TSTP Solution File: SEV045^5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEV045^5 : 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 : n013.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 04:14:19 EDT 2024
% Result : Theorem 0.20s 0.38s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 68
% Syntax : Number of formulae : 237 ( 15 unt; 18 typ; 0 def)
% Number of atoms : 3232 ( 483 equ; 0 cnn)
% Maximal formula atoms : 19 ( 14 avg)
% Number of connectives : 1143 ( 458 ~; 532 |; 54 &; 0 @)
% ( 46 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 25 ( 24 >; 1 *; 0 +; 0 <<)
% Number of symbols : 64 ( 61 usr; 50 con; 0-6 aty)
% Number of variables : 372 ( 0 ^ 358 !; 8 ?; 372 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
g: a > b ).
thf(func_def_3,type,
f: a > b ).
thf(func_def_4,type,
cQ: a > b > b > $o ).
thf(func_def_5,type,
cP: a > a > $o ).
thf(func_def_9,type,
sK0: a ).
thf(func_def_10,type,
sK1: 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(f1063,plain,
$false,
inference(avatar_sat_refutation,[],[f25,f30,f34,f66,f75,f81,f90,f94,f102,f106,f117,f123,f138,f145,f149,f191,f197,f202,f213,f221,f246,f260,f264,f282,f307,f325,f329,f333,f337,f341,f375,f492,f497,f512,f516,f520,f863,f867,f871,f921,f925,f929,f961,f980,f1011,f1015,f1062]) ).
thf(f1062,plain,
( ~ spl2_19
| ~ spl2_17
| ~ spl2_18
| ~ spl2_45 ),
inference(avatar_split_clause,[],[f1032,f1009,f199,f194,f210]) ).
thf(f210,plain,
( spl2_19
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
thf(f194,plain,
( spl2_17
<=> ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK0)),vAPP(a,b,f,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
thf(f199,plain,
( spl2_18
<=> ( $false = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK0)),vAPP(a,b,g,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
thf(f1009,plain,
( spl2_45
<=> ! [X0: a,X1: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),vAPP(a,b,g,X0)) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),vAPP(a,b,f,X0)) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_45])]) ).
thf(f1032,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),sK1) )
| ~ spl2_17
| ~ spl2_18
| ~ spl2_45 ),
inference(trivial_inequality_removal,[],[f1031]) ).
thf(f1031,plain,
( ( $true = $false )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),sK1) )
| ~ spl2_17
| ~ spl2_18
| ~ spl2_45 ),
inference(forward_demodulation,[],[f1028,f201]) ).
thf(f201,plain,
( ( $false = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK0)),vAPP(a,b,g,sK1)) )
| ~ spl2_18 ),
inference(avatar_component_clause,[],[f199]) ).
thf(f1028,plain,
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK0)),vAPP(a,b,g,sK1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),sK1) )
| ~ spl2_17
| ~ spl2_45 ),
inference(trivial_inequality_removal,[],[f1017]) ).
thf(f1017,plain,
( ( $true != $true )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK0)),vAPP(a,b,g,sK1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),sK1) )
| ~ spl2_17
| ~ spl2_45 ),
inference(superposition,[],[f1010,f196]) ).
thf(f196,plain,
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK0)),vAPP(a,b,f,sK1)) )
| ~ spl2_17 ),
inference(avatar_component_clause,[],[f194]) ).
thf(f1010,plain,
( ! [X0: a,X1: b] :
( ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),vAPP(a,b,f,X0)) )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),vAPP(a,b,g,X0)) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true ) )
| ~ spl2_45 ),
inference(avatar_component_clause,[],[f1009]) ).
thf(f1015,plain,
( spl2_46
| ~ spl2_22
| ~ spl2_25 ),
inference(avatar_split_clause,[],[f321,f305,f258,f1013]) ).
thf(f1013,plain,
( spl2_46
<=> ! [X0: a,X1: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),X1) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( $false = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,g,X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_46])]) ).
thf(f258,plain,
( spl2_22
<=> ! [X0: a] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,g,X0)) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).
thf(f305,plain,
( spl2_25
<=> ! [X0: a,X3: b,X2: b,X1: b] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X3),X2) = $true )
| ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X3),X1) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),X2) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_25])]) ).
thf(f321,plain,
( ! [X0: a,X1: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),X1) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( $false = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,g,X0)),X1) ) )
| ~ spl2_22
| ~ spl2_25 ),
inference(trivial_inequality_removal,[],[f320]) ).
thf(f320,plain,
( ! [X0: a,X1: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),X1) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( $false = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,g,X0)),X1) )
| ( $true = $false ) )
| ~ spl2_22
| ~ spl2_25 ),
inference(inner_rewriting,[],[f316]) ).
thf(f316,plain,
( ! [X0: a,X1: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),X1) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( $false = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,g,X0)),X1) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) = $false ) )
| ~ spl2_22
| ~ spl2_25 ),
inference(trivial_inequality_removal,[],[f311]) ).
thf(f311,plain,
( ! [X0: a,X1: b] :
( ( $true != $true )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),X1) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( $false = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,g,X0)),X1) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) = $false ) )
| ~ spl2_22
| ~ spl2_25 ),
inference(superposition,[],[f306,f259]) ).
thf(f259,plain,
( ! [X0: a] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,g,X0)) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) = $false ) )
| ~ spl2_22 ),
inference(avatar_component_clause,[],[f258]) ).
thf(f306,plain,
( ! [X2: b,X3: b,X0: a,X1: b] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X3),X1) != $true )
| ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X3),X2) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),X2) = $false ) )
| ~ spl2_25 ),
inference(avatar_component_clause,[],[f305]) ).
thf(f1011,plain,
( spl2_45
| ~ spl2_12
| ~ spl2_22 ),
inference(avatar_split_clause,[],[f271,f258,f121,f1009]) ).
thf(f121,plain,
( spl2_12
<=> ! [X5: b,X4: a,X7: b,X6: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X5),X7) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X6),X7) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X5),X6) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X4),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
thf(f271,plain,
( ! [X0: a,X1: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),vAPP(a,b,g,X0)) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),vAPP(a,b,f,X0)) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true ) )
| ~ spl2_12
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f270]) ).
thf(f270,plain,
( ! [X0: a,X1: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),vAPP(a,b,g,X0)) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),vAPP(a,b,f,X0)) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( $true = $false ) )
| ~ spl2_12
| ~ spl2_22 ),
inference(inner_rewriting,[],[f269]) ).
thf(f269,plain,
( ! [X0: a,X1: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),vAPP(a,b,g,X0)) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),vAPP(a,b,f,X0)) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) = $false ) )
| ~ spl2_12
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f266]) ).
thf(f266,plain,
( ! [X0: a,X1: b] :
( ( $true != $true )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),vAPP(a,b,g,X0)) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),vAPP(a,b,f,X0)) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) = $false ) )
| ~ spl2_12
| ~ spl2_22 ),
inference(superposition,[],[f122,f259]) ).
thf(f122,plain,
( ! [X6: b,X7: b,X4: a,X5: b] :
( ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X6),X7) )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X5),X7) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X5),X6) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X4),X4) ) )
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f121]) ).
thf(f980,plain,
( spl2_44
| ~ spl2_11
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f277,f262,f115,f978]) ).
thf(f978,plain,
( spl2_44
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X1)),vAPP(a,b,f,X0)) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_44])]) ).
thf(f115,plain,
( spl2_11
<=> ! [X9: b,X8: b,X4: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X9),X8) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X8),X9) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X4),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
thf(f262,plain,
( spl2_23
<=> ! [X0: a,X1: a] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,f,X1)) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_23])]) ).
thf(f277,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X1)),vAPP(a,b,f,X0)) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) )
| ~ spl2_11
| ~ spl2_23 ),
inference(trivial_inequality_removal,[],[f276]) ).
thf(f276,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X1)),vAPP(a,b,f,X0)) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) )
| ~ spl2_11
| ~ spl2_23 ),
inference(superposition,[],[f116,f263]) ).
thf(f263,plain,
( ! [X0: a,X1: a] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,f,X1)) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) )
| ~ spl2_23 ),
inference(avatar_component_clause,[],[f262]) ).
thf(f116,plain,
( ! [X8: b,X9: b,X4: a] :
( ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X8),X9) )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X9),X8) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X4),X4) ) )
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f115]) ).
thf(f961,plain,
( ~ spl2_31
| spl2_43
| ~ spl2_11
| ~ spl2_13 ),
inference(avatar_split_clause,[],[f141,f135,f115,f959,f372]) ).
thf(f372,plain,
( spl2_31
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_31])]) ).
thf(f959,plain,
( spl2_43
<=> ! [X0: b,X1: b] :
( ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),X0),X1) )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_43])]) ).
thf(f135,plain,
( spl2_13
<=> ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK0) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
thf(f141,plain,
( ! [X0: b,X1: b] :
( ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),X0),X1) )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),X1),X0) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),sK0) ) )
| ~ spl2_11
| ~ spl2_13 ),
inference(superposition,[],[f116,f137]) ).
thf(f137,plain,
( ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK0) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1) )
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f135]) ).
thf(f929,plain,
( spl2_42
| ~ spl2_3
| ~ spl2_26 ),
inference(avatar_split_clause,[],[f348,f323,f32,f927]) ).
thf(f927,plain,
( spl2_42
<=> ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_42])]) ).
thf(f32,plain,
( spl2_3
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
thf(f323,plain,
( spl2_26
<=> ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK0) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_26])]) ).
thf(f348,plain,
( ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK1) ) )
| ~ spl2_3
| ~ spl2_26 ),
inference(trivial_inequality_removal,[],[f347]) ).
thf(f347,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK1) ) )
| ~ spl2_3
| ~ spl2_26 ),
inference(superposition,[],[f324,f33]) ).
thf(f33,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f324,plain,
( ! [X0: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK0) ) )
| ~ spl2_26 ),
inference(avatar_component_clause,[],[f323]) ).
thf(f925,plain,
( spl2_41
| ~ spl2_17
| ~ spl2_19
| ~ spl2_25 ),
inference(avatar_split_clause,[],[f319,f305,f210,f194,f923]) ).
thf(f923,plain,
( spl2_41
<=> ! [X0: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK0)),X0) )
| ( $false = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK1)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_41])]) ).
thf(f319,plain,
( ! [X0: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK0)),X0) )
| ( $false = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK1)),X0) ) )
| ~ spl2_17
| ~ spl2_19
| ~ spl2_25 ),
inference(trivial_inequality_removal,[],[f318]) ).
thf(f318,plain,
( ! [X0: b] :
( ( $true != $true )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK0)),X0) )
| ( $false = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK1)),X0) ) )
| ~ spl2_17
| ~ spl2_19
| ~ spl2_25 ),
inference(forward_demodulation,[],[f317,f212]) ).
thf(f212,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),sK1) )
| ~ spl2_19 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f317,plain,
( ! [X0: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK0)),X0) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),sK1) )
| ( $false = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK1)),X0) ) )
| ~ spl2_17
| ~ spl2_25 ),
inference(trivial_inequality_removal,[],[f309]) ).
thf(f309,plain,
( ! [X0: b] :
( ( $true != $true )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK0)),X0) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),sK1) )
| ( $false = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK1)),X0) ) )
| ~ spl2_17
| ~ spl2_25 ),
inference(superposition,[],[f306,f196]) ).
thf(f921,plain,
( spl2_40
| ~ spl2_7
| ~ spl2_12
| ~ spl2_15
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f208,f194,f147,f121,f87,f919]) ).
thf(f919,plain,
( spl2_40
<=> ! [X0: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),X0),vAPP(a,b,f,sK1)) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),X0),vAPP(a,b,f,sK0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_40])]) ).
thf(f87,plain,
( spl2_7
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
thf(f147,plain,
( spl2_15
<=> ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK1) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
thf(f208,plain,
( ! [X0: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),X0),vAPP(a,b,f,sK1)) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),X0),vAPP(a,b,f,sK0)) ) )
| ~ spl2_7
| ~ spl2_12
| ~ spl2_15
| ~ spl2_17 ),
inference(trivial_inequality_removal,[],[f207]) ).
thf(f207,plain,
( ! [X0: b] :
( ( $true != $true )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),X0),vAPP(a,b,f,sK1)) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),X0),vAPP(a,b,f,sK0)) ) )
| ~ spl2_7
| ~ spl2_12
| ~ spl2_15
| ~ spl2_17 ),
inference(forward_demodulation,[],[f206,f186]) ).
thf(f186,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),sK1) )
| ~ spl2_7
| ~ spl2_15 ),
inference(trivial_inequality_removal,[],[f180]) ).
thf(f180,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),sK1) )
| ~ spl2_7
| ~ spl2_15 ),
inference(superposition,[],[f148,f89]) ).
thf(f89,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),sK0) )
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f87]) ).
thf(f148,plain,
( ! [X0: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK1) ) )
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f147]) ).
thf(f206,plain,
( ! [X0: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),X0),vAPP(a,b,f,sK1)) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),X0),vAPP(a,b,f,sK0)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),sK1) ) )
| ~ spl2_12
| ~ spl2_17 ),
inference(trivial_inequality_removal,[],[f203]) ).
thf(f203,plain,
( ! [X0: b] :
( ( $true != $true )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),X0),vAPP(a,b,f,sK1)) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),X0),vAPP(a,b,f,sK0)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),sK1) ) )
| ~ spl2_12
| ~ spl2_17 ),
inference(superposition,[],[f122,f196]) ).
thf(f871,plain,
( spl2_39
| ~ spl2_13
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f274,f262,f135,f869]) ).
thf(f869,plain,
( spl2_39
<=> ! [X0: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK0)),vAPP(a,b,f,X0)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_39])]) ).
thf(f274,plain,
( ! [X0: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK0)),vAPP(a,b,f,X0)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),X0) ) )
| ~ spl2_13
| ~ spl2_23 ),
inference(superposition,[],[f263,f137]) ).
thf(f867,plain,
( spl2_38
| ~ spl2_11
| ~ spl2_22 ),
inference(avatar_split_clause,[],[f273,f258,f115,f865]) ).
thf(f865,plain,
( spl2_38
<=> ! [X0: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,g,X0)),vAPP(a,b,f,X0)) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_38])]) ).
thf(f273,plain,
( ! [X0: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,g,X0)),vAPP(a,b,f,X0)) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true ) )
| ~ spl2_11
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f272]) ).
thf(f272,plain,
( ! [X0: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,g,X0)),vAPP(a,b,f,X0)) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( $true = $false ) )
| ~ spl2_11
| ~ spl2_22 ),
inference(inner_rewriting,[],[f268]) ).
thf(f268,plain,
( ! [X0: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,g,X0)),vAPP(a,b,f,X0)) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) = $false ) )
| ~ spl2_11
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f267]) ).
thf(f267,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,g,X0)),vAPP(a,b,f,X0)) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) = $false ) )
| ~ spl2_11
| ~ spl2_22 ),
inference(superposition,[],[f116,f259]) ).
thf(f863,plain,
( spl2_37
| ~ spl2_10
| ~ spl2_14 ),
inference(avatar_split_clause,[],[f174,f143,f104,f861]) ).
thf(f861,plain,
( spl2_37
<=> ! [X0: a,X1: a] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,f,X1)) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X0) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_37])]) ).
thf(f104,plain,
( spl2_10
<=> ! [X16: a,X15: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X15),vAPP(a,b,f,X15)),vAPP(a,b,f,X16)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X15),X16) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
thf(f143,plain,
( spl2_14
<=> ! [X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X0) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
thf(f174,plain,
( ! [X0: a,X1: a] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,f,X1)) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X0) = $false ) )
| ~ spl2_10
| ~ spl2_14 ),
inference(trivial_inequality_removal,[],[f156]) ).
thf(f156,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,f,X1)) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X0) = $false ) )
| ~ spl2_10
| ~ spl2_14 ),
inference(superposition,[],[f105,f144]) ).
thf(f144,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X0) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) )
| ~ spl2_14 ),
inference(avatar_component_clause,[],[f143]) ).
thf(f105,plain,
( ! [X16: a,X15: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X15),X16) )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X15),vAPP(a,b,f,X15)),vAPP(a,b,f,X16)) ) )
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f104]) ).
thf(f520,plain,
( spl2_36
| ~ spl2_14
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f254,f244,f143,f518]) ).
thf(f518,plain,
( spl2_36
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X2) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X2) = $false )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X0) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_36])]) ).
thf(f244,plain,
( spl2_21
<=> ! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X1) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X0) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).
thf(f254,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X2) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X2) = $false )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X0) = $false ) )
| ~ spl2_14
| ~ spl2_21 ),
inference(trivial_inequality_removal,[],[f251]) ).
thf(f251,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X2) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X2) = $false )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X0) = $false ) )
| ~ spl2_14
| ~ spl2_21 ),
inference(superposition,[],[f245,f144]) ).
thf(f245,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X1) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) )
| ~ spl2_21 ),
inference(avatar_component_clause,[],[f244]) ).
thf(f516,plain,
( spl2_35
| ~ spl2_3
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f253,f244,f32,f514]) ).
thf(f514,plain,
( spl2_35
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X2) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X2) = $false )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_35])]) ).
thf(f253,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X2) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X2) = $false )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) )
| ~ spl2_3
| ~ spl2_21 ),
inference(trivial_inequality_removal,[],[f252]) ).
thf(f252,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X2) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X2) = $false )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) )
| ~ spl2_3
| ~ spl2_21 ),
inference(superposition,[],[f245,f33]) ).
thf(f512,plain,
( spl2_34
| ~ spl2_8
| ~ spl2_14 ),
inference(avatar_split_clause,[],[f173,f143,f92,f510]) ).
thf(f510,plain,
( spl2_34
<=> ! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X1) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X0) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X0) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_34])]) ).
thf(f92,plain,
( spl2_8
<=> ! [X11: a,X12: a,X10: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X10),X12) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X11),X12) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X10),X11) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
thf(f173,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X1) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X0) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X0) = $false ) )
| ~ spl2_8
| ~ spl2_14 ),
inference(trivial_inequality_removal,[],[f157]) ).
thf(f157,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X1) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X0) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X0) = $false ) )
| ~ spl2_8
| ~ spl2_14 ),
inference(superposition,[],[f93,f144]) ).
thf(f93,plain,
( ! [X10: a,X11: a,X12: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X11),X12) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X10),X12) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X10),X11) ) )
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f497,plain,
( ~ spl2_33
| spl2_5
| ~ spl2_13 ),
inference(avatar_split_clause,[],[f139,f135,f72,f494]) ).
thf(f494,plain,
( spl2_33
<=> ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK0)),vAPP(a,b,g,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_33])]) ).
thf(f72,plain,
( spl2_5
<=> ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK0),vAPP(a,b,f,sK0)),vAPP(a,b,g,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
thf(f139,plain,
( ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK0)),vAPP(a,b,g,sK1)) )
| spl2_5
| ~ spl2_13 ),
inference(superposition,[],[f74,f137]) ).
thf(f74,plain,
( ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK0),vAPP(a,b,f,sK0)),vAPP(a,b,g,sK1)) )
| spl2_5 ),
inference(avatar_component_clause,[],[f72]) ).
thf(f492,plain,
( spl2_32
| ~ spl2_7
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f133,f104,f87,f489]) ).
thf(f489,plain,
( spl2_32
<=> ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK1)),vAPP(a,b,f,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_32])]) ).
thf(f133,plain,
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK1)),vAPP(a,b,f,sK0)) )
| ~ spl2_7
| ~ spl2_10 ),
inference(trivial_inequality_removal,[],[f126]) ).
thf(f126,plain,
( ( $true != $true )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK1)),vAPP(a,b,f,sK0)) )
| ~ spl2_7
| ~ spl2_10 ),
inference(superposition,[],[f105,f89]) ).
thf(f375,plain,
( spl2_31
| ~ spl2_2
| ~ spl2_26 ),
inference(avatar_split_clause,[],[f351,f323,f27,f372]) ).
thf(f27,plain,
( spl2_2
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
thf(f351,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),sK0) )
| ~ spl2_2
| ~ spl2_26 ),
inference(trivial_inequality_removal,[],[f342]) ).
thf(f342,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),sK0) )
| ~ spl2_2
| ~ spl2_26 ),
inference(superposition,[],[f324,f29]) ).
thf(f29,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),sK1) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f341,plain,
( spl2_30
| ~ spl2_2
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f256,f244,f27,f339]) ).
thf(f339,plain,
( spl2_30
<=> ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_30])]) ).
thf(f256,plain,
( ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),X0) ) )
| ~ spl2_2
| ~ spl2_21 ),
inference(trivial_inequality_removal,[],[f247]) ).
thf(f247,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),X0) ) )
| ~ spl2_2
| ~ spl2_21 ),
inference(superposition,[],[f245,f29]) ).
thf(f337,plain,
( spl2_29
| ~ spl2_7
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f255,f244,f87,f335]) ).
thf(f335,plain,
( spl2_29
<=> ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_29])]) ).
thf(f255,plain,
( ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),X0) ) )
| ~ spl2_7
| ~ spl2_21 ),
inference(trivial_inequality_removal,[],[f248]) ).
thf(f248,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),X0) ) )
| ~ spl2_7
| ~ spl2_21 ),
inference(superposition,[],[f245,f89]) ).
thf(f333,plain,
( spl2_28
| ~ spl2_14
| ~ spl2_15 ),
inference(avatar_split_clause,[],[f185,f147,f143,f331]) ).
thf(f331,plain,
( spl2_28
<=> ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_28])]) ).
thf(f185,plain,
( ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),X0) ) )
| ~ spl2_14
| ~ spl2_15 ),
inference(trivial_inequality_removal,[],[f182]) ).
thf(f182,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),X0) ) )
| ~ spl2_14
| ~ spl2_15 ),
inference(superposition,[],[f148,f144]) ).
thf(f329,plain,
( spl2_27
| ~ spl2_3
| ~ spl2_15 ),
inference(avatar_split_clause,[],[f184,f147,f32,f327]) ).
thf(f327,plain,
( spl2_27
<=> ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_27])]) ).
thf(f184,plain,
( ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK0) ) )
| ~ spl2_3
| ~ spl2_15 ),
inference(trivial_inequality_removal,[],[f183]) ).
thf(f183,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK0) ) )
| ~ spl2_3
| ~ spl2_15 ),
inference(superposition,[],[f148,f33]) ).
thf(f325,plain,
( spl2_26
| ~ spl2_7
| ~ spl2_8 ),
inference(avatar_split_clause,[],[f132,f92,f87,f323]) ).
thf(f132,plain,
( ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK0) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK1) ) )
| ~ spl2_7
| ~ spl2_8 ),
inference(trivial_inequality_removal,[],[f127]) ).
thf(f127,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK0) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK1) ) )
| ~ spl2_7
| ~ spl2_8 ),
inference(superposition,[],[f93,f89]) ).
thf(f307,plain,
( spl2_25
| ~ spl2_3
| ~ spl2_12 ),
inference(avatar_split_clause,[],[f125,f121,f32,f305]) ).
thf(f125,plain,
( ! [X2: b,X3: b,X0: a,X1: b] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X3),X2) = $true )
| ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X3),X1) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),X2) = $false ) )
| ~ spl2_3
| ~ spl2_12 ),
inference(trivial_inequality_removal,[],[f124]) ).
thf(f124,plain,
( ! [X2: b,X3: b,X0: a,X1: b] :
( ( $true != $true )
| ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X3),X2) = $true )
| ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X3),X1) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),X2) = $false ) )
| ~ spl2_3
| ~ spl2_12 ),
inference(superposition,[],[f122,f33]) ).
thf(f282,plain,
( spl2_24
| ~ spl2_3
| ~ spl2_11 ),
inference(avatar_split_clause,[],[f119,f115,f32,f280]) ).
thf(f280,plain,
( spl2_24
<=> ! [X2: b,X0: a,X1: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X2),X1) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),X2) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_24])]) ).
thf(f119,plain,
( ! [X2: b,X0: a,X1: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X2),X1) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),X2) = $false ) )
| ~ spl2_3
| ~ spl2_11 ),
inference(trivial_inequality_removal,[],[f118]) ).
thf(f118,plain,
( ! [X2: b,X0: a,X1: b] :
( ( $true != $true )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X2),X1) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true )
| ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),X2) = $false ) )
| ~ spl2_3
| ~ spl2_11 ),
inference(superposition,[],[f116,f33]) ).
thf(f264,plain,
( spl2_23
| ~ spl2_3
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f111,f104,f32,f262]) ).
thf(f111,plain,
( ! [X0: a,X1: a] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,f,X1)) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) )
| ~ spl2_3
| ~ spl2_10 ),
inference(trivial_inequality_removal,[],[f110]) ).
thf(f110,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,f,X1)) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) )
| ~ spl2_3
| ~ spl2_10 ),
inference(superposition,[],[f105,f33]) ).
thf(f260,plain,
( spl2_22
| ~ spl2_3
| ~ spl2_9 ),
inference(avatar_split_clause,[],[f108,f100,f32,f258]) ).
thf(f100,plain,
( spl2_9
<=> ! [X17: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X17),vAPP(a,b,f,X17)),vAPP(a,b,g,X17)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X17),X17) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
thf(f108,plain,
( ! [X0: a] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,g,X0)) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) = $false ) )
| ~ spl2_3
| ~ spl2_9 ),
inference(trivial_inequality_removal,[],[f107]) ).
thf(f107,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,g,X0)) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) = $false ) )
| ~ spl2_3
| ~ spl2_9 ),
inference(superposition,[],[f101,f33]) ).
thf(f101,plain,
( ! [X17: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X17),X17) )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X17),vAPP(a,b,f,X17)),vAPP(a,b,g,X17)) ) )
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f100]) ).
thf(f246,plain,
( spl2_21
| ~ spl2_3
| ~ spl2_8 ),
inference(avatar_split_clause,[],[f97,f92,f32,f244]) ).
thf(f97,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X1) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X0) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) )
| ~ spl2_3
| ~ spl2_8 ),
inference(trivial_inequality_removal,[],[f96]) ).
thf(f96,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X1) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X0) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) )
| ~ spl2_3
| ~ spl2_8 ),
inference(superposition,[],[f93,f33]) ).
thf(f221,plain,
( spl2_20
| ~ spl2_3
| ~ spl2_6 ),
inference(avatar_split_clause,[],[f84,f79,f32,f219]) ).
thf(f219,plain,
( spl2_20
<=> ! [X0: a,X1: a] :
( ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X1) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).
thf(f79,plain,
( spl2_6
<=> ! [X2: a,X3: a] :
( ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X2) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
thf(f84,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X1) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) )
| ~ spl2_3
| ~ spl2_6 ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f83,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X1) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) )
| ~ spl2_3
| ~ spl2_6 ),
inference(superposition,[],[f80,f33]) ).
thf(f80,plain,
( ! [X2: a,X3: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X3) )
| ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X2) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X3) ) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f79]) ).
thf(f213,plain,
( spl2_19
| ~ spl2_7
| ~ spl2_15 ),
inference(avatar_split_clause,[],[f186,f147,f87,f210]) ).
thf(f202,plain,
( spl2_18
| ~ spl2_13
| ~ spl2_16 ),
inference(avatar_split_clause,[],[f192,f188,f135,f199]) ).
thf(f188,plain,
( spl2_16
<=> ( $false = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK0),vAPP(a,b,f,sK0)),vAPP(a,b,g,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
thf(f192,plain,
( ( $false = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK0)),vAPP(a,b,g,sK1)) )
| ~ spl2_13
| ~ spl2_16 ),
inference(forward_demodulation,[],[f190,f137]) ).
thf(f190,plain,
( ( $false = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK0),vAPP(a,b,f,sK0)),vAPP(a,b,g,sK1)) )
| ~ spl2_16 ),
inference(avatar_component_clause,[],[f188]) ).
thf(f197,plain,
( spl2_17
| ~ spl2_2
| ~ spl2_6
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f113,f104,f79,f27,f194]) ).
thf(f113,plain,
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1),vAPP(a,b,f,sK0)),vAPP(a,b,f,sK1)) )
| ~ spl2_2
| ~ spl2_6
| ~ spl2_10 ),
inference(forward_demodulation,[],[f112,f85]) ).
thf(f85,plain,
( ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK0) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1) )
| ~ spl2_2
| ~ spl2_6 ),
inference(trivial_inequality_removal,[],[f82]) ).
thf(f82,plain,
( ( $true != $true )
| ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK0) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK1) )
| ~ spl2_2
| ~ spl2_6 ),
inference(superposition,[],[f80,f29]) ).
thf(f112,plain,
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK0),vAPP(a,b,f,sK0)),vAPP(a,b,f,sK1)) )
| ~ spl2_2
| ~ spl2_10 ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f109,plain,
( ( $true != $true )
| ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK0),vAPP(a,b,f,sK0)),vAPP(a,b,f,sK1)) )
| ~ spl2_2
| ~ spl2_10 ),
inference(superposition,[],[f105,f29]) ).
thf(f191,plain,
( spl2_16
| ~ spl2_3
| spl2_5 ),
inference(avatar_split_clause,[],[f77,f72,f32,f188]) ).
thf(f77,plain,
( ( $false = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK0),vAPP(a,b,f,sK0)),vAPP(a,b,g,sK1)) )
| ~ spl2_3
| spl2_5 ),
inference(trivial_inequality_removal,[],[f76]) ).
thf(f76,plain,
( ( $true != $true )
| ( $false = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK0),vAPP(a,b,f,sK0)),vAPP(a,b,g,sK1)) )
| ~ spl2_3
| spl2_5 ),
inference(superposition,[],[f74,f33]) ).
thf(f149,plain,
( spl2_15
| ~ spl2_2
| ~ spl2_8 ),
inference(avatar_split_clause,[],[f98,f92,f27,f147]) ).
thf(f98,plain,
( ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK1) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK0) ) )
| ~ spl2_2
| ~ spl2_8 ),
inference(trivial_inequality_removal,[],[f95]) ).
thf(f95,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK1) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),sK0) ) )
| ~ spl2_2
| ~ spl2_8 ),
inference(superposition,[],[f93,f29]) ).
thf(f145,plain,
( spl2_14
| ~ spl2_3
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f69,f64,f32,f143]) ).
thf(f64,plain,
( spl2_4
<=> ! [X13: a,X14: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X14),X13) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X13),X14) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
thf(f69,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X0) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) )
| ~ spl2_3
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f68]) ).
thf(f68,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X0) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $false ) )
| ~ spl2_3
| ~ spl2_4 ),
inference(superposition,[],[f65,f33]) ).
thf(f65,plain,
( ! [X14: a,X13: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X13),X14) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X14),X13) ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f64]) ).
thf(f138,plain,
( spl2_13
| ~ spl2_2
| ~ spl2_6 ),
inference(avatar_split_clause,[],[f85,f79,f27,f135]) ).
thf(f123,plain,
spl2_12,
inference(avatar_split_clause,[],[f17,f121]) ).
thf(f17,plain,
! [X6: b,X7: b,X4: a,X5: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X5),X7) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X6),X7) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X5),X6) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X4),X4) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f11,plain,
( ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK0),vAPP(a,b,f,sK0)),vAPP(a,b,g,sK1)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),sK1) )
& ! [X2: a,X3: a] :
( ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X2) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X3) ) )
& ! [X4: a] :
( ( ! [X5: b,X6: b,X7: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X5),X7) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X6),X7) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X5),X6) ) )
& ! [X8: b,X9: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X9),X8) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X8),X9) ) ) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X4),X4) ) )
& ! [X10: a,X11: a,X12: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X10),X12) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X11),X12) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X10),X11) ) )
& ! [X13: a,X14: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X14),X13) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X13),X14) ) )
& ! [X15: a,X16: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X15),vAPP(a,b,f,X15)),vAPP(a,b,f,X16)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X15),X16) ) )
& ! [X17: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X17),vAPP(a,b,f,X17)),vAPP(a,b,g,X17)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X17),X17) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: a,X1: a] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,g,X1)) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $true ) )
=> ( ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK0),vAPP(a,b,f,sK0)),vAPP(a,b,g,sK1)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),sK1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f9,plain,
( ? [X0: a,X1: a] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,g,X1)) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) = $true ) )
& ! [X2: a,X3: a] :
( ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X2) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X3) ) )
& ! [X4: a] :
( ( ! [X5: b,X6: b,X7: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X5),X7) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X6),X7) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X5),X6) ) )
& ! [X8: b,X9: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X9),X8) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X8),X9) ) ) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X4),X4) ) )
& ! [X10: a,X11: a,X12: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X10),X12) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X11),X12) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X10),X11) ) )
& ! [X13: a,X14: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X14),X13) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X13),X14) ) )
& ! [X15: a,X16: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X15),vAPP(a,b,f,X15)),vAPP(a,b,f,X16)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X15),X16) ) )
& ! [X17: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X17),vAPP(a,b,f,X17)),vAPP(a,b,g,X17)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X17),X17) ) ) ),
inference(rectify,[],[f8]) ).
thf(f8,plain,
( ? [X16: a,X17: a] :
( ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X16),vAPP(a,b,f,X16)),vAPP(a,b,g,X17)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X16),X17) ) )
& ! [X8: a,X9: a] :
( ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X8) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X9) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X8),X9) ) )
& ! [X10: a] :
( ( ! [X11: b,X12: b,X13: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X11),X13) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X12),X13) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X11),X12) ) )
& ! [X14: b,X15: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X15),X14) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X14),X15) ) ) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X10),X10) ) )
& ! [X3: a,X4: a,X5: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X3),X5) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X4),X5) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X3),X4) ) )
& ! [X6: a,X7: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X7),X6) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X6),X7) ) )
& ! [X1: a,X2: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X1),vAPP(a,b,f,X1)),vAPP(a,b,f,X2)) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X2) != $true ) )
& ! [X0: a] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,g,X0)) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
( ? [X16: a,X17: a] :
( ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X16),vAPP(a,b,f,X16)),vAPP(a,b,g,X17)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X16),X17) ) )
& ! [X8: a,X9: a] :
( ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X8) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X9) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X8),X9) ) )
& ! [X10: a] :
( ( ! [X11: b,X12: b,X13: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X11),X13) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X12),X13) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X11),X12) ) )
& ! [X14: b,X15: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X15),X14) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X14),X15) ) ) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X10),X10) ) )
& ! [X3: a,X4: a,X5: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X3),X5) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X4),X5) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X3),X4) ) )
& ! [X6: a,X7: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X7),X6) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X6),X7) ) )
& ! [X1: a,X2: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X1),vAPP(a,b,f,X1)),vAPP(a,b,f,X2)) )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X2) != $true ) )
& ! [X0: a] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,g,X0)) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) != $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ( ! [X0: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0) = $true )
=> ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,g,X0)) = $true ) )
=> ( ! [X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X2) = $true )
=> ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X1),vAPP(a,b,f,X1)),vAPP(a,b,f,X2)) ) )
=> ( ( ! [X3: a,X4: a,X5: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X4),X5) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X3),X4) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X3),X5) ) )
& ! [X6: a,X7: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X6),X7) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X7),X6) ) ) )
=> ( ( ! [X8: a,X9: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X8),X9) )
=> ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X8) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X9) ) )
& ! [X10: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X10),X10) )
=> ( ! [X11: b,X12: b,X13: b] :
( ( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X12),X13) )
& ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X11),X12) ) )
=> ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X11),X13) ) )
& ! [X14: b,X15: b] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X14),X15) )
=> ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X15),X14) ) ) ) ) )
=> ! [X16: a,X17: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X16),X17) )
=> ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X16),vAPP(a,b,f,X16)),vAPP(a,b,g,X17)) ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ( ! [X0: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0)
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,g,X0)) )
=> ( ! [X1: a,X2: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X2)
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X1),vAPP(a,b,f,X1)),vAPP(a,b,f,X2)) )
=> ( ( ! [X3: a,X4: a,X5: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X4),X5)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X3),X4) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X3),X5) )
& ! [X6: a,X7: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X6),X7)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X7),X6) ) )
=> ( ( ! [X8: a,X9: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X8),X9)
=> ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X8) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X9) ) )
& ! [X10: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X10),X10)
=> ( ! [X11: b,X12: b,X13: b] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X12),X13)
& vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X11),X12) )
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X11),X13) )
& ! [X14: b,X15: b] :
( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X14),X15)
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X10),X15),X14) ) ) ) )
=> ! [X16: a,X17: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X16),X17)
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X16),vAPP(a,b,f,X16)),vAPP(a,b,g,X17)) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0)
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,g,X0)) )
=> ( ! [X0: a,X1: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1)
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,f,X1)) )
=> ( ( ! [X0: a,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X2)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X2) )
& ! [X0: a,X1: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X0) ) )
=> ( ( ! [X0: a,X1: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1)
=> ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X1) ) )
& ! [X0: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0)
=> ( ! [X3: b,X1: b,X2: b] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),X2)
& vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X3),X1) )
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X3),X2) )
& ! [X3: b,X1: b] :
( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X3),X1)
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),X3) ) ) ) )
=> ! [X0: a,X1: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1)
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,g,X1)) ) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ! [X0: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0)
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,g,X0)) )
=> ( ! [X0: a,X1: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1)
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,f,X1)) )
=> ( ( ! [X0: a,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X2)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X2) )
& ! [X0: a,X1: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X1),X0) ) )
=> ( ( ! [X0: a,X1: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1)
=> ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X1) ) )
& ! [X0: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X0)
=> ( ! [X3: b,X1: b,X2: b] :
( ( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),X2)
& vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X3),X1) )
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X3),X2) )
& ! [X3: b,X1: b] :
( vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X3),X1)
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),X1),X3) ) ) ) )
=> ! [X0: a,X1: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X0),X1)
=> vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X0),vAPP(a,b,f,X0)),vAPP(a,b,g,X1)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM509_pme) ).
thf(f117,plain,
spl2_11,
inference(avatar_split_clause,[],[f16,f115]) ).
thf(f16,plain,
! [X8: b,X9: b,X4: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X9),X8) )
| ( $true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X4),X8),X9) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X4),X4) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f106,plain,
spl2_10,
inference(avatar_split_clause,[],[f13,f104]) ).
thf(f13,plain,
! [X16: a,X15: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X15),vAPP(a,b,f,X15)),vAPP(a,b,f,X16)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X15),X16) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f102,plain,
spl2_9,
inference(avatar_split_clause,[],[f12,f100]) ).
thf(f12,plain,
! [X17: a] :
( ( $true = vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X17),vAPP(a,b,f,X17)),vAPP(a,b,g,X17)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X17),X17) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f94,plain,
spl2_8,
inference(avatar_split_clause,[],[f15,f92]) ).
thf(f15,plain,
! [X10: a,X11: a,X12: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X10),X12) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X11),X12) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X10),X11) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f90,plain,
( spl2_7
| ~ spl2_2
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f70,f64,f27,f87]) ).
thf(f70,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),sK0) )
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f67,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK1),sK0) )
| ~ spl2_2
| ~ spl2_4 ),
inference(superposition,[],[f65,f29]) ).
thf(f81,plain,
spl2_6,
inference(avatar_split_clause,[],[f18,f79]) ).
thf(f18,plain,
! [X2: a,X3: a] :
( ( vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X2) = vAPP(a,sTfun(b,sTfun(b,$o)),cQ,X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X2),X3) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f75,plain,
~ spl2_5,
inference(avatar_split_clause,[],[f20,f72]) ).
thf(f20,plain,
$true != vAPP(b,$o,vAPP(b,sTfun(b,$o),vAPP(a,sTfun(b,sTfun(b,$o)),cQ,sK0),vAPP(a,b,f,sK0)),vAPP(a,b,g,sK1)),
inference(cnf_transformation,[],[f11]) ).
thf(f66,plain,
spl2_4,
inference(avatar_split_clause,[],[f14,f64]) ).
thf(f14,plain,
! [X14: a,X13: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X14),X13) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,X13),X14) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f34,plain,
spl2_3,
inference(avatar_split_clause,[],[f4,f32]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f30,plain,
spl2_2,
inference(avatar_split_clause,[],[f19,f27]) ).
thf(f19,plain,
$true = vAPP(a,$o,vAPP(a,sTfun(a,$o),cP,sK0),sK1),
inference(cnf_transformation,[],[f11]) ).
thf(f25,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f3,f22]) ).
thf(f22,plain,
( spl2_1
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
thf(f3,plain,
$true != $false,
introduced(fool_axiom,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEV045^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 18:50:23 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (16492)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (16499)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)
% 0.13/0.36 % (16497)WARNING: value z3 for option sas not known
% 0.13/0.36 % (16498)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 % (16497)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)
% 0.13/0.36 % (16501)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)
% 0.13/0.36 % (16500)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)
% 0.13/0.36 % (16496)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36 % (16495)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36 % Exception at run slice level
% 0.13/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % (16501)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.38 % (16499)First to succeed.
% 0.20/0.38 % (16515)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.38 % (16516)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)
% 0.20/0.38 % (16517)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)
% 0.20/0.38 % (16515)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.38 % Exception at run slice level
% 0.20/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.38 % (16516)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.38 % (16499)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16492"
% 0.20/0.38 % (16499)Refutation found. Thanks to Tanya!
% 0.20/0.38 % SZS status Theorem for theBenchmark
% 0.20/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.39 % (16499)------------------------------
% 0.20/0.39 % (16499)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.39 % (16499)Termination reason: Refutation
% 0.20/0.39
% 0.20/0.39 % (16499)Memory used [KB]: 1117
% 0.20/0.39 % (16499)Time elapsed: 0.027 s
% 0.20/0.39 % (16499)Instructions burned: 94 (million)
% 0.20/0.39 % (16492)Success in time 0.035 s
%------------------------------------------------------------------------------