TSTP Solution File: SYO500^1.003 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYO500^1.003 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n022.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 : Tue May 21 09:11:34 EDT 2024
% Result : Theorem 0.17s 0.45s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 63
% Syntax : Number of formulae : 710 ( 5 unt; 12 typ; 0 def)
% Number of atoms : 6653 ( 595 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 3236 (1474 ~;1713 |; 0 &; 0 @)
% ( 49 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 21 ( 20 >; 1 *; 0 +; 0 <<)
% Number of symbols : 65 ( 62 usr; 52 con; 0-6 aty)
% Number of variables : 20 ( 0 ^ 14 !; 0 ?; 20 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: $o ).
thf(func_def_1,type,
f0: $o > $o ).
thf(func_def_2,type,
f1: $o > $o ).
thf(func_def_3,type,
f2: $o > $o ).
thf(func_def_8,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_9,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_10,type,
vAND: $o > $o > $o ).
thf(func_def_11,type,
vOR: $o > $o > $o ).
thf(func_def_12,type,
vIMP: $o > $o > $o ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(func_def_14,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f3216,plain,
$false,
inference(avatar_sat_refutation,[],[f17,f26,f68,f86,f95,f104,f107,f241,f315,f404,f427,f430,f437,f498,f501,f507,f513,f535,f546,f549,f560,f563,f567,f577,f580,f582,f587,f592,f655,f671,f702,f752,f789,f810,f813,f821,f832,f921,f924,f969,f975,f980,f985,f1022,f1024,f1032,f1033,f1112,f1137,f1144,f1147,f1150,f1165,f1179,f1203,f1208,f1213,f1216,f1248,f1300,f1317,f1318,f1330,f1335,f1338,f1340,f1350,f1352,f1355,f1415,f1423,f1434,f1443,f1480,f1482,f1483,f1496,f1499,f1513,f1634,f1639,f1684,f1698,f1732,f1762,f1874,f1877,f1901,f1980,f2000,f2098,f2106,f2120,f2392,f2404,f2429,f2470,f2484,f2486,f2490,f2500,f2507,f2509,f2512,f2543,f2567,f2592,f2652,f2664,f2672,f2680,f2731,f2738,f2740,f2778,f2841,f2846,f2849,f2870,f2875,f2925,f2933,f2943,f2982,f2989,f2992,f3011,f3030,f3033,f3041,f3047,f3050,f3092,f3096,f3099,f3123,f3145,f3153,f3164,f3172,f3215]) ).
thf(f3215,plain,
( ~ spl0_4
| spl0_11
| ~ spl0_25
| ~ spl0_53
| ~ spl0_60
| ~ spl0_68 ),
inference(avatar_contradiction_clause,[],[f3214]) ).
thf(f3214,plain,
( $false
| ~ spl0_4
| spl0_11
| ~ spl0_25
| ~ spl0_53
| ~ spl0_60
| ~ spl0_68 ),
inference(trivial_inequality_removal,[],[f3213]) ).
thf(f3213,plain,
( ( $true = $false )
| ~ spl0_4
| spl0_11
| ~ spl0_25
| ~ spl0_53
| ~ spl0_60
| ~ spl0_68 ),
inference(forward_demodulation,[],[f3212,f255]) ).
thf(f255,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f253]) ).
thf(f253,plain,
( spl0_25
<=> ( $false = vAPP($o,$o,f0,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
thf(f3212,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_4
| spl0_11
| ~ spl0_53
| ~ spl0_60
| ~ spl0_68 ),
inference(forward_demodulation,[],[f3208,f1265]) ).
thf(f1265,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f1263]) ).
thf(f1263,plain,
( spl0_60
<=> ( $true = vAPP($o,$o,f0,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
thf(f3208,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_4
| spl0_11
| ~ spl0_53
| ~ spl0_68 ),
inference(backward_demodulation,[],[f2499,f3205]) ).
thf(f3205,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_4
| spl0_11
| ~ spl0_53 ),
inference(subsumption_resolution,[],[f3199,f3144]) ).
thf(f3144,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| spl0_11
| ~ spl0_53 ),
inference(backward_demodulation,[],[f89,f1103]) ).
thf(f1103,plain,
( ( vAPP($o,$o,f2,x) = $true )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f1101]) ).
thf(f1101,plain,
( spl0_53
<=> ( vAPP($o,$o,f2,x) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
thf(f89,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x))) != $false )
| spl0_11 ),
inference(avatar_component_clause,[],[f88]) ).
thf(f88,plain,
( spl0_11
<=> ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f3199,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_4
| ~ spl0_53 ),
inference(superposition,[],[f3146,f4]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f3146,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_4
| ~ spl0_53 ),
inference(forward_demodulation,[],[f25,f1103]) ).
thf(f25,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x))))) = $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f23,plain,
( spl0_4
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x))))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f2499,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f2497]) ).
thf(f2497,plain,
( spl0_68
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
thf(f3172,plain,
( ~ spl0_60
| spl0_12
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f3166,f310,f92,f1263]) ).
thf(f92,plain,
( spl0_12
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f310,plain,
( spl0_30
<=> ( $false = vAPP($o,$o,f1,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
thf(f3166,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| spl0_12
| ~ spl0_30 ),
inference(backward_demodulation,[],[f93,f312]) ).
thf(f312,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f310]) ).
thf(f93,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_12 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f3164,plain,
( spl0_60
| ~ spl0_25
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f3163,f392,f253,f1263]) ).
thf(f392,plain,
( spl0_32
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
thf(f3163,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_25
| ~ spl0_32 ),
inference(forward_demodulation,[],[f394,f255]) ).
thf(f394,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f392]) ).
thf(f3153,plain,
( spl0_60
| ~ spl0_1
| ~ spl0_53
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f3152,f1194,f1101,f10,f1263]) ).
thf(f10,plain,
( spl0_1
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))))) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f1194,plain,
( spl0_57
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
thf(f3152,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_1
| ~ spl0_53
| ~ spl0_57 ),
inference(forward_demodulation,[],[f3151,f3149]) ).
thf(f3149,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_53
| ~ spl0_57 ),
inference(forward_demodulation,[],[f1196,f1103]) ).
thf(f1196,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))))) = $false )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f1194]) ).
thf(f3151,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_1
| ~ spl0_53 ),
inference(forward_demodulation,[],[f12,f1103]) ).
thf(f12,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))))) = $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f10]) ).
thf(f3145,plain,
( ~ spl0_67
| spl0_44
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f3143,f1101,f699,f2492]) ).
thf(f2492,plain,
( spl0_67
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
thf(f699,plain,
( spl0_44
<=> ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
thf(f3143,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| spl0_44
| ~ spl0_53 ),
inference(backward_demodulation,[],[f700,f1103]) ).
thf(f700,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))) != $false )
| spl0_44 ),
inference(avatar_component_clause,[],[f699]) ).
thf(f3123,plain,
( spl0_60
| ~ spl0_31
| ~ spl0_53
| ~ spl0_57
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f3121,f2497,f1194,f1101,f379,f1263]) ).
thf(f379,plain,
( spl0_31
<=> ( x = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
thf(f3121,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_31
| ~ spl0_53
| ~ spl0_57
| ~ spl0_68 ),
inference(backward_demodulation,[],[f2499,f3120]) ).
thf(f3120,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true))) )
| ~ spl0_31
| ~ spl0_53
| ~ spl0_57 ),
inference(forward_demodulation,[],[f3119,f3106]) ).
thf(f3106,plain,
( ( $true = vAPP($o,$o,f2,$true) )
| ~ spl0_31
| ~ spl0_53 ),
inference(forward_demodulation,[],[f1103,f381]) ).
thf(f381,plain,
( ( x = $true )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f379]) ).
thf(f3119,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true)))) )
| ~ spl0_31
| ~ spl0_53
| ~ spl0_57 ),
inference(forward_demodulation,[],[f3109,f3106]) ).
thf(f3109,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_31
| ~ spl0_53
| ~ spl0_57 ),
inference(backward_demodulation,[],[f3037,f3106]) ).
thf(f3037,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_31
| ~ spl0_57 ),
inference(forward_demodulation,[],[f1196,f381]) ).
thf(f3099,plain,
( ~ spl0_60
| ~ spl0_25
| spl0_32 ),
inference(avatar_split_clause,[],[f3063,f392,f253,f1263]) ).
thf(f3063,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| ~ spl0_25
| spl0_32 ),
inference(backward_demodulation,[],[f393,f255]) ).
thf(f393,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| spl0_32 ),
inference(avatar_component_clause,[],[f392]) ).
thf(f3096,plain,
( spl0_60
| ~ spl0_1
| ~ spl0_31
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f3095,f1194,f379,f10,f1263]) ).
thf(f3095,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_57 ),
inference(forward_demodulation,[],[f2821,f3037]) ).
thf(f2821,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ~ spl0_1
| ~ spl0_31 ),
inference(forward_demodulation,[],[f12,f381]) ).
thf(f3092,plain,
( ~ spl0_67
| ~ spl0_31
| spl0_43 ),
inference(avatar_split_clause,[],[f3009,f631,f379,f2492]) ).
thf(f631,plain,
( spl0_43
<=> ( vAPP($o,$o,f2,vAPP($o,$o,f2,x)) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
thf(f3009,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_31
| spl0_43 ),
inference(forward_demodulation,[],[f632,f381]) ).
thf(f632,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f2,x)) != $false )
| spl0_43 ),
inference(avatar_component_clause,[],[f631]) ).
thf(f3050,plain,
( spl0_40
| ~ spl0_45
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f3048,f747,f743,f518]) ).
thf(f518,plain,
( spl0_40
<=> ( $false = vAPP($o,$o,f0,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
thf(f743,plain,
( spl0_45
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
thf(f747,plain,
( spl0_46
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
thf(f3048,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_45
| ~ spl0_46 ),
inference(backward_demodulation,[],[f749,f745]) ).
thf(f745,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f743]) ).
thf(f749,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false))) )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f747]) ).
thf(f3047,plain,
( ~ spl0_40
| spl0_42
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f3043,f747,f530,f518]) ).
thf(f530,plain,
( spl0_42
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
thf(f3043,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_42
| ~ spl0_46 ),
inference(backward_demodulation,[],[f531,f749]) ).
thf(f531,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_42 ),
inference(avatar_component_clause,[],[f530]) ).
thf(f3041,plain,
( spl0_46
| ~ spl0_20
| ~ spl0_31
| ~ spl0_52
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f3040,f1194,f982,f379,f226,f747]) ).
thf(f226,plain,
( spl0_20
<=> ( $true = vAPP($o,$o,f2,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
thf(f982,plain,
( spl0_52
<=> ( $false = vAPP($o,$o,f2,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
thf(f3040,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false))) )
| ~ spl0_20
| ~ spl0_31
| ~ spl0_52
| ~ spl0_57 ),
inference(forward_demodulation,[],[f3039,f983]) ).
thf(f983,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f982]) ).
thf(f3039,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true)))) )
| ~ spl0_20
| ~ spl0_31
| ~ spl0_52
| ~ spl0_57 ),
inference(forward_demodulation,[],[f3038,f228]) ).
thf(f228,plain,
( ( $true = vAPP($o,$o,f2,$false) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f226]) ).
thf(f3038,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_31
| ~ spl0_52
| ~ spl0_57 ),
inference(forward_demodulation,[],[f3037,f983]) ).
thf(f3033,plain,
( spl0_45
| ~ spl0_4
| ~ spl0_7
| ~ spl0_15
| ~ spl0_20
| spl0_27 ),
inference(avatar_split_clause,[],[f3032,f264,f226,f199,f70,f23,f743]) ).
thf(f70,plain,
( spl0_7
<=> ( vAPP($o,$o,f2,x) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f199,plain,
( spl0_15
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
thf(f264,plain,
( spl0_27
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
thf(f3032,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_15
| ~ spl0_20
| spl0_27 ),
inference(forward_demodulation,[],[f2746,f3031]) ).
thf(f3031,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_15
| ~ spl0_20
| spl0_27 ),
inference(subsumption_resolution,[],[f2967,f3014]) ).
thf(f3014,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_15
| ~ spl0_20
| spl0_27 ),
inference(backward_demodulation,[],[f3001,f228]) ).
thf(f3001,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_15
| spl0_27 ),
inference(forward_demodulation,[],[f265,f201]) ).
thf(f201,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f199]) ).
thf(f265,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| spl0_27 ),
inference(avatar_component_clause,[],[f264]) ).
thf(f2967,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f2746,f4]) ).
thf(f2746,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_4
| ~ spl0_7 ),
inference(backward_demodulation,[],[f25,f72]) ).
thf(f72,plain,
( ( vAPP($o,$o,f2,x) = $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f3030,plain,
( ~ spl0_4
| ~ spl0_7
| spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f3029]) ).
thf(f3029,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f3028]) ).
thf(f3028,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f94,f2983]) ).
thf(f2983,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_4
| ~ spl0_7
| spl0_11 ),
inference(subsumption_resolution,[],[f2967,f2750]) ).
thf(f2750,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_7
| spl0_11 ),
inference(backward_demodulation,[],[f89,f72]) ).
thf(f94,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f3011,plain,
( ~ spl0_29
| ~ spl0_31
| spl0_43
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f3010,f982,f631,f379,f306]) ).
thf(f306,plain,
( spl0_29
<=> ( $false = vAPP($o,$o,f2,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
thf(f3010,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_31
| spl0_43
| ~ spl0_52 ),
inference(forward_demodulation,[],[f3009,f983]) ).
thf(f2992,plain,
( ~ spl0_37
| ~ spl0_7
| spl0_57 ),
inference(avatar_split_clause,[],[f2753,f1194,f70,f419]) ).
thf(f419,plain,
( spl0_37
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
thf(f2753,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_7
| spl0_57 ),
inference(forward_demodulation,[],[f1195,f72]) ).
thf(f1195,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))))) != $false )
| spl0_57 ),
inference(avatar_component_clause,[],[f1194]) ).
thf(f2989,plain,
( ~ spl0_4
| ~ spl0_7
| spl0_13
| spl0_25 ),
inference(avatar_contradiction_clause,[],[f2988]) ).
thf(f2988,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| spl0_13
| spl0_25 ),
inference(subsumption_resolution,[],[f2976,f2749]) ).
thf(f2749,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_7
| spl0_13 ),
inference(backward_demodulation,[],[f98,f72]) ).
thf(f98,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x)))) != $false )
| spl0_13 ),
inference(avatar_component_clause,[],[f97]) ).
thf(f97,plain,
( spl0_13
<=> ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x)))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f2976,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_4
| ~ spl0_7
| spl0_25 ),
inference(trivial_inequality_removal,[],[f2971]) ).
thf(f2971,plain,
( ( $false != $false )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_4
| ~ spl0_7
| spl0_25 ),
inference(superposition,[],[f1542,f2746]) ).
thf(f1542,plain,
( ! [X0: $o] :
( ( $false != vAPP($o,$o,f0,X0) )
| ( $false = X0 ) )
| spl0_25 ),
inference(superposition,[],[f254,f4]) ).
thf(f254,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| spl0_25 ),
inference(avatar_component_clause,[],[f253]) ).
thf(f2982,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_30
| spl0_45
| spl0_54 ),
inference(avatar_contradiction_clause,[],[f2981]) ).
thf(f2981,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_30
| spl0_45
| spl0_54 ),
inference(subsumption_resolution,[],[f2980,f744]) ).
thf(f744,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_45 ),
inference(avatar_component_clause,[],[f743]) ).
thf(f2980,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_30
| spl0_54 ),
inference(forward_demodulation,[],[f2979,f312]) ).
thf(f2979,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_4
| ~ spl0_7
| spl0_54 ),
inference(subsumption_resolution,[],[f2966,f1121]) ).
thf(f1121,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| spl0_54 ),
inference(avatar_component_clause,[],[f1120]) ).
thf(f1120,plain,
( spl0_54
<=> ( $false = vAPP($o,$o,f1,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
thf(f2966,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f2746,f4]) ).
thf(f2943,plain,
( ~ spl0_42
| spl0_16
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f2914,f982,f203,f530]) ).
thf(f203,plain,
( spl0_16
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
thf(f2914,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_16
| ~ spl0_52 ),
inference(forward_demodulation,[],[f204,f983]) ).
thf(f204,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_16 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f2933,plain,
( ~ spl0_42
| spl0_3
| ~ spl0_29
| ~ spl0_31
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f2932,f982,f379,f306,f19,f530]) ).
thf(f19,plain,
( spl0_3
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f2932,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_3
| ~ spl0_29
| ~ spl0_31
| ~ spl0_52 ),
inference(forward_demodulation,[],[f2931,f308]) ).
thf(f308,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f306]) ).
thf(f2931,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_3
| ~ spl0_29
| ~ spl0_31
| ~ spl0_52 ),
inference(forward_demodulation,[],[f2819,f308]) ).
thf(f2819,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_3
| ~ spl0_31
| ~ spl0_52 ),
inference(forward_demodulation,[],[f2818,f983]) ).
thf(f2818,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| spl0_3
| ~ spl0_31 ),
inference(forward_demodulation,[],[f20,f381]) ).
thf(f20,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))))) != $false )
| spl0_3 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f2925,plain,
( ~ spl0_45
| ~ spl0_29
| spl0_38 ),
inference(avatar_split_clause,[],[f2924,f424,f306,f743]) ).
thf(f424,plain,
( spl0_38
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
thf(f2924,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_29
| spl0_38 ),
inference(forward_demodulation,[],[f2923,f308]) ).
thf(f2923,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_29
| spl0_38 ),
inference(forward_demodulation,[],[f425,f308]) ).
thf(f425,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| spl0_38 ),
inference(avatar_component_clause,[],[f424]) ).
thf(f2875,plain,
( spl0_14
| ~ spl0_32
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f2874,f401,f392,f101]) ).
thf(f101,plain,
( spl0_14
<=> ( $true = vAPP($o,$o,f0,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f401,plain,
( spl0_34
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
thf(f2874,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_32
| ~ spl0_34 ),
inference(backward_demodulation,[],[f403,f394]) ).
thf(f403,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f401]) ).
thf(f2870,plain,
( spl0_29
| ~ spl0_31
| ~ spl0_43
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f2869,f982,f631,f379,f306]) ).
thf(f2869,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_31
| ~ spl0_43
| ~ spl0_52 ),
inference(forward_demodulation,[],[f2868,f983]) ).
thf(f2868,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_31
| ~ spl0_43 ),
inference(forward_demodulation,[],[f633,f381]) ).
thf(f633,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f2,x)) = $false )
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f631]) ).
thf(f2849,plain,
( spl0_15
| ~ spl0_20
| ~ spl0_52 ),
inference(avatar_contradiction_clause,[],[f2848]) ).
thf(f2848,plain,
( $false
| spl0_15
| ~ spl0_20
| ~ spl0_52 ),
inference(subsumption_resolution,[],[f2847,f983]) ).
thf(f2847,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f200,f228]) ).
thf(f200,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| spl0_15 ),
inference(avatar_component_clause,[],[f199]) ).
thf(f2846,plain,
( ~ spl0_16
| spl0_42
| ~ spl0_52 ),
inference(avatar_contradiction_clause,[],[f2845]) ).
thf(f2845,plain,
( $false
| ~ spl0_16
| spl0_42
| ~ spl0_52 ),
inference(subsumption_resolution,[],[f2844,f531]) ).
thf(f2844,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_16
| ~ spl0_52 ),
inference(forward_demodulation,[],[f205,f983]) ).
thf(f205,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f2841,plain,
( ~ spl0_20
| ~ spl0_27
| ~ spl0_40
| spl0_49
| ~ spl0_52 ),
inference(avatar_contradiction_clause,[],[f2840]) ).
thf(f2840,plain,
( $false
| ~ spl0_20
| ~ spl0_27
| ~ spl0_40
| spl0_49
| ~ spl0_52 ),
inference(subsumption_resolution,[],[f2839,f520]) ).
thf(f520,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f518]) ).
thf(f2839,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_20
| ~ spl0_27
| ~ spl0_40
| spl0_49
| ~ spl0_52 ),
inference(forward_demodulation,[],[f2838,f520]) ).
thf(f2838,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_20
| ~ spl0_27
| spl0_49
| ~ spl0_52 ),
inference(backward_demodulation,[],[f819,f2837]) ).
thf(f2837,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_20
| ~ spl0_27
| ~ spl0_52 ),
inference(forward_demodulation,[],[f2836,f228]) ).
thf(f2836,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_20
| ~ spl0_27
| ~ spl0_52 ),
inference(forward_demodulation,[],[f2830,f983]) ).
thf(f2830,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| ~ spl0_20
| ~ spl0_27 ),
inference(backward_demodulation,[],[f266,f228]) ).
thf(f266,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f264]) ).
thf(f819,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| spl0_49 ),
inference(avatar_component_clause,[],[f818]) ).
thf(f818,plain,
( spl0_49
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
thf(f2778,plain,
( ~ spl0_1
| ~ spl0_29
| ~ spl0_40
| ~ spl0_43
| ~ spl0_46 ),
inference(avatar_contradiction_clause,[],[f2777]) ).
thf(f2777,plain,
( $false
| ~ spl0_1
| ~ spl0_29
| ~ spl0_40
| ~ spl0_43
| ~ spl0_46 ),
inference(trivial_inequality_removal,[],[f2776]) ).
thf(f2776,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_29
| ~ spl0_40
| ~ spl0_43
| ~ spl0_46 ),
inference(forward_demodulation,[],[f2774,f520]) ).
thf(f2774,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_1
| ~ spl0_29
| ~ spl0_43
| ~ spl0_46 ),
inference(backward_demodulation,[],[f2742,f749]) ).
thf(f2742,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_1
| ~ spl0_29
| ~ spl0_43 ),
inference(forward_demodulation,[],[f2741,f308]) ).
thf(f2741,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_1
| ~ spl0_43 ),
inference(forward_demodulation,[],[f12,f633]) ).
thf(f2740,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_13
| spl0_25
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[],[f2739]) ).
thf(f2739,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| spl0_13
| spl0_25
| ~ spl0_29 ),
inference(subsumption_resolution,[],[f2721,f2655]) ).
thf(f2655,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_5
| spl0_13
| ~ spl0_29 ),
inference(forward_demodulation,[],[f2654,f308]) ).
thf(f2654,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) )
| ~ spl0_5
| spl0_13 ),
inference(forward_demodulation,[],[f98,f63]) ).
thf(f63,plain,
( ( x = $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f61]) ).
thf(f61,plain,
( spl0_5
<=> ( x = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f2721,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_4
| ~ spl0_5
| spl0_25
| ~ spl0_29 ),
inference(trivial_inequality_removal,[],[f2716]) ).
thf(f2716,plain,
( ( $false != $false )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_4
| ~ spl0_5
| spl0_25
| ~ spl0_29 ),
inference(superposition,[],[f1542,f2569]) ).
thf(f2569,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_29 ),
inference(forward_demodulation,[],[f2568,f308]) ).
thf(f2568,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f25,f63]) ).
thf(f2738,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_13
| ~ spl0_14
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[],[f2737]) ).
thf(f2737,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| spl0_13
| ~ spl0_14
| ~ spl0_29 ),
inference(subsumption_resolution,[],[f2722,f2655]) ).
thf(f2722,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_29 ),
inference(trivial_inequality_removal,[],[f2715]) ).
thf(f2715,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_29 ),
inference(superposition,[],[f2602,f2569]) ).
thf(f2602,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,f0,X0) )
| ( $false = X0 ) )
| ~ spl0_14 ),
inference(duplicate_literal_removal,[],[f2600]) ).
thf(f2600,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,f0,X0) )
| ( $false = X0 )
| ( $false = X0 ) )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f2595]) ).
thf(f2595,plain,
( ! [X0: $o] :
( ( vAPP($o,$o,f0,X0) = X0 )
| ( $false = X0 ) )
| ~ spl0_14 ),
inference(superposition,[],[f103,f4]) ).
thf(f103,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f101]) ).
thf(f2731,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_11
| ~ spl0_12
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[],[f2730]) ).
thf(f2730,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| spl0_11
| ~ spl0_12
| ~ spl0_29 ),
inference(trivial_inequality_removal,[],[f2729]) ).
thf(f2729,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_5
| spl0_11
| ~ spl0_12
| ~ spl0_29 ),
inference(backward_demodulation,[],[f94,f2728]) ).
thf(f2728,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_4
| ~ spl0_5
| spl0_11
| ~ spl0_29 ),
inference(subsumption_resolution,[],[f2710,f2701]) ).
thf(f2701,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_5
| spl0_11
| ~ spl0_29 ),
inference(forward_demodulation,[],[f2700,f308]) ).
thf(f2700,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_5
| spl0_11 ),
inference(forward_demodulation,[],[f89,f63]) ).
thf(f2710,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_29 ),
inference(superposition,[],[f2569,f4]) ).
thf(f2680,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_29
| ~ spl0_40
| ~ spl0_46 ),
inference(avatar_contradiction_clause,[],[f2679]) ).
thf(f2679,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_29
| ~ spl0_40
| ~ spl0_46 ),
inference(trivial_inequality_removal,[],[f2678]) ).
thf(f2678,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_29
| ~ spl0_40
| ~ spl0_46 ),
inference(forward_demodulation,[],[f2674,f520]) ).
thf(f2674,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_29
| ~ spl0_46 ),
inference(backward_demodulation,[],[f2580,f749]) ).
thf(f2580,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_29 ),
inference(forward_demodulation,[],[f2579,f308]) ).
thf(f2579,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_29 ),
inference(forward_demodulation,[],[f2578,f308]) ).
thf(f2578,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_29 ),
inference(forward_demodulation,[],[f2577,f308]) ).
thf(f2577,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_demodulation,[],[f12,f63]) ).
thf(f2672,plain,
( ~ spl0_46
| spl0_26
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f2588,f306,f259,f747]) ).
thf(f259,plain,
( spl0_26
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
thf(f2588,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false))) )
| spl0_26
| ~ spl0_29 ),
inference(forward_demodulation,[],[f2587,f308]) ).
thf(f2587,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) )
| spl0_26
| ~ spl0_29 ),
inference(forward_demodulation,[],[f2586,f308]) ).
thf(f2586,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| spl0_26
| ~ spl0_29 ),
inference(forward_demodulation,[],[f260,f308]) ).
thf(f260,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_26 ),
inference(avatar_component_clause,[],[f259]) ).
thf(f2664,plain,
( spl0_45
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f2659,f306,f88,f61,f23,f743]) ).
thf(f2659,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_29 ),
inference(backward_demodulation,[],[f2569,f2657]) ).
thf(f2657,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_5
| ~ spl0_11
| ~ spl0_29 ),
inference(forward_demodulation,[],[f2656,f308]) ).
thf(f2656,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_5
| ~ spl0_11 ),
inference(forward_demodulation,[],[f90,f63]) ).
thf(f90,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x))) = $false )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f88]) ).
thf(f2652,plain,
( ~ spl0_5
| spl0_11
| ~ spl0_29
| ~ spl0_30
| spl0_54 ),
inference(avatar_contradiction_clause,[],[f2651]) ).
thf(f2651,plain,
( $false
| ~ spl0_5
| spl0_11
| ~ spl0_29
| ~ spl0_30
| spl0_54 ),
inference(subsumption_resolution,[],[f2650,f1121]) ).
thf(f2650,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_5
| spl0_11
| ~ spl0_29
| ~ spl0_30 ),
inference(subsumption_resolution,[],[f2646,f312]) ).
thf(f2646,plain,
( ( $false != vAPP($o,$o,f1,$true) )
| ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_5
| spl0_11
| ~ spl0_29 ),
inference(superposition,[],[f2530,f4]) ).
thf(f2530,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_5
| spl0_11
| ~ spl0_29 ),
inference(backward_demodulation,[],[f2442,f308]) ).
thf(f2442,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_5
| spl0_11 ),
inference(forward_demodulation,[],[f89,f63]) ).
thf(f2592,plain,
( ~ spl0_42
| spl0_3
| ~ spl0_5
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f2574,f306,f61,f19,f530]) ).
thf(f2574,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_3
| ~ spl0_5
| ~ spl0_29 ),
inference(forward_demodulation,[],[f2573,f308]) ).
thf(f2573,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_3
| ~ spl0_5
| ~ spl0_29 ),
inference(forward_demodulation,[],[f2572,f308]) ).
thf(f2572,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_3
| ~ spl0_5
| ~ spl0_29 ),
inference(forward_demodulation,[],[f2571,f308]) ).
thf(f2571,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f20,f63]) ).
thf(f2567,plain,
( ~ spl0_5
| ~ spl0_29
| spl0_43 ),
inference(avatar_contradiction_clause,[],[f2566]) ).
thf(f2566,plain,
( $false
| ~ spl0_5
| ~ spl0_29
| spl0_43 ),
inference(subsumption_resolution,[],[f2565,f308]) ).
thf(f2565,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_5
| ~ spl0_29
| spl0_43 ),
inference(forward_demodulation,[],[f2564,f308]) ).
thf(f2564,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_5
| spl0_43 ),
inference(forward_demodulation,[],[f632,f63]) ).
thf(f2543,plain,
( ~ spl0_29
| spl0_37
| ~ spl0_40
| ~ spl0_45 ),
inference(avatar_contradiction_clause,[],[f2542]) ).
thf(f2542,plain,
( $false
| ~ spl0_29
| spl0_37
| ~ spl0_40
| ~ spl0_45 ),
inference(subsumption_resolution,[],[f2541,f520]) ).
thf(f2541,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_29
| spl0_37
| ~ spl0_45 ),
inference(forward_demodulation,[],[f2540,f745]) ).
thf(f2540,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false))) )
| ~ spl0_29
| spl0_37 ),
inference(forward_demodulation,[],[f2528,f308]) ).
thf(f2528,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) )
| ~ spl0_29
| spl0_37 ),
inference(backward_demodulation,[],[f420,f308]) ).
thf(f420,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| spl0_37 ),
inference(avatar_component_clause,[],[f419]) ).
thf(f2512,plain,
( ~ spl0_40
| ~ spl0_45
| spl0_46 ),
inference(avatar_contradiction_clause,[],[f2511]) ).
thf(f2511,plain,
( $false
| ~ spl0_40
| ~ spl0_45
| spl0_46 ),
inference(subsumption_resolution,[],[f2510,f520]) ).
thf(f2510,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_45
| spl0_46 ),
inference(forward_demodulation,[],[f748,f745]) ).
thf(f748,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false))) )
| spl0_46 ),
inference(avatar_component_clause,[],[f747]) ).
thf(f2509,plain,
( ~ spl0_26
| ~ spl0_5
| spl0_57 ),
inference(avatar_split_clause,[],[f2508,f1194,f61,f259]) ).
thf(f2508,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_5
| spl0_57 ),
inference(forward_demodulation,[],[f1195,f63]) ).
thf(f2507,plain,
( ~ spl0_21
| ~ spl0_5
| spl0_58 ),
inference(avatar_split_clause,[],[f2506,f1198,f61,f234]) ).
thf(f234,plain,
( spl0_21
<=> ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
thf(f1198,plain,
( spl0_58
<=> ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
thf(f2506,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_5
| spl0_58 ),
inference(forward_demodulation,[],[f1199,f63]) ).
thf(f1199,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))) != $false )
| spl0_58 ),
inference(avatar_component_clause,[],[f1198]) ).
thf(f2500,plain,
( spl0_67
| spl0_68
| ~ spl0_1
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f2162,f1101,f10,f2497,f2492]) ).
thf(f2162,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_1
| ~ spl0_53 ),
inference(superposition,[],[f1902,f4]) ).
thf(f1902,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_1
| ~ spl0_53 ),
inference(backward_demodulation,[],[f12,f1103]) ).
thf(f2490,plain,
( spl0_20
| ~ spl0_5
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f2137,f1101,f61,f226]) ).
thf(f2137,plain,
( ( $true = vAPP($o,$o,f2,$false) )
| ~ spl0_5
| ~ spl0_53 ),
inference(backward_demodulation,[],[f1103,f63]) ).
thf(f2486,plain,
( ~ spl0_66
| spl0_3
| ~ spl0_40
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f2485,f1101,f518,f19,f2481]) ).
thf(f2481,plain,
( spl0_66
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
thf(f2485,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| spl0_3
| ~ spl0_40
| ~ spl0_53 ),
inference(subsumption_resolution,[],[f2282,f520]) ).
thf(f2282,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| spl0_3
| ~ spl0_40
| ~ spl0_53 ),
inference(constrained_superposition,[],[f1903,f520]) ).
thf(f1903,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| spl0_3
| ~ spl0_53 ),
inference(backward_demodulation,[],[f20,f1103]) ).
thf(f2484,plain,
( spl0_66
| spl0_14
| ~ spl0_1
| ~ spl0_40
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f2479,f1101,f518,f10,f101,f2481]) ).
thf(f2479,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| ~ spl0_1
| ~ spl0_40
| ~ spl0_53 ),
inference(subsumption_resolution,[],[f2182,f2180]) ).
thf(f2180,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_1
| ~ spl0_40
| ~ spl0_53 ),
inference(trivial_inequality_removal,[],[f2175]) ).
thf(f2175,plain,
( ( $true = $false )
| ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_1
| ~ spl0_40
| ~ spl0_53 ),
inference(constrained_superposition,[],[f1902,f520]) ).
thf(f2182,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_1
| ~ spl0_53 ),
inference(binary_proxy_clausification,[],[f2173]) ).
thf(f2173,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_1
| ~ spl0_53 ),
inference(constrained_superposition,[],[f1902,f1902]) ).
thf(f2470,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_20
| ~ spl0_40
| ~ spl0_53
| ~ spl0_58 ),
inference(avatar_contradiction_clause,[],[f2469]) ).
thf(f2469,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_20
| ~ spl0_40
| ~ spl0_53
| ~ spl0_58 ),
inference(subsumption_resolution,[],[f2468,f2461]) ).
thf(f2461,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| spl0_3
| ~ spl0_40
| ~ spl0_53 ),
inference(subsumption_resolution,[],[f2460,f520]) ).
thf(f2460,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| spl0_3
| ~ spl0_40
| ~ spl0_53 ),
inference(forward_demodulation,[],[f2276,f520]) ).
thf(f2276,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| spl0_3
| ~ spl0_40
| ~ spl0_53 ),
inference(constrained_superposition,[],[f1903,f520]) ).
thf(f2468,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| ~ spl0_5
| ~ spl0_20
| ~ spl0_58 ),
inference(forward_demodulation,[],[f2467,f228]) ).
thf(f2467,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_5
| ~ spl0_58 ),
inference(forward_demodulation,[],[f1200,f63]) ).
thf(f1200,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))) = $false )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f1198]) ).
thf(f2429,plain,
( spl0_14
| ~ spl0_1
| ~ spl0_53
| spl0_57 ),
inference(avatar_split_clause,[],[f2428,f1194,f1101,f10,f101]) ).
thf(f2428,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_1
| ~ spl0_53
| spl0_57 ),
inference(subsumption_resolution,[],[f2174,f1908]) ).
thf(f1908,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_53
| spl0_57 ),
inference(backward_demodulation,[],[f1195,f1103]) ).
thf(f2174,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_1
| ~ spl0_53 ),
inference(superposition,[],[f1902,f4]) ).
thf(f2404,plain,
( spl0_30
| ~ spl0_11
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f2340,f1101,f88,f310]) ).
thf(f2340,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_11
| ~ spl0_53 ),
inference(duplicate_literal_removal,[],[f2326]) ).
thf(f2326,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_11
| ~ spl0_53 ),
inference(superposition,[],[f2131,f4]) ).
thf(f2131,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_11
| ~ spl0_53 ),
inference(forward_demodulation,[],[f90,f1103]) ).
thf(f2392,plain,
( ~ spl0_49
| spl0_3
| spl0_44
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f2304,f1101,f699,f19,f818]) ).
thf(f2304,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| spl0_3
| spl0_44
| ~ spl0_53 ),
inference(subsumption_resolution,[],[f2272,f1907]) ).
thf(f1907,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| spl0_44
| ~ spl0_53 ),
inference(backward_demodulation,[],[f700,f1103]) ).
thf(f2272,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| spl0_3
| ~ spl0_53 ),
inference(superposition,[],[f1903,f4]) ).
thf(f2120,plain,
( spl0_16
| ~ spl0_40
| ~ spl0_50 ),
inference(avatar_contradiction_clause,[],[f2119]) ).
thf(f2119,plain,
( $false
| spl0_16
| ~ spl0_40
| ~ spl0_50 ),
inference(subsumption_resolution,[],[f2118,f520]) ).
thf(f2118,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_16
| ~ spl0_40
| ~ spl0_50 ),
inference(forward_demodulation,[],[f2117,f520]) ).
thf(f2117,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_16
| ~ spl0_40
| ~ spl0_50 ),
inference(forward_demodulation,[],[f2113,f520]) ).
thf(f2113,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_16
| ~ spl0_50 ),
inference(backward_demodulation,[],[f204,f974]) ).
thf(f974,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f972]) ).
thf(f972,plain,
( spl0_50
<=> ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
thf(f2106,plain,
( ~ spl0_1
| spl0_12
| ~ spl0_31
| ~ spl0_40
| ~ spl0_53 ),
inference(avatar_contradiction_clause,[],[f2105]) ).
thf(f2105,plain,
( $false
| ~ spl0_1
| spl0_12
| ~ spl0_31
| ~ spl0_40
| ~ spl0_53 ),
inference(subsumption_resolution,[],[f2085,f2061]) ).
thf(f2061,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_40
| ~ spl0_53 ),
inference(trivial_inequality_removal,[],[f2060]) ).
thf(f2060,plain,
( ( $true = $false )
| ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_40
| ~ spl0_53 ),
inference(forward_demodulation,[],[f2035,f520]) ).
thf(f2035,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_40
| ~ spl0_53 ),
inference(constrained_superposition,[],[f1930,f520]) ).
thf(f1930,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_53 ),
inference(forward_demodulation,[],[f1921,f1912]) ).
thf(f1912,plain,
( ( $true = vAPP($o,$o,f2,$true) )
| ~ spl0_31
| ~ spl0_53 ),
inference(backward_demodulation,[],[f1103,f381]) ).
thf(f1921,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_53 ),
inference(backward_demodulation,[],[f1902,f1912]) ).
thf(f2085,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_12 ),
inference(trivial_inequality_removal,[],[f2084]) ).
thf(f2084,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_12 ),
inference(superposition,[],[f93,f4]) ).
thf(f2098,plain,
( spl0_12
| ~ spl0_14
| spl0_30 ),
inference(avatar_contradiction_clause,[],[f2097]) ).
thf(f2097,plain,
( $false
| spl0_12
| ~ spl0_14
| spl0_30 ),
inference(subsumption_resolution,[],[f2090,f311]) ).
thf(f311,plain,
( ( $false != vAPP($o,$o,f1,$true) )
| spl0_30 ),
inference(avatar_component_clause,[],[f310]) ).
thf(f2090,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| spl0_12
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f2080]) ).
thf(f2080,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f1,$true) )
| spl0_12
| ~ spl0_14 ),
inference(superposition,[],[f93,f1541]) ).
thf(f1541,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,f0,X0) )
| ( $false = X0 ) )
| ~ spl0_14 ),
inference(duplicate_literal_removal,[],[f1539]) ).
thf(f1539,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,f0,X0) )
| ( $false = X0 )
| ( $false = X0 ) )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f1537]) ).
thf(f1537,plain,
( ! [X0: $o] :
( ( vAPP($o,$o,f0,X0) = X0 )
| ( $false = X0 ) )
| ~ spl0_14 ),
inference(superposition,[],[f103,f4]) ).
thf(f2000,plain,
( spl0_15
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[],[f1999]) ).
thf(f1999,plain,
( $false
| spl0_15
| ~ spl0_29 ),
inference(subsumption_resolution,[],[f1993,f308]) ).
thf(f1993,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| spl0_15
| ~ spl0_29 ),
inference(backward_demodulation,[],[f200,f308]) ).
thf(f1980,plain,
( ~ spl0_11
| spl0_30
| ~ spl0_31
| ~ spl0_53 ),
inference(avatar_contradiction_clause,[],[f1979]) ).
thf(f1979,plain,
( $false
| ~ spl0_11
| spl0_30
| ~ spl0_31
| ~ spl0_53 ),
inference(subsumption_resolution,[],[f1978,f311]) ).
thf(f1978,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_11
| ~ spl0_31
| ~ spl0_53 ),
inference(duplicate_literal_removal,[],[f1972]) ).
thf(f1972,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_11
| ~ spl0_31
| ~ spl0_53 ),
inference(superposition,[],[f1940,f4]) ).
thf(f1940,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_11
| ~ spl0_31
| ~ spl0_53 ),
inference(forward_demodulation,[],[f1939,f1912]) ).
thf(f1939,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))) )
| ~ spl0_11
| ~ spl0_31 ),
inference(forward_demodulation,[],[f90,f381]) ).
thf(f1901,plain,
( ~ spl0_5
| ~ spl0_20
| spl0_53 ),
inference(avatar_contradiction_clause,[],[f1900]) ).
thf(f1900,plain,
( $false
| ~ spl0_5
| ~ spl0_20
| spl0_53 ),
inference(subsumption_resolution,[],[f1899,f228]) ).
thf(f1899,plain,
( ( $true != vAPP($o,$o,f2,$false) )
| ~ spl0_5
| spl0_53 ),
inference(forward_demodulation,[],[f1102,f63]) ).
thf(f1102,plain,
( ( vAPP($o,$o,f2,x) != $true )
| spl0_53 ),
inference(avatar_component_clause,[],[f1101]) ).
thf(f1877,plain,
( ~ spl0_4
| spl0_13
| spl0_25
| ~ spl0_53 ),
inference(avatar_contradiction_clause,[],[f1876]) ).
thf(f1876,plain,
( $false
| ~ spl0_4
| spl0_13
| spl0_25
| ~ spl0_53 ),
inference(subsumption_resolution,[],[f1875,f1833]) ).
thf(f1833,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_13
| ~ spl0_53 ),
inference(forward_demodulation,[],[f98,f1103]) ).
thf(f1875,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_4
| spl0_25
| ~ spl0_53 ),
inference(subsumption_resolution,[],[f1858,f254]) ).
thf(f1858,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_4
| ~ spl0_53 ),
inference(superposition,[],[f1826,f4]) ).
thf(f1826,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_4
| ~ spl0_53 ),
inference(backward_demodulation,[],[f25,f1103]) ).
thf(f1874,plain,
( ~ spl0_4
| spl0_11
| ~ spl0_12
| ~ spl0_53 ),
inference(avatar_contradiction_clause,[],[f1873]) ).
thf(f1873,plain,
( $false
| ~ spl0_4
| spl0_11
| ~ spl0_12
| ~ spl0_53 ),
inference(trivial_inequality_removal,[],[f1872]) ).
thf(f1872,plain,
( ( $true = $false )
| ~ spl0_4
| spl0_11
| ~ spl0_12
| ~ spl0_53 ),
inference(backward_demodulation,[],[f94,f1871]) ).
thf(f1871,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_4
| spl0_11
| ~ spl0_53 ),
inference(subsumption_resolution,[],[f1856,f1834]) ).
thf(f1834,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| spl0_11
| ~ spl0_53 ),
inference(forward_demodulation,[],[f89,f1103]) ).
thf(f1856,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_4
| ~ spl0_53 ),
inference(superposition,[],[f1826,f4]) ).
thf(f1762,plain,
( ~ spl0_12
| spl0_25
| ~ spl0_31
| ~ spl0_53
| ~ spl0_57 ),
inference(avatar_contradiction_clause,[],[f1761]) ).
thf(f1761,plain,
( $false
| ~ spl0_12
| spl0_25
| ~ spl0_31
| ~ spl0_53
| ~ spl0_57 ),
inference(subsumption_resolution,[],[f1760,f254]) ).
thf(f1760,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_12
| ~ spl0_31
| ~ spl0_53
| ~ spl0_57 ),
inference(backward_demodulation,[],[f1748,f94]) ).
thf(f1748,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true))) )
| ~ spl0_31
| ~ spl0_53
| ~ spl0_57 ),
inference(forward_demodulation,[],[f1747,f1667]) ).
thf(f1667,plain,
( ( $true = vAPP($o,$o,f2,$true) )
| ~ spl0_31
| ~ spl0_53 ),
inference(forward_demodulation,[],[f1103,f381]) ).
thf(f1747,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true)))) )
| ~ spl0_31
| ~ spl0_53
| ~ spl0_57 ),
inference(forward_demodulation,[],[f1746,f1667]) ).
thf(f1746,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_31
| ~ spl0_53
| ~ spl0_57 ),
inference(forward_demodulation,[],[f1745,f1667]) ).
thf(f1745,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_31
| ~ spl0_57 ),
inference(forward_demodulation,[],[f1196,f381]) ).
thf(f1732,plain,
( ~ spl0_31
| spl0_49
| ~ spl0_51
| ~ spl0_53 ),
inference(avatar_contradiction_clause,[],[f1731]) ).
thf(f1731,plain,
( $false
| ~ spl0_31
| spl0_49
| ~ spl0_51
| ~ spl0_53 ),
inference(subsumption_resolution,[],[f1690,f819]) ).
thf(f1690,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_31
| ~ spl0_51
| ~ spl0_53 ),
inference(forward_demodulation,[],[f1689,f1667]) ).
thf(f1689,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_31
| ~ spl0_51
| ~ spl0_53 ),
inference(forward_demodulation,[],[f1688,f1667]) ).
thf(f1688,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_31
| ~ spl0_51
| ~ spl0_53 ),
inference(forward_demodulation,[],[f979,f1667]) ).
thf(f979,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f977]) ).
thf(f977,plain,
( spl0_51
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
thf(f1698,plain,
( spl0_30
| ~ spl0_31
| ~ spl0_53
| ~ spl0_58 ),
inference(avatar_contradiction_clause,[],[f1697]) ).
thf(f1697,plain,
( $false
| spl0_30
| ~ spl0_31
| ~ spl0_53
| ~ spl0_58 ),
inference(subsumption_resolution,[],[f1696,f311]) ).
thf(f1696,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_31
| ~ spl0_53
| ~ spl0_58 ),
inference(forward_demodulation,[],[f1695,f1667]) ).
thf(f1695,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_31
| ~ spl0_53
| ~ spl0_58 ),
inference(forward_demodulation,[],[f1694,f1667]) ).
thf(f1694,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| ~ spl0_31
| ~ spl0_53
| ~ spl0_58 ),
inference(forward_demodulation,[],[f1693,f1667]) ).
thf(f1693,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| ~ spl0_31
| ~ spl0_58 ),
inference(forward_demodulation,[],[f1200,f381]) ).
thf(f1684,plain,
( ~ spl0_31
| ~ spl0_44
| spl0_52
| ~ spl0_53 ),
inference(avatar_contradiction_clause,[],[f1683]) ).
thf(f1683,plain,
( $false
| ~ spl0_31
| ~ spl0_44
| spl0_52
| ~ spl0_53 ),
inference(subsumption_resolution,[],[f1682,f984]) ).
thf(f984,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| spl0_52 ),
inference(avatar_component_clause,[],[f982]) ).
thf(f1682,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_31
| ~ spl0_44
| ~ spl0_53 ),
inference(forward_demodulation,[],[f1676,f1667]) ).
thf(f1676,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_31
| ~ spl0_44
| ~ spl0_53 ),
inference(backward_demodulation,[],[f1521,f1667]) ).
thf(f1521,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| ~ spl0_31
| ~ spl0_44 ),
inference(backward_demodulation,[],[f701,f381]) ).
thf(f701,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))) = $false )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f699]) ).
thf(f1639,plain,
( ~ spl0_31
| spl0_52
| spl0_53 ),
inference(avatar_contradiction_clause,[],[f1638]) ).
thf(f1638,plain,
( $false
| ~ spl0_31
| spl0_52
| spl0_53 ),
inference(trivial_inequality_removal,[],[f1604]) ).
thf(f1604,plain,
( ( $true = $false )
| ~ spl0_31
| spl0_52
| spl0_53 ),
inference(backward_demodulation,[],[f381,f1603]) ).
thf(f1603,plain,
( ! [X0: $o] : ( $false = X0 )
| ~ spl0_31
| spl0_52
| spl0_53 ),
inference(subsumption_resolution,[],[f1602,f1053]) ).
thf(f1053,plain,
( ! [X0: $o] :
( ( $false != vAPP($o,$o,f2,X0) )
| ( $false = X0 ) )
| spl0_52 ),
inference(superposition,[],[f984,f4]) ).
thf(f1602,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f2,X0) )
| ( $false = X0 ) )
| ~ spl0_31
| spl0_53 ),
inference(duplicate_literal_removal,[],[f1601]) ).
thf(f1601,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f2,X0) )
| ( $false = X0 )
| ( $false = X0 ) )
| ~ spl0_31
| spl0_53 ),
inference(binary_proxy_clausification,[],[f1595]) ).
thf(f1595,plain,
( ! [X0: $o] :
( ( vAPP($o,$o,f2,X0) != X0 )
| ( $false = X0 ) )
| ~ spl0_31
| spl0_53 ),
inference(superposition,[],[f1522,f4]) ).
thf(f1522,plain,
( ( $true != vAPP($o,$o,f2,$true) )
| ~ spl0_31
| spl0_53 ),
inference(backward_demodulation,[],[f1102,f381]) ).
thf(f1634,plain,
( ~ spl0_20
| ~ spl0_31
| spl0_52
| spl0_53 ),
inference(avatar_contradiction_clause,[],[f1633]) ).
thf(f1633,plain,
( $false
| ~ spl0_20
| ~ spl0_31
| spl0_52
| spl0_53 ),
inference(trivial_inequality_removal,[],[f1622]) ).
thf(f1622,plain,
( ( $true = $false )
| ~ spl0_20
| ~ spl0_31
| spl0_52
| spl0_53 ),
inference(backward_demodulation,[],[f228,f1603]) ).
thf(f1513,plain,
( spl0_5
| spl0_31 ),
inference(avatar_contradiction_clause,[],[f1512]) ).
thf(f1512,plain,
( $false
| spl0_5
| spl0_31 ),
inference(subsumption_resolution,[],[f1511,f62]) ).
thf(f62,plain,
( ( x != $false )
| spl0_5 ),
inference(avatar_component_clause,[],[f61]) ).
thf(f1511,plain,
( ( x = $false )
| spl0_31 ),
inference(trivial_inequality_removal,[],[f1510]) ).
thf(f1510,plain,
( ( $true != $true )
| ( x = $false )
| spl0_31 ),
inference(superposition,[],[f380,f4]) ).
thf(f380,plain,
( ( x != $true )
| spl0_31 ),
inference(avatar_component_clause,[],[f379]) ).
thf(f1499,plain,
( ~ spl0_40
| spl0_45
| ~ spl0_54 ),
inference(avatar_contradiction_clause,[],[f1498]) ).
thf(f1498,plain,
( $false
| ~ spl0_40
| spl0_45
| ~ spl0_54 ),
inference(subsumption_resolution,[],[f1497,f520]) ).
thf(f1497,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_45
| ~ spl0_54 ),
inference(forward_demodulation,[],[f744,f1122]) ).
thf(f1122,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f1120]) ).
thf(f1496,plain,
( ~ spl0_6
| ~ spl0_40
| ~ spl0_50
| ~ spl0_54 ),
inference(avatar_contradiction_clause,[],[f1495]) ).
thf(f1495,plain,
( $false
| ~ spl0_6
| ~ spl0_40
| ~ spl0_50
| ~ spl0_54 ),
inference(trivial_inequality_removal,[],[f1494]) ).
thf(f1494,plain,
( ( $true = $false )
| ~ spl0_6
| ~ spl0_40
| ~ spl0_50
| ~ spl0_54 ),
inference(forward_demodulation,[],[f1493,f520]) ).
thf(f1493,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_6
| ~ spl0_50
| ~ spl0_54 ),
inference(forward_demodulation,[],[f1487,f1122]) ).
thf(f1487,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_6
| ~ spl0_50
| ~ spl0_54 ),
inference(backward_demodulation,[],[f1418,f1122]) ).
thf(f1418,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_6
| ~ spl0_50 ),
inference(backward_demodulation,[],[f67,f974]) ).
thf(f67,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f65]) ).
thf(f65,plain,
( spl0_6
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f1483,plain,
( ~ spl0_54
| ~ spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f1462,f97,f88,f1120]) ).
thf(f1462,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_11
| spl0_13 ),
inference(backward_demodulation,[],[f98,f90]) ).
thf(f1482,plain,
( spl0_54
| ~ spl0_9
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f1470,f88,f79,f1120]) ).
thf(f79,plain,
( spl0_9
<=> ( vAPP($o,$o,f1,vAPP($o,$o,f2,x)) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f1470,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_9
| ~ spl0_11 ),
inference(backward_demodulation,[],[f90,f81]) ).
thf(f81,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f2,x)) = $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f79]) ).
thf(f1480,plain,
( spl0_47
| ~ spl0_2
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f1461,f88,f14,f756]) ).
thf(f756,plain,
( spl0_47
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
thf(f14,plain,
( spl0_2
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x))))) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f1461,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_2
| ~ spl0_11 ),
inference(backward_demodulation,[],[f16,f90]) ).
thf(f16,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x))))) = $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f14]) ).
thf(f1443,plain,
( spl0_46
| ~ spl0_44
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f1442,f1194,f699,f747]) ).
thf(f1442,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false))) )
| ~ spl0_44
| ~ spl0_57 ),
inference(forward_demodulation,[],[f1196,f701]) ).
thf(f1434,plain,
( ~ spl0_12
| ~ spl0_30
| ~ spl0_40 ),
inference(avatar_contradiction_clause,[],[f1433]) ).
thf(f1433,plain,
( $false
| ~ spl0_12
| ~ spl0_30
| ~ spl0_40 ),
inference(trivial_inequality_removal,[],[f1432]) ).
thf(f1432,plain,
( ( $true = $false )
| ~ spl0_12
| ~ spl0_30
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1431,f520]) ).
thf(f1431,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_12
| ~ spl0_30 ),
inference(forward_demodulation,[],[f94,f312]) ).
thf(f1423,plain,
( ~ spl0_30
| ~ spl0_40
| spl0_49 ),
inference(avatar_contradiction_clause,[],[f1422]) ).
thf(f1422,plain,
( $false
| ~ spl0_30
| ~ spl0_40
| spl0_49 ),
inference(subsumption_resolution,[],[f1421,f520]) ).
thf(f1421,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_30
| ~ spl0_40
| spl0_49 ),
inference(forward_demodulation,[],[f1420,f520]) ).
thf(f1420,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_30
| ~ spl0_40
| spl0_49 ),
inference(forward_demodulation,[],[f1419,f520]) ).
thf(f1419,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_30
| spl0_49 ),
inference(forward_demodulation,[],[f819,f312]) ).
thf(f1415,plain,
( spl0_47
| ~ spl0_10
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f1391,f310,f83,f756]) ).
thf(f83,plain,
( spl0_10
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f1391,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_10
| ~ spl0_30 ),
inference(backward_demodulation,[],[f85,f312]) ).
thf(f85,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f83]) ).
thf(f1355,plain,
( spl0_45
| ~ spl0_15
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f1354,f424,f199,f743]) ).
thf(f1354,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_15
| ~ spl0_38 ),
inference(forward_demodulation,[],[f426,f201]) ).
thf(f426,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f424]) ).
thf(f1352,plain,
( spl0_46
| ~ spl0_15
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f1351,f419,f199,f747]) ).
thf(f1351,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false))) )
| ~ spl0_15
| ~ spl0_37 ),
inference(forward_demodulation,[],[f421,f201]) ).
thf(f421,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f419]) ).
thf(f1350,plain,
( spl0_54
| ~ spl0_15
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f1349,f397,f199,f1120]) ).
thf(f397,plain,
( spl0_33
<=> ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
thf(f1349,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_15
| ~ spl0_33 ),
inference(backward_demodulation,[],[f399,f201]) ).
thf(f399,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f397]) ).
thf(f1340,plain,
( ~ spl0_7
| spl0_11
| ~ spl0_54 ),
inference(avatar_contradiction_clause,[],[f1339]) ).
thf(f1339,plain,
( $false
| ~ spl0_7
| spl0_11
| ~ spl0_54 ),
inference(subsumption_resolution,[],[f1326,f1122]) ).
thf(f1326,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_7
| spl0_11
| ~ spl0_54 ),
inference(backward_demodulation,[],[f1316,f1122]) ).
thf(f1316,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_7
| spl0_11 ),
inference(forward_demodulation,[],[f89,f72]) ).
thf(f1338,plain,
( ~ spl0_7
| spl0_13
| ~ spl0_54 ),
inference(avatar_contradiction_clause,[],[f1337]) ).
thf(f1337,plain,
( $false
| ~ spl0_7
| spl0_13
| ~ spl0_54 ),
inference(subsumption_resolution,[],[f1336,f1122]) ).
thf(f1336,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_7
| spl0_13
| ~ spl0_54 ),
inference(forward_demodulation,[],[f1325,f1122]) ).
thf(f1325,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_7
| spl0_13
| ~ spl0_54 ),
inference(backward_demodulation,[],[f1228,f1122]) ).
thf(f1228,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_7
| spl0_13 ),
inference(forward_demodulation,[],[f98,f72]) ).
thf(f1335,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_40
| ~ spl0_54 ),
inference(avatar_contradiction_clause,[],[f1334]) ).
thf(f1334,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_40
| ~ spl0_54 ),
inference(trivial_inequality_removal,[],[f1333]) ).
thf(f1333,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_40
| ~ spl0_54 ),
inference(forward_demodulation,[],[f1332,f520]) ).
thf(f1332,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_54 ),
inference(forward_demodulation,[],[f1331,f1122]) ).
thf(f1331,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_54 ),
inference(forward_demodulation,[],[f1324,f1122]) ).
thf(f1324,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_54 ),
inference(backward_demodulation,[],[f1220,f1122]) ).
thf(f1220,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_2
| ~ spl0_7 ),
inference(backward_demodulation,[],[f16,f72]) ).
thf(f1330,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_40
| ~ spl0_54 ),
inference(avatar_contradiction_clause,[],[f1329]) ).
thf(f1329,plain,
( $false
| spl0_4
| ~ spl0_7
| ~ spl0_40
| ~ spl0_54 ),
inference(subsumption_resolution,[],[f1328,f520]) ).
thf(f1328,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_4
| ~ spl0_7
| ~ spl0_54 ),
inference(forward_demodulation,[],[f1327,f1122]) ).
thf(f1327,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_4
| ~ spl0_7
| ~ spl0_54 ),
inference(forward_demodulation,[],[f1323,f1122]) ).
thf(f1323,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| spl0_4
| ~ spl0_7
| ~ spl0_54 ),
inference(backward_demodulation,[],[f1219,f1122]) ).
thf(f1219,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| spl0_4
| ~ spl0_7 ),
inference(backward_demodulation,[],[f24,f72]) ).
thf(f24,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x))))) != $false )
| spl0_4 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f1318,plain,
( spl0_54
| ~ spl0_7
| ~ spl0_29
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f1293,f1198,f306,f70,f1120]) ).
thf(f1293,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_7
| ~ spl0_29
| ~ spl0_58 ),
inference(forward_demodulation,[],[f1292,f308]) ).
thf(f1292,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_7
| ~ spl0_29
| ~ spl0_58 ),
inference(forward_demodulation,[],[f1291,f308]) ).
thf(f1291,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_7
| ~ spl0_58 ),
inference(forward_demodulation,[],[f1200,f72]) ).
thf(f1317,plain,
( spl0_54
| ~ spl0_29
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f1311,f397,f306,f1120]) ).
thf(f1311,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_29
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1310,f308]) ).
thf(f1310,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_29
| ~ spl0_33 ),
inference(forward_demodulation,[],[f399,f308]) ).
thf(f1300,plain,
( spl0_40
| ~ spl0_7
| ~ spl0_29
| ~ spl0_45
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f1299,f1194,f743,f306,f70,f518]) ).
thf(f1299,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_7
| ~ spl0_29
| ~ spl0_45
| ~ spl0_57 ),
inference(forward_demodulation,[],[f1298,f745]) ).
thf(f1298,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false))) )
| ~ spl0_7
| ~ spl0_29
| ~ spl0_57 ),
inference(forward_demodulation,[],[f1297,f308]) ).
thf(f1297,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) )
| ~ spl0_7
| ~ spl0_29
| ~ spl0_57 ),
inference(forward_demodulation,[],[f1296,f308]) ).
thf(f1296,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_7
| ~ spl0_57 ),
inference(forward_demodulation,[],[f1196,f72]) ).
thf(f1248,plain,
( ~ spl0_12
| ~ spl0_14
| spl0_25
| ~ spl0_49 ),
inference(avatar_contradiction_clause,[],[f1247]) ).
thf(f1247,plain,
( $false
| ~ spl0_12
| ~ spl0_14
| spl0_25
| ~ spl0_49 ),
inference(subsumption_resolution,[],[f1246,f254]) ).
thf(f1246,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_12
| ~ spl0_14
| ~ spl0_49 ),
inference(forward_demodulation,[],[f1245,f103]) ).
thf(f1245,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_12
| ~ spl0_49 ),
inference(backward_demodulation,[],[f820,f94]) ).
thf(f820,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f818]) ).
thf(f1216,plain,
( spl0_57
| ~ spl0_3
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f1215,f101,f19,f1194]) ).
thf(f1215,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))))) = $false )
| ~ spl0_3
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f1214]) ).
thf(f1214,plain,
( ( $true = $false )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))))) = $false )
| ~ spl0_3
| ~ spl0_14 ),
inference(forward_demodulation,[],[f615,f103]) ).
thf(f615,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))))) = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f21,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))))) = $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f1213,plain,
( spl0_58
| ~ spl0_3
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f1212,f101,f19,f1198]) ).
thf(f1212,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))) = $false )
| ~ spl0_3
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f1211]) ).
thf(f1211,plain,
( ( $true = $false )
| ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))) = $false )
| ~ spl0_3
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1210,f103]) ).
thf(f1210,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))) = $false )
| ~ spl0_3
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1209,f103]) ).
thf(f1209,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))) = $false )
| ~ spl0_3
| ~ spl0_14 ),
inference(forward_demodulation,[],[f609,f103]) ).
thf(f609,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))) = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f1208,plain,
( spl0_25
| ~ spl0_14
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f1207,f238,f101,f253]) ).
thf(f238,plain,
( spl0_22
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
thf(f1207,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1206,f103]) ).
thf(f1206,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_demodulation,[],[f240,f103]) ).
thf(f240,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f238]) ).
thf(f1203,plain,
( spl0_25
| ~ spl0_3
| spl0_18
| spl0_40 ),
inference(avatar_split_clause,[],[f1127,f518,f214,f19,f253]) ).
thf(f214,plain,
( spl0_18
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
thf(f1127,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_3
| spl0_18
| spl0_40 ),
inference(forward_demodulation,[],[f822,f826]) ).
thf(f826,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_3
| spl0_18
| spl0_40 ),
inference(forward_demodulation,[],[f825,f711]) ).
thf(f711,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))) = $false )
| ~ spl0_3
| spl0_18 ),
inference(subsumption_resolution,[],[f612,f215]) ).
thf(f215,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| spl0_18 ),
inference(avatar_component_clause,[],[f214]) ).
thf(f612,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))) = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f825,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))))) = $true )
| ~ spl0_3
| spl0_18
| spl0_40 ),
inference(trivial_inequality_removal,[],[f824]) ).
thf(f824,plain,
( ( $true = $false )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))))) = $true )
| ~ spl0_3
| spl0_18
| spl0_40 ),
inference(forward_demodulation,[],[f649,f711]) ).
thf(f649,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))) = $true )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))))) = $true )
| ~ spl0_3
| spl0_40 ),
inference(subsumption_resolution,[],[f624,f519]) ).
thf(f519,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_40 ),
inference(avatar_component_clause,[],[f518]) ).
thf(f624,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))) = $true )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))))) = $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f614]) ).
thf(f614,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))) != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))))) )
| ~ spl0_3 ),
inference(constrained_superposition,[],[f21,f21]) ).
thf(f822,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_3
| spl0_18 ),
inference(backward_demodulation,[],[f21,f711]) ).
thf(f1179,plain,
( ~ spl0_7
| ~ spl0_31
| spl0_52 ),
inference(avatar_contradiction_clause,[],[f1178]) ).
thf(f1178,plain,
( $false
| ~ spl0_7
| ~ spl0_31
| spl0_52 ),
inference(subsumption_resolution,[],[f1177,f984]) ).
thf(f1177,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_7
| ~ spl0_31 ),
inference(forward_demodulation,[],[f72,f381]) ).
thf(f1165,plain,
( ~ spl0_14
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f1164]) ).
thf(f1164,plain,
( $false
| ~ spl0_14
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f1163]) ).
thf(f1163,plain,
( ( $true = $false )
| ~ spl0_14
| ~ spl0_25 ),
inference(forward_demodulation,[],[f103,f255]) ).
thf(f1150,plain,
( spl0_45
| ~ spl0_29
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f1149,f424,f306,f743]) ).
thf(f1149,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_29
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1148,f308]) ).
thf(f1148,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_29
| ~ spl0_38 ),
inference(forward_demodulation,[],[f426,f308]) ).
thf(f1147,plain,
( ~ spl0_29
| ~ spl0_43
| spl0_44 ),
inference(avatar_contradiction_clause,[],[f1146]) ).
thf(f1146,plain,
( $false
| ~ spl0_29
| ~ spl0_43
| spl0_44 ),
inference(subsumption_resolution,[],[f1145,f308]) ).
thf(f1145,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_43
| spl0_44 ),
inference(forward_demodulation,[],[f700,f633]) ).
thf(f1144,plain,
( ~ spl0_3
| spl0_18
| ~ spl0_25
| ~ spl0_30
| spl0_40
| ~ spl0_49 ),
inference(avatar_contradiction_clause,[],[f1143]) ).
thf(f1143,plain,
( $false
| ~ spl0_3
| spl0_18
| ~ spl0_25
| ~ spl0_30
| spl0_40
| ~ spl0_49 ),
inference(subsumption_resolution,[],[f1142,f519]) ).
thf(f1142,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_3
| spl0_18
| ~ spl0_25
| ~ spl0_30
| spl0_40
| ~ spl0_49 ),
inference(forward_demodulation,[],[f1141,f255]) ).
thf(f1141,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_3
| spl0_18
| ~ spl0_30
| spl0_40
| ~ spl0_49 ),
inference(forward_demodulation,[],[f1140,f826]) ).
thf(f1140,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_30
| ~ spl0_49 ),
inference(forward_demodulation,[],[f820,f312]) ).
thf(f1137,plain,
( spl0_45
| ~ spl0_3
| spl0_18
| ~ spl0_29
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f1136,f631,f306,f214,f19,f743]) ).
thf(f1136,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_3
| spl0_18
| ~ spl0_29
| ~ spl0_43 ),
inference(forward_demodulation,[],[f1135,f308]) ).
thf(f1135,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_3
| spl0_18
| ~ spl0_43 ),
inference(forward_demodulation,[],[f711,f633]) ).
thf(f1112,plain,
( spl0_5
| spl0_7
| ~ spl0_43 ),
inference(avatar_contradiction_clause,[],[f1111]) ).
thf(f1111,plain,
( $false
| spl0_5
| spl0_7
| ~ spl0_43 ),
inference(subsumption_resolution,[],[f1110,f71]) ).
thf(f71,plain,
( ( vAPP($o,$o,f2,x) != $false )
| spl0_7 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f1110,plain,
( ( vAPP($o,$o,f2,x) = $false )
| spl0_5
| spl0_7
| ~ spl0_43 ),
inference(subsumption_resolution,[],[f1079,f62]) ).
thf(f1079,plain,
( ( x = $false )
| ( vAPP($o,$o,f2,x) = $false )
| spl0_7
| ~ spl0_43 ),
inference(binary_proxy_clausification,[],[f1077]) ).
thf(f1077,plain,
( ( x != vAPP($o,$o,f2,x) )
| spl0_7
| ~ spl0_43 ),
inference(trivial_inequality_removal,[],[f1074]) ).
thf(f1074,plain,
( ( $false != $false )
| ( x != vAPP($o,$o,f2,x) )
| spl0_7
| ~ spl0_43 ),
inference(constrained_superposition,[],[f71,f633]) ).
thf(f1033,plain,
( ~ spl0_29
| ~ spl0_5
| spl0_7 ),
inference(avatar_split_clause,[],[f989,f70,f61,f306]) ).
thf(f989,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_5
| spl0_7 ),
inference(backward_demodulation,[],[f71,f63]) ).
thf(f1032,plain,
( spl0_29
| spl0_20 ),
inference(avatar_split_clause,[],[f1029,f226,f306]) ).
thf(f1029,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| spl0_20 ),
inference(trivial_inequality_removal,[],[f1028]) ).
thf(f1028,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f2,$false) )
| spl0_20 ),
inference(superposition,[],[f227,f4]) ).
thf(f227,plain,
( ( $true != vAPP($o,$o,f2,$false) )
| spl0_20 ),
inference(avatar_component_clause,[],[f226]) ).
thf(f1024,plain,
( ~ spl0_52
| ~ spl0_5
| ~ spl0_20
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f1017,f699,f226,f61,f982]) ).
thf(f1017,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| ~ spl0_5
| ~ spl0_20
| ~ spl0_44 ),
inference(trivial_inequality_removal,[],[f1014]) ).
thf(f1014,plain,
( ( $true = $false )
| ( $false != vAPP($o,$o,f2,$true) )
| ~ spl0_5
| ~ spl0_20
| ~ spl0_44 ),
inference(constrained_superposition,[],[f228,f993]) ).
thf(f993,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_5
| ~ spl0_20
| ~ spl0_44 ),
inference(forward_demodulation,[],[f991,f228]) ).
thf(f991,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_5
| ~ spl0_44 ),
inference(backward_demodulation,[],[f701,f63]) ).
thf(f1022,plain,
( spl0_52
| ~ spl0_5
| ~ spl0_20
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f1020,f699,f226,f61,f982]) ).
thf(f1020,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_5
| ~ spl0_20
| ~ spl0_44 ),
inference(duplicate_literal_removal,[],[f1011]) ).
thf(f1011,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_5
| ~ spl0_20
| ~ spl0_44 ),
inference(superposition,[],[f993,f4]) ).
thf(f985,plain,
( spl0_5
| ~ spl0_52
| spl0_7 ),
inference(avatar_split_clause,[],[f598,f70,f982,f61]) ).
thf(f598,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| ( x = $false )
| spl0_7 ),
inference(superposition,[],[f71,f4]) ).
thf(f980,plain,
( spl0_5
| spl0_51
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f605,f19,f977,f61]) ).
thf(f605,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ( x = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f975,plain,
( spl0_5
| spl0_50
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f956,f79,f972,f61]) ).
thf(f956,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ( x = $false )
| ~ spl0_9 ),
inference(superposition,[],[f81,f4]) ).
thf(f969,plain,
( ~ spl0_2
| spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_25
| spl0_40 ),
inference(avatar_contradiction_clause,[],[f968]) ).
thf(f968,plain,
( $false
| ~ spl0_2
| spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_25
| spl0_40 ),
inference(subsumption_resolution,[],[f967,f519]) ).
thf(f967,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_2
| spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_25 ),
inference(forward_demodulation,[],[f966,f255]) ).
thf(f966,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_2
| spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f964,f584]) ).
thf(f584,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_2
| ~ spl0_13 ),
inference(forward_demodulation,[],[f16,f99]) ).
thf(f99,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x)))) = $false )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f97]) ).
thf(f964,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_5
| ~ spl0_9
| ~ spl0_16 ),
inference(backward_demodulation,[],[f205,f963]) ).
thf(f963,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| spl0_5
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f956,f62]) ).
thf(f924,plain,
( ~ spl0_45
| ~ spl0_47 ),
inference(avatar_contradiction_clause,[],[f923]) ).
thf(f923,plain,
( $false
| ~ spl0_45
| ~ spl0_47 ),
inference(trivial_inequality_removal,[],[f922]) ).
thf(f922,plain,
( ( $true = $false )
| ~ spl0_45
| ~ spl0_47 ),
inference(backward_demodulation,[],[f758,f745]) ).
thf(f758,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f756]) ).
thf(f921,plain,
( ~ spl0_25
| spl0_46
| ~ spl0_47 ),
inference(avatar_contradiction_clause,[],[f920]) ).
thf(f920,plain,
( $false
| ~ spl0_25
| spl0_46
| ~ spl0_47 ),
inference(subsumption_resolution,[],[f919,f255]) ).
thf(f919,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| spl0_46
| ~ spl0_47 ),
inference(forward_demodulation,[],[f748,f758]) ).
thf(f832,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_13
| ~ spl0_25
| spl0_40
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f831]) ).
thf(f831,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_13
| ~ spl0_25
| spl0_40
| ~ spl0_42 ),
inference(subsumption_resolution,[],[f830,f519]) ).
thf(f830,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_13
| ~ spl0_25
| ~ spl0_42 ),
inference(forward_demodulation,[],[f829,f255]) ).
thf(f829,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_13
| ~ spl0_42 ),
inference(forward_demodulation,[],[f828,f584]) ).
thf(f828,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_11
| ~ spl0_13
| ~ spl0_42 ),
inference(forward_demodulation,[],[f532,f811]) ).
thf(f811,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_11
| ~ spl0_13 ),
inference(backward_demodulation,[],[f99,f90]) ).
thf(f532,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f530]) ).
thf(f821,plain,
( spl0_44
| spl0_49
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f608,f19,f818,f699]) ).
thf(f608,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))) = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f813,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_11
| ~ spl0_13
| spl0_18
| ~ spl0_44 ),
inference(avatar_contradiction_clause,[],[f812]) ).
thf(f812,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_11
| ~ spl0_13
| spl0_18
| ~ spl0_44 ),
inference(subsumption_resolution,[],[f811,f766]) ).
thf(f766,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_13
| spl0_18
| ~ spl0_44 ),
inference(forward_demodulation,[],[f708,f701]) ).
thf(f708,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))) != $false )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_13
| spl0_18 ),
inference(subsumption_resolution,[],[f610,f215]) ).
thf(f610,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))) != $false )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_13 ),
inference(constrained_superposition,[],[f21,f584]) ).
thf(f810,plain,
( ~ spl0_12
| ~ spl0_25
| spl0_30 ),
inference(avatar_contradiction_clause,[],[f809]) ).
thf(f809,plain,
( $false
| ~ spl0_12
| ~ spl0_25
| spl0_30 ),
inference(trivial_inequality_removal,[],[f808]) ).
thf(f808,plain,
( ( $true = $false )
| ~ spl0_12
| ~ spl0_25
| spl0_30 ),
inference(forward_demodulation,[],[f807,f255]) ).
thf(f807,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_12
| spl0_30 ),
inference(subsumption_resolution,[],[f798,f311]) ).
thf(f798,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_12 ),
inference(superposition,[],[f94,f4]) ).
thf(f789,plain,
( ~ spl0_30
| spl0_7
| spl0_9 ),
inference(avatar_split_clause,[],[f788,f79,f70,f310]) ).
thf(f788,plain,
( ( $false != vAPP($o,$o,f1,$true) )
| spl0_7
| spl0_9 ),
inference(subsumption_resolution,[],[f785,f71]) ).
thf(f785,plain,
( ( $false != vAPP($o,$o,f1,$true) )
| ( vAPP($o,$o,f2,x) = $false )
| spl0_9 ),
inference(superposition,[],[f80,f4]) ).
thf(f80,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f2,x)) != $false )
| spl0_9 ),
inference(avatar_component_clause,[],[f79]) ).
thf(f752,plain,
( ~ spl0_46
| ~ spl0_2
| ~ spl0_3
| ~ spl0_13
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f751,f699,f97,f19,f14,f747]) ).
thf(f751,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false))) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_13
| ~ spl0_44 ),
inference(forward_demodulation,[],[f621,f701]) ).
thf(f621,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))))) != $false )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f618]) ).
thf(f618,plain,
( ( $true = $false )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))))) != $false )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_13 ),
inference(constrained_superposition,[],[f584,f21]) ).
thf(f702,plain,
( spl0_44
| spl0_18
| ~ spl0_3
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f635,f92,f19,f214,f699]) ).
thf(f635,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))) = $false )
| ~ spl0_3
| ~ spl0_12 ),
inference(forward_demodulation,[],[f608,f94]) ).
thf(f671,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_13
| spl0_25 ),
inference(avatar_contradiction_clause,[],[f670]) ).
thf(f670,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_13
| spl0_25 ),
inference(subsumption_resolution,[],[f656,f621]) ).
thf(f656,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))))) = $false )
| ~ spl0_3
| spl0_25 ),
inference(subsumption_resolution,[],[f615,f254]) ).
thf(f655,plain,
( ~ spl0_3
| ~ spl0_18
| spl0_25
| spl0_40 ),
inference(avatar_contradiction_clause,[],[f654]) ).
thf(f654,plain,
( $false
| ~ spl0_3
| ~ spl0_18
| spl0_25
| spl0_40 ),
inference(subsumption_resolution,[],[f653,f519]) ).
thf(f653,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_3
| ~ spl0_18
| spl0_25
| spl0_40 ),
inference(forward_demodulation,[],[f652,f637]) ).
thf(f637,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))) = $false )
| ~ spl0_3
| ~ spl0_18
| spl0_40 ),
inference(subsumption_resolution,[],[f636,f519]) ).
thf(f636,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))) = $false )
| ~ spl0_3
| ~ spl0_18 ),
inference(forward_demodulation,[],[f609,f216]) ).
thf(f216,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f214]) ).
thf(f652,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))) = $false )
| ~ spl0_3
| spl0_25
| spl0_40 ),
inference(subsumption_resolution,[],[f651,f601]) ).
thf(f601,plain,
( ! [X0: $o] :
( ( $false != vAPP($o,$o,f0,X0) )
| ( $false = X0 ) )
| spl0_25 ),
inference(superposition,[],[f254,f4]) ).
thf(f651,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))) = $false )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))))) = $false )
| ~ spl0_3
| spl0_40 ),
inference(subsumption_resolution,[],[f625,f519]) ).
thf(f625,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))) = $false )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x)))))) = $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f614]) ).
thf(f592,plain,
( ~ spl0_40
| spl0_4
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f588,f97,f23,f518]) ).
thf(f588,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_4
| ~ spl0_13 ),
inference(forward_demodulation,[],[f24,f99]) ).
thf(f587,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_40 ),
inference(avatar_contradiction_clause,[],[f586]) ).
thf(f586,plain,
( $false
| ~ spl0_2
| ~ spl0_13
| ~ spl0_40 ),
inference(trivial_inequality_removal,[],[f585]) ).
thf(f585,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_13
| ~ spl0_40 ),
inference(forward_demodulation,[],[f584,f520]) ).
thf(f582,plain,
( spl0_40
| ~ spl0_4
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f581,f97,f23,f518]) ).
thf(f581,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_13 ),
inference(backward_demodulation,[],[f25,f99]) ).
thf(f580,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f579]) ).
thf(f579,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f578]) ).
thf(f578,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f16,f25]) ).
thf(f577,plain,
( ~ spl0_42
| spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f576,f226,f70,f61,f19,f530]) ).
thf(f576,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_demodulation,[],[f575,f344]) ).
thf(f344,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| spl0_5
| ~ spl0_7 ),
inference(subsumption_resolution,[],[f341,f62]) ).
thf(f341,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ( x = $false )
| ~ spl0_7 ),
inference(superposition,[],[f72,f4]) ).
thf(f575,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_3
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_demodulation,[],[f574,f228]) ).
thf(f574,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_3
| ~ spl0_7 ),
inference(forward_demodulation,[],[f20,f72]) ).
thf(f567,plain,
( spl0_40
| ~ spl0_18
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f566,f238,f214,f518]) ).
thf(f566,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_demodulation,[],[f240,f216]) ).
thf(f563,plain,
( ~ spl0_20
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[],[f562]) ).
thf(f562,plain,
( $false
| ~ spl0_20
| ~ spl0_29 ),
inference(trivial_inequality_removal,[],[f561]) ).
thf(f561,plain,
( ( $true = $false )
| ~ spl0_20
| ~ spl0_29 ),
inference(forward_demodulation,[],[f228,f308]) ).
thf(f560,plain,
( spl0_42
| ~ spl0_3
| ~ spl0_7
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f559,f306,f70,f19,f530]) ).
thf(f559,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_29 ),
inference(forward_demodulation,[],[f558,f308]) ).
thf(f558,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_29 ),
inference(backward_demodulation,[],[f459,f308]) ).
thf(f459,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_demodulation,[],[f21,f72]) ).
thf(f549,plain,
( ~ spl0_7
| spl0_9
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f548]) ).
thf(f548,plain,
( $false
| ~ spl0_7
| spl0_9
| ~ spl0_11
| ~ spl0_13 ),
inference(subsumption_resolution,[],[f547,f538]) ).
thf(f538,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_7
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f324,f336]) ).
thf(f336,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f90,f72]) ).
thf(f324,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_7
| ~ spl0_13 ),
inference(forward_demodulation,[],[f99,f72]) ).
thf(f547,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_7
| spl0_9 ),
inference(forward_demodulation,[],[f80,f72]) ).
thf(f546,plain,
( spl0_40
| ~ spl0_18
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f545,f253,f214,f518]) ).
thf(f545,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_18
| ~ spl0_25 ),
inference(forward_demodulation,[],[f216,f255]) ).
thf(f535,plain,
( spl0_29
| spl0_42
| ~ spl0_3
| spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f488,f70,f61,f19,f530,f306]) ).
thf(f488,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_3
| spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f464,f344]) ).
thf(f464,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f459,f4]) ).
thf(f513,plain,
( spl0_37
| spl0_25
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f473,f70,f19,f253,f419]) ).
thf(f473,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f459,f4]) ).
thf(f507,plain,
( spl0_38
| spl0_18
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f470,f70,f19,f214,f424]) ).
thf(f470,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f459,f4]) ).
thf(f501,plain,
( spl0_33
| spl0_22
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f467,f70,f19,f238,f397]) ).
thf(f467,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f459,f4]) ).
thf(f498,plain,
( spl0_29
| spl0_18
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f497,f79,f70,f61,f19,f14,f214,f306]) ).
thf(f497,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f496,f450]) ).
thf(f450,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f449,f330]) ).
thf(f330,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f81,f72]) ).
thf(f449,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f448,f330]) ).
thf(f448,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f447,f330]) ).
thf(f447,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[],[f16,f72]) ).
thf(f496,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f495,f330]) ).
thf(f495,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_3
| spl0_5
| ~ spl0_7 ),
inference(subsumption_resolution,[],[f487,f62]) ).
thf(f487,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ( x = $false )
| ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_3
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f465]) ).
thf(f465,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ( x != vAPP($o,$o,f2,$false) )
| ~ spl0_3
| ~ spl0_7 ),
inference(constrained_superposition,[],[f459,f72]) ).
thf(f437,plain,
( spl0_37
| spl0_14
| ~ spl0_1
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f355,f70,f10,f101,f419]) ).
thf(f355,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f322,f4]) ).
thf(f322,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_1
| ~ spl0_7 ),
inference(backward_demodulation,[],[f12,f72]) ).
thf(f430,plain,
( ~ spl0_38
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f429,f97,f70,f23,f10,f424]) ).
thf(f429,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f428]) ).
thf(f428,plain,
( ( $true = $false )
| ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13 ),
inference(forward_demodulation,[],[f353,f328]) ).
thf(f328,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13 ),
inference(forward_demodulation,[],[f327,f324]) ).
thf(f327,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f25,f72]) ).
thf(f353,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13 ),
inference(constrained_superposition,[],[f322,f328]) ).
thf(f427,plain,
( spl0_38
| spl0_32
| ~ spl0_1
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f352,f70,f10,f392,f424]) ).
thf(f352,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f322,f4]) ).
thf(f404,plain,
( spl0_33
| spl0_34
| ~ spl0_1
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f349,f70,f10,f401,f397]) ).
thf(f349,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f322,f4]) ).
thf(f315,plain,
( spl0_29
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f314,f70,f61,f306]) ).
thf(f314,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f72,f63]) ).
thf(f241,plain,
( spl0_21
| spl0_22
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f178,f61,f19,f238,f234]) ).
thf(f178,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f158,f4]) ).
thf(f158,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f21,f63]) ).
thf(f107,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f106]) ).
thf(f106,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f105]) ).
thf(f105,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[],[f12,f21]) ).
thf(f104,plain,
( spl0_13
| spl0_14
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f59,f14,f101,f97]) ).
thf(f59,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x)))) = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f95,plain,
( spl0_11
| spl0_12
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f58,f14,f92,f88]) ).
thf(f58,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x))) = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f86,plain,
( spl0_9
| spl0_10
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f57,f14,f83,f79]) ).
thf(f57,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f2,x)) = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f68,plain,
( spl0_5
| spl0_6
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f55,f14,f65,f61]) ).
thf(f55,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ( x = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f26,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f8,f23,f19]) ).
thf(f8,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x))))) = $false )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))))) = $false ) ),
inference(binary_proxy_clausification,[],[f6]) ).
thf(f6,plain,
vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x))))) != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))))),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x))))) != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))))),
inference(flattening,[],[f2]) ).
thf(f2,negated_conjecture,
vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x))))) != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))))),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x))))) = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kaminski3) ).
thf(f17,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f7,f14,f10]) ).
thf(f7,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,x))))) = $true )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,x))))))) = $true ) ),
inference(binary_proxy_clausification,[],[f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO500^1.003 : TPTP v8.2.0. Released v4.1.0.
% 0.10/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon May 20 08:39:07 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % (28164)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.35 % (28167)WARNING: value z3 for option sas not known
% 0.12/0.35 % (28167)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)
% 0.12/0.35 % (28168)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.35 % (28171)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)
% 0.12/0.35 % (28166)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.35 % (28169)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)
% 0.12/0.35 % (28170)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)
% 0.12/0.35 % (28171)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.35 % Exception at run slice level% Exception at run slice level
% 0.12/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.35
% 0.12/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.35 % (28165)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.35 % Exception at run slice level
% 0.12/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.36 % (28172)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.12/0.36 % (28172)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.36 % (28173)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)
% 0.12/0.36 % Exception at run slice level
% 0.12/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.36 % (28173)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.37 % (28174)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)
% 0.12/0.38 % (28175)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)
% 0.17/0.44 % (28174)First to succeed.
% 0.17/0.44 % (28174)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-28164"
% 0.17/0.45 % (28174)Refutation found. Thanks to Tanya!
% 0.17/0.45 % SZS status Theorem for theBenchmark
% 0.17/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.45 % (28174)------------------------------
% 0.17/0.45 % (28174)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.17/0.45 % (28174)Termination reason: Refutation
% 0.17/0.45
% 0.17/0.45 % (28174)Memory used [KB]: 1588
% 0.17/0.45 % (28174)Time elapsed: 0.080 s
% 0.17/0.45 % (28174)Instructions burned: 193 (million)
% 0.17/0.45 % (28164)Success in time 0.114 s
%------------------------------------------------------------------------------