TSTP Solution File: LCL808-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL808-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n010.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 : Fri Sep 1 18:55:55 EDT 2023
% Result : Unsatisfiable 0.22s 0.44s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 148
% Syntax : Number of formulae : 292 ( 88 unt; 0 def)
% Number of atoms : 675 ( 106 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 698 ( 315 ~; 297 |; 0 &)
% ( 86 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 99 ( 97 usr; 87 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-4 aty)
% Number of variables : 443 (; 443 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f693,plain,
$false,
inference(avatar_sat_refutation,[],[f81,f87,f92,f97,f102,f107,f112,f117,f122,f127,f132,f136,f140,f144,f149,f153,f157,f161,f165,f169,f173,f177,f181,f185,f189,f193,f197,f201,f205,f209,f213,f218,f226,f230,f234,f238,f242,f253,f257,f261,f265,f269,f273,f277,f281,f285,f289,f293,f308,f312,f338,f342,f347,f359,f363,f367,f429,f433,f437,f441,f445,f449,f453,f508,f527,f545,f551,f564,f568,f572,f576,f584,f588,f592,f602,f608,f612,f616,f620,f642,f650,f654,f679,f683,f687,f691,f692]) ).
fof(f692,plain,
( ~ spl0_4
| ~ spl0_15
| spl0_2
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f646,f618,f84,f146,f94]) ).
fof(f94,plain,
( spl0_4
<=> c_InductTermi_OIT(v_u____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f146,plain,
( spl0_15
<=> c_Type_Otyping(v_e____,v_u____,v_T____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f84,plain,
( spl0_2
<=> c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_n____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f618,plain,
( spl0_79
<=> ! [X0] :
( ~ c_Type_Otyping(v_e____,X0,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,X0,v_n____))
| ~ c_InductTermi_OIT(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f646,plain,
( ~ c_Type_Otyping(v_e____,v_u____,v_T____)
| ~ c_InductTermi_OIT(v_u____)
| spl0_2
| ~ spl0_79 ),
inference(resolution,[],[f619,f86]) ).
fof(f86,plain,
( ~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_n____))
| spl0_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f619,plain,
( ! [X0] :
( c_InductTermi_OIT(c_Lambda_Osubst(v_b____,X0,v_n____))
| ~ c_Type_Otyping(v_e____,X0,v_T____)
| ~ c_InductTermi_OIT(X0) )
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f618]) ).
fof(f691,plain,
( spl0_86
| ~ spl0_48
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f424,f365,f291,f689]) ).
fof(f689,plain,
( spl0_86
<=> ! [X38,X34,X36,X35,X37] :
( c_Lambda_Olift(c_Lambda_OdB_OApp(X34,X36),X35) != c_Lambda_OdB_OApp(X37,X38)
| c_Lambda_Olift(X34,X35) = X37 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f291,plain,
( spl0_48
<=> ! [X19,X20,X9,X8] :
( X8 = X19
| c_Lambda_OdB_OApp(X8,X9) != c_Lambda_OdB_OApp(X19,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f365,plain,
( spl0_56
<=> ! [X11,X12,X15] : c_Lambda_Olift(c_Lambda_OdB_OApp(X11,X12),X15) = c_Lambda_OdB_OApp(c_Lambda_Olift(X11,X15),c_Lambda_Olift(X12,X15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f424,plain,
( ! [X38,X36,X37,X34,X35] :
( c_Lambda_Olift(c_Lambda_OdB_OApp(X34,X36),X35) != c_Lambda_OdB_OApp(X37,X38)
| c_Lambda_Olift(X34,X35) = X37 )
| ~ spl0_48
| ~ spl0_56 ),
inference(superposition,[],[f292,f366]) ).
fof(f366,plain,
( ! [X11,X15,X12] : c_Lambda_Olift(c_Lambda_OdB_OApp(X11,X12),X15) = c_Lambda_OdB_OApp(c_Lambda_Olift(X11,X15),c_Lambda_Olift(X12,X15))
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f292,plain,
( ! [X8,X19,X9,X20] :
( c_Lambda_OdB_OApp(X8,X9) != c_Lambda_OdB_OApp(X19,X20)
| X8 = X19 )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f687,plain,
( spl0_85
| ~ spl0_47
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f422,f365,f287,f685]) ).
fof(f685,plain,
( spl0_85
<=> ! [X28,X24,X27,X25,X26] :
( c_Lambda_Olift(c_Lambda_OdB_OApp(X24,X26),X25) != c_Lambda_OdB_OApp(X27,X28)
| c_Lambda_Olift(X26,X25) = X28 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f287,plain,
( spl0_47
<=> ! [X20,X9,X8,X19] :
( X9 = X20
| c_Lambda_OdB_OApp(X8,X9) != c_Lambda_OdB_OApp(X19,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f422,plain,
( ! [X28,X26,X27,X24,X25] :
( c_Lambda_Olift(c_Lambda_OdB_OApp(X24,X26),X25) != c_Lambda_OdB_OApp(X27,X28)
| c_Lambda_Olift(X26,X25) = X28 )
| ~ spl0_47
| ~ spl0_56 ),
inference(superposition,[],[f288,f366]) ).
fof(f288,plain,
( ! [X8,X19,X9,X20] :
( c_Lambda_OdB_OApp(X8,X9) != c_Lambda_OdB_OApp(X19,X20)
| X9 = X20 )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f683,plain,
( spl0_84
| ~ spl0_35
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f349,f340,f232,f681]) ).
fof(f681,plain,
( spl0_84
<=> ! [X0,X1] :
( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1)
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f232,plain,
( spl0_35
<=> ! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f340,plain,
( spl0_52
<=> ! [X21,X16,X14] :
( ~ c_HOL_Oord__class_Oless(X21,X14,tc_nat)
| c_Lambda_OdB_OVar(X21) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X21),X16,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f349,plain,
( ! [X0,X1] :
( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1)
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
| ~ spl0_35
| ~ spl0_52 ),
inference(resolution,[],[f341,f233]) ).
fof(f233,plain,
( ! [X2] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2 )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f341,plain,
( ! [X21,X16,X14] :
( ~ c_HOL_Oord__class_Oless(X21,X14,tc_nat)
| c_Lambda_OdB_OVar(X21) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X21),X16,X14) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f679,plain,
( spl0_83
| ~ spl0_49
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f333,f310,f306,f677]) ).
fof(f677,plain,
( spl0_83
<=> ! [X2,X1] :
( c_Lambda_OdB_OVar(X1) = c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f306,plain,
( spl0_49
<=> ! [X2,X1] :
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f310,plain,
( spl0_50
<=> ! [X14,X15] :
( ~ c_HOL_Oord__class_Oless(X14,X15,tc_nat)
| c_Lambda_OdB_OVar(X14) = c_Lambda_Olift(c_Lambda_OdB_OVar(X14),X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f333,plain,
( ! [X2,X1] :
( c_Lambda_OdB_OVar(X1) = c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X1 = X2 )
| ~ spl0_49
| ~ spl0_50 ),
inference(resolution,[],[f311,f307]) ).
fof(f307,plain,
( ! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f311,plain,
( ! [X14,X15] :
( ~ c_HOL_Oord__class_Oless(X14,X15,tc_nat)
| c_Lambda_OdB_OVar(X14) = c_Lambda_Olift(c_Lambda_OdB_OVar(X14),X15) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f654,plain,
( ~ spl0_5
| spl0_82
| ~ spl0_35
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f471,f439,f232,f652,f99]) ).
fof(f99,plain,
( spl0_5
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f652,plain,
( spl0_82
<=> ! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f439,plain,
( spl0_60
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f471,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat) )
| ~ spl0_35
| ~ spl0_60 ),
inference(resolution,[],[f440,f233]) ).
fof(f440,plain,
( ! [X2,X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f650,plain,
( spl0_81
| ~ spl0_35
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f332,f310,f232,f648]) ).
fof(f648,plain,
( spl0_81
<=> ! [X0] :
( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f332,plain,
( ! [X0] :
( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_35
| ~ spl0_50 ),
inference(resolution,[],[f311,f233]) ).
fof(f642,plain,
( spl0_80
| ~ spl0_14
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f631,f610,f142,f640]) ).
fof(f640,plain,
( spl0_80
<=> ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f142,plain,
( spl0_14
<=> ! [X12,X14] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X14),X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f610,plain,
( spl0_77
<=> ! [X5,X4,X6,X3] :
( c_Lambda_Obeta(X3,c_Lambda_Osubst(X6,X5,X4))
| ~ c_Lambda_Obeta(c_Lambda_Olift(X3,X4),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f631,plain,
( ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1),X2)
| ~ spl0_14
| ~ spl0_77 ),
inference(resolution,[],[f611,f143]) ).
fof(f143,plain,
( ! [X14,X12] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X14),X12)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f611,plain,
( ! [X3,X6,X4,X5] :
( c_Lambda_Obeta(X3,c_Lambda_Osubst(X6,X5,X4))
| ~ c_Lambda_Obeta(c_Lambda_Olift(X3,X4),X6) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f620,plain,
( spl0_79
| ~ spl0_32
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f546,f543,f215,f618]) ).
fof(f215,plain,
( spl0_32
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_b____,v_Ua____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f543,plain,
( spl0_66
<=> ! [X24,X23,X25,X26] :
( ~ c_InductTermi_OIT(X23)
| ~ c_Type_Otyping(X25,X23,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,X23,X24))
| ~ c_Type_Otyping(c_Type_Oshift(X25,X24,v_T____,tc_Type_Otype),v_b____,X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f546,plain,
( ! [X0] :
( ~ c_Type_Otyping(v_e____,X0,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,X0,v_n____))
| ~ c_InductTermi_OIT(X0) )
| ~ spl0_32
| ~ spl0_66 ),
inference(resolution,[],[f544,f217]) ).
fof(f217,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_b____,v_Ua____)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f544,plain,
( ! [X26,X24,X25,X23] :
( ~ c_Type_Otyping(c_Type_Oshift(X25,X24,v_T____,tc_Type_Otype),v_b____,X26)
| ~ c_Type_Otyping(X25,X23,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,X23,X24))
| ~ c_InductTermi_OIT(X23) )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f616,plain,
( spl0_78
| ~ spl0_31
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f355,f345,f211,f614]) ).
fof(f614,plain,
( spl0_78
<=> ! [X5,X4,X6,X3] :
( c_Lambda_Obeta(c_Lambda_Osubst(X6,X5,X4),X3)
| ~ c_Lambda_Obeta(X6,c_Lambda_Olift(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f211,plain,
( spl0_31
<=> ! [X11,X12,X15] : c_Lambda_Osubst(c_Lambda_Olift(X12,X15),X11,X15) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f345,plain,
( spl0_53
<=> ! [X11,X13,X14,X12] :
( ~ c_Lambda_Obeta(X13,X11)
| c_Lambda_Obeta(c_Lambda_Osubst(X13,X12,X14),c_Lambda_Osubst(X11,X12,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f355,plain,
( ! [X3,X6,X4,X5] :
( c_Lambda_Obeta(c_Lambda_Osubst(X6,X5,X4),X3)
| ~ c_Lambda_Obeta(X6,c_Lambda_Olift(X3,X4)) )
| ~ spl0_31
| ~ spl0_53 ),
inference(superposition,[],[f346,f212]) ).
fof(f212,plain,
( ! [X11,X15,X12] : c_Lambda_Osubst(c_Lambda_Olift(X12,X15),X11,X15) = X12
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f346,plain,
( ! [X11,X14,X12,X13] :
( c_Lambda_Obeta(c_Lambda_Osubst(X13,X12,X14),c_Lambda_Osubst(X11,X12,X14))
| ~ c_Lambda_Obeta(X13,X11) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f612,plain,
( spl0_77
| ~ spl0_31
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f353,f345,f211,f610]) ).
fof(f353,plain,
( ! [X3,X6,X4,X5] :
( c_Lambda_Obeta(X3,c_Lambda_Osubst(X6,X5,X4))
| ~ c_Lambda_Obeta(c_Lambda_Olift(X3,X4),X6) )
| ~ spl0_31
| ~ spl0_53 ),
inference(superposition,[],[f346,f212]) ).
fof(f608,plain,
( spl0_76
| ~ spl0_27
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f297,f263,f195,f606]) ).
fof(f606,plain,
( spl0_76
<=> ! [X0,X1] :
( c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X0,c_Lambda_OdB_OAbs(X1)))
| ~ c_Lambda_Obeta(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f195,plain,
( spl0_27
<=> ! [X11,X12] :
( ~ c_Lambda_Obeta(X11,X12)
| c_Lambda_Obeta(c_Lambda_OdB_OAbs(X11),c_Lambda_OdB_OAbs(X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f263,plain,
( spl0_41
<=> ! [X13,X11] :
( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X13),X11)
| c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X13,X11)) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f297,plain,
( ! [X0,X1] :
( c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X0,c_Lambda_OdB_OAbs(X1)))
| ~ c_Lambda_Obeta(X0,X1) )
| ~ spl0_27
| ~ spl0_41 ),
inference(resolution,[],[f264,f196]) ).
fof(f196,plain,
( ! [X11,X12] :
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X11),c_Lambda_OdB_OAbs(X12))
| ~ c_Lambda_Obeta(X11,X12) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f264,plain,
( ! [X11,X13] :
( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X13),X11)
| c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X13,X11)) = X11 )
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f602,plain,
( spl0_75
| ~ spl0_26
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f354,f345,f191,f600]) ).
fof(f600,plain,
( spl0_75
<=> ! [X2,X0,X1] :
( c_Lambda_Obeta(c_Lambda_Osubst(X2,X1,X0),X1)
| ~ c_Lambda_Obeta(X2,c_Lambda_OdB_OVar(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f191,plain,
( spl0_26
<=> ! [X16,X15] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X15),X16,X15) = X16 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f354,plain,
( ! [X2,X0,X1] :
( c_Lambda_Obeta(c_Lambda_Osubst(X2,X1,X0),X1)
| ~ c_Lambda_Obeta(X2,c_Lambda_OdB_OVar(X0)) )
| ~ spl0_26
| ~ spl0_53 ),
inference(superposition,[],[f346,f192]) ).
fof(f192,plain,
( ! [X16,X15] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X15),X16,X15) = X16
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f592,plain,
( spl0_74
| ~ spl0_23
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f533,f525,f179,f590]) ).
fof(f590,plain,
( spl0_74
<=> ! [X5,X9,X7,X6,X8] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X5,X8),X6,X7) != c_Lambda_OdB_OAbs(X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f179,plain,
( spl0_23
<=> ! [X20,X17,X19] : c_Lambda_OdB_OAbs(X17) != c_Lambda_OdB_OApp(X19,X20) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f525,plain,
( spl0_65
<=> ! [X15,X11,X12,X16] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X12,X16),X11,X15) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X12,X11,X15),c_Lambda_Osubst(X16,X11,X15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f533,plain,
( ! [X8,X6,X9,X7,X5] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X5,X8),X6,X7) != c_Lambda_OdB_OAbs(X9)
| ~ spl0_23
| ~ spl0_65 ),
inference(superposition,[],[f180,f526]) ).
fof(f526,plain,
( ! [X11,X16,X15,X12] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X12,X16),X11,X15) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X12,X11,X15),c_Lambda_Osubst(X16,X11,X15))
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f525]) ).
fof(f180,plain,
( ! [X19,X17,X20] : c_Lambda_OdB_OAbs(X17) != c_Lambda_OdB_OApp(X19,X20)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f588,plain,
( spl0_73
| ~ spl0_22
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f532,f525,f175,f586]) ).
fof(f586,plain,
( spl0_73
<=> ! [X4,X0,X3,X2,X1] : c_Lambda_OdB_OVar(X4) != c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f175,plain,
( spl0_22
<=> ! [X9,X8,X10] : c_Lambda_OdB_OApp(X8,X9) != c_Lambda_OdB_OVar(X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f532,plain,
( ! [X2,X3,X0,X1,X4] : c_Lambda_OdB_OVar(X4) != c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2)
| ~ spl0_22
| ~ spl0_65 ),
inference(superposition,[],[f176,f526]) ).
fof(f176,plain,
( ! [X10,X8,X9] : c_Lambda_OdB_OApp(X8,X9) != c_Lambda_OdB_OVar(X10)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f584,plain,
( spl0_72
| ~ spl0_31
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f302,f283,f211,f582]) ).
fof(f582,plain,
( spl0_72
<=> ! [X2,X1] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat))),X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f283,plain,
( spl0_46
<=> ! [X11,X12] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X11),X12),c_Lambda_Osubst(X11,X12,c_HOL_Ozero__class_Ozero(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f302,plain,
( ! [X2,X1] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat))),X2),X1)
| ~ spl0_31
| ~ spl0_46 ),
inference(superposition,[],[f284,f212]) ).
fof(f284,plain,
( ! [X11,X12] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X11),X12),c_Lambda_Osubst(X11,X12,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f576,plain,
( spl0_71
| ~ spl0_23
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f417,f365,f179,f574]) ).
fof(f574,plain,
( spl0_71
<=> ! [X6,X4,X5,X7] : c_Lambda_Olift(c_Lambda_OdB_OApp(X4,X6),X5) != c_Lambda_OdB_OAbs(X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f417,plain,
( ! [X6,X7,X4,X5] : c_Lambda_Olift(c_Lambda_OdB_OApp(X4,X6),X5) != c_Lambda_OdB_OAbs(X7)
| ~ spl0_23
| ~ spl0_56 ),
inference(superposition,[],[f180,f366]) ).
fof(f572,plain,
( spl0_70
| ~ spl0_22
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f416,f365,f175,f570]) ).
fof(f570,plain,
( spl0_70
<=> ! [X2,X0,X1,X3] : c_Lambda_OdB_OVar(X3) != c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f416,plain,
( ! [X2,X3,X0,X1] : c_Lambda_OdB_OVar(X3) != c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1)
| ~ spl0_22
| ~ spl0_56 ),
inference(superposition,[],[f176,f366]) ).
fof(f568,plain,
( spl0_69
| ~ spl0_26
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f301,f283,f191,f566]) ).
fof(f566,plain,
( spl0_69
<=> ! [X0] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f301,plain,
( ! [X0] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),X0),X0)
| ~ spl0_26
| ~ spl0_46 ),
inference(superposition,[],[f284,f192]) ).
fof(f564,plain,
( spl0_68
| ~ spl0_36
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f486,f427,f236,f562]) ).
fof(f562,plain,
( spl0_68
<=> ! [X2,X3] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X2)))),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f236,plain,
( spl0_36
<=> ! [X13,X11] :
( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X13),X11)
| c_Lambda_Obeta(X13,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X13,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f427,plain,
( spl0_57
<=> ! [X2,X3] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X2))),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f486,plain,
( ! [X2,X3] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X2)))),X3)
| ~ spl0_36
| ~ spl0_57 ),
inference(resolution,[],[f428,f237]) ).
fof(f237,plain,
( ! [X11,X13] :
( c_Lambda_Obeta(X13,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X13,X11))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X13),X11) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f428,plain,
( ! [X2,X3] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X2))),X3)
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f427]) ).
fof(f551,plain,
( spl0_67
| ~ spl0_6
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f243,f228,f104,f548]) ).
fof(f548,plain,
( spl0_67
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f104,plain,
( spl0_6
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f228,plain,
( spl0_34
<=> ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f243,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_6
| ~ spl0_34 ),
inference(resolution,[],[f229,f106]) ).
fof(f106,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f229,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f545,plain,
spl0_66,
inference(avatar_split_clause,[],[f66,f543]) ).
fof(f66,axiom,
! [X26,X24,X25,X23] :
( ~ c_InductTermi_OIT(X23)
| ~ c_Type_Otyping(X25,X23,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,X23,X24))
| ~ c_Type_Otyping(c_Type_Oshift(X25,X24,v_T____,tc_Type_Otype),v_b____,X26) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_CHAINED_0_01) ).
fof(f527,plain,
spl0_65,
inference(avatar_split_clause,[],[f54,f525]) ).
fof(f54,axiom,
! [X11,X16,X15,X12] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X12,X16),X11,X15) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X12,X11,X15),c_Lambda_Osubst(X16,X11,X15)),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_subst__App_0) ).
fof(f508,plain,
spl0_64,
inference(avatar_split_clause,[],[f39,f506]) ).
fof(f506,plain,
( spl0_64
<=> ! [X11,X14,X15] :
( X14 = X15
| c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| c_Lambda_OdB_OVar(X14) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X14),X11,X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f39,axiom,
! [X11,X14,X15] :
( X14 = X15
| c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| c_Lambda_OdB_OVar(X14) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X14),X11,X15) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_subst__Var_2) ).
fof(f453,plain,
spl0_63,
inference(avatar_split_clause,[],[f27,f451]) ).
fof(f451,plain,
( spl0_63
<=> ! [X5,X0,X6,X7] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X7,X5,X0)
| c_HOL_Oord__class_Oless(X7,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f27,axiom,
! [X0,X6,X7,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X7,X5,X0)
| c_HOL_Oord__class_Oless(X7,X6,X0) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_xt1_I10_J_0) ).
fof(f449,plain,
spl0_62,
inference(avatar_split_clause,[],[f26,f447]) ).
fof(f447,plain,
( spl0_62
<=> ! [X6,X0,X5,X7] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(X6,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f26,axiom,
! [X0,X6,X7,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(X6,X7,X0) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_order__less__trans_0) ).
fof(f445,plain,
spl0_61,
inference(avatar_split_clause,[],[f13,f443]) ).
fof(f443,plain,
( spl0_61
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f13,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_of__nat__0__less__iff_1) ).
fof(f441,plain,
spl0_60,
inference(avatar_split_clause,[],[f12,f439]) ).
fof(f12,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_of__nat__0__less__iff_0) ).
fof(f437,plain,
spl0_59,
inference(avatar_split_clause,[],[f5,f435]) ).
fof(f435,plain,
( spl0_59
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_of__nat__less__iff_0) ).
fof(f433,plain,
spl0_58,
inference(avatar_split_clause,[],[f4,f431]) ).
fof(f431,plain,
( spl0_58
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_of__nat__less__iff_1) ).
fof(f429,plain,
( spl0_57
| ~ spl0_36
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f300,f275,f236,f427]) ).
fof(f275,plain,
( spl0_44
<=> ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f300,plain,
( ! [X2,X3] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X2))),X3)
| ~ spl0_36
| ~ spl0_44 ),
inference(resolution,[],[f276,f237]) ).
fof(f276,plain,
( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f367,plain,
spl0_56,
inference(avatar_split_clause,[],[f40,f365]) ).
fof(f40,axiom,
! [X11,X15,X12] : c_Lambda_Olift(c_Lambda_OdB_OApp(X11,X12),X15) = c_Lambda_OdB_OApp(c_Lambda_Olift(X11,X15),c_Lambda_Olift(X12,X15)),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_lift_Osimps_I2_J_0) ).
fof(f363,plain,
spl0_55,
inference(avatar_split_clause,[],[f20,f361]) ).
fof(f361,plain,
( spl0_55
<=> ! [X6,X0,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X5 = X6
| c_HOL_Oord__class_Oless(X6,X5,X0)
| c_HOL_Oord__class_Oless(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f20,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X5 = X6
| c_HOL_Oord__class_Oless(X6,X5,X0)
| c_HOL_Oord__class_Oless(X5,X6,X0) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_linorder__neqE__ordered__idom_0) ).
fof(f359,plain,
spl0_54,
inference(avatar_split_clause,[],[f15,f357]) ).
fof(f357,plain,
( spl0_54
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| X5 = X6
| c_HOL_Oord__class_Oless(X5,X6,X0)
| c_HOL_Oord__class_Oless(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f15,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| X5 = X6
| c_HOL_Oord__class_Oless(X5,X6,X0)
| c_HOL_Oord__class_Oless(X6,X5,X0) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_linorder__less__linear_0) ).
fof(f347,plain,
spl0_53,
inference(avatar_split_clause,[],[f60,f345]) ).
fof(f60,axiom,
! [X11,X14,X12,X13] :
( ~ c_Lambda_Obeta(X13,X11)
| c_Lambda_Obeta(c_Lambda_Osubst(X13,X12,X14),c_Lambda_Osubst(X11,X12,X14)) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_subst__preserves__beta_0) ).
fof(f342,plain,
spl0_52,
inference(avatar_split_clause,[],[f49,f340]) ).
fof(f49,axiom,
! [X21,X16,X14] :
( ~ c_HOL_Oord__class_Oless(X21,X14,tc_nat)
| c_Lambda_OdB_OVar(X21) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X21),X16,X14) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_subst__lt_0) ).
fof(f338,plain,
spl0_51,
inference(avatar_split_clause,[],[f3,f336]) ).
fof(f336,plain,
( spl0_51
<=> ! [X2,X0,X1] :
( ~ class_Nat_Osemiring__char__0(X0)
| X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X0) != c_Nat_Osemiring__1__class_Oof__nat(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ class_Nat_Osemiring__char__0(X0)
| X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X0) != c_Nat_Osemiring__1__class_Oof__nat(X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_of__nat__eq__iff_0) ).
fof(f312,plain,
spl0_50,
inference(avatar_split_clause,[],[f35,f310]) ).
fof(f35,axiom,
! [X14,X15] :
( ~ c_HOL_Oord__class_Oless(X14,X15,tc_nat)
| c_Lambda_OdB_OVar(X14) = c_Lambda_Olift(c_Lambda_OdB_OVar(X14),X15) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_lift_Osimps_I1_J_0) ).
fof(f308,plain,
spl0_49,
inference(avatar_split_clause,[],[f18,f306]) ).
fof(f18,axiom,
! [X2,X1] :
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_nat__neq__iff_0) ).
fof(f293,plain,
spl0_48,
inference(avatar_split_clause,[],[f46,f291]) ).
fof(f46,axiom,
! [X8,X19,X9,X20] :
( X8 = X19
| c_Lambda_OdB_OApp(X8,X9) != c_Lambda_OdB_OApp(X19,X20) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_dB_Osimps_I2_J_0) ).
fof(f289,plain,
spl0_47,
inference(avatar_split_clause,[],[f45,f287]) ).
fof(f45,axiom,
! [X8,X19,X9,X20] :
( X9 = X20
| c_Lambda_OdB_OApp(X8,X9) != c_Lambda_OdB_OApp(X19,X20) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_dB_Osimps_I2_J_1) ).
fof(f285,plain,
spl0_46,
inference(avatar_split_clause,[],[f44,f283]) ).
fof(f44,axiom,
! [X11,X12] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X11),X12),c_Lambda_Osubst(X11,X12,c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_beta_0) ).
fof(f281,plain,
spl0_45,
inference(avatar_split_clause,[],[f37,f279]) ).
fof(f279,plain,
( spl0_45
<=> ! [X11,X16,X12] :
( ~ c_Lambda_Obeta(X11,X12)
| c_Lambda_Obeta(c_Lambda_OdB_OApp(X16,X11),c_Lambda_OdB_OApp(X16,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f37,axiom,
! [X11,X16,X12] :
( ~ c_Lambda_Obeta(X11,X12)
| c_Lambda_Obeta(c_Lambda_OdB_OApp(X16,X11),c_Lambda_OdB_OApp(X16,X12)) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_appR_0) ).
fof(f277,plain,
( spl0_44
| ~ spl0_14
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f249,f236,f142,f275]) ).
fof(f249,plain,
( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1)
| ~ spl0_14
| ~ spl0_36 ),
inference(resolution,[],[f237,f143]) ).
fof(f273,plain,
spl0_43,
inference(avatar_split_clause,[],[f36,f271]) ).
fof(f271,plain,
( spl0_43
<=> ! [X11,X16,X12] :
( ~ c_Lambda_Obeta(X11,X12)
| c_Lambda_Obeta(c_Lambda_OdB_OApp(X11,X16),c_Lambda_OdB_OApp(X12,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f36,axiom,
! [X11,X16,X12] :
( ~ c_Lambda_Obeta(X11,X12)
| c_Lambda_Obeta(c_Lambda_OdB_OApp(X11,X16),c_Lambda_OdB_OApp(X12,X16)) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_appL_0) ).
fof(f269,plain,
spl0_42,
inference(avatar_split_clause,[],[f34,f267]) ).
fof(f267,plain,
( spl0_42
<=> ! [X13,X11,X14] :
( ~ c_Lambda_Obeta(X13,X11)
| c_Lambda_Obeta(c_Lambda_Olift(X13,X14),c_Lambda_Olift(X11,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f34,axiom,
! [X11,X14,X13] :
( ~ c_Lambda_Obeta(X13,X11)
| c_Lambda_Obeta(c_Lambda_Olift(X13,X14),c_Lambda_Olift(X11,X14)) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_lift__preserves__beta_0) ).
fof(f265,plain,
spl0_41,
inference(avatar_split_clause,[],[f32,f263]) ).
fof(f32,axiom,
! [X11,X13] :
( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X13),X11)
| c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X13,X11)) = X11 ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_beta__cases_I2_J_0) ).
fof(f261,plain,
spl0_40,
inference(avatar_split_clause,[],[f9,f259]) ).
fof(f259,plain,
( spl0_40
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f9,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_xt1_I9_J_0) ).
fof(f257,plain,
spl0_39,
inference(avatar_split_clause,[],[f8,f255]) ).
fof(f255,plain,
( spl0_39
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f8,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_not__less__iff__gr__or__eq_1) ).
fof(f253,plain,
spl0_38,
inference(avatar_split_clause,[],[f6,f251]) ).
fof(f251,plain,
( spl0_38
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f6,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_order__less__asym_H_0) ).
fof(f242,plain,
( spl0_37
| ~ spl0_30
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f222,f211,f207,f240]) ).
fof(f240,plain,
( spl0_37
<=> ! [X0,X1] :
( c_InductTermi_OIT(X0)
| ~ c_InductTermi_OIT(c_Lambda_Olift(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f207,plain,
( spl0_30
<=> ! [X13,X21,X14] :
( ~ c_InductTermi_OIT(X13)
| c_InductTermi_OIT(c_Lambda_Osubst(X13,c_Lambda_OdB_OVar(X14),X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f222,plain,
( ! [X0,X1] :
( c_InductTermi_OIT(X0)
| ~ c_InductTermi_OIT(c_Lambda_Olift(X0,X1)) )
| ~ spl0_30
| ~ spl0_31 ),
inference(superposition,[],[f208,f212]) ).
fof(f208,plain,
( ! [X21,X14,X13] :
( c_InductTermi_OIT(c_Lambda_Osubst(X13,c_Lambda_OdB_OVar(X14),X21))
| ~ c_InductTermi_OIT(X13) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f238,plain,
spl0_36,
inference(avatar_split_clause,[],[f48,f236]) ).
fof(f48,axiom,
! [X11,X13] :
( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X13),X11)
| c_Lambda_Obeta(X13,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X13,X11)) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_beta__cases_I2_J_1) ).
fof(f234,plain,
spl0_35,
inference(avatar_split_clause,[],[f11,f232]) ).
fof(f11,axiom,
! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_gr0I_0) ).
fof(f230,plain,
spl0_34,
inference(avatar_split_clause,[],[f2,f228]) ).
fof(f2,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_of__nat__0_0) ).
fof(f226,plain,
spl0_33,
inference(avatar_split_clause,[],[f1,f224]) ).
fof(f224,plain,
( spl0_33
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_of__nat__less__0__iff_0) ).
fof(f218,plain,
spl0_32,
inference(avatar_split_clause,[],[f76,f215]) ).
fof(f76,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_b____,v_Ua____),
inference(forward_demodulation,[],[f65,f58]) ).
fof(f58,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_True_0) ).
fof(f65,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_CHAINED_0) ).
fof(f213,plain,
spl0_31,
inference(avatar_split_clause,[],[f64,f211]) ).
fof(f64,axiom,
! [X11,X15,X12] : c_Lambda_Osubst(c_Lambda_Olift(X12,X15),X11,X15) = X12,
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_subst__lift_0) ).
fof(f209,plain,
spl0_30,
inference(avatar_split_clause,[],[f56,f207]) ).
fof(f56,axiom,
! [X21,X14,X13] :
( ~ c_InductTermi_OIT(X13)
| c_InductTermi_OIT(c_Lambda_Osubst(X13,c_Lambda_OdB_OVar(X14),X21)) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_subst__Var__IT_0) ).
fof(f205,plain,
spl0_29,
inference(avatar_split_clause,[],[f51,f203]) ).
fof(f203,plain,
( spl0_29
<=> ! [X22,X10] :
( X10 = X22
| c_Lambda_OdB_OVar(X10) != c_Lambda_OdB_OVar(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f51,axiom,
! [X10,X22] :
( X10 = X22
| c_Lambda_OdB_OVar(X10) != c_Lambda_OdB_OVar(X22) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_dB_Osimps_I1_J_0) ).
fof(f201,plain,
spl0_28,
inference(avatar_split_clause,[],[f42,f199]) ).
fof(f199,plain,
( spl0_28
<=> ! [X18,X17] :
( X17 = X18
| c_Lambda_OdB_OAbs(X17) != c_Lambda_OdB_OAbs(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f42,axiom,
! [X18,X17] :
( X17 = X18
| c_Lambda_OdB_OAbs(X17) != c_Lambda_OdB_OAbs(X18) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_dB_Osimps_I3_J_0) ).
fof(f197,plain,
spl0_27,
inference(avatar_split_clause,[],[f31,f195]) ).
fof(f31,axiom,
! [X11,X12] :
( ~ c_Lambda_Obeta(X11,X12)
| c_Lambda_Obeta(c_Lambda_OdB_OAbs(X11),c_Lambda_OdB_OAbs(X12)) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_abs_0) ).
fof(f193,plain,
spl0_26,
inference(avatar_split_clause,[],[f55,f191]) ).
fof(f55,axiom,
! [X16,X15] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X15),X16,X15) = X16,
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_subst__eq_0) ).
fof(f189,plain,
spl0_25,
inference(avatar_split_clause,[],[f33,f187]) ).
fof(f187,plain,
( spl0_25
<=> ! [X12,X14] :
( ~ c_InductTermi_OIT(X12)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(X12,c_Lambda_OdB_OVar(X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f33,axiom,
! [X14,X12] :
( ~ c_InductTermi_OIT(X12)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(X12,c_Lambda_OdB_OVar(X14))) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_app__Var__IT_0) ).
fof(f185,plain,
spl0_24,
inference(avatar_split_clause,[],[f57,f183]) ).
fof(f183,plain,
( spl0_24
<=> ! [X12,X14] :
( ~ c_InductTermi_OIT(X12)
| c_InductTermi_OIT(c_Lambda_Olift(X12,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f57,axiom,
! [X14,X12] :
( ~ c_InductTermi_OIT(X12)
| c_InductTermi_OIT(c_Lambda_Olift(X12,X14)) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_lift__IT_0) ).
fof(f181,plain,
spl0_23,
inference(avatar_split_clause,[],[f52,f179]) ).
fof(f52,axiom,
! [X19,X17,X20] : c_Lambda_OdB_OAbs(X17) != c_Lambda_OdB_OApp(X19,X20),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_dB_Osimps_I8_J_0) ).
fof(f177,plain,
spl0_22,
inference(avatar_split_clause,[],[f30,f175]) ).
fof(f30,axiom,
! [X10,X8,X9] : c_Lambda_OdB_OApp(X8,X9) != c_Lambda_OdB_OVar(X10),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_dB_Osimps_I5_J_0) ).
fof(f173,plain,
spl0_21,
inference(avatar_split_clause,[],[f23,f171]) ).
fof(f171,plain,
( spl0_21
<=> ! [X6,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f23,axiom,
! [X0,X6] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X6,X0) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_order__less__le_1) ).
fof(f169,plain,
spl0_20,
inference(avatar_split_clause,[],[f22,f167]) ).
fof(f167,plain,
( spl0_20
<=> ! [X6,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f22,axiom,
! [X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X6,X0) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_linorder__neq__iff_1) ).
fof(f165,plain,
spl0_19,
inference(avatar_split_clause,[],[f21,f163]) ).
fof(f163,plain,
( spl0_19
<=> ! [X6,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f21,axiom,
! [X0,X6] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X6,X0) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_order__less__irrefl_0) ).
fof(f161,plain,
spl0_18,
inference(avatar_split_clause,[],[f62,f159]) ).
fof(f159,plain,
( spl0_18
<=> ! [X13] :
( ~ c_InductTermi_OIT(X13)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f62,axiom,
! [X13] :
( ~ c_InductTermi_OIT(X13)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X13)) ),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_Lambda_0) ).
fof(f157,plain,
spl0_17,
inference(avatar_split_clause,[],[f41,f155]) ).
fof(f155,plain,
( spl0_17
<=> ! [X17,X10] : c_Lambda_OdB_OVar(X10) != c_Lambda_OdB_OAbs(X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f41,axiom,
! [X10,X17] : c_Lambda_OdB_OVar(X10) != c_Lambda_OdB_OAbs(X17),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_dB_Osimps_I6_J_0) ).
fof(f153,plain,
spl0_16,
inference(avatar_split_clause,[],[f28,f151]) ).
fof(f151,plain,
( spl0_16
<=> ! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f28,axiom,
! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_gr__implies__not0_0) ).
fof(f149,plain,
spl0_15,
inference(avatar_split_clause,[],[f68,f146]) ).
fof(f68,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_CHAINED_0_03) ).
fof(f144,plain,
spl0_14,
inference(avatar_split_clause,[],[f47,f142]) ).
fof(f47,axiom,
! [X14,X12] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X14),X12),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_beta__cases_I1_J_0) ).
fof(f140,plain,
spl0_13,
inference(avatar_split_clause,[],[f24,f138]) ).
fof(f138,plain,
( spl0_13
<=> ! [X2] : ~ c_HOL_Oord__class_Oless(X2,X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f24,axiom,
! [X2] : ~ c_HOL_Oord__class_Oless(X2,X2,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_less__not__refl_0) ).
fof(f136,plain,
spl0_12,
inference(avatar_split_clause,[],[f59,f134]) ).
fof(f134,plain,
( spl0_12
<=> ! [X2] : c_InductTermi_OIT(c_Lambda_OdB_OVar(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f59,axiom,
! [X2] : c_InductTermi_OIT(c_Lambda_OdB_OVar(X2)),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_Var__IT_0) ).
fof(f132,plain,
spl0_11,
inference(avatar_split_clause,[],[f58,f129]) ).
fof(f129,plain,
( spl0_11
<=> v_n____ = v_i____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f127,plain,
spl0_10,
inference(avatar_split_clause,[],[f75,f124]) ).
fof(f124,plain,
( spl0_10
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f75,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',clsarity_nat__Orderings_Oorder) ).
fof(f122,plain,
spl0_9,
inference(avatar_split_clause,[],[f74,f119]) ).
fof(f119,plain,
( spl0_9
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f74,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',clsarity_nat__Orderings_Olinorder) ).
fof(f117,plain,
spl0_8,
inference(avatar_split_clause,[],[f73,f114]) ).
fof(f114,plain,
( spl0_8
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f73,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',clsarity_nat__Orderings_Opreorder) ).
fof(f112,plain,
spl0_7,
inference(avatar_split_clause,[],[f72,f109]) ).
fof(f109,plain,
( spl0_7
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f72,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f107,plain,
spl0_6,
inference(avatar_split_clause,[],[f71,f104]) ).
fof(f71,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f102,plain,
spl0_5,
inference(avatar_split_clause,[],[f70,f99]) ).
fof(f70,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f97,plain,
spl0_4,
inference(avatar_split_clause,[],[f63,f94]) ).
fof(f63,axiom,
c_InductTermi_OIT(v_u____),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_uIT_0) ).
fof(f92,plain,
spl0_3,
inference(avatar_split_clause,[],[f61,f89]) ).
fof(f89,plain,
( spl0_3
<=> c_InductTermi_OIT(v_ua______) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f61,axiom,
c_InductTermi_OIT(v_ua______),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_Var_I3_J_0) ).
fof(f87,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f82,f78,f84]) ).
fof(f78,plain,
( spl0_1
<=> c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f82,plain,
( ~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_n____))
| spl0_1 ),
inference(forward_demodulation,[],[f80,f58]) ).
fof(f80,plain,
( ~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____))
| spl0_1 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f69,f78]) ).
fof(f69,axiom,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)),
file('/export/starexec/sandbox/tmp/tmp.DwpXPcx3cT/Vampire---4.8_12893',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : LCL808-1 : TPTP v8.1.2. Released v4.1.0.
% 0.14/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.36 % Computer : n010.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Wed Aug 30 14:35:03 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.22/0.42 % (13014)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (13016)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.22/0.42 % (13019)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.42 % (13017)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.22/0.42 % (13018)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.22/0.42 % (13020)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.22/0.42 % (13022)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.22/0.42 % (13021)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.22/0.43 TRYING [1]
% 0.22/0.43 TRYING [2]
% 0.22/0.43 TRYING [3]
% 0.22/0.44 TRYING [1]
% 0.22/0.44 % (13020)First to succeed.
% 0.22/0.44 TRYING [1]
% 0.22/0.44 TRYING [2]
% 0.22/0.44 TRYING [2]
% 0.22/0.44 % (13020)Refutation found. Thanks to Tanya!
% 0.22/0.44 % SZS status Unsatisfiable for Vampire---4
% 0.22/0.44 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.45 % (13020)------------------------------
% 0.22/0.45 % (13020)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.45 % (13020)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.45 % (13020)Termination reason: Refutation
% 0.22/0.45
% 0.22/0.45 % (13020)Memory used [KB]: 5884
% 0.22/0.45 % (13020)Time elapsed: 0.021 s
% 0.22/0.45 % (13020)------------------------------
% 0.22/0.45 % (13020)------------------------------
% 0.22/0.45 % (13014)Success in time 0.084 s
% 0.22/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------