TSTP Solution File: SEU998^5 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU998^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n020.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 04:07:10 EDT 2024
% Result : Theorem 0.11s 0.40s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 134
% Syntax : Number of formulae : 427 ( 82 unt; 17 typ; 0 def)
% Number of atoms : 3552 ( 700 equ; 0 cnn)
% Maximal formula atoms : 78 ( 8 avg)
% Number of connectives : 1525 ( 573 ~; 438 |; 394 &; 0 @)
% ( 112 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 50 ( 49 >; 1 *; 0 +; 0 <<)
% Number of symbols : 131 ( 128 usr; 119 con; 0-6 aty)
% Number of variables : 497 ( 0 ^ 438 !; 53 ?; 497 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > a > a ).
thf(func_def_5,type,
sK1: a > a > a ).
thf(func_def_6,type,
sK2: a ).
thf(func_def_7,type,
sK3: a ).
thf(func_def_8,type,
sK4: a ).
thf(func_def_9,type,
sK5: a ).
thf(func_def_10,type,
sK6: a ).
thf(func_def_12,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_13,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_14,type,
vAND: $o > $o > $o ).
thf(func_def_15,type,
vOR: $o > $o > $o ).
thf(func_def_16,type,
vIMP: $o > $o > $o ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(func_def_18,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f3017,plain,
$false,
inference(avatar_sat_refutation,[],[f55,f60,f65,f70,f75,f80,f85,f90,f95,f100,f105,f109,f113,f118,f123,f128,f133,f138,f143,f148,f153,f158,f163,f168,f173,f178,f183,f188,f193,f198,f203,f208,f213,f217,f221,f225,f229,f293,f325,f329,f334,f386,f447,f452,f457,f462,f467,f472,f477,f514,f518,f522,f526,f646,f650,f654,f658,f662,f667,f671,f675,f679,f683,f687,f691,f695,f699,f703,f707,f712,f716,f720,f724,f728,f732,f736,f740,f744,f748,f786,f959,f1212,f1317,f1321,f1325,f1330,f1334,f1338,f1342,f1348,f1352,f1356,f1361,f1365,f1369,f1373,f1377,f1381,f1385,f1389,f1403,f1407,f1411,f1415,f1419,f1423,f1427,f1431,f1435,f1439,f1453,f1457,f3016]) ).
thf(f3016,plain,
( spl7_4
| ~ spl7_34
| ~ spl7_35
| ~ spl7_42
| ~ spl7_45
| ~ spl7_50
| ~ spl7_52
| ~ spl7_54
| ~ spl7_63
| ~ spl7_73
| ~ spl7_97
| ~ spl7_98
| ~ spl7_99
| ~ spl7_101 ),
inference(avatar_split_clause,[],[f2780,f1401,f1383,f1379,f1375,f722,f681,f644,f520,f512,f454,f384,f219,f215,f67]) ).
thf(f67,plain,
( spl7_4
<=> ( sK3 = sK4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).
thf(f215,plain,
( spl7_34
<=> ! [X16: a,X17: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X16),X17) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X17),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_34])]) ).
thf(f219,plain,
( spl7_35
<=> ! [X14: a,X15: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X14),X15) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X15),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_35])]) ).
thf(f384,plain,
( spl7_42
<=> ! [X4: a,X2: a,X3: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X3),X4)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X2),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X2),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_42])]) ).
thf(f454,plain,
( spl7_45
<=> ( sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_45])]) ).
thf(f512,plain,
( spl7_50
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),X0)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_50])]) ).
thf(f520,plain,
( spl7_52
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),X0)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_52])]) ).
thf(f644,plain,
( spl7_54
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_54])]) ).
thf(f681,plain,
( spl7_63
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_63])]) ).
thf(f722,plain,
( spl7_73
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_73])]) ).
thf(f1375,plain,
( spl7_97
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_97])]) ).
thf(f1379,plain,
( spl7_98
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_98])]) ).
thf(f1383,plain,
( spl7_99
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_99])]) ).
thf(f1401,plain,
( spl7_101
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_101])]) ).
thf(f2780,plain,
( ( sK3 = sK4 )
| ~ spl7_34
| ~ spl7_35
| ~ spl7_42
| ~ spl7_45
| ~ spl7_50
| ~ spl7_52
| ~ spl7_54
| ~ spl7_63
| ~ spl7_73
| ~ spl7_97
| ~ spl7_98
| ~ spl7_99
| ~ spl7_101 ),
inference(forward_demodulation,[],[f2779,f2648]) ).
thf(f2648,plain,
( ! [X0: a] : ( sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) )
| ~ spl7_34
| ~ spl7_42
| ~ spl7_45
| ~ spl7_50
| ~ spl7_54
| ~ spl7_63
| ~ spl7_97
| ~ spl7_98
| ~ spl7_99 ),
inference(forward_demodulation,[],[f2623,f2529]) ).
thf(f2529,plain,
( ! [X0: a] : ( sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) )
| ~ spl7_34
| ~ spl7_42
| ~ spl7_45
| ~ spl7_50
| ~ spl7_54
| ~ spl7_63
| ~ spl7_97
| ~ spl7_98 ),
inference(forward_demodulation,[],[f2528,f545]) ).
thf(f545,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1)) = X0 )
| ~ spl7_34
| ~ spl7_50 ),
inference(superposition,[],[f513,f216]) ).
thf(f216,plain,
( ! [X16: a,X17: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X16),X17) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X17),X16) )
| ~ spl7_34 ),
inference(avatar_component_clause,[],[f215]) ).
thf(f513,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),X0)),X1) = X1 )
| ~ spl7_50 ),
inference(avatar_component_clause,[],[f512]) ).
thf(f2528,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) )
| ~ spl7_42
| ~ spl7_45
| ~ spl7_54
| ~ spl7_63
| ~ spl7_97
| ~ spl7_98 ),
inference(forward_demodulation,[],[f2527,f485]) ).
thf(f485,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) )
| ~ spl7_42
| ~ spl7_45 ),
inference(superposition,[],[f385,f456]) ).
thf(f456,plain,
( ( sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK2) )
| ~ spl7_45 ),
inference(avatar_component_clause,[],[f454]) ).
thf(f385,plain,
( ! [X2: a,X3: a,X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X3),X4)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X2),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X2),X4)) )
| ~ spl7_42 ),
inference(avatar_component_clause,[],[f384]) ).
thf(f2527,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0)) )
| ~ spl7_54
| ~ spl7_63
| ~ spl7_97
| ~ spl7_98 ),
inference(forward_demodulation,[],[f2526,f645]) ).
thf(f645,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1)) )
| ~ spl7_54 ),
inference(avatar_component_clause,[],[f644]) ).
thf(f2526,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0))) )
| ~ spl7_63
| ~ spl7_97
| ~ spl7_98 ),
inference(forward_demodulation,[],[f2498,f1380]) ).
thf(f1380,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0)) )
| ~ spl7_98 ),
inference(avatar_component_clause,[],[f1379]) ).
thf(f2498,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0))) )
| ~ spl7_63
| ~ spl7_97 ),
inference(superposition,[],[f1376,f682]) ).
thf(f682,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0)) )
| ~ spl7_63 ),
inference(avatar_component_clause,[],[f681]) ).
thf(f1376,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) )
| ~ spl7_97 ),
inference(avatar_component_clause,[],[f1375]) ).
thf(f2623,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0))) )
| ~ spl7_54
| ~ spl7_99 ),
inference(superposition,[],[f1384,f645]) ).
thf(f1384,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) )
| ~ spl7_99 ),
inference(avatar_component_clause,[],[f1383]) ).
thf(f2779,plain,
( ! [X0: a] : ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0))) )
| ~ spl7_35
| ~ spl7_52
| ~ spl7_73
| ~ spl7_101 ),
inference(forward_demodulation,[],[f2751,f598]) ).
thf(f598,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1)) = X0 )
| ~ spl7_35
| ~ spl7_52 ),
inference(superposition,[],[f521,f220]) ).
thf(f220,plain,
( ! [X14: a,X15: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X14),X15) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X15),X14) )
| ~ spl7_35 ),
inference(avatar_component_clause,[],[f219]) ).
thf(f521,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),X0)),X1) = X1 )
| ~ spl7_52 ),
inference(avatar_component_clause,[],[f520]) ).
thf(f2751,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0))) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) )
| ~ spl7_73
| ~ spl7_101 ),
inference(superposition,[],[f723,f1402]) ).
thf(f1402,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) )
| ~ spl7_101 ),
inference(avatar_component_clause,[],[f1401]) ).
thf(f723,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)) )
| ~ spl7_73 ),
inference(avatar_component_clause,[],[f722]) ).
thf(f1457,plain,
( spl7_112
| ~ spl7_32
| ~ spl7_34
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f442,f384,f215,f205,f1455]) ).
thf(f1455,plain,
( spl7_112
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_112])]) ).
thf(f205,plain,
( spl7_32
<=> ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_32])]) ).
thf(f442,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK3)) )
| ~ spl7_32
| ~ spl7_34
| ~ spl7_42 ),
inference(forward_demodulation,[],[f416,f216]) ).
thf(f416,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK3)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),X0)),sK3) )
| ~ spl7_32
| ~ spl7_42 ),
inference(superposition,[],[f385,f207]) ).
thf(f207,plain,
( ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),sK3) )
| ~ spl7_32 ),
inference(avatar_component_clause,[],[f205]) ).
thf(f1453,plain,
( spl7_111
| ~ spl7_30
| ~ spl7_34
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f441,f384,f215,f195,f1451]) ).
thf(f1451,plain,
( spl7_111
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_111])]) ).
thf(f195,plain,
( spl7_30
<=> ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_30])]) ).
thf(f441,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK3)) )
| ~ spl7_30
| ~ spl7_34
| ~ spl7_42 ),
inference(forward_demodulation,[],[f415,f216]) ).
thf(f415,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)),sK3) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK3)) )
| ~ spl7_30
| ~ spl7_42 ),
inference(superposition,[],[f385,f197]) ).
thf(f197,plain,
( ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),sK3) )
| ~ spl7_30 ),
inference(avatar_component_clause,[],[f195]) ).
thf(f1439,plain,
( spl7_110
| ~ spl7_28
| ~ spl7_34
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f440,f384,f215,f185,f1437]) ).
thf(f1437,plain,
( spl7_110
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_110])]) ).
thf(f185,plain,
( spl7_28
<=> ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_28])]) ).
thf(f440,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK6)) )
| ~ spl7_28
| ~ spl7_34
| ~ spl7_42 ),
inference(forward_demodulation,[],[f414,f216]) ).
thf(f414,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)),sK3) )
| ~ spl7_28
| ~ spl7_42 ),
inference(superposition,[],[f385,f187]) ).
thf(f187,plain,
( ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),sK6) )
| ~ spl7_28 ),
inference(avatar_component_clause,[],[f185]) ).
thf(f1435,plain,
( spl7_109
| ~ spl7_26
| ~ spl7_34
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f439,f384,f215,f175,f1433]) ).
thf(f1433,plain,
( spl7_109
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_109])]) ).
thf(f175,plain,
( spl7_26
<=> ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_26])]) ).
thf(f439,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK3)) )
| ~ spl7_26
| ~ spl7_34
| ~ spl7_42 ),
inference(forward_demodulation,[],[f413,f216]) ).
thf(f413,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)),sK3) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK3)) )
| ~ spl7_26
| ~ spl7_42 ),
inference(superposition,[],[f385,f177]) ).
thf(f177,plain,
( ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK3) )
| ~ spl7_26 ),
inference(avatar_component_clause,[],[f175]) ).
thf(f1431,plain,
( spl7_108
| ~ spl7_24
| ~ spl7_34
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f438,f384,f215,f165,f1429]) ).
thf(f1429,plain,
( spl7_108
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_108])]) ).
thf(f165,plain,
( spl7_24
<=> ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_24])]) ).
thf(f438,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK6)) )
| ~ spl7_24
| ~ spl7_34
| ~ spl7_42 ),
inference(forward_demodulation,[],[f412,f216]) ).
thf(f412,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)),sK3) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK6)) )
| ~ spl7_24
| ~ spl7_42 ),
inference(superposition,[],[f385,f167]) ).
thf(f167,plain,
( ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK6) )
| ~ spl7_24 ),
inference(avatar_component_clause,[],[f165]) ).
thf(f1427,plain,
( spl7_107
| ~ spl7_22
| ~ spl7_34
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f437,f384,f215,f155,f1425]) ).
thf(f1425,plain,
( spl7_107
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_107])]) ).
thf(f155,plain,
( spl7_22
<=> ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_22])]) ).
thf(f437,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK5)) )
| ~ spl7_22
| ~ spl7_34
| ~ spl7_42 ),
inference(forward_demodulation,[],[f411,f216]) ).
thf(f411,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK5)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)),sK3) )
| ~ spl7_22
| ~ spl7_42 ),
inference(superposition,[],[f385,f157]) ).
thf(f157,plain,
( ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK5) )
| ~ spl7_22 ),
inference(avatar_component_clause,[],[f155]) ).
thf(f1423,plain,
( spl7_106
| ~ spl7_20
| ~ spl7_34
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f436,f384,f215,f145,f1421]) ).
thf(f1421,plain,
( spl7_106
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_106])]) ).
thf(f145,plain,
( spl7_20
<=> ( sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_20])]) ).
thf(f436,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK6)) )
| ~ spl7_20
| ~ spl7_34
| ~ spl7_42 ),
inference(forward_demodulation,[],[f410,f216]) ).
thf(f410,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)),sK6) )
| ~ spl7_20
| ~ spl7_42 ),
inference(superposition,[],[f385,f147]) ).
thf(f147,plain,
( ( sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK6) )
| ~ spl7_20 ),
inference(avatar_component_clause,[],[f145]) ).
thf(f1419,plain,
( spl7_105
| ~ spl7_18
| ~ spl7_34
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f435,f384,f215,f135,f1417]) ).
thf(f1417,plain,
( spl7_105
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_105])]) ).
thf(f135,plain,
( spl7_18
<=> ( sK5 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_18])]) ).
thf(f435,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK5)) )
| ~ spl7_18
| ~ spl7_34
| ~ spl7_42 ),
inference(forward_demodulation,[],[f409,f216]) ).
thf(f409,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK5)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)),sK5) )
| ~ spl7_18
| ~ spl7_42 ),
inference(superposition,[],[f385,f137]) ).
thf(f137,plain,
( ( sK5 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK5) )
| ~ spl7_18 ),
inference(avatar_component_clause,[],[f135]) ).
thf(f1415,plain,
( spl7_104
| ~ spl7_16
| ~ spl7_34
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f434,f384,f215,f125,f1413]) ).
thf(f1413,plain,
( spl7_104
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_104])]) ).
thf(f125,plain,
( spl7_16
<=> ( sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_16])]) ).
thf(f434,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK4)) )
| ~ spl7_16
| ~ spl7_34
| ~ spl7_42 ),
inference(forward_demodulation,[],[f408,f216]) ).
thf(f408,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK4)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)),sK4) )
| ~ spl7_16
| ~ spl7_42 ),
inference(superposition,[],[f385,f127]) ).
thf(f127,plain,
( ( sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK4) )
| ~ spl7_16 ),
inference(avatar_component_clause,[],[f125]) ).
thf(f1411,plain,
( spl7_103
| ~ spl7_14
| ~ spl7_34
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f433,f384,f215,f115,f1409]) ).
thf(f1409,plain,
( spl7_103
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_103])]) ).
thf(f115,plain,
( spl7_14
<=> ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_14])]) ).
thf(f433,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK3)) )
| ~ spl7_14
| ~ spl7_34
| ~ spl7_42 ),
inference(forward_demodulation,[],[f407,f216]) ).
thf(f407,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),sK3)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)),sK3) )
| ~ spl7_14
| ~ spl7_42 ),
inference(superposition,[],[f385,f117]) ).
thf(f117,plain,
( ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK3) )
| ~ spl7_14 ),
inference(avatar_component_clause,[],[f115]) ).
thf(f1407,plain,
( spl7_102
| ~ spl7_32
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f401,f384,f205,f1405]) ).
thf(f1405,plain,
( spl7_102
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_102])]) ).
thf(f401,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),X0)) )
| ~ spl7_32
| ~ spl7_42 ),
inference(superposition,[],[f385,f207]) ).
thf(f1403,plain,
( spl7_101
| ~ spl7_30
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f400,f384,f195,f1401]) ).
thf(f400,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) )
| ~ spl7_30
| ~ spl7_42 ),
inference(superposition,[],[f385,f197]) ).
thf(f1389,plain,
( spl7_100
| ~ spl7_28
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f399,f384,f185,f1387]) ).
thf(f1387,plain,
( spl7_100
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_100])]) ).
thf(f399,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)) )
| ~ spl7_28
| ~ spl7_42 ),
inference(superposition,[],[f385,f187]) ).
thf(f1385,plain,
( spl7_99
| ~ spl7_26
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f398,f384,f175,f1383]) ).
thf(f398,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) )
| ~ spl7_26
| ~ spl7_42 ),
inference(superposition,[],[f385,f177]) ).
thf(f1381,plain,
( spl7_98
| ~ spl7_24
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f397,f384,f165,f1379]) ).
thf(f397,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0)) )
| ~ spl7_24
| ~ spl7_42 ),
inference(superposition,[],[f385,f167]) ).
thf(f1377,plain,
( spl7_97
| ~ spl7_22
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f396,f384,f155,f1375]) ).
thf(f396,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) )
| ~ spl7_22
| ~ spl7_42 ),
inference(superposition,[],[f385,f157]) ).
thf(f1373,plain,
( spl7_96
| ~ spl7_20
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f395,f384,f145,f1371]) ).
thf(f1371,plain,
( spl7_96
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_96])]) ).
thf(f395,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)) )
| ~ spl7_20
| ~ spl7_42 ),
inference(superposition,[],[f385,f147]) ).
thf(f1369,plain,
( spl7_95
| ~ spl7_18
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f394,f384,f135,f1367]) ).
thf(f1367,plain,
( spl7_95
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_95])]) ).
thf(f394,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)) )
| ~ spl7_18
| ~ spl7_42 ),
inference(superposition,[],[f385,f137]) ).
thf(f1365,plain,
( spl7_94
| ~ spl7_16
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f393,f384,f125,f1363]) ).
thf(f1363,plain,
( spl7_94
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_94])]) ).
thf(f393,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)) )
| ~ spl7_16
| ~ spl7_42 ),
inference(superposition,[],[f385,f127]) ).
thf(f1361,plain,
( spl7_93
| ~ spl7_14
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f392,f384,f115,f1359]) ).
thf(f1359,plain,
( spl7_93
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_93])]) ).
thf(f392,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),X0)) )
| ~ spl7_14
| ~ spl7_42 ),
inference(superposition,[],[f385,f117]) ).
thf(f1356,plain,
( spl7_92
| ~ spl7_13
| ~ spl7_42 ),
inference(avatar_split_clause,[],[f387,f384,f111,f1354]) ).
thf(f1354,plain,
( spl7_92
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_92])]) ).
thf(f111,plain,
( spl7_13
<=> ! [X24: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X24),X24) = X24 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_13])]) ).
thf(f387,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1)) )
| ~ spl7_13
| ~ spl7_42 ),
inference(superposition,[],[f385,f112]) ).
thf(f112,plain,
( ! [X24: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X24),X24) = X24 )
| ~ spl7_13 ),
inference(avatar_component_clause,[],[f111]) ).
thf(f1352,plain,
( spl7_91
| ~ spl7_35
| ~ spl7_40 ),
inference(avatar_split_clause,[],[f375,f327,f219,f1350]) ).
thf(f1350,plain,
( spl7_91
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X2),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_91])]) ).
thf(f327,plain,
( spl7_40
<=> ! [X20: a,X18: a,X19: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X18),X19)),X20) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X18),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X19),X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_40])]) ).
thf(f375,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X2),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1)) )
| ~ spl7_35
| ~ spl7_40 ),
inference(superposition,[],[f328,f220]) ).
thf(f328,plain,
( ! [X18: a,X19: a,X20: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X18),X19)),X20) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X18),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X19),X20)) )
| ~ spl7_40 ),
inference(avatar_component_clause,[],[f327]) ).
thf(f1348,plain,
( spl7_90
| ~ spl7_33
| ~ spl7_53 ),
inference(avatar_split_clause,[],[f630,f524,f210,f1345]) ).
thf(f1345,plain,
( spl7_90
<=> ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_90])]) ).
thf(f210,plain,
( spl7_33
<=> ( sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_33])]) ).
thf(f524,plain,
( spl7_53
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_53])]) ).
thf(f630,plain,
( ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),sK6) )
| ~ spl7_33
| ~ spl7_53 ),
inference(superposition,[],[f525,f212]) ).
thf(f212,plain,
( ( sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),sK3) )
| ~ spl7_33 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f525,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1)) = X1 )
| ~ spl7_53 ),
inference(avatar_component_clause,[],[f524]) ).
thf(f1342,plain,
( spl7_89
| ~ spl7_13
| ~ spl7_40 ),
inference(avatar_split_clause,[],[f374,f327,f111,f1340]) ).
thf(f1340,plain,
( spl7_89
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_89])]) ).
thf(f374,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1))) )
| ~ spl7_13
| ~ spl7_40 ),
inference(superposition,[],[f328,f112]) ).
thf(f1338,plain,
( spl7_88
| ~ spl7_37
| ~ spl7_40 ),
inference(avatar_split_clause,[],[f362,f327,f227,f1336]) ).
thf(f1336,plain,
( spl7_88
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_88])]) ).
thf(f227,plain,
( spl7_37
<=> ! [X11: a,X10: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X10),X11)),X11) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_37])]) ).
thf(f362,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),X2)) )
| ~ spl7_37
| ~ spl7_40 ),
inference(superposition,[],[f328,f228]) ).
thf(f228,plain,
( ! [X10: a,X11: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X10),X11)),X11) = X11 )
| ~ spl7_37 ),
inference(avatar_component_clause,[],[f227]) ).
thf(f1334,plain,
( spl7_87
| ~ spl7_35
| ~ spl7_40 ),
inference(avatar_split_clause,[],[f360,f327,f219,f1332]) ).
thf(f1332,plain,
( spl7_87
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_87])]) ).
thf(f360,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),X0)),X2) )
| ~ spl7_35
| ~ spl7_40 ),
inference(superposition,[],[f328,f220]) ).
thf(f1330,plain,
( spl7_86
| ~ spl7_34
| ~ spl7_39 ),
inference(avatar_split_clause,[],[f351,f323,f215,f1328]) ).
thf(f1328,plain,
( spl7_86
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_86])]) ).
thf(f323,plain,
( spl7_39
<=> ! [X22: a,X21: a,X23: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X21),X22)),X23) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X21),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X22),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_39])]) ).
thf(f351,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1)) )
| ~ spl7_34
| ~ spl7_39 ),
inference(superposition,[],[f324,f216]) ).
thf(f324,plain,
( ! [X21: a,X22: a,X23: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X21),X22)),X23) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X21),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X22),X23)) )
| ~ spl7_39 ),
inference(avatar_component_clause,[],[f323]) ).
thf(f1325,plain,
( spl7_85
| ~ spl7_12
| ~ spl7_39 ),
inference(avatar_split_clause,[],[f350,f323,f107,f1323]) ).
thf(f1323,plain,
( spl7_85
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_85])]) ).
thf(f107,plain,
( spl7_12
<=> ! [X25: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X25),X25) = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_12])]) ).
thf(f350,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1))) )
| ~ spl7_12
| ~ spl7_39 ),
inference(superposition,[],[f324,f108]) ).
thf(f108,plain,
( ! [X25: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X25),X25) = X25 )
| ~ spl7_12 ),
inference(avatar_component_clause,[],[f107]) ).
thf(f1321,plain,
( spl7_84
| ~ spl7_36
| ~ spl7_39 ),
inference(avatar_split_clause,[],[f338,f323,f223,f1319]) ).
thf(f1319,plain,
( spl7_84
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_84])]) ).
thf(f223,plain,
( spl7_36
<=> ! [X13: a,X12: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X12),X13)),X13) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_36])]) ).
thf(f338,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),X2)) )
| ~ spl7_36
| ~ spl7_39 ),
inference(superposition,[],[f324,f224]) ).
thf(f224,plain,
( ! [X12: a,X13: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X12),X13)),X13) = X13 )
| ~ spl7_36 ),
inference(avatar_component_clause,[],[f223]) ).
thf(f1317,plain,
( spl7_83
| ~ spl7_34
| ~ spl7_39 ),
inference(avatar_split_clause,[],[f336,f323,f215,f1315]) ).
thf(f1315,plain,
( spl7_83
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_83])]) ).
thf(f336,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),X0)),X2) )
| ~ spl7_34
| ~ spl7_39 ),
inference(superposition,[],[f324,f216]) ).
thf(f1212,plain,
( spl7_82
| ~ spl7_31
| ~ spl7_53 ),
inference(avatar_split_clause,[],[f628,f524,f200,f1209]) ).
thf(f1209,plain,
( spl7_82
<=> ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_82])]) ).
thf(f200,plain,
( spl7_31
<=> ( sK5 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_31])]) ).
thf(f628,plain,
( ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),sK5) )
| ~ spl7_31
| ~ spl7_53 ),
inference(superposition,[],[f525,f202]) ).
thf(f202,plain,
( ( sK5 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),sK3) )
| ~ spl7_31 ),
inference(avatar_component_clause,[],[f200]) ).
thf(f959,plain,
( spl7_81
| ~ spl7_27
| ~ spl7_53 ),
inference(avatar_split_clause,[],[f624,f524,f180,f956]) ).
thf(f956,plain,
( spl7_81
<=> ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_81])]) ).
thf(f180,plain,
( spl7_27
<=> ( sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_27])]) ).
thf(f624,plain,
( ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),sK4) )
| ~ spl7_27
| ~ spl7_53 ),
inference(superposition,[],[f525,f182]) ).
thf(f182,plain,
( ( sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK3) )
| ~ spl7_27 ),
inference(avatar_component_clause,[],[f180]) ).
thf(f786,plain,
( spl7_80
| ~ spl7_15
| ~ spl7_53 ),
inference(avatar_split_clause,[],[f617,f524,f120,f783]) ).
thf(f783,plain,
( spl7_80
<=> ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_80])]) ).
thf(f120,plain,
( spl7_15
<=> ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_15])]) ).
thf(f617,plain,
( ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),sK2) )
| ~ spl7_15
| ~ spl7_53 ),
inference(superposition,[],[f525,f122]) ).
thf(f122,plain,
( ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK3) )
| ~ spl7_15 ),
inference(avatar_component_clause,[],[f120]) ).
thf(f748,plain,
( spl7_79
| ~ spl7_36
| ~ spl7_40 ),
inference(avatar_split_clause,[],[f378,f327,f223,f746]) ).
thf(f746,plain,
( spl7_79
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),X2))),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_79])]) ).
thf(f378,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),X2))),X2) = X2 )
| ~ spl7_36
| ~ spl7_40 ),
inference(superposition,[],[f224,f328]) ).
thf(f744,plain,
( spl7_78
| ~ spl7_32
| ~ spl7_40 ),
inference(avatar_split_clause,[],[f373,f327,f205,f742]) ).
thf(f742,plain,
( spl7_78
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_78])]) ).
thf(f373,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0)) )
| ~ spl7_32
| ~ spl7_40 ),
inference(superposition,[],[f328,f207]) ).
thf(f740,plain,
( spl7_77
| ~ spl7_30
| ~ spl7_40 ),
inference(avatar_split_clause,[],[f372,f327,f195,f738]) ).
thf(f738,plain,
( spl7_77
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_77])]) ).
thf(f372,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0)) )
| ~ spl7_30
| ~ spl7_40 ),
inference(superposition,[],[f328,f197]) ).
thf(f736,plain,
( spl7_76
| ~ spl7_28
| ~ spl7_40 ),
inference(avatar_split_clause,[],[f371,f327,f185,f734]) ).
thf(f734,plain,
( spl7_76
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_76])]) ).
thf(f371,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),X0)) )
| ~ spl7_28
| ~ spl7_40 ),
inference(superposition,[],[f328,f187]) ).
thf(f732,plain,
( spl7_75
| ~ spl7_26
| ~ spl7_40 ),
inference(avatar_split_clause,[],[f370,f327,f175,f730]) ).
thf(f730,plain,
( spl7_75
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_75])]) ).
thf(f370,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0)) )
| ~ spl7_26
| ~ spl7_40 ),
inference(superposition,[],[f328,f177]) ).
thf(f728,plain,
( spl7_74
| ~ spl7_24
| ~ spl7_40 ),
inference(avatar_split_clause,[],[f369,f327,f165,f726]) ).
thf(f726,plain,
( spl7_74
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_74])]) ).
thf(f369,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),X0)) )
| ~ spl7_24
| ~ spl7_40 ),
inference(superposition,[],[f328,f167]) ).
thf(f724,plain,
( spl7_73
| ~ spl7_22
| ~ spl7_40 ),
inference(avatar_split_clause,[],[f368,f327,f155,f722]) ).
thf(f368,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)) )
| ~ spl7_22
| ~ spl7_40 ),
inference(superposition,[],[f328,f157]) ).
thf(f720,plain,
( spl7_72
| ~ spl7_20
| ~ spl7_40 ),
inference(avatar_split_clause,[],[f367,f327,f145,f718]) ).
thf(f718,plain,
( spl7_72
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_72])]) ).
thf(f367,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),X0)) )
| ~ spl7_20
| ~ spl7_40 ),
inference(superposition,[],[f328,f147]) ).
thf(f716,plain,
( spl7_71
| ~ spl7_18
| ~ spl7_40 ),
inference(avatar_split_clause,[],[f366,f327,f135,f714]) ).
thf(f714,plain,
( spl7_71
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_71])]) ).
thf(f366,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),X0)) )
| ~ spl7_18
| ~ spl7_40 ),
inference(superposition,[],[f328,f137]) ).
thf(f712,plain,
( spl7_70
| ~ spl7_26
| ~ spl7_50 ),
inference(avatar_split_clause,[],[f537,f512,f175,f709]) ).
thf(f709,plain,
( spl7_70
<=> ( sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_70])]) ).
thf(f537,plain,
( ( sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),sK4) )
| ~ spl7_26
| ~ spl7_50 ),
inference(superposition,[],[f513,f177]) ).
thf(f707,plain,
( spl7_69
| ~ spl7_16
| ~ spl7_40 ),
inference(avatar_split_clause,[],[f365,f327,f125,f705]) ).
thf(f705,plain,
( spl7_69
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_69])]) ).
thf(f365,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),X0)) )
| ~ spl7_16
| ~ spl7_40 ),
inference(superposition,[],[f328,f127]) ).
thf(f703,plain,
( spl7_68
| ~ spl7_14
| ~ spl7_40 ),
inference(avatar_split_clause,[],[f364,f327,f115,f701]) ).
thf(f701,plain,
( spl7_68
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_68])]) ).
thf(f364,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK3),X0)) )
| ~ spl7_14
| ~ spl7_40 ),
inference(superposition,[],[f328,f117]) ).
thf(f699,plain,
( spl7_67
| ~ spl7_13
| ~ spl7_40 ),
inference(avatar_split_clause,[],[f359,f327,f111,f697]) ).
thf(f697,plain,
( spl7_67
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_67])]) ).
thf(f359,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1)) )
| ~ spl7_13
| ~ spl7_40 ),
inference(superposition,[],[f328,f112]) ).
thf(f695,plain,
( spl7_66
| ~ spl7_37
| ~ spl7_39 ),
inference(avatar_split_clause,[],[f354,f323,f227,f693]) ).
thf(f693,plain,
( spl7_66
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),X2))),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_66])]) ).
thf(f354,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),X2))),X2) = X2 )
| ~ spl7_37
| ~ spl7_39 ),
inference(superposition,[],[f228,f324]) ).
thf(f691,plain,
( spl7_65
| ~ spl7_33
| ~ spl7_39 ),
inference(avatar_split_clause,[],[f349,f323,f210,f689]) ).
thf(f689,plain,
( spl7_65
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_65])]) ).
thf(f349,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) )
| ~ spl7_33
| ~ spl7_39 ),
inference(superposition,[],[f324,f212]) ).
thf(f687,plain,
( spl7_64
| ~ spl7_31
| ~ spl7_39 ),
inference(avatar_split_clause,[],[f348,f323,f200,f685]) ).
thf(f685,plain,
( spl7_64
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_64])]) ).
thf(f348,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) )
| ~ spl7_31
| ~ spl7_39 ),
inference(superposition,[],[f324,f202]) ).
thf(f683,plain,
( spl7_63
| ~ spl7_29
| ~ spl7_39 ),
inference(avatar_split_clause,[],[f347,f323,f190,f681]) ).
thf(f190,plain,
( spl7_29
<=> ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_29])]) ).
thf(f347,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0)) )
| ~ spl7_29
| ~ spl7_39 ),
inference(superposition,[],[f324,f192]) ).
thf(f192,plain,
( ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),sK6) )
| ~ spl7_29 ),
inference(avatar_component_clause,[],[f190]) ).
thf(f679,plain,
( spl7_62
| ~ spl7_27
| ~ spl7_39 ),
inference(avatar_split_clause,[],[f346,f323,f180,f677]) ).
thf(f677,plain,
( spl7_62
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_62])]) ).
thf(f346,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) )
| ~ spl7_27
| ~ spl7_39 ),
inference(superposition,[],[f324,f182]) ).
thf(f675,plain,
( spl7_61
| ~ spl7_25
| ~ spl7_39 ),
inference(avatar_split_clause,[],[f345,f323,f170,f673]) ).
thf(f673,plain,
( spl7_61
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_61])]) ).
thf(f170,plain,
( spl7_25
<=> ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_25])]) ).
thf(f345,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0)) )
| ~ spl7_25
| ~ spl7_39 ),
inference(superposition,[],[f324,f172]) ).
thf(f172,plain,
( ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK6) )
| ~ spl7_25 ),
inference(avatar_component_clause,[],[f170]) ).
thf(f671,plain,
( spl7_60
| ~ spl7_23
| ~ spl7_39 ),
inference(avatar_split_clause,[],[f344,f323,f160,f669]) ).
thf(f669,plain,
( spl7_60
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_60])]) ).
thf(f160,plain,
( spl7_23
<=> ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_23])]) ).
thf(f344,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),X0)) )
| ~ spl7_23
| ~ spl7_39 ),
inference(superposition,[],[f324,f162]) ).
thf(f162,plain,
( ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK5) )
| ~ spl7_23 ),
inference(avatar_component_clause,[],[f160]) ).
thf(f667,plain,
( spl7_59
| ~ spl7_14
| ~ spl7_50 ),
inference(avatar_split_clause,[],[f532,f512,f115,f664]) ).
thf(f664,plain,
( spl7_59
<=> ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_59])]) ).
thf(f532,plain,
( ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),sK2) )
| ~ spl7_14
| ~ spl7_50 ),
inference(superposition,[],[f513,f117]) ).
thf(f662,plain,
( spl7_58
| ~ spl7_21
| ~ spl7_39 ),
inference(avatar_split_clause,[],[f343,f323,f150,f660]) ).
thf(f660,plain,
( spl7_58
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_58])]) ).
thf(f150,plain,
( spl7_21
<=> ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_21])]) ).
thf(f343,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),X0)) )
| ~ spl7_21
| ~ spl7_39 ),
inference(superposition,[],[f324,f152]) ).
thf(f152,plain,
( ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK6) )
| ~ spl7_21 ),
inference(avatar_component_clause,[],[f150]) ).
thf(f658,plain,
( spl7_57
| ~ spl7_19
| ~ spl7_39 ),
inference(avatar_split_clause,[],[f342,f323,f140,f656]) ).
thf(f656,plain,
( spl7_57
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_57])]) ).
thf(f140,plain,
( spl7_19
<=> ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_19])]) ).
thf(f342,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),X0)) )
| ~ spl7_19
| ~ spl7_39 ),
inference(superposition,[],[f324,f142]) ).
thf(f142,plain,
( ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK5) )
| ~ spl7_19 ),
inference(avatar_component_clause,[],[f140]) ).
thf(f654,plain,
( spl7_56
| ~ spl7_17
| ~ spl7_39 ),
inference(avatar_split_clause,[],[f341,f323,f130,f652]) ).
thf(f652,plain,
( spl7_56
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_56])]) ).
thf(f130,plain,
( spl7_17
<=> ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_17])]) ).
thf(f341,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),X0)) )
| ~ spl7_17
| ~ spl7_39 ),
inference(superposition,[],[f324,f132]) ).
thf(f132,plain,
( ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK4) )
| ~ spl7_17 ),
inference(avatar_component_clause,[],[f130]) ).
thf(f650,plain,
( spl7_55
| ~ spl7_15
| ~ spl7_39 ),
inference(avatar_split_clause,[],[f340,f323,f120,f648]) ).
thf(f648,plain,
( spl7_55
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_55])]) ).
thf(f340,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),X0) )
| ~ spl7_15
| ~ spl7_39 ),
inference(superposition,[],[f324,f122]) ).
thf(f646,plain,
( spl7_54
| ~ spl7_12
| ~ spl7_39 ),
inference(avatar_split_clause,[],[f335,f323,f107,f644]) ).
thf(f335,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1)) )
| ~ spl7_12
| ~ spl7_39 ),
inference(superposition,[],[f324,f108]) ).
thf(f526,plain,
( spl7_53
| ~ spl7_35
| ~ spl7_37 ),
inference(avatar_split_clause,[],[f285,f227,f219,f524]) ).
thf(f285,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X0),X1)) = X1 )
| ~ spl7_35
| ~ spl7_37 ),
inference(superposition,[],[f228,f220]) ).
thf(f522,plain,
( spl7_52
| ~ spl7_34
| ~ spl7_37 ),
inference(avatar_split_clause,[],[f272,f227,f215,f520]) ).
thf(f272,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),X0)),X1) = X1 )
| ~ spl7_34
| ~ spl7_37 ),
inference(superposition,[],[f228,f216]) ).
thf(f518,plain,
( spl7_51
| ~ spl7_34
| ~ spl7_36 ),
inference(avatar_split_clause,[],[f267,f223,f215,f516]) ).
thf(f516,plain,
( spl7_51
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_51])]) ).
thf(f267,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X1),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X0),X1)) = X1 )
| ~ spl7_34
| ~ spl7_36 ),
inference(superposition,[],[f224,f216]) ).
thf(f514,plain,
( spl7_50
| ~ spl7_35
| ~ spl7_36 ),
inference(avatar_split_clause,[],[f255,f223,f219,f512]) ).
thf(f255,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X1),X0)),X1) = X1 )
| ~ spl7_35
| ~ spl7_36 ),
inference(superposition,[],[f224,f220]) ).
thf(f477,plain,
( spl7_49
| ~ spl7_24
| ~ spl7_36 ),
inference(avatar_split_clause,[],[f262,f223,f165,f474]) ).
thf(f474,plain,
( spl7_49
<=> ( sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_49])]) ).
thf(f262,plain,
( ( sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),sK6) )
| ~ spl7_24
| ~ spl7_36 ),
inference(superposition,[],[f224,f167]) ).
thf(f472,plain,
( spl7_48
| ~ spl7_22
| ~ spl7_36 ),
inference(avatar_split_clause,[],[f261,f223,f155,f469]) ).
thf(f469,plain,
( spl7_48
<=> ( sK5 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_48])]) ).
thf(f261,plain,
( ( sK5 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK3),sK5) )
| ~ spl7_22
| ~ spl7_36 ),
inference(superposition,[],[f224,f157]) ).
thf(f467,plain,
( spl7_47
| ~ spl7_20
| ~ spl7_35 ),
inference(avatar_split_clause,[],[f244,f219,f145,f464]) ).
thf(f464,plain,
( spl7_47
<=> ( sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_47])]) ).
thf(f244,plain,
( ( sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),sK2) )
| ~ spl7_20
| ~ spl7_35 ),
inference(superposition,[],[f220,f147]) ).
thf(f462,plain,
( spl7_46
| ~ spl7_18
| ~ spl7_35 ),
inference(avatar_split_clause,[],[f243,f219,f135,f459]) ).
thf(f459,plain,
( spl7_46
<=> ( sK5 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_46])]) ).
thf(f243,plain,
( ( sK5 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),sK2) )
| ~ spl7_18
| ~ spl7_35 ),
inference(superposition,[],[f220,f137]) ).
thf(f457,plain,
( spl7_45
| ~ spl7_16
| ~ spl7_35 ),
inference(avatar_split_clause,[],[f242,f219,f125,f454]) ).
thf(f242,plain,
( ( sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK2) )
| ~ spl7_16
| ~ spl7_35 ),
inference(superposition,[],[f220,f127]) ).
thf(f452,plain,
( spl7_44
| ~ spl7_21
| ~ spl7_34 ),
inference(avatar_split_clause,[],[f232,f215,f150,f449]) ).
thf(f449,plain,
( spl7_44
<=> ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_44])]) ).
thf(f232,plain,
( ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),sK2) )
| ~ spl7_21
| ~ spl7_34 ),
inference(superposition,[],[f216,f152]) ).
thf(f447,plain,
( spl7_43
| ~ spl7_19
| ~ spl7_34 ),
inference(avatar_split_clause,[],[f231,f215,f140,f444]) ).
thf(f444,plain,
( spl7_43
<=> ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_43])]) ).
thf(f231,plain,
( ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),sK2) )
| ~ spl7_19
| ~ spl7_34 ),
inference(superposition,[],[f216,f142]) ).
thf(f386,plain,
spl7_42,
inference(avatar_split_clause,[],[f50,f384]) ).
thf(f50,plain,
! [X2: a,X3: a,X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X3),X4)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X2),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X2),X4)) ),
inference(cnf_transformation,[],[f11]) ).
thf(f11,plain,
( ! [X2: a,X3: a,X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X3),X4)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X2),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X2),X4)) )
& ( sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),sK3) )
& ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),sK3) )
& ( sK5 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),sK3) )
& ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),sK3) )
& ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),sK6) )
& ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),sK6) )
& ( sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK3) )
& ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK3) )
& ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK6) )
& ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK6) )
& ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK5) )
& ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK5) )
& ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK6) )
& ( sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK6) )
& ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK5) )
& ( sK5 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK5) )
& ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK4) )
& ( sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK4) )
& ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK3) )
& ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK3) )
& ( sK2 != sK3 )
& ( sK3 != sK6 )
& ( sK2 != sK6 )
& ( sK3 != sK5 )
& ( sK2 != sK5 )
& ( sK5 != sK6 )
& ( sK3 != sK4 )
& ( sK2 != sK4 )
& ( sK4 != sK6 )
& ( sK4 != sK5 )
& ! [X10: a,X11: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X10),X11)),X11) = X11 )
& ! [X12: a,X13: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X12),X13)),X13) = X13 )
& ! [X14: a,X15: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X14),X15) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X15),X14) )
& ! [X16: a,X17: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X16),X17) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X17),X16) )
& ! [X18: a,X19: a,X20: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X18),X19)),X20) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X18),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X19),X20)) )
& ! [X21: a,X22: a,X23: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X21),X22)),X23) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X21),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X22),X23)) )
& ! [X24: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X24),X24) = X24 )
& ! [X25: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X25),X25) = X25 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > a > a,X1: a > a > a] :
( ! [X2: a,X3: a,X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X3),X4)) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X4)) )
& ? [X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X9),X6) = X9 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X9),X6) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X8),X6) = X8 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X8),X6) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X8),X9) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X8),X9) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X7),X6) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X7),X6) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X7),X9) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X7),X9) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X7),X8) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X7),X8) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X9) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X9) = X9 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X8) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X8) = X8 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X7) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X7) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X6) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X6) = X6 )
& ( X5 != X6 )
& ( X6 != X9 )
& ( X5 != X9 )
& ( X6 != X8 )
& ( X5 != X8 )
& ( X8 != X9 )
& ( X6 != X7 )
& ( X5 != X7 )
& ( X7 != X9 )
& ( X7 != X8 ) )
& ! [X10: a,X11: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X10),X11)),X11) = X11 )
& ! [X12: a,X13: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X12),X13)),X13) = X13 )
& ! [X14: a,X15: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X14),X15) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X15),X14) )
& ! [X16: a,X17: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X16),X17) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X17),X16) )
& ! [X18: a,X19: a,X20: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),X19)),X20) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X19),X20)) )
& ! [X21: a,X22: a,X23: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X21),X22)),X23) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X21),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X22),X23)) )
& ! [X24: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X24),X24) = X24 )
& ! [X25: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X25),X25) = X25 ) )
=> ( ! [X4: a,X3: a,X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X2),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X3),X4)) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X2),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X2),X4)) )
& ? [X9: a,X8: a,X7: a,X6: a,X5: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X9),X6) = X9 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X9),X6) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X8),X6) = X8 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X8),X6) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X8),X9) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X8),X9) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X7),X6) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X7),X6) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X7),X9) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X7),X9) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X7),X8) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X7),X8) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X5),X9) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X5),X9) = X9 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X5),X8) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X5),X8) = X8 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X5),X7) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X5),X7) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X5),X6) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X5),X6) = X6 )
& ( X5 != X6 )
& ( X6 != X9 )
& ( X5 != X9 )
& ( X6 != X8 )
& ( X5 != X8 )
& ( X8 != X9 )
& ( X6 != X7 )
& ( X5 != X7 )
& ( X7 != X9 )
& ( X7 != X8 ) )
& ! [X11: a,X10: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X10),X11)),X11) = X11 )
& ! [X13: a,X12: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X12),X13)),X13) = X13 )
& ! [X15: a,X14: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X14),X15) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X15),X14) )
& ! [X17: a,X16: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X16),X17) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X17),X16) )
& ! [X20: a,X19: a,X18: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X18),X19)),X20) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X18),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X19),X20)) )
& ! [X23: a,X22: a,X21: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X21),X22)),X23) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X21),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X22),X23)) )
& ! [X24: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X24),X24) = X24 )
& ! [X25: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X25),X25) = X25 ) ) ),
introduced(choice_axiom,[]) ).
thf(f10,plain,
( ? [X9: a,X8: a,X7: a,X6: a,X5: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X9),X6) = X9 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X9),X6) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X8),X6) = X8 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X8),X6) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X8),X9) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X8),X9) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X7),X6) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X7),X6) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X7),X9) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X7),X9) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X7),X8) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X7),X8) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X5),X9) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X5),X9) = X9 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X5),X8) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X5),X8) = X8 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X5),X7) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X5),X7) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X5),X6) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X5),X6) = X6 )
& ( X5 != X6 )
& ( X6 != X9 )
& ( X5 != X9 )
& ( X6 != X8 )
& ( X5 != X8 )
& ( X8 != X9 )
& ( X6 != X7 )
& ( X5 != X7 )
& ( X7 != X9 )
& ( X7 != X8 ) )
=> ( ( sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),sK3) )
& ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),sK3) )
& ( sK5 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),sK3) )
& ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),sK3) )
& ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),sK6) )
& ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),sK6) )
& ( sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK3) )
& ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK3) )
& ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK6) )
& ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK6) )
& ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK5) )
& ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK5) )
& ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK6) )
& ( sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK6) )
& ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK5) )
& ( sK5 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK5) )
& ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK4) )
& ( sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK4) )
& ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK3) )
& ( sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK3) )
& ( sK2 != sK3 )
& ( sK3 != sK6 )
& ( sK2 != sK6 )
& ( sK3 != sK5 )
& ( sK2 != sK5 )
& ( sK5 != sK6 )
& ( sK3 != sK4 )
& ( sK2 != sK4 )
& ( sK4 != sK6 )
& ( sK4 != sK5 ) ) ),
introduced(choice_axiom,[]) ).
thf(f8,plain,
? [X0: a > a > a,X1: a > a > a] :
( ! [X2: a,X3: a,X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X3),X4)) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X4)) )
& ? [X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X9),X6) = X9 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X9),X6) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X8),X6) = X8 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X8),X6) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X8),X9) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X8),X9) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X7),X6) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X7),X6) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X7),X9) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X7),X9) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X7),X8) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X7),X8) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X9) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X9) = X9 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X8) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X8) = X8 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X7) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X7) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X6) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X6) = X6 )
& ( X5 != X6 )
& ( X6 != X9 )
& ( X5 != X9 )
& ( X6 != X8 )
& ( X5 != X8 )
& ( X8 != X9 )
& ( X6 != X7 )
& ( X5 != X7 )
& ( X7 != X9 )
& ( X7 != X8 ) )
& ! [X10: a,X11: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X10),X11)),X11) = X11 )
& ! [X12: a,X13: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X12),X13)),X13) = X13 )
& ! [X14: a,X15: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X14),X15) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X15),X14) )
& ! [X16: a,X17: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X16),X17) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X17),X16) )
& ! [X18: a,X19: a,X20: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),X19)),X20) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X19),X20)) )
& ! [X21: a,X22: a,X23: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X21),X22)),X23) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X21),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X22),X23)) )
& ! [X24: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X24),X24) = X24 )
& ! [X25: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X25),X25) = X25 ) ),
inference(rectify,[],[f7]) ).
thf(f7,plain,
? [X0: a > a > a,X1: a > a > a] :
( ! [X23: a,X24: a,X25: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X23),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X24),X25)) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X23),X24)),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X23),X25)) )
& ? [X18: a,X19: a,X20: a,X21: a,X22: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X22),X19) = X22 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X22),X19) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X21),X19) = X21 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X21),X19) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X21),X22) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X21),X22) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X20),X19) = X20 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X20),X19) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X20),X22) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X20),X22) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X20),X21) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X20),X21) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X18),X22) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),X22) = X22 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X18),X21) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),X21) = X21 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X18),X20) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),X20) = X20 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X18),X19) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),X19) = X19 )
& ( X18 != X19 )
& ( X19 != X22 )
& ( X18 != X22 )
& ( X19 != X21 )
& ( X18 != X21 )
& ( X21 != X22 )
& ( X19 != X20 )
& ( X18 != X20 )
& ( X20 != X22 )
& ( X20 != X21 ) )
& ! [X2: a,X3: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X3)),X3) = X3 )
& ! [X4: a,X5: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5)),X5) = X5 )
& ! [X6: a,X7: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X6),X7) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X7),X6) )
& ! [X8: a,X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X8),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X9),X8) )
& ! [X10: a,X11: a,X12: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X10),X11)),X12) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X10),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X11),X12)) )
& ! [X13: a,X14: a,X15: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X13),X14)),X15) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X13),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X14),X15)) )
& ! [X16: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X16),X16) = X16 )
& ! [X17: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X17),X17) = X17 ) ),
inference(flattening,[],[f6]) ).
thf(f6,plain,
? [X0: a > a > a,X1: a > a > a] :
( ! [X23: a,X24: a,X25: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X23),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X24),X25)) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X23),X24)),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X23),X25)) )
& ? [X18: a,X19: a,X20: a,X21: a,X22: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X22),X19) = X22 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X22),X19) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X21),X19) = X21 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X21),X19) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X21),X22) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X21),X22) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X20),X19) = X20 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X20),X19) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X20),X22) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X20),X22) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X20),X21) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X20),X21) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X18),X22) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),X22) = X22 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X18),X21) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),X21) = X21 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X18),X20) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),X20) = X20 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X18),X19) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),X19) = X19 )
& ( X18 != X19 )
& ( X19 != X22 )
& ( X18 != X22 )
& ( X19 != X21 )
& ( X18 != X21 )
& ( X21 != X22 )
& ( X19 != X20 )
& ( X18 != X20 )
& ( X20 != X22 )
& ( X20 != X21 ) )
& ! [X2: a,X3: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X3)),X3) = X3 )
& ! [X4: a,X5: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5)),X5) = X5 )
& ! [X6: a,X7: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X6),X7) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X7),X6) )
& ! [X8: a,X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X8),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X9),X8) )
& ! [X10: a,X11: a,X12: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X10),X11)),X12) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X10),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X11),X12)) )
& ! [X13: a,X14: a,X15: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X13),X14)),X15) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X13),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X14),X15)) )
& ! [X16: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X16),X16) = X16 )
& ! [X17: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X17),X17) = X17 ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f5,plain,
~ ! [X0: a > a > a,X1: a > a > a] :
( ( ! [X2: a,X3: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X3)),X3) = X3 )
& ! [X4: a,X5: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X4),X5)),X5) = X5 )
& ! [X6: a,X7: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X6),X7) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X7),X6) )
& ! [X8: a,X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X8),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X9),X8) )
& ! [X10: a,X11: a,X12: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X10),X11)),X12) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X10),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X11),X12)) )
& ! [X13: a,X14: a,X15: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X13),X14)),X15) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X13),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X14),X15)) )
& ! [X16: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X16),X16) = X16 )
& ! [X17: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X17),X17) = X17 ) )
=> ( ? [X18: a,X19: a,X20: a,X21: a,X22: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X22),X19) = X22 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X22),X19) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X21),X19) = X21 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X21),X19) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X21),X22) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X21),X22) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X20),X19) = X20 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X20),X19) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X20),X22) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X20),X22) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X20),X21) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X20),X21) = X19 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X18),X22) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),X22) = X22 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X18),X21) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),X21) = X21 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X18),X20) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),X20) = X20 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X18),X19) = X18 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X18),X19) = X19 )
& ( X18 != X19 )
& ( X19 != X22 )
& ( X18 != X22 )
& ( X19 != X21 )
& ( X18 != X21 )
& ( X21 != X22 )
& ( X19 != X20 )
& ( X18 != X20 )
& ( X20 != X22 )
& ( X20 != X21 ) )
=> ~ ! [X23: a,X24: a,X25: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X23),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X24),X25)) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X23),X24)),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X23),X25)) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > a,X1: a > a > a] :
( ( ! [X2: a,X3: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X3)),X3) = X3 )
& ! [X2: a,X3: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X3)),X3) = X3 )
& ! [X2: a,X3: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X3),X2) )
& ! [X2: a,X3: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X3),X2) )
& ! [X2: a,X3: a,X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X3)),X4) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X3),X4)) )
& ! [X2: a,X3: a,X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X3)),X4) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X3),X4)) )
& ! [X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X2) = X2 )
& ! [X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X2) = X2 ) )
=> ( ? [X2: a,X3: a,X5: a,X6: a,X7: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X7),X3) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X7),X3) = X3 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X6),X3) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X6),X3) = X3 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X6),X7) = X2 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X6),X7) = X3 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X3) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X3) = X3 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X7) = X2 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X7) = X3 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X6) = X2 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X6) = X3 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X7) = X2 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X7) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X6) = X2 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X6) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X5) = X2 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X5) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X3) = X2 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X3) = X3 )
& ( X2 != X3 )
& ( X3 != X7 )
& ( X2 != X7 )
& ( X3 != X6 )
& ( X2 != X6 )
& ( X6 != X7 )
& ( X3 != X5 )
& ( X2 != X5 )
& ( X5 != X7 )
& ( X5 != X6 ) )
=> ~ ! [X2: a,X3: a,X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X3),X4)) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X4)) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > a,X1: a > a > a] :
( ( ! [X2: a,X3: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X3)),X3) = X3 )
& ! [X2: a,X3: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X3)),X3) = X3 )
& ! [X2: a,X3: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X3),X2) )
& ! [X2: a,X3: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X3),X2) )
& ! [X2: a,X3: a,X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X3)),X4) = vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X3),X4)) )
& ! [X2: a,X3: a,X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X3)),X4) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X3),X4)) )
& ! [X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X2) = X2 )
& ! [X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X2) = X2 ) )
=> ( ? [X2: a,X3: a,X5: a,X6: a,X7: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X7),X3) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X7),X3) = X3 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X6),X3) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X6),X3) = X3 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X6),X7) = X2 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X6),X7) = X3 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X3) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X3) = X3 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X7) = X2 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X7) = X3 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X5),X6) = X2 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X5),X6) = X3 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X7) = X2 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X7) = X7 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X6) = X2 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X6) = X6 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X5) = X2 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X5) = X5 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X0,X2),X3) = X2 )
& ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X3) = X3 )
& ( X2 != X3 )
& ( X3 != X7 )
& ( X2 != X7 )
& ( X3 != X6 )
& ( X2 != X6 )
& ( X6 != X7 )
& ( X3 != X5 )
& ( X2 != X5 )
& ( X5 != X7 )
& ( X5 != X6 ) )
=> ~ ! [X2: a,X3: a,X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),vAPP(a,a,vAPP(a,sTfun(a,a),X0,X3),X4)) = vAPP(a,a,vAPP(a,sTfun(a,a),X0,vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),X1,X2),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c3_DIAMOND_THM_pme) ).
thf(f334,plain,
( spl7_41
| ~ spl7_17
| ~ spl7_34 ),
inference(avatar_split_clause,[],[f230,f215,f130,f331]) ).
thf(f331,plain,
( spl7_41
<=> ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_41])]) ).
thf(f230,plain,
( ( sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK2) )
| ~ spl7_17
| ~ spl7_34 ),
inference(superposition,[],[f216,f132]) ).
thf(f329,plain,
spl7_40,
inference(avatar_split_clause,[],[f15,f327]) ).
thf(f15,plain,
! [X18: a,X19: a,X20: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X18),X19)),X20) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X18),vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X19),X20)) ),
inference(cnf_transformation,[],[f11]) ).
thf(f325,plain,
spl7_39,
inference(avatar_split_clause,[],[f14,f323]) ).
thf(f14,plain,
! [X21: a,X22: a,X23: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X21),X22)),X23) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X21),vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X22),X23)) ),
inference(cnf_transformation,[],[f11]) ).
thf(f293,plain,
spl7_38,
inference(avatar_split_clause,[],[f4,f291]) ).
thf(f291,plain,
( spl7_38
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_38])]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f229,plain,
spl7_37,
inference(avatar_split_clause,[],[f19,f227]) ).
thf(f19,plain,
! [X10: a,X11: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X10),X11)),X11) = X11 ),
inference(cnf_transformation,[],[f11]) ).
thf(f225,plain,
spl7_36,
inference(avatar_split_clause,[],[f18,f223]) ).
thf(f18,plain,
! [X12: a,X13: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X12),X13)),X13) = X13 ),
inference(cnf_transformation,[],[f11]) ).
thf(f221,plain,
spl7_35,
inference(avatar_split_clause,[],[f17,f219]) ).
thf(f17,plain,
! [X14: a,X15: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X14),X15) = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X15),X14) ),
inference(cnf_transformation,[],[f11]) ).
thf(f217,plain,
spl7_34,
inference(avatar_split_clause,[],[f16,f215]) ).
thf(f16,plain,
! [X16: a,X17: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X16),X17) = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X17),X16) ),
inference(cnf_transformation,[],[f11]) ).
thf(f213,plain,
spl7_33,
inference(avatar_split_clause,[],[f49,f210]) ).
thf(f49,plain,
sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK6),sK3),
inference(cnf_transformation,[],[f11]) ).
thf(f208,plain,
spl7_32,
inference(avatar_split_clause,[],[f48,f205]) ).
thf(f48,plain,
sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK6),sK3),
inference(cnf_transformation,[],[f11]) ).
thf(f203,plain,
spl7_31,
inference(avatar_split_clause,[],[f47,f200]) ).
thf(f47,plain,
sK5 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),sK3),
inference(cnf_transformation,[],[f11]) ).
thf(f198,plain,
spl7_30,
inference(avatar_split_clause,[],[f46,f195]) ).
thf(f46,plain,
sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),sK3),
inference(cnf_transformation,[],[f11]) ).
thf(f193,plain,
spl7_29,
inference(avatar_split_clause,[],[f45,f190]) ).
thf(f45,plain,
sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK5),sK6),
inference(cnf_transformation,[],[f11]) ).
thf(f188,plain,
spl7_28,
inference(avatar_split_clause,[],[f44,f185]) ).
thf(f44,plain,
sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK5),sK6),
inference(cnf_transformation,[],[f11]) ).
thf(f183,plain,
spl7_27,
inference(avatar_split_clause,[],[f43,f180]) ).
thf(f43,plain,
sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK3),
inference(cnf_transformation,[],[f11]) ).
thf(f178,plain,
spl7_26,
inference(avatar_split_clause,[],[f42,f175]) ).
thf(f42,plain,
sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK3),
inference(cnf_transformation,[],[f11]) ).
thf(f173,plain,
spl7_25,
inference(avatar_split_clause,[],[f41,f170]) ).
thf(f41,plain,
sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK6),
inference(cnf_transformation,[],[f11]) ).
thf(f168,plain,
spl7_24,
inference(avatar_split_clause,[],[f40,f165]) ).
thf(f40,plain,
sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK6),
inference(cnf_transformation,[],[f11]) ).
thf(f163,plain,
spl7_23,
inference(avatar_split_clause,[],[f39,f160]) ).
thf(f39,plain,
sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK4),sK5),
inference(cnf_transformation,[],[f11]) ).
thf(f158,plain,
spl7_22,
inference(avatar_split_clause,[],[f38,f155]) ).
thf(f38,plain,
sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK4),sK5),
inference(cnf_transformation,[],[f11]) ).
thf(f153,plain,
spl7_21,
inference(avatar_split_clause,[],[f37,f150]) ).
thf(f37,plain,
sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK6),
inference(cnf_transformation,[],[f11]) ).
thf(f148,plain,
spl7_20,
inference(avatar_split_clause,[],[f36,f145]) ).
thf(f36,plain,
sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK6),
inference(cnf_transformation,[],[f11]) ).
thf(f143,plain,
spl7_19,
inference(avatar_split_clause,[],[f35,f140]) ).
thf(f35,plain,
sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK5),
inference(cnf_transformation,[],[f11]) ).
thf(f138,plain,
spl7_18,
inference(avatar_split_clause,[],[f34,f135]) ).
thf(f34,plain,
sK5 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK5),
inference(cnf_transformation,[],[f11]) ).
thf(f133,plain,
spl7_17,
inference(avatar_split_clause,[],[f33,f130]) ).
thf(f33,plain,
sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK4),
inference(cnf_transformation,[],[f11]) ).
thf(f128,plain,
spl7_16,
inference(avatar_split_clause,[],[f32,f125]) ).
thf(f32,plain,
sK4 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK4),
inference(cnf_transformation,[],[f11]) ).
thf(f123,plain,
spl7_15,
inference(avatar_split_clause,[],[f31,f120]) ).
thf(f31,plain,
sK2 = vAPP(a,a,vAPP(a,sTfun(a,a),sK0,sK2),sK3),
inference(cnf_transformation,[],[f11]) ).
thf(f118,plain,
spl7_14,
inference(avatar_split_clause,[],[f30,f115]) ).
thf(f30,plain,
sK3 = vAPP(a,a,vAPP(a,sTfun(a,a),sK1,sK2),sK3),
inference(cnf_transformation,[],[f11]) ).
thf(f113,plain,
spl7_13,
inference(avatar_split_clause,[],[f13,f111]) ).
thf(f13,plain,
! [X24: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK1,X24),X24) = X24 ),
inference(cnf_transformation,[],[f11]) ).
thf(f109,plain,
spl7_12,
inference(avatar_split_clause,[],[f12,f107]) ).
thf(f12,plain,
! [X25: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),sK0,X25),X25) = X25 ),
inference(cnf_transformation,[],[f11]) ).
thf(f105,plain,
~ spl7_11,
inference(avatar_split_clause,[],[f3,f102]) ).
thf(f102,plain,
( spl7_11
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_11])]) ).
thf(f3,plain,
$true != $false,
introduced(fool_axiom,[]) ).
thf(f100,plain,
~ spl7_10,
inference(avatar_split_clause,[],[f29,f97]) ).
thf(f97,plain,
( spl7_10
<=> ( sK2 = sK3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_10])]) ).
thf(f29,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f11]) ).
thf(f95,plain,
~ spl7_9,
inference(avatar_split_clause,[],[f28,f92]) ).
thf(f92,plain,
( spl7_9
<=> ( sK3 = sK6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_9])]) ).
thf(f28,plain,
sK3 != sK6,
inference(cnf_transformation,[],[f11]) ).
thf(f90,plain,
~ spl7_8,
inference(avatar_split_clause,[],[f27,f87]) ).
thf(f87,plain,
( spl7_8
<=> ( sK2 = sK6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_8])]) ).
thf(f27,plain,
sK2 != sK6,
inference(cnf_transformation,[],[f11]) ).
thf(f85,plain,
~ spl7_7,
inference(avatar_split_clause,[],[f26,f82]) ).
thf(f82,plain,
( spl7_7
<=> ( sK3 = sK5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_7])]) ).
thf(f26,plain,
sK3 != sK5,
inference(cnf_transformation,[],[f11]) ).
thf(f80,plain,
~ spl7_6,
inference(avatar_split_clause,[],[f25,f77]) ).
thf(f77,plain,
( spl7_6
<=> ( sK2 = sK5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_6])]) ).
thf(f25,plain,
sK2 != sK5,
inference(cnf_transformation,[],[f11]) ).
thf(f75,plain,
~ spl7_5,
inference(avatar_split_clause,[],[f24,f72]) ).
thf(f72,plain,
( spl7_5
<=> ( sK5 = sK6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).
thf(f24,plain,
sK5 != sK6,
inference(cnf_transformation,[],[f11]) ).
thf(f70,plain,
~ spl7_4,
inference(avatar_split_clause,[],[f23,f67]) ).
thf(f23,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f11]) ).
thf(f65,plain,
~ spl7_3,
inference(avatar_split_clause,[],[f22,f62]) ).
thf(f62,plain,
( spl7_3
<=> ( sK2 = sK4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).
thf(f22,plain,
sK2 != sK4,
inference(cnf_transformation,[],[f11]) ).
thf(f60,plain,
~ spl7_2,
inference(avatar_split_clause,[],[f21,f57]) ).
thf(f57,plain,
( spl7_2
<=> ( sK4 = sK6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
thf(f21,plain,
sK4 != sK6,
inference(cnf_transformation,[],[f11]) ).
thf(f55,plain,
~ spl7_1,
inference(avatar_split_clause,[],[f20,f52]) ).
thf(f52,plain,
( spl7_1
<=> ( sK4 = sK5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
thf(f20,plain,
sK4 != sK5,
inference(cnf_transformation,[],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU998^5 : TPTP v8.2.0. Released v4.0.0.
% 0.00/0.08 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.07/0.27 % Computer : n020.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Sun May 19 17:10:22 EDT 2024
% 0.07/0.27 % CPUTime :
% 0.07/0.27 % (1854)Running in auto input_syntax mode. Trying TPTP
% 0.07/0.28 % (1857)WARNING: value z3 for option sas not known
% 0.07/0.28 % (1856)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.07/0.28 % (1861)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)
% 0.07/0.28 % (1858)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.07/0.28 % (1860)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)
% 0.07/0.28 % (1855)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.07/0.28 % (1857)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)
% 0.07/0.28 % (1862)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)
% 0.07/0.28 % (1862)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.07/0.28 % Exception at run slice level% Exception at run slice level
% 0.07/0.28
% 0.07/0.28 % Exception at run slice level
% 0.07/0.28 User error: User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructsFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.07/0.28 User error:
% 0.07/0.28 Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.29 % (1863)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.11/0.29 % (1865)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)
% 0.11/0.29 % (1864)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)
% 0.11/0.29 % (1863)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.29 % Exception at run slice level
% 0.11/0.29 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.29 % (1864)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.30 % (1866)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)
% 0.11/0.39 % (1860)First to succeed.
% 0.11/0.40 % (1860)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1854"
% 0.11/0.40 % (1860)Refutation found. Thanks to Tanya!
% 0.11/0.40 % SZS status Theorem for theBenchmark
% 0.11/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.40 % (1860)------------------------------
% 0.11/0.40 % (1860)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.40 % (1860)Termination reason: Refutation
% 0.11/0.40
% 0.11/0.40 % (1860)Memory used [KB]: 2921
% 0.11/0.40 % (1860)Time elapsed: 0.116 s
% 0.11/0.40 % (1860)Instructions burned: 433 (million)
% 0.11/0.40 % (1854)Success in time 0.126 s
%------------------------------------------------------------------------------