TSTP Solution File: NUM390+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM390+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 : n014.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 10:21:54 EDT 2023
% Result : Theorem 0.19s 0.74s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM390+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 11:45:48 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.19/0.73 %-------------------------------------------
% 0.19/0.73 % File :CSE---1.6
% 0.19/0.73 % Problem :theBenchmark
% 0.19/0.73 % Transform :cnf
% 0.19/0.73 % Format :tptp:raw
% 0.19/0.73 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.73
% 0.19/0.73 % Result :Theorem 0.110000s
% 0.19/0.73 % Output :CNFRefutation 0.110000s
% 0.19/0.73 %-------------------------------------------
% 0.19/0.73 %------------------------------------------------------------------------------
% 0.19/0.73 % File : NUM390+1 : TPTP v8.1.2. Released v3.2.0.
% 0.19/0.73 % Domain : Number Theory (Ordinals)
% 0.19/0.73 % Problem : Ordinal numbers, theorem 22
% 0.19/0.73 % Version : [Urb06] axioms : Especial.
% 0.19/0.73 % English :
% 0.19/0.73
% 0.19/0.74 % Refs : [Ban90] Bancerek (1990), The Ordinal Numbers
% 0.19/0.74 % [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.19/0.74 % Source : [Urb06]
% 0.19/0.74 % Names : ordinal1__t22_ordinal1 [Urb06]
% 0.19/0.74
% 0.19/0.74 % Status : Theorem
% 0.19/0.74 % 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
% 0.19/0.74 % Syntax : Number of formulae : 38 ( 6 unt; 0 def)
% 0.19/0.74 % Number of atoms : 95 ( 3 equ)
% 0.19/0.74 % Maximal formula atoms : 6 ( 2 avg)
% 0.19/0.74 % Number of connectives : 68 ( 11 ~; 1 |; 33 &)
% 0.19/0.74 % ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% 0.19/0.74 % Maximal formula depth : 9 ( 4 avg)
% 0.19/0.74 % Maximal term depth : 2 ( 1 avg)
% 0.19/0.74 % Number of predicates : 14 ( 13 usr; 0 prp; 1-2 aty)
% 0.19/0.74 % Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% 0.19/0.74 % Number of variables : 57 ( 45 !; 12 ?)
% 0.19/0.74 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.74
% 0.19/0.74 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.19/0.74 % library, www.mizar.org
% 0.19/0.74 %------------------------------------------------------------------------------
% 0.19/0.74 fof(antisymmetry_r2_hidden,axiom,
% 0.19/0.74 ! [A,B] :
% 0.19/0.74 ( in(A,B)
% 0.19/0.74 => ~ in(B,A) ) ).
% 0.19/0.74
% 0.19/0.74 fof(antisymmetry_r2_xboole_0,axiom,
% 0.19/0.74 ! [A,B] :
% 0.19/0.74 ( proper_subset(A,B)
% 0.19/0.74 => ~ proper_subset(B,A) ) ).
% 0.19/0.74
% 0.19/0.74 fof(cc1_funct_1,axiom,
% 0.19/0.74 ! [A] :
% 0.19/0.74 ( empty(A)
% 0.19/0.74 => function(A) ) ).
% 0.19/0.74
% 0.19/0.74 fof(cc1_ordinal1,axiom,
% 0.19/0.74 ! [A] :
% 0.19/0.74 ( ordinal(A)
% 0.19/0.74 => ( epsilon_transitive(A)
% 0.19/0.74 & epsilon_connected(A) ) ) ).
% 0.19/0.74
% 0.19/0.74 fof(cc1_relat_1,axiom,
% 0.19/0.74 ! [A] :
% 0.19/0.74 ( empty(A)
% 0.19/0.74 => relation(A) ) ).
% 0.19/0.74
% 0.19/0.74 fof(cc2_funct_1,axiom,
% 0.19/0.74 ! [A] :
% 0.19/0.74 ( ( relation(A)
% 0.19/0.74 & empty(A)
% 0.19/0.74 & function(A) )
% 0.19/0.74 => ( relation(A)
% 0.19/0.74 & function(A)
% 0.19/0.74 & one_to_one(A) ) ) ).
% 0.19/0.74
% 0.19/0.74 fof(cc2_ordinal1,axiom,
% 0.19/0.74 ! [A] :
% 0.19/0.74 ( ( epsilon_transitive(A)
% 0.19/0.74 & epsilon_connected(A) )
% 0.19/0.74 => ordinal(A) ) ).
% 0.19/0.74
% 0.19/0.74 fof(d2_ordinal1,axiom,
% 0.19/0.74 ! [A] :
% 0.19/0.74 ( epsilon_transitive(A)
% 0.19/0.74 <=> ! [B] :
% 0.19/0.74 ( in(B,A)
% 0.19/0.74 => subset(B,A) ) ) ).
% 0.19/0.74
% 0.19/0.74 fof(d8_xboole_0,axiom,
% 0.19/0.74 ! [A,B] :
% 0.19/0.74 ( proper_subset(A,B)
% 0.19/0.74 <=> ( subset(A,B)
% 0.19/0.74 & A != B ) ) ).
% 0.19/0.74
% 0.19/0.74 fof(existence_m1_subset_1,axiom,
% 0.19/0.74 ! [A] :
% 0.19/0.74 ? [B] : element(B,A) ).
% 0.19/0.74
% 0.19/0.74 fof(fc12_relat_1,axiom,
% 0.19/0.74 ( empty(empty_set)
% 0.19/0.74 & relation(empty_set)
% 0.19/0.74 & relation_empty_yielding(empty_set) ) ).
% 0.19/0.74
% 0.19/0.74 fof(fc1_xboole_0,axiom,
% 0.19/0.74 empty(empty_set) ).
% 0.19/0.74
% 0.19/0.74 fof(fc4_relat_1,axiom,
% 0.19/0.74 ( empty(empty_set)
% 0.19/0.74 & relation(empty_set) ) ).
% 0.19/0.74
% 0.19/0.74 fof(irreflexivity_r2_xboole_0,axiom,
% 0.19/0.74 ! [A,B] : ~ proper_subset(A,A) ).
% 0.19/0.74
% 0.19/0.74 fof(rc1_funct_1,axiom,
% 0.19/0.74 ? [A] :
% 0.19/0.74 ( relation(A)
% 0.19/0.74 & function(A) ) ).
% 0.19/0.74
% 0.19/0.74 fof(rc1_ordinal1,axiom,
% 0.19/0.74 ? [A] :
% 0.19/0.74 ( epsilon_transitive(A)
% 0.19/0.74 & epsilon_connected(A)
% 0.19/0.74 & ordinal(A) ) ).
% 0.19/0.74
% 0.19/0.74 fof(rc1_relat_1,axiom,
% 0.19/0.74 ? [A] :
% 0.19/0.74 ( empty(A)
% 0.19/0.74 & relation(A) ) ).
% 0.19/0.74
% 0.19/0.74 fof(rc1_xboole_0,axiom,
% 0.19/0.74 ? [A] : empty(A) ).
% 0.19/0.74
% 0.19/0.74 fof(rc2_funct_1,axiom,
% 0.19/0.74 ? [A] :
% 0.19/0.74 ( relation(A)
% 0.19/0.74 & empty(A)
% 0.19/0.74 & function(A) ) ).
% 0.19/0.74
% 0.19/0.74 fof(rc2_relat_1,axiom,
% 0.19/0.74 ? [A] :
% 0.19/0.74 ( ~ empty(A)
% 0.19/0.74 & relation(A) ) ).
% 0.19/0.74
% 0.19/0.74 fof(rc2_xboole_0,axiom,
% 0.19/0.74 ? [A] : ~ empty(A) ).
% 0.19/0.74
% 0.19/0.74 fof(rc3_funct_1,axiom,
% 0.19/0.74 ? [A] :
% 0.19/0.74 ( relation(A)
% 0.19/0.74 & function(A)
% 0.19/0.74 & one_to_one(A) ) ).
% 0.19/0.74
% 0.19/0.74 fof(rc3_relat_1,axiom,
% 0.19/0.74 ? [A] :
% 0.19/0.74 ( relation(A)
% 0.19/0.74 & relation_empty_yielding(A) ) ).
% 0.19/0.74
% 0.19/0.74 fof(rc4_funct_1,axiom,
% 0.19/0.74 ? [A] :
% 0.19/0.74 ( relation(A)
% 0.19/0.74 & relation_empty_yielding(A)
% 0.19/0.74 & function(A) ) ).
% 0.19/0.74
% 0.19/0.74 fof(rc5_funct_1,axiom,
% 0.19/0.74 ? [A] :
% 0.19/0.74 ( relation(A)
% 0.19/0.74 & relation_non_empty(A)
% 0.19/0.74 & function(A) ) ).
% 0.19/0.74
% 0.19/0.74 fof(reflexivity_r1_tarski,axiom,
% 0.19/0.74 ! [A,B] : subset(A,A) ).
% 0.19/0.74
% 0.19/0.74 fof(t1_subset,axiom,
% 0.19/0.74 ! [A,B] :
% 0.19/0.74 ( in(A,B)
% 0.19/0.74 => element(A,B) ) ).
% 0.19/0.74
% 0.19/0.74 fof(t1_xboole_1,axiom,
% 0.19/0.74 ! [A,B,C] :
% 0.19/0.74 ( ( subset(A,B)
% 0.19/0.74 & subset(B,C) )
% 0.19/0.74 => subset(A,C) ) ).
% 0.19/0.74
% 0.19/0.74 fof(t21_ordinal1,axiom,
% 0.19/0.74 ! [A] :
% 0.19/0.74 ( epsilon_transitive(A)
% 0.19/0.74 => ! [B] :
% 0.19/0.74 ( ordinal(B)
% 0.19/0.74 => ( proper_subset(A,B)
% 0.19/0.74 => in(A,B) ) ) ) ).
% 0.19/0.74
% 0.19/0.74 fof(t22_ordinal1,conjecture,
% 0.19/0.74 ! [A] :
% 0.19/0.74 ( epsilon_transitive(A)
% 0.19/0.74 => ! [B] :
% 0.19/0.74 ( ordinal(B)
% 0.19/0.74 => ! [C] :
% 0.19/0.74 ( ordinal(C)
% 0.19/0.74 => ( ( subset(A,B)
% 0.19/0.74 & in(B,C) )
% 0.19/0.74 => in(A,C) ) ) ) ) ).
% 0.19/0.74
% 0.19/0.74 fof(t2_subset,axiom,
% 0.19/0.74 ! [A,B] :
% 0.19/0.74 ( element(A,B)
% 0.19/0.74 => ( empty(B)
% 0.19/0.74 | in(A,B) ) ) ).
% 0.19/0.74
% 0.19/0.74 fof(t3_subset,axiom,
% 0.19/0.74 ! [A,B] :
% 0.19/0.74 ( element(A,powerset(B))
% 0.19/0.74 <=> subset(A,B) ) ).
% 0.19/0.74
% 0.19/0.74 fof(t4_subset,axiom,
% 0.19/0.74 ! [A,B,C] :
% 0.19/0.74 ( ( in(A,B)
% 0.19/0.74 & element(B,powerset(C)) )
% 0.19/0.74 => element(A,C) ) ).
% 0.19/0.74
% 0.19/0.74 fof(t5_subset,axiom,
% 0.19/0.74 ! [A,B,C] :
% 0.19/0.74 ~ ( in(A,B)
% 0.19/0.74 & element(B,powerset(C))
% 0.19/0.74 & empty(C) ) ).
% 0.19/0.74
% 0.19/0.74 fof(t6_boole,axiom,
% 0.19/0.74 ! [A] :
% 0.19/0.74 ( empty(A)
% 0.19/0.74 => A = empty_set ) ).
% 0.19/0.74
% 0.19/0.74 fof(t7_boole,axiom,
% 0.19/0.74 ! [A,B] :
% 0.19/0.74 ~ ( in(A,B)
% 0.19/0.74 & empty(B) ) ).
% 0.19/0.74
% 0.19/0.74 fof(t7_ordinal1,axiom,
% 0.19/0.74 ! [A,B] :
% 0.19/0.74 ~ ( in(A,B)
% 0.19/0.74 & subset(B,A) ) ).
% 0.19/0.74
% 0.19/0.74 fof(t8_boole,axiom,
% 0.19/0.74 ! [A,B] :
% 0.19/0.74 ~ ( empty(A)
% 0.19/0.74 & A != B
% 0.19/0.74 & empty(B) ) ).
% 0.19/0.74
% 0.19/0.74 %------------------------------------------------------------------------------
% 0.19/0.74 %-------------------------------------------
% 0.19/0.74 % Proof found
% 0.19/0.74 % SZS status Theorem for theBenchmark
% 0.19/0.74 % SZS output start Proof
% 0.19/0.74 %ClaNum:89(EqnAxiom:23)
% 0.19/0.74 %VarNum:107(SingletonVarNum:49)
% 0.19/0.74 %MaxLitNum:4
% 0.19/0.74 %MaxfuncDepth:1
% 0.19/0.74 %SharedTerms:49
% 0.19/0.75 %goalClause: 36 37 39 56 57 62
% 0.19/0.75 %singleGoalClaCount:6
% 0.19/0.75 [26]P1(a1)
% 0.19/0.75 [27]P1(a2)
% 0.19/0.75 [28]P1(a14)
% 0.19/0.75 [29]P1(a15)
% 0.19/0.75 [30]P3(a3)
% 0.19/0.75 [31]P3(a15)
% 0.19/0.75 [32]P3(a4)
% 0.19/0.75 [33]P3(a5)
% 0.19/0.75 [34]P3(a7)
% 0.19/0.75 [35]P6(a13)
% 0.19/0.75 [36]P6(a8)
% 0.19/0.75 [37]P6(a10)
% 0.19/0.75 [38]P4(a13)
% 0.19/0.75 [39]P4(a9)
% 0.19/0.75 [40]P5(a13)
% 0.19/0.75 [42]P9(a1)
% 0.19/0.75 [43]P9(a3)
% 0.19/0.75 [44]P9(a2)
% 0.19/0.75 [45]P9(a15)
% 0.19/0.75 [46]P9(a16)
% 0.19/0.75 [47]P9(a4)
% 0.19/0.75 [48]P9(a6)
% 0.19/0.75 [49]P9(a5)
% 0.19/0.75 [50]P9(a7)
% 0.19/0.75 [51]P7(a4)
% 0.19/0.75 [52]P11(a1)
% 0.19/0.75 [53]P11(a6)
% 0.19/0.75 [54]P11(a5)
% 0.19/0.75 [55]P12(a7)
% 0.19/0.75 [56]P8(a8,a10)
% 0.19/0.75 [57]P13(a9,a8)
% 0.19/0.75 [60]~P1(a16)
% 0.19/0.75 [61]~P1(a17)
% 0.19/0.75 [62]~P8(a9,a10)
% 0.19/0.75 [58]P13(x581,x581)
% 0.19/0.75 [63]~P10(x631,x631)
% 0.19/0.75 [59]P2(f11(x591),x591)
% 0.19/0.75 [64]~P1(x641)+E(x641,a1)
% 0.19/0.75 [65]~P1(x651)+P3(x651)
% 0.19/0.75 [66]~P6(x661)+P4(x661)
% 0.19/0.75 [67]~P6(x671)+P5(x671)
% 0.19/0.75 [68]~P1(x681)+P9(x681)
% 0.19/0.75 [71]P4(x711)+P8(f12(x711),x711)
% 0.19/0.75 [75]P4(x751)+~P13(f12(x751),x751)
% 0.19/0.75 [73]~P10(x731,x732)+~E(x731,x732)
% 0.19/0.75 [74]~P1(x741)+~P8(x742,x741)
% 0.19/0.75 [76]~P10(x761,x762)+P13(x761,x762)
% 0.19/0.75 [77]~P8(x771,x772)+P2(x771,x772)
% 0.19/0.75 [82]~P8(x822,x821)+~P8(x821,x822)
% 0.19/0.75 [83]~P13(x832,x831)+~P8(x831,x832)
% 0.19/0.75 [84]~P10(x842,x841)+~P10(x841,x842)
% 0.19/0.75 [80]~P13(x801,x802)+P2(x801,f18(x802))
% 0.19/0.75 [85]P13(x851,x852)+~P2(x851,f18(x852))
% 0.19/0.75 [70]~P4(x701)+~P5(x701)+P6(x701)
% 0.19/0.75 [69]~P1(x692)+~P1(x691)+E(x691,x692)
% 0.19/0.75 [78]P10(x781,x782)+~P13(x781,x782)+E(x781,x782)
% 0.19/0.75 [79]~P2(x792,x791)+P1(x791)+P8(x792,x791)
% 0.19/0.75 [81]~P4(x812)+~P8(x811,x812)+P13(x811,x812)
% 0.19/0.75 [87]~P13(x871,x873)+P13(x871,x872)+~P13(x873,x872)
% 0.19/0.75 [88]~P1(x881)+~P8(x882,x883)+~P2(x883,f18(x881))
% 0.19/0.75 [89]P2(x891,x892)+~P8(x891,x893)+~P2(x893,f18(x892))
% 0.19/0.75 [72]~P1(x721)+~P3(x721)+~P9(x721)+P7(x721)
% 0.19/0.75 [86]~P6(x862)+~P4(x861)+~P10(x861,x862)+P8(x861,x862)
% 0.19/0.75 %EqnAxiom
% 0.19/0.75 [1]E(x11,x11)
% 0.19/0.75 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.75 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.75 [4]~E(x41,x42)+E(f11(x41),f11(x42))
% 0.19/0.75 [5]~E(x51,x52)+E(f12(x51),f12(x52))
% 0.19/0.75 [6]~E(x61,x62)+E(f18(x61),f18(x62))
% 0.19/0.75 [7]~P1(x71)+P1(x72)+~E(x71,x72)
% 0.19/0.75 [8]P2(x82,x83)+~E(x81,x82)+~P2(x81,x83)
% 0.19/0.75 [9]P2(x93,x92)+~E(x91,x92)+~P2(x93,x91)
% 0.19/0.75 [10]P8(x102,x103)+~E(x101,x102)+~P8(x101,x103)
% 0.19/0.75 [11]P8(x113,x112)+~E(x111,x112)+~P8(x113,x111)
% 0.19/0.75 [12]P10(x122,x123)+~E(x121,x122)+~P10(x121,x123)
% 0.19/0.75 [13]P10(x133,x132)+~E(x131,x132)+~P10(x133,x131)
% 0.19/0.75 [14]P13(x142,x143)+~E(x141,x142)+~P13(x141,x143)
% 0.19/0.75 [15]P13(x153,x152)+~E(x151,x152)+~P13(x153,x151)
% 0.19/0.75 [16]~P3(x161)+P3(x162)+~E(x161,x162)
% 0.19/0.75 [17]~P9(x171)+P9(x172)+~E(x171,x172)
% 0.19/0.75 [18]~P6(x181)+P6(x182)+~E(x181,x182)
% 0.19/0.75 [19]~P5(x191)+P5(x192)+~E(x191,x192)
% 0.19/0.75 [20]~P11(x201)+P11(x202)+~E(x201,x202)
% 0.19/0.75 [21]~P4(x211)+P4(x212)+~E(x211,x212)
% 0.19/0.75 [22]~P7(x221)+P7(x222)+~E(x221,x222)
% 0.19/0.75 [23]~P12(x231)+P12(x232)+~E(x231,x232)
% 0.19/0.75
% 0.19/0.75 %-------------------------------------------
% 0.19/0.75 cnf(90,plain,
% 0.19/0.75 (~P13(a10,a8)),
% 0.19/0.75 inference(scs_inference,[],[56,83])).
% 0.19/0.75 cnf(91,plain,
% 0.19/0.75 (~P8(a10,a8)),
% 0.19/0.75 inference(scs_inference,[],[56,83,82])).
% 0.19/0.75 cnf(94,plain,
% 0.19/0.75 (~P8(x941,a1)),
% 0.19/0.75 inference(scs_inference,[],[56,26,83,82,76,74])).
% 0.19/0.75 cnf(97,plain,
% 0.19/0.75 (P2(f11(x971),x971)),
% 0.19/0.75 inference(rename_variables,[],[59])).
% 0.19/0.75 cnf(99,plain,
% 0.19/0.75 (P4(a1)),
% 0.19/0.75 inference(scs_inference,[],[56,26,59,83,82,76,74,85,71])).
% 0.19/0.75 cnf(102,plain,
% 0.19/0.75 (P13(x1021,x1021)),
% 0.19/0.75 inference(rename_variables,[],[58])).
% 0.19/0.75 cnf(104,plain,
% 0.19/0.75 (~E(a8,a9)),
% 0.19/0.75 inference(scs_inference,[],[58,102,56,62,26,59,83,82,76,74,85,71,15,14,10])).
% 0.19/0.75 cnf(105,plain,
% 0.19/0.75 (P13(f11(f18(a9)),a8)),
% 0.19/0.75 inference(scs_inference,[],[58,102,56,57,62,26,59,83,82,76,74,85,71,15,14,10,87])).
% 0.19/0.75 cnf(107,plain,
% 0.19/0.75 (P8(f11(a16),a16)),
% 0.19/0.75 inference(scs_inference,[],[58,102,56,57,62,26,60,59,97,83,82,76,74,85,71,15,14,10,87,79])).
% 0.19/0.75 cnf(120,plain,
% 0.19/0.75 (P3(a1)),
% 0.19/0.75 inference(scs_inference,[],[36,58,102,56,57,62,26,28,29,31,45,60,59,97,83,82,76,74,85,71,15,14,10,87,79,72,2,77,68,67,66,65])).
% 0.19/0.75 cnf(122,plain,
% 0.19/0.75 (E(a2,a1)),
% 0.19/0.75 inference(scs_inference,[],[36,58,102,56,57,62,26,27,28,29,31,45,60,59,97,83,82,76,74,85,71,15,14,10,87,79,72,2,77,68,67,66,65,64])).
% 0.19/0.75 cnf(126,plain,
% 0.19/0.75 (E(f18(a2),f18(a1))),
% 0.19/0.75 inference(scs_inference,[],[36,58,102,56,57,62,26,27,28,29,31,45,60,59,97,83,82,76,74,85,71,15,14,10,87,79,72,2,77,68,67,66,65,64,80,6])).
% 0.19/0.75 cnf(127,plain,
% 0.19/0.75 (E(f12(a2),f12(a1))),
% 0.19/0.75 inference(scs_inference,[],[36,58,102,56,57,62,26,27,28,29,31,45,60,59,97,83,82,76,74,85,71,15,14,10,87,79,72,2,77,68,67,66,65,64,80,6,5])).
% 0.19/0.75 cnf(128,plain,
% 0.19/0.75 (E(f11(a2),f11(a1))),
% 0.19/0.75 inference(scs_inference,[],[36,58,102,56,57,62,26,27,28,29,31,45,60,59,97,83,82,76,74,85,71,15,14,10,87,79,72,2,77,68,67,66,65,64,80,6,5,4])).
% 0.19/0.75 cnf(133,plain,
% 0.19/0.75 (~E(a1,a16)),
% 0.19/0.75 inference(scs_inference,[],[36,58,102,63,56,57,62,26,27,28,29,31,45,55,60,59,97,83,82,76,74,85,71,15,14,10,87,79,72,2,77,68,67,66,65,64,80,6,5,4,23,13,12,11,7])).
% 0.19/0.75 cnf(134,plain,
% 0.19/0.75 (P10(a9,a8)),
% 0.19/0.75 inference(scs_inference,[],[36,58,102,63,56,57,62,26,27,28,29,31,45,55,60,59,97,83,82,76,74,85,71,15,14,10,87,79,72,2,77,68,67,66,65,64,80,6,5,4,23,13,12,11,7,78])).
% 0.19/0.75 cnf(136,plain,
% 0.19/0.75 (~P2(a10,f18(a1))),
% 0.19/0.75 inference(scs_inference,[],[36,58,102,63,56,57,62,26,27,28,29,31,45,55,60,59,97,83,82,76,74,85,71,15,14,10,87,79,72,2,77,68,67,66,65,64,80,6,5,4,23,13,12,11,7,78,88])).
% 0.19/0.75 cnf(138,plain,
% 0.19/0.75 (~P10(a9,a10)),
% 0.19/0.75 inference(scs_inference,[],[36,58,102,63,37,39,56,57,62,26,27,28,29,31,45,55,60,59,97,83,82,76,74,85,71,15,14,10,87,79,72,2,77,68,67,66,65,64,80,6,5,4,23,13,12,11,7,78,88,86])).
% 0.19/0.75 cnf(140,plain,
% 0.19/0.75 (~P10(a8,a9)),
% 0.19/0.75 inference(scs_inference,[],[36,58,102,63,37,39,56,57,62,26,27,28,29,31,45,55,60,59,97,83,82,76,74,85,71,15,14,10,87,79,72,2,77,68,67,66,65,64,80,6,5,4,23,13,12,11,7,78,88,86,84])).
% 0.19/0.75 cnf(162,plain,
% 0.19/0.75 (~P2(a10,f18(a8))),
% 0.19/0.75 inference(scs_inference,[],[56,90,107,136,82,77,74,85])).
% 0.19/0.75 cnf(164,plain,
% 0.19/0.75 (~P13(a10,a1)),
% 0.19/0.75 inference(scs_inference,[],[56,90,107,136,82,77,74,85,80])).
% 0.19/0.75 cnf(166,plain,
% 0.19/0.75 (~P8(x1661,x1661)),
% 0.19/0.75 inference(scs_inference,[],[58,56,90,107,136,82,77,74,85,80,83])).
% 0.19/0.75 cnf(171,plain,
% 0.19/0.75 (~P10(x1711,x1711)),
% 0.19/0.75 inference(rename_variables,[],[63])).
% 0.19/0.75 cnf(174,plain,
% 0.19/0.75 (P2(f11(x1741),x1741)),
% 0.19/0.75 inference(rename_variables,[],[59])).
% 0.19/0.75 cnf(176,plain,
% 0.19/0.75 (P2(f11(x1761),x1761)),
% 0.19/0.75 inference(rename_variables,[],[59])).
% 0.19/0.75 cnf(177,plain,
% 0.19/0.75 (~E(a2,a17)),
% 0.19/0.75 inference(scs_inference,[],[61,58,27,59,174,63,56,90,94,122,127,107,136,82,77,74,85,80,83,14,12,11,9,8,7])).
% 0.19/0.75 cnf(180,plain,
% 0.19/0.75 (~P13(a8,a9)),
% 0.19/0.75 inference(scs_inference,[],[61,58,27,59,174,63,62,56,90,94,122,127,107,136,104,140,82,77,74,85,80,83,14,12,11,9,8,7,79,78])).
% 0.19/0.75 cnf(182,plain,
% 0.19/0.75 (~P2(a10,f18(a2))),
% 0.19/0.75 inference(scs_inference,[],[61,58,27,59,174,63,62,56,90,94,122,127,107,136,104,140,82,77,74,85,80,83,14,12,11,9,8,7,79,78,88])).
% 0.19/0.75 cnf(186,plain,
% 0.19/0.75 (E(a1,a2)),
% 0.19/0.75 inference(scs_inference,[],[42,61,58,27,59,174,63,62,26,56,90,94,122,127,107,136,104,120,140,82,77,74,85,80,83,14,12,11,9,8,7,79,78,88,72,2])).
% 0.19/0.75 cnf(200,plain,
% 0.19/0.75 (P8(a9,a8)),
% 0.19/0.75 inference(scs_inference,[],[36,42,51,52,61,58,27,59,174,176,63,171,39,62,26,56,90,94,122,126,127,107,136,99,104,120,133,134,140,82,77,74,85,80,83,14,12,11,9,8,7,79,78,88,72,2,13,15,22,21,20,16,81,89,3,86])).
% 0.19/0.75 cnf(202,plain,
% 0.19/0.75 (~E(a9,a10)),
% 0.19/0.75 inference(scs_inference,[],[36,42,51,52,61,58,27,59,174,176,63,171,39,62,26,56,90,91,94,122,126,127,107,136,99,104,120,133,134,140,82,77,74,85,80,83,14,12,11,9,8,7,79,78,88,72,2,13,15,22,21,20,16,81,89,3,86,10])).
% 0.19/0.75 cnf(212,plain,
% 0.19/0.75 (~P8(x2121,f11(f18(a14)))),
% 0.19/0.75 inference(scs_inference,[],[28,59,57,200,107,77,80,74,83,88])).
% 0.19/0.75 cnf(213,plain,
% 0.19/0.75 (P2(f11(x2131),x2131)),
% 0.19/0.75 inference(rename_variables,[],[59])).
% 0.19/0.75 cnf(217,plain,
% 0.19/0.75 (~P8(x2171,x2171)),
% 0.19/0.75 inference(rename_variables,[],[166])).
% 0.19/0.75 cnf(220,plain,
% 0.19/0.75 (P13(a2,a1)),
% 0.19/0.75 inference(scs_inference,[],[28,59,213,57,58,166,202,162,186,200,107,77,80,74,83,88,2,11,8,14])).
% 0.19/0.75 cnf(221,plain,
% 0.19/0.75 (P13(x2211,x2211)),
% 0.19/0.75 inference(rename_variables,[],[58])).
% 0.19/0.75 cnf(227,plain,
% 0.19/0.75 (~P2(a8,f18(a9))),
% 0.19/0.75 inference(scs_inference,[],[40,28,59,213,57,58,221,166,217,202,162,180,186,200,128,107,77,80,74,83,88,2,11,8,14,15,10,19,85])).
% 0.19/0.75 cnf(248,plain,
% 0.19/0.75 (~P8(x2481,f11(f18(a14)))),
% 0.19/0.75 inference(rename_variables,[],[212])).
% 0.19/0.75 cnf(249,plain,
% 0.19/0.75 (P2(f11(x2491),x2491)),
% 0.19/0.75 inference(rename_variables,[],[59])).
% 0.19/0.75 cnf(261,plain,
% 0.19/0.75 (P2(f11(x2611),x2611)),
% 0.19/0.75 inference(rename_variables,[],[59])).
% 0.19/0.75 cnf(278,plain,
% 0.19/0.75 (~P4(a10)),
% 0.19/0.75 inference(scs_inference,[],[37,61,29,59,249,261,57,56,212,248,182,138,220,227,177,164,105,166,202,126,128,107,122,77,78,79,88,74,89,83,3,8,2,11,7,14,9,10,18,87,80,85,81])).
% 0.19/0.75 cnf(294,plain,
% 0.19/0.75 ($false),
% 0.19/0.75 inference(scs_inference,[],[278,37,66]),
% 0.19/0.75 ['proof']).
% 0.19/0.75 % SZS output end Proof
% 0.19/0.75 % Total time :0.110000s
%------------------------------------------------------------------------------