TSTP Solution File: DAT297^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT297^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.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 May 20 19:52:05 EDT 2024
% Result : Theorem 2.20s 0.68s
% Output : Refutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 56
% Syntax : Number of formulae : 317 ( 20 unt; 20 typ; 0 def)
% Number of atoms : 3767 ( 703 equ; 0 cnn)
% Maximal formula atoms : 7 ( 12 avg)
% Number of connectives : 1006 ( 273 ~; 703 |; 0 &; 0 @)
% ( 29 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 239 ( 238 >; 1 *; 0 +; 0 <<)
% Number of symbols : 54 ( 51 usr; 34 con; 0-6 aty)
% Number of variables : 588 ( 0 ^ 565 !; 12 ?; 588 :)
% ( 11 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
'type/ind_types/list': $tType > $tType ).
thf(type_def_7,type,
sK0: $tType ).
thf(type_def_8,type,
sK1: $tType ).
thf(func_def_0,type,
'type/ind_types/list': $tType > $tType ).
thf(func_def_1,type,
'const/lists/ITLIST':
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 > X1 ) > 'type/ind_types/list'(X0) > X1 > X1 ) ).
thf(func_def_2,type,
'const/lists/APPEND':
!>[X0: $tType] : ( 'type/ind_types/list'(X0) > 'type/ind_types/list'(X0) > 'type/ind_types/list'(X0) ) ).
thf(func_def_3,type,
'const/ind_types/NIL':
!>[X0: $tType] : 'type/ind_types/list'(X0) ).
thf(func_def_4,type,
'const/ind_types/CONS':
!>[X0: $tType] : ( X0 > 'type/ind_types/list'(X0) > 'type/ind_types/list'(X0) ) ).
thf(func_def_8,type,
sK2: sK0 > sK1 > sK1 ).
thf(func_def_9,type,
sK3: sK0 ).
thf(func_def_10,type,
sK4: sK1 ).
thf(func_def_11,type,
sK5: 'type/ind_types/list'(sK0) ).
thf(func_def_13,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_14,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_15,type,
vAND: $o > $o > $o ).
thf(func_def_16,type,
vOR: $o > $o > $o ).
thf(func_def_17,type,
vIMP: $o > $o > $o ).
thf(func_def_18,type,
vNOT: $o > $o ).
thf(func_def_19,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f5824,plain,
$false,
inference(avatar_sat_refutation,[],[f19,f24,f462,f463,f666,f1314,f1318,f1322,f1326,f1330,f1334,f1338,f1343,f1344,f1345,f1347,f1348,f1349,f1350,f1351,f1354,f3070,f3074,f3078,f3082,f3201,f3206,f3211,f3212,f3213,f3214,f3215,f3216,f3217,f3218,f3219,f3220,f3337,f3338,f3339,f3340,f3463,f3464,f3465,f3466,f4150,f4154,f4485,f4489,f4493,f4494,f4496,f4497,f4498,f5508,f5822]) ).
thf(f5822,plain,
spl6_2,
inference(avatar_contradiction_clause,[],[f5821]) ).
thf(f5821,plain,
( $false
| spl6_2 ),
inference(subsumption_resolution,[],[f23,f5608]) ).
thf(f5608,plain,
! [X1: $tType,X0: $tType,X2: X1 > X0 > X0,X3: X1,X4: X0,X5: 'type/ind_types/list'(X1)] : ( vAPP(X0,X0,vAPP('type/ind_types/list'(X1),sTfun(X0,X0),vAPP(sTfun(X1,sTfun(X0,X0)),sTfun('type/ind_types/list'(X1),sTfun(X0,X0)),'const/lists/ITLIST'(X1,X0),X2),vAPP('type/ind_types/list'(X1),'type/ind_types/list'(X1),vAPP('type/ind_types/list'(X1),sTfun('type/ind_types/list'(X1),'type/ind_types/list'(X1)),'const/lists/APPEND'(X1),X5),vAPP('type/ind_types/list'(X1),'type/ind_types/list'(X1),vAPP(X1,sTfun('type/ind_types/list'(X1),'type/ind_types/list'(X1)),'const/ind_types/CONS'(X1),X3),'const/ind_types/NIL'(X1)))),X4) = vAPP(X0,X0,vAPP('type/ind_types/list'(X1),sTfun(X0,X0),vAPP(sTfun(X1,sTfun(X0,X0)),sTfun('type/ind_types/list'(X1),sTfun(X0,X0)),'const/lists/ITLIST'(X1,X0),X2),X5),vAPP(X0,X0,vAPP(X1,sTfun(X0,X0),X2,X3),X4)) ),
inference(superposition,[],[f14,f65]) ).
thf(f65,plain,
! [X1: $tType,X0: $tType,X2: X1 > X0 > X0,X3: X0,X4: X1] : ( vAPP(X0,X0,vAPP('type/ind_types/list'(X1),sTfun(X0,X0),vAPP(sTfun(X1,sTfun(X0,X0)),sTfun('type/ind_types/list'(X1),sTfun(X0,X0)),'const/lists/ITLIST'(X1,X0),X2),vAPP('type/ind_types/list'(X1),'type/ind_types/list'(X1),vAPP(X1,sTfun('type/ind_types/list'(X1),'type/ind_types/list'(X1)),'const/ind_types/CONS'(X1),X4),'const/ind_types/NIL'(X1))),X3) = vAPP(X0,X0,vAPP(X1,sTfun(X0,X0),X2,X4),X3) ),
inference(superposition,[],[f13,f12]) ).
thf(f12,plain,
! [X1: $tType,X0: $tType,X2: X0 > X1 > X1,X3: X1] : ( vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X2),'const/ind_types/NIL'(X0)),X3) = X3 ),
inference(cnf_transformation,[],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X1] : ( vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X2),'const/ind_types/NIL'(X0)),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/ITLIST_0') ).
thf(f13,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X0 > X1 > X1,X4: 'type/ind_types/list'(X0),X5: X1] : ( vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X3),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),X4)),X5) = vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X3,X2),vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X3),X4),X5)) ),
inference(cnf_transformation,[],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: $tType,X2: X0,X3: X0 > X1 > X1,X4: 'type/ind_types/list'(X0),X5: X1] : ( vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X3),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),X4)),X5) = vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X3,X2),vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X3),X4),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/ITLIST_1') ).
thf(f14,plain,
! [X1: $tType,X0: $tType,X2: X0 > X1 > X1,X3: X1,X4: 'type/ind_types/list'(X0),X5: 'type/ind_types/list'(X0)] : ( vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X2),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/lists/APPEND'(X0),X4),X5)),X3) = vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X2),X4),vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X2),X5),X3)) ),
inference(cnf_transformation,[],[f3]) ).
thf(f3,axiom,
! [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X1,X4: 'type/ind_types/list'(X0),X5: 'type/ind_types/list'(X0)] : ( vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X2),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/lists/APPEND'(X0),X4),X5)),X3) = vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X2),X4),vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X2),X5),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/ITLIST_APPEND_') ).
thf(f23,plain,
( ( vAPP(sK1,sK1,vAPP('type/ind_types/list'(sK0),sTfun(sK1,sK1),vAPP(sTfun(sK0,sTfun(sK1,sK1)),sTfun('type/ind_types/list'(sK0),sTfun(sK1,sK1)),'const/lists/ITLIST'(sK0,sK1),sK2),vAPP('type/ind_types/list'(sK0),'type/ind_types/list'(sK0),vAPP('type/ind_types/list'(sK0),sTfun('type/ind_types/list'(sK0),'type/ind_types/list'(sK0)),'const/lists/APPEND'(sK0),sK5),vAPP('type/ind_types/list'(sK0),'type/ind_types/list'(sK0),vAPP(sK0,sTfun('type/ind_types/list'(sK0),'type/ind_types/list'(sK0)),'const/ind_types/CONS'(sK0),sK3),'const/ind_types/NIL'(sK0)))),sK4) != vAPP(sK1,sK1,vAPP('type/ind_types/list'(sK0),sTfun(sK1,sK1),vAPP(sTfun(sK0,sTfun(sK1,sK1)),sTfun('type/ind_types/list'(sK0),sTfun(sK1,sK1)),'const/lists/ITLIST'(sK0,sK1),sK2),sK5),vAPP(sK1,sK1,vAPP(sK0,sTfun(sK1,sK1),sK2,sK3),sK4)) )
| spl6_2 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f21,plain,
( spl6_2
<=> ( vAPP(sK1,sK1,vAPP('type/ind_types/list'(sK0),sTfun(sK1,sK1),vAPP(sTfun(sK0,sTfun(sK1,sK1)),sTfun('type/ind_types/list'(sK0),sTfun(sK1,sK1)),'const/lists/ITLIST'(sK0,sK1),sK2),vAPP('type/ind_types/list'(sK0),'type/ind_types/list'(sK0),vAPP('type/ind_types/list'(sK0),sTfun('type/ind_types/list'(sK0),'type/ind_types/list'(sK0)),'const/lists/APPEND'(sK0),sK5),vAPP('type/ind_types/list'(sK0),'type/ind_types/list'(sK0),vAPP(sK0,sTfun('type/ind_types/list'(sK0),'type/ind_types/list'(sK0)),'const/ind_types/CONS'(sK0),sK3),'const/ind_types/NIL'(sK0)))),sK4) = vAPP(sK1,sK1,vAPP('type/ind_types/list'(sK0),sTfun(sK1,sK1),vAPP(sTfun(sK0,sTfun(sK1,sK1)),sTfun('type/ind_types/list'(sK0),sTfun(sK1,sK1)),'const/lists/ITLIST'(sK0,sK1),sK2),sK5),vAPP(sK1,sK1,vAPP(sK0,sTfun(sK1,sK1),sK2,sK3),sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
thf(f5508,plain,
( spl6_3
| spl6_29 ),
inference(avatar_split_clause,[],[f5504,f5506,f457]) ).
thf(f457,plain,
( spl6_3
<=> ! [X3: $o] : ( $true = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).
thf(f5506,plain,
( spl6_29
<=> ! [X0: $tType,X4: $o,X2: X0,X1: X0 > $o > $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false)) )
| ( $true = X4 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_29])]) ).
thf(f5504,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false)) )
| ( $true = X3 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X4) )
| ( $true = X4 ) ),
inference(forward_demodulation,[],[f5392,f65]) ).
thf(f5392,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),$false)) )
| ( $true = X3 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X4) )
| ( $true = X4 ) ),
inference(trivial_inequality_removal,[],[f5391]) ).
thf(f5391,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),$false)) )
| ( $true = X3 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X4) )
| ( $true = X4 ) ),
inference(duplicate_literal_removal,[],[f5087]) ).
thf(f5087,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),$false)) )
| ( $true = X3 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X4) )
| ( $true = X4 )
| ( $true = X3 ) ),
inference(superposition,[],[f4952,f776]) ).
thf(f776,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o] :
( ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X3) )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),X4) )
| ( $true = X3 )
| ( $true = X4 ) ),
inference(trivial_inequality_removal,[],[f688]) ).
thf(f688,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),X4) )
| ( $true = X4 )
| ( $true = X3 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X3) ) ),
inference(superposition,[],[f541,f79]) ).
thf(f79,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),X3) )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X3) ) ),
inference(superposition,[],[f65,f7]) ).
thf(f7,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f541,plain,
! [X2: $o,X0: $o > $o,X1: $o] :
( ( $true = vAPP($o,$o,X0,X2) )
| ( $false = vAPP($o,$o,X0,X1) )
| ( $true = X1 )
| ( $true = X2 ) ),
inference(trivial_inequality_removal,[],[f483]) ).
thf(f483,plain,
! [X2: $o,X0: $o > $o,X1: $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,X0,X1) )
| ( $true = X1 )
| ( $true = vAPP($o,$o,X0,X2) )
| ( $true = X2 ) ),
inference(superposition,[],[f452,f208]) ).
thf(f208,plain,
! [X2: $o > $o,X3: $o] :
( ( $false = vAPP($o,$o,X2,$false) )
| ( $true = vAPP($o,$o,X2,X3) )
| ( $true = X3 ) ),
inference(forward_demodulation,[],[f126,f12]) ).
thf(f126,plain,
! [X0: $tType,X2: $o > $o,X3: $o,X1: X0 > ( $o > $o ) > $o > $o] :
( ( $false = vAPP($o,$o,X2,$false) )
| ( $true = vAPP($o,$o,vAPP(sTfun($o,$o),sTfun($o,$o),vAPP('type/ind_types/list'(X0),sTfun(sTfun($o,$o),sTfun($o,$o)),vAPP(sTfun(X0,sTfun(sTfun($o,$o),sTfun($o,$o))),sTfun('type/ind_types/list'(X0),sTfun(sTfun($o,$o),sTfun($o,$o))),'const/lists/ITLIST'(X0,sTfun($o,$o)),X1),'const/ind_types/NIL'(X0)),X2),X3) )
| ( $true = X3 ) ),
inference(superposition,[],[f111,f12]) ).
thf(f111,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X3) )
| ( $true = X3 ) ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f99,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $true = X3 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X3) ) ),
inference(superposition,[],[f77,f79]) ).
thf(f77,plain,
! [X0: $tType,X2: $o,X3: X0,X1: X0 > $o > $o] :
( ( $true = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X3),'const/ind_types/NIL'(X0))),X2) )
| ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X3),$false) ) ),
inference(binary_proxy_clausification,[],[f63]) ).
thf(f63,plain,
! [X0: $tType,X2: $o,X3: X0,X1: X0 > $o > $o] :
( ( vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X3),'const/ind_types/NIL'(X0))),X2) = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X3),$false) )
| ( $true = X2 ) ),
inference(superposition,[],[f13,f53]) ).
thf(f53,plain,
! [X0: $tType,X2: $o,X1: X0 > $o > $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),'const/ind_types/NIL'(X0)),X2) )
| ( $true = X2 ) ),
inference(superposition,[],[f12,f7]) ).
thf(f452,plain,
! [X2: $o > $o,X3: $o] :
( ( $true = vAPP($o,$o,X2,$false) )
| ( $false = vAPP($o,$o,X2,X3) )
| ( $true = X3 ) ),
inference(forward_demodulation,[],[f345,f12]) ).
thf(f345,plain,
! [X0: $tType,X2: $o > $o,X3: $o,X1: X0 > ( $o > $o ) > $o > $o] :
( ( $true = vAPP($o,$o,X2,$false) )
| ( $false = vAPP($o,$o,vAPP(sTfun($o,$o),sTfun($o,$o),vAPP('type/ind_types/list'(X0),sTfun(sTfun($o,$o),sTfun($o,$o)),vAPP(sTfun(X0,sTfun(sTfun($o,$o),sTfun($o,$o))),sTfun('type/ind_types/list'(X0),sTfun(sTfun($o,$o),sTfun($o,$o))),'const/lists/ITLIST'(X0,sTfun($o,$o)),X1),'const/ind_types/NIL'(X0)),X2),X3) )
| ( $true = X3 ) ),
inference(superposition,[],[f331,f12]) ).
thf(f331,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X3) )
| ( $true = X3 ) ),
inference(forward_demodulation,[],[f311,f12]) ).
thf(f311,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),'const/ind_types/NIL'(X0)),X3)) )
| ( $true = X3 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ),
inference(superposition,[],[f78,f13]) ).
thf(f78,plain,
! [X0: $tType,X2: $o,X3: X0,X1: X0 > $o > $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X3),'const/ind_types/NIL'(X0))),X2) )
| ( $true = X2 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X3),$false) ) ),
inference(binary_proxy_clausification,[],[f63]) ).
thf(f4952,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X3) )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false)) )
| ( $true = X3 ) ),
inference(trivial_inequality_removal,[],[f4951]) ).
thf(f4951,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false)) )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X3) )
| ( $true = X3 ) ),
inference(duplicate_literal_removal,[],[f4789]) ).
thf(f4789,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false)) )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X3) )
| ( $true = X3 )
| ( $true = $false ) ),
inference(superposition,[],[f668,f776]) ).
thf(f668,plain,
! [X0: $tType,X2: X0,X1: X0 > $o > $o] :
( ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false)) )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),$false) ) ),
inference(forward_demodulation,[],[f608,f65]) ).
thf(f608,plain,
! [X0: $tType,X2: X0,X1: X0 > $o > $o] :
( ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),$false)) )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),$false) ) ),
inference(superposition,[],[f515,f65]) ).
thf(f515,plain,
! [X0: $o > $o] :
( ( $false = vAPP($o,$o,X0,vAPP($o,$o,X0,$false)) )
| ( $true = vAPP($o,$o,X0,$false) ) ),
inference(trivial_inequality_removal,[],[f513]) ).
thf(f513,plain,
! [X0: $o > $o] :
( ( $true != $true )
| ( $false = vAPP($o,$o,X0,vAPP($o,$o,X0,$false)) )
| ( $true = vAPP($o,$o,X0,$false) ) ),
inference(equality_factoring,[],[f452]) ).
thf(f4498,plain,
( spl6_26
| spl6_3 ),
inference(avatar_split_clause,[],[f4322,f457,f4483]) ).
thf(f4483,plain,
( spl6_26
<=> ! [X0: $tType,X1: X0 > $o > $o,X3: $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X3) )
| ( $true = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_26])]) ).
thf(f4322,plain,
! [X0: $tType,X2: $o,X3: $o,X1: X0 > $o > $o] :
( ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X3) )
| ( $true = X3 ) ),
inference(duplicate_literal_removal,[],[f4242]) ).
thf(f4242,plain,
! [X0: $tType,X2: $o,X3: $o,X1: X0 > $o > $o] :
( ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X3) )
| ( $true = X2 )
| ( $true = X3 ) ),
inference(superposition,[],[f12,f776]) ).
thf(f4497,plain,
( spl6_28
| spl6_3 ),
inference(avatar_split_clause,[],[f4355,f457,f4491]) ).
thf(f4491,plain,
( spl6_28
<=> ! [X0: $tType,X4: $o,X2: X0,X1: X0 > $o > $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) )
| ( $true = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_28])]) ).
thf(f4355,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o] :
( ( $true = X3 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = X4 ) ),
inference(trivial_inequality_removal,[],[f4354]) ).
thf(f4354,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o] :
( ( $true = $false )
| ( $true = X3 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = X4 ) ),
inference(duplicate_literal_removal,[],[f4224]) ).
thf(f4224,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o] :
( ( $true = $false )
| ( $true = X3 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = X3 )
| ( $true = X4 ) ),
inference(superposition,[],[f78,f776]) ).
thf(f4496,plain,
( spl6_26
| spl6_3 ),
inference(avatar_split_clause,[],[f4357,f457,f4483]) ).
thf(f4357,plain,
! [X0: $tType,X2: $o,X3: $o,X1: X0 > $o > $o] :
( ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X3) )
| ( $true = X3 ) ),
inference(trivial_inequality_removal,[],[f4356]) ).
thf(f4356,plain,
! [X0: $tType,X2: $o,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X3) )
| ( $true = X3 ) ),
inference(duplicate_literal_removal,[],[f4223]) ).
thf(f4223,plain,
! [X0: $tType,X2: $o,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X3) )
| ( $true = X2 )
| ( $true = X3 ) ),
inference(superposition,[],[f53,f776]) ).
thf(f4494,plain,
( spl6_26
| spl6_3 ),
inference(avatar_split_clause,[],[f4421,f457,f4483]) ).
thf(f4421,plain,
! [X0: $tType,X2: $o,X3: $o,X1: X0 > $o > $o] :
( ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X3) )
| ( $true = X3 ) ),
inference(duplicate_literal_removal,[],[f4193]) ).
thf(f4193,plain,
! [X0: $tType,X2: $o,X3: $o,X1: X0 > $o > $o] :
( ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X3) )
| ( $true = X2 )
| ( $true = X3 ) ),
inference(superposition,[],[f776,f12]) ).
thf(f4493,plain,
( spl6_3
| spl6_28 ),
inference(avatar_split_clause,[],[f4440,f4491,f457]) ).
thf(f4440,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = X3 )
| ( $true = X4 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ),
inference(trivial_inequality_removal,[],[f4439]) ).
thf(f4439,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = X3 )
| ( $true = X4 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ),
inference(duplicate_literal_removal,[],[f4183]) ).
thf(f4183,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = X3 )
| ( $true = X4 )
| ( $true = X3 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ),
inference(superposition,[],[f776,f78]) ).
thf(f4489,plain,
( spl6_3
| spl6_27 ),
inference(avatar_split_clause,[],[f4442,f4487,f457]) ).
thf(f4487,plain,
( spl6_27
<=> ! [X0: $tType,X4: $o,X5: $o,X2: X0,X1: X0 > $o > $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = X5 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X5) )
| ( $true = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_27])]) ).
thf(f4442,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o,X5: $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = X3 )
| ( $true = X4 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X5) )
| ( $true = X5 ) ),
inference(trivial_inequality_removal,[],[f4441]) ).
thf(f4441,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o,X5: $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = X3 )
| ( $true = X4 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X5) )
| ( $true = X5 ) ),
inference(duplicate_literal_removal,[],[f4182]) ).
thf(f4182,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o,X5: $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = X3 )
| ( $true = X4 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X5) )
| ( $true = X5 )
| ( $true = X3 ) ),
inference(superposition,[],[f776,f776]) ).
thf(f4485,plain,
( spl6_3
| spl6_26 ),
inference(avatar_split_clause,[],[f4460,f4483,f457]) ).
thf(f4460,plain,
! [X0: $tType,X2: $o,X3: $o,X1: X0 > $o > $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X3) )
| ( $true = X2 )
| ( $true = X3 ) ),
inference(trivial_inequality_removal,[],[f4459]) ).
thf(f4459,plain,
! [X0: $tType,X2: $o,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X3) )
| ( $true = X2 )
| ( $true = X3 ) ),
inference(duplicate_literal_removal,[],[f4173]) ).
thf(f4173,plain,
! [X0: $tType,X2: $o,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X3) )
| ( $true = X2 )
| ( $true = X3 )
| ( $true = X2 ) ),
inference(superposition,[],[f776,f53]) ).
thf(f4154,plain,
( spl6_3
| spl6_25 ),
inference(avatar_split_clause,[],[f4123,f4152,f457]) ).
thf(f4152,plain,
( spl6_25
<=> ! [X0: $tType,X4: $o,X2: X0,X1: X0 > $o > $o] :
( ( $true = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) )
| ( $true = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_25])]) ).
thf(f4123,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o] :
( ( $true = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = X3 )
| ( $true = X4 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ),
inference(trivial_inequality_removal,[],[f4122]) ).
thf(f4122,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o] :
( ( $true = $false )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = X3 )
| ( $true = X4 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ),
inference(duplicate_literal_removal,[],[f3888]) ).
thf(f3888,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o] :
( ( $true = $false )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = X3 )
| ( $true = X4 )
| ( $true = X3 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ),
inference(superposition,[],[f704,f77]) ).
thf(f704,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o] :
( ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X3) )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),X4) )
| ( $true = X3 )
| ( $true = X4 ) ),
inference(superposition,[],[f541,f65]) ).
thf(f4150,plain,
( spl6_3
| spl6_24 ),
inference(avatar_split_clause,[],[f4125,f4148,f457]) ).
thf(f4148,plain,
( spl6_24
<=> ! [X0: $tType,X4: $o,X5: $o,X2: X0,X1: X0 > $o > $o] :
( ( $true = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = X5 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X5) )
| ( $true = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_24])]) ).
thf(f4125,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o,X5: $o] :
( ( $true = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = X3 )
| ( $true = X4 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X5) )
| ( $true = X5 ) ),
inference(trivial_inequality_removal,[],[f4124]) ).
thf(f4124,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o,X5: $o] :
( ( $true = $false )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = X3 )
| ( $true = X4 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X5) )
| ( $true = X5 ) ),
inference(duplicate_literal_removal,[],[f3887]) ).
thf(f3887,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o,X4: $o,X5: $o] :
( ( $true = $false )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),X4) )
| ( $true = X3 )
| ( $true = X4 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X5) )
| ( $true = X5 )
| ( $true = X3 ) ),
inference(superposition,[],[f704,f704]) ).
thf(f3466,plain,
( ~ spl6_23
| spl6_3
| ~ spl6_6
| ~ spl6_16 ),
inference(avatar_split_clause,[],[f3407,f3076,f1312,f457,f3460]) ).
thf(f3460,plain,
( spl6_23
<=> ( vAND = vEQ($o) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_23])]) ).
thf(f1312,plain,
( spl6_6
<=> ! [X0: $o] : ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vAND),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).
thf(f3076,plain,
( spl6_16
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vEQ($o)),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_16])]) ).
thf(f3407,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( vAND != vEQ($o) ) )
| ~ spl6_6
| ~ spl6_16 ),
inference(trivial_inequality_removal,[],[f3366]) ).
thf(f3366,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $true = X0 )
| ( vAND != vEQ($o) ) )
| ~ spl6_6
| ~ spl6_16 ),
inference(constrained_superposition,[],[f1313,f3077]) ).
thf(f3077,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vEQ($o)),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X0 ) )
| ~ spl6_16 ),
inference(avatar_component_clause,[],[f3076]) ).
thf(f1313,plain,
( ! [X0: $o] : ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vAND),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f1312]) ).
thf(f3465,plain,
( ~ spl6_23
| spl6_3
| ~ spl6_6
| ~ spl6_16 ),
inference(avatar_split_clause,[],[f3420,f3076,f1312,f457,f3460]) ).
thf(f3420,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( vAND != vEQ($o) ) )
| ~ spl6_6
| ~ spl6_16 ),
inference(trivial_inequality_removal,[],[f3419]) ).
thf(f3419,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $true = X0 )
| ( vAND != vEQ($o) ) )
| ~ spl6_6
| ~ spl6_16 ),
inference(duplicate_literal_removal,[],[f3360]) ).
thf(f3360,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $true = $false )
| ( $true = X0 )
| ( vAND != vEQ($o) ) )
| ~ spl6_6
| ~ spl6_16 ),
inference(constrained_superposition,[],[f2095,f3077]) ).
thf(f2095,plain,
( ! [X0: $o,X1: $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vAND),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),X1) )
| ( $true = X1 ) )
| ~ spl6_6 ),
inference(trivial_inequality_removal,[],[f2094]) ).
thf(f2094,plain,
( ! [X0: $o,X1: $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vAND),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),X1) )
| ( $true = X1 ) )
| ~ spl6_6 ),
inference(duplicate_literal_removal,[],[f2066]) ).
thf(f2066,plain,
( ! [X0: $o,X1: $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vAND),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),X1) )
| ( $true = X1 )
| ( $true = $false ) )
| ~ spl6_6 ),
inference(superposition,[],[f1313,f541]) ).
thf(f3464,plain,
( ~ spl6_23
| spl6_3
| ~ spl6_6
| ~ spl6_16 ),
inference(avatar_split_clause,[],[f3453,f3076,f1312,f457,f3460]) ).
thf(f3453,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( vAND != vEQ($o) ) )
| ~ spl6_6
| ~ spl6_16 ),
inference(trivial_inequality_removal,[],[f3452]) ).
thf(f3452,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $true = X0 )
| ( vAND != vEQ($o) ) )
| ~ spl6_6
| ~ spl6_16 ),
inference(duplicate_literal_removal,[],[f3345]) ).
thf(f3345,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $true = X0 )
| ( $true = $false )
| ( vAND != vEQ($o) ) )
| ~ spl6_6
| ~ spl6_16 ),
inference(constrained_superposition,[],[f3077,f2095]) ).
thf(f3463,plain,
( ~ spl6_23
| spl6_3
| ~ spl6_6
| ~ spl6_16 ),
inference(avatar_split_clause,[],[f3458,f3076,f1312,f457,f3460]) ).
thf(f3458,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( vAND != vEQ($o) ) )
| ~ spl6_6
| ~ spl6_16 ),
inference(trivial_inequality_removal,[],[f3341]) ).
thf(f3341,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $true = X0 )
| ( vAND != vEQ($o) ) )
| ~ spl6_6
| ~ spl6_16 ),
inference(constrained_superposition,[],[f3077,f1313]) ).
thf(f3340,plain,
( ~ spl6_22
| spl6_3
| ~ spl6_6
| ~ spl6_15 ),
inference(avatar_split_clause,[],[f3282,f3072,f1312,f457,f3334]) ).
thf(f3334,plain,
( spl6_22
<=> ( vAND = vIMP ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_22])]) ).
thf(f3072,plain,
( spl6_15
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vIMP),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_15])]) ).
thf(f3282,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( vAND != vIMP ) )
| ~ spl6_6
| ~ spl6_15 ),
inference(trivial_inequality_removal,[],[f3246]) ).
thf(f3246,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $true = X0 )
| ( vAND != vIMP ) )
| ~ spl6_6
| ~ spl6_15 ),
inference(constrained_superposition,[],[f1313,f3073]) ).
thf(f3073,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vIMP),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X0 ) )
| ~ spl6_15 ),
inference(avatar_component_clause,[],[f3072]) ).
thf(f3339,plain,
( ~ spl6_22
| spl6_3
| ~ spl6_6
| ~ spl6_15 ),
inference(avatar_split_clause,[],[f3297,f3072,f1312,f457,f3334]) ).
thf(f3297,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( vAND != vIMP ) )
| ~ spl6_6
| ~ spl6_15 ),
inference(trivial_inequality_removal,[],[f3296]) ).
thf(f3296,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $true = X0 )
| ( vAND != vIMP ) )
| ~ spl6_6
| ~ spl6_15 ),
inference(duplicate_literal_removal,[],[f3240]) ).
thf(f3240,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $true = $false )
| ( $true = X0 )
| ( vAND != vIMP ) )
| ~ spl6_6
| ~ spl6_15 ),
inference(constrained_superposition,[],[f2095,f3073]) ).
thf(f3338,plain,
( ~ spl6_22
| spl6_3
| ~ spl6_6
| ~ spl6_15 ),
inference(avatar_split_clause,[],[f3327,f3072,f1312,f457,f3334]) ).
thf(f3327,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( vAND != vIMP ) )
| ~ spl6_6
| ~ spl6_15 ),
inference(trivial_inequality_removal,[],[f3326]) ).
thf(f3326,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $true = X0 )
| ( vAND != vIMP ) )
| ~ spl6_6
| ~ spl6_15 ),
inference(duplicate_literal_removal,[],[f3225]) ).
thf(f3225,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $true = X0 )
| ( $true = $false )
| ( vAND != vIMP ) )
| ~ spl6_6
| ~ spl6_15 ),
inference(constrained_superposition,[],[f3073,f2095]) ).
thf(f3337,plain,
( ~ spl6_22
| spl6_3
| ~ spl6_6
| ~ spl6_15 ),
inference(avatar_split_clause,[],[f3332,f3072,f1312,f457,f3334]) ).
thf(f3332,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( vAND != vIMP ) )
| ~ spl6_6
| ~ spl6_15 ),
inference(trivial_inequality_removal,[],[f3221]) ).
thf(f3221,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $true = X0 )
| ( vAND != vIMP ) )
| ~ spl6_6
| ~ spl6_15 ),
inference(constrained_superposition,[],[f3073,f1313]) ).
thf(f3220,plain,
( ~ spl6_21
| spl6_19
| ~ spl6_10
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f3143,f3068,f1328,f3199,f3208]) ).
thf(f3208,plain,
( spl6_21
<=> ( vOR = vEQ($o) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_21])]) ).
thf(f3199,plain,
( spl6_19
<=> ! [X0: $o] : ( $false = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_19])]) ).
thf(f1328,plain,
( spl6_10
<=> ! [X0: $o] :
( ( $false = X0 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vEQ($o)),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).
thf(f3068,plain,
( spl6_14
<=> ! [X0: $o] :
( ( $false = X0 )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vOR),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_14])]) ).
thf(f3143,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( vOR != vEQ($o) ) )
| ~ spl6_10
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f3142]) ).
thf(f3142,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( vOR != vEQ($o) ) )
| ~ spl6_10
| ~ spl6_14 ),
inference(duplicate_literal_removal,[],[f3114]) ).
thf(f3114,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( $false = X0 )
| ( vOR != vEQ($o) ) )
| ~ spl6_10
| ~ spl6_14 ),
inference(constrained_superposition,[],[f1329,f3069]) ).
thf(f3069,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vOR),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $false = X0 ) )
| ~ spl6_14 ),
inference(avatar_component_clause,[],[f3068]) ).
thf(f1329,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vEQ($o)),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $false = X0 ) )
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f1328]) ).
thf(f3219,plain,
( ~ spl6_20
| spl6_19
| ~ spl6_9
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f3145,f3068,f1324,f3199,f3203]) ).
thf(f3203,plain,
( spl6_20
<=> ( vOR = vIMP ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_20])]) ).
thf(f1324,plain,
( spl6_9
<=> ! [X0: $o] :
( ( $false = X0 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vIMP),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).
thf(f3145,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( vOR != vIMP ) )
| ~ spl6_9
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f3144]) ).
thf(f3144,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( vOR != vIMP ) )
| ~ spl6_9
| ~ spl6_14 ),
inference(duplicate_literal_removal,[],[f3113]) ).
thf(f3113,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( $false = X0 )
| ( vOR != vIMP ) )
| ~ spl6_9
| ~ spl6_14 ),
inference(constrained_superposition,[],[f1325,f3069]) ).
thf(f1325,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vIMP),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $false = X0 ) )
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f1324]) ).
thf(f3218,plain,
( ~ spl6_18
| spl6_19
| ~ spl6_6
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f3147,f3068,f1312,f3199,f3195]) ).
thf(f3195,plain,
( spl6_18
<=> ( vAND = vOR ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_18])]) ).
thf(f3147,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( vAND != vOR ) )
| ~ spl6_6
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f3111]) ).
thf(f3111,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( vAND != vOR ) )
| ~ spl6_6
| ~ spl6_14 ),
inference(constrained_superposition,[],[f1313,f3069]) ).
thf(f3217,plain,
( ~ spl6_21
| spl6_19
| ~ spl6_10
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f3154,f3068,f1328,f3199,f3208]) ).
thf(f3154,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( vOR != vEQ($o) ) )
| ~ spl6_10
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f3153]) ).
thf(f3153,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( vOR != vEQ($o) ) )
| ~ spl6_10
| ~ spl6_14 ),
inference(duplicate_literal_removal,[],[f3108]) ).
thf(f3108,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( $true = $false )
| ( $false = X0 )
| ( vOR != vEQ($o) ) )
| ~ spl6_10
| ~ spl6_14 ),
inference(constrained_superposition,[],[f2231,f3069]) ).
thf(f2231,plain,
( ! [X0: $o,X1: $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vEQ($o)),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),X1) )
| ( $false = X0 )
| ( $true = X1 ) )
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f2230]) ).
thf(f2230,plain,
( ! [X0: $o,X1: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vEQ($o)),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),X1) )
| ( $true = X1 ) )
| ~ spl6_10 ),
inference(duplicate_literal_removal,[],[f2196]) ).
thf(f2196,plain,
( ! [X0: $o,X1: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vEQ($o)),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),X1) )
| ( $true = X1 )
| ( $true = $false ) )
| ~ spl6_10 ),
inference(superposition,[],[f1329,f541]) ).
thf(f3216,plain,
( ~ spl6_20
| spl6_19
| ~ spl6_9
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f3156,f3068,f1324,f3199,f3203]) ).
thf(f3156,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( vOR != vIMP ) )
| ~ spl6_9
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f3155]) ).
thf(f3155,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( vOR != vIMP ) )
| ~ spl6_9
| ~ spl6_14 ),
inference(duplicate_literal_removal,[],[f3107]) ).
thf(f3107,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( $true = $false )
| ( $false = X0 )
| ( vOR != vIMP ) )
| ~ spl6_9
| ~ spl6_14 ),
inference(constrained_superposition,[],[f2161,f3069]) ).
thf(f2161,plain,
( ! [X0: $o,X1: $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vIMP),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),X1) )
| ( $false = X0 )
| ( $true = X1 ) )
| ~ spl6_9 ),
inference(trivial_inequality_removal,[],[f2160]) ).
thf(f2160,plain,
( ! [X0: $o,X1: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vIMP),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),X1) )
| ( $true = X1 ) )
| ~ spl6_9 ),
inference(duplicate_literal_removal,[],[f2128]) ).
thf(f2128,plain,
( ! [X0: $o,X1: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vIMP),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),X1) )
| ( $true = X1 )
| ( $true = $false ) )
| ~ spl6_9 ),
inference(superposition,[],[f1325,f541]) ).
thf(f3215,plain,
( ~ spl6_18
| spl6_19
| ~ spl6_6
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f3160,f3068,f1312,f3199,f3195]) ).
thf(f3160,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( vAND != vOR ) )
| ~ spl6_6
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f3159]) ).
thf(f3159,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( vAND != vOR ) )
| ~ spl6_6
| ~ spl6_14 ),
inference(duplicate_literal_removal,[],[f3105]) ).
thf(f3105,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $true = $false )
| ( $false = X0 )
| ( vAND != vOR ) )
| ~ spl6_6
| ~ spl6_14 ),
inference(constrained_superposition,[],[f2095,f3069]) ).
thf(f3214,plain,
( ~ spl6_21
| spl6_19
| ~ spl6_10
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f3181,f3068,f1328,f3199,f3208]) ).
thf(f3181,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( vOR != vEQ($o) ) )
| ~ spl6_10
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f3180]) ).
thf(f3180,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( vOR != vEQ($o) ) )
| ~ spl6_10
| ~ spl6_14 ),
inference(duplicate_literal_removal,[],[f3093]) ).
thf(f3093,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( $false = X0 )
| ( $true = $false )
| ( vOR != vEQ($o) ) )
| ~ spl6_10
| ~ spl6_14 ),
inference(constrained_superposition,[],[f3069,f2231]) ).
thf(f3213,plain,
( ~ spl6_20
| spl6_19
| ~ spl6_9
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f3183,f3068,f1324,f3199,f3203]) ).
thf(f3183,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( vOR != vIMP ) )
| ~ spl6_9
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f3182]) ).
thf(f3182,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( vOR != vIMP ) )
| ~ spl6_9
| ~ spl6_14 ),
inference(duplicate_literal_removal,[],[f3092]) ).
thf(f3092,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( $false = X0 )
| ( $true = $false )
| ( vOR != vIMP ) )
| ~ spl6_9
| ~ spl6_14 ),
inference(constrained_superposition,[],[f3069,f2161]) ).
thf(f3212,plain,
( ~ spl6_18
| spl6_19
| ~ spl6_6
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f3187,f3068,f1312,f3199,f3195]) ).
thf(f3187,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( vAND != vOR ) )
| ~ spl6_6
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f3186]) ).
thf(f3186,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( vAND != vOR ) )
| ~ spl6_6
| ~ spl6_14 ),
inference(duplicate_literal_removal,[],[f3090]) ).
thf(f3090,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( $true = $false )
| ( vAND != vOR ) )
| ~ spl6_6
| ~ spl6_14 ),
inference(constrained_superposition,[],[f3069,f2095]) ).
thf(f3211,plain,
( ~ spl6_21
| spl6_19
| ~ spl6_10
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f3189,f3068,f1328,f3199,f3208]) ).
thf(f3189,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( vOR != vEQ($o) ) )
| ~ spl6_10
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f3188]) ).
thf(f3188,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( vOR != vEQ($o) ) )
| ~ spl6_10
| ~ spl6_14 ),
inference(duplicate_literal_removal,[],[f3089]) ).
thf(f3089,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( $false = X0 )
| ( vOR != vEQ($o) ) )
| ~ spl6_10
| ~ spl6_14 ),
inference(constrained_superposition,[],[f3069,f1329]) ).
thf(f3206,plain,
( ~ spl6_20
| spl6_19
| ~ spl6_9
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f3191,f3068,f1324,f3199,f3203]) ).
thf(f3191,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( vOR != vIMP ) )
| ~ spl6_9
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f3190]) ).
thf(f3190,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( vOR != vIMP ) )
| ~ spl6_9
| ~ spl6_14 ),
inference(duplicate_literal_removal,[],[f3088]) ).
thf(f3088,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( $false = X0 )
| ( vOR != vIMP ) )
| ~ spl6_9
| ~ spl6_14 ),
inference(constrained_superposition,[],[f3069,f1325]) ).
thf(f3201,plain,
( ~ spl6_18
| spl6_19
| ~ spl6_6
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f3193,f3068,f1312,f3199,f3195]) ).
thf(f3193,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( vAND != vOR ) )
| ~ spl6_6
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f3086]) ).
thf(f3086,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( vAND != vOR ) )
| ~ spl6_6
| ~ spl6_14 ),
inference(constrained_superposition,[],[f3069,f1313]) ).
thf(f3082,plain,
( spl6_3
| spl6_17 ),
inference(avatar_split_clause,[],[f3057,f3080,f457]) ).
thf(f3080,plain,
( spl6_17
<=> ! [X0: $tType,X2: X0,X1: X0 > $o > $o] :
( ( $true = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_17])]) ).
thf(f3057,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) )
| ( $true = X3 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ),
inference(trivial_inequality_removal,[],[f3056]) ).
thf(f3056,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) )
| ( $true = X3 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ),
inference(duplicate_literal_removal,[],[f2868]) ).
thf(f2868,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) )
| ( $true = X3 )
| ( $true = X3 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ),
inference(superposition,[],[f367,f77]) ).
thf(f367,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X3) )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),$false) )
| ( $true = X3 ) ),
inference(superposition,[],[f331,f65]) ).
thf(f3078,plain,
( spl6_3
| spl6_16 ),
inference(avatar_split_clause,[],[f3061,f3076,f457]) ).
thf(f3061,plain,
! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vEQ($o)),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 ) ),
inference(duplicate_literal_removal,[],[f3059]) ).
thf(f3059,plain,
! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vEQ($o)),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 )
| ( $true = X1 ) ),
inference(binary_proxy_clausification,[],[f3058]) ).
thf(f3058,plain,
! [X0: $o,X1: $o] :
( ( X0 != X1 )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vEQ($o)),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 ) ),
inference(equality_proxy_clausification,[],[f2863]) ).
thf(f2863,plain,
! [X0: $o,X1: $o] :
( ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),X0),X1) )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vEQ($o)),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 ) ),
inference(primitive_instantiation,[],[f367]) ).
thf(f3074,plain,
( spl6_3
| spl6_15 ),
inference(avatar_split_clause,[],[f3063,f3072,f457]) ).
thf(f3063,plain,
! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vIMP),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 ) ),
inference(binary_proxy_clausification,[],[f2860]) ).
thf(f2860,plain,
! [X0: $o,X1: $o] :
( ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vIMP,X0),X1) )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vIMP),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 ) ),
inference(primitive_instantiation,[],[f367]) ).
thf(f3070,plain,
( spl6_3
| spl6_14 ),
inference(avatar_split_clause,[],[f3065,f3068,f457]) ).
thf(f3065,plain,
! [X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vOR),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 ) ),
inference(binary_proxy_clausification,[],[f2859]) ).
thf(f2859,plain,
! [X0: $o,X1: $o] :
( ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X0),X1) )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vOR),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 ) ),
inference(primitive_instantiation,[],[f367]) ).
thf(f1354,plain,
( spl6_1
| ~ spl6_3 ),
inference(avatar_contradiction_clause,[],[f1353]) ).
thf(f1353,plain,
( $false
| spl6_1
| ~ spl6_3 ),
inference(subsumption_resolution,[],[f18,f458]) ).
thf(f458,plain,
( ! [X3: $o] : ( $true = X3 )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f457]) ).
thf(f18,plain,
( ( $true != $false )
| spl6_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f16,plain,
( spl6_1
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
thf(f1351,plain,
( spl6_11
| spl6_3 ),
inference(avatar_split_clause,[],[f1233,f457,f1332]) ).
thf(f1332,plain,
( spl6_11
<=> ! [X0: $tType,X1: X0 > $o > $o] : ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_11])]) ).
thf(f1233,plain,
! [X0: $tType,X2: $o,X1: X0 > $o > $o] :
( ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) ) ),
inference(duplicate_literal_removal,[],[f1203]) ).
thf(f1203,plain,
! [X0: $tType,X2: $o,X1: X0 > $o > $o] :
( ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) )
| ( $true = X2 ) ),
inference(superposition,[],[f12,f174]) ).
thf(f174,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X3) )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),$false) )
| ( $true = X3 ) ),
inference(trivial_inequality_removal,[],[f140]) ).
thf(f140,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),$false) )
| ( $true = X3 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),X3) ) ),
inference(superposition,[],[f111,f79]) ).
thf(f1350,plain,
( spl6_13
| spl6_3
| ~ spl6_5 ),
inference(avatar_split_clause,[],[f1249,f663,f457,f1340]) ).
thf(f1340,plain,
( spl6_13
<=> ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o),vAPP(sTfun(sTfun($o,$o),sTfun($o,$o)),sTfun('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o)),'const/lists/ITLIST'(sTfun($o,$o),$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT)),vAPP('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o)),vAPP(sTfun($o,$o),sTfun('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o))),'const/ind_types/CONS'(sTfun($o,$o)),vAPP($o,sTfun($o,$o),vEQ($o),$false)),'const/ind_types/NIL'(sTfun($o,$o)))),$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_13])]) ).
thf(f663,plain,
( spl6_5
<=> ( $false = vAPP($o,$o,vAPP(sTfun($o,$o),sTfun($o,$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT),vAPP($o,sTfun($o,$o),vEQ($o),$false)),$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).
thf(f1249,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o),vAPP(sTfun(sTfun($o,$o),sTfun($o,$o)),sTfun('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o)),'const/lists/ITLIST'(sTfun($o,$o),$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT)),vAPP('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o)),vAPP(sTfun($o,$o),sTfun('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o))),'const/ind_types/CONS'(sTfun($o,$o)),vAPP($o,sTfun($o,$o),vEQ($o),$false)),'const/ind_types/NIL'(sTfun($o,$o)))),$false) ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f1248]) ).
thf(f1248,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o),vAPP(sTfun(sTfun($o,$o),sTfun($o,$o)),sTfun('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o)),'const/lists/ITLIST'(sTfun($o,$o),$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT)),vAPP('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o)),vAPP(sTfun($o,$o),sTfun('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o))),'const/ind_types/CONS'(sTfun($o,$o)),vAPP($o,sTfun($o,$o),vEQ($o),$false)),'const/ind_types/NIL'(sTfun($o,$o)))),$false) ) )
| ~ spl6_5 ),
inference(duplicate_literal_removal,[],[f1194]) ).
thf(f1194,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o),vAPP(sTfun(sTfun($o,$o),sTfun($o,$o)),sTfun('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o)),'const/lists/ITLIST'(sTfun($o,$o),$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT)),vAPP('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o)),vAPP(sTfun($o,$o),sTfun('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o))),'const/ind_types/CONS'(sTfun($o,$o)),vAPP($o,sTfun($o,$o),vEQ($o),$false)),'const/ind_types/NIL'(sTfun($o,$o)))),$false) )
| ( $true = X0 ) )
| ~ spl6_5 ),
inference(superposition,[],[f1004,f174]) ).
thf(f1004,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,vAPP(sTfun($o,$o),sTfun($o,$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT),vAPP($o,sTfun($o,$o),vEQ($o),$false)),X0) )
| ( $true = X0 ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f1003]) ).
thf(f1003,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP(sTfun($o,$o),sTfun($o,$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT),vAPP($o,sTfun($o,$o),vEQ($o),$false)),X0) )
| ( $true = X0 ) )
| ~ spl6_5 ),
inference(duplicate_literal_removal,[],[f984]) ).
thf(f984,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP(sTfun($o,$o),sTfun($o,$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT),vAPP($o,sTfun($o,$o),vEQ($o),$false)),X0) )
| ( $true = X0 )
| ( $true = $false ) )
| ~ spl6_5 ),
inference(superposition,[],[f665,f541]) ).
thf(f665,plain,
( ( $false = vAPP($o,$o,vAPP(sTfun($o,$o),sTfun($o,$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT),vAPP($o,sTfun($o,$o),vEQ($o),$false)),$false) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f663]) ).
thf(f1349,plain,
( spl6_13
| ~ spl6_5 ),
inference(avatar_split_clause,[],[f1255,f663,f1340]) ).
thf(f1255,plain,
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o),vAPP(sTfun(sTfun($o,$o),sTfun($o,$o)),sTfun('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o)),'const/lists/ITLIST'(sTfun($o,$o),$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT)),vAPP('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o)),vAPP(sTfun($o,$o),sTfun('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o))),'const/ind_types/CONS'(sTfun($o,$o)),vAPP($o,sTfun($o,$o),vEQ($o),$false)),'const/ind_types/NIL'(sTfun($o,$o)))),$false) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f1254]) ).
thf(f1254,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o),vAPP(sTfun(sTfun($o,$o),sTfun($o,$o)),sTfun('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o)),'const/lists/ITLIST'(sTfun($o,$o),$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT)),vAPP('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o)),vAPP(sTfun($o,$o),sTfun('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o))),'const/ind_types/CONS'(sTfun($o,$o)),vAPP($o,sTfun($o,$o),vEQ($o),$false)),'const/ind_types/NIL'(sTfun($o,$o)))),$false) )
| ~ spl6_5 ),
inference(duplicate_literal_removal,[],[f1191]) ).
thf(f1191,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o),vAPP(sTfun(sTfun($o,$o),sTfun($o,$o)),sTfun('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o)),'const/lists/ITLIST'(sTfun($o,$o),$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT)),vAPP('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o)),vAPP(sTfun($o,$o),sTfun('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o))),'const/ind_types/CONS'(sTfun($o,$o)),vAPP($o,sTfun($o,$o),vEQ($o),$false)),'const/ind_types/NIL'(sTfun($o,$o)))),$false) )
| ( $true = $false )
| ~ spl6_5 ),
inference(superposition,[],[f665,f174]) ).
thf(f1348,plain,
( spl6_12
| spl6_3 ),
inference(avatar_split_clause,[],[f1258,f457,f1336]) ).
thf(f1336,plain,
( spl6_12
<=> ! [X0: $tType,X2: X0,X1: X0 > $o > $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_12])]) ).
thf(f1258,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = X3 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) ) ),
inference(trivial_inequality_removal,[],[f1257]) ).
thf(f1257,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $true = X3 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) ) ),
inference(duplicate_literal_removal,[],[f1189]) ).
thf(f1189,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $true = X3 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) )
| ( $true = X3 ) ),
inference(superposition,[],[f78,f174]) ).
thf(f1347,plain,
( spl6_11
| spl6_3 ),
inference(avatar_split_clause,[],[f1260,f457,f1332]) ).
thf(f1260,plain,
! [X0: $tType,X2: $o,X1: X0 > $o > $o] :
( ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) ) ),
inference(trivial_inequality_removal,[],[f1259]) ).
thf(f1259,plain,
! [X0: $tType,X2: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) ) ),
inference(duplicate_literal_removal,[],[f1188]) ).
thf(f1188,plain,
! [X0: $tType,X2: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) )
| ( $true = X2 ) ),
inference(superposition,[],[f53,f174]) ).
thf(f1345,plain,
( spl6_11
| spl6_3 ),
inference(avatar_split_clause,[],[f1272,f457,f1332]) ).
thf(f1272,plain,
! [X0: $tType,X2: $o,X1: X0 > $o > $o] :
( ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) ) ),
inference(duplicate_literal_removal,[],[f1175]) ).
thf(f1175,plain,
! [X0: $tType,X2: $o,X1: X0 > $o > $o] :
( ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) )
| ( $true = X2 ) ),
inference(superposition,[],[f174,f12]) ).
thf(f1344,plain,
( spl6_3
| spl6_13
| ~ spl6_5 ),
inference(avatar_split_clause,[],[f1290,f663,f1340,f457]) ).
thf(f1290,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o),vAPP(sTfun(sTfun($o,$o),sTfun($o,$o)),sTfun('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o)),'const/lists/ITLIST'(sTfun($o,$o),$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT)),vAPP('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o)),vAPP(sTfun($o,$o),sTfun('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o))),'const/ind_types/CONS'(sTfun($o,$o)),vAPP($o,sTfun($o,$o),vEQ($o),$false)),'const/ind_types/NIL'(sTfun($o,$o)))),$false) )
| ( $true = X0 ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f1289]) ).
thf(f1289,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o),vAPP(sTfun(sTfun($o,$o),sTfun($o,$o)),sTfun('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o)),'const/lists/ITLIST'(sTfun($o,$o),$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT)),vAPP('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o)),vAPP(sTfun($o,$o),sTfun('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o))),'const/ind_types/CONS'(sTfun($o,$o)),vAPP($o,sTfun($o,$o),vEQ($o),$false)),'const/ind_types/NIL'(sTfun($o,$o)))),$false) )
| ( $true = X0 ) )
| ~ spl6_5 ),
inference(duplicate_literal_removal,[],[f1166]) ).
thf(f1166,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o),vAPP(sTfun(sTfun($o,$o),sTfun($o,$o)),sTfun('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o)),'const/lists/ITLIST'(sTfun($o,$o),$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT)),vAPP('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o)),vAPP(sTfun($o,$o),sTfun('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o))),'const/ind_types/CONS'(sTfun($o,$o)),vAPP($o,sTfun($o,$o),vEQ($o),$false)),'const/ind_types/NIL'(sTfun($o,$o)))),$false) )
| ( $true = X0 )
| ( $true = X0 ) )
| ~ spl6_5 ),
inference(superposition,[],[f174,f1004]) ).
thf(f1343,plain,
( spl6_13
| ~ spl6_5 ),
inference(avatar_split_clause,[],[f1292,f663,f1340]) ).
thf(f1292,plain,
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o),vAPP(sTfun(sTfun($o,$o),sTfun($o,$o)),sTfun('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o)),'const/lists/ITLIST'(sTfun($o,$o),$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT)),vAPP('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o)),vAPP(sTfun($o,$o),sTfun('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o))),'const/ind_types/CONS'(sTfun($o,$o)),vAPP($o,sTfun($o,$o),vEQ($o),$false)),'const/ind_types/NIL'(sTfun($o,$o)))),$false) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f1291]) ).
thf(f1291,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o),vAPP(sTfun(sTfun($o,$o),sTfun($o,$o)),sTfun('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o)),'const/lists/ITLIST'(sTfun($o,$o),$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT)),vAPP('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o)),vAPP(sTfun($o,$o),sTfun('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o))),'const/ind_types/CONS'(sTfun($o,$o)),vAPP($o,sTfun($o,$o),vEQ($o),$false)),'const/ind_types/NIL'(sTfun($o,$o)))),$false) )
| ~ spl6_5 ),
inference(duplicate_literal_removal,[],[f1165]) ).
thf(f1165,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o),vAPP(sTfun(sTfun($o,$o),sTfun($o,$o)),sTfun('type/ind_types/list'(sTfun($o,$o)),sTfun($o,$o)),'const/lists/ITLIST'(sTfun($o,$o),$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT)),vAPP('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o)),vAPP(sTfun($o,$o),sTfun('type/ind_types/list'(sTfun($o,$o)),'type/ind_types/list'(sTfun($o,$o))),'const/ind_types/CONS'(sTfun($o,$o)),vAPP($o,sTfun($o,$o),vEQ($o),$false)),'const/ind_types/NIL'(sTfun($o,$o)))),$false) )
| ( $true = $false )
| ~ spl6_5 ),
inference(superposition,[],[f174,f665]) ).
thf(f1338,plain,
( spl6_3
| spl6_12 ),
inference(avatar_split_clause,[],[f1297,f1336,f457]) ).
thf(f1297,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) )
| ( $true = X3 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ),
inference(trivial_inequality_removal,[],[f1296]) ).
thf(f1296,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) )
| ( $true = X3 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ),
inference(duplicate_literal_removal,[],[f1162]) ).
thf(f1162,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) )
| ( $true = X3 )
| ( $true = X3 )
| ( $true = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ),
inference(superposition,[],[f174,f78]) ).
thf(f1334,plain,
( spl6_3
| spl6_11 ),
inference(avatar_split_clause,[],[f1299,f1332,f457]) ).
thf(f1299,plain,
! [X0: $tType,X2: $o,X1: X0 > $o > $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) )
| ( $true = X2 ) ),
inference(trivial_inequality_removal,[],[f1298]) ).
thf(f1298,plain,
! [X0: $tType,X2: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) )
| ( $true = X2 ) ),
inference(duplicate_literal_removal,[],[f1161]) ).
thf(f1161,plain,
! [X0: $tType,X2: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o),vAPP(sTfun('type/ind_types/list'(X0),sTfun($o,$o)),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),sTfun($o,$o)),'const/lists/ITLIST'('type/ind_types/list'(X0),$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1)),vAPP('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0)),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'('type/ind_types/list'(X0)),'type/ind_types/list'('type/ind_types/list'(X0))),'const/ind_types/CONS'('type/ind_types/list'(X0)),'const/ind_types/NIL'(X0)),'const/ind_types/NIL'('type/ind_types/list'(X0)))),$false) )
| ( $true = X2 )
| ( $true = X2 ) ),
inference(superposition,[],[f174,f53]) ).
thf(f1330,plain,
( spl6_3
| spl6_10 ),
inference(avatar_split_clause,[],[f1303,f1328,f457]) ).
thf(f1303,plain,
! [X0: $o,X1: $o] :
( ( $false = X0 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vEQ($o)),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 ) ),
inference(duplicate_literal_removal,[],[f1302]) ).
thf(f1302,plain,
! [X0: $o,X1: $o] :
( ( $false = X0 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vEQ($o)),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 )
| ( $true = X1 ) ),
inference(binary_proxy_clausification,[],[f1300]) ).
thf(f1300,plain,
! [X0: $o,X1: $o] :
( ( X0 = X1 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vEQ($o)),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 ) ),
inference(equality_proxy_clausification,[],[f1156]) ).
thf(f1156,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),X0),X1) )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vEQ($o)),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 ) ),
inference(primitive_instantiation,[],[f174]) ).
thf(f1326,plain,
( spl6_3
| spl6_9 ),
inference(avatar_split_clause,[],[f1305,f1324,f457]) ).
thf(f1305,plain,
! [X0: $o,X1: $o] :
( ( $false = X0 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vIMP),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 ) ),
inference(duplicate_literal_removal,[],[f1304]) ).
thf(f1304,plain,
! [X0: $o,X1: $o] :
( ( $false = X0 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vIMP),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 )
| ( $true = X1 ) ),
inference(binary_proxy_clausification,[],[f1153]) ).
thf(f1153,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vIMP,X0),X1) )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vIMP),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 ) ),
inference(primitive_instantiation,[],[f174]) ).
thf(f1322,plain,
( spl6_8
| spl6_3 ),
inference(avatar_split_clause,[],[f1307,f457,f1320]) ).
thf(f1320,plain,
( spl6_8
<=> ! [X0: $o] :
( ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vOR),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).
thf(f1307,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vOR),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X0 ) ),
inference(duplicate_literal_removal,[],[f1306]) ).
thf(f1306,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vOR),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 )
| ( $true = X0 ) ),
inference(binary_proxy_clausification,[],[f1152]) ).
thf(f1152,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X0),X1) )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vOR),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 ) ),
inference(primitive_instantiation,[],[f174]) ).
thf(f1318,plain,
( spl6_3
| spl6_7 ),
inference(avatar_split_clause,[],[f1309,f1316,f457]) ).
thf(f1316,plain,
( spl6_7
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vAND),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).
thf(f1309,plain,
! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vAND),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 ) ),
inference(binary_proxy_clausification,[],[f1151]) ).
thf(f1151,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,X0),X1) )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vAND),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 ) ),
inference(primitive_instantiation,[],[f174]) ).
thf(f1314,plain,
( spl6_6
| spl6_3 ),
inference(avatar_split_clause,[],[f1310,f457,f1312]) ).
thf(f1310,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vAND),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) ) ),
inference(duplicate_literal_removal,[],[f1308]) ).
thf(f1308,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP('type/ind_types/list'($o),sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun('type/ind_types/list'($o),sTfun($o,$o)),'const/lists/ITLIST'($o,$o),vAND),vAPP('type/ind_types/list'($o),'type/ind_types/list'($o),vAPP($o,sTfun('type/ind_types/list'($o),'type/ind_types/list'($o)),'const/ind_types/CONS'($o),X0),'const/ind_types/NIL'($o))),$false) )
| ( $true = X1 ) ),
inference(binary_proxy_clausification,[],[f1151]) ).
thf(f666,plain,
spl6_5,
inference(avatar_split_clause,[],[f581,f663]) ).
thf(f581,plain,
$false = vAPP($o,$o,vAPP(sTfun($o,$o),sTfun($o,$o),vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),sTfun($o,$o)),bCOMB,vNOT),vAPP($o,sTfun($o,$o),vEQ($o),$false)),$false),
inference(leibniz_equality_elimination,[],[f515]) ).
thf(f463,plain,
( spl6_4
| spl6_3 ),
inference(avatar_split_clause,[],[f394,f457,f460]) ).
thf(f460,plain,
( spl6_4
<=> ! [X0: $tType,X2: X0,X1: X0 > $o > $o] :
( ( $true = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),$false) )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).
thf(f394,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = X3 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),$false) ) ),
inference(trivial_inequality_removal,[],[f393]) ).
thf(f393,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $true = X3 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),$false) ) ),
inference(duplicate_literal_removal,[],[f378]) ).
thf(f378,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $true = X3 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),$false) )
| ( $true = X3 ) ),
inference(superposition,[],[f77,f331]) ).
thf(f462,plain,
( spl6_3
| spl6_4 ),
inference(avatar_split_clause,[],[f410,f460,f457]) ).
thf(f410,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),$false) )
| ( $true = X3 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ),
inference(trivial_inequality_removal,[],[f409]) ).
thf(f409,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),$false) )
| ( $true = X3 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ),
inference(duplicate_literal_removal,[],[f361]) ).
thf(f361,plain,
! [X0: $tType,X2: X0,X3: $o,X1: X0 > $o > $o] :
( ( $true = $false )
| ( $true = vAPP($o,$o,vAPP('type/ind_types/list'(X0),sTfun($o,$o),vAPP(sTfun(X0,sTfun($o,$o)),sTfun('type/ind_types/list'(X0),sTfun($o,$o)),'const/lists/ITLIST'(X0,$o),X1),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X2),'const/ind_types/NIL'(X0))),$false) )
| ( $true = X3 )
| ( $true = X3 )
| ( $false = vAPP($o,$o,vAPP(X0,sTfun($o,$o),X1,X2),$false) ) ),
inference(superposition,[],[f331,f77]) ).
thf(f24,plain,
~ spl6_2,
inference(avatar_split_clause,[],[f11,f21]) ).
thf(f11,plain,
vAPP(sK1,sK1,vAPP('type/ind_types/list'(sK0),sTfun(sK1,sK1),vAPP(sTfun(sK0,sTfun(sK1,sK1)),sTfun('type/ind_types/list'(sK0),sTfun(sK1,sK1)),'const/lists/ITLIST'(sK0,sK1),sK2),vAPP('type/ind_types/list'(sK0),'type/ind_types/list'(sK0),vAPP('type/ind_types/list'(sK0),sTfun('type/ind_types/list'(sK0),'type/ind_types/list'(sK0)),'const/lists/APPEND'(sK0),sK5),vAPP('type/ind_types/list'(sK0),'type/ind_types/list'(sK0),vAPP(sK0,sTfun('type/ind_types/list'(sK0),'type/ind_types/list'(sK0)),'const/ind_types/CONS'(sK0),sK3),'const/ind_types/NIL'(sK0)))),sK4) != vAPP(sK1,sK1,vAPP('type/ind_types/list'(sK0),sTfun(sK1,sK1),vAPP(sTfun(sK0,sTfun(sK1,sK1)),sTfun('type/ind_types/list'(sK0),sTfun(sK1,sK1)),'const/lists/ITLIST'(sK0,sK1),sK2),sK5),vAPP(sK1,sK1,vAPP(sK0,sTfun(sK1,sK1),sK2,sK3),sK4)),
inference(cnf_transformation,[],[f10]) ).
thf(f10,plain,
vAPP(sK1,sK1,vAPP('type/ind_types/list'(sK0),sTfun(sK1,sK1),vAPP(sTfun(sK0,sTfun(sK1,sK1)),sTfun('type/ind_types/list'(sK0),sTfun(sK1,sK1)),'const/lists/ITLIST'(sK0,sK1),sK2),vAPP('type/ind_types/list'(sK0),'type/ind_types/list'(sK0),vAPP('type/ind_types/list'(sK0),sTfun('type/ind_types/list'(sK0),'type/ind_types/list'(sK0)),'const/lists/APPEND'(sK0),sK5),vAPP('type/ind_types/list'(sK0),'type/ind_types/list'(sK0),vAPP(sK0,sTfun('type/ind_types/list'(sK0),'type/ind_types/list'(sK0)),'const/ind_types/CONS'(sK0),sK3),'const/ind_types/NIL'(sK0)))),sK4) != vAPP(sK1,sK1,vAPP('type/ind_types/list'(sK0),sTfun(sK1,sK1),vAPP(sTfun(sK0,sTfun(sK1,sK1)),sTfun('type/ind_types/list'(sK0),sTfun(sK1,sK1)),'const/lists/ITLIST'(sK0,sK1),sK2),sK5),vAPP(sK1,sK1,vAPP(sK0,sTfun(sK1,sK1),sK2,sK3),sK4)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X0,X4: X1,X5: 'type/ind_types/list'(X0)] : ( vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X2),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/lists/APPEND'(X0),X5),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X3),'const/ind_types/NIL'(X0)))),X4) != vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X2),X5),vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X2,X3),X4)) )
=> ( vAPP(sK1,sK1,vAPP('type/ind_types/list'(sK0),sTfun(sK1,sK1),vAPP(sTfun(sK0,sTfun(sK1,sK1)),sTfun('type/ind_types/list'(sK0),sTfun(sK1,sK1)),'const/lists/ITLIST'(sK0,sK1),sK2),vAPP('type/ind_types/list'(sK0),'type/ind_types/list'(sK0),vAPP('type/ind_types/list'(sK0),sTfun('type/ind_types/list'(sK0),'type/ind_types/list'(sK0)),'const/lists/APPEND'(sK0),sK5),vAPP('type/ind_types/list'(sK0),'type/ind_types/list'(sK0),vAPP(sK0,sTfun('type/ind_types/list'(sK0),'type/ind_types/list'(sK0)),'const/ind_types/CONS'(sK0),sK3),'const/ind_types/NIL'(sK0)))),sK4) != vAPP(sK1,sK1,vAPP('type/ind_types/list'(sK0),sTfun(sK1,sK1),vAPP(sTfun(sK0,sTfun(sK1,sK1)),sTfun('type/ind_types/list'(sK0),sTfun(sK1,sK1)),'const/lists/ITLIST'(sK0,sK1),sK2),sK5),vAPP(sK1,sK1,vAPP(sK0,sTfun(sK1,sK1),sK2,sK3),sK4)) ) ),
introduced(choice_axiom,[]) ).
thf(f8,plain,
? [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X0,X4: X1,X5: 'type/ind_types/list'(X0)] : ( vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X2),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/lists/APPEND'(X0),X5),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X3),'const/ind_types/NIL'(X0)))),X4) != vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X2),X5),vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X2,X3),X4)) ),
inference(ennf_transformation,[],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X0,X4: X1,X5: 'type/ind_types/list'(X0)] : ( vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X2),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/lists/APPEND'(X0),X5),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X3),'const/ind_types/NIL'(X0)))),X4) = vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X2),X5),vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X2,X3),X4)) ),
inference(negated_conjecture,[],[f4]) ).
thf(f4,conjecture,
! [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X0,X4: X1,X5: 'type/ind_types/list'(X0)] : ( vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X2),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP('type/ind_types/list'(X0),sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/lists/APPEND'(X0),X5),vAPP('type/ind_types/list'(X0),'type/ind_types/list'(X0),vAPP(X0,sTfun('type/ind_types/list'(X0),'type/ind_types/list'(X0)),'const/ind_types/CONS'(X0),X3),'const/ind_types/NIL'(X0)))),X4) = vAPP(X1,X1,vAPP('type/ind_types/list'(X0),sTfun(X1,X1),vAPP(sTfun(X0,sTfun(X1,X1)),sTfun('type/ind_types/list'(X0),sTfun(X1,X1)),'const/lists/ITLIST'(X0,X1),X2),X5),vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X2,X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/ITLIST_EXTRA_') ).
thf(f19,plain,
~ spl6_1,
inference(avatar_split_clause,[],[f6,f16]) ).
thf(f6,plain,
$true != $false,
introduced(fool_axiom,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT297^1 : TPTP v8.2.0. Released v7.0.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 23:17:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.35 % (4247)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (4250)WARNING: value z3 for option sas not known
% 0.21/0.37 % (4254)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 theBenchmark for (497ds/0Mi)
% 0.21/0.37 % (4252)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 theBenchmark for (531ds/0Mi)
% 0.21/0.37 % (4248)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37 % (4251)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.37 % (4249)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37 % (4253)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 theBenchmark for (522ds/0Mi)
% 0.21/0.37 % (4250)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 theBenchmark for (569ds/0Mi)
% 0.21/0.37 % (4254)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.37 % Exception at run slice level% Exception at run slice level
% 0.21/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.37 % Exception at run slice level
% 0.21/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.37
% 0.21/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.39 % (4255)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.39 % (4256)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.21/0.39 % (4257)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.21/0.39 % (4256)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.39 % (4255)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.39 % Exception at run slice level
% 0.21/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.41 % (4258)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 2.20/0.67 % (4258)First to succeed.
% 2.20/0.68 % (4258)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4247"
% 2.20/0.68 % (4258)Refutation found. Thanks to Tanya!
% 2.20/0.68 % SZS status Theorem for theBenchmark
% 2.20/0.68 % SZS output start Proof for theBenchmark
% See solution above
% 2.20/0.68 % (4258)------------------------------
% 2.20/0.68 % (4258)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.20/0.68 % (4258)Termination reason: Refutation
% 2.20/0.68
% 2.20/0.68 % (4258)Memory used [KB]: 2430
% 2.20/0.68 % (4258)Time elapsed: 0.271 s
% 2.20/0.68 % (4258)Instructions burned: 812 (million)
% 2.20/0.68 % (4247)Success in time 0.324 s
%------------------------------------------------------------------------------