,81,78,69,79,66,65,64,63,62,77,5,4,24,10,6,70,84,82])).
% 0.81/0.88 cnf(130,plain,
% 0.81/0.88 (E(a1,a2)),
% 0.81/0.88 inference(scs_inference,[],[37,56,57,38,61,27,28,29,30,32,36,45,55,59,58,93,74,73,72,71,80,20,13,76,81,78,69,79,66,65,64,63,62,77,5,4,24,10,6,70,84,82,2])).
% 0.81/0.88 cnf(148,plain,
% 0.81/0.88 (~P2(a7,f16(a8))),
% 0.81/0.88 inference(scs_inference,[],[52,86,113,130,22,16,80])).
% 0.81/0.88 cnf(152,plain,
% 0.81/0.88 (P11(a8,a7)),
% 0.81/0.88 inference(scs_inference,[],[37,52,38,126,86,113,128,130,22,16,80,77,78])).
% 0.81/0.88 cnf(417,plain,
% 0.81/0.88 ($false),
% 0.81/0.88 inference(scs_inference,[],[87,148,152,38,37,75,82]),
% 0.81/0.88 ['proof']).
% 0.81/0.88 % SZS output end Proof
% 0.81/0.88 % Total time :0.210000s
%------------------------------------------------------------------------------