%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n025.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 5 06:58:55 PM UTC 2026
% Result : Theorem 1.82s 1.55s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 28
% Syntax : Number of formulae : 412 ( 24 unt; 0 typ; 25 def)
% Number of atoms : 9506 (1554 equ; 0 cnn)
% Maximal formula atoms : 24 ( 23 avg)
% Number of connectives : 15663 (2533 ~;3326 |; 294 &;8358 @)
% ( 25 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 218 ( 218 >; 0 *; 0 +; 0 <<)
% Number of symbols : 87 ( 83 usr; 49 con; 0-3 aty)
% (1121 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 2292 (1495 ^; 790 !; 7 ?;2292 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
d_unsorted: $tType ).
thf(func_def_0,type,
unsorted: $tType ).
thf(func_def_1,type,
irel: $i > $i > $o ).
thf(func_def_2,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
iatom: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
inot: ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
itrue: $i > $o ).
thf(func_def_10,type,
ifalse: $i > $o ).
thf(func_def_11,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_16,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
ivalid: ( $i > $o ) > $o ).
thf(func_def_18,type,
isatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_20,type,
iinvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
d_unsorted: $tType ).
thf(func_def_22,type,
d2unsorted: d_unsorted > $i ).
thf(func_def_23,type,
d_unsorted_0: d_unsorted ).
thf(func_def_41,type,
sK0: $i > d_unsorted ).
thf(func_def_43,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
sK3: $i > $o ).
thf(func_def_45,type,
sK4: $i > $o ).
thf(func_def_47,type,
sK6: $i > $i ).
thf(func_def_48,type,
sK7: $i > $i ).
thf(func_def_49,type,
sK8: $i > $i ).
thf(func_def_50,type,
sK9: $i > $i ).
thf(func_def_51,type,
sK10: $i > $i ).
thf(func_def_52,type,
sK11: $i > $i ).
thf(func_def_53,type,
sK12: $i > $i ).
thf(func_def_54,type,
sK13: $i > $i ).
thf(func_def_55,type,
sK14: $i > $i ).
thf(func_def_56,type,
sK15: $i > $i ).
thf(func_def_57,type,
sK16: $i > $i ).
thf(func_def_58,type,
sK17: $i > $i ).
thf(f3345,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2035,f2118,f2120,f2133,f2135,f2306,f2311,f2324,f2326,f2810,f2882,f2915,f2998,f3066,f3079,f3085,f3087,f3089,f3118,f3131,f3151,f3276,f3283,f3306,f3310,f3326,f3332,f3340,f3344]) ).
thf(f3344,plain,
( ~ spl1_1
| ~ spl1_169 ),
inference(avatar_contradiction_clause,[status(thm)],[f3343]) ).
thf(f3343,plain,
( $false
| ~ spl1_1
| ~ spl1_169 ),
inference(trivial_inequality_removal,[status(thm)],[f3342]) ).
thf(f3342,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_169 ),
inference(forward_demodulation,[status(thm)],[f2030,f3053]) ).
thf(f3053,plain,
( ! [X0: $i] :
( ( irel @ sK5 @ X0 )
= $false )
| ~ spl1_169 ),
inference(avatar_component_clause,[status(thm)],[f3052]) ).
thf(f3052,definition,
( spl1_169
<=> ! [X0: $i] :
( ( irel @ sK5 @ X0 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_169])],[avatar_definition]) ).
thf(f2030,plain,
( ( $true
= ( irel @ sK5 @ sK22 ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f2028]) ).
thf(f2028,definition,
( spl1_1
<=> ( $true
= ( irel @ sK5 @ sK22 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f3340,plain,
( ~ spl1_2
| ~ spl1_169 ),
inference(avatar_contradiction_clause,[status(thm)],[f3339]) ).
thf(f3339,plain,
( $false
| ~ spl1_2
| ~ spl1_169 ),
inference(trivial_inequality_removal,[status(thm)],[f3338]) ).
thf(f3338,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_169 ),
inference(backward_demodulation,[status(thm)],[f2959,f3053]) ).
thf(f2959,plain,
( ! [X0: $i] :
( ( irel @ sK5 @ X0 )
= $true )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f2034,f2945]) ).
thf(f2945,plain,
! [X0: $i,X1: $i] : ( X0 = X1 ),
inference(superposition,[status(thm)],[f41,f41]) ).
thf(f41,plain,
! [X1: $i] :
( ( d2unsorted @ d_unsorted_0 )
= X1 ),
inference(forward_demodulation,[status(thm)],[f36,f37]) ).
thf(f37,plain,
! [X0: d_unsorted] : ( d_unsorted_0 = X0 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ! [X1: $i] :
( ( d2unsorted @ ( sK0 @ X1 ) )
= X1 )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( X3 = X4 )
| ( ( d2unsorted @ X3 )
!= ( d2unsorted @ X4 ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( irel @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ( Y0 @ Y3 )
| ~ ( irel @ Y4 @ Y3 )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( ( Y0 @ Y4 )
| ~ ( irel @ Y7 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y3 @ Y8 )
| ( Y1 @ Y8 ) ) )
| ~ ( irel @ Y3 @ Y4 ) )
& ( ~ ( irel @ Y7 @ Y6 )
| ( Y1 @ Y5 )
| ~ ( irel @ Y6 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y6 @ Y8 )
| ( Y0 @ Y8 ) ) ) ) )
| ~ ( irel @ Y2 @ Y7 ) ) ) ) ) ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f13]) ).
thf(f13,plain,
! [X1: $i] :
( ? [X2: d_unsorted] :
( ( d2unsorted @ X2 )
= X1 )
=> ( ( d2unsorted @ ( sK0 @ X1 ) )
= X1 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ! [X1: $i] :
? [X2: d_unsorted] :
( ( d2unsorted @ X2 )
= X1 )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( X3 = X4 )
| ( ( d2unsorted @ X3 )
!= ( d2unsorted @ X4 ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( irel @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ( Y0 @ Y3 )
| ~ ( irel @ Y4 @ Y3 )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( ( Y0 @ Y4 )
| ~ ( irel @ Y7 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y3 @ Y8 )
| ( Y1 @ Y8 ) ) )
| ~ ( irel @ Y3 @ Y4 ) )
& ( ~ ( irel @ Y7 @ Y6 )
| ( Y1 @ Y5 )
| ~ ( irel @ Y6 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y6 @ Y8 )
| ( Y0 @ Y8 ) ) ) ) )
| ~ ( irel @ Y2 @ Y7 ) ) ) ) ) ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) )
& ! [X1: $i] :
? [X2: d_unsorted] :
( ( d2unsorted @ X2 )
= X1 )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( ( d2unsorted @ X3 )
= ( d2unsorted @ X4 ) )
=> ( X3 = X4 ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( irel @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ( Y0 @ Y3 )
| ~ ( irel @ Y4 @ Y3 )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( ( Y0 @ Y4 )
| ~ ( irel @ Y7 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y3 @ Y8 )
| ( Y1 @ Y8 ) ) )
| ~ ( irel @ Y3 @ Y4 ) )
& ( ~ ( irel @ Y7 @ Y6 )
| ( Y1 @ Y5 )
| ~ ( irel @ Y6 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y6 @ Y8 )
| ( Y0 @ Y8 ) ) ) ) )
| ~ ( irel @ Y2 @ Y7 ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ! [X1: $i] :
? [X2: d_unsorted] :
( ( d2unsorted @ X2 )
= X1 )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( irel @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ( Y0 @ Y3 )
| ~ ( irel @ Y4 @ Y3 )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( ( d2unsorted @ X3 )
= ( d2unsorted @ X4 ) )
=> ( X3 = X4 ) )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( ( Y0 @ Y4 )
| ~ ( irel @ Y7 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y3 @ Y8 )
| ( Y1 @ Y8 ) ) )
| ~ ( irel @ Y3 @ Y4 ) )
& ( ~ ( irel @ Y7 @ Y6 )
| ( Y1 @ Y5 )
| ~ ( irel @ Y6 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y6 @ Y8 )
| ( Y0 @ Y8 ) ) ) ) )
| ~ ( irel @ Y2 @ Y7 ) ) ) ) ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ! [X5: d_unsorted] : ( d_unsorted_0 = X5 )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ! [X16: $i] :
? [X17: d_unsorted] :
( ( d2unsorted @ X17 )
= X16 )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( irel @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ( Y0 @ Y3 )
| ~ ( irel @ Y4 @ Y3 )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ! [X42: d_unsorted,X43: d_unsorted] :
( ( ( d2unsorted @ X43 )
= ( d2unsorted @ X42 ) )
=> ( X42 = X43 ) )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( ( Y0 @ Y4 )
| ~ ( irel @ Y7 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y3 @ Y8 )
| ( Y1 @ Y8 ) ) )
| ~ ( irel @ Y3 @ Y4 ) )
& ( ~ ( irel @ Y7 @ Y6 )
| ( Y1 @ Y5 )
| ~ ( irel @ Y6 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y6 @ Y8 )
| ( Y0 @ Y8 ) ) ) ) )
| ~ ( irel @ Y2 @ Y7 ) ) ) ) ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( ( iand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ! [X3: $i] :
( ~ ( irel @ X2 @ X3 )
| ( X0 @ X3 ) )
& ! [X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( X1 @ X4 ) ) ) ) )
& ! [X5: d_unsorted] : ( d_unsorted_0 = X5 )
& ( ( ^ [X6: $i > $o,X7: $i] :
~ ! [X8: $i] :
( ~ ( irel @ X7 @ X8 )
| ( X6 @ X8 ) ) )
= inot )
& ( ( ^ [X9: $i > $o,X10: $i > $o,X11: $i] :
( ( X9 @ X11 )
& ( X10 @ X11 ) ) )
= mand )
& ( icountersatisfiable
= ( ^ [X12: $i > $o] :
~ ! [X13: $i] : ( X12 @ X13 ) ) )
& ( iinvalid
= ( ^ [X14: $i > $o] :
! [X15: $i] :
~ ( X14 @ X15 ) ) )
& ! [X16: $i] :
? [X17: d_unsorted] :
( ( d2unsorted @ X17 )
= X16 )
& ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
& ( ( ^ [X18: $i > $o,X19: $i > $o,X20: $i] :
( ! [X21: $i] :
( ~ ( irel @ X20 @ X21 )
| ( X19 @ X21 ) )
| ! [X22: $i] :
( ( X18 @ X22 )
| ~ ( irel @ X20 @ X22 ) ) ) )
= ior )
& ( iequiv
= ( ^ [X23: $i > $o,X24: $i > $o,X25: $i] :
( ! [X26: $i,X27: $i] :
( ~ ( irel @ X25 @ X26 )
| ~ ( irel @ X26 @ X27 )
| ( X23 @ X27 )
| ~ ! [X28: $i] :
( ( X24 @ X28 )
| ~ ( irel @ X26 @ X28 ) ) )
& ! [X29: $i,X30: $i] :
( ( X24 @ X29 )
| ~ ( irel @ X30 @ X29 )
| ~ ( irel @ X25 @ X30 )
| ~ ! [X31: $i] :
( ~ ( irel @ X30 @ X31 )
| ( X23 @ X31 ) ) ) ) ) )
& ( ( ^ [X32: $i > $o,X33: $i > $o,X34: $i] :
( ! [X35: $i] :
( ( X32 @ X35 )
| ~ ( irel @ X34 @ X35 ) )
| ~ ! [X36: $i] :
( ~ ( irel @ X34 @ X36 )
| ( X33 @ X36 ) ) ) )
= iimplied )
& ( ( ^ [X37: $i > $o,X38: $i > $o,X39: $i] :
( ~ ( X37 @ X39 )
| ( X38 @ X39 ) ) )
= mimplies )
& ( ( ^ [X40: $i > $o] :
! [X41: $i] : ( X40 @ X41 ) )
= ivalid )
& ! [X42: d_unsorted,X43: d_unsorted] :
( ( ( d2unsorted @ X43 )
= ( d2unsorted @ X42 ) )
=> ( X42 = X43 ) )
& ( ixor
= ( ^ [X44: $i > $o,X45: $i > $o,X46: $i] :
~ ! [X47: $i,X48: $i,X49: $i,X50: $i,X51: $i] :
( ~ ( irel @ X46 @ X47 )
| ( ( ~ ! [X52: $i] :
( ( X44 @ X52 )
| ~ ( irel @ X48 @ X52 ) )
| ~ ( irel @ X48 @ X49 )
| ( X45 @ X49 )
| ~ ( irel @ X47 @ X48 ) )
& ( ~ ( irel @ X51 @ X50 )
| ~ ! [X53: $i] :
( ( X45 @ X53 )
| ~ ( irel @ X51 @ X53 ) )
| ~ ( irel @ X47 @ X51 )
| ( X44 @ X50 ) ) ) ) ) )
& ( ( ^ [X54: $i > $o,X55: $i > $o,X56: $i] :
( ! [X57: $i] :
( ( X55 @ X57 )
| ~ ( irel @ X56 @ X57 ) )
| ~ ! [X58: $i] :
( ( X54 @ X58 )
| ~ ( irel @ X56 @ X58 ) ) ) )
= iimplies )
& ( mnot
= ( ^ [X59: $i > $o,X60: $i] :
~ ( X59 @ X60 ) ) )
& ( ( ^ [X61: $i > $o,X62: $i > $o,X63: $i] :
( ( X62 @ X63 )
| ( X61 @ X63 ) ) )
= mor )
& ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
& ( iatom
= ( ^ [X64: $i > $o,X65: $i] : ( X64 @ X65 ) ) )
& ( ( ^ [X66: $i > $o,X67: $i] :
! [X68: $i] :
( ~ ( irel @ X67 @ X68 )
| ( X66 @ X68 ) ) )
= mbox_s4 )
& ( isatisfiable
= ( ^ [X69: $i > $o] :
~ ! [X70: $i] :
~ ( X69 @ X70 ) ) )
& ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( iand
= ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X8 @ X5 ) )
& ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X9 @ X5 ) ) ) ) )
& ! [X1: d_unsorted] : ( d_unsorted_0 = X1 )
& ( ( ^ [X8: $i > $o,X7: $i] :
~ ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X8 @ X5 ) ) )
= inot )
& ( ( ^ [X4: $i > $o,X5: $i > $o,X0: $i] :
( ( X4 @ X0 )
& ( X5 @ X0 ) ) )
= mand )
& ( icountersatisfiable
= ( ^ [X18: $i > $o] :
~ ! [X19: $i] : ( X18 @ X19 ) ) )
& ( iinvalid
= ( ^ [X18: $i > $o] :
! [X19: $i] :
~ ( X18 @ X19 ) ) )
& ! [X0: $i] :
? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 )
& ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X9 @ X5 ) )
| ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) ) )
= ior )
& ( iequiv
= ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ! [X5: $i,X12: $i] :
( ~ ( irel @ X7 @ X5 )
| ~ ( irel @ X5 @ X12 )
| ( X8 @ X12 )
| ~ ! [X13: $i] :
( ( X9 @ X13 )
| ~ ( irel @ X5 @ X13 ) ) )
& ! [X10: $i,X5: $i] :
( ( X9 @ X10 )
| ~ ( irel @ X5 @ X10 )
| ~ ( irel @ X7 @ X5 )
| ~ ! [X11: $i] :
( ~ ( irel @ X5 @ X11 )
| ( X8 @ X11 ) ) ) ) ) )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) )
| ~ ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X9 @ X5 ) ) ) )
= iimplied )
& ( ( ^ [X0: $i > $o,X6: $i > $o,X7: $i] :
( ~ ( X0 @ X7 )
| ( X6 @ X7 ) ) )
= mimplies )
& ( ( ^ [X18: $i > $o] :
! [X19: $i] : ( X18 @ X19 ) )
= ivalid )
& ! [X3: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X2 )
= ( d2unsorted @ X3 ) )
=> ( X2 = X3 ) )
& ( ixor
= ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
~ ! [X5: $i,X14: $i,X15: $i,X17: $i,X16: $i] :
( ~ ( irel @ X7 @ X5 )
| ( ( ~ ! [X11: $i] :
( ( X8 @ X11 )
| ~ ( irel @ X14 @ X11 ) )
| ~ ( irel @ X14 @ X15 )
| ( X9 @ X15 )
| ~ ( irel @ X5 @ X14 ) )
& ( ~ ( irel @ X16 @ X17 )
| ~ ! [X13: $i] :
( ( X9 @ X13 )
| ~ ( irel @ X16 @ X13 ) )
| ~ ( irel @ X5 @ X16 )
| ( X8 @ X17 ) ) ) ) ) )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ! [X5: $i] :
( ( X9 @ X5 )
| ~ ( irel @ X7 @ X5 ) )
| ~ ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) ) )
= iimplies )
& ( mnot
= ( ^ [X4: $i > $o,X0: $i] :
~ ( X4 @ X0 ) ) )
& ( ( ^ [X4: $i > $o,X5: $i > $o,X0: $i] :
( ( X5 @ X0 )
| ( X4 @ X0 ) ) )
= mor )
& ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
& ( iatom
= ( ^ [X8: $i > $o,X7: $i] : ( X8 @ X7 ) ) )
& ( ( ^ [X8: $i > $o,X4: $i] :
! [X5: $i] :
( ~ ( irel @ X4 @ X5 )
| ( X8 @ X5 ) ) )
= mbox_s4 )
& ( isatisfiable
= ( ^ [X18: $i > $o] :
~ ! [X19: $i] :
~ ( X18 @ X19 ) ) )
& ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YfK2dOMluu/DTF2THF_2576.p',lcl696_1) ).
thf(f36,plain,
! [X1: $i] :
( ( d2unsorted @ ( sK0 @ X1 ) )
= X1 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f2034,plain,
( ( ( irel @ sK5 @ sK23 )
= $true )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f2032]) ).
thf(f2032,definition,
( spl1_2
<=> ( ( irel @ sK5 @ sK23 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f3332,plain,
( ~ spl1_22
| ~ spl1_49
| ~ spl1_50 ),
inference(avatar_contradiction_clause,[status(thm)],[f3331]) ).
thf(f3331,plain,
( $false
| ~ spl1_22
| ~ spl1_49
| ~ spl1_50 ),
inference(trivial_inequality_removal,[status(thm)],[f3330]) ).
thf(f3330,plain,
( ( $true = $false )
| ~ spl1_22
| ~ spl1_49
| ~ spl1_50 ),
inference(forward_demodulation,[status(thm)],[f2305,f3329]) ).
thf(f3329,plain,
( ! [X3: $i] :
( ( irel @ sK66 @ X3 )
= $false )
| ~ spl1_22
| ~ spl1_50 ),
inference(trivial_inequality_removal,[status(thm)],[f3328]) ).
thf(f3328,plain,
( ! [X3: $i] :
( ( ( irel @ sK66 @ X3 )
= $false )
| ( $true = $false ) )
| ~ spl1_22
| ~ spl1_50 ),
inference(forward_demodulation,[status(thm)],[f2310,f3092]) ).
thf(f3092,plain,
( ! [X0: $i] :
( ( sK4 @ X0 )
= $false )
| ~ spl1_22 ),
inference(superposition,[status(thm)],[f2144,f2945]) ).
thf(f2144,plain,
( ( ( sK4 @ sK20 )
= $false )
| ~ spl1_22 ),
inference(avatar_component_clause,[status(thm)],[f2142]) ).
thf(f2142,definition,
( spl1_22
<=> ( ( sK4 @ sK20 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_22])],[avatar_definition]) ).
thf(f2310,plain,
( ! [X3: $i] :
( ( $true
= ( sK4 @ X3 ) )
| ( ( irel @ sK66 @ X3 )
= $false ) )
| ~ spl1_50 ),
inference(avatar_component_clause,[status(thm)],[f2309]) ).
thf(f2309,definition,
( spl1_50
<=> ! [X3: $i] :
( ( ( irel @ sK66 @ X3 )
= $false )
| ( $true
= ( sK4 @ X3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_50])],[avatar_definition]) ).
thf(f2305,plain,
( ( ( irel @ sK66 @ sK65 )
= $true )
| ~ spl1_49 ),
inference(avatar_component_clause,[status(thm)],[f2303]) ).
thf(f2303,definition,
( spl1_49
<=> ( ( irel @ sK66 @ sK65 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_49])],[avatar_definition]) ).
thf(f3326,plain,
( ~ spl1_6
| ~ spl1_48
| ~ spl1_52 ),
inference(avatar_contradiction_clause,[status(thm)],[f3325]) ).
thf(f3325,plain,
( $false
| ~ spl1_6
| ~ spl1_48
| ~ spl1_52 ),
inference(trivial_inequality_removal,[status(thm)],[f3324]) ).
thf(f3324,plain,
( ( $true = $false )
| ~ spl1_6
| ~ spl1_48
| ~ spl1_52 ),
inference(forward_demodulation,[status(thm)],[f2300,f3320]) ).
thf(f3320,plain,
( ! [X2: $i] :
( ( irel @ sK63 @ X2 )
= $false )
| ~ spl1_6
| ~ spl1_52 ),
inference(trivial_inequality_removal,[status(thm)],[f3319]) ).
thf(f3319,plain,
( ! [X2: $i] :
( ( ( irel @ sK63 @ X2 )
= $false )
| ( $true = $false ) )
| ~ spl1_6
| ~ spl1_52 ),
inference(forward_demodulation,[status(thm)],[f2322,f3286]) ).
thf(f3286,plain,
( ! [X0: $i] :
( ( sK3 @ X0 )
= $false )
| ~ spl1_6 ),
inference(superposition,[status(thm)],[f2053,f2945]) ).
thf(f2053,plain,
( ( ( sK3 @ sK81 )
= $false )
| ~ spl1_6 ),
inference(avatar_component_clause,[status(thm)],[f2051]) ).
thf(f2051,definition,
( spl1_6
<=> ( ( sK3 @ sK81 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition]) ).
thf(f2322,plain,
( ! [X2: $i] :
( ( ( irel @ sK63 @ X2 )
= $false )
| ( $true
= ( sK3 @ X2 ) ) )
| ~ spl1_52 ),
inference(avatar_component_clause,[status(thm)],[f2321]) ).
thf(f2321,definition,
( spl1_52
<=> ! [X2: $i] :
( ( ( irel @ sK63 @ X2 )
= $false )
| ( $true
= ( sK3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_52])],[avatar_definition]) ).
thf(f2300,plain,
( ( $true
= ( irel @ sK63 @ sK64 ) )
| ~ spl1_48 ),
inference(avatar_component_clause,[status(thm)],[f2298]) ).
thf(f2298,definition,
( spl1_48
<=> ( $true
= ( irel @ sK63 @ sK64 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_48])],[avatar_definition]) ).
thf(f3310,plain,
( spl1_169
| ~ spl1_6
| ~ spl1_170 ),
inference(avatar_split_clause,[status(thm)],[f3295,f3077,f2051,f3052]) ).
thf(f3077,definition,
( spl1_170
<=> ! [X0: $i] :
( ( ( sK3 @ X0 )
= $true )
| ( ( irel @ sK5 @ X0 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl1_170])],[avatar_definition]) ).
thf(f3295,plain,
( ! [X0: $i] :
( ( irel @ sK5 @ X0 )
= $false )
| ~ spl1_6
| ~ spl1_170 ),
inference(trivial_inequality_removal,[status(thm)],[f3292]) ).
thf(f3292,plain,
( ! [X0: $i] :
( ( ( irel @ sK5 @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl1_6
| ~ spl1_170 ),
inference(backward_demodulation,[status(thm)],[f3078,f3286]) ).
thf(f3078,plain,
( ! [X0: $i] :
( ( ( irel @ sK5 @ X0 )
= $false )
| ( ( sK3 @ X0 )
= $true ) )
| ~ spl1_170 ),
inference(avatar_component_clause,[status(thm)],[f3077]) ).
thf(f3306,plain,
( ~ spl1_6
| ~ spl1_18
| ~ spl1_20 ),
inference(avatar_contradiction_clause,[status(thm)],[f3305]) ).
thf(f3305,plain,
( $false
| ~ spl1_6
| ~ spl1_18
| ~ spl1_20 ),
inference(trivial_inequality_removal,[status(thm)],[f3304]) ).
thf(f3304,plain,
( ( $true = $false )
| ~ spl1_6
| ~ spl1_18
| ~ spl1_20 ),
inference(backward_demodulation,[status(thm)],[f2116,f3297]) ).
thf(f3297,plain,
( ! [X2: $i] :
( ( irel @ sK77 @ X2 )
= $false )
| ~ spl1_6
| ~ spl1_20 ),
inference(trivial_inequality_removal,[status(thm)],[f3287]) ).
thf(f3287,plain,
( ! [X2: $i] :
( ( ( irel @ sK77 @ X2 )
= $false )
| ( $true = $false ) )
| ~ spl1_6
| ~ spl1_20 ),
inference(backward_demodulation,[status(thm)],[f2128,f3286]) ).
thf(f2128,plain,
( ! [X2: $i] :
( ( ( irel @ sK77 @ X2 )
= $false )
| ( $true
= ( sK3 @ X2 ) ) )
| ~ spl1_20 ),
inference(avatar_component_clause,[status(thm)],[f2127]) ).
thf(f2127,definition,
( spl1_20
<=> ! [X2: $i] :
( ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK77 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl1_20])],[avatar_definition]) ).
thf(f2116,plain,
( ( ( irel @ sK77 @ sK78 )
= $true )
| ~ spl1_18 ),
inference(avatar_component_clause,[status(thm)],[f2114]) ).
thf(f2114,definition,
( spl1_18
<=> ( ( irel @ sK77 @ sK78 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_18])],[avatar_definition]) ).
thf(f3283,plain,
( ~ spl1_15
| ~ spl1_17
| ~ spl1_22 ),
inference(avatar_contradiction_clause,[status(thm)],[f3282]) ).
thf(f3282,plain,
( $false
| ~ spl1_15
| ~ spl1_17
| ~ spl1_22 ),
inference(trivial_inequality_removal,[status(thm)],[f3281]) ).
thf(f3281,plain,
( ( $true = $false )
| ~ spl1_15
| ~ spl1_17
| ~ spl1_22 ),
inference(backward_demodulation,[status(thm)],[f2102,f3280]) ).
thf(f3280,plain,
( ! [X2: $i] :
( ( irel @ sK79 @ X2 )
= $false )
| ~ spl1_17
| ~ spl1_22 ),
inference(trivial_inequality_removal,[status(thm)],[f3279]) ).
thf(f3279,plain,
( ! [X2: $i] :
( ( ( irel @ sK79 @ X2 )
= $false )
| ( $true = $false ) )
| ~ spl1_17
| ~ spl1_22 ),
inference(forward_demodulation,[status(thm)],[f2111,f3092]) ).
thf(f2111,plain,
( ! [X2: $i] :
( ( ( irel @ sK79 @ X2 )
= $false )
| ( ( sK4 @ X2 )
= $true ) )
| ~ spl1_17 ),
inference(avatar_component_clause,[status(thm)],[f2110]) ).
thf(f2110,definition,
( spl1_17
<=> ! [X2: $i] :
( ( ( irel @ sK79 @ X2 )
= $false )
| ( ( sK4 @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1_17])],[avatar_definition]) ).
thf(f2102,plain,
( ( ( irel @ sK79 @ sK76 )
= $true )
| ~ spl1_15 ),
inference(avatar_component_clause,[status(thm)],[f2100]) ).
thf(f2100,definition,
( spl1_15
<=> ( ( irel @ sK79 @ sK76 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_15])],[avatar_definition]) ).
thf(f3276,plain,
~ spl1_168,
inference(avatar_contradiction_clause,[status(thm)],[f3275]) ).
thf(f3275,plain,
( $false
| ~ spl1_168 ),
inference(trivial_inequality_removal,[status(thm)],[f3274]) ).
thf(f3274,plain,
( ( $true = $false )
| ~ spl1_168 ),
inference(backward_demodulation,[status(thm)],[f21,f3273]) ).
thf(f3273,plain,
( ! [X0: $i] :
( ( irel @ X0 @ X0 )
= $false )
| ~ spl1_168 ),
inference(superposition,[status(thm)],[f3050,f2945]) ).
thf(f3050,plain,
( ( ( irel @ sK5 @ sK5 )
= $false )
| ~ spl1_168 ),
inference(avatar_component_clause,[status(thm)],[f3048]) ).
thf(f3048,definition,
( spl1_168
<=> ( ( irel @ sK5 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_168])],[avatar_definition]) ).
thf(f21,plain,
( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f3151,plain,
( spl1_169
| spl1_168
| spl1_6
| ~ spl1_22
| ~ spl1_160 ),
inference(avatar_split_clause,[status(thm)],[f3150,f2913,f2142,f2051,f3048,f3052]) ).
thf(f2913,definition,
( spl1_160
<=> ! [X5: $i,X7: $i,X8: $i] :
( ( ( sK3 @ ( sK10 @ X7 ) )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( $true
= ( sK4 @ X5 ) )
| ( ( irel @ X7 @ X5 )
= $false )
| ( ( irel @ X8 @ X7 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl1_160])],[avatar_definition]) ).
thf(f3150,plain,
( ! [X0: $i] :
( ( ( irel @ sK5 @ sK5 )
= $false )
| ( ( irel @ sK5 @ X0 )
= $false ) )
| spl1_6
| ~ spl1_22
| ~ spl1_160 ),
inference(trivial_inequality_removal,[status(thm)],[f3148]) ).
thf(f3148,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ sK5 @ sK5 )
= $false )
| ( ( irel @ sK5 @ X0 )
= $false ) )
| spl1_6
| ~ spl1_22
| ~ spl1_160 ),
inference(equality_factoring,[status(thm)],[f3144]) ).
thf(f3144,plain,
( ! [X8: $i,X7: $i,X5: $i] :
( ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ X7 @ X5 )
= $false )
| ( ( irel @ X8 @ X7 )
= $false ) )
| spl1_6
| ~ spl1_22
| ~ spl1_160 ),
inference(trivial_inequality_removal,[status(thm)],[f3143]) ).
thf(f3143,plain,
( ! [X8: $i,X7: $i,X5: $i] :
( ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ X7 @ X5 )
= $false )
| ( ( irel @ X8 @ X7 )
= $false )
| ( $true = $false ) )
| spl1_6
| ~ spl1_22
| ~ spl1_160 ),
inference(forward_demodulation,[status(thm)],[f3142,f3092]) ).
thf(f3142,plain,
( ! [X8: $i,X7: $i,X5: $i] :
( ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ X7 @ X5 )
= $false )
| ( $true
= ( sK4 @ X5 ) )
| ( ( irel @ X8 @ X7 )
= $false ) )
| spl1_6
| ~ spl1_160 ),
inference(subsumption_resolution,[status(thm)],[f2914,f3068]) ).
thf(f3068,plain,
( ! [X0: $i] :
( ( sK3 @ X0 )
!= $false )
| spl1_6 ),
inference(superposition,[status(thm)],[f2052,f2945]) ).
thf(f2052,plain,
( ( ( sK3 @ sK81 )
!= $false )
| spl1_6 ),
inference(avatar_component_clause,[status(thm)],[f2051]) ).
thf(f2914,plain,
( ! [X8: $i,X7: $i,X5: $i] :
( ( ( sK3 @ ( sK10 @ X7 ) )
= $false )
| ( ( irel @ X8 @ X7 )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( $true
= ( sK4 @ X5 ) )
| ( ( irel @ X7 @ X5 )
= $false ) )
| ~ spl1_160 ),
inference(avatar_component_clause,[status(thm)],[f2913]) ).
thf(f3131,plain,
( spl1_168
| spl1_169
| spl1_6
| ~ spl1_22
| ~ spl1_159 ),
inference(avatar_split_clause,[status(thm)],[f3130,f2910,f2142,f2051,f3052,f3048]) ).
thf(f2910,definition,
( spl1_159
<=> ! [X6: $i,X4: $i,X1: $i] :
( ( ( sK3 @ ( sK9 @ X4 ) )
= $false )
| ( ( sK4 @ X6 )
= $true )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X4 @ X6 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl1_159])],[avatar_definition]) ).
thf(f3130,plain,
( ! [X0: $i] :
( ( ( irel @ sK5 @ sK5 )
= $false )
| ( ( irel @ sK5 @ X0 )
= $false ) )
| spl1_6
| ~ spl1_22
| ~ spl1_159 ),
inference(trivial_inequality_removal,[status(thm)],[f3127]) ).
thf(f3127,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ sK5 @ X0 )
= $false )
| ( ( irel @ sK5 @ sK5 )
= $false ) )
| spl1_6
| ~ spl1_22
| ~ spl1_159 ),
inference(equality_factoring,[status(thm)],[f3112]) ).
thf(f3112,plain,
( ! [X1: $i,X6: $i,X4: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X4 @ X6 )
= $false ) )
| spl1_6
| ~ spl1_22
| ~ spl1_159 ),
inference(subsumption_resolution,[status(thm)],[f3111,f3068]) ).
thf(f3111,plain,
( ! [X1: $i,X6: $i,X4: $i] :
( ( ( sK3 @ ( sK9 @ X4 ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ X4 @ X6 )
= $false ) )
| ~ spl1_22
| ~ spl1_159 ),
inference(trivial_inequality_removal,[status(thm)],[f3100]) ).
thf(f3100,plain,
( ! [X1: $i,X6: $i,X4: $i] :
( ( ( irel @ X4 @ X6 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( sK3 @ ( sK9 @ X4 ) )
= $false )
| ( $true = $false )
| ( ( irel @ sK5 @ X1 )
= $false ) )
| ~ spl1_22
| ~ spl1_159 ),
inference(backward_demodulation,[status(thm)],[f2911,f3092]) ).
thf(f2911,plain,
( ! [X1: $i,X6: $i,X4: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( sK4 @ X6 )
= $true )
| ( ( irel @ X4 @ X6 )
= $false )
| ( ( sK3 @ ( sK9 @ X4 ) )
= $false ) )
| ~ spl1_159 ),
inference(avatar_component_clause,[status(thm)],[f2910]) ).
thf(f3118,plain,
( ~ spl1_11
| ~ spl1_22
| ~ spl1_41 ),
inference(avatar_contradiction_clause,[status(thm)],[f3117]) ).
thf(f3117,plain,
( $false
| ~ spl1_11
| ~ spl1_22
| ~ spl1_41 ),
inference(trivial_inequality_removal,[status(thm)],[f3113]) ).
thf(f3113,plain,
( ( $true = $false )
| ~ spl1_11
| ~ spl1_22
| ~ spl1_41 ),
inference(backward_demodulation,[status(thm)],[f3029,f3109]) ).
thf(f3109,plain,
( ! [X2: $i] :
( ( irel @ sK18 @ X2 )
= $false )
| ~ spl1_22
| ~ spl1_41 ),
inference(trivial_inequality_removal,[status(thm)],[f3095]) ).
thf(f3095,plain,
( ! [X2: $i] :
( ( ( irel @ sK18 @ X2 )
= $false )
| ( $true = $false ) )
| ~ spl1_22
| ~ spl1_41 ),
inference(backward_demodulation,[status(thm)],[f2265,f3092]) ).
thf(f2265,plain,
( ! [X2: $i] :
( ( ( irel @ sK18 @ X2 )
= $false )
| ( ( sK4 @ X2 )
= $true ) )
| ~ spl1_41 ),
inference(avatar_component_clause,[status(thm)],[f2264]) ).
thf(f2264,definition,
( spl1_41
<=> ! [X2: $i] :
( ( ( sK4 @ X2 )
= $true )
| ( ( irel @ sK18 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl1_41])],[avatar_definition]) ).
thf(f3029,plain,
( ! [X0: $i] :
( $true
= ( irel @ sK18 @ X0 ) )
| ~ spl1_11 ),
inference(superposition,[status(thm)],[f2085,f2945]) ).
thf(f2085,plain,
( ( $true
= ( irel @ sK18 @ sK19 ) )
| ~ spl1_11 ),
inference(avatar_component_clause,[status(thm)],[f2083]) ).
thf(f2083,definition,
( spl1_11
<=> ( $true
= ( irel @ sK18 @ sK19 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_11])],[avatar_definition]) ).
thf(f3089,plain,
( spl1_22
| ~ spl1_140 ),
inference(avatar_contradiction_clause,[status(thm)],[f3088]) ).
thf(f3088,plain,
( $false
| spl1_22
| ~ spl1_140 ),
inference(subsumption_resolution,[status(thm)],[f2809,f3027]) ).
thf(f3027,plain,
( ! [X0: $i] :
( ( sK4 @ X0 )
!= $false )
| spl1_22 ),
inference(superposition,[status(thm)],[f2143,f2945]) ).
thf(f2143,plain,
( ( ( sK4 @ sK20 )
!= $false )
| spl1_22 ),
inference(avatar_component_clause,[status(thm)],[f2142]) ).
thf(f2809,plain,
( ( ( sK4 @ sK28 )
= $false )
| ~ spl1_140 ),
inference(avatar_component_clause,[status(thm)],[f2807]) ).
thf(f2807,definition,
( spl1_140
<=> ( ( sK4 @ sK28 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_140])],[avatar_definition]) ).
thf(f3087,plain,
( spl1_6
| ~ spl1_135 ),
inference(avatar_contradiction_clause,[status(thm)],[f3086]) ).
thf(f3086,plain,
( $false
| spl1_6
| ~ spl1_135 ),
inference(subsumption_resolution,[status(thm)],[f2782,f3068]) ).
thf(f2782,plain,
( ( ( sK3 @ sK24 )
= $false )
| ~ spl1_135 ),
inference(avatar_component_clause,[status(thm)],[f2780]) ).
thf(f2780,definition,
( spl1_135
<=> ( ( sK3 @ sK24 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_135])],[avatar_definition]) ).
thf(f3085,plain,
( spl1_6
| ~ spl1_86 ),
inference(avatar_contradiction_clause,[status(thm)],[f3084]) ).
thf(f3084,plain,
( $false
| spl1_6
| ~ spl1_86 ),
inference(subsumption_resolution,[status(thm)],[f3081,f3068]) ).
thf(f3081,plain,
( ! [X0: $i] :
( ( sK3 @ X0 )
= $false )
| ~ spl1_86 ),
inference(superposition,[status(thm)],[f2501,f2945]) ).
thf(f2501,plain,
( ( $false
= ( sK3 @ sK19 ) )
| ~ spl1_86 ),
inference(avatar_component_clause,[status(thm)],[f2499]) ).
thf(f2499,definition,
( spl1_86
<=> ( $false
= ( sK3 @ sK19 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_86])],[avatar_definition]) ).
thf(f3079,plain,
( spl1_170
| spl1_168
| spl1_22
| ~ spl1_151 ),
inference(avatar_split_clause,[status(thm)],[f3075,f2880,f2142,f3048,f3077]) ).
thf(f2880,definition,
( spl1_151
<=> ! [X4: $i,X2: $i,X8: $i] :
( ( ( sK3 @ X4 )
= $true )
| ( ( sK4 @ ( sK12 @ X2 ) )
= $false )
| ( ( irel @ X8 @ X2 )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl1_151])],[avatar_definition]) ).
thf(f3075,plain,
( ! [X0: $i] :
( ( ( irel @ sK5 @ sK5 )
= $false )
| ( ( sK3 @ X0 )
= $true )
| ( ( irel @ sK5 @ X0 )
= $false ) )
| spl1_22
| ~ spl1_151 ),
inference(trivial_inequality_removal,[status(thm)],[f3073]) ).
thf(f3073,plain,
( ! [X0: $i] :
( ( ( irel @ sK5 @ X0 )
= $false )
| ( ( sK3 @ X0 )
= $true )
| ( $false != $false )
| ( ( irel @ sK5 @ sK5 )
= $false ) )
| spl1_22
| ~ spl1_151 ),
inference(equality_factoring,[status(thm)],[f3067]) ).
thf(f3067,plain,
( ! [X2: $i,X8: $i,X4: $i] :
( ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( sK3 @ X4 )
= $true )
| ( ( irel @ X8 @ X2 )
= $false ) )
| spl1_22
| ~ spl1_151 ),
inference(subsumption_resolution,[status(thm)],[f2881,f3027]) ).
thf(f2881,plain,
( ! [X2: $i,X8: $i,X4: $i] :
( ( ( irel @ X8 @ X2 )
= $false )
| ( ( sK3 @ X4 )
= $true )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( sK4 @ ( sK12 @ X2 ) )
= $false )
| ( ( irel @ X2 @ X4 )
= $false ) )
| ~ spl1_151 ),
inference(avatar_component_clause,[status(thm)],[f2880]) ).
thf(f3066,plain,
( spl1_168
| spl1_169
| ~ spl1_6
| spl1_22
| ~ spl1_150 ),
inference(avatar_split_clause,[status(thm)],[f3064,f2877,f2142,f2051,f3052,f3048]) ).
thf(f2877,definition,
( spl1_150
<=> ! [X1: $i,X7: $i,X3: $i] :
( ( ( irel @ X1 @ X7 )
= $false )
| ( ( sK4 @ ( sK14 @ X7 ) )
= $false )
| ( $true
= ( sK3 @ X3 ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ X7 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl1_150])],[avatar_definition]) ).
thf(f3064,plain,
( ! [X0: $i] :
( ( ( irel @ sK5 @ X0 )
= $false )
| ( ( irel @ sK5 @ sK5 )
= $false ) )
| ~ spl1_6
| spl1_22
| ~ spl1_150 ),
inference(trivial_inequality_removal,[status(thm)],[f3063]) ).
thf(f3063,plain,
( ! [X0: $i] :
( ( ( irel @ sK5 @ X0 )
= $false )
| ( $false != $false )
| ( ( irel @ sK5 @ sK5 )
= $false ) )
| ~ spl1_6
| spl1_22
| ~ spl1_150 ),
inference(equality_factoring,[status(thm)],[f3059]) ).
thf(f3059,plain,
( ! [X3: $i,X1: $i,X7: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ X7 @ X3 )
= $false )
| ( ( irel @ X1 @ X7 )
= $false ) )
| ~ spl1_6
| spl1_22
| ~ spl1_150 ),
inference(trivial_inequality_removal,[status(thm)],[f3058]) ).
thf(f3058,plain,
( ! [X3: $i,X1: $i,X7: $i] :
( ( ( irel @ X7 @ X3 )
= $false )
| ( $true = $false )
| ( ( irel @ X1 @ X7 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false ) )
| ~ spl1_6
| spl1_22
| ~ spl1_150 ),
inference(forward_demodulation,[status(thm)],[f3057,f2960]) ).
thf(f2960,plain,
( ! [X0: $i] :
( ( sK3 @ X0 )
= $false )
| ~ spl1_6 ),
inference(superposition,[status(thm)],[f2053,f2945]) ).
thf(f3057,plain,
( ! [X3: $i,X1: $i,X7: $i] :
( ( ( irel @ X7 @ X3 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( sK3 @ X3 ) )
| ( ( irel @ X1 @ X7 )
= $false ) )
| spl1_22
| ~ spl1_150 ),
inference(subsumption_resolution,[status(thm)],[f2878,f3027]) ).
thf(f2878,plain,
( ! [X3: $i,X1: $i,X7: $i] :
( ( ( irel @ X1 @ X7 )
= $false )
| ( $true
= ( sK3 @ X3 ) )
| ( ( irel @ X7 @ X3 )
= $false )
| ( ( sK4 @ ( sK14 @ X7 ) )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false ) )
| ~ spl1_150 ),
inference(avatar_component_clause,[status(thm)],[f2877]) ).
thf(f2998,plain,
( ~ spl1_6
| ~ spl1_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f2997]) ).
thf(f2997,plain,
( $false
| ~ spl1_6
| ~ spl1_12 ),
inference(trivial_inequality_removal,[status(thm)],[f2985]) ).
thf(f2985,plain,
( ( $true = $false )
| ~ spl1_6
| ~ spl1_12 ),
inference(backward_demodulation,[status(thm)],[f21,f2983]) ).
thf(f2983,plain,
( ! [X0: $i,X1: $i] :
( ( irel @ X0 @ X1 )
= $false )
| ~ spl1_6
| ~ spl1_12 ),
inference(trivial_inequality_removal,[status(thm)],[f2982]) ).
thf(f2982,plain,
( ! [X0: $i,X1: $i] :
( ( ( irel @ X0 @ X1 )
= $false )
| ( $true = $false ) )
| ~ spl1_6
| ~ spl1_12 ),
inference(forward_demodulation,[status(thm)],[f2957,f2960]) ).
thf(f2957,plain,
( ! [X0: $i,X1: $i] :
( ( ( irel @ X0 @ X1 )
= $false )
| ( $true
= ( sK3 @ X1 ) ) )
| ~ spl1_12 ),
inference(superposition,[status(thm)],[f2088,f2945]) ).
thf(f2088,plain,
( ! [X1: $i] :
( ( ( irel @ sK21 @ X1 )
= $false )
| ( $true
= ( sK3 @ X1 ) ) )
| ~ spl1_12 ),
inference(avatar_component_clause,[status(thm)],[f2087]) ).
thf(f2087,definition,
( spl1_12
<=> ! [X1: $i] :
( ( ( irel @ sK21 @ X1 )
= $false )
| ( $true
= ( sK3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_12])],[avatar_definition]) ).
thf(f2915,plain,
( spl1_159
| spl1_160 ),
inference(avatar_split_clause,[status(thm)],[f126,f2913,f2910]) ).
thf(f126,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( sK3 @ ( sK10 @ X7 ) )
= $false )
| ( ( irel @ X8 @ X7 )
= $false )
| ( ( sK3 @ ( sK9 @ X4 ) )
= $false )
| ( ( irel @ X4 @ X6 )
= $false )
| ( ( irel @ X7 @ X5 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( sK4 @ X5 ) )
| ( ( sK4 @ X6 )
= $true )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f125]) ).
thf(f125,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( sK4 @ X5 ) )
| ( ( ~ ( irel @ X7 @ ( sK10 @ X7 ) )
| ( sK3 @ ( sK10 @ X7 ) ) )
= $false )
| ( ( sK3 @ ( sK9 @ X4 ) )
= $false )
| ( ( sK4 @ X6 )
= $true )
| ( ( irel @ X7 @ X5 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X4 @ X6 )
= $false )
| ( ( irel @ X8 @ X7 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f124]) ).
thf(f124,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( sK3 @ ( sK9 @ X4 ) )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( sK4 @ X5 ) )
| ( ( sK4 @ X6 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) )
@ ( sK10 @ X7 ) )
= $false )
| ( ( irel @ X7 @ X5 )
= $false )
| ( ( irel @ X8 @ X7 )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ X4 @ X6 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f123]) ).
thf(f123,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X8 @ X7 )
= $false )
| ( $true
= ( sK4 @ X5 ) )
| ( ( sK4 @ X6 )
= $true )
| ( ( sK3 @ ( sK9 @ X4 ) )
= $false )
| ( ( irel @ X4 @ X6 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ X7 @ X5 )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( sK3 @ ( sK9 @ X4 ) )
= $false )
| ( $true
= ( ~ ( irel @ X8 @ X7 ) ) )
| ( ( irel @ X4 @ X6 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( sK4 @ X5 ) )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ X7 @ X5 )
= $false )
| ( ( sK4 @ X6 )
= $true )
| ( ( irel @ sK5 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f121]) ).
thf(f121,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ X7 @ X5 )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( $true
= ( sK4 @ X5 ) )
| ( ( sK4 @ X6 )
= $true )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X4 @ X6 )
= $false )
| ( ( sK3 @ ( sK9 @ X4 ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( irel @ X8 @ X7 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f120]) ).
thf(f120,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( sK4 @ X5 ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ X7 @ X5 )
= $false )
| ( $true
= ( ~ ( irel @ X4 @ X6 ) ) )
| ( $true
= ( ~ ( irel @ X8 @ X7 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( ( sK4 @ X6 )
= $true )
| ( ( sK3 @ ( sK9 @ X4 ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f118]) ).
thf(f118,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X7 @ X5 )
= $false )
| ( ( ( sK3 @ ( sK9 @ X4 ) )
| ~ ( irel @ X4 @ ( sK9 @ X4 ) ) )
= $false )
| ( ( sK4 @ X6 )
= $true )
| ( $true
= ( ~ ( irel @ X8 @ X7 ) ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( ~ ( irel @ X4 @ X6 ) ) )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( $true
= ( sK4 @ X5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f117]) ).
thf(f117,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( sK4 @ X6 )
= $true )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( ~ ( irel @ X7 @ X5 ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( sK4 @ X5 ) )
| ( ( ( sK3 @ ( sK9 @ X4 ) )
| ~ ( irel @ X4 @ ( sK9 @ X4 ) ) )
= $false )
| ( $true
= ( ~ ( irel @ X4 @ X6 ) ) )
| ( $true
= ( ~ ( irel @ X8 @ X7 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f116]) ).
thf(f116,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( irel @ sK5 @ X8 )
= $false )
| ( $true
= ( sK4 @ X5 ) )
| ( $true
= ( ~ ( irel @ X8 @ X7 ) ) )
| ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) )
@ ( sK9 @ X4 ) )
= $false )
| ( ( ~ ( irel @ X7 @ X5 ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( sK4 @ X6 )
= $true )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( ~ ( irel @ X4 @ X6 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f115]) ).
thf(f115,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( sK4 @ X6 )
= $true )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( $true
= ( sK4 @ X5 ) )
| ( ( ~ ( irel @ X7 @ X5 ) )
= $true )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( ~ ( irel @ X8 @ X7 ) ) )
| ( $true
= ( ~ ( irel @ X4 @ X6 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f114]) ).
thf(f114,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( ~ ( irel @ X8 @ X7 )
| ( sK4 @ X5 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
= $false )
| ( ( ~ ( irel @ X7 @ X5 ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( irel @ X4 @ X6 ) ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( sK4 @ X6 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f113,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( irel @ X8 @ X7 )
| ( sK4 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( $true
= ( ~ ( irel @ X4 @ X6 ) ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( sK4 @ X6 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f112]) ).
thf(f112,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( irel @ X4 @ X6 ) ) )
| ( $true
= ( ~ ( irel @ X8 @ X7 )
| ( sK4 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( sK4 @ X6 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( irel @ sK5 @ X8 )
= $false )
| ( $true
= ( ~ ( irel @ X8 @ X7 )
| ( sK4 @ X5 )
| ~ ( irel @ X7 @ X5 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( ( sK4 @ X6 )
= $true )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( irel @ X4 @ X6 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( irel @ X1 @ X4 ) ) )
| ( $true
= ( ~ ( irel @ X4 @ X6 ) ) )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( $true
= ( ~ ( irel @ X8 @ X7 )
| ( sK4 @ X5 )
| ~ ( irel @ X7 @ X5 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( sK4 @ X6 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X1 @ X4 ) ) )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( ~ ( irel @ X8 @ X7 )
| ( sK4 @ X5 )
| ~ ( irel @ X7 @ X5 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( ( sK4 @ X6 )
= $true )
| ( $true
= ( ~ ( irel @ X4 @ X6 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
! [X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X1 @ X4 )
| ~ ( irel @ X4 @ X6 ) )
= $true )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( sK4 @ X6 )
= $true )
| ( $true
= ( ~ ( irel @ X8 @ X7 )
| ( sK4 @ X5 )
| ~ ( irel @ X7 @ X5 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( ( ( sK3 @ X3 )
| ~ ( irel @ X8 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( irel @ X2 @ X3 ) )
& ( ~ ( irel @ X8 @ X7 )
| ( sK4 @ X5 )
| ~ ( irel @ X7 @ X5 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X1 @ X4 )
| ~ ( irel @ X4 @ X6 ) )
= $true )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( sK4 @ X6 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( irel @ sK5 @ X8 ) ) )
| ( ( sK4 @ X6 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X1 @ X4 )
| ~ ( irel @ X4 @ X6 ) )
= $true )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( ( ( sK3 @ X3 )
| ~ ( irel @ X8 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( irel @ X2 @ X3 ) )
& ( ~ ( irel @ X8 @ X7 )
| ( sK4 @ X5 )
| ~ ( irel @ X7 @ X5 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( ( ( ( sK3 @ X3 )
| ~ ( irel @ X8 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( irel @ X2 @ X3 ) )
& ( ~ ( irel @ X8 @ X7 )
| ( sK4 @ X5 )
| ~ ( irel @ X7 @ X5 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ~ ( irel @ sK5 @ X8 ) )
= $true )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X1 @ X4 )
| ~ ( irel @ X4 @ X6 ) )
= $true )
| ( ( sK4 @ X6 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( ( sK4 @ X6 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X1 @ X4 )
| ~ ( irel @ X4 @ X6 ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( ( ( sK3 @ X3 )
| ~ ( irel @ Y0 @ X2 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ X2 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( irel @ X2 @ X3 ) )
& ( ~ ( irel @ Y0 @ X7 )
| ( sK4 @ X5 )
| ~ ( irel @ X7 @ X5 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ X7 @ Y1 )
| ( sK3 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) )
@ X8 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ( sK3 @ X3 )
| ~ ( irel @ Y0 @ X2 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ X2 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( irel @ X2 @ X3 ) )
& ( ~ ( irel @ Y0 @ X7 )
| ( sK4 @ X5 )
| ~ ( irel @ X7 @ X5 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ X7 @ Y1 )
| ( sK3 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $true )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X1 @ X4 )
| ~ ( irel @ X4 @ X6 ) )
= $true )
| ( ( sK4 @ X6 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X1 @ X4 )
| ~ ( irel @ X4 @ X6 ) )
= $true )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( sK4 @ X6 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK3 @ X3 )
| ~ ( irel @ Y1 @ X2 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ X2 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ~ ( irel @ X2 @ X3 ) )
& ( ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ X5 )
| ~ ( irel @ Y0 @ X5 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) )
@ X7 ) ) ),
inference(pi_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK3 @ X3 )
| ~ ( irel @ Y1 @ X2 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ X2 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ~ ( irel @ X2 @ X3 ) )
& ( ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ X5 )
| ~ ( irel @ Y0 @ X5 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X1 @ X4 )
| ~ ( irel @ X4 @ X6 ) )
= $true )
| ( ( sK4 @ X6 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X1 @ X4 )
| ~ ( irel @ X4 @ X6 )
| ( sK4 @ X6 ) )
= $true )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK3 @ X3 )
| ~ ( irel @ Y1 @ X2 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ X2 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ~ ( irel @ X2 @ X3 ) )
& ( ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ X5 )
| ~ ( irel @ Y0 @ X5 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X1 @ X4 )
| ~ ( irel @ X4 @ Y0 )
| ( sK4 @ Y0 ) )
@ X6 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK3 @ X3 )
| ~ ( irel @ Y1 @ X2 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ X2 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ~ ( irel @ X2 @ X3 ) )
& ( ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ X5 )
| ~ ( irel @ Y0 @ X5 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X1 @ X4 )
| ~ ( irel @ X4 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK3 @ X3 )
| ~ ( irel @ Y1 @ X2 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ X2 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ~ ( irel @ X2 @ X3 ) )
& ( ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ X5 )
| ~ ( irel @ Y0 @ X5 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X1 @ X4 )
| ~ ( irel @ X4 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK3 @ X3 )
| ~ ( irel @ Y2 @ X2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ X2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ~ ( irel @ X2 @ X3 ) )
& ( ~ ( irel @ Y2 @ Y1 )
| ( sK4 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y1 @ Y3 )
| ( sK3 @ Y3 ) ) ) ) )
| ~ ( irel @ sK5 @ Y2 ) ) ) )
@ X5 ) )
| ( ( irel @ sK5 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK3 @ X3 )
| ~ ( irel @ Y2 @ X2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ X2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ~ ( irel @ X2 @ X3 ) )
& ( ~ ( irel @ Y2 @ Y1 )
| ( sK4 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y1 @ Y3 )
| ( sK3 @ Y3 ) ) ) ) )
| ~ ( irel @ sK5 @ Y2 ) ) ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X1 @ X4 )
| ~ ( irel @ X4 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ X1 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
@ X4 ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK3 @ X3 )
| ~ ( irel @ Y2 @ X2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ X2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ~ ( irel @ X2 @ X3 ) )
& ( ~ ( irel @ Y2 @ Y1 )
| ( sK4 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y1 @ Y3 )
| ( sK3 @ Y3 ) ) ) ) )
| ~ ( irel @ sK5 @ Y2 ) ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ X1 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK3 @ X3 )
| ~ ( irel @ Y2 @ X2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ X2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ~ ( irel @ X2 @ X3 ) )
& ( ~ ( irel @ Y2 @ Y1 )
| ( sK4 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y1 @ Y3 )
| ( sK3 @ Y3 ) ) ) ) )
| ~ ( irel @ sK5 @ Y2 ) ) ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK5 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK3 @ X3 )
| ~ ( irel @ Y2 @ X2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ X2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ~ ( irel @ X2 @ X3 ) )
& ( ~ ( irel @ Y2 @ Y1 )
| ( sK4 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y1 @ Y3 )
| ( sK3 @ Y3 ) ) ) ) )
| ~ ( irel @ sK5 @ Y2 ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ X1 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK5 @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ( sK3 @ Y0 )
| ~ ( irel @ Y3 @ X2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ X2 @ Y4 )
| ( sK4 @ Y4 ) ) )
| ~ ( irel @ X2 @ Y0 ) )
& ( ~ ( irel @ Y3 @ Y2 )
| ( sK4 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y2 @ Y4 )
| ( sK3 @ Y4 ) ) ) ) )
| ~ ( irel @ sK5 @ Y3 ) ) ) ) )
@ X3 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ X1 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ( sK3 @ Y0 )
| ~ ( irel @ Y3 @ X2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ X2 @ Y4 )
| ( sK4 @ Y4 ) ) )
| ~ ( irel @ X2 @ Y0 ) )
& ( ~ ( irel @ Y3 @ Y2 )
| ( sK4 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y2 @ Y4 )
| ( sK3 @ Y4 ) ) ) ) )
| ~ ( irel @ sK5 @ Y3 ) ) ) ) ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ X1 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ X1 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ X1 @ Y1 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ( sK3 @ Y0 )
| ~ ( irel @ Y3 @ X2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ X2 @ Y4 )
| ( sK4 @ Y4 ) ) )
| ~ ( irel @ X2 @ Y0 ) )
& ( ~ ( irel @ Y3 @ Y2 )
| ( sK4 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y2 @ Y4 )
| ( sK3 @ Y4 ) ) ) ) )
| ~ ( irel @ sK5 @ Y3 ) ) ) ) ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK5 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( ( sK3 @ Y1 )
| ~ ( irel @ Y4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y0 @ Y5 )
| ( sK4 @ Y5 ) ) )
| ~ ( irel @ Y0 @ Y1 ) )
& ( ~ ( irel @ Y4 @ Y3 )
| ( sK4 @ Y2 )
| ~ ( irel @ Y3 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( sK3 @ Y5 ) ) ) ) )
| ~ ( irel @ sK5 @ Y4 ) ) ) ) ) )
@ X2 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ X1 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ X1 @ Y1 ) ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( ( sK3 @ Y1 )
| ~ ( irel @ Y4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y0 @ Y5 )
| ( sK4 @ Y5 ) ) )
| ~ ( irel @ Y0 @ Y1 ) )
& ( ~ ( irel @ Y4 @ Y3 )
| ( sK4 @ Y2 )
| ~ ( irel @ Y3 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( sK3 @ Y5 ) ) ) ) )
| ~ ( irel @ sK5 @ Y4 ) ) ) ) ) ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ X1 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ X1 @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: $i] :
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ X1 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ X1 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ X1 ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( ( sK3 @ Y1 )
| ~ ( irel @ Y4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y0 @ Y5 )
| ( sK4 @ Y5 ) ) )
| ~ ( irel @ Y0 @ Y1 ) )
& ( ~ ( irel @ Y4 @ Y3 )
| ( sK4 @ Y2 )
| ~ ( irel @ Y3 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( sK3 @ Y5 ) ) ) ) )
| ~ ( irel @ sK5 @ Y4 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( ( sK3 @ Y1 )
| ~ ( irel @ Y4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y0 @ Y5 )
| ( sK4 @ Y5 ) ) )
| ~ ( irel @ Y0 @ Y1 ) )
& ( ~ ( irel @ Y4 @ Y3 )
| ( sK4 @ Y2 )
| ~ ( irel @ Y3 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( sK3 @ Y5 ) ) ) ) )
| ~ ( irel @ sK5 @ Y4 ) ) ) ) ) ) ) )
= $false )
| ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ X1 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ X1 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ X1 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) )
@ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( ( sK3 @ Y1 )
| ~ ( irel @ Y4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y0 @ Y5 )
| ( sK4 @ Y5 ) ) )
| ~ ( irel @ Y0 @ Y1 ) )
& ( ~ ( irel @ Y4 @ Y3 )
| ( sK4 @ Y2 )
| ~ ( irel @ Y3 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( sK3 @ Y5 ) ) ) ) )
| ~ ( irel @ sK5 @ Y4 ) ) ) ) ) ) ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( ( sK3 @ Y1 )
| ~ ( irel @ Y4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y0 @ Y5 )
| ( sK4 @ Y5 ) ) )
| ~ ( irel @ Y0 @ Y1 ) )
& ( ~ ( irel @ Y4 @ Y3 )
| ( sK4 @ Y2 )
| ~ ( irel @ Y3 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( sK3 @ Y5 ) ) ) ) )
| ~ ( irel @ sK5 @ Y4 ) ) ) ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( ( sK3 @ Y1 )
| ~ ( irel @ Y4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y0 @ Y5 )
| ( sK4 @ Y5 ) ) )
| ~ ( irel @ Y0 @ Y1 ) )
& ( ~ ( irel @ Y4 @ Y3 )
| ( sK4 @ Y2 )
| ~ ( irel @ Y3 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( sK3 @ Y5 ) ) ) ) )
| ~ ( irel @ sK5 @ Y4 ) ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( ( sK3 @ Y1 )
| ~ ( irel @ Y4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y0 @ Y5 )
| ( sK4 @ Y5 ) ) )
| ~ ( irel @ Y0 @ Y1 ) )
& ( ~ ( irel @ Y4 @ Y3 )
| ( sK4 @ Y2 )
| ~ ( irel @ Y3 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( sK3 @ Y5 ) ) ) ) )
| ~ ( irel @ sK5 @ Y4 ) ) ) ) ) ) ) )
!= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( sK3 @ Y4 )
| ~ ( irel @ Y2 @ Y4 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ( sK4 @ Y4 ) ) )
| ( sK3 @ Y2 )
| ~ ( irel @ Y3 @ Y2 )
| ~ ( irel @ Y1 @ Y3 ) ) ) ) )
| ~ ( irel @ Y0 @ Y1 ) ) )
@ sK5 )
!= ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( ( sK3 @ Y2 )
| ~ ( irel @ Y5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y1 @ Y6 )
| ( sK4 @ Y6 ) ) )
| ~ ( irel @ Y1 @ Y2 ) )
& ( ~ ( irel @ Y5 @ Y4 )
| ( sK4 @ Y3 )
| ~ ( irel @ Y4 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y4 @ Y6 )
| ( sK3 @ Y6 ) ) ) ) )
| ~ ( irel @ Y0 @ Y5 ) ) ) ) ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( sK3 @ Y4 )
| ~ ( irel @ Y2 @ Y4 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ( sK4 @ Y4 ) ) )
| ( sK3 @ Y2 )
| ~ ( irel @ Y3 @ Y2 )
| ~ ( irel @ Y1 @ Y3 ) ) ) ) )
| ~ ( irel @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( ( sK3 @ Y2 )
| ~ ( irel @ Y5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y1 @ Y6 )
| ( sK4 @ Y6 ) ) )
| ~ ( irel @ Y1 @ Y2 ) )
& ( ~ ( irel @ Y5 @ Y4 )
| ( sK4 @ Y3 )
| ~ ( irel @ Y4 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y4 @ Y6 )
| ( sK3 @ Y6 ) ) ) ) )
| ~ ( irel @ Y0 @ Y5 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( sK3 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( irel @ Y3 @ Y4 )
| ( Y0 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ( sK3 @ Y3 )
| ~ ( irel @ Y4 @ Y3 )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) )
| ~ ( irel @ Y1 @ Y2 ) ) )
@ sK4 )
!= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( ( sK3 @ Y3 )
| ~ ( irel @ Y6 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( ~ ( irel @ Y2 @ Y7 )
| ( Y0 @ Y7 ) ) )
| ~ ( irel @ Y2 @ Y3 ) )
& ( ~ ( irel @ Y6 @ Y5 )
| ( Y0 @ Y4 )
| ~ ( irel @ Y5 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( ~ ( irel @ Y5 @ Y7 )
| ( sK3 @ Y7 ) ) ) ) )
| ~ ( irel @ Y1 @ Y6 ) ) ) ) ) ) )
@ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( sK3 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( irel @ Y3 @ Y4 )
| ( Y0 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ( sK3 @ Y3 )
| ~ ( irel @ Y4 @ Y3 )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) )
| ~ ( irel @ Y1 @ Y2 ) ) ) )
!= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( ( sK3 @ Y3 )
| ~ ( irel @ Y6 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( ~ ( irel @ Y2 @ Y7 )
| ( Y0 @ Y7 ) ) )
| ~ ( irel @ Y2 @ Y3 ) )
& ( ~ ( irel @ Y6 @ Y5 )
| ( Y0 @ Y4 )
| ~ ( irel @ Y5 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( ~ ( irel @ Y5 @ Y7 )
| ( sK3 @ Y7 ) ) ) ) )
| ~ ( irel @ Y1 @ Y6 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( ( Y0 @ Y4 )
| ~ ( irel @ Y7 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y3 @ Y8 )
| ( Y1 @ Y8 ) ) )
| ~ ( irel @ Y3 @ Y4 ) )
& ( ~ ( irel @ Y7 @ Y6 )
| ( Y1 @ Y5 )
| ~ ( irel @ Y6 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y6 @ Y8 )
| ( Y0 @ Y8 ) ) ) ) )
| ~ ( irel @ Y2 @ Y7 ) ) ) ) ) ) )
@ sK3 )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y3 @ Y4 )
| ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y5 @ Y6 )
| ( Y1 @ Y6 ) ) )
| ( Y0 @ Y4 )
| ~ ( irel @ Y5 @ Y4 )
| ~ ( irel @ Y3 @ Y5 ) ) ) ) )
| ~ ( irel @ Y2 @ Y3 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y3 @ Y4 )
| ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y5 @ Y6 )
| ( Y1 @ Y6 ) ) )
| ( Y0 @ Y4 )
| ~ ( irel @ Y5 @ Y4 )
| ~ ( irel @ Y3 @ Y5 ) ) ) ) )
| ~ ( irel @ Y2 @ Y3 ) ) ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( ( Y0 @ Y4 )
| ~ ( irel @ Y7 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y3 @ Y8 )
| ( Y1 @ Y8 ) ) )
| ~ ( irel @ Y3 @ Y4 ) )
& ( ~ ( irel @ Y7 @ Y6 )
| ( Y1 @ Y5 )
| ~ ( irel @ Y6 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y6 @ Y8 )
| ( Y0 @ Y8 ) ) ) ) )
| ~ ( irel @ Y2 @ Y7 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( ( Y0 @ Y4 )
| ~ ( irel @ Y7 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y3 @ Y8 )
| ( Y1 @ Y8 ) ) )
| ~ ( irel @ Y3 @ Y4 ) )
& ( ~ ( irel @ Y7 @ Y6 )
| ( Y1 @ Y5 )
| ~ ( irel @ Y6 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y6 @ Y8 )
| ( Y0 @ Y8 ) ) ) ) )
| ~ ( irel @ Y2 @ Y7 ) ) ) ) ) ) ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( irel @ Y3 @ Y4 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 )
| ~ ( irel @ Y5 @ Y7 ) ) )
| ~ ( irel @ Y4 @ Y5 )
| ~ ( irel @ Y5 @ Y6 )
| ( Y3 @ Y6 ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ~ ( irel @ Y6 @ Y7 )
| ( Y3 @ Y7 ) ) )
| ( Y2 @ Y5 )
| ~ ( irel @ Y6 @ Y5 )
| ~ ( irel @ Y4 @ Y6 ) ) ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f38,f17,f24,f25]) ).
thf(f25,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( irel @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ( Y0 @ Y3 )
| ~ ( irel @ Y4 @ Y3 )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f24,plain,
( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f17,plain,
( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( ( Y0 @ Y4 )
| ~ ( irel @ Y7 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y3 @ Y8 )
| ( Y1 @ Y8 ) ) )
| ~ ( irel @ Y3 @ Y4 ) )
& ( ~ ( irel @ Y7 @ Y6 )
| ( Y1 @ Y5 )
| ~ ( irel @ Y6 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y6 @ Y8 )
| ( Y0 @ Y8 ) ) ) ) )
| ~ ( irel @ Y2 @ Y7 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f38,plain,
( ixor
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( inot @ ( iequiv @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ixor
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( inot @ ( iequiv @ Y0 @ Y1 ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ixor
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( inot @ ( iequiv @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( inot @ ( iequiv @ X0 @ X1 ) ) )
!= ixor ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( ( ^ [X8: $i > $o,X9: $i > $o] : ( inot @ ( iequiv @ X8 @ X9 ) ) )
!= ixor ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( ^ [X8: $i > $o,X9: $i > $o] : ( inot @ ( iequiv @ X8 @ X9 ) ) )
= ixor ),
file('/export/starexec/sandbox/tmp/tmp.YfK2dOMluu/DTF2THF_2576.p',ixor) ).
thf(f2882,plain,
( spl1_150
| spl1_151 ),
inference(avatar_split_clause,[status(thm)],[f180,f2880,f2877]) ).
thf(f180,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( ( sK3 @ X4 )
= $true )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ X1 @ X7 )
= $false )
| ( ( irel @ X8 @ X2 )
= $false )
| ( ( irel @ X7 @ X3 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( sK3 @ X3 ) )
| ( ( sK4 @ ( sK14 @ X7 ) )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( sK4 @ ( sK12 @ X2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f179]) ).
thf(f179,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( ( sK3 @ X4 )
= $true )
| ( ( irel @ X7 @ X3 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( sK3 @ X3 ) )
| ( ( ~ ( irel @ X7 @ ( sK14 @ X7 ) )
| ( sK4 @ ( sK14 @ X7 ) ) )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ X8 @ X2 )
= $false )
| ( ( sK4 @ ( sK12 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X7 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f178]) ).
thf(f178,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) )
@ ( sK14 @ X7 ) )
= $false )
| ( ( irel @ X8 @ X2 )
= $false )
| ( ( irel @ X1 @ X7 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X7 @ X3 )
= $false )
| ( $true
= ( sK3 @ X3 ) )
| ( ( sK4 @ ( sK12 @ X2 ) )
= $false )
| ( ( sK3 @ X4 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f177]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( $true
= ( sK3 @ X3 ) )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ X1 @ X7 )
= $false )
| ( ( sK3 @ X4 )
= $true )
| ( ( irel @ X7 @ X3 )
= $false )
| ( ( sK4 @ ( sK12 @ X2 ) )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X8 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f168]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( ( irel @ sK5 @ X8 )
= $false )
| ( ( sK4 @ ( sK12 @ X2 ) )
= $false )
| ( ( sK3 @ X4 )
= $true )
| ( ( irel @ X1 @ X7 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ X7 @ X3 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( irel @ X8 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f167]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X7 @ X3 )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( ~ ( irel @ X2 @ ( sK12 @ X2 ) )
| ( sK4 @ ( sK12 @ X2 ) ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( sK3 @ X4 )
= $true )
| ( ( irel @ X8 @ X2 )
= $false )
| ( ( irel @ X1 @ X7 )
= $false )
| ( $true
= ( sK3 @ X3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f166]) ).
thf(f166,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( ~ ( irel @ X8 @ X2 ) ) )
| ( ( irel @ X1 @ X7 )
= $false )
| ( ( sK3 @ X4 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( irel @ X7 @ X3 )
= $false )
| ( $true
= ( sK3 @ X3 ) )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( ~ ( irel @ X2 @ ( sK12 @ X2 ) )
| ( sK4 @ ( sK12 @ X2 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f165]) ).
thf(f165,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( ( ( sK3 @ X4 )
| ~ ( irel @ X8 @ X2 ) )
= $true )
| ( ( irel @ X1 @ X7 )
= $false )
| ( ( ~ ( irel @ X2 @ ( sK12 @ X2 ) )
| ( sK4 @ ( sK12 @ X2 ) ) )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( $true
= ( sK3 @ X3 ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ X7 @ X3 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f164]) ).
thf(f164,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( ( irel @ X7 @ X3 )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( $true
= ( ~ ( irel @ X2 @ X4 ) ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ X1 @ X7 )
= $false )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( ( sK3 @ X4 )
| ~ ( irel @ X8 @ X2 ) )
= $true )
| ( ( ~ ( irel @ X2 @ ( sK12 @ X2 ) )
| ( sK4 @ ( sK12 @ X2 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f163]) ).
thf(f163,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X3 ) )
= $true )
| ( ( ~ ( irel @ X2 @ ( sK12 @ X2 ) )
| ( sK4 @ ( sK12 @ X2 ) ) )
= $false )
| ( ( irel @ X7 @ X3 )
= $false )
| ( $true
= ( ~ ( irel @ X2 @ X4 ) ) )
| ( ( ( sK3 @ X4 )
| ~ ( irel @ X8 @ X2 ) )
= $true )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ X1 @ X7 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f162]) ).
thf(f162,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( ( ( sK3 @ X4 )
| ~ ( irel @ X8 @ X2 ) )
= $true )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( $true
= ( ~ ( irel @ X2 @ X4 ) ) )
| ( ( irel @ X1 @ X7 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) )
@ ( sK12 @ X2 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X3 ) )
= $true )
| ( ( irel @ X7 @ X3 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f161]) ).
thf(f161,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $true
= ( ~ ( irel @ X2 @ X4 ) ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X3 ) )
= $true )
| ( ( irel @ X1 @ X7 )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ X7 @ X3 )
= $false )
| ( ( ( sK3 @ X4 )
| ~ ( irel @ X8 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f160]) ).
thf(f160,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( ~ ( irel @ X1 @ X7 ) ) )
| ( ( ( sK3 @ X4 )
| ~ ( irel @ X8 @ X2 ) )
= $true )
| ( $true
= ( ~ ( irel @ X2 @ X4 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X3 ) )
= $true )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ X7 @ X3 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f159]) ).
thf(f159,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( ( ~ ( irel @ X7 @ X3 ) )
= $true )
| ( ( ( sK3 @ X4 )
| ~ ( irel @ X8 @ X2 ) )
= $true )
| ( $true
= ( ~ ( irel @ X1 @ X7 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X3 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( ~ ( irel @ X2 @ X4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f158]) ).
thf(f158,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ X7 @ X3 ) ) )
| ( $true
= ( ~ ( irel @ X2 @ X4 ) ) )
| ( ( ( sK3 @ X4 )
| ~ ( irel @ X8 @ X2 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( $true
= ( ~ ( irel @ X1 @ X7 ) ) )
| ( ( irel @ sK5 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f157]) ).
thf(f157,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( ( irel @ sK5 @ X8 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ~ ( irel @ X2 @ X4 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ X7 @ X3 ) ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( ( sK3 @ X4 )
| ~ ( irel @ X8 @ X2 ) )
= $true )
| ( $true
= ( ~ ( irel @ X1 @ X7 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f156]) ).
thf(f156,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( $true
= ( ( sK3 @ X4 )
| ~ ( irel @ X8 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( irel @ X1 @ X7 ) ) )
| ( $true
= ( ~ ( irel @ X2 @ X4 ) ) )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ X7 @ X3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f155]) ).
thf(f155,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ sK5 @ X8 )
= $false )
| ( $true
= ( ( sK3 @ X4 )
| ~ ( irel @ X8 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ X7 @ X3 ) ) )
| ( $true
= ( ~ ( irel @ X1 @ X7 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f154]) ).
thf(f154,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X7: $i,X4: $i] :
( ( ( irel @ sK5 @ X8 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ X7 @ X3 )
| ~ ( irel @ X1 @ X7 ) ) )
| ( $true
= ( ( sK3 @ X4 )
| ~ ( irel @ X8 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f152]) ).
thf(f152,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( irel @ sK5 @ X8 )
= $false )
| ( $true
= ( ( ( sK3 @ X4 )
| ~ ( irel @ X8 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) )
& ( ~ ( irel @ X8 @ X6 )
| ( sK4 @ X5 )
| ~ ( irel @ X6 @ X5 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X6 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ X7 @ X3 )
| ~ ( irel @ X1 @ X7 ) ) )
| ( ( irel @ sK5 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f151]) ).
thf(f151,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( ~ ( irel @ sK5 @ X8 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ X7 @ X3 )
| ~ ( irel @ X1 @ X7 ) ) )
| ( $true
= ( ( ( sK3 @ X4 )
| ~ ( irel @ X8 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) )
& ( ~ ( irel @ X8 @ X6 )
| ( sK4 @ X5 )
| ~ ( irel @ X6 @ X5 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X6 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f150]) ).
thf(f150,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( ( ( ( ( sK3 @ X4 )
| ~ ( irel @ X8 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) )
& ( ~ ( irel @ X8 @ X6 )
| ( sK4 @ X5 )
| ~ ( irel @ X6 @ X5 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X6 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ~ ( irel @ sK5 @ X8 ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ X7 @ X3 )
| ~ ( irel @ X1 @ X7 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f149]) ).
thf(f149,plain,
! [X2: $i,X3: $i,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ X7 @ X3 )
| ~ ( irel @ X1 @ X7 ) ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( ( ( sK3 @ X4 )
| ~ ( irel @ Y0 @ X2 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ X2 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( irel @ X2 @ X4 ) )
& ( ~ ( irel @ Y0 @ X6 )
| ( sK4 @ X5 )
| ~ ( irel @ X6 @ X5 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ X6 @ Y1 )
| ( sK3 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) )
@ X8 ) ) ),
inference(pi_clausification,[status(thm)],[f148]) ).
thf(f148,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ( sK3 @ X4 )
| ~ ( irel @ Y0 @ X2 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ X2 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( irel @ X2 @ X4 ) )
& ( ~ ( irel @ Y0 @ X6 )
| ( sK4 @ X5 )
| ~ ( irel @ X6 @ X5 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ X6 @ Y1 )
| ( sK3 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X7 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ X7 @ X3 )
| ~ ( irel @ X1 @ X7 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f147]) ).
thf(f147,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ Y0 @ X3 )
| ~ ( irel @ X1 @ Y0 ) )
@ X7 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ( sK3 @ X4 )
| ~ ( irel @ Y0 @ X2 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ X2 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( irel @ X2 @ X4 ) )
& ( ~ ( irel @ Y0 @ X6 )
| ( sK4 @ X5 )
| ~ ( irel @ X6 @ X5 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ X6 @ Y1 )
| ( sK3 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f146]) ).
thf(f146,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ Y0 @ X3 )
| ~ ( irel @ X1 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ( sK3 @ X4 )
| ~ ( irel @ Y0 @ X2 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ X2 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( irel @ X2 @ X4 ) )
& ( ~ ( irel @ Y0 @ X6 )
| ( sK4 @ X5 )
| ~ ( irel @ X6 @ X5 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ X6 @ Y1 )
| ( sK3 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f145]) ).
thf(f145,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ Y0 @ X3 )
| ~ ( irel @ X1 @ Y0 ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK3 @ X4 )
| ~ ( irel @ Y1 @ X2 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ X2 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ~ ( irel @ X2 @ X4 ) )
& ( ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ X5 )
| ~ ( irel @ Y0 @ X5 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) )
@ X6 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK3 @ X4 )
| ~ ( irel @ Y1 @ X2 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ X2 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ~ ( irel @ X2 @ X4 ) )
& ( ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ X5 )
| ~ ( irel @ Y0 @ X5 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ Y0 @ X3 )
| ~ ( irel @ X1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f143]) ).
thf(f143,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ Y0 @ X3 )
| ~ ( irel @ X1 @ Y0 ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK3 @ X4 )
| ~ ( irel @ Y2 @ X2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ X2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ~ ( irel @ X2 @ X4 ) )
& ( ~ ( irel @ Y2 @ Y1 )
| ( sK4 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y1 @ Y3 )
| ( sK3 @ Y3 ) ) ) ) )
| ~ ( irel @ sK5 @ Y2 ) ) ) )
@ X5 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f142]) ).
thf(f142,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK3 @ X4 )
| ~ ( irel @ Y2 @ X2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ X2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ~ ( irel @ X2 @ X4 ) )
& ( ~ ( irel @ Y2 @ Y1 )
| ( sK4 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y1 @ Y3 )
| ( sK3 @ Y3 ) ) ) ) )
| ~ ( irel @ sK5 @ Y2 ) ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ Y0 @ X3 )
| ~ ( irel @ X1 @ Y0 ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f141]) ).
thf(f141,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ Y0 @ X3 )
| ~ ( irel @ X1 @ Y0 ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ( sK3 @ Y0 )
| ~ ( irel @ Y3 @ X2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ X2 @ Y4 )
| ( sK4 @ Y4 ) ) )
| ~ ( irel @ X2 @ Y0 ) )
& ( ~ ( irel @ Y3 @ Y2 )
| ( sK4 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y2 @ Y4 )
| ( sK3 @ Y4 ) ) ) ) )
| ~ ( irel @ sK5 @ Y3 ) ) ) ) )
@ X4 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ( sK3 @ Y0 )
| ~ ( irel @ Y3 @ X2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ X2 @ Y4 )
| ( sK4 @ Y4 ) ) )
| ~ ( irel @ X2 @ Y0 ) )
& ( ~ ( irel @ Y3 @ Y2 )
| ( sK4 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y2 @ Y4 )
| ( sK3 @ Y4 ) ) ) ) )
| ~ ( irel @ sK5 @ Y3 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ X3 )
| ~ ( irel @ Y0 @ X3 )
| ~ ( irel @ X1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f139]) ).
thf(f139,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ( sK3 @ Y0 )
| ~ ( irel @ Y3 @ X2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ X2 @ Y4 )
| ( sK4 @ Y4 ) ) )
| ~ ( irel @ X2 @ Y0 ) )
& ( ~ ( irel @ Y3 @ Y2 )
| ( sK4 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y2 @ Y4 )
| ( sK3 @ Y4 ) ) ) ) )
| ~ ( irel @ sK5 @ Y3 ) ) ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ X1 @ Y1 ) ) )
@ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f138]) ).
thf(f138,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ X1 @ Y1 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ( sK3 @ Y0 )
| ~ ( irel @ Y3 @ X2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ X2 @ Y4 )
| ( sK4 @ Y4 ) ) )
| ~ ( irel @ X2 @ Y0 ) )
& ( ~ ( irel @ Y3 @ Y2 )
| ( sK4 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y2 @ Y4 )
| ( sK3 @ Y4 ) ) ) ) )
| ~ ( irel @ sK5 @ Y3 ) ) ) ) ) ) )
| ( ( irel @ sK5 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK5 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ X1 @ Y1 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ( sK3 @ Y0 )
| ~ ( irel @ Y3 @ X2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ X2 @ Y4 )
| ( sK4 @ Y4 ) ) )
| ~ ( irel @ X2 @ Y0 ) )
& ( ~ ( irel @ Y3 @ Y2 )
| ( sK4 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y2 @ Y4 )
| ( sK3 @ Y4 ) ) ) ) )
| ~ ( irel @ sK5 @ Y3 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f2810,plain,
( spl1_86
| spl1_22
| spl1_140
| spl1_135 ),
inference(avatar_split_clause,[status(thm)],[f446,f2780,f2807,f2142,f2499]) ).
thf(f446,plain,
( ( ( sK3 @ sK24 )
= $false )
| ( ( sK4 @ sK28 )
= $false )
| ( $false
= ( sK3 @ sK19 ) )
| ( ( sK4 @ sK20 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f410]) ).
thf(f410,plain,
( ( ( sK4 @ sK28 )
= $false )
| ( ( sK4 @ sK20 )
= $false )
| ( $false
= ( sK3 @ sK19 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK26 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK24 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f409]) ).
thf(f409,plain,
( ( ( sK4 @ sK20 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK25 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK25 )
| ~ ( irel @ sK25 @ sK28 )
| ( sK4 @ sK28 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK26 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK24 ) )
= $false )
| ( $false
= ( sK3 @ sK19 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f408]) ).
thf(f408,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK26 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK24 ) )
= $false )
| ( $false
= ( sK3 @ sK19 ) )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ sK25 @ Y1 ) ) )
| ~ ( irel @ sK23 @ sK25 )
| ~ ( irel @ sK25 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK28 )
= $false )
| ( ( sK4 @ sK20 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f407]) ).
thf(f407,plain,
( ( ( sK4 @ sK20 )
= $false )
| ( $false
= ( sK3 @ sK19 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ sK25 @ Y1 ) ) )
| ~ ( irel @ sK23 @ sK25 )
| ~ ( irel @ sK25 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK26 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK24 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f405]) ).
thf(f405,plain,
( ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ sK25 @ Y1 ) ) )
| ~ ( irel @ sK23 @ sK25 )
| ~ ( irel @ sK25 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK26 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK24 ) )
= $false )
| ( ( sK4 @ sK20 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f256]) ).
thf(f256,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK26 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK24 )
| ~ ( irel @ sK26 @ sK24 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ sK25 @ Y1 ) ) )
| ~ ( irel @ sK23 @ sK25 )
| ~ ( irel @ sK25 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 ) )
= $false )
| ( ( sK4 @ sK20 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f255]) ).
thf(f255,plain,
( ( ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK26 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK24 )
| ~ ( irel @ sK26 @ sK24 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ sK25 @ Y1 ) ) )
| ~ ( irel @ sK23 @ sK25 )
| ~ ( irel @ sK25 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f253]) ).
thf(f253,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK26 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK24 )
| ~ ( irel @ sK26 @ sK24 )
| ~ ( irel @ sK23 @ sK26 ) )
= $false )
| ( ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ sK25 @ Y1 ) ) )
| ~ ( irel @ sK23 @ sK25 )
| ~ ( irel @ sK25 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f252]) ).
thf(f252,plain,
( ( ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ sK25 @ Y1 ) ) )
| ~ ( irel @ sK23 @ sK25 )
| ~ ( irel @ sK25 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ sK24 )
| ~ ( irel @ Y0 @ sK24 )
| ~ ( irel @ sK23 @ Y0 ) )
@ sK26 )
= $false )
| ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f251]) ).
thf(f251,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ sK24 )
| ~ ( irel @ Y0 @ sK24 )
| ~ ( irel @ sK23 @ Y0 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ sK25 @ Y1 ) ) )
| ~ ( irel @ sK23 @ sK25 )
| ~ ( irel @ sK25 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 ) )
= $false )
| ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f250]) ).
thf(f250,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
@ sK25 )
= $false )
| ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 ) )
= $false )
| ( ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ sK24 )
| ~ ( irel @ Y0 @ sK24 )
| ~ ( irel @ sK23 @ Y0 ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f249]) ).
thf(f249,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
= $false )
| ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ sK24 )
| ~ ( irel @ Y0 @ sK24 )
| ~ ( irel @ sK23 @ Y0 ) ) )
= $false )
| ( ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f248]) ).
thf(f248,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
= $false )
| ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 ) )
= $false )
| ( ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 ) )
= $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) )
@ sK24 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f247]) ).
thf(f247,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) )
= $false )
| ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f245]) ).
thf(f245,plain,
( ( ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 )
| ~ ( irel @ sK21 @ sK20 ) )
= $false )
| ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f243]) ).
thf(f243,plain,
( ( ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 )
| ~ ( irel @ sK21 @ sK20 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f242]) ).
thf(f242,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) ) )
= $false )
| ( ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 )
| ~ ( irel @ sK21 @ sK20 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f240]) ).
thf(f240,plain,
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ sK23 ) )
= $false )
| ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 ) )
= $false )
| ( ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 )
| ~ ( irel @ sK21 @ sK20 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f238]) ).
thf(f238,plain,
( ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK18 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 )
| ~ ( irel @ sK21 @ sK20 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ sK23 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f236]) ).
thf(f236,plain,
( ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK18 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( irel @ sK18 @ sK19 ) )
= $false )
| ( ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 )
| ~ ( irel @ sK21 @ sK20 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ sK23 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f235]) ).
thf(f235,plain,
( ( ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK18 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( irel @ sK18 @ sK19 ) )
& ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 )
| ~ ( irel @ sK21 @ sK20 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
= $false )
| ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ sK23 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f233]) ).
thf(f233,plain,
( ( ( ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK18 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( irel @ sK18 @ sK19 ) )
& ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 )
| ~ ( irel @ sK21 @ sK20 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ~ ( irel @ sK5 @ sK22 ) )
= $false )
| ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ sK23 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f232]) ).
thf(f232,plain,
( ( ( ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK18 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( irel @ sK18 @ sK19 ) )
& ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 )
| ~ ( irel @ sK21 @ sK20 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ~ ( irel @ sK5 @ sK22 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) )
@ sK23 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f231]) ).
thf(f231,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false )
| ( ( ( ( ( sK3 @ sK19 )
| ~ ( irel @ sK22 @ sK18 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK18 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( irel @ sK18 @ sK19 ) )
& ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 )
| ~ ( irel @ sK21 @ sK20 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ~ ( irel @ sK5 @ sK22 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f230]) ).
thf(f230,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( ( ( sK3 @ sK19 )
| ~ ( irel @ Y0 @ sK18 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK18 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( irel @ sK18 @ sK19 ) )
& ( ~ ( irel @ Y0 @ sK21 )
| ( sK4 @ sK20 )
| ~ ( irel @ sK21 @ sK20 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK21 @ Y1 )
| ( sK3 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) )
@ sK22 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f229]) ).
thf(f229,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ( sK3 @ sK19 )
| ~ ( irel @ Y0 @ sK18 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK18 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( irel @ sK18 @ sK19 ) )
& ( ~ ( irel @ Y0 @ sK21 )
| ( sK4 @ sK20 )
| ~ ( irel @ sK21 @ sK20 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK21 @ Y1 )
| ( sK3 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f228]) ).
thf(f228,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK3 @ sK19 )
| ~ ( irel @ Y1 @ sK18 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ sK18 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ~ ( irel @ sK18 @ sK19 ) )
& ( ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ sK20 )
| ~ ( irel @ Y0 @ sK20 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) )
@ sK21 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f227]) ).
thf(f227,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK3 @ sK19 )
| ~ ( irel @ Y1 @ sK18 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ sK18 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ~ ( irel @ sK18 @ sK19 ) )
& ( ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ sK20 )
| ~ ( irel @ Y0 @ sK20 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f226]) ).
thf(f226,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK3 @ sK19 )
| ~ ( irel @ Y2 @ sK18 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ sK18 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ~ ( irel @ sK18 @ sK19 ) )
& ( ~ ( irel @ Y2 @ Y1 )
| ( sK4 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y1 @ Y3 )
| ( sK3 @ Y3 ) ) ) ) )
| ~ ( irel @ sK5 @ Y2 ) ) ) )
@ sK20 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f225]) ).
thf(f225,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK3 @ sK19 )
| ~ ( irel @ Y2 @ sK18 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ sK18 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ~ ( irel @ sK18 @ sK19 ) )
& ( ~ ( irel @ Y2 @ Y1 )
| ( sK4 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y1 @ Y3 )
| ( sK3 @ Y3 ) ) ) ) )
| ~ ( irel @ sK5 @ Y2 ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f224]) ).
thf(f224,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ( sK3 @ Y0 )
| ~ ( irel @ Y3 @ sK18 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ sK18 @ Y4 )
| ( sK4 @ Y4 ) ) )
| ~ ( irel @ sK18 @ Y0 ) )
& ( ~ ( irel @ Y3 @ Y2 )
| ( sK4 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y2 @ Y4 )
| ( sK3 @ Y4 ) ) ) ) )
| ~ ( irel @ sK5 @ Y3 ) ) ) ) )
@ sK19 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f223]) ).
thf(f223,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ( sK3 @ Y0 )
| ~ ( irel @ Y3 @ sK18 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ sK18 @ Y4 )
| ( sK4 @ Y4 ) ) )
| ~ ( irel @ sK18 @ Y0 ) )
& ( ~ ( irel @ Y3 @ Y2 )
| ( sK4 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y2 @ Y4 )
| ( sK3 @ Y4 ) ) ) ) )
| ~ ( irel @ sK5 @ Y3 ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f222]) ).
thf(f222,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ( sK3 @ Y0 )
| ~ ( irel @ Y3 @ sK18 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ sK18 @ Y4 )
| ( sK4 @ Y4 ) ) )
| ~ ( irel @ sK18 @ Y0 ) )
& ( ~ ( irel @ Y3 @ Y2 )
| ( sK4 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y2 @ Y4 )
| ( sK3 @ Y4 ) ) ) ) )
| ~ ( irel @ sK5 @ Y3 ) ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f221]) ).
thf(f221,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( ( sK3 @ Y1 )
| ~ ( irel @ Y4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y0 @ Y5 )
| ( sK4 @ Y5 ) ) )
| ~ ( irel @ Y0 @ Y1 ) )
& ( ~ ( irel @ Y4 @ Y3 )
| ( sK4 @ Y2 )
| ~ ( irel @ Y3 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( sK3 @ Y5 ) ) ) ) )
| ~ ( irel @ sK5 @ Y4 ) ) ) ) ) )
@ sK18 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f220]) ).
thf(f220,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( ( sK3 @ Y1 )
| ~ ( irel @ Y4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y0 @ Y5 )
| ( sK4 @ Y5 ) ) )
| ~ ( irel @ Y0 @ Y1 ) )
& ( ~ ( irel @ Y4 @ Y3 )
| ( sK4 @ Y2 )
| ~ ( irel @ Y3 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( sK3 @ Y5 ) ) ) ) )
| ~ ( irel @ sK5 @ Y4 ) ) ) ) ) ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( ( sK3 @ Y1 )
| ~ ( irel @ Y4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y0 @ Y5 )
| ( sK4 @ Y5 ) ) )
| ~ ( irel @ Y0 @ Y1 ) )
& ( ~ ( irel @ Y4 @ Y3 )
| ( sK4 @ Y2 )
| ~ ( irel @ Y3 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( sK3 @ Y5 ) ) ) ) )
| ~ ( irel @ sK5 @ Y4 ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 )
| ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f2326,plain,
( spl1_50
| spl1_41
| spl1_52
| spl1_12 ),
inference(avatar_split_clause,[status(thm)],[f1405,f2087,f2321,f2264,f2309]) ).
thf(f1405,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK66 @ X4 )
= $false )
| ( ( irel @ sK63 @ X2 )
= $false )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( sK3 @ X3 ) )
| ( ( irel @ sK21 @ X3 )
= $false )
| ( $true
= ( sK4 @ X4 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1404]) ).
thf(f1404,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK21 @ X3 )
= $false )
| ( $true
= ( sK4 @ X4 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK63 @ X2 )
= $false )
| ( ( ~ ( irel @ sK66 @ X4 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1403]) ).
thf(f1403,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK21 @ X3 )
= $false )
| ( ( irel @ sK63 @ X2 )
= $false )
| ( ( ~ ( irel @ sK66 @ X4 )
| ( sK4 @ X4 ) )
= $true )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK18 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1402]) ).
thf(f1402,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) )
@ X4 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( ( irel @ sK63 @ X2 )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK21 @ X3 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f1401]) ).
thf(f1401,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK63 @ X2 )
= $false )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( ( irel @ sK21 @ X3 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1400]) ).
thf(f1400,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK63 @ X2 ) ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK21 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1399]) ).
thf(f1399,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK3 @ X3 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( ~ ( irel @ sK63 @ X2 ) ) )
| ( ( irel @ sK21 @ X3 )
= $false )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1398]) ).
thf(f1398,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK63 @ X2 ) ) )
| ( ( irel @ sK21 @ X3 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( $true
= ( sK3 @ X3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1397]) ).
thf(f1397,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK21 @ X3 ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK63 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1395]) ).
thf(f1395,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 ) )
= $false )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( ~ ( irel @ sK21 @ X3 ) ) )
| ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK63 @ X2 ) ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1394]) ).
thf(f1394,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK21 @ X3 )
| ( sK3 @ X3 ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK63 @ X2 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1393]) ).
thf(f1393,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK18 @ X1 ) ) )
| ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK63 @ X2 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK21 @ X3 )
| ( sK3 @ X3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1391]) ).
thf(f1391,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ sK66 @ sK65 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK21 @ X3 )
| ( sK3 @ X3 ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK18 @ X1 ) ) )
| ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK63 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1390]) ).
thf(f1390,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK18 @ X1 ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ sK66 @ sK65 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK63 @ X2 ) ) ) ),
inference(pi_clausification,[status(thm)],[f1389]) ).
thf(f1389,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ sK66 @ sK65 ) )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK63 @ X2 ) ) )
| ( $true
= ( ~ ( irel @ sK18 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1387]) ).
thf(f1387,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ sK66 @ sK65 )
| ~ ( irel @ sK23 @ sK66 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK18 @ X1 ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK63 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1386]) ).
thf(f1386,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK18 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ sK66 @ sK65 )
| ~ ( irel @ sK23 @ sK66 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK63 @ Y0 ) )
@ X2 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f1385]) ).
thf(f1385,plain,
! [X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK63 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( irel @ sK18 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ sK66 @ sK65 )
| ~ ( irel @ sK23 @ sK66 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1384]) ).
thf(f1384,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK63 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ sK66 @ sK65 )
| ~ ( irel @ sK23 @ sK66 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK18 @ X1 ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1383]) ).
thf(f1383,plain,
! [X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ~ ( irel @ sK18 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ sK66 @ sK65 )
| ~ ( irel @ sK23 @ sK66 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK63 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1382]) ).
thf(f1382,plain,
! [X1: $i] :
( ( $true
= ( ~ ( irel @ sK18 @ X1 )
| ( sK4 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ sK66 @ sK65 )
| ~ ( irel @ sK23 @ sK66 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK63 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1380]) ).
thf(f1380,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK63 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK63 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK18 @ X1 )
| ( sK4 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ sK66 @ sK65 )
| ~ ( irel @ sK23 @ sK66 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1378]) ).
thf(f1378,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK63 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK63 )
| ~ ( irel @ sK63 @ sK64 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ~ ( irel @ sK18 @ X1 )
| ( sK4 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ sK66 @ sK65 )
| ~ ( irel @ sK23 @ sK66 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1377]) ).
thf(f1377,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK63 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK63 )
| ~ ( irel @ sK63 @ sK64 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ Y0 @ sK65 )
| ~ ( irel @ sK23 @ Y0 ) )
@ sK66 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ~ ( irel @ sK18 @ X1 )
| ( sK4 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f1376]) ).
thf(f1376,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ Y0 @ sK65 )
| ~ ( irel @ sK23 @ Y0 ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ~ ( irel @ sK18 @ X1 )
| ( sK4 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK63 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK63 )
| ~ ( irel @ sK63 @ sK64 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1374]) ).
thf(f1374,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK63 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK63 )
| ~ ( irel @ sK63 @ sK64 )
| ( sK4 @ sK64 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ~ ( irel @ sK18 @ X1 )
| ( sK4 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ Y0 @ sK65 )
| ~ ( irel @ sK23 @ Y0 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1373]) ).
thf(f1373,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) )
@ sK65 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK63 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK63 )
| ~ ( irel @ sK63 @ sK64 )
| ( sK4 @ sK64 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK18 @ X1 )
| ( sK4 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f1372]) ).
thf(f1372,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK63 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK63 )
| ~ ( irel @ sK63 @ sK64 )
| ( sK4 @ sK64 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK18 @ X1 )
| ( sK4 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1371]) ).
thf(f1371,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ sK63 @ Y1 ) ) )
| ~ ( irel @ sK23 @ sK63 )
| ~ ( irel @ sK63 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK64 )
= $false )
| ( $true
= ( ~ ( irel @ sK18 @ X1 )
| ( sK4 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f1370]) ).
thf(f1370,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ sK63 @ Y1 ) ) )
| ~ ( irel @ sK23 @ sK63 )
| ~ ( irel @ sK63 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $true
= ( ~ ( irel @ sK18 @ X1 )
| ( sK4 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1369]) ).
thf(f1369,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ~ ( irel @ sK18 @ X1 )
| ( sK4 @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
@ sK63 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f1368]) ).
thf(f1368,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ~ ( irel @ sK18 @ X1 )
| ( sK4 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1367]) ).
thf(f1367,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK18 @ Y0 )
| ( sK4 @ Y0 ) )
@ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f1366]) ).
thf(f1366,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK18 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1365]) ).
thf(f1365,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK18 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1047]) ).
thf(f1047,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK18 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1046]) ).
thf(f1046,plain,
( ( ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 )
| ~ ( irel @ sK21 @ sK20 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK18 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f239]) ).
thf(f239,plain,
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ sK23 ) )
= $false )
| ( ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 )
| ~ ( irel @ sK21 @ sK20 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK18 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f238]) ).
thf(f2324,plain,
( spl1_12
| spl1_52
| spl1_49
| spl1_41 ),
inference(avatar_split_clause,[status(thm)],[f1414,f2264,f2303,f2321,f2087]) ).
thf(f1414,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK66 @ sK65 )
= $true )
| ( ( irel @ sK63 @ X2 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( ( irel @ sK21 @ X3 )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK3 @ X3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1413]) ).
thf(f1413,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK3 @ X3 ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( ( irel @ sK21 @ X3 )
= $false )
| ( ( ~ ( irel @ sK66 @ sK65 ) )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK63 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1412]) ).
thf(f1412,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( ~ ( irel @ sK21 @ X3 ) ) )
| ( $true
= ( sK3 @ X2 ) )
| ( ( ~ ( irel @ sK66 @ sK65 ) )
= $false )
| ( ( irel @ sK63 @ X2 )
= $false )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1411]) ).
thf(f1411,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK63 @ X2 ) ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( ~ ( irel @ sK21 @ X3 ) ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( ( ~ ( irel @ sK66 @ sK65 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1410]) ).
thf(f1410,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK21 @ X3 )
| ( sK3 @ X3 ) ) )
| ( ( ~ ( irel @ sK66 @ sK65 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK63 @ X2 ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK18 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1409]) ).
thf(f1409,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK63 @ X2 ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( ( ~ ( irel @ sK66 @ sK65 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK21 @ X3 )
| ( sK3 @ X3 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1392]) ).
thf(f1392,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK18 @ X1 ) ) )
| ( ( ~ ( irel @ sK66 @ sK65 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK21 @ X3 )
| ( sK3 @ X3 ) ) )
| ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK63 @ X2 ) ) )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1391]) ).
thf(f2311,plain,
( spl1_41
| spl1_50
| spl1_12
| spl1_48 ),
inference(avatar_split_clause,[status(thm)],[f1474,f2298,f2087,f2309,f2264]) ).
thf(f1474,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK21 @ X2 )
= $false )
| ( $true
= ( irel @ sK63 @ sK64 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK66 @ X3 )
= $false )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK4 @ X3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1473]) ).
thf(f1473,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ sK63 @ sK64 ) )
| ( ( irel @ sK21 @ X2 )
= $false )
| ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( ~ ( irel @ sK66 @ X3 ) ) )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1472]) ).
thf(f1472,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK66 @ X3 )
| ( sK4 @ X3 ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( irel @ sK63 @ sK64 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK21 @ X2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1471]) ).
thf(f1471,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) )
@ X3 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK21 @ X2 )
= $false )
| ( $true
= ( irel @ sK63 @ sK64 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK18 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f1470]) ).
thf(f1470,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( irel @ sK63 @ sK64 ) )
| ( ( irel @ sK21 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1469]) ).
thf(f1469,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK21 @ X2 )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( irel @ sK63 @ sK64 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1468]) ).
thf(f1468,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( irel @ sK63 @ sK64 ) )
| ( ( ~ ( irel @ sK21 @ X2 ) )
= $true )
| ( $true
= ( sK4 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1467]) ).
thf(f1467,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK21 @ X2 )
| ( sK3 @ X2 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( irel @ sK63 @ sK64 ) )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1466]) ).
thf(f1466,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) )
@ X2 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( $true
= ( irel @ sK63 @ sK64 ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f1465]) ).
thf(f1465,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK63 @ sK64 ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1463]) ).
thf(f1463,plain,
! [X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( irel @ sK63 @ sK64 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1461]) ).
thf(f1461,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK63 @ sK64 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ sK66 @ sK65 ) )
= $false )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1460]) ).
thf(f1460,plain,
! [X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK18 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ sK66 @ sK65 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( irel @ sK63 @ sK64 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1459]) ).
thf(f1459,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( irel @ sK63 @ sK64 ) )
| ( $true
= ( ~ ( irel @ sK18 @ X1 ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ sK66 @ sK65 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1457]) ).
thf(f1457,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK63 @ sK64 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ sK66 @ sK65 )
| ~ ( irel @ sK23 @ sK66 ) )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK18 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1456]) ).
thf(f1456,plain,
! [X1: $i] :
( ( ( ~ ( irel @ sK63 @ sK64 ) )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ sK66 @ sK65 )
| ~ ( irel @ sK23 @ sK66 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK18 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1379]) ).
thf(f1379,plain,
! [X1: $i] :
( ( $true
= ( ~ ( irel @ sK18 @ X1 )
| ( sK4 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK66 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK65 )
| ~ ( irel @ sK66 @ sK65 )
| ~ ( irel @ sK23 @ sK66 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK63 @ sK64 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1378]) ).
thf(f2306,plain,
( spl1_49
| spl1_41
| spl1_48
| spl1_12 ),
inference(avatar_split_clause,[status(thm)],[f1483,f2087,f2298,f2264,f2303]) ).
thf(f1483,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK66 @ sK65 )
= $true )
| ( ( irel @ sK18 @ X1 )
= $false )
| ( ( irel @ sK21 @ X2 )
= $false )
| ( $true
= ( irel @ sK63 @ sK64 ) )
| ( $true
= ( sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1482]) ).
thf(f1482,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK63 @ sK64 ) )
| ( ( irel @ sK21 @ X2 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( ( ~ ( irel @ sK66 @ sK65 ) )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK18 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1481]) ).
thf(f1481,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK63 @ sK64 ) )
| ( ( ~ ( irel @ sK21 @ X2 ) )
= $true )
| ( ( ~ ( irel @ sK66 @ sK65 ) )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK18 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1480]) ).
thf(f1480,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK21 @ X2 )
| ( sK3 @ X2 ) ) )
| ( $true
= ( irel @ sK63 @ sK64 ) )
| ( ( ~ ( irel @ sK66 @ sK65 ) )
= $false )
| ( ( irel @ sK18 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1479]) ).
thf(f1479,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) )
@ X2 )
= $true )
| ( $true
= ( irel @ sK63 @ sK64 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( ~ ( irel @ sK66 @ sK65 ) )
= $false )
| ( ( irel @ sK18 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f1462]) ).
thf(f1462,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( ~ ( irel @ sK66 @ sK65 ) )
= $false )
| ( $true
= ( irel @ sK63 @ sK64 ) )
| ( ( irel @ sK18 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1461]) ).
thf(f2135,plain,
( spl1_17
| spl1_20
| spl1_12
| spl1_11 ),
inference(avatar_split_clause,[status(thm)],[f1871,f2083,f2087,f2127,f2110]) ).
thf(f1871,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK79 @ X3 )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK77 @ X2 )
= $false )
| ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( sK3 @ X1 ) )
| ( ( irel @ sK21 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1870]) ).
thf(f1870,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( irel @ sK21 @ X1 )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( ( ~ ( irel @ sK79 @ X3 ) )
= $true )
| ( ( irel @ sK77 @ X2 )
= $false )
| ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( sK4 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1869]) ).
thf(f1869,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ sK18 @ sK19 ) )
| ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK79 @ X3 )
| ( sK4 @ X3 ) ) )
| ( ( irel @ sK77 @ X2 )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK21 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1868]) ).
thf(f1868,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ sK18 @ sK19 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK21 @ X1 )
= $false )
| ( $true
= ( sK3 @ X1 ) )
| ( ( irel @ sK77 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) )
@ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f1867]) ).
thf(f1867,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( irel @ sK77 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( ( irel @ sK21 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1866]) ).
thf(f1866,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( ( irel @ sK77 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( irel @ sK21 @ X1 )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( irel @ sK18 @ sK19 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1864]) ).
thf(f1864,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK77 @ X2 )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( irel @ sK21 @ X1 )
= $false )
| ( $true
= ( sK3 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1863]) ).
thf(f1863,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK77 @ X2 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 ) )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK21 @ X1 )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1861]) ).
thf(f1861,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ sK79 @ sK76 ) )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( $true
= ( ~ ( irel @ sK77 @ X2 ) ) )
| ( ( irel @ sK21 @ X1 )
= $false )
| ( $true
= ( sK3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1860]) ).
thf(f1860,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK3 @ X2 )
| ~ ( irel @ sK77 @ X2 ) )
= $true )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( $true
= ( sK3 @ X1 ) )
| ( ( irel @ sK21 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ sK79 @ sK76 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1859]) ).
thf(f1859,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK77 @ Y0 ) )
@ X2 ) )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( irel @ sK21 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ sK79 @ sK76 ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f1858]) ).
thf(f1858,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK77 @ Y0 ) ) )
= $true )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ sK79 @ sK76 ) )
= $false )
| ( $true
= ( sK3 @ X1 ) )
| ( ( irel @ sK21 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1857]) ).
thf(f1857,plain,
! [X1: $i] :
( ( $true
= ( ~ ( irel @ sK21 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ sK79 @ sK76 ) )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( $true
= ( sK3 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK77 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f1856]) ).
thf(f1856,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK77 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ~ ( irel @ sK21 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ sK79 @ sK76 ) )
= $false )
| ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( irel @ sK18 @ sK19 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1854]) ).
thf(f1854,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK77 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK77 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK21 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ sK79 @ sK76 ) )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1852]) ).
thf(f1852,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ sK79 @ sK76 )
| ~ ( irel @ sK23 @ sK79 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK21 @ X1 ) ) )
| ( $true
= ( sK3 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK77 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK77 ) )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1850]) ).
thf(f1850,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK77 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK77 )
| ~ ( irel @ sK77 @ sK78 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK21 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ sK79 @ sK76 )
| ~ ( irel @ sK23 @ sK79 ) )
= $false )
| ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( irel @ sK18 @ sK19 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1848]) ).
thf(f1848,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK77 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK77 )
| ~ ( irel @ sK77 @ sK78 )
| ( sK4 @ sK78 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK21 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ sK79 @ sK76 )
| ~ ( irel @ sK23 @ sK79 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1847]) ).
thf(f1847,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( ~ ( irel @ sK21 @ X1 )
| ( sK3 @ X1 ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK77 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK77 )
| ~ ( irel @ sK77 @ sK78 )
| ( sK4 @ sK78 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ sK79 @ sK76 )
| ~ ( irel @ sK23 @ sK79 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1846]) ).
thf(f1846,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) )
@ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ sK79 @ sK76 )
| ~ ( irel @ sK23 @ sK79 ) )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK77 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK77 )
| ~ ( irel @ sK77 @ sK78 )
| ( sK4 @ sK78 ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f1845]) ).
thf(f1845,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ sK79 @ sK76 )
| ~ ( irel @ sK23 @ sK79 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK77 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK77 )
| ~ ( irel @ sK77 @ sK78 )
| ( sK4 @ sK78 ) )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1844]) ).
thf(f1844,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK77 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK77 )
| ~ ( irel @ sK77 @ sK78 )
| ( sK4 @ sK78 ) )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ Y0 @ sK76 )
| ~ ( irel @ sK23 @ Y0 ) )
@ sK79 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f1843]) ).
thf(f1843,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ Y0 @ sK76 )
| ~ ( irel @ sK23 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK77 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK77 )
| ~ ( irel @ sK77 @ sK78 )
| ( sK4 @ sK78 ) )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1842]) ).
thf(f1842,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ Y0 @ sK76 )
| ~ ( irel @ sK23 @ Y0 ) ) )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK77 @ Y0 ) ) )
| ~ ( irel @ sK23 @ sK77 )
| ~ ( irel @ sK77 @ sK78 )
| ( sK4 @ sK78 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1841]) ).
thf(f1841,plain,
( ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ sK77 @ Y1 ) ) )
| ~ ( irel @ sK23 @ sK77 )
| ~ ( irel @ sK77 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK78 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ Y0 @ sK76 )
| ~ ( irel @ sK23 @ Y0 ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f1840]) ).
thf(f1840,plain,
( ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ sK77 @ Y1 ) ) )
| ~ ( irel @ sK23 @ sK77 )
| ~ ( irel @ sK77 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ Y0 @ sK76 )
| ~ ( irel @ sK23 @ Y0 ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1839]) ).
thf(f1839,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
@ sK77 )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ Y0 @ sK76 )
| ~ ( irel @ sK23 @ Y0 ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f1838]) ).
thf(f1838,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ Y0 @ sK76 )
| ~ ( irel @ sK23 @ Y0 ) ) )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1837]) ).
thf(f1837,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) )
@ sK76 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f1836]) ).
thf(f1836,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1835]) ).
thf(f1835,plain,
( ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1834]) ).
thf(f1834,plain,
( ( ( ~ ( irel @ sK18 @ sK19 ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1549]) ).
thf(f1549,plain,
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ sK23 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK18 @ sK19 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f237]) ).
thf(f237,plain,
( ( ( ~ ( irel @ sK22 @ sK21 )
| ( sK4 @ sK20 )
| ~ ( irel @ sK21 @ sK20 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK21 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK18 @ sK19 ) )
= $false )
| ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ sK23 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f236]) ).
thf(f2133,plain,
( spl1_12
| spl1_15
| spl1_20
| spl1_11 ),
inference(avatar_split_clause,[status(thm)],[f1873,f2083,f2127,f2100,f2087]) ).
thf(f1873,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK77 @ X2 )
= $false )
| ( ( irel @ sK79 @ sK76 )
= $true )
| ( ( irel @ sK21 @ X1 )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( $true
= ( sK3 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1872]) ).
thf(f1872,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK21 @ X1 )
= $false )
| ( ( irel @ sK77 @ X2 )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK3 @ X1 ) )
| ( ( ~ ( irel @ sK79 @ sK76 ) )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1862]) ).
thf(f1862,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK18 @ sK19 ) )
| ( $true
= ( ~ ( irel @ sK77 @ X2 ) ) )
| ( ( irel @ sK21 @ X1 )
= $false )
| ( $true
= ( sK3 @ X1 ) )
| ( ( ~ ( irel @ sK79 @ sK76 ) )
= $false )
| ( $true
= ( sK3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1861]) ).
thf(f2120,plain,
( spl1_18
| spl1_11
| spl1_12
| spl1_17 ),
inference(avatar_split_clause,[status(thm)],[f1912,f2110,f2087,f2083,f2114]) ).
thf(f1912,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK79 @ X2 )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( sK4 @ X2 )
= $true )
| ( ( irel @ sK77 @ sK78 )
= $true )
| ( $true
= ( sK3 @ X1 ) )
| ( ( irel @ sK21 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1911]) ).
thf(f1911,plain,
! [X2: $i,X1: $i] :
( ( ( sK4 @ X2 )
= $true )
| ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK79 @ X2 ) ) )
| ( ( irel @ sK77 @ sK78 )
= $true )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( irel @ sK21 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1910]) ).
thf(f1910,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK77 @ sK78 )
= $true )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( $true
= ( ~ ( irel @ sK79 @ X2 )
| ( sK4 @ X2 ) ) )
| ( ( irel @ sK21 @ X1 )
= $false )
| ( $true
= ( sK3 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1909]) ).
thf(f1909,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK21 @ X1 )
= $false )
| ( ( irel @ sK77 @ sK78 )
= $true )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( $true
= ( sK3 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f1908]) ).
thf(f1908,plain,
! [X1: $i] :
( ( ( irel @ sK21 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( irel @ sK77 @ sK78 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f1907]) ).
thf(f1907,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( irel @ sK77 @ sK78 )
= $true )
| ( $true
= ( sK3 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( irel @ sK21 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1905]) ).
thf(f1905,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( ( irel @ sK77 @ sK78 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 ) )
= $false )
| ( ( irel @ sK21 @ X1 )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1903]) ).
thf(f1903,plain,
! [X1: $i] :
( ( ( irel @ sK77 @ sK78 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ sK79 @ sK76 ) )
= $false )
| ( ( irel @ sK21 @ X1 )
= $false )
| ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( irel @ sK18 @ sK19 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1902]) ).
thf(f1902,plain,
! [X1: $i] :
( ( ( irel @ sK21 @ X1 )
= $false )
| ( $true
= ( sK3 @ X1 ) )
| ( ( ~ ( irel @ sK77 @ sK78 ) )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ sK79 @ sK76 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1901]) ).
thf(f1901,plain,
! [X1: $i] :
( ( $true
= ( ~ ( irel @ sK21 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ sK79 @ sK76 ) )
= $false )
| ( ( ~ ( irel @ sK77 @ sK78 ) )
= $false )
| ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( irel @ sK18 @ sK19 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1851]) ).
thf(f1851,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK79 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK76 )
| ~ ( irel @ sK79 @ sK76 )
| ~ ( irel @ sK23 @ sK79 ) )
= $false )
| ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK21 @ X1 ) ) )
| ( ( ~ ( irel @ sK77 @ sK78 ) )
= $false )
| ( $true
= ( irel @ sK18 @ sK19 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1850]) ).
thf(f2118,plain,
( spl1_15
| spl1_11
| spl1_12
| spl1_18 ),
inference(avatar_split_clause,[status(thm)],[f1913,f2114,f2087,f2083,f2100]) ).
thf(f1913,plain,
! [X1: $i] :
( ( ( irel @ sK21 @ X1 )
= $false )
| ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( irel @ sK77 @ sK78 )
= $true )
| ( ( irel @ sK79 @ sK76 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f1904]) ).
thf(f1904,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( irel @ sK18 @ sK19 ) )
| ( ( irel @ sK21 @ X1 )
= $false )
| ( ( ~ ( irel @ sK79 @ sK76 ) )
= $false )
| ( ( irel @ sK77 @ sK78 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1903]) ).
thf(f2035,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f2026,f2032,f2028]) ).
thf(f2026,plain,
( ( $true
= ( irel @ sK5 @ sK22 ) )
| ( ( irel @ sK5 @ sK23 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f2025]) ).
thf(f2025,plain,
( ( $true
= ( irel @ sK5 @ sK22 ) )
| ( ( ~ ( irel @ sK5 @ sK23 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1938]) ).
thf(f1938,plain,
( ( ( ~ ( irel @ sK5 @ sK22 ) )
= $false )
| ( ( ~ ( irel @ sK5 @ sK23 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f234]) ).
thf(f234,plain,
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ sK23 @ Y0 )
| ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 )
| ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK23 @ Y1 ) ) ) ) )
| ~ ( irel @ sK5 @ sK23 ) )
= $false )
| ( ( ~ ( irel @ sK5 @ sK22 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n025.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue May 5 09:26:13 EDT 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.19/0.47 % Domain : Software Verification
% 0.19/0.47 % Problem : Benchmark: LCL696^1, Active target: ixor
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English :
% 0.19/0.47
% 0.19/0.47 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.19/0.47 % Source : [Kon26]
% 0.19/0.47 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : ? v9.3.0
% 0.19/0.47 % Syntax : Number of formulae : 26 ( 1 unt; 24 typ; 0 def)
% 0.19/0.47 % Number of atoms : 68 ( 22 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 24 ( 34 avg)
% 0.19/0.47 % Number of connectives : 187 ( 38 ~; 32 |; 26 &; 90 @)
% 0.19/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 26 ( 14 avg)
% 0.19/0.47 % Number of types : 4 ( 2 usr)
% 0.19/0.47 % Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 23 ( 22 usr; 1 con; 0-3 aty)
% 0.19/0.47 % Number of variables : 73 ( 41 ^; 31 !; 1 ?; 73 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments :
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(unsorted_type,type,
% 0.19/0.47 unsorted: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(irel_decl,type,
% 0.19/0.47 irel: $i > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(mnot_decl,type,
% 0.19/0.47 mnot: ( $i > $o ) > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(mor_decl,type,
% 0.19/0.47 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(mand_decl,type,
% 0.19/0.47 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(mimplies_decl,type,
% 0.19/0.47 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(mbox_s4_decl,type,
% 0.19/0.47 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(iatom_decl,type,
% 0.19/0.47 iatom: ( $i > $o ) > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(inot_decl,type,
% 0.19/0.47 inot: ( $i > $o ) > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(itrue_decl,type,
% 0.19/0.47 itrue: $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(ifalse_decl,type,
% 0.19/0.47 ifalse: $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(iand_decl,type,
% 0.19/0.47 iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(ior_decl,type,
% 0.19/0.47 ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(iimplies_decl,type,
% 0.19/0.47 iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(iimplied_decl,type,
% 0.19/0.47 iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(iequiv_decl,type,
% 0.19/0.47 iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(ixor_decl,type,
% 0.19/0.47 ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(ivalid_decl,type,
% 0.19/0.47 ivalid: ( $i > $o ) > $o ).
% 0.19/0.47
% 0.19/0.47 thf(isatisfiable_decl,type,
% 0.19/0.47 isatisfiable: ( $i > $o ) > $o ).
% 0.19/0.47
% 0.19/0.47 thf(icountersatisfiable_decl,type,
% 0.19/0.47 icountersatisfiable: ( $i > $o ) > $o ).
% 0.19/0.47
% 0.19/0.47 thf(iinvalid_decl,type,
% 0.19/0.47 iinvalid: ( $i > $o ) > $o ).
% 0.19/0.47
% 0.19/0.47 %----Types of the domains
% 0.19/0.47 thf(d_unsorted_type,type,
% 0.19/0.47 d_unsorted: $tType ).
% 0.19/0.47
% 0.19/0.47 %----Types of the promotion functions
% 0.19/0.47 thf(d2unsorted_decl,type,
% 0.19/0.47 d2unsorted: d_unsorted > $i ).
% 0.19/0.47
% 0.19/0.47 %----Types of the domain elements
% 0.19/0.47 thf(d_unsorted_0_decl,type,
% 0.19/0.47 d_unsorted_0: d_unsorted ).
% 0.19/0.47
% 0.19/0.47 thf(lcl696_1,axiom,
% 0.19/0.47 ( ! [U: $i] :
% 0.19/0.47 ? [DU: d_unsorted] :
% 0.19/0.47 ( U
% 0.19/0.47 = ( d2unsorted @ DU ) )
% 0.19/0.47 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 0.19/0.47 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 0.19/0.47 ( ( ( d2unsorted @ DU1 )
% 0.19/0.47 = ( d2unsorted @ DU2 ) )
% 0.19/0.47 => ( DU1 = DU2 ) )
% 0.19/0.47 & ( mnot
% 0.19/0.47 = ( ^ [X: $i > $o,U: $i] :
% 0.19/0.47 ~ ( X @ U ) ) )
% 0.19/0.47 & ( mor
% 0.19/0.47 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.19/0.47 ( ( X @ U )
% 0.19/0.47 | ( Y @ U ) ) ) )
% 0.19/0.47 & ( mand
% 0.19/0.47 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.19/0.47 ( ( X @ U )
% 0.19/0.47 & ( Y @ U ) ) ) )
% 0.19/0.47 & ( mimplies
% 0.19/0.47 = ( ^ [U: $i > $o,V: $i > $o,Flatten_var_0: $i] :
% 0.19/0.47 ( ~ ( U @ Flatten_var_0 )
% 0.19/0.47 | ( V @ Flatten_var_0 ) ) ) )
% 0.19/0.47 & ( mbox_s4
% 0.19/0.47 = ( ^ [P: $i > $o,X: $i] :
% 0.19/0.47 ! [Y: $i] :
% 0.19/0.47 ( ~ ( irel @ X @ Y )
% 0.19/0.47 | ( P @ Y ) ) ) )
% 0.19/0.47 & ( iatom
% 0.19/0.47 = ( ^ [P: $i > $o,Flatten_var_0: $i] : ( P @ Flatten_var_0 ) ) )
% 0.19/0.47 & ( inot
% 0.19/0.47 = ( ^ [P: $i > $o,Flatten_var_0: $i] :
% 0.19/0.47 ~ ! [Y: $i] :
% 0.19/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.19/0.47 | ( P @ Y ) ) ) )
% 0.19/0.47 & ( iand
% 0.19/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.19/0.47 ( ! [Y: $i] :
% 0.19/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.19/0.47 | ( P @ Y ) )
% 0.19/0.47 & ! [Y: $i] :
% 0.19/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.19/0.47 | ( Q @ Y ) ) ) ) )
% 0.19/0.47 & ( ior
% 0.19/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.19/0.47 ( ! [Y: $i] :
% 0.19/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.19/0.47 | ( P @ Y ) )
% 0.19/0.47 | ! [Y: $i] :
% 0.19/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.19/0.47 | ( Q @ Y ) ) ) ) )
% 0.19/0.47 & ( iimplies
% 0.19/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.19/0.47 ( ~ ! [Y: $i] :
% 0.19/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.19/0.47 | ( P @ Y ) )
% 0.19/0.47 | ! [Y: $i] :
% 0.19/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.19/0.47 | ( Q @ Y ) ) ) ) )
% 0.19/0.47 & ( iimplied
% 0.19/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.19/0.47 ( ~ ! [Y: $i] :
% 0.19/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.19/0.47 | ( Q @ Y ) )
% 0.19/0.47 | ! [Y: $i] :
% 0.19/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.19/0.47 | ( P @ Y ) ) ) ) )
% 0.19/0.47 & ( iequiv
% 0.19/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.19/0.47 ( ! [Y: $i,Bound_variable_718: $i] :
% 0.19/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.19/0.47 | ~ ! [Bound_variable_693: $i] :
% 0.19/0.47 ( ~ ( irel @ Y @ Bound_variable_693 )
% 0.19/0.47 | ( P @ Bound_variable_693 ) )
% 0.19/0.47 | ~ ( irel @ Y @ Bound_variable_718 )
% 0.19/0.47 | ( Q @ Bound_variable_718 ) )
% 0.19/0.47 & ! [Y: $i,Bound_variable_771: $i] :
% 0.19/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.19/0.47 | ~ ! [Bound_variable_746: $i] :
% 0.19/0.47 ( ~ ( irel @ Y @ Bound_variable_746 )
% 0.19/0.47 | ( Q @ Bound_variable_746 ) )
% 0.19/0.47 | ~ ( irel @ Y @ Bound_variable_771 )
% 0.19/0.47 | ( P @ Bound_variable_771 ) ) ) ) )
% 0.19/0.47 & ( ixor
% 0.19/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.19/0.47 ~ ! [Y: $i,Bound_variable_849: $i,Bound_variable_851: $i,Bound_variable_864: $i,Bound_variable_866: $i] :
% 0.19/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.19/0.47 | ( ( ~ ( irel @ Y @ Bound_variable_849 )
% 0.19/0.47 | ~ ! [Bound_variable_693: $i] :
% 0.19/0.47 ( ~ ( irel @ Bound_variable_849 @ Bound_variable_693 )
% 0.19/0.47 | ( P @ Bound_variable_693 ) )
% 0.19/0.47 | ~ ( irel @ Bound_variable_849 @ Bound_variable_851 )
% 0.19/0.47 | ( Q @ Bound_variable_851 ) )
% 0.19/0.47 & ( ~ ( irel @ Y @ Bound_variable_864 )
% 0.19/0.47 | ~ ! [Bound_variable_746: $i] :
% 0.19/0.47 ( ~ ( irel @ Bound_variable_864 @ Bound_variable_746 )
% 0.19/0.47 | ( Q @ Bound_variable_746 ) )
% 0.19/0.47 | ~ ( irel @ Bound_variable_864 @ Bound_variable_866 )
% 0.19/0.47 | ( P @ Bound_variable_866 ) ) ) ) ) )
% 0.19/0.47 & ( ivalid
% 0.19/0.47 = ( ^ [Phi: $i > $o] :
% 0.19/0.47 ! [W: $i] : ( Phi @ W ) ) )
% 0.19/0.47 & ( isatisfiable
% 0.19/0.47 = ( ^ [Phi: $i > $o] :
% 0.19/0.47 ~ ! [W: $i] :
% 0.19/0.47 ~ ( Phi @ W ) ) )
% 0.19/0.47 & ( icountersatisfiable
% 0.19/0.47 = ( ^ [Phi: $i > $o] :
% 0.19/0.47 ~ ! [W: $i] : ( Phi @ W ) ) )
% 0.19/0.47 & ( iinvalid
% 0.19/0.47 = ( ^ [Phi: $i > $o] :
% 0.19/0.47 ! [W: $i] :
% 0.19/0.47 ~ ( Phi @ W ) ) )
% 0.19/0.47 & ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
% 0.19/0.47 & ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
% 0.19/0.47 & ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(ixor,conjecture,
% 0.19/0.47 ( ixor
% 0.19/0.47 = ( ^ [P: $i > $o,Q: $i > $o] : ( inot @ ( iequiv @ P @ Q ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.79/1.31 ---- Embedded in THF ---
% 1.79/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.79/1.31 %%% Generated on Tue May 05 09:26:14 EDT 2026
% 1.79/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.79/1.31 %%% Logic specification used:
% 1.79/1.31 %%% thf(spec, logic, $$dhol).
% 1.79/1.31
% 1.79/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.YfK2dOMluu/DTF2DTF2576.p
% See solution above
% 1.79/1.31 ------------------------
% 1.79/1.32 ---- Cleaned THF ---
% 1.79/1.32 thf(unsorted_type,type,
% 1.79/1.32 unsorted: $tType ).
% 1.79/1.32
% 1.79/1.32 thf(irel_decl,type,
% 1.79/1.32 irel: $i > $i > $o ).
% 1.79/1.32
% 1.79/1.32 thf(mnot_decl,type,
% 1.79/1.32 mnot: ( $i > $o ) > $i > $o ).
% 1.79/1.32
% 1.79/1.32 thf(mor_decl,type,
% 1.79/1.32 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.79/1.32
% 1.79/1.32 thf(mand_decl,type,
% 1.79/1.32 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.79/1.32
% 1.79/1.32 thf(mimplies_decl,type,
% 1.79/1.32 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.79/1.32
% 1.79/1.32 thf(mbox_s4_decl,type,
% 1.79/1.32 mbox_s4: ( $i > $o ) > $i > $o ).
% 1.79/1.32
% 1.79/1.32 thf(iatom_decl,type,
% 1.79/1.32 iatom: ( $i > $o ) > $i > $o ).
% 1.79/1.32
% 1.79/1.32 thf(inot_decl,type,
% 1.79/1.32 inot: ( $i > $o ) > $i > $o ).
% 1.79/1.32
% 1.79/1.32 thf(itrue_decl,type,
% 1.79/1.32 itrue: $i > $o ).
% 1.79/1.32
% 1.79/1.32 thf(ifalse_decl,type,
% 1.79/1.32 ifalse: $i > $o ).
% 1.79/1.32
% 1.79/1.32 thf(iand_decl,type,
% 1.79/1.32 iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.79/1.32
% 1.79/1.32 thf(ior_decl,type,
% 1.79/1.32 ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.79/1.32
% 1.79/1.32 thf(iimplies_decl,type,
% 1.79/1.32 iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.79/1.32
% 1.79/1.32 thf(iimplied_decl,type,
% 1.79/1.32 iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.79/1.32
% 1.79/1.32 thf(iequiv_decl,type,
% 1.79/1.32 iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.79/1.32
% 1.79/1.32 thf(ixor_decl,type,
% 1.79/1.32 ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.79/1.32
% 1.79/1.32 thf(ivalid_decl,type,
% 1.79/1.32 ivalid: ( $i > $o ) > $o ).
% 1.79/1.32
% 1.79/1.32 thf(isatisfiable_decl,type,
% 1.79/1.32 isatisfiable: ( $i > $o ) > $o ).
% 1.79/1.32
% 1.79/1.32 thf(icountersatisfiable_decl,type,
% 1.79/1.32 icountersatisfiable: ( $i > $o ) > $o ).
% 1.79/1.32
% 1.79/1.32 thf(iinvalid_decl,type,
% 1.79/1.32 iinvalid: ( $i > $o ) > $o ).
% 1.79/1.32
% 1.79/1.32 thf(d_unsorted_type,type,
% 1.79/1.32 d_unsorted: $tType ).
% 1.79/1.32
% 1.79/1.32 thf(d2unsorted_decl,type,
% 1.79/1.32 d2unsorted: d_unsorted > $i ).
% 1.79/1.32
% 1.79/1.32 thf(d_unsorted_0_decl,type,
% 1.79/1.32 d_unsorted_0: d_unsorted ).
% 1.79/1.32
% 1.79/1.32 thf(lcl696_1,axiom,
% 1.79/1.32 ( ! [U: $i] :
% 1.79/1.32 ? [DU: d_unsorted] :
% 1.79/1.32 ( U
% 1.79/1.32 = ( d2unsorted @ DU ) )
% 1.79/1.32 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 1.79/1.32 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 1.79/1.32 ( ( ( d2unsorted @ DU1 )
% 1.79/1.32 = ( d2unsorted @ DU2 ) )
% 1.79/1.32 => ( DU1 = DU2 ) )
% 1.79/1.32 & ( mnot
% 1.79/1.32 = ( ^ [X: $i > $o,U: $i] :
% 1.79/1.32 ~ ( X @ U ) ) )
% 1.79/1.32 & ( mor
% 1.79/1.32 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 1.79/1.32 ( ( X @ U )
% 1.79/1.32 | ( Y @ U ) ) ) )
% 1.79/1.32 & ( mand
% 1.79/1.32 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 1.79/1.32 ( ( X @ U )
% 1.79/1.32 & ( Y @ U ) ) ) )
% 1.79/1.32 & ( mimplies
% 1.79/1.32 = ( ^ [U: $i > $o,V: $i > $o,Flatten_var_0: $i] :
% 1.79/1.32 ( ~ ( U @ Flatten_var_0 )
% 1.79/1.32 | ( V @ Flatten_var_0 ) ) ) )
% 1.79/1.32 & ( mbox_s4
% 1.79/1.32 = ( ^ [P: $i > $o,X: $i] :
% 1.79/1.32 ! [Y: $i] :
% 1.79/1.32 ( ~ ( irel @ X @ Y )
% 1.79/1.32 | ( P @ Y ) ) ) )
% 1.79/1.32 & ( iatom
% 1.79/1.32 = ( ^ [P: $i > $o,Flatten_var_0: $i] : ( P @ Flatten_var_0 ) ) )
% 1.79/1.32 & ( inot
% 1.79/1.32 = ( ^ [P: $i > $o,Flatten_var_0: $i] :
% 1.79/1.32 ~ ! [Y: $i] :
% 1.79/1.32 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.79/1.32 | ( P @ Y ) ) ) )
% 1.79/1.32 & ( iand
% 1.79/1.32 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.79/1.32 ( ! [Y: $i] :
% 1.79/1.32 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.79/1.32 | ( P @ Y ) )
% 1.79/1.32 & ! [Y: $i] :
% 1.79/1.32 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.79/1.32 | ( Q @ Y ) ) ) ) )
% 1.79/1.32 & ( ior
% 1.79/1.32 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.79/1.32 ( ! [Y: $i] :
% 1.79/1.32 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.79/1.32 | ( P @ Y ) )
% 1.79/1.32 | ! [Y: $i] :
% 1.79/1.32 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.79/1.32 | ( Q @ Y ) ) ) ) )
% 1.79/1.32 & ( iimplies
% 1.79/1.32 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.79/1.32 ( ~ ! [Y: $i] :
% 1.79/1.32 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.79/1.32 | ( P @ Y ) )
% 1.79/1.32 | ! [Y: $i] :
% 1.79/1.32 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.79/1.32 | ( Q @ Y ) ) ) ) )
% 1.79/1.32 & ( iimplied
% 1.79/1.32 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.79/1.32 ( ~ ! [Y: $i] :
% 1.79/1.32 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.79/1.32 | ( Q @ Y ) )
% 1.79/1.32 | ! [Y: $i] :
% 1.79/1.32 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.79/1.32 | ( P @ Y ) ) ) ) )
% 1.79/1.32 & ( iequiv
% 1.79/1.32 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.79/1.32 ( ! [Y: $i,Bound_variable_718: $i] :
% 1.79/1.32 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.79/1.32 | ~ ! [Bound_variable_693: $i] :
% 1.79/1.32 ( ~ ( irel @ Y @ Bound_variable_693 )
% 1.79/1.32 | ( P @ Bound_variable_693 ) )
% 1.79/1.32 | ~ ( irel @ Y @ Bound_variable_718 )
% 1.79/1.32 | ( Q @ Bound_variable_718 ) )
% 1.79/1.32 & ! [Y: $i,Bound_variable_771: $i] :
% 1.79/1.32 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.79/1.32 | ~ ! [Bound_variable_746: $i] :
% 1.79/1.32 ( ~ ( irel @ Y @ Bound_variable_746 )
% 1.79/1.32 | ( Q @ Bound_variable_746 ) )
% 1.79/1.32 | ~ ( irel @ Y @ Bound_variable_771 )
% 1.79/1.32 | ( P @ Bound_variable_771 ) ) ) ) )
% 1.79/1.32 & ( ixor
% 1.79/1.32 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.79/1.32 ~ ! [Y: $i,Bound_variable_849: $i,Bound_variable_851: $i,Bound_variable_864: $i,Bound_variable_866: $i] :
% 1.79/1.32 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.79/1.32 | ( ( ~ ( irel @ Y @ Bound_variable_849 )
% 1.79/1.32 | ~ ! [Bound_variable_693: $i] :
% 1.79/1.32 ( ~ ( irel @ Bound_variable_849 @ Bound_variable_693 )
% 1.79/1.32 | ( P @ Bound_variable_693 ) )
% 1.79/1.32 | ~ ( irel @ Bound_variable_849 @ Bound_variable_851 )
% 1.79/1.32 | ( Q @ Bound_variable_851 ) )
% 1.79/1.32 & ( ~ ( irel @ Y @ Bound_variable_864 )
% 1.79/1.32 | ~ ! [Bound_variable_746: $i] :
% 1.79/1.32 ( ~ ( irel @ Bound_variable_864 @ Bound_variable_746 )
% 1.79/1.32 | ( Q @ Bound_variable_746 ) )
% 1.79/1.32 | ~ ( irel @ Bound_variable_864 @ Bound_variable_866 )
% 1.79/1.32 | ( P @ Bound_variable_866 ) ) ) ) ) )
% 1.79/1.32 & ( ivalid
% 1.79/1.32 = ( ^ [Phi: $i > $o] :
% 1.79/1.32 ! [W: $i] : ( Phi @ W ) ) )
% 1.79/1.32 & ( isatisfiable
% 1.79/1.32 = ( ^ [Phi: $i > $o] :
% 1.79/1.32 ~ ! [W: $i] :
% 1.79/1.32 ~ ( Phi @ W ) ) )
% 1.79/1.32 & ( icountersatisfiable
% 1.79/1.32 = ( ^ [Phi: $i > $o] :
% 1.79/1.32 ~ ! [W: $i] : ( Phi @ W ) ) )
% 1.79/1.32 & ( iinvalid
% 1.79/1.32 = ( ^ [Phi: $i > $o] :
% 1.79/1.32 ! [W: $i] :
% 1.79/1.32 ~ ( Phi @ W ) ) )
% 1.79/1.32 & ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
% 1.79/1.32 & ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
% 1.79/1.32 & ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ) ).
% 1.79/1.32
% 1.79/1.32 thf(ixor,conjecture,
% 1.79/1.32 ( ixor
% 1.79/1.32 = ( ^ [P: $i > $o,Q: $i > $o] : ( inot @ ( iequiv @ P @ Q ) ) ) ) ).
% 1.79/1.32 ------------------------
% 1.79/1.34 % (2913)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/183Mi)
% 1.79/1.34 % (2914)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/4Mi)
% 1.79/1.34 % (2915)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/27Mi)
% 1.79/1.34 % (2914)Instruction limit reached!
% 1.79/1.34 % (2914)------------------------------
% 1.79/1.34 % (2914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.34 % (2914)Termination reason: Unknown
% 1.79/1.34 % (2914)Termination phase: shuffling
% 1.79/1.34
% 1.79/1.34 % (2914)Memory used [KB]: 1023
% 1.79/1.34 % (2914)Time elapsed: 0.002 s
% 1.79/1.34 % (2914)Instructions burned: 4 (million)
% 1.79/1.34 % (2914)------------------------------
% 1.79/1.34 % (2914)------------------------------
% 1.79/1.35 % (2916)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/2Mi)
% 1.79/1.35 % (2917)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/2Mi)
% 1.79/1.35 % (2918)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/275Mi)
% 1.79/1.35 % (2919)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/18Mi)
% 1.79/1.35 % (2916)Instruction limit reached!
% 1.79/1.35 % (2916)------------------------------
% 1.79/1.35 % (2916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.35 % (2916)Termination reason: Unknown
% 1.79/1.35 % (2916)Termination phase: shuffling
% 1.79/1.35
% 1.79/1.35 % (2916)Memory used [KB]: 1023
% 1.79/1.35 % (2916)Time elapsed: 0.003 s
% 1.79/1.35 % (2916)Instructions burned: 2 (million)
% 1.79/1.35 % (2916)------------------------------
% 1.79/1.35 % (2916)------------------------------
% 1.79/1.35 % (2917)Instruction limit reached!
% 1.79/1.35 % (2917)------------------------------
% 1.79/1.35 % (2917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.35 % (2917)Termination reason: Unknown
% 1.79/1.35 % (2917)Termination phase: shuffling
% 1.79/1.35
% 1.79/1.35 % (2917)Memory used [KB]: 1023
% 1.79/1.35 % (2917)Time elapsed: 0.003 s
% 1.79/1.35 % (2917)Instructions burned: 2 (million)
% 1.79/1.35 % (2917)------------------------------
% 1.79/1.35 % (2917)------------------------------
% 1.79/1.35 % (2915)Instruction limit reached!
% 1.79/1.35 % (2915)------------------------------
% 1.79/1.35 % (2915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.35 % (2915)Termination reason: Unknown
% 1.79/1.35 % (2915)Termination phase: Saturation
% 1.79/1.35
% 1.79/1.35 % (2915)Memory used [KB]: 5756
% 1.79/1.35 % (2915)Time elapsed: 0.011 s
% 1.79/1.35 % (2915)Instructions burned: 27 (million)
% 1.79/1.35 % (2915)------------------------------
% 1.79/1.35 % (2915)------------------------------
% 1.79/1.35 % (2920)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/3Mi)
% 1.79/1.35 % (2918)Refutation not found, incomplete strategy
% 1.79/1.35 % (2918)------------------------------
% 1.79/1.35 % (2918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.35 % (2918)Termination reason: Refutation not found, incomplete strategy
% 1.79/1.35
% 1.79/1.35
% 1.79/1.35 % (2918)Memory used [KB]: 5628
% 1.79/1.35 % (2918)Time elapsed: 0.006 s
% 1.79/1.35 % (2918)Instructions burned: 6 (million)
% 1.79/1.35 % (2918)------------------------------
% 1.79/1.35 % (2918)------------------------------
% 1.79/1.35 % (2920)Instruction limit reached!
% 1.79/1.35 % (2920)------------------------------
% 1.79/1.35 % (2920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.35 % (2920)Termination reason: Unknown
% 1.79/1.35 % (2920)Termination phase: Property scanning
% 1.79/1.35
% 1.79/1.35 % (2920)Memory used [KB]: 1023
% 1.79/1.35 % (2920)Time elapsed: 0.003 s
% 1.79/1.35 % (2920)Instructions burned: 5 (million)
% 1.79/1.35 % (2920)------------------------------
% 1.79/1.35 % (2920)------------------------------
% 1.79/1.36 % (2919)Instruction limit reached!
% 1.79/1.36 % (2919)------------------------------
% 1.79/1.36 % (2919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.36 % (2919)Termination reason: Unknown
% 1.79/1.36 % (2919)Termination phase: Saturation
% 1.79/1.36
% 1.79/1.36 % (2919)Memory used [KB]: 5628
% 1.79/1.36 % (2919)Time elapsed: 0.013 s
% 1.79/1.36 % (2919)Instructions burned: 19 (million)
% 1.79/1.36 % (2919)------------------------------
% 1.79/1.36 % (2919)------------------------------
% 1.79/1.36 % (2923)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/3Mi)
% 1.79/1.36 % (2923)Instruction limit reached!
% 1.79/1.36 % (2923)------------------------------
% 1.79/1.36 % (2923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.36 % (2923)Termination reason: Unknown
% 1.79/1.36 % (2923)Termination phase: shuffling
% 1.79/1.36
% 1.79/1.36 % (2923)Memory used [KB]: 1023
% 1.79/1.36 % (2923)Time elapsed: 0.002 s
% 1.79/1.36 % (2923)Instructions burned: 3 (million)
% 1.79/1.36 % (2923)------------------------------
% 1.79/1.36 % (2923)------------------------------
% 1.79/1.36 % (2925)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/7Mi)
% 1.79/1.36 % (2925)Instruction limit reached!
% 1.79/1.36 % (2925)------------------------------
% 1.79/1.36 % (2925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.36 % (2925)Termination reason: Unknown
% 1.79/1.36 % (2925)Termination phase: Saturation
% 1.79/1.36
% 1.79/1.36 % (2925)Memory used [KB]: 1023
% 1.79/1.36 % (2925)Time elapsed: 0.004 s
% 1.79/1.36 % (2925)Instructions burned: 8 (million)
% 1.79/1.36 % (2925)------------------------------
% 1.79/1.36 % (2925)------------------------------
% 1.79/1.36 % (2921)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/37Mi)
% 1.79/1.36 % (2922)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/15Mi)
% 1.79/1.37 % (2924)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/1041Mi)
% 1.79/1.37 % (2927)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/3Mi)
% 1.79/1.37 % (2927)Instruction limit reached!
% 1.79/1.37 % (2927)------------------------------
% 1.79/1.37 % (2927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.37 % (2927)Termination reason: Unknown
% 1.79/1.37 % (2927)Termination phase: Property scanning
% 1.79/1.37
% 1.79/1.37 % (2927)Memory used [KB]: 1023
% 1.79/1.37 % (2927)Time elapsed: 0.003 s
% 1.79/1.37 % (2927)Instructions burned: 5 (million)
% 1.79/1.37 % (2927)------------------------------
% 1.79/1.37 % (2927)------------------------------
% 1.79/1.37 % (2922)Instruction limit reached!
% 1.79/1.37 % (2922)------------------------------
% 1.79/1.37 % (2922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.37 % (2922)Termination reason: Unknown
% 1.79/1.37 % (2922)Termination phase: Saturation
% 1.79/1.37
% 1.79/1.37 % (2922)Memory used [KB]: 5884
% 1.79/1.37 % (2922)Time elapsed: 0.010 s
% 1.79/1.37 % (2922)Instructions burned: 15 (million)
% 1.79/1.37 % (2922)------------------------------
% 1.79/1.37 % (2922)------------------------------
% 1.79/1.37 % (2928)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/3Mi)
% 1.79/1.37 % (2926)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/16Mi)
% 1.79/1.37 % (2928)Instruction limit reached!
% 1.79/1.37 % (2928)------------------------------
% 1.79/1.37 % (2928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.37 % (2928)Termination reason: Unknown
% 1.79/1.37 % (2928)Termination phase: Property scanning
% 1.79/1.37
% 1.79/1.37 % (2928)Memory used [KB]: 1023
% 1.79/1.37 % (2928)Time elapsed: 0.003 s
% 1.79/1.37 % (2928)Instructions burned: 5 (million)
% 1.79/1.37 % (2928)------------------------------
% 1.79/1.37 % (2928)------------------------------
% 1.79/1.38 % (2929)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/7Mi)
% 1.79/1.38 % (2929)Instruction limit reached!
% 1.79/1.38 % (2929)------------------------------
% 1.79/1.38 % (2929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.38 % (2929)Termination reason: Unknown
% 1.79/1.38 % (2929)Termination phase: Property scanning
% 1.79/1.38
% 1.79/1.38 % (2929)Memory used [KB]: 1023
% 1.79/1.38 % (2929)Time elapsed: 0.004 s
% 1.79/1.38 % (2929)Instructions burned: 8 (million)
% 1.79/1.38 % (2929)------------------------------
% 1.79/1.38 % (2929)------------------------------
% 1.79/1.38 % (2921)Instruction limit reached!
% 1.79/1.38 % (2921)------------------------------
% 1.79/1.38 % (2921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.38 % (2921)Termination reason: Unknown
% 1.79/1.38 % (2921)Termination phase: Saturation
% 1.79/1.38
% 1.79/1.38 % (2921)Memory used [KB]: 5628
% 1.79/1.38 % (2921)Time elapsed: 0.022 s
% 1.79/1.38 % (2921)Instructions burned: 37 (million)
% 1.79/1.38 % (2921)------------------------------
% 1.79/1.38 % (2921)------------------------------
% 1.79/1.38 % (2926)Instruction limit reached!
% 1.79/1.38 % (2926)------------------------------
% 1.79/1.38 % (2926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.38 % (2926)Termination reason: Unknown
% 1.79/1.38 % (2926)Termination phase: Saturation
% 1.79/1.38
% 1.79/1.38 % (2926)Memory used [KB]: 5756
% 1.79/1.38 % (2926)Time elapsed: 0.012 s
% 1.79/1.38 % (2926)Instructions burned: 17 (million)
% 1.79/1.38 % (2926)------------------------------
% 1.79/1.38 % (2926)------------------------------
% 1.79/1.38 % (2931)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/4Mi)
% 1.79/1.38 % (2931)Instruction limit reached!
% 1.79/1.38 % (2931)------------------------------
% 1.79/1.38 % (2931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.38 % (2931)Termination reason: Unknown
% 1.79/1.38 % (2931)Termination phase: Property scanning
% 1.79/1.38
% 1.79/1.38 % (2931)Memory used [KB]: 1023
% 1.79/1.38 % (2931)Time elapsed: 0.003 s
% 1.79/1.39 % (2931)Instructions burned: 5 (million)
% 1.79/1.39 % (2931)------------------------------
% 1.79/1.39 % (2931)------------------------------
% 1.79/1.39 % (2930)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/3Mi)
% 1.79/1.39 % (2913)Instruction limit reached!
% 1.79/1.39 % (2913)------------------------------
% 1.79/1.39 % (2913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.39 % (2913)Termination reason: Unknown
% 1.79/1.39 % (2913)Termination phase: Saturation
% 1.79/1.39
% 1.79/1.39 % (2913)Memory used [KB]: 6396
% 1.79/1.39 % (2913)Time elapsed: 0.054 s
% 1.79/1.39 % (2913)Instructions burned: 184 (million)
% 1.79/1.39 % (2913)------------------------------
% 1.79/1.39 % (2913)------------------------------
% 1.79/1.39 % (2930)Instruction limit reached!
% 1.79/1.39 % (2930)------------------------------
% 1.79/1.39 % (2930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.39 % (2930)Termination reason: Unknown
% 1.79/1.39 % (2930)Termination phase: Property scanning
% 1.79/1.39
% 1.79/1.39 % (2930)Memory used [KB]: 1023
% 1.79/1.39 % (2930)Time elapsed: 0.004 s
% 1.79/1.39 % (2930)Instructions burned: 4 (million)
% 1.79/1.39 % (2930)------------------------------
% 1.79/1.39 % (2930)------------------------------
% 1.79/1.39 % (2932)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/18Mi)
% 1.79/1.39 % (2935)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/902Mi)
% 1.82/1.40 % (2935)Refutation not found, incomplete strategy
% 1.82/1.40 % (2935)------------------------------
% 1.82/1.40 % (2935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.40 % (2935)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.40
% 1.82/1.40
% 1.82/1.40 % (2935)Memory used [KB]: 5628
% 1.82/1.40 % (2935)Time elapsed: 0.005 s
% 1.82/1.40 % (2935)Instructions burned: 10 (million)
% 1.82/1.40 % (2935)------------------------------
% 1.82/1.40 % (2935)------------------------------
% 1.82/1.40 % (2932)Instruction limit reached!
% 1.82/1.40 % (2932)------------------------------
% 1.82/1.40 % (2932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.40 % (2936)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/21Mi)
% 1.82/1.40 % (2932)Termination reason: Unknown
% 1.82/1.40 % (2932)Termination phase: Saturation
% 1.82/1.40
% 1.82/1.40 % (2932)Memory used [KB]: 5628
% 1.82/1.40 % (2932)Time elapsed: 0.008 s
% 1.82/1.40 % (2932)Instructions burned: 19 (million)
% 1.82/1.40 % (2932)------------------------------
% 1.82/1.40 % (2932)------------------------------
% 1.82/1.40 % (2933)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/710Mi)
% 1.82/1.40 % (2934)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/6Mi)
% 1.82/1.41 % (2934)Instruction limit reached!
% 1.82/1.41 % (2934)------------------------------
% 1.82/1.41 % (2934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.41 % (2934)Termination reason: Unknown
% 1.82/1.41 % (2934)Termination phase: Function definition elimination
% 1.82/1.41
% 1.82/1.41 % (2934)Memory used [KB]: 1023
% 1.82/1.41 % (2934)Time elapsed: 0.006 s
% 1.82/1.41 % (2934)Instructions burned: 8 (million)
% 1.82/1.41 % (2934)------------------------------
% 1.82/1.41 % (2934)------------------------------
% 1.82/1.41 % (2936)Instruction limit reached!
% 1.82/1.41 % (2936)------------------------------
% 1.82/1.41 % (2936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.41 % (2936)Termination reason: Unknown
% 1.82/1.41 % (2936)Termination phase: Saturation
% 1.82/1.41
% 1.82/1.41 % (2936)Memory used [KB]: 5628
% 1.82/1.41 % (2936)Time elapsed: 0.008 s
% 1.82/1.41 % (2936)Instructions burned: 22 (million)
% 1.82/1.41 % (2936)------------------------------
% 1.82/1.41 % (2936)------------------------------
% 1.82/1.41 % (2937)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/5Mi)
% 1.82/1.41 % (2938)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/6Mi)
% 1.82/1.41 % (2939)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/377Mi)
% 1.82/1.41 % (2938)Instruction limit reached!
% 1.82/1.41 % (2938)------------------------------
% 1.82/1.41 % (2938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.41 % (2938)Termination reason: Unknown
% 1.82/1.41 % (2938)Termination phase: Saturation
% 1.82/1.41
% 1.82/1.41 % (2938)Memory used [KB]: 5628
% 1.82/1.41 % (2938)Time elapsed: 0.004 s
% 1.82/1.41 % (2938)Instructions burned: 7 (million)
% 1.82/1.41 % (2938)------------------------------
% 1.82/1.41 % (2938)------------------------------
% 1.82/1.41 % (2937)Instruction limit reached!
% 1.82/1.41 % (2937)------------------------------
% 1.82/1.41 % (2937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.41 % (2937)Termination reason: Unknown
% 1.82/1.41 % (2937)Termination phase: Property scanning
% 1.82/1.41
% 1.82/1.41 % (2937)Memory used [KB]: 1023
% 1.82/1.41 % (2937)Time elapsed: 0.005 s
% 1.82/1.41 % (2937)Instructions burned: 7 (million)
% 1.82/1.41 % (2937)------------------------------
% 1.82/1.41 % (2937)------------------------------
% 1.82/1.42 % (2941)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/19Mi)
% 1.82/1.42 % (2941)Refutation not found, incomplete strategy
% 1.82/1.42 % (2941)------------------------------
% 1.82/1.42 % (2941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.42 % (2941)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.42
% 1.82/1.42
% 1.82/1.42 % (2941)Memory used [KB]: 5628
% 1.82/1.42 % (2941)Time elapsed: 0.003 s
% 1.82/1.42 % (2941)Instructions burned: 7 (million)
% 1.82/1.42 % (2941)------------------------------
% 1.82/1.42 % (2941)------------------------------
% 1.82/1.42 % (2942)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/879Mi)
% 1.82/1.42 % (2940)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/779Mi)
% 1.82/1.43 % (2944)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/3Mi)
% 1.82/1.43 % (2944)Instruction limit reached!
% 1.82/1.43 % (2944)------------------------------
% 1.82/1.43 % (2944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.43 % (2944)Termination reason: Unknown
% 1.82/1.43 % (2944)Termination phase: Property scanning
% 1.82/1.43
% 1.82/1.43 % (2944)Memory used [KB]: 1023
% 1.82/1.43 % (2944)Time elapsed: 0.002 s
% 1.82/1.43 % (2944)Instructions burned: 4 (million)
% 1.82/1.43 % (2944)------------------------------
% 1.82/1.43 % (2944)------------------------------
% 1.82/1.43 % (2943)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/17Mi)
% 1.82/1.44 % (2943)Instruction limit reached!
% 1.82/1.44 % (2943)------------------------------
% 1.82/1.44 % (2943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.44 % (2943)Termination reason: Unknown
% 1.82/1.44 % (2943)Termination phase: Saturation
% 1.82/1.44
% 1.82/1.44 % (2943)Memory used [KB]: 6012
% 1.82/1.44 % (2943)Time elapsed: 0.010 s
% 1.82/1.44 % (2943)Instructions burned: 18 (million)
% 1.82/1.44 % (2943)------------------------------
% 1.82/1.44 % (2943)------------------------------
% 1.82/1.44 % (2945)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/30Mi)
% 1.82/1.44 % (2945)Refutation not found, incomplete strategy
% 1.82/1.44 % (2945)------------------------------
% 1.82/1.44 % (2945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.44 % (2945)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.44
% 1.82/1.44
% 1.82/1.44 % (2945)Memory used [KB]: 5628
% 1.82/1.44 % (2945)Time elapsed: 0.008 s
% 1.82/1.44 % (2945)Instructions burned: 23 (million)
% 1.82/1.44 % (2945)------------------------------
% 1.82/1.44 % (2945)------------------------------
% 1.82/1.45 % (2946)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_2576 for (2999ds/127Mi)
% 1.82/1.45 % (2947)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_2576 for (2998ds/100Mi)
% 1.82/1.49 % (2946)Instruction limit reached!
% 1.82/1.49 % (2946)------------------------------
% 1.82/1.49 % (2946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.49 % (2946)Termination reason: Unknown
% 1.82/1.49 % (2946)Termination phase: Saturation
% 1.82/1.49
% 1.82/1.49 % (2946)Memory used [KB]: 6140
% 1.82/1.49 % (2946)Time elapsed: 0.039 s
% 1.82/1.49 % (2946)Instructions burned: 128 (million)
% 1.82/1.49 % (2946)------------------------------
% 1.82/1.49 % (2946)------------------------------
% 1.82/1.49 % (2947)Instruction limit reached!
% 1.82/1.49 % (2947)------------------------------
% 1.82/1.49 % (2947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.49 % (2947)Termination reason: Unknown
% 1.82/1.49 % (2947)Termination phase: Saturation
% 1.82/1.49
% 1.82/1.49 % (2947)Memory used [KB]: 5884
% 1.82/1.49 % (2947)Time elapsed: 0.054 s
% 1.82/1.49 % (2947)Instructions burned: 101 (million)
% 1.82/1.49 % (2947)------------------------------
% 1.82/1.49 % (2947)------------------------------
% 1.82/1.49 % (2949)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_2576 for (2998ds/20Mi)
% 1.82/1.50 % (2948)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_2576 for (2998ds/3Mi)
% 1.82/1.50 % (2948)Instruction limit reached!
% 1.82/1.50 % (2948)------------------------------
% 1.82/1.50 % (2948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.50 % (2948)Termination reason: Unknown
% 1.82/1.50 % (2948)Termination phase: Property scanning
% 1.82/1.50
% 1.82/1.50 % (2948)Memory used [KB]: 1023
% 1.82/1.50 % (2948)Time elapsed: 0.003 s
% 1.82/1.50 % (2948)Instructions burned: 5 (million)
% 1.82/1.50 % (2948)------------------------------
% 1.82/1.50 % (2948)------------------------------
% 1.82/1.50 % (2949)Refutation not found, incomplete strategy
% 1.82/1.50 % (2949)------------------------------
% 1.82/1.50 % (2949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.50 % (2949)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.50
% 1.82/1.50
% 1.82/1.50 % (2949)Memory used [KB]: 5500
% 1.82/1.50 % (2949)Time elapsed: 0.002 s
% 1.82/1.50 % (2949)Instructions burned: 4 (million)
% 1.82/1.50 % (2949)------------------------------
% 1.82/1.50 % (2949)------------------------------
% 1.82/1.51 % (2951)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_2576 for (2998ds/107Mi)
% 1.82/1.51 % (2950)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_2576 for (2998ds/86Mi)
% 1.82/1.53 % (2942)First to succeed.
% 1.82/1.53 % (2950)Instruction limit reached!
% 1.82/1.53 % (2950)------------------------------
% 1.82/1.53 % (2950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.53 % (2950)Termination reason: Unknown
% 1.82/1.53 % (2950)Termination phase: Saturation
% 1.82/1.53
% 1.82/1.53 % (2950)Memory used [KB]: 5884
% 1.82/1.53 % (2950)Time elapsed: 0.048 s
% 1.82/1.53 % (2950)Instructions burned: 86 (million)
% 1.82/1.53 % (2950)------------------------------
% 1.82/1.53 % (2950)------------------------------
% 1.82/1.53 % (2939)Instruction limit reached!
% 1.82/1.53 % (2939)------------------------------
% 1.82/1.53 % (2939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.53 % (2939)Termination reason: Unknown
% 1.82/1.53 % (2939)Termination phase: Saturation
% 1.82/1.53
% 1.82/1.53 % (2939)Memory used [KB]: 6908
% 1.82/1.53 % (2939)Time elapsed: 0.126 s
% 1.82/1.53 % (2939)Instructions burned: 377 (million)
% 1.82/1.53 % (2939)------------------------------
% 1.82/1.53 % (2939)------------------------------
% 1.82/1.54 % (2951)Instruction limit reached!
% 1.82/1.54 % (2951)------------------------------
% 1.82/1.54 % (2951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.54 % (2951)Termination reason: Unknown
% 1.82/1.54 % (2951)Termination phase: Saturation
% 1.82/1.54
% 1.82/1.54 % (2951)Memory used [KB]: 6140
% 1.82/1.54 % (2951)Time elapsed: 0.052 s
% 1.82/1.54 % (2951)Instructions burned: 107 (million)
% 1.82/1.54 % (2951)------------------------------
% 1.82/1.54 % (2951)------------------------------
% 1.82/1.54 % (2952)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_2576 for (2998ds/39Mi)
% 1.82/1.54 % (2953)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_2576 for (2998ds/448Mi)
% 1.82/1.55 % (2954)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_2576 for (2998ds/46Mi)
% 1.82/1.55 % (2953)Refutation not found, incomplete strategy
% 1.82/1.55 % (2953)------------------------------
% 1.82/1.55 % (2953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.55 % (2953)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.55
% 1.82/1.55
% 1.82/1.55 % (2953)Memory used [KB]: 5628
% 1.82/1.55 % (2953)Time elapsed: 0.004 s
% 1.82/1.55 % (2953)Instructions burned: 8 (million)
% 1.82/1.55 % (2953)------------------------------
% 1.82/1.55 % (2953)------------------------------
% 1.82/1.55 % (2942)Refutation found. Thanks to Tanya!
% 1.82/1.55 % SZS status Theorem for DTF2THF_2576
% 1.82/1.55 % SZS output start Proof for DTF2THF_2576
% 1.82/1.55 thf(type_def_6, type, d_unsorted: $tType).
% 1.82/1.55 thf(func_def_0, type, unsorted: $tType).
% 1.82/1.55 thf(func_def_1, type, irel: $i > $i > $o).
% 1.82/1.55 thf(func_def_2, type, mnot: ($i > $o) > $i > $o).
% 1.82/1.55 thf(func_def_3, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 1.82/1.55 thf(func_def_4, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 1.82/1.55 thf(func_def_5, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 1.82/1.55 thf(func_def_6, type, mbox_s4: ($i > $o) > $i > $o).
% 1.82/1.55 thf(func_def_7, type, iatom: ($i > $o) > $i > $o).
% 1.82/1.55 thf(func_def_8, type, inot: ($i > $o) > $i > $o).
% 1.82/1.55 thf(func_def_9, type, itrue: $i > $o).
% 1.82/1.55 thf(func_def_10, type, ifalse: $i > $o).
% 1.82/1.55 thf(func_def_11, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 1.82/1.55 thf(func_def_12, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 1.82/1.55 thf(func_def_13, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 1.82/1.55 thf(func_def_14, type, iimplied: ($i > $o) > ($i > $o) > $i > $o).
% 1.82/1.55 thf(func_def_15, type, iequiv: ($i > $o) > ($i > $o) > $i > $o).
% 1.82/1.55 thf(func_def_16, type, ixor: ($i > $o) > ($i > $o) > $i > $o).
% 1.82/1.55 thf(func_def_17, type, ivalid: ($i > $o) > $o).
% 1.82/1.55 thf(func_def_18, type, isatisfiable: ($i > $o) > $o).
% 1.82/1.55 thf(func_def_19, type, icountersatisfiable: ($i > $o) > $o).
% 1.82/1.55 thf(func_def_20, type, iinvalid: ($i > $o) > $o).
% 1.82/1.55 thf(func_def_21, type, d_unsorted: $tType).
% 1.82/1.55 thf(func_def_22, type, d2unsorted: d_unsorted > $i).
% 1.82/1.55 thf(func_def_23, type, d_unsorted_0: d_unsorted).
% 1.82/1.55 thf(func_def_41, type, sK0: $i > d_unsorted).
% 1.82/1.55 thf(func_def_43, type, ph2: !>[X0: $tType]:(X0)).
% 1.82/1.55 thf(func_def_44, type, sK3: $i > $o).
% 1.82/1.55 thf(func_def_45, type, sK4: $i > $o).
% 1.82/1.55 thf(func_def_47, type, sK6: $i > $i).
% 1.82/1.55 thf(func_def_48, type, sK7: $i > $i).
% 1.82/1.55 thf(func_def_49, type, sK8: $i > $i).
% 1.82/1.55 thf(func_def_50, type, sK9: $i > $i).
% 1.82/1.55 thf(func_def_51, type, sK10: $i > $i).
% 1.82/1.55 thf(func_def_52, type, sK11: $i > $i).
% 1.82/1.55 thf(func_def_53, type, sK12: $i > $i).
% 1.82/1.55 thf(func_def_54, type, sK13: $i > $i).
% 1.82/1.55 thf(func_def_55, type, sK14: $i > $i).
% 1.82/1.55 thf(func_def_56, type, sK15: $i > $i).
% 1.82/1.55 thf(func_def_57, type, sK16: $i > $i).
% 1.82/1.55 thf(func_def_58, type, sK17: $i > $i).
% 1.82/1.55 thf(f3345,plain,(
% 1.82/1.55 $false),
% 1.82/1.55 inference(avatar_sat_refutation,[status(thm)],[f2035,f2118,f2120,f2133,f2135,f2306,f2311,f2324,f2326,f2810,f2882,f2915,f2998,f3066,f3079,f3085,f3087,f3089,f3118,f3131,f3151,f3276,f3283,f3306,f3310,f3326,f3332,f3340,f3344])).
% 1.82/1.55 thf(f3344,plain,(
% 1.82/1.55 ~spl1_1 | ~spl1_169),
% 1.82/1.55 inference(avatar_contradiction_clause,[status(thm)],[f3343])).
% 1.82/1.55 thf(f3343,plain,(
% 1.82/1.55 $false | (~spl1_1 | ~spl1_169)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3342])).
% 1.82/1.55 thf(f3342,plain,(
% 1.82/1.55 ($true = $false) | (~spl1_1 | ~spl1_169)),
% 1.82/1.55 inference(forward_demodulation,[status(thm)],[f2030,f3053])).
% 1.82/1.55 thf(f3053,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((irel @ sK5 @ X0) = $false)) ) | ~spl1_169),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f3052])).
% 1.82/1.55 thf(f3052,definition,(
% 1.82/1.55 spl1_169 <=> ! [X0 : $i] : ((irel @ sK5 @ X0) = $false)),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_169])],[avatar_definition])).
% 1.82/1.55 thf(f2030,plain,(
% 1.82/1.55 ($true = (irel @ sK5 @ sK22)) | ~spl1_1),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2028])).
% 1.82/1.55 thf(f2028,definition,(
% 1.82/1.55 spl1_1 <=> ($true = (irel @ sK5 @ sK22))),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.82/1.55 thf(f3340,plain,(
% 1.82/1.55 ~spl1_2 | ~spl1_169),
% 1.82/1.55 inference(avatar_contradiction_clause,[status(thm)],[f3339])).
% 1.82/1.55 thf(f3339,plain,(
% 1.82/1.55 $false | (~spl1_2 | ~spl1_169)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3338])).
% 1.82/1.55 thf(f3338,plain,(
% 1.82/1.55 ($true = $false) | (~spl1_2 | ~spl1_169)),
% 1.82/1.55 inference(backward_demodulation,[status(thm)],[f2959,f3053])).
% 1.82/1.55 thf(f2959,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((irel @ sK5 @ X0) = $true)) ) | ~spl1_2),
% 1.82/1.55 inference(superposition,[status(thm)],[f2034,f2945])).
% 1.82/1.55 thf(f2945,plain,(
% 1.82/1.55 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 1.82/1.55 inference(superposition,[status(thm)],[f41,f41])).
% 1.82/1.55 thf(f41,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((d2unsorted @ d_unsorted_0) = X1)) )),
% 1.82/1.55 inference(forward_demodulation,[status(thm)],[f36,f37])).
% 1.82/1.55 thf(f37,plain,(
% 1.82/1.55 ( ! [X0 : d_unsorted] : ((d_unsorted_0 = X0)) )),
% 1.82/1.55 inference(cnf_transformation,[status(thm)],[f14])).
% 1.82/1.55 thf(f14,plain,(
% 1.82/1.55 ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & ! [X1 : $i] : ((d2unsorted @ (sK0 @ X1)) = X1) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((X3 = X4) | ((d2unsorted @ X3) != (d2unsorted @ X4))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))) | (Y1 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5))))) | (Y0 @ Y3)) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4)))))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y0 @ Y4) | (~ (irel @ Y7 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y3 @ Y4))) & ((((~ (irel @ Y7 @ Y6)) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8))))))) | (~ (irel @ Y2 @ Y7)))))))))))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))))),
% 1.82/1.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f13])).
% 1.82/1.55 thf(f13,plain,(
% 1.82/1.55 ! [X1 : $i] : (? [X2 : d_unsorted] : ((d2unsorted @ X2) = X1) => ((d2unsorted @ (sK0 @ X1)) = X1))),
% 1.82/1.55 introduced(definition,[],[choice_axiom])).
% 1.82/1.55 thf(f12,plain,(
% 1.82/1.55 ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & ! [X1 : $i] : ? [X2 : d_unsorted] : ((d2unsorted @ X2) = X1) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((X3 = X4) | ((d2unsorted @ X3) != (d2unsorted @ X4))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))) | (Y1 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5))))) | (Y0 @ Y3)) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4)))))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y0 @ Y4) | (~ (irel @ Y7 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y3 @ Y4))) & ((((~ (irel @ Y7 @ Y6)) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8))))))) | (~ (irel @ Y2 @ Y7)))))))))))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))))),
% 1.82/1.55 inference(ennf_transformation,[status(thm)],[f11])).
% 1.82/1.55 thf(f11,plain,(
% 1.82/1.55 (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & ! [X1 : $i] : ? [X2 : d_unsorted] : ((d2unsorted @ X2) = X1) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : (((d2unsorted @ X3) = (d2unsorted @ X4)) => (X3 = X4)) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))) | (Y1 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5))))) | (Y0 @ Y3)) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4)))))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y0 @ Y4) | (~ (irel @ Y7 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y3 @ Y4))) & ((((~ (irel @ Y7 @ Y6)) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8))))))) | (~ (irel @ Y2 @ Y7))))))))))))))))))))),
% 1.82/1.55 inference(flattening,[status(thm)],[f10])).
% 1.82/1.55 thf(f10,plain,(
% 1.82/1.55 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X1 : $i] : ? [X2 : d_unsorted] : ((d2unsorted @ X2) = X1) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))) | (Y1 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5))))) | (Y0 @ Y3)) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4)))))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : (((d2unsorted @ X3) = (d2unsorted @ X4)) => (X3 = X4)) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y0 @ Y4) | (~ (irel @ Y7 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y3 @ Y4))) & ((((~ (irel @ Y7 @ Y6)) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8))))))) | (~ (irel @ Y2 @ Y7)))))))))))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ~((ifalse @ (d2unsorted @ d_unsorted_0)) = $true)),
% 1.82/1.55 inference(rectify,[status(thm)],[f6])).
% 1.82/1.55 thf(f6,plain,(
% 1.82/1.55 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X5 : d_unsorted] : (d_unsorted_0 = X5) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X16 : $i] : ? [X17 : d_unsorted] : ((d2unsorted @ X17) = X16) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))) | (Y1 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5))))) | (Y0 @ Y3)) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4)))))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ! [X42 : d_unsorted,X43 : d_unsorted] : (((d2unsorted @ X43) = (d2unsorted @ X42)) => (X42 = X43)) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y0 @ Y4) | (~ (irel @ Y7 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y3 @ Y4))) & ((((~ (irel @ Y7 @ Y6)) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8))))))) | (~ (irel @ Y2 @ Y7)))))))))))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ~((ifalse @ (d2unsorted @ d_unsorted_0)) = $true)),
% 1.82/1.55 inference(fool_elimination,[status(thm)],[f5])).
% 1.82/1.55 thf(f5,plain,(
% 1.82/1.55 (iand = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : (! [X3 : $i] : (~(irel @ X2 @ X3) | (X0 @ X3)) & ! [X4 : $i] : (~(irel @ X2 @ X4) | (X1 @ X4))))) & ! [X5 : d_unsorted] : (d_unsorted_0 = X5) & ((^[X6 : $i > $o, X7 : $i] : (~! [X8 : $i] : (~(irel @ X7 @ X8) | (X6 @ X8)))) = inot) & ((^[X9 : $i > $o, X10 : $i > $o, X11 : $i] : ((X9 @ X11) & (X10 @ X11))) = mand) & (icountersatisfiable = (^[X12 : $i > $o] : (~! [X13 : $i] : (X12 @ X13)))) & (iinvalid = (^[X14 : $i > $o] : (! [X15 : $i] : ~(X14 @ X15)))) & ! [X16 : $i] : ? [X17 : d_unsorted] : ((d2unsorted @ X17) = X16) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ((^[X18 : $i > $o, X19 : $i > $o, X20 : $i] : (! [X21 : $i] : (~(irel @ X20 @ X21) | (X19 @ X21)) | ! [X22 : $i] : ((X18 @ X22) | ~(irel @ X20 @ X22)))) = ior) & (iequiv = (^[X23 : $i > $o, X24 : $i > $o, X25 : $i] : (! [X26 : $i,X27 : $i] : (~(irel @ X25 @ X26) | ~(irel @ X26 @ X27) | (X23 @ X27) | ~! [X28 : $i] : ((X24 @ X28) | ~(irel @ X26 @ X28))) & ! [X29 : $i,X30 : $i] : ((X24 @ X29) | ~(irel @ X30 @ X29) | ~(irel @ X25 @ X30) | ~! [X31 : $i] : (~(irel @ X30 @ X31) | (X23 @ X31)))))) & ((^[X32 : $i > $o, X33 : $i > $o, X34 : $i] : (! [X35 : $i] : ((X32 @ X35) | ~(irel @ X34 @ X35)) | ~! [X36 : $i] : (~(irel @ X34 @ X36) | (X33 @ X36)))) = iimplied) & ((^[X37 : $i > $o, X38 : $i > $o, X39 : $i] : (~(X37 @ X39) | (X38 @ X39))) = mimplies) & ((^[X40 : $i > $o] : (! [X41 : $i] : (X40 @ X41))) = ivalid) & ! [X42 : d_unsorted,X43 : d_unsorted] : (((d2unsorted @ X43) = (d2unsorted @ X42)) => (X42 = X43)) & (ixor = (^[X44 : $i > $o, X45 : $i > $o, X46 : $i] : (~! [X47 : $i,X48 : $i,X49 : $i,X50 : $i,X51 : $i] : (~(irel @ X46 @ X47) | ((~! [X52 : $i] : ((X44 @ X52) | ~(irel @ X48 @ X52)) | ~(irel @ X48 @ X49) | (X45 @ X49) | ~(irel @ X47 @ X48)) & (~(irel @ X51 @ X50) | ~! [X53 : $i] : ((X45 @ X53) | ~(irel @ X51 @ X53)) | ~(irel @ X47 @ X51) | (X44 @ X50))))))) & ((^[X54 : $i > $o, X55 : $i > $o, X56 : $i] : (! [X57 : $i] : ((X55 @ X57) | ~(irel @ X56 @ X57)) | ~! [X58 : $i] : ((X54 @ X58) | ~(irel @ X56 @ X58)))) = iimplies) & (mnot = (^[X59 : $i > $o, X60 : $i] : (~(X59 @ X60)))) & ((^[X61 : $i > $o, X62 : $i > $o, X63 : $i] : ((X62 @ X63) | (X61 @ X63))) = mor) & (itrue @ (d2unsorted @ d_unsorted_0)) & (iatom = (^[X64 : $i > $o, X65 : $i] : (X64 @ X65))) & ((^[X66 : $i > $o, X67 : $i] : (! [X68 : $i] : (~(irel @ X67 @ X68) | (X66 @ X68)))) = mbox_s4) & (isatisfiable = (^[X69 : $i > $o] : (~! [X70 : $i] : ~(X69 @ X70)))) & ~(ifalse @ (d2unsorted @ d_unsorted_0))),
% 1.82/1.55 inference(rectify,[status(thm)],[f1])).
% 1.82/1.55 thf(f1,axiom,(
% 1.82/1.55 (iand = (^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)) & ! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5))))) & ! [X1 : d_unsorted] : (d_unsorted_0 = X1) & ((^[X8 : $i > $o, X7 : $i] : (~! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)))) = inot) & ((^[X4 : $i > $o, X5 : $i > $o, X0 : $i] : ((X4 @ X0) & (X5 @ X0))) = mand) & (icountersatisfiable = (^[X18 : $i > $o] : (~! [X19 : $i] : (X18 @ X19)))) & (iinvalid = (^[X18 : $i > $o] : (! [X19 : $i] : ~(X18 @ X19)))) & ! [X0 : $i] : ? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)) | ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)))) = ior) & (iequiv = (^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (! [X5 : $i,X12 : $i] : (~(irel @ X7 @ X5) | ~(irel @ X5 @ X12) | (X8 @ X12) | ~! [X13 : $i] : ((X9 @ X13) | ~(irel @ X5 @ X13))) & ! [X10 : $i,X5 : $i] : ((X9 @ X10) | ~(irel @ X5 @ X10) | ~(irel @ X7 @ X5) | ~! [X11 : $i] : (~(irel @ X5 @ X11) | (X8 @ X11)))))) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)) | ~! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)))) = iimplied) & ((^[X0 : $i > $o, X6 : $i > $o, X7 : $i] : (~(X0 @ X7) | (X6 @ X7))) = mimplies) & ((^[X18 : $i > $o] : (! [X19 : $i] : (X18 @ X19))) = ivalid) & ! [X3 : d_unsorted,X2 : d_unsorted] : (((d2unsorted @ X2) = (d2unsorted @ X3)) => (X2 = X3)) & (ixor = (^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (~! [X5 : $i,X14 : $i,X15 : $i,X17 : $i,X16 : $i] : (~(irel @ X7 @ X5) | ((~! [X11 : $i] : ((X8 @ X11) | ~(irel @ X14 @ X11)) | ~(irel @ X14 @ X15) | (X9 @ X15) | ~(irel @ X5 @ X14)) & (~(irel @ X16 @ X17) | ~! [X13 : $i] : ((X9 @ X13) | ~(irel @ X16 @ X13)) | ~(irel @ X5 @ X16) | (X8 @ X17))))))) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)) | ~! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)))) = iimplies) & (mnot = (^[X4 : $i > $o, X0 : $i] : (~(X4 @ X0)))) & ((^[X4 : $i > $o, X5 : $i > $o, X0 : $i] : ((X5 @ X0) | (X4 @ X0))) = mor) & (itrue @ (d2unsorted @ d_unsorted_0)) & (iatom = (^[X8 : $i > $o, X7 : $i] : (X8 @ X7))) & ((^[X8 : $i > $o, X4 : $i] : (! [X5 : $i] : (~(irel @ X4 @ X5) | (X8 @ X5)))) = mbox_s4) & (isatisfiable = (^[X18 : $i > $o] : (~! [X19 : $i] : ~(X18 @ X19)))) & ~(ifalse @ (d2unsorted @ d_unsorted_0))),
% 1.82/1.55 file('/export/starexec/sandbox/tmp/tmp.YfK2dOMluu/DTF2THF_2576.p',lcl696_1)).
% 1.82/1.55 thf(f36,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((d2unsorted @ (sK0 @ X1)) = X1)) )),
% 1.82/1.55 inference(cnf_transformation,[status(thm)],[f14])).
% 1.82/1.55 thf(f2034,plain,(
% 1.82/1.55 ((irel @ sK5 @ sK23) = $true) | ~spl1_2),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2032])).
% 1.82/1.55 thf(f2032,definition,(
% 1.82/1.55 spl1_2 <=> ((irel @ sK5 @ sK23) = $true)),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.82/1.55 thf(f3332,plain,(
% 1.82/1.55 ~spl1_22 | ~spl1_49 | ~spl1_50),
% 1.82/1.55 inference(avatar_contradiction_clause,[status(thm)],[f3331])).
% 1.82/1.55 thf(f3331,plain,(
% 1.82/1.55 $false | (~spl1_22 | ~spl1_49 | ~spl1_50)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3330])).
% 1.82/1.55 thf(f3330,plain,(
% 1.82/1.55 ($true = $false) | (~spl1_22 | ~spl1_49 | ~spl1_50)),
% 1.82/1.55 inference(forward_demodulation,[status(thm)],[f2305,f3329])).
% 1.82/1.55 thf(f3329,plain,(
% 1.82/1.55 ( ! [X3 : $i] : (((irel @ sK66 @ X3) = $false)) ) | (~spl1_22 | ~spl1_50)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3328])).
% 1.82/1.55 thf(f3328,plain,(
% 1.82/1.55 ( ! [X3 : $i] : (((irel @ sK66 @ X3) = $false) | ($true = $false)) ) | (~spl1_22 | ~spl1_50)),
% 1.82/1.55 inference(forward_demodulation,[status(thm)],[f2310,f3092])).
% 1.82/1.55 thf(f3092,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((sK4 @ X0) = $false)) ) | ~spl1_22),
% 1.82/1.55 inference(superposition,[status(thm)],[f2144,f2945])).
% 1.82/1.55 thf(f2144,plain,(
% 1.82/1.55 ((sK4 @ sK20) = $false) | ~spl1_22),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2142])).
% 1.82/1.55 thf(f2142,definition,(
% 1.82/1.55 spl1_22 <=> ((sK4 @ sK20) = $false)),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_22])],[avatar_definition])).
% 1.82/1.55 thf(f2310,plain,(
% 1.82/1.55 ( ! [X3 : $i] : (($true = (sK4 @ X3)) | ((irel @ sK66 @ X3) = $false)) ) | ~spl1_50),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2309])).
% 1.82/1.55 thf(f2309,definition,(
% 1.82/1.55 spl1_50 <=> ! [X3 : $i] : (((irel @ sK66 @ X3) = $false) | ($true = (sK4 @ X3)))),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_50])],[avatar_definition])).
% 1.82/1.55 thf(f2305,plain,(
% 1.82/1.55 ((irel @ sK66 @ sK65) = $true) | ~spl1_49),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2303])).
% 1.82/1.55 thf(f2303,definition,(
% 1.82/1.55 spl1_49 <=> ((irel @ sK66 @ sK65) = $true)),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_49])],[avatar_definition])).
% 1.82/1.55 thf(f3326,plain,(
% 1.82/1.55 ~spl1_6 | ~spl1_48 | ~spl1_52),
% 1.82/1.55 inference(avatar_contradiction_clause,[status(thm)],[f3325])).
% 1.82/1.55 thf(f3325,plain,(
% 1.82/1.55 $false | (~spl1_6 | ~spl1_48 | ~spl1_52)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3324])).
% 1.82/1.55 thf(f3324,plain,(
% 1.82/1.55 ($true = $false) | (~spl1_6 | ~spl1_48 | ~spl1_52)),
% 1.82/1.55 inference(forward_demodulation,[status(thm)],[f2300,f3320])).
% 1.82/1.55 thf(f3320,plain,(
% 1.82/1.55 ( ! [X2 : $i] : (((irel @ sK63 @ X2) = $false)) ) | (~spl1_6 | ~spl1_52)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3319])).
% 1.82/1.55 thf(f3319,plain,(
% 1.82/1.55 ( ! [X2 : $i] : (((irel @ sK63 @ X2) = $false) | ($true = $false)) ) | (~spl1_6 | ~spl1_52)),
% 1.82/1.55 inference(forward_demodulation,[status(thm)],[f2322,f3286])).
% 1.82/1.55 thf(f3286,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((sK3 @ X0) = $false)) ) | ~spl1_6),
% 1.82/1.55 inference(superposition,[status(thm)],[f2053,f2945])).
% 1.82/1.55 thf(f2053,plain,(
% 1.82/1.55 ((sK3 @ sK81) = $false) | ~spl1_6),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2051])).
% 1.82/1.55 thf(f2051,definition,(
% 1.82/1.55 spl1_6 <=> ((sK3 @ sK81) = $false)),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition])).
% 1.82/1.55 thf(f2322,plain,(
% 1.82/1.55 ( ! [X2 : $i] : (((irel @ sK63 @ X2) = $false) | ($true = (sK3 @ X2))) ) | ~spl1_52),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2321])).
% 1.82/1.55 thf(f2321,definition,(
% 1.82/1.55 spl1_52 <=> ! [X2 : $i] : (((irel @ sK63 @ X2) = $false) | ($true = (sK3 @ X2)))),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_52])],[avatar_definition])).
% 1.82/1.55 thf(f2300,plain,(
% 1.82/1.55 ($true = (irel @ sK63 @ sK64)) | ~spl1_48),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2298])).
% 1.82/1.55 thf(f2298,definition,(
% 1.82/1.55 spl1_48 <=> ($true = (irel @ sK63 @ sK64))),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_48])],[avatar_definition])).
% 1.82/1.55 thf(f3310,plain,(
% 1.82/1.55 spl1_169 | ~spl1_6 | ~spl1_170),
% 1.82/1.55 inference(avatar_split_clause,[status(thm)],[f3295,f3077,f2051,f3052])).
% 1.82/1.55 thf(f3077,definition,(
% 1.82/1.55 spl1_170 <=> ! [X0 : $i] : (((sK3 @ X0) = $true) | ((irel @ sK5 @ X0) = $false))),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_170])],[avatar_definition])).
% 1.82/1.55 thf(f3295,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((irel @ sK5 @ X0) = $false)) ) | (~spl1_6 | ~spl1_170)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3292])).
% 1.82/1.55 thf(f3292,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((irel @ sK5 @ X0) = $false) | ($true = $false)) ) | (~spl1_6 | ~spl1_170)),
% 1.82/1.55 inference(backward_demodulation,[status(thm)],[f3078,f3286])).
% 1.82/1.55 thf(f3078,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((irel @ sK5 @ X0) = $false) | ((sK3 @ X0) = $true)) ) | ~spl1_170),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f3077])).
% 1.82/1.55 thf(f3306,plain,(
% 1.82/1.55 ~spl1_6 | ~spl1_18 | ~spl1_20),
% 1.82/1.55 inference(avatar_contradiction_clause,[status(thm)],[f3305])).
% 1.82/1.55 thf(f3305,plain,(
% 1.82/1.55 $false | (~spl1_6 | ~spl1_18 | ~spl1_20)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3304])).
% 1.82/1.55 thf(f3304,plain,(
% 1.82/1.55 ($true = $false) | (~spl1_6 | ~spl1_18 | ~spl1_20)),
% 1.82/1.55 inference(backward_demodulation,[status(thm)],[f2116,f3297])).
% 1.82/1.55 thf(f3297,plain,(
% 1.82/1.55 ( ! [X2 : $i] : (((irel @ sK77 @ X2) = $false)) ) | (~spl1_6 | ~spl1_20)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3287])).
% 1.82/1.55 thf(f3287,plain,(
% 1.82/1.55 ( ! [X2 : $i] : (((irel @ sK77 @ X2) = $false) | ($true = $false)) ) | (~spl1_6 | ~spl1_20)),
% 1.82/1.55 inference(backward_demodulation,[status(thm)],[f2128,f3286])).
% 1.82/1.55 thf(f2128,plain,(
% 1.82/1.55 ( ! [X2 : $i] : (((irel @ sK77 @ X2) = $false) | ($true = (sK3 @ X2))) ) | ~spl1_20),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2127])).
% 1.82/1.55 thf(f2127,definition,(
% 1.82/1.55 spl1_20 <=> ! [X2 : $i] : (($true = (sK3 @ X2)) | ((irel @ sK77 @ X2) = $false))),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_20])],[avatar_definition])).
% 1.82/1.55 thf(f2116,plain,(
% 1.82/1.55 ((irel @ sK77 @ sK78) = $true) | ~spl1_18),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2114])).
% 1.82/1.55 thf(f2114,definition,(
% 1.82/1.55 spl1_18 <=> ((irel @ sK77 @ sK78) = $true)),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_18])],[avatar_definition])).
% 1.82/1.55 thf(f3283,plain,(
% 1.82/1.55 ~spl1_15 | ~spl1_17 | ~spl1_22),
% 1.82/1.55 inference(avatar_contradiction_clause,[status(thm)],[f3282])).
% 1.82/1.55 thf(f3282,plain,(
% 1.82/1.55 $false | (~spl1_15 | ~spl1_17 | ~spl1_22)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3281])).
% 1.82/1.55 thf(f3281,plain,(
% 1.82/1.55 ($true = $false) | (~spl1_15 | ~spl1_17 | ~spl1_22)),
% 1.82/1.55 inference(backward_demodulation,[status(thm)],[f2102,f3280])).
% 1.82/1.55 thf(f3280,plain,(
% 1.82/1.55 ( ! [X2 : $i] : (((irel @ sK79 @ X2) = $false)) ) | (~spl1_17 | ~spl1_22)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3279])).
% 1.82/1.55 thf(f3279,plain,(
% 1.82/1.55 ( ! [X2 : $i] : (((irel @ sK79 @ X2) = $false) | ($true = $false)) ) | (~spl1_17 | ~spl1_22)),
% 1.82/1.55 inference(forward_demodulation,[status(thm)],[f2111,f3092])).
% 1.82/1.55 thf(f2111,plain,(
% 1.82/1.55 ( ! [X2 : $i] : (((irel @ sK79 @ X2) = $false) | ((sK4 @ X2) = $true)) ) | ~spl1_17),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2110])).
% 1.82/1.55 thf(f2110,definition,(
% 1.82/1.55 spl1_17 <=> ! [X2 : $i] : (((irel @ sK79 @ X2) = $false) | ((sK4 @ X2) = $true))),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_17])],[avatar_definition])).
% 1.82/1.55 thf(f2102,plain,(
% 1.82/1.55 ((irel @ sK79 @ sK76) = $true) | ~spl1_15),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2100])).
% 1.82/1.55 thf(f2100,definition,(
% 1.82/1.55 spl1_15 <=> ((irel @ sK79 @ sK76) = $true)),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_15])],[avatar_definition])).
% 1.82/1.55 thf(f3276,plain,(
% 1.82/1.55 ~spl1_168),
% 1.82/1.55 inference(avatar_contradiction_clause,[status(thm)],[f3275])).
% 1.82/1.55 thf(f3275,plain,(
% 1.82/1.55 $false | ~spl1_168),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3274])).
% 1.82/1.55 thf(f3274,plain,(
% 1.82/1.55 ($true = $false) | ~spl1_168),
% 1.82/1.55 inference(backward_demodulation,[status(thm)],[f21,f3273])).
% 1.82/1.55 thf(f3273,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((irel @ X0 @ X0) = $false)) ) | ~spl1_168),
% 1.82/1.55 inference(superposition,[status(thm)],[f3050,f2945])).
% 1.82/1.55 thf(f3050,plain,(
% 1.82/1.55 ((irel @ sK5 @ sK5) = $false) | ~spl1_168),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f3048])).
% 1.82/1.55 thf(f3048,definition,(
% 1.82/1.55 spl1_168 <=> ((irel @ sK5 @ sK5) = $false)),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_168])],[avatar_definition])).
% 1.82/1.55 thf(f21,plain,(
% 1.82/1.55 ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true)),
% 1.82/1.55 inference(cnf_transformation,[status(thm)],[f14])).
% 1.82/1.55 thf(f3151,plain,(
% 1.82/1.55 spl1_169 | spl1_168 | spl1_6 | ~spl1_22 | ~spl1_160),
% 1.82/1.55 inference(avatar_split_clause,[status(thm)],[f3150,f2913,f2142,f2051,f3048,f3052])).
% 1.82/1.55 thf(f2913,definition,(
% 1.82/1.55 spl1_160 <=> ! [X5 : $i,X7 : $i,X8 : $i] : (((sK3 @ (sK10 @ X7)) = $false) | ((irel @ sK5 @ X8) = $false) | ($true = (sK4 @ X5)) | ((irel @ X7 @ X5) = $false) | ((irel @ X8 @ X7) = $false))),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_160])],[avatar_definition])).
% 1.82/1.55 thf(f3150,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((irel @ sK5 @ sK5) = $false) | ((irel @ sK5 @ X0) = $false)) ) | (spl1_6 | ~spl1_22 | ~spl1_160)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3148])).
% 1.82/1.55 thf(f3148,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (($false != $false) | ((irel @ sK5 @ sK5) = $false) | ((irel @ sK5 @ X0) = $false)) ) | (spl1_6 | ~spl1_22 | ~spl1_160)),
% 1.82/1.55 inference(equality_factoring,[status(thm)],[f3144])).
% 1.82/1.55 thf(f3144,plain,(
% 1.82/1.55 ( ! [X8 : $i,X7 : $i,X5 : $i] : (((irel @ sK5 @ X8) = $false) | ((irel @ X7 @ X5) = $false) | ((irel @ X8 @ X7) = $false)) ) | (spl1_6 | ~spl1_22 | ~spl1_160)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3143])).
% 1.82/1.55 thf(f3143,plain,(
% 1.82/1.55 ( ! [X8 : $i,X7 : $i,X5 : $i] : (((irel @ sK5 @ X8) = $false) | ((irel @ X7 @ X5) = $false) | ((irel @ X8 @ X7) = $false) | ($true = $false)) ) | (spl1_6 | ~spl1_22 | ~spl1_160)),
% 1.82/1.55 inference(forward_demodulation,[status(thm)],[f3142,f3092])).
% 1.82/1.55 thf(f3142,plain,(
% 1.82/1.55 ( ! [X8 : $i,X7 : $i,X5 : $i] : (((irel @ sK5 @ X8) = $false) | ((irel @ X7 @ X5) = $false) | ($true = (sK4 @ X5)) | ((irel @ X8 @ X7) = $false)) ) | (spl1_6 | ~spl1_160)),
% 1.82/1.55 inference(subsumption_resolution,[status(thm)],[f2914,f3068])).
% 1.82/1.55 thf(f3068,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((sK3 @ X0) != $false)) ) | spl1_6),
% 1.82/1.55 inference(superposition,[status(thm)],[f2052,f2945])).
% 1.82/1.55 thf(f2052,plain,(
% 1.82/1.55 ((sK3 @ sK81) != $false) | spl1_6),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2051])).
% 1.82/1.55 thf(f2914,plain,(
% 1.82/1.55 ( ! [X8 : $i,X7 : $i,X5 : $i] : (((sK3 @ (sK10 @ X7)) = $false) | ((irel @ X8 @ X7) = $false) | ((irel @ sK5 @ X8) = $false) | ($true = (sK4 @ X5)) | ((irel @ X7 @ X5) = $false)) ) | ~spl1_160),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2913])).
% 1.82/1.55 thf(f3131,plain,(
% 1.82/1.55 spl1_168 | spl1_169 | spl1_6 | ~spl1_22 | ~spl1_159),
% 1.82/1.55 inference(avatar_split_clause,[status(thm)],[f3130,f2910,f2142,f2051,f3052,f3048])).
% 1.82/1.55 thf(f2910,definition,(
% 1.82/1.55 spl1_159 <=> ! [X6 : $i,X4 : $i,X1 : $i] : (((sK3 @ (sK9 @ X4)) = $false) | ((sK4 @ X6) = $true) | ((irel @ sK5 @ X1) = $false) | ((irel @ X1 @ X4) = $false) | ((irel @ X4 @ X6) = $false))),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_159])],[avatar_definition])).
% 1.82/1.55 thf(f3130,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((irel @ sK5 @ sK5) = $false) | ((irel @ sK5 @ X0) = $false)) ) | (spl1_6 | ~spl1_22 | ~spl1_159)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3127])).
% 1.82/1.55 thf(f3127,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (($false != $false) | ((irel @ sK5 @ X0) = $false) | ((irel @ sK5 @ sK5) = $false)) ) | (spl1_6 | ~spl1_22 | ~spl1_159)),
% 1.82/1.55 inference(equality_factoring,[status(thm)],[f3112])).
% 1.82/1.55 thf(f3112,plain,(
% 1.82/1.55 ( ! [X1 : $i,X6 : $i,X4 : $i] : (((irel @ sK5 @ X1) = $false) | ((irel @ X1 @ X4) = $false) | ((irel @ X4 @ X6) = $false)) ) | (spl1_6 | ~spl1_22 | ~spl1_159)),
% 1.82/1.55 inference(subsumption_resolution,[status(thm)],[f3111,f3068])).
% 1.82/1.55 thf(f3111,plain,(
% 1.82/1.55 ( ! [X1 : $i,X6 : $i,X4 : $i] : (((sK3 @ (sK9 @ X4)) = $false) | ((irel @ X1 @ X4) = $false) | ((irel @ sK5 @ X1) = $false) | ((irel @ X4 @ X6) = $false)) ) | (~spl1_22 | ~spl1_159)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3100])).
% 1.82/1.55 thf(f3100,plain,(
% 1.82/1.55 ( ! [X1 : $i,X6 : $i,X4 : $i] : (((irel @ X4 @ X6) = $false) | ((irel @ X1 @ X4) = $false) | ((sK3 @ (sK9 @ X4)) = $false) | ($true = $false) | ((irel @ sK5 @ X1) = $false)) ) | (~spl1_22 | ~spl1_159)),
% 1.82/1.55 inference(backward_demodulation,[status(thm)],[f2911,f3092])).
% 1.82/1.55 thf(f2911,plain,(
% 1.82/1.55 ( ! [X1 : $i,X6 : $i,X4 : $i] : (((irel @ X1 @ X4) = $false) | ((irel @ sK5 @ X1) = $false) | ((sK4 @ X6) = $true) | ((irel @ X4 @ X6) = $false) | ((sK3 @ (sK9 @ X4)) = $false)) ) | ~spl1_159),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2910])).
% 1.82/1.55 thf(f3118,plain,(
% 1.82/1.55 ~spl1_11 | ~spl1_22 | ~spl1_41),
% 1.82/1.55 inference(avatar_contradiction_clause,[status(thm)],[f3117])).
% 1.82/1.55 thf(f3117,plain,(
% 1.82/1.55 $false | (~spl1_11 | ~spl1_22 | ~spl1_41)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3113])).
% 1.82/1.55 thf(f3113,plain,(
% 1.82/1.55 ($true = $false) | (~spl1_11 | ~spl1_22 | ~spl1_41)),
% 1.82/1.55 inference(backward_demodulation,[status(thm)],[f3029,f3109])).
% 1.82/1.55 thf(f3109,plain,(
% 1.82/1.55 ( ! [X2 : $i] : (((irel @ sK18 @ X2) = $false)) ) | (~spl1_22 | ~spl1_41)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3095])).
% 1.82/1.55 thf(f3095,plain,(
% 1.82/1.55 ( ! [X2 : $i] : (((irel @ sK18 @ X2) = $false) | ($true = $false)) ) | (~spl1_22 | ~spl1_41)),
% 1.82/1.55 inference(backward_demodulation,[status(thm)],[f2265,f3092])).
% 1.82/1.55 thf(f2265,plain,(
% 1.82/1.55 ( ! [X2 : $i] : (((irel @ sK18 @ X2) = $false) | ((sK4 @ X2) = $true)) ) | ~spl1_41),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2264])).
% 1.82/1.55 thf(f2264,definition,(
% 1.82/1.55 spl1_41 <=> ! [X2 : $i] : (((sK4 @ X2) = $true) | ((irel @ sK18 @ X2) = $false))),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_41])],[avatar_definition])).
% 1.82/1.55 thf(f3029,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (($true = (irel @ sK18 @ X0))) ) | ~spl1_11),
% 1.82/1.55 inference(superposition,[status(thm)],[f2085,f2945])).
% 1.82/1.55 thf(f2085,plain,(
% 1.82/1.55 ($true = (irel @ sK18 @ sK19)) | ~spl1_11),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2083])).
% 1.82/1.55 thf(f2083,definition,(
% 1.82/1.55 spl1_11 <=> ($true = (irel @ sK18 @ sK19))),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_11])],[avatar_definition])).
% 1.82/1.55 thf(f3089,plain,(
% 1.82/1.55 spl1_22 | ~spl1_140),
% 1.82/1.55 inference(avatar_contradiction_clause,[status(thm)],[f3088])).
% 1.82/1.55 thf(f3088,plain,(
% 1.82/1.55 $false | (spl1_22 | ~spl1_140)),
% 1.82/1.55 inference(subsumption_resolution,[status(thm)],[f2809,f3027])).
% 1.82/1.55 thf(f3027,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((sK4 @ X0) != $false)) ) | spl1_22),
% 1.82/1.55 inference(superposition,[status(thm)],[f2143,f2945])).
% 1.82/1.55 thf(f2143,plain,(
% 1.82/1.55 ((sK4 @ sK20) != $false) | spl1_22),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2142])).
% 1.82/1.55 thf(f2809,plain,(
% 1.82/1.55 ((sK4 @ sK28) = $false) | ~spl1_140),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2807])).
% 1.82/1.55 thf(f2807,definition,(
% 1.82/1.55 spl1_140 <=> ((sK4 @ sK28) = $false)),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_140])],[avatar_definition])).
% 1.82/1.55 thf(f3087,plain,(
% 1.82/1.55 spl1_6 | ~spl1_135),
% 1.82/1.55 inference(avatar_contradiction_clause,[status(thm)],[f3086])).
% 1.82/1.55 thf(f3086,plain,(
% 1.82/1.55 $false | (spl1_6 | ~spl1_135)),
% 1.82/1.55 inference(subsumption_resolution,[status(thm)],[f2782,f3068])).
% 1.82/1.55 thf(f2782,plain,(
% 1.82/1.55 ((sK3 @ sK24) = $false) | ~spl1_135),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2780])).
% 1.82/1.55 thf(f2780,definition,(
% 1.82/1.55 spl1_135 <=> ((sK3 @ sK24) = $false)),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_135])],[avatar_definition])).
% 1.82/1.55 thf(f3085,plain,(
% 1.82/1.55 spl1_6 | ~spl1_86),
% 1.82/1.55 inference(avatar_contradiction_clause,[status(thm)],[f3084])).
% 1.82/1.55 thf(f3084,plain,(
% 1.82/1.55 $false | (spl1_6 | ~spl1_86)),
% 1.82/1.55 inference(subsumption_resolution,[status(thm)],[f3081,f3068])).
% 1.82/1.55 thf(f3081,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((sK3 @ X0) = $false)) ) | ~spl1_86),
% 1.82/1.55 inference(superposition,[status(thm)],[f2501,f2945])).
% 1.82/1.55 thf(f2501,plain,(
% 1.82/1.55 ($false = (sK3 @ sK19)) | ~spl1_86),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2499])).
% 1.82/1.55 thf(f2499,definition,(
% 1.82/1.55 spl1_86 <=> ($false = (sK3 @ sK19))),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_86])],[avatar_definition])).
% 1.82/1.55 thf(f3079,plain,(
% 1.82/1.55 spl1_170 | spl1_168 | spl1_22 | ~spl1_151),
% 1.82/1.55 inference(avatar_split_clause,[status(thm)],[f3075,f2880,f2142,f3048,f3077])).
% 1.82/1.55 thf(f2880,definition,(
% 1.82/1.55 spl1_151 <=> ! [X4 : $i,X2 : $i,X8 : $i] : (((sK3 @ X4) = $true) | ((sK4 @ (sK12 @ X2)) = $false) | ((irel @ X8 @ X2) = $false) | ((irel @ sK5 @ X8) = $false) | ((irel @ X2 @ X4) = $false))),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_151])],[avatar_definition])).
% 1.82/1.55 thf(f3075,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((irel @ sK5 @ sK5) = $false) | ((sK3 @ X0) = $true) | ((irel @ sK5 @ X0) = $false)) ) | (spl1_22 | ~spl1_151)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3073])).
% 1.82/1.55 thf(f3073,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((irel @ sK5 @ X0) = $false) | ((sK3 @ X0) = $true) | ($false != $false) | ((irel @ sK5 @ sK5) = $false)) ) | (spl1_22 | ~spl1_151)),
% 1.82/1.55 inference(equality_factoring,[status(thm)],[f3067])).
% 1.82/1.55 thf(f3067,plain,(
% 1.82/1.55 ( ! [X2 : $i,X8 : $i,X4 : $i] : (((irel @ sK5 @ X8) = $false) | ((irel @ X2 @ X4) = $false) | ((sK3 @ X4) = $true) | ((irel @ X8 @ X2) = $false)) ) | (spl1_22 | ~spl1_151)),
% 1.82/1.55 inference(subsumption_resolution,[status(thm)],[f2881,f3027])).
% 1.82/1.55 thf(f2881,plain,(
% 1.82/1.55 ( ! [X2 : $i,X8 : $i,X4 : $i] : (((irel @ X8 @ X2) = $false) | ((sK3 @ X4) = $true) | ((irel @ sK5 @ X8) = $false) | ((sK4 @ (sK12 @ X2)) = $false) | ((irel @ X2 @ X4) = $false)) ) | ~spl1_151),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2880])).
% 1.82/1.55 thf(f3066,plain,(
% 1.82/1.55 spl1_168 | spl1_169 | ~spl1_6 | spl1_22 | ~spl1_150),
% 1.82/1.55 inference(avatar_split_clause,[status(thm)],[f3064,f2877,f2142,f2051,f3052,f3048])).
% 1.82/1.55 thf(f2877,definition,(
% 1.82/1.55 spl1_150 <=> ! [X1 : $i,X7 : $i,X3 : $i] : (((irel @ X1 @ X7) = $false) | ((sK4 @ (sK14 @ X7)) = $false) | ($true = (sK3 @ X3)) | ((irel @ sK5 @ X1) = $false) | ((irel @ X7 @ X3) = $false))),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_150])],[avatar_definition])).
% 1.82/1.55 thf(f3064,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((irel @ sK5 @ X0) = $false) | ((irel @ sK5 @ sK5) = $false)) ) | (~spl1_6 | spl1_22 | ~spl1_150)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3063])).
% 1.82/1.55 thf(f3063,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((irel @ sK5 @ X0) = $false) | ($false != $false) | ((irel @ sK5 @ sK5) = $false)) ) | (~spl1_6 | spl1_22 | ~spl1_150)),
% 1.82/1.55 inference(equality_factoring,[status(thm)],[f3059])).
% 1.82/1.55 thf(f3059,plain,(
% 1.82/1.55 ( ! [X3 : $i,X1 : $i,X7 : $i] : (((irel @ sK5 @ X1) = $false) | ((irel @ X7 @ X3) = $false) | ((irel @ X1 @ X7) = $false)) ) | (~spl1_6 | spl1_22 | ~spl1_150)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f3058])).
% 1.82/1.55 thf(f3058,plain,(
% 1.82/1.55 ( ! [X3 : $i,X1 : $i,X7 : $i] : (((irel @ X7 @ X3) = $false) | ($true = $false) | ((irel @ X1 @ X7) = $false) | ((irel @ sK5 @ X1) = $false)) ) | (~spl1_6 | spl1_22 | ~spl1_150)),
% 1.82/1.55 inference(forward_demodulation,[status(thm)],[f3057,f2960])).
% 1.82/1.55 thf(f2960,plain,(
% 1.82/1.55 ( ! [X0 : $i] : (((sK3 @ X0) = $false)) ) | ~spl1_6),
% 1.82/1.55 inference(superposition,[status(thm)],[f2053,f2945])).
% 1.82/1.55 thf(f3057,plain,(
% 1.82/1.55 ( ! [X3 : $i,X1 : $i,X7 : $i] : (((irel @ X7 @ X3) = $false) | ((irel @ sK5 @ X1) = $false) | ($true = (sK3 @ X3)) | ((irel @ X1 @ X7) = $false)) ) | (spl1_22 | ~spl1_150)),
% 1.82/1.55 inference(subsumption_resolution,[status(thm)],[f2878,f3027])).
% 1.82/1.55 thf(f2878,plain,(
% 1.82/1.55 ( ! [X3 : $i,X1 : $i,X7 : $i] : (((irel @ X1 @ X7) = $false) | ($true = (sK3 @ X3)) | ((irel @ X7 @ X3) = $false) | ((sK4 @ (sK14 @ X7)) = $false) | ((irel @ sK5 @ X1) = $false)) ) | ~spl1_150),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2877])).
% 1.82/1.55 thf(f2998,plain,(
% 1.82/1.55 ~spl1_6 | ~spl1_12),
% 1.82/1.55 inference(avatar_contradiction_clause,[status(thm)],[f2997])).
% 1.82/1.55 thf(f2997,plain,(
% 1.82/1.55 $false | (~spl1_6 | ~spl1_12)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f2985])).
% 1.82/1.55 thf(f2985,plain,(
% 1.82/1.55 ($true = $false) | (~spl1_6 | ~spl1_12)),
% 1.82/1.55 inference(backward_demodulation,[status(thm)],[f21,f2983])).
% 1.82/1.55 thf(f2983,plain,(
% 1.82/1.55 ( ! [X0 : $i,X1 : $i] : (((irel @ X0 @ X1) = $false)) ) | (~spl1_6 | ~spl1_12)),
% 1.82/1.55 inference(trivial_inequality_removal,[status(thm)],[f2982])).
% 1.82/1.55 thf(f2982,plain,(
% 1.82/1.55 ( ! [X0 : $i,X1 : $i] : (((irel @ X0 @ X1) = $false) | ($true = $false)) ) | (~spl1_6 | ~spl1_12)),
% 1.82/1.55 inference(forward_demodulation,[status(thm)],[f2957,f2960])).
% 1.82/1.55 thf(f2957,plain,(
% 1.82/1.55 ( ! [X0 : $i,X1 : $i] : (((irel @ X0 @ X1) = $false) | ($true = (sK3 @ X1))) ) | ~spl1_12),
% 1.82/1.55 inference(superposition,[status(thm)],[f2088,f2945])).
% 1.82/1.55 thf(f2088,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((irel @ sK21 @ X1) = $false) | ($true = (sK3 @ X1))) ) | ~spl1_12),
% 1.82/1.55 inference(avatar_component_clause,[status(thm)],[f2087])).
% 1.82/1.55 thf(f2087,definition,(
% 1.82/1.55 spl1_12 <=> ! [X1 : $i] : (((irel @ sK21 @ X1) = $false) | ($true = (sK3 @ X1)))),
% 1.82/1.55 introduced(definition,[new_symbols(naming,[spl1_12])],[avatar_definition])).
% 1.82/1.55 thf(f2915,plain,(
% 1.82/1.55 spl1_159 | spl1_160),
% 1.82/1.55 inference(avatar_split_clause,[status(thm)],[f126,f2913,f2910])).
% 1.82/1.55 thf(f126,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((sK3 @ (sK10 @ X7)) = $false) | ((irel @ X8 @ X7) = $false) | ((sK3 @ (sK9 @ X4)) = $false) | ((irel @ X4 @ X6) = $false) | ((irel @ X7 @ X5) = $false) | ((irel @ sK5 @ X1) = $false) | ($true = (sK4 @ X5)) | ((sK4 @ X6) = $true) | ((irel @ sK5 @ X8) = $false) | ((irel @ X1 @ X4) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f125])).
% 1.82/1.55 thf(f125,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (sK4 @ X5)) | (((~ (irel @ X7 @ (sK10 @ X7))) | (sK3 @ (sK10 @ X7))) = $false) | ((sK3 @ (sK9 @ X4)) = $false) | ((sK4 @ X6) = $true) | ((irel @ X7 @ X5) = $false) | ((irel @ X1 @ X4) = $false) | ((irel @ X4 @ X6) = $false) | ((irel @ X8 @ X7) = $false) | ((irel @ sK5 @ X1) = $false) | ((irel @ sK5 @ X8) = $false)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f124])).
% 1.82/1.55 thf(f124,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((sK3 @ (sK9 @ X4)) = $false) | ((irel @ sK5 @ X1) = $false) | ($true = (sK4 @ X5)) | ((sK4 @ X6) = $true) | (((^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0))) @ (sK10 @ X7)) = $false) | ((irel @ X7 @ X5) = $false) | ((irel @ X8 @ X7) = $false) | ((irel @ sK5 @ X8) = $false) | ((irel @ X4 @ X6) = $false) | ((irel @ X1 @ X4) = $false)) )),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f123])).
% 1.82/1.55 thf(f123,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((irel @ X1 @ X4) = $false) | ((irel @ X8 @ X7) = $false) | ($true = (sK4 @ X5)) | ((sK4 @ X6) = $true) | ((sK3 @ (sK9 @ X4)) = $false) | ((irel @ X4 @ X6) = $false) | ((irel @ sK5 @ X1) = $false) | ((irel @ X7 @ X5) = $false) | ((irel @ sK5 @ X8) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0)))) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f122])).
% 1.82/1.55 thf(f122,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((sK3 @ (sK9 @ X4)) = $false) | ($true = (~ (irel @ X8 @ X7))) | ((irel @ X4 @ X6) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0)))) = $false) | ((irel @ X1 @ X4) = $false) | ($true = (sK4 @ X5)) | ((irel @ sK5 @ X8) = $false) | ((irel @ X7 @ X5) = $false) | ((sK4 @ X6) = $true) | ((irel @ sK5 @ X1) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f121])).
% 1.82/1.55 thf(f121,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((irel @ sK5 @ X1) = $false) | ((irel @ X7 @ X5) = $false) | ((irel @ sK5 @ X8) = $false) | ($true = (sK4 @ X5)) | ((sK4 @ X6) = $true) | ((irel @ X1 @ X4) = $false) | ((irel @ X4 @ X6) = $false) | ((sK3 @ (sK9 @ X4)) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0)))))) | ($true = (~ (irel @ X8 @ X7)))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f120])).
% 1.82/1.55 thf(f120,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (sK4 @ X5)) | ((irel @ sK5 @ X1) = $false) | ((irel @ sK5 @ X8) = $false) | ((irel @ X7 @ X5) = $false) | ($true = (~ (irel @ X4 @ X6))) | ($true = (~ (irel @ X8 @ X7))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0)))))) | ((sK4 @ X6) = $true) | ((sK3 @ (sK9 @ X4)) = $false) | ((irel @ X1 @ X4) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f118])).
% 1.82/1.55 thf(f118,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((irel @ X1 @ X4) = $false) | ((irel @ X7 @ X5) = $false) | (((sK3 @ (sK9 @ X4)) | (~ (irel @ X4 @ (sK9 @ X4)))) = $false) | ((sK4 @ X6) = $true) | ($true = (~ (irel @ X8 @ X7))) | ((irel @ sK5 @ X1) = $false) | ($true = (~ (irel @ X4 @ X6))) | ((irel @ sK5 @ X8) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0)))))) | ($true = (sK4 @ X5))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f117])).
% 1.82/1.55 thf(f117,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((sK4 @ X6) = $true) | ((irel @ sK5 @ X8) = $false) | ((irel @ sK5 @ X1) = $false) | ((~ (irel @ X7 @ X5)) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0)))))) | ((irel @ X1 @ X4) = $false) | ($true = (sK4 @ X5)) | (((sK3 @ (sK9 @ X4)) | (~ (irel @ X4 @ (sK9 @ X4)))) = $false) | ($true = (~ (irel @ X4 @ X6))) | ($true = (~ (irel @ X8 @ X7)))) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f116])).
% 1.82/1.55 thf(f116,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((irel @ sK5 @ X8) = $false) | ($true = (sK4 @ X5)) | ($true = (~ (irel @ X8 @ X7))) | (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))) @ (sK9 @ X4)) = $false) | ((~ (irel @ X7 @ X5)) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0)))))) | ((irel @ sK5 @ X1) = $false) | ((sK4 @ X6) = $true) | ((irel @ X1 @ X4) = $false) | ($true = (~ (irel @ X4 @ X6)))) )),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f115])).
% 1.82/1.55 thf(f115,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((sK4 @ X6) = $true) | ((irel @ sK5 @ X8) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0))))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0)))))) | ($true = (sK4 @ X5)) | ((~ (irel @ X7 @ X5)) = $true) | ((irel @ X1 @ X4) = $false) | ((irel @ sK5 @ X1) = $false) | ($true = (~ (irel @ X8 @ X7))) | ($true = (~ (irel @ X4 @ X6)))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f114])).
% 1.82/1.55 thf(f114,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((~ (irel @ X8 @ X7)) | (sK4 @ X5)) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0))))) = $false) | ((~ (irel @ X7 @ X5)) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0)))))) | ($true = (~ (irel @ X4 @ X6))) | ((irel @ X1 @ X4) = $false) | ((irel @ sK5 @ X1) = $false) | ((irel @ sK5 @ X8) = $false) | ((sK4 @ X6) = $true)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.82/1.55 thf(f113,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (((~ (irel @ X8 @ X7)) | (sK4 @ X5)) | (~ (irel @ X7 @ X5)))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0)))))) | ((irel @ sK5 @ X1) = $false) | ((irel @ sK5 @ X8) = $false) | ($true = (~ (irel @ X4 @ X6))) | ((irel @ X1 @ X4) = $false) | ((sK4 @ X6) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0))))) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f112])).
% 1.82/1.55 thf(f112,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((irel @ X1 @ X4) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0))))))) | ($true = (~ (irel @ X4 @ X6))) | ($true = (((~ (irel @ X8 @ X7)) | (sK4 @ X5)) | (~ (irel @ X7 @ X5)))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0)))))) | ((irel @ sK5 @ X8) = $false) | ((irel @ sK5 @ X1) = $false) | ((sK4 @ X6) = $true)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f111])).
% 1.82/1.55 thf(f111,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((irel @ sK5 @ X8) = $false) | ($true = ((((~ (irel @ X8 @ X7)) | (sK4 @ X5)) | (~ (irel @ X7 @ X5))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0))))))) | ((sK4 @ X6) = $true) | ((irel @ sK5 @ X1) = $false) | ((irel @ X1 @ X4) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0))))))) | ($true = (~ (irel @ X4 @ X6)))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f110])).
% 1.82/1.55 thf(f110,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (~ (irel @ X1 @ X4))) | ($true = (~ (irel @ X4 @ X6))) | ((irel @ sK5 @ X8) = $false) | ($true = ((((~ (irel @ X8 @ X7)) | (sK4 @ X5)) | (~ (irel @ X7 @ X5))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0))))))) | ((irel @ sK5 @ X1) = $false) | ((sK4 @ X6) = $true)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.82/1.55 thf(f109,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X1 @ X4)))) | ((irel @ sK5 @ X8) = $false) | ((irel @ sK5 @ X1) = $false) | ($true = ((((~ (irel @ X8 @ X7)) | (sK4 @ X5)) | (~ (irel @ X7 @ X5))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0))))))) | ((sK4 @ X6) = $true) | ($true = (~ (irel @ X4 @ X6)))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.82/1.55 thf(f78,plain,(
% 1.82/1.55 ( ! [X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X1 @ X4))) | (~ (irel @ X4 @ X6))) = $true) | ((irel @ sK5 @ X1) = $false) | ((irel @ sK5 @ X8) = $false) | ((sK4 @ X6) = $true) | ($true = ((((~ (irel @ X8 @ X7)) | (sK4 @ X5)) | (~ (irel @ X7 @ X5))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0)))))))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.82/1.55 thf(f77,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (((((sK3 @ X3) | (~ (irel @ X8 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | (~ (irel @ X2 @ X3))) & ((((~ (irel @ X8 @ X7)) | (sK4 @ X5)) | (~ (irel @ X7 @ X5))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0)))))))) | ((irel @ sK5 @ X1) = $false) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X1 @ X4))) | (~ (irel @ X4 @ X6))) = $true) | ((irel @ sK5 @ X8) = $false) | ((sK4 @ X6) = $true)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f76])).
% 1.82/1.55 thf(f76,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (~ (irel @ sK5 @ X8))) | ((sK4 @ X6) = $true) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X1 @ X4))) | (~ (irel @ X4 @ X6))) = $true) | ((irel @ sK5 @ X1) = $false) | ($true = (((((sK3 @ X3) | (~ (irel @ X8 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | (~ (irel @ X2 @ X3))) & ((((~ (irel @ X8 @ X7)) | (sK4 @ X5)) | (~ (irel @ X7 @ X5))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0))))))))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 1.82/1.55 thf(f75,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((((((sK3 @ X3) | (~ (irel @ X8 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | (~ (irel @ X2 @ X3))) & ((((~ (irel @ X8 @ X7)) | (sK4 @ X5)) | (~ (irel @ X7 @ X5))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK3 @ Y0))))))) | (~ (irel @ sK5 @ X8))) = $true) | ((irel @ sK5 @ X1) = $false) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X1 @ X4))) | (~ (irel @ X4 @ X6))) = $true) | ((sK4 @ X6) = $true)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f74])).
% 1.82/1.55 thf(f74,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((irel @ sK5 @ X1) = $false) | ((sK4 @ X6) = $true) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X1 @ X4))) | (~ (irel @ X4 @ X6))) = $true) | (((^[Y0 : $i]: ((((((sK3 @ X3) | (~ (irel @ Y0 @ X2))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X2 @ Y1)) | (sK4 @ Y1)))))) | (~ (irel @ X2 @ X3))) & ((((~ (irel @ Y0 @ X7)) | (sK4 @ X5)) | (~ (irel @ X7 @ X5))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X7 @ Y1)) | (sK3 @ Y1))))))) | (~ (irel @ sK5 @ Y0)))) @ X8) = $true)) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f73])).
% 1.82/1.55 thf(f73,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((((((sK3 @ X3) | (~ (irel @ Y0 @ X2))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X2 @ Y1)) | (sK4 @ Y1)))))) | (~ (irel @ X2 @ X3))) & ((((~ (irel @ Y0 @ X7)) | (sK4 @ X5)) | (~ (irel @ X7 @ X5))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X7 @ Y1)) | (sK3 @ Y1))))))) | (~ (irel @ sK5 @ Y0))))) = $true) | ((irel @ sK5 @ X1) = $false) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X1 @ X4))) | (~ (irel @ X4 @ X6))) = $true) | ((sK4 @ X6) = $true)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.82/1.55 thf(f72,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X1 @ X4))) | (~ (irel @ X4 @ X6))) = $true) | ((irel @ sK5 @ X1) = $false) | ((sK4 @ X6) = $true) | ($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK3 @ X3) | (~ (irel @ Y1 @ X2))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X2 @ Y2)) | (sK4 @ Y2)))))) | (~ (irel @ X2 @ X3))) & ((((~ (irel @ Y1 @ Y0)) | (sK4 @ X5)) | (~ (irel @ Y0 @ X5))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2))))))) | (~ (irel @ sK5 @ Y1)))))) @ X7))) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f71])).
% 1.82/1.55 thf(f71,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK3 @ X3) | (~ (irel @ Y1 @ X2))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X2 @ Y2)) | (sK4 @ Y2)))))) | (~ (irel @ X2 @ X3))) & ((((~ (irel @ Y1 @ Y0)) | (sK4 @ X5)) | (~ (irel @ Y0 @ X5))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2))))))) | (~ (irel @ sK5 @ Y1)))))))) | ((irel @ sK5 @ X1) = $false) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X1 @ X4))) | (~ (irel @ X4 @ X6))) = $true) | ((sK4 @ X6) = $true)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.82/1.55 thf(f70,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : ((((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X1 @ X4))) | (~ (irel @ X4 @ X6))) | (sK4 @ X6)) = $true) | ((irel @ sK5 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK3 @ X3) | (~ (irel @ Y1 @ X2))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X2 @ Y2)) | (sK4 @ Y2)))))) | (~ (irel @ X2 @ X3))) & ((((~ (irel @ Y1 @ Y0)) | (sK4 @ X5)) | (~ (irel @ Y0 @ X5))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2))))))) | (~ (irel @ sK5 @ Y1))))))))) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.82/1.55 thf(f69,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : ((((^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X1 @ X4))) | (~ (irel @ X4 @ Y0))) | (sK4 @ Y0))) @ X6) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK3 @ X3) | (~ (irel @ Y1 @ X2))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X2 @ Y2)) | (sK4 @ Y2)))))) | (~ (irel @ X2 @ X3))) & ((((~ (irel @ Y1 @ Y0)) | (sK4 @ X5)) | (~ (irel @ Y0 @ X5))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2))))))) | (~ (irel @ sK5 @ Y1)))))))) | ((irel @ sK5 @ X1) = $false)) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f68])).
% 1.82/1.55 thf(f68,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X1 @ X4))) | (~ (irel @ X4 @ Y0))) | (sK4 @ Y0))))) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK3 @ X3) | (~ (irel @ Y1 @ X2))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X2 @ Y2)) | (sK4 @ Y2)))))) | (~ (irel @ X2 @ X3))) & ((((~ (irel @ Y1 @ Y0)) | (sK4 @ X5)) | (~ (irel @ Y0 @ X5))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2))))))) | (~ (irel @ sK5 @ Y1)))))))) | ((irel @ sK5 @ X1) = $false)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.82/1.55 thf(f67,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X1 @ X4))) | (~ (irel @ X4 @ Y0))) | (sK4 @ Y0))))) | ($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK3 @ X3) | (~ (irel @ Y2 @ X2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X2 @ Y3)) | (sK4 @ Y3)))))) | (~ (irel @ X2 @ X3))) & ((((~ (irel @ Y2 @ Y1)) | (sK4 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK3 @ Y3))))))) | (~ (irel @ sK5 @ Y2)))))))) @ X5)) | ((irel @ sK5 @ X1) = $false)) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f66])).
% 1.82/1.55 thf(f66,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK3 @ X3) | (~ (irel @ Y2 @ X2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X2 @ Y3)) | (sK4 @ Y3)))))) | (~ (irel @ X2 @ X3))) & ((((~ (irel @ Y2 @ Y1)) | (sK4 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK3 @ Y3))))))) | (~ (irel @ sK5 @ Y2)))))))))) | ((irel @ sK5 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X1 @ X4))) | (~ (irel @ X4 @ Y0))) | (sK4 @ Y0)))))) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f65])).
% 1.82/1.55 thf(f65,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ X1 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1))))) @ X4)) | ((irel @ sK5 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK3 @ X3) | (~ (irel @ Y2 @ X2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X2 @ Y3)) | (sK4 @ Y3)))))) | (~ (irel @ X2 @ X3))) & ((((~ (irel @ Y2 @ Y1)) | (sK4 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK3 @ Y3))))))) | (~ (irel @ sK5 @ Y2))))))))))) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f64])).
% 1.82/1.55 thf(f64,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ X1 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK3 @ X3) | (~ (irel @ Y2 @ X2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X2 @ Y3)) | (sK4 @ Y3)))))) | (~ (irel @ X2 @ X3))) & ((((~ (irel @ Y2 @ Y1)) | (sK4 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK3 @ Y3))))))) | (~ (irel @ sK5 @ Y2)))))))))) | ((irel @ sK5 @ X1) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f63])).
% 1.82/1.55 thf(f63,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (irel @ sK5 @ X1))) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK3 @ X3) | (~ (irel @ Y2 @ X2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X2 @ Y3)) | (sK4 @ Y3)))))) | (~ (irel @ X2 @ X3))) & ((((~ (irel @ Y2 @ Y1)) | (sK4 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK3 @ Y3))))))) | (~ (irel @ sK5 @ Y2)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ X1 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) = $true)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f62])).
% 1.82/1.55 thf(f62,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (irel @ sK5 @ X1))) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK3 @ Y0) | (~ (irel @ Y3 @ X2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ X2 @ Y4)) | (sK4 @ Y4)))))) | (~ (irel @ X2 @ Y0))) & ((((~ (irel @ Y3 @ Y2)) | (sK4 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK3 @ Y4))))))) | (~ (irel @ sK5 @ Y3)))))))))) @ X3) = $true) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ X1 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) = $true)) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f61])).
% 1.82/1.55 thf(f61,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK3 @ Y0) | (~ (irel @ Y3 @ X2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ X2 @ Y4)) | (sK4 @ Y4)))))) | (~ (irel @ X2 @ Y0))) & ((((~ (irel @ Y3 @ Y2)) | (sK4 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK3 @ Y4))))))) | (~ (irel @ sK5 @ Y3)))))))))))) | ($true = (~ (irel @ sK5 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ X1 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) = $true)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.82/1.55 thf(f59,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ X1 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ X1 @ Y1))))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK3 @ Y0) | (~ (irel @ Y3 @ X2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ X2 @ Y4)) | (sK4 @ Y4)))))) | (~ (irel @ X2 @ Y0))) & ((((~ (irel @ Y3 @ Y2)) | (sK4 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK3 @ Y4))))))) | (~ (irel @ sK5 @ Y3)))))))))))) | ($true = (~ (irel @ sK5 @ X1)))) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.82/1.55 thf(f58,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = (~ (irel @ sK5 @ X1))) | ($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK3 @ Y1) | (~ (irel @ Y4 @ Y0))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK4 @ Y5)))))) | (~ (irel @ Y0 @ Y1))) & ((((~ (irel @ Y4 @ Y3)) | (sK4 @ Y2)) | (~ (irel @ Y3 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK3 @ Y5))))))) | (~ (irel @ sK5 @ Y4)))))))))))) @ X2)) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ X1 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ X1 @ Y1)))))))))) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f57])).
% 1.82/1.55 thf(f57,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK3 @ Y1) | (~ (irel @ Y4 @ Y0))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK4 @ Y5)))))) | (~ (irel @ Y0 @ Y1))) & ((((~ (irel @ Y4 @ Y3)) | (sK4 @ Y2)) | (~ (irel @ Y3 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK3 @ Y5))))))) | (~ (irel @ sK5 @ Y4)))))))))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ X1 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ X1 @ Y1))))))))) | ($true = (~ (irel @ sK5 @ X1)))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.82/1.55 thf(f56,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ X1 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ X1 @ Y1)))))))) | (~ (irel @ sK5 @ X1))) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK3 @ Y1) | (~ (irel @ Y4 @ Y0))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK4 @ Y5)))))) | (~ (irel @ Y0 @ Y1))) & ((((~ (irel @ Y4 @ Y3)) | (sK4 @ Y2)) | (~ (irel @ Y3 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK3 @ Y5))))))) | (~ (irel @ sK5 @ Y4))))))))))))))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f55])).
% 1.82/1.55 thf(f55,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK3 @ Y1) | (~ (irel @ Y4 @ Y0))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK4 @ Y5)))))) | (~ (irel @ Y0 @ Y1))) & ((((~ (irel @ Y4 @ Y3)) | (sK4 @ Y2)) | (~ (irel @ Y3 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK3 @ Y5))))))) | (~ (irel @ sK5 @ Y4)))))))))))))) = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ X1 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ X1 @ Y1)))))))) | (~ (irel @ sK5 @ X1))) = $true)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.82/1.55 thf(f54,plain,(
% 1.82/1.55 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0)))) @ X1) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK3 @ Y1) | (~ (irel @ Y4 @ Y0))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK4 @ Y5)))))) | (~ (irel @ Y0 @ Y1))) & ((((~ (irel @ Y4 @ Y3)) | (sK4 @ Y2)) | (~ (irel @ Y3 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK3 @ Y5))))))) | (~ (irel @ sK5 @ Y4)))))))))))))) = $false)) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f53])).
% 1.82/1.55 thf(f53,plain,(
% 1.82/1.55 ($true = (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK3 @ Y1) | (~ (irel @ Y4 @ Y0))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK4 @ Y5)))))) | (~ (irel @ Y0 @ Y1))) & ((((~ (irel @ Y4 @ Y3)) | (sK4 @ Y2)) | (~ (irel @ Y3 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK3 @ Y5))))))) | (~ (irel @ sK5 @ Y4)))))))))))))) = $false)),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f52])).
% 1.82/1.55 thf(f52,plain,(
% 1.82/1.55 ((~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0)))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK3 @ Y1) | (~ (irel @ Y4 @ Y0))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK4 @ Y5)))))) | (~ (irel @ Y0 @ Y1))) & ((((~ (irel @ Y4 @ Y3)) | (sK4 @ Y2)) | (~ (irel @ Y3 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK3 @ Y5))))))) | (~ (irel @ sK5 @ Y4)))))))))))))) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.82/1.55 thf(f50,plain,(
% 1.82/1.55 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK3 @ Y1) | (~ (irel @ Y4 @ Y0))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK4 @ Y5)))))) | (~ (irel @ Y0 @ Y1))) & ((((~ (irel @ Y4 @ Y3)) | (sK4 @ Y2)) | (~ (irel @ Y3 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK3 @ Y5))))))) | (~ (irel @ sK5 @ Y4)))))))))))))) != (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0)))))))),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.82/1.55 thf(f49,plain,(
% 1.82/1.55 (((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (!! @ $i @ (^[Y4 : $i]: ((sK3 @ Y4) | (~ (irel @ Y2 @ Y4)))))) | (~ (irel @ Y1 @ Y2))) | (~ (irel @ Y2 @ Y3))) | (sK4 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (sK4 @ Y4))))) | (sK3 @ Y2)) | (~ (irel @ Y3 @ Y2))) | (~ (irel @ Y1 @ Y3)))))))) | (~ (irel @ Y0 @ Y1))))))) @ sK5) != ((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((sK3 @ Y2) | (~ (irel @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y1 @ Y6)) | (sK4 @ Y6)))))) | (~ (irel @ Y1 @ Y2))) & ((((~ (irel @ Y5 @ Y4)) | (sK4 @ Y3)) | (~ (irel @ Y4 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (sK3 @ Y6))))))) | (~ (irel @ Y0 @ Y5))))))))))))))) @ sK5))),
% 1.82/1.55 inference(negative_extensionality,[status(thm)],[f46])).
% 1.82/1.55 thf(f46,plain,(
% 1.82/1.55 ((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (!! @ $i @ (^[Y4 : $i]: ((sK3 @ Y4) | (~ (irel @ Y2 @ Y4)))))) | (~ (irel @ Y1 @ Y2))) | (~ (irel @ Y2 @ Y3))) | (sK4 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (sK4 @ Y4))))) | (sK3 @ Y2)) | (~ (irel @ Y3 @ Y2))) | (~ (irel @ Y1 @ Y3)))))))) | (~ (irel @ Y0 @ Y1))))))) != (^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((sK3 @ Y2) | (~ (irel @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y1 @ Y6)) | (sK4 @ Y6)))))) | (~ (irel @ Y1 @ Y2))) & ((((~ (irel @ Y5 @ Y4)) | (sK4 @ Y3)) | (~ (irel @ Y4 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (sK3 @ Y6))))))) | (~ (irel @ Y0 @ Y5))))))))))))))))),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.82/1.55 thf(f45,plain,(
% 1.82/1.55 (((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((sK3 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))) | (Y0 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y0 @ Y5))))) | (sK3 @ Y3)) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4)))))))) | (~ (irel @ Y1 @ Y2))))))))) @ sK4) != ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((((((sK3 @ Y3) | (~ (irel @ Y6 @ Y2))) | (~ (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y7)) | (Y0 @ Y7)))))) | (~ (irel @ Y2 @ Y3))) & ((((~ (irel @ Y6 @ Y5)) | (Y0 @ Y4)) | (~ (irel @ Y5 @ Y4))) | (~ (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y5 @ Y7)) | (sK3 @ Y7))))))) | (~ (irel @ Y1 @ Y6))))))))))))))))) @ sK4))),
% 1.82/1.55 inference(negative_extensionality,[status(thm)],[f43])).
% 1.82/1.55 thf(f43,plain,(
% 1.82/1.55 ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((sK3 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))) | (Y0 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y0 @ Y5))))) | (sK3 @ Y3)) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4)))))))) | (~ (irel @ Y1 @ Y2))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((((((sK3 @ Y3) | (~ (irel @ Y6 @ Y2))) | (~ (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y7)) | (Y0 @ Y7)))))) | (~ (irel @ Y2 @ Y3))) & ((((~ (irel @ Y6 @ Y5)) | (Y0 @ Y4)) | (~ (irel @ Y5 @ Y4))) | (~ (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y5 @ Y7)) | (sK3 @ Y7))))))) | (~ (irel @ Y1 @ Y6))))))))))))))))))),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.82/1.55 thf(f42,plain,(
% 1.82/1.55 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y0 @ Y4) | (~ (irel @ Y7 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y3 @ Y4))) & ((((~ (irel @ Y7 @ Y6)) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8))))))) | (~ (irel @ Y2 @ Y7))))))))))))))))))) @ sK3) != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y3 @ Y4))) | (~ (irel @ Y4 @ Y5))) | (Y1 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y5 @ Y6)) | (Y1 @ Y6))))) | (Y0 @ Y4)) | (~ (irel @ Y5 @ Y4))) | (~ (irel @ Y3 @ Y5)))))))) | (~ (irel @ Y2 @ Y3))))))))))) @ sK3))),
% 1.82/1.55 inference(negative_extensionality,[status(thm)],[f40])).
% 1.82/1.55 thf(f40,plain,(
% 1.82/1.55 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y3 @ Y4))) | (~ (irel @ Y4 @ Y5))) | (Y1 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y5 @ Y6)) | (Y1 @ Y6))))) | (Y0 @ Y4)) | (~ (irel @ Y5 @ Y4))) | (~ (irel @ Y3 @ Y5)))))))) | (~ (irel @ Y2 @ Y3))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y0 @ Y4) | (~ (irel @ Y7 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y3 @ Y4))) & ((((~ (irel @ Y7 @ Y6)) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8))))))) | (~ (irel @ Y2 @ Y7))))))))))))))))))))),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.82/1.55 thf(f39,plain,(
% 1.82/1.55 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y0 @ Y4) | (~ (irel @ Y7 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y3 @ Y4))) & ((((~ (irel @ Y7 @ Y6)) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8))))))) | (~ (irel @ Y2 @ Y7))))))))))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (irel @ Y3 @ Y4))))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((((~ (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7) | (~ (irel @ Y5 @ Y7)))))) | (~ (irel @ Y4 @ Y5))) | (~ (irel @ Y5 @ Y6))) | (Y3 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((((~ (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y6 @ Y7)) | (Y3 @ Y7))))) | (Y2 @ Y5)) | (~ (irel @ Y6 @ Y5))) | (~ (irel @ Y4 @ Y6))))))))))))) @ Y0 @ Y1))))))),
% 1.82/1.55 inference(definition_unfolding,[status(thm)],[f38,f17,f24,f25])).
% 1.82/1.55 thf(f25,plain,(
% 1.82/1.55 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))) | (Y1 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5))))) | (Y0 @ Y3)) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4))))))))))))))),
% 1.82/1.55 inference(cnf_transformation,[status(thm)],[f14])).
% 1.82/1.55 thf(f24,plain,(
% 1.82/1.55 (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))))),
% 1.82/1.55 inference(cnf_transformation,[status(thm)],[f14])).
% 1.82/1.55 thf(f17,plain,(
% 1.82/1.55 (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y0 @ Y4) | (~ (irel @ Y7 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y3 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y3 @ Y4))) & ((((~ (irel @ Y7 @ Y6)) | (Y1 @ Y5)) | (~ (irel @ Y6 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8))))))) | (~ (irel @ Y2 @ Y7))))))))))))))))))))),
% 1.82/1.55 inference(cnf_transformation,[status(thm)],[f14])).
% 1.82/1.55 thf(f38,plain,(
% 1.82/1.55 (ixor != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (inot @ (iequiv @ Y0 @ Y1))))))),
% 1.82/1.55 inference(cnf_transformation,[status(thm)],[f9])).
% 1.82/1.55 thf(f9,plain,(
% 1.82/1.55 (ixor != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (inot @ (iequiv @ Y0 @ Y1))))))),
% 1.82/1.55 inference(flattening,[status(thm)],[f8])).
% 1.82/1.55 thf(f8,plain,(
% 1.82/1.55 ~(ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (inot @ (iequiv @ Y0 @ Y1))))))),
% 1.82/1.55 inference(fool_elimination,[status(thm)],[f7])).
% 1.82/1.55 thf(f7,plain,(
% 1.82/1.55 ~((^[X0 : $i > $o, X1 : $i > $o] : (inot @ (iequiv @ X0 @ X1))) = ixor)),
% 1.82/1.55 inference(rectify,[status(thm)],[f3])).
% 1.82/1.55 thf(f3,negated_conjecture,(
% 1.82/1.55 ~((^[X8 : $i > $o, X9 : $i > $o] : (inot @ (iequiv @ X8 @ X9))) = ixor)),
% 1.82/1.55 inference(negated_conjecture,[status(cth)],[f2])).
% 1.82/1.55 thf(f2,conjecture,(
% 1.82/1.55 ((^[X8 : $i > $o, X9 : $i > $o] : (inot @ (iequiv @ X8 @ X9))) = ixor)),
% 1.82/1.55 file('/export/starexec/sandbox/tmp/tmp.YfK2dOMluu/DTF2THF_2576.p',ixor)).
% 1.82/1.55 thf(f2882,plain,(
% 1.82/1.55 spl1_150 | spl1_151),
% 1.82/1.55 inference(avatar_split_clause,[status(thm)],[f180,f2880,f2877])).
% 1.82/1.55 thf(f180,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (((sK3 @ X4) = $true) | ((irel @ sK5 @ X8) = $false) | ((irel @ X1 @ X7) = $false) | ((irel @ X8 @ X2) = $false) | ((irel @ X7 @ X3) = $false) | ((irel @ sK5 @ X1) = $false) | ($true = (sK3 @ X3)) | ((sK4 @ (sK14 @ X7)) = $false) | ((irel @ X2 @ X4) = $false) | ((sK4 @ (sK12 @ X2)) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f179])).
% 1.82/1.55 thf(f179,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (((sK3 @ X4) = $true) | ((irel @ X7 @ X3) = $false) | ((irel @ X2 @ X4) = $false) | ($true = (sK3 @ X3)) | (((~ (irel @ X7 @ (sK14 @ X7))) | (sK4 @ (sK14 @ X7))) = $false) | ((irel @ sK5 @ X8) = $false) | ((irel @ sK5 @ X1) = $false) | ((irel @ X8 @ X2) = $false) | ((sK4 @ (sK12 @ X2)) = $false) | ((irel @ X1 @ X7) = $false)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f178])).
% 1.82/1.55 thf(f178,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (((irel @ sK5 @ X8) = $false) | ((irel @ sK5 @ X1) = $false) | (((^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0))) @ (sK14 @ X7)) = $false) | ((irel @ X8 @ X2) = $false) | ((irel @ X1 @ X7) = $false) | ((irel @ X2 @ X4) = $false) | ((irel @ X7 @ X3) = $false) | ($true = (sK3 @ X3)) | ((sK4 @ (sK12 @ X2)) = $false) | ((sK3 @ X4) = $true)) )),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f177])).
% 1.82/1.55 thf(f177,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (($true = (sK3 @ X3)) | ((irel @ sK5 @ X8) = $false) | ((irel @ X1 @ X7) = $false) | ((sK3 @ X4) = $true) | ((irel @ X7 @ X3) = $false) | ((sK4 @ (sK12 @ X2)) = $false) | ((irel @ X2 @ X4) = $false) | ((irel @ X8 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0)))) = $false) | ((irel @ sK5 @ X1) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f168])).
% 1.82/1.55 thf(f168,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (((irel @ sK5 @ X8) = $false) | ((sK4 @ (sK12 @ X2)) = $false) | ((sK3 @ X4) = $true) | ((irel @ X1 @ X7) = $false) | ((irel @ sK5 @ X1) = $false) | ((irel @ X7 @ X3) = $false) | ((irel @ X2 @ X4) = $false) | ($true = (sK3 @ X3)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0)))))) | ((irel @ X8 @ X2) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f167])).
% 1.82/1.55 thf(f167,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (((irel @ sK5 @ X1) = $false) | ((irel @ X2 @ X4) = $false) | ((irel @ X7 @ X3) = $false) | ((irel @ sK5 @ X8) = $false) | (((~ (irel @ X2 @ (sK12 @ X2))) | (sK4 @ (sK12 @ X2))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0)))))) | ((sK3 @ X4) = $true) | ((irel @ X8 @ X2) = $false) | ((irel @ X1 @ X7) = $false) | ($true = (sK3 @ X3))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f166])).
% 1.82/1.55 thf(f166,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (((irel @ sK5 @ X1) = $false) | ($true = (~ (irel @ X8 @ X2))) | ((irel @ X1 @ X7) = $false) | ((sK3 @ X4) = $true) | ((irel @ X2 @ X4) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0)))))) | ((irel @ X7 @ X3) = $false) | ($true = (sK3 @ X3)) | ((irel @ sK5 @ X8) = $false) | (((~ (irel @ X2 @ (sK12 @ X2))) | (sK4 @ (sK12 @ X2))) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f165])).
% 1.82/1.55 thf(f165,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (((irel @ X2 @ X4) = $false) | (((sK3 @ X4) | (~ (irel @ X8 @ X2))) = $true) | ((irel @ X1 @ X7) = $false) | (((~ (irel @ X2 @ (sK12 @ X2))) | (sK4 @ (sK12 @ X2))) = $false) | ((irel @ sK5 @ X8) = $false) | ($true = (sK3 @ X3)) | ((irel @ sK5 @ X1) = $false) | ((irel @ X7 @ X3) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0))))))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f164])).
% 1.82/1.55 thf(f164,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (((irel @ X7 @ X3) = $false) | ((irel @ sK5 @ X8) = $false) | ($true = (~ (irel @ X2 @ X4))) | ((irel @ sK5 @ X1) = $false) | ((irel @ X1 @ X7) = $false) | ($true = (sK3 @ X3)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0)))))) | (((sK3 @ X4) | (~ (irel @ X8 @ X2))) = $true) | (((~ (irel @ X2 @ (sK12 @ X2))) | (sK4 @ (sK12 @ X2))) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f163])).
% 1.82/1.55 thf(f163,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (((irel @ sK5 @ X1) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ X3)) = $true) | (((~ (irel @ X2 @ (sK12 @ X2))) | (sK4 @ (sK12 @ X2))) = $false) | ((irel @ X7 @ X3) = $false) | ($true = (~ (irel @ X2 @ X4))) | (((sK3 @ X4) | (~ (irel @ X8 @ X2))) = $true) | ((irel @ sK5 @ X8) = $false) | ((irel @ X1 @ X7) = $false)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f162])).
% 1.82/1.55 thf(f162,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : ((((sK3 @ X4) | (~ (irel @ X8 @ X2))) = $true) | ((irel @ sK5 @ X8) = $false) | ($true = (~ (irel @ X2 @ X4))) | ((irel @ X1 @ X7) = $false) | ((irel @ sK5 @ X1) = $false) | (((^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0))) @ (sK12 @ X2)) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ X3)) = $true) | ((irel @ X7 @ X3) = $false)) )),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f161])).
% 1.82/1.55 thf(f161,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) = $false) | ($true = (~ (irel @ X2 @ X4))) | ((irel @ sK5 @ X1) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ X3)) = $true) | ((irel @ X1 @ X7) = $false) | ((irel @ sK5 @ X8) = $false) | ((irel @ X7 @ X3) = $false) | (((sK3 @ X4) | (~ (irel @ X8 @ X2))) = $true)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f160])).
% 1.82/1.55 thf(f160,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (((irel @ sK5 @ X1) = $false) | ($true = (~ (irel @ X1 @ X7))) | (((sK3 @ X4) | (~ (irel @ X8 @ X2))) = $true) | ($true = (~ (irel @ X2 @ X4))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ X3)) = $true) | ((irel @ sK5 @ X8) = $false) | ((irel @ X7 @ X3) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f159])).
% 1.82/1.55 thf(f159,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (((~ (irel @ X7 @ X3)) = $true) | (((sK3 @ X4) | (~ (irel @ X8 @ X2))) = $true) | ($true = (~ (irel @ X1 @ X7))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ X3)) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) = $false) | ((irel @ sK5 @ X8) = $false) | ((irel @ sK5 @ X1) = $false) | ($true = (~ (irel @ X2 @ X4)))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f158])).
% 1.82/1.55 thf(f158,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ X3)) | (~ (irel @ X7 @ X3)))) | ($true = (~ (irel @ X2 @ X4))) | (((sK3 @ X4) | (~ (irel @ X8 @ X2))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) = $false) | ((irel @ sK5 @ X8) = $false) | ($true = (~ (irel @ X1 @ X7))) | ((irel @ sK5 @ X1) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f157])).
% 1.82/1.55 thf(f157,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (((irel @ sK5 @ X8) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0))))) = $true) | ($true = (~ (irel @ X2 @ X4))) | ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ X3)) | (~ (irel @ X7 @ X3)))) | ((irel @ sK5 @ X1) = $false) | (((sK3 @ X4) | (~ (irel @ X8 @ X2))) = $true) | ($true = (~ (irel @ X1 @ X7)))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f156])).
% 1.82/1.55 thf(f156,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (($true = (((sK3 @ X4) | (~ (irel @ X8 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0))))))) | ($true = (~ (irel @ X1 @ X7))) | ($true = (~ (irel @ X2 @ X4))) | ((irel @ sK5 @ X8) = $false) | ((irel @ sK5 @ X1) = $false) | ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ X3)) | (~ (irel @ X7 @ X3))))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f155])).
% 1.82/1.55 thf(f155,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (((irel @ sK5 @ X1) = $false) | ((irel @ sK5 @ X8) = $false) | ($true = ((((sK3 @ X4) | (~ (irel @ X8 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | (~ (irel @ X2 @ X4)))) | ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ X3)) | (~ (irel @ X7 @ X3)))) | ($true = (~ (irel @ X1 @ X7)))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f154])).
% 1.82/1.55 thf(f154,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X7 : $i,X4 : $i] : (((irel @ sK5 @ X8) = $false) | ((irel @ sK5 @ X1) = $false) | ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ X3)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X1 @ X7)))) | ($true = ((((sK3 @ X4) | (~ (irel @ X8 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | (~ (irel @ X2 @ X4))))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f152])).
% 1.82/1.55 thf(f152,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((irel @ sK5 @ X8) = $false) | ($true = (((((sK3 @ X4) | (~ (irel @ X8 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | (~ (irel @ X2 @ X4))) & ((((~ (irel @ X8 @ X6)) | (sK4 @ X5)) | (~ (irel @ X6 @ X5))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X6 @ Y0)) | (sK3 @ Y0)))))))) | ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ X3)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X1 @ X7)))) | ((irel @ sK5 @ X1) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f151])).
% 1.82/1.55 thf(f151,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((irel @ sK5 @ X1) = $false) | ($true = (~ (irel @ sK5 @ X8))) | ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ X3)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X1 @ X7)))) | ($true = (((((sK3 @ X4) | (~ (irel @ X8 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | (~ (irel @ X2 @ X4))) & ((((~ (irel @ X8 @ X6)) | (sK4 @ X5)) | (~ (irel @ X6 @ X5))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X6 @ Y0)) | (sK3 @ Y0))))))))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f150])).
% 1.82/1.55 thf(f150,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((irel @ sK5 @ X1) = $false) | (((((((sK3 @ X4) | (~ (irel @ X8 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | (~ (irel @ X2 @ X4))) & ((((~ (irel @ X8 @ X6)) | (sK4 @ X5)) | (~ (irel @ X6 @ X5))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X6 @ Y0)) | (sK3 @ Y0))))))) | (~ (irel @ sK5 @ X8))) = $true) | ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ X3)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X1 @ X7))))) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f149])).
% 1.82/1.55 thf(f149,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ X3)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X1 @ X7)))) | ((irel @ sK5 @ X1) = $false) | ($true = ((^[Y0 : $i]: ((((((sK3 @ X4) | (~ (irel @ Y0 @ X2))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X2 @ Y1)) | (sK4 @ Y1)))))) | (~ (irel @ X2 @ X4))) & ((((~ (irel @ Y0 @ X6)) | (sK4 @ X5)) | (~ (irel @ X6 @ X5))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X6 @ Y1)) | (sK3 @ Y1))))))) | (~ (irel @ sK5 @ Y0)))) @ X8))) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f148])).
% 1.82/1.55 thf(f148,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((((((sK3 @ X4) | (~ (irel @ Y0 @ X2))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X2 @ Y1)) | (sK4 @ Y1)))))) | (~ (irel @ X2 @ X4))) & ((((~ (irel @ Y0 @ X6)) | (sK4 @ X5)) | (~ (irel @ X6 @ X5))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X6 @ Y1)) | (sK3 @ Y1))))))) | (~ (irel @ sK5 @ Y0)))))) | ((irel @ sK5 @ X1) = $false) | ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ X3)) | (~ (irel @ X7 @ X3))) | (~ (irel @ X1 @ X7))))) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f147])).
% 1.82/1.55 thf(f147,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ X3)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X1 @ Y0)))) @ X7) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((((((sK3 @ X4) | (~ (irel @ Y0 @ X2))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X2 @ Y1)) | (sK4 @ Y1)))))) | (~ (irel @ X2 @ X4))) & ((((~ (irel @ Y0 @ X6)) | (sK4 @ X5)) | (~ (irel @ X6 @ X5))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X6 @ Y1)) | (sK3 @ Y1))))))) | (~ (irel @ sK5 @ Y0)))))) | ((irel @ sK5 @ X1) = $false)) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f146])).
% 1.82/1.55 thf(f146,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ X3)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X1 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((((((sK3 @ X4) | (~ (irel @ Y0 @ X2))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X2 @ Y1)) | (sK4 @ Y1)))))) | (~ (irel @ X2 @ X4))) & ((((~ (irel @ Y0 @ X6)) | (sK4 @ X5)) | (~ (irel @ X6 @ X5))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X6 @ Y1)) | (sK3 @ Y1))))))) | (~ (irel @ sK5 @ Y0)))))) | ((irel @ sK5 @ X1) = $false)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f145])).
% 1.82/1.55 thf(f145,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ X3)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X1 @ Y0)))))) | ((irel @ sK5 @ X1) = $false) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK3 @ X4) | (~ (irel @ Y1 @ X2))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X2 @ Y2)) | (sK4 @ Y2)))))) | (~ (irel @ X2 @ X4))) & ((((~ (irel @ Y1 @ Y0)) | (sK4 @ X5)) | (~ (irel @ Y0 @ X5))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2))))))) | (~ (irel @ sK5 @ Y1)))))) @ X6) = $true)) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f144])).
% 1.82/1.55 thf(f144,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK3 @ X4) | (~ (irel @ Y1 @ X2))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ X2 @ Y2)) | (sK4 @ Y2)))))) | (~ (irel @ X2 @ X4))) & ((((~ (irel @ Y1 @ Y0)) | (sK4 @ X5)) | (~ (irel @ Y0 @ X5))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2))))))) | (~ (irel @ sK5 @ Y1)))))))) | ((irel @ sK5 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ X3)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X1 @ Y0))))))) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f143])).
% 1.82/1.55 thf(f143,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ X3)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X1 @ Y0)))))) | ((irel @ sK5 @ X1) = $false) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK3 @ X4) | (~ (irel @ Y2 @ X2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X2 @ Y3)) | (sK4 @ Y3)))))) | (~ (irel @ X2 @ X4))) & ((((~ (irel @ Y2 @ Y1)) | (sK4 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK3 @ Y3))))))) | (~ (irel @ sK5 @ Y2)))))))) @ X5) = $true)) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f142])).
% 1.82/1.55 thf(f142,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK3 @ X4) | (~ (irel @ Y2 @ X2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ X2 @ Y3)) | (sK4 @ Y3)))))) | (~ (irel @ X2 @ X4))) & ((((~ (irel @ Y2 @ Y1)) | (sK4 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK3 @ Y3))))))) | (~ (irel @ sK5 @ Y2))))))))) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ X3)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X1 @ Y0)))))) | ((irel @ sK5 @ X1) = $false)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f141])).
% 1.82/1.55 thf(f141,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ X3)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X1 @ Y0)))))) | ((irel @ sK5 @ X1) = $false) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK3 @ Y0) | (~ (irel @ Y3 @ X2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ X2 @ Y4)) | (sK4 @ Y4)))))) | (~ (irel @ X2 @ Y0))) & ((((~ (irel @ Y3 @ Y2)) | (sK4 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK3 @ Y4))))))) | (~ (irel @ sK5 @ Y3)))))))))) @ X4) = $true)) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f140])).
% 1.82/1.55 thf(f140,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ sK5 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK3 @ Y0) | (~ (irel @ Y3 @ X2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ X2 @ Y4)) | (sK4 @ Y4)))))) | (~ (irel @ X2 @ Y0))) & ((((~ (irel @ Y3 @ Y2)) | (sK4 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK3 @ Y4))))))) | (~ (irel @ sK5 @ Y3)))))))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ X3)) | (~ (irel @ Y0 @ X3))) | (~ (irel @ X1 @ Y0))))))) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f139])).
% 1.82/1.55 thf(f139,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ sK5 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK3 @ Y0) | (~ (irel @ Y3 @ X2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ X2 @ Y4)) | (sK4 @ Y4)))))) | (~ (irel @ X2 @ Y0))) & ((((~ (irel @ Y3 @ Y2)) | (sK4 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK3 @ Y4))))))) | (~ (irel @ sK5 @ Y3)))))))))))) | ($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ X1 @ Y1)))))) @ X3))) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f138])).
% 1.82/1.55 thf(f138,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ X1 @ Y1)))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK3 @ Y0) | (~ (irel @ Y3 @ X2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ X2 @ Y4)) | (sK4 @ Y4)))))) | (~ (irel @ X2 @ Y0))) & ((((~ (irel @ Y3 @ Y2)) | (sK4 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK3 @ Y4))))))) | (~ (irel @ sK5 @ Y3)))))))))))) | ((irel @ sK5 @ X1) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f60])).
% 1.82/1.55 thf(f60,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = (~ (irel @ sK5 @ X1))) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ X1 @ Y1)))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK3 @ Y0) | (~ (irel @ Y3 @ X2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ X2 @ Y4)) | (sK4 @ Y4)))))) | (~ (irel @ X2 @ Y0))) & ((((~ (irel @ Y3 @ Y2)) | (sK4 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK3 @ Y4))))))) | (~ (irel @ sK5 @ Y3))))))))))))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.82/1.55 thf(f2810,plain,(
% 1.82/1.55 spl1_86 | spl1_22 | spl1_140 | spl1_135),
% 1.82/1.55 inference(avatar_split_clause,[status(thm)],[f446,f2780,f2807,f2142,f2499])).
% 1.82/1.55 thf(f446,plain,(
% 1.82/1.55 ((sK3 @ sK24) = $false) | ((sK4 @ sK28) = $false) | ($false = (sK3 @ sK19)) | ((sK4 @ sK20) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f410])).
% 1.82/1.55 thf(f410,plain,(
% 1.82/1.55 ((sK4 @ sK28) = $false) | ((sK4 @ sK20) = $false) | ($false = (sK3 @ sK19)) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK24)) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f409])).
% 1.82/1.55 thf(f409,plain,(
% 1.82/1.55 ((sK4 @ sK20) = $false) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK25 @ Y0)))))) | (~ (irel @ sK23 @ sK25))) | (~ (irel @ sK25 @ sK28))) | (sK4 @ sK28)) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK24)) = $false) | ($false = (sK3 @ sK19))),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f408])).
% 1.82/1.55 thf(f408,plain,(
% 1.82/1.55 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK24)) = $false) | ($false = (sK3 @ sK19)) | (((^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ sK25 @ Y1)))))) | (~ (irel @ sK23 @ sK25))) | (~ (irel @ sK25 @ Y0))) | (sK4 @ Y0))) @ sK28) = $false) | ((sK4 @ sK20) = $false)),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f407])).
% 1.82/1.55 thf(f407,plain,(
% 1.82/1.55 ((sK4 @ sK20) = $false) | ($false = (sK3 @ sK19)) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ sK25 @ Y1)))))) | (~ (irel @ sK23 @ sK25))) | (~ (irel @ sK25 @ Y0))) | (sK4 @ Y0)))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK24)) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f405])).
% 1.82/1.55 thf(f405,plain,(
% 1.82/1.55 (((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ sK25 @ Y1)))))) | (~ (irel @ sK23 @ sK25))) | (~ (irel @ sK25 @ Y0))) | (sK4 @ Y0)))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK24)) = $false) | ((sK4 @ sK20) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f256])).
% 1.82/1.55 thf(f256,plain,(
% 1.82/1.55 ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK24)) | (~ (irel @ sK26 @ sK24))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ sK25 @ Y1)))))) | (~ (irel @ sK23 @ sK25))) | (~ (irel @ sK25 @ Y0))) | (sK4 @ Y0)))) = $false) | (((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) = $false) | ((sK4 @ sK20) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f255])).
% 1.82/1.55 thf(f255,plain,(
% 1.82/1.55 (((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) = $false) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK24)) | (~ (irel @ sK26 @ sK24))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ sK25 @ Y1)))))) | (~ (irel @ sK23 @ sK25))) | (~ (irel @ sK25 @ Y0))) | (sK4 @ Y0)))) = $false) | (((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f253])).
% 1.82/1.55 thf(f253,plain,(
% 1.82/1.55 (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK24)) | (~ (irel @ sK26 @ sK24))) | (~ (irel @ sK23 @ sK26))) = $false) | (((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ sK25 @ Y1)))))) | (~ (irel @ sK23 @ sK25))) | (~ (irel @ sK25 @ Y0))) | (sK4 @ Y0)))) = $false) | (((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) = $false)),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f252])).
% 1.82/1.55 thf(f252,plain,(
% 1.82/1.55 (((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ sK25 @ Y1)))))) | (~ (irel @ sK23 @ sK25))) | (~ (irel @ sK25 @ Y0))) | (sK4 @ Y0)))) = $false) | (((^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ sK24)) | (~ (irel @ Y0 @ sK24))) | (~ (irel @ sK23 @ Y0)))) @ sK26) = $false) | (((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) = $false)),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f251])).
% 1.82/1.55 thf(f251,plain,(
% 1.82/1.55 ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ sK24)) | (~ (irel @ Y0 @ sK24))) | (~ (irel @ sK23 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ sK25 @ Y1)))))) | (~ (irel @ sK23 @ sK25))) | (~ (irel @ sK25 @ Y0))) | (sK4 @ Y0)))) = $false) | (((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) = $false) | (((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) = $false)),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f250])).
% 1.82/1.55 thf(f250,plain,(
% 1.82/1.55 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1))))) @ sK25) = $false) | (((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) = $false) | (((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ sK24)) | (~ (irel @ Y0 @ sK24))) | (~ (irel @ sK23 @ Y0))))) = $false)),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f249])).
% 1.82/1.55 thf(f249,plain,(
% 1.82/1.55 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) = $false) | (((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ sK24)) | (~ (irel @ Y0 @ sK24))) | (~ (irel @ sK23 @ Y0))))) = $false) | (((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) = $false)),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f248])).
% 1.82/1.55 thf(f248,plain,(
% 1.82/1.55 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) = $false) | (((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) = $false) | (((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) = $false) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))) @ sK24) = $false)),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f247])).
% 1.82/1.55 thf(f247,plain,(
% 1.82/1.55 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1))))))) = $false) | (((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) = $false) | (((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f245])).
% 1.82/1.55 thf(f245,plain,(
% 1.82/1.55 ((((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) | (~ (irel @ sK21 @ sK20))) = $false) | (((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1))))))) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f243])).
% 1.82/1.55 thf(f243,plain,(
% 1.82/1.55 (((((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) | (~ (irel @ sK21 @ sK20))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0)))))) = $false) | (((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1))))))) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f242])).
% 1.82/1.55 thf(f242,plain,(
% 1.82/1.55 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))))) = $false) | (((((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) | (~ (irel @ sK21 @ sK20))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0)))))) = $false) | (((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f240])).
% 1.82/1.55 thf(f240,plain,(
% 1.82/1.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))))) | (~ (irel @ sK5 @ sK23))) = $false) | (((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) = $false) | (((((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) | (~ (irel @ sK21 @ sK20))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0)))))) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f238])).
% 1.82/1.55 thf(f238,plain,(
% 1.82/1.55 ((((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK4 @ Y0)))))) = $false) | (((((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) | (~ (irel @ sK21 @ sK20))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0)))))) = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))))) | (~ (irel @ sK5 @ sK23))) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f236])).
% 1.82/1.55 thf(f236,plain,(
% 1.82/1.55 (((((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK4 @ Y0)))))) | (~ (irel @ sK18 @ sK19))) = $false) | (((((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) | (~ (irel @ sK21 @ sK20))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0)))))) = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))))) | (~ (irel @ sK5 @ sK23))) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f235])).
% 1.82/1.55 thf(f235,plain,(
% 1.82/1.55 ((((((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK4 @ Y0)))))) | (~ (irel @ sK18 @ sK19))) & ((((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) | (~ (irel @ sK21 @ sK20))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))))) = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))))) | (~ (irel @ sK5 @ sK23))) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f233])).
% 1.82/1.55 thf(f233,plain,(
% 1.82/1.55 (((((((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK4 @ Y0)))))) | (~ (irel @ sK18 @ sK19))) & ((((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) | (~ (irel @ sK21 @ sK20))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))))) | (~ (irel @ sK5 @ sK22))) = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))))) | (~ (irel @ sK5 @ sK23))) = $false)),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f232])).
% 1.82/1.55 thf(f232,plain,(
% 1.82/1.55 (((((((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK4 @ Y0)))))) | (~ (irel @ sK18 @ sK19))) & ((((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) | (~ (irel @ sK21 @ sK20))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))))) | (~ (irel @ sK5 @ sK22))) = $false) | (((^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0)))) @ sK23) = $false)),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f231])).
% 1.82/1.55 thf(f231,plain,(
% 1.82/1.55 ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0))))) = $false) | (((((((sK3 @ sK19) | (~ (irel @ sK22 @ sK18))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK4 @ Y0)))))) | (~ (irel @ sK18 @ sK19))) & ((((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) | (~ (irel @ sK21 @ sK20))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))))) | (~ (irel @ sK5 @ sK22))) = $false)),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f230])).
% 1.82/1.55 thf(f230,plain,(
% 1.82/1.55 ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0))))) = $false) | (((^[Y0 : $i]: ((((((sK3 @ sK19) | (~ (irel @ Y0 @ sK18))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK4 @ Y1)))))) | (~ (irel @ sK18 @ sK19))) & ((((~ (irel @ Y0 @ sK21)) | (sK4 @ sK20)) | (~ (irel @ sK21 @ sK20))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK21 @ Y1)) | (sK3 @ Y1))))))) | (~ (irel @ sK5 @ Y0)))) @ sK22) = $false)),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f229])).
% 1.82/1.55 thf(f229,plain,(
% 1.82/1.55 ((!! @ $i @ (^[Y0 : $i]: ((((((sK3 @ sK19) | (~ (irel @ Y0 @ sK18))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK4 @ Y1)))))) | (~ (irel @ sK18 @ sK19))) & ((((~ (irel @ Y0 @ sK21)) | (sK4 @ sK20)) | (~ (irel @ sK21 @ sK20))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK21 @ Y1)) | (sK3 @ Y1))))))) | (~ (irel @ sK5 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0))))) = $false)),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f228])).
% 1.82/1.55 thf(f228,plain,(
% 1.82/1.55 ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0))))) = $false) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK3 @ sK19) | (~ (irel @ Y1 @ sK18))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK4 @ Y2)))))) | (~ (irel @ sK18 @ sK19))) & ((((~ (irel @ Y1 @ Y0)) | (sK4 @ sK20)) | (~ (irel @ Y0 @ sK20))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2))))))) | (~ (irel @ sK5 @ Y1)))))) @ sK21) = $false)),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f227])).
% 1.82/1.55 thf(f227,plain,(
% 1.82/1.55 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK3 @ sK19) | (~ (irel @ Y1 @ sK18))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ sK18 @ Y2)) | (sK4 @ Y2)))))) | (~ (irel @ sK18 @ sK19))) & ((((~ (irel @ Y1 @ Y0)) | (sK4 @ sK20)) | (~ (irel @ Y0 @ sK20))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2))))))) | (~ (irel @ sK5 @ Y1))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0))))) = $false)),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f226])).
% 1.82/1.55 thf(f226,plain,(
% 1.82/1.55 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK3 @ sK19) | (~ (irel @ Y2 @ sK18))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ sK18 @ Y3)) | (sK4 @ Y3)))))) | (~ (irel @ sK18 @ sK19))) & ((((~ (irel @ Y2 @ Y1)) | (sK4 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK3 @ Y3))))))) | (~ (irel @ sK5 @ Y2)))))))) @ sK20) = $false) | ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0))))) = $false)),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f225])).
% 1.82/1.55 thf(f225,plain,(
% 1.82/1.55 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK3 @ sK19) | (~ (irel @ Y2 @ sK18))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ sK18 @ Y3)) | (sK4 @ Y3)))))) | (~ (irel @ sK18 @ sK19))) & ((((~ (irel @ Y2 @ Y1)) | (sK4 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK3 @ Y3))))))) | (~ (irel @ sK5 @ Y2))))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0))))) = $false)),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f224])).
% 1.82/1.55 thf(f224,plain,(
% 1.82/1.55 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK3 @ Y0) | (~ (irel @ Y3 @ sK18))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ sK18 @ Y4)) | (sK4 @ Y4)))))) | (~ (irel @ sK18 @ Y0))) & ((((~ (irel @ Y3 @ Y2)) | (sK4 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK3 @ Y4))))))) | (~ (irel @ sK5 @ Y3)))))))))) @ sK19) = $false) | ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0))))) = $false)),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f223])).
% 1.82/1.55 thf(f223,plain,(
% 1.82/1.55 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK3 @ Y0) | (~ (irel @ Y3 @ sK18))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ sK18 @ Y4)) | (sK4 @ Y4)))))) | (~ (irel @ sK18 @ Y0))) & ((((~ (irel @ Y3 @ Y2)) | (sK4 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK3 @ Y4))))))) | (~ (irel @ sK5 @ Y3))))))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0))))) = $false)),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f222])).
% 1.82/1.55 thf(f222,plain,(
% 1.82/1.55 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK3 @ Y0) | (~ (irel @ Y3 @ sK18))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ sK18 @ Y4)) | (sK4 @ Y4)))))) | (~ (irel @ sK18 @ Y0))) & ((((~ (irel @ Y3 @ Y2)) | (sK4 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK3 @ Y4))))))) | (~ (irel @ sK5 @ Y3))))))))))) = $false)),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f221])).
% 1.82/1.55 thf(f221,plain,(
% 1.82/1.55 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK3 @ Y1) | (~ (irel @ Y4 @ Y0))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK4 @ Y5)))))) | (~ (irel @ Y0 @ Y1))) & ((((~ (irel @ Y4 @ Y3)) | (sK4 @ Y2)) | (~ (irel @ Y3 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK3 @ Y5))))))) | (~ (irel @ sK5 @ Y4)))))))))))) @ sK18) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0)))))))),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f220])).
% 1.82/1.55 thf(f220,plain,(
% 1.82/1.55 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK3 @ Y1) | (~ (irel @ Y4 @ Y0))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK4 @ Y5)))))) | (~ (irel @ Y0 @ Y1))) & ((((~ (irel @ Y4 @ Y3)) | (sK4 @ Y2)) | (~ (irel @ Y3 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK3 @ Y5))))))) | (~ (irel @ sK5 @ Y4))))))))))))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0)))))))),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f51])).
% 1.82/1.55 thf(f51,plain,(
% 1.82/1.55 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK3 @ Y1) | (~ (irel @ Y4 @ Y0))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y0 @ Y5)) | (sK4 @ Y5)))))) | (~ (irel @ Y0 @ Y1))) & ((((~ (irel @ Y4 @ Y3)) | (sK4 @ Y2)) | (~ (irel @ Y3 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK3 @ Y5))))))) | (~ (irel @ sK5 @ Y4)))))))))))))) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))) | (sK4 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3))))) | (sK3 @ Y1)) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2)))))))) | (~ (irel @ sK5 @ Y0)))))))),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.82/1.55 thf(f2326,plain,(
% 1.82/1.55 spl1_50 | spl1_41 | spl1_52 | spl1_12),
% 1.82/1.55 inference(avatar_split_clause,[status(thm)],[f1405,f2087,f2321,f2264,f2309])).
% 1.82/1.55 thf(f1405,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((irel @ sK66 @ X4) = $false) | ((irel @ sK63 @ X2) = $false) | ((irel @ sK18 @ X1) = $false) | ($true = (sK3 @ X3)) | ((irel @ sK21 @ X3) = $false) | ($true = (sK4 @ X4)) | ($true = (sK3 @ X2)) | ($true = (sK4 @ X1))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1404])).
% 1.82/1.55 thf(f1404,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((irel @ sK21 @ X3) = $false) | ($true = (sK4 @ X4)) | ($true = (sK3 @ X3)) | ($true = (sK3 @ X2)) | ((irel @ sK18 @ X1) = $false) | ($true = (sK4 @ X1)) | ((irel @ sK63 @ X2) = $false) | ((~ (irel @ sK66 @ X4)) = $true)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1403])).
% 1.82/1.55 thf(f1403,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((irel @ sK21 @ X3) = $false) | ((irel @ sK63 @ X2) = $false) | (((~ (irel @ sK66 @ X4)) | (sK4 @ X4)) = $true) | ($true = (sK3 @ X2)) | ($true = (sK3 @ X3)) | ($true = (sK4 @ X1)) | ((irel @ sK18 @ X1) = $false)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1402])).
% 1.82/1.55 thf(f1402,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))) @ X4)) | ($true = (sK3 @ X3)) | ($true = (sK4 @ X1)) | ((irel @ sK18 @ X1) = $false) | ((irel @ sK63 @ X2) = $false) | ($true = (sK3 @ X2)) | ((irel @ sK21 @ X3) = $false)) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f1401])).
% 1.82/1.55 thf(f1401,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ sK63 @ X2) = $false) | ($true = (sK3 @ X3)) | ($true = (sK3 @ X2)) | ($true = (sK4 @ X1)) | ((irel @ sK18 @ X1) = $false) | ((irel @ sK21 @ X3) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0)))))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1400])).
% 1.82/1.55 thf(f1400,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (irel @ sK63 @ X2))) | ((irel @ sK18 @ X1) = $false) | ($true = (sK3 @ X3)) | ($true = (sK4 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | ($true = (sK3 @ X2)) | ((irel @ sK21 @ X3) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1399])).
% 1.82/1.55 thf(f1399,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK3 @ X3)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) = $false) | ($true = (sK3 @ X2)) | ($true = (~ (irel @ sK63 @ X2))) | ((irel @ sK21 @ X3) = $false) | ((irel @ sK18 @ X1) = $false) | ($true = (sK4 @ X1))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1398])).
% 1.82/1.55 thf(f1398,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((sK3 @ X2) | (~ (irel @ sK63 @ X2)))) | ((irel @ sK21 @ X3) = $false) | ($true = (sK4 @ X1)) | ((irel @ sK18 @ X1) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) = $false) | ($true = (sK3 @ X3))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1397])).
% 1.82/1.55 thf(f1397,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (irel @ sK21 @ X3))) | ($true = (sK4 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) = $false) | ((irel @ sK18 @ X1) = $false) | ($true = (sK3 @ X3)) | ($true = ((sK3 @ X2) | (~ (irel @ sK63 @ X2))))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1395])).
% 1.82/1.55 thf(f1395,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) = $false) | ((irel @ sK18 @ X1) = $false) | ($true = (~ (irel @ sK21 @ X3))) | ($true = ((sK3 @ X2) | (~ (irel @ sK63 @ X2)))) | ($true = (sK3 @ X3)) | ($true = (sK4 @ X1))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1394])).
% 1.82/1.55 thf(f1394,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((~ (irel @ sK21 @ X3)) | (sK3 @ X3))) | ($true = (sK4 @ X1)) | ((irel @ sK18 @ X1) = $false) | ($true = ((sK3 @ X2) | (~ (irel @ sK63 @ X2)))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1393])).
% 1.82/1.55 thf(f1393,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK4 @ X1)) | ($true = (~ (irel @ sK18 @ X1))) | ($true = ((sK3 @ X2) | (~ (irel @ sK63 @ X2)))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) = $false) | ($true = ((~ (irel @ sK21 @ X3)) | (sK3 @ X3)))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1391])).
% 1.82/1.55 thf(f1391,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) | (~ (irel @ sK66 @ sK65))) = $false) | ($true = ((~ (irel @ sK21 @ X3)) | (sK3 @ X3))) | ($true = (sK4 @ X1)) | ($true = (~ (irel @ sK18 @ X1))) | ($true = ((sK3 @ X2) | (~ (irel @ sK63 @ X2))))) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1390])).
% 1.82/1.55 thf(f1390,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (irel @ sK18 @ X1))) | ($true = (sK4 @ X1)) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) | (~ (irel @ sK66 @ sK65))) = $false) | (((^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))) @ X3) = $true) | ($true = ((sK3 @ X2) | (~ (irel @ sK63 @ X2))))) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f1389])).
% 1.82/1.55 thf(f1389,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) | (~ (irel @ sK66 @ sK65))) = $false) | ($true = (sK4 @ X1)) | ($true = ((sK3 @ X2) | (~ (irel @ sK63 @ X2)))) | ($true = (~ (irel @ sK18 @ X1)))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1387])).
% 1.82/1.55 thf(f1387,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : ((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) | (~ (irel @ sK66 @ sK65))) | (~ (irel @ sK23 @ sK66))) = $false) | ($true = (~ (irel @ sK18 @ X1))) | ($true = (sK4 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) | ($true = ((sK3 @ X2) | (~ (irel @ sK63 @ X2))))) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1386])).
% 1.82/1.55 thf(f1386,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = (~ (irel @ sK18 @ X1))) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) | (~ (irel @ sK66 @ sK65))) | (~ (irel @ sK23 @ sK66))) = $false) | ($true = ((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK63 @ Y0)))) @ X2)) | ($true = (sK4 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0)))))) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f1385])).
% 1.82/1.55 thf(f1385,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = (sK4 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK63 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) | ($true = (~ (irel @ sK18 @ X1))) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) | (~ (irel @ sK66 @ sK65))) | (~ (irel @ sK23 @ sK66))) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1384])).
% 1.82/1.55 thf(f1384,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK63 @ Y0)))))) = $false) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) | (~ (irel @ sK66 @ sK65))) | (~ (irel @ sK23 @ sK66))) = $false) | ($true = (~ (irel @ sK18 @ X1))) | ($true = (sK4 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0)))))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1383])).
% 1.82/1.55 thf(f1383,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = (sK4 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = (~ (irel @ sK18 @ X1))) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) | (~ (irel @ sK66 @ sK65))) | (~ (irel @ sK23 @ sK66))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK63 @ Y0)))))) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1382])).
% 1.82/1.55 thf(f1382,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = ((~ (irel @ sK18 @ X1)) | (sK4 @ X1))) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) | (~ (irel @ sK66 @ sK65))) | (~ (irel @ sK23 @ sK66))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK63 @ Y0)))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1380])).
% 1.82/1.55 thf(f1380,plain,(
% 1.82/1.55 ( ! [X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK63 @ Y0)))))) | (~ (irel @ sK23 @ sK63))) = $false) | ($true = ((~ (irel @ sK18 @ X1)) | (sK4 @ X1))) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) | (~ (irel @ sK66 @ sK65))) | (~ (irel @ sK23 @ sK66))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1378])).
% 1.82/1.55 thf(f1378,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK63 @ Y0)))))) | (~ (irel @ sK23 @ sK63))) | (~ (irel @ sK63 @ sK64))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = ((~ (irel @ sK18 @ X1)) | (sK4 @ X1))) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) | (~ (irel @ sK66 @ sK65))) | (~ (irel @ sK23 @ sK66))) = $false)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1377])).
% 1.82/1.55 thf(f1377,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK63 @ Y0)))))) | (~ (irel @ sK23 @ sK63))) | (~ (irel @ sK63 @ sK64))) = $false) | (((^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ sK65)) | (~ (irel @ Y0 @ sK65))) | (~ (irel @ sK23 @ Y0)))) @ sK66) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = ((~ (irel @ sK18 @ X1)) | (sK4 @ X1)))) )),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f1376])).
% 1.82/1.55 thf(f1376,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ sK65)) | (~ (irel @ Y0 @ sK65))) | (~ (irel @ sK23 @ Y0))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = ((~ (irel @ sK18 @ X1)) | (sK4 @ X1))) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK63 @ Y0)))))) | (~ (irel @ sK23 @ sK63))) | (~ (irel @ sK63 @ sK64))) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1374])).
% 1.82/1.55 thf(f1374,plain,(
% 1.82/1.55 ( ! [X1 : $i] : ((((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK63 @ Y0)))))) | (~ (irel @ sK23 @ sK63))) | (~ (irel @ sK63 @ sK64))) | (sK4 @ sK64)) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = ((~ (irel @ sK18 @ X1)) | (sK4 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ sK65)) | (~ (irel @ Y0 @ sK65))) | (~ (irel @ sK23 @ Y0))))) = $false)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1373])).
% 1.82/1.55 thf(f1373,plain,(
% 1.82/1.55 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))) @ sK65) = $false) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK63 @ Y0)))))) | (~ (irel @ sK23 @ sK63))) | (~ (irel @ sK63 @ sK64))) | (sK4 @ sK64)) = $false) | ($true = ((~ (irel @ sK18 @ X1)) | (sK4 @ X1))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false)) )),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f1372])).
% 1.82/1.55 thf(f1372,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1))))))) = $false) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK63 @ Y0)))))) | (~ (irel @ sK23 @ sK63))) | (~ (irel @ sK63 @ sK64))) | (sK4 @ sK64)) = $false) | ($true = ((~ (irel @ sK18 @ X1)) | (sK4 @ X1))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1371])).
% 1.82/1.55 thf(f1371,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1))))))) = $false) | (((^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ sK63 @ Y1)))))) | (~ (irel @ sK23 @ sK63))) | (~ (irel @ sK63 @ Y0))) | (sK4 @ Y0))) @ sK64) = $false) | ($true = ((~ (irel @ sK18 @ X1)) | (sK4 @ X1)))) )),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f1370])).
% 1.82/1.55 thf(f1370,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ sK63 @ Y1)))))) | (~ (irel @ sK23 @ sK63))) | (~ (irel @ sK63 @ Y0))) | (sK4 @ Y0)))) = $false) | ($true = ((~ (irel @ sK18 @ X1)) | (sK4 @ X1))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1))))))) = $false)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1369])).
% 1.82/1.55 thf(f1369,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1))))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = ((~ (irel @ sK18 @ X1)) | (sK4 @ X1))) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1))))) @ sK63) = $false)) )),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f1368])).
% 1.82/1.55 thf(f1368,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = ((~ (irel @ sK18 @ X1)) | (sK4 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1))))))) = $false)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1367])).
% 1.82/1.55 thf(f1367,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) = $false) | ($true = ((^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK4 @ Y0))) @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1))))))) = $false)) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f1366])).
% 1.82/1.55 thf(f1366,plain,(
% 1.82/1.55 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK4 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1))))))) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1365])).
% 1.82/1.55 thf(f1365,plain,(
% 1.82/1.55 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK4 @ Y0)))))),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1047])).
% 1.82/1.55 thf(f1047,plain,(
% 1.82/1.55 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK4 @ Y0))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))))) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1046])).
% 1.82/1.55 thf(f1046,plain,(
% 1.82/1.55 (((((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) | (~ (irel @ sK21 @ sK20))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0)))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK4 @ Y0))))) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f239])).
% 1.82/1.55 thf(f239,plain,(
% 1.82/1.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))))) | (~ (irel @ sK5 @ sK23))) = $false) | (((((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) | (~ (irel @ sK21 @ sK20))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0)))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK4 @ Y0))))) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f238])).
% 1.82/1.55 thf(f2324,plain,(
% 1.82/1.55 spl1_12 | spl1_52 | spl1_49 | spl1_41),
% 1.82/1.55 inference(avatar_split_clause,[status(thm)],[f1414,f2264,f2303,f2321,f2087])).
% 1.82/1.55 thf(f1414,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ sK66 @ sK65) = $true) | ((irel @ sK63 @ X2) = $false) | ($true = (sK4 @ X1)) | ((irel @ sK18 @ X1) = $false) | ((irel @ sK21 @ X3) = $false) | ($true = (sK3 @ X2)) | ($true = (sK3 @ X3))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1413])).
% 1.82/1.55 thf(f1413,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK3 @ X3)) | ((irel @ sK18 @ X1) = $false) | ((irel @ sK21 @ X3) = $false) | ((~ (irel @ sK66 @ sK65)) = $false) | ($true = (sK3 @ X2)) | ($true = (sK4 @ X1)) | ((irel @ sK63 @ X2) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1412])).
% 1.82/1.55 thf(f1412,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK3 @ X3)) | ($true = (~ (irel @ sK21 @ X3))) | ($true = (sK3 @ X2)) | ((~ (irel @ sK66 @ sK65)) = $false) | ((irel @ sK63 @ X2) = $false) | ((irel @ sK18 @ X1) = $false) | ($true = (sK4 @ X1))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1411])).
% 1.82/1.55 thf(f1411,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK4 @ X1)) | ($true = (~ (irel @ sK63 @ X2))) | ((irel @ sK18 @ X1) = $false) | ($true = (~ (irel @ sK21 @ X3))) | ($true = (sK3 @ X3)) | ($true = (sK3 @ X2)) | ((~ (irel @ sK66 @ sK65)) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1410])).
% 1.82/1.55 thf(f1410,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((~ (irel @ sK21 @ X3)) | (sK3 @ X3))) | ((~ (irel @ sK66 @ sK65)) = $false) | ($true = (~ (irel @ sK63 @ X2))) | ($true = (sK4 @ X1)) | ($true = (sK3 @ X2)) | ((irel @ sK18 @ X1) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1409])).
% 1.82/1.55 thf(f1409,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((sK3 @ X2) | (~ (irel @ sK63 @ X2)))) | ($true = (sK4 @ X1)) | ((irel @ sK18 @ X1) = $false) | ((~ (irel @ sK66 @ sK65)) = $false) | ($true = ((~ (irel @ sK21 @ X3)) | (sK3 @ X3)))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1392])).
% 1.82/1.55 thf(f1392,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (irel @ sK18 @ X1))) | ((~ (irel @ sK66 @ sK65)) = $false) | ($true = ((~ (irel @ sK21 @ X3)) | (sK3 @ X3))) | ($true = ((sK3 @ X2) | (~ (irel @ sK63 @ X2)))) | ($true = (sK4 @ X1))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1391])).
% 1.82/1.55 thf(f2311,plain,(
% 1.82/1.55 spl1_41 | spl1_50 | spl1_12 | spl1_48),
% 1.82/1.55 inference(avatar_split_clause,[status(thm)],[f1474,f2298,f2087,f2309,f2264])).
% 1.82/1.55 thf(f1474,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ sK21 @ X2) = $false) | ($true = (irel @ sK63 @ sK64)) | ($true = (sK4 @ X1)) | ((irel @ sK66 @ X3) = $false) | ((irel @ sK18 @ X1) = $false) | ($true = (sK3 @ X2)) | ($true = (sK4 @ X3))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1473])).
% 1.82/1.55 thf(f1473,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (irel @ sK63 @ sK64)) | ((irel @ sK21 @ X2) = $false) | ($true = (sK4 @ X3)) | ($true = (sK3 @ X2)) | ((irel @ sK18 @ X1) = $false) | ($true = (~ (irel @ sK66 @ X3))) | ($true = (sK4 @ X1))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1472])).
% 1.82/1.55 thf(f1472,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((~ (irel @ sK66 @ X3)) | (sK4 @ X3))) | ($true = (sK4 @ X1)) | ((irel @ sK18 @ X1) = $false) | ($true = (irel @ sK63 @ sK64)) | ($true = (sK3 @ X2)) | ((irel @ sK21 @ X2) = $false)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1471])).
% 1.82/1.55 thf(f1471,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))) @ X3)) | ($true = (sK3 @ X2)) | ((irel @ sK21 @ X2) = $false) | ($true = (irel @ sK63 @ sK64)) | ($true = (sK4 @ X1)) | ((irel @ sK18 @ X1) = $false)) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f1470])).
% 1.82/1.55 thf(f1470,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = (sK4 @ X1)) | ((irel @ sK18 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | ($true = (sK3 @ X2)) | ($true = (irel @ sK63 @ sK64)) | ((irel @ sK21 @ X2) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1469])).
% 1.82/1.55 thf(f1469,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (((irel @ sK21 @ X2) = $false) | ($true = (sK3 @ X2)) | ($true = (sK4 @ X1)) | ((irel @ sK18 @ X1) = $false) | ($true = (irel @ sK63 @ sK64)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1468])).
% 1.82/1.55 thf(f1468,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = (sK3 @ X2)) | ((irel @ sK18 @ X1) = $false) | ($true = (irel @ sK63 @ sK64)) | ((~ (irel @ sK21 @ X2)) = $true) | ($true = (sK4 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1467])).
% 1.82/1.55 thf(f1467,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (irel @ sK21 @ X2)) | (sK3 @ X2))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) = $false) | ((irel @ sK18 @ X1) = $false) | ($true = (irel @ sK63 @ sK64)) | ($true = (sK4 @ X1))) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1466])).
% 1.82/1.55 thf(f1466,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))) @ X2) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) = $false) | ($true = (irel @ sK63 @ sK64)) | ((irel @ sK18 @ X1) = $false) | ($true = (sK4 @ X1))) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f1465])).
% 1.82/1.55 thf(f1465,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = (irel @ sK63 @ sK64)) | ((irel @ sK18 @ X1) = $false) | ($true = (sK4 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1463])).
% 1.82/1.55 thf(f1463,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = (sK4 @ X1)) | ((irel @ sK18 @ X1) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) | ($true = (irel @ sK63 @ sK64))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1461])).
% 1.82/1.55 thf(f1461,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = (irel @ sK63 @ sK64)) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) | (~ (irel @ sK66 @ sK65))) = $false) | ((irel @ sK18 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) | ($true = (sK4 @ X1))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1460])).
% 1.82/1.55 thf(f1460,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = (sK4 @ X1)) | ($true = (~ (irel @ sK18 @ X1))) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) | (~ (irel @ sK66 @ sK65))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) | ($true = (irel @ sK63 @ sK64))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1459])).
% 1.82/1.55 thf(f1459,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = (irel @ sK63 @ sK64)) | ($true = (~ (irel @ sK18 @ X1))) | ($true = (sK4 @ X1)) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) | (~ (irel @ sK66 @ sK65))) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1457])).
% 1.82/1.55 thf(f1457,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = (irel @ sK63 @ sK64)) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) | (~ (irel @ sK66 @ sK65))) | (~ (irel @ sK23 @ sK66))) = $false) | ($true = (sK4 @ X1)) | ($true = (~ (irel @ sK18 @ X1))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1456])).
% 1.82/1.55 thf(f1456,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((~ (irel @ sK63 @ sK64)) = $false) | ($true = (sK4 @ X1)) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) | (~ (irel @ sK66 @ sK65))) | (~ (irel @ sK23 @ sK66))) = $false) | ($true = (~ (irel @ sK18 @ X1))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1379])).
% 1.82/1.55 thf(f1379,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = ((~ (irel @ sK18 @ X1)) | (sK4 @ X1))) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK66 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK65)) | (~ (irel @ sK66 @ sK65))) | (~ (irel @ sK23 @ sK66))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ((~ (irel @ sK63 @ sK64)) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1378])).
% 1.82/1.55 thf(f2306,plain,(
% 1.82/1.55 spl1_49 | spl1_41 | spl1_48 | spl1_12),
% 1.82/1.55 inference(avatar_split_clause,[status(thm)],[f1483,f2087,f2298,f2264,f2303])).
% 1.82/1.55 thf(f1483,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = (sK4 @ X1)) | ((irel @ sK66 @ sK65) = $true) | ((irel @ sK18 @ X1) = $false) | ((irel @ sK21 @ X2) = $false) | ($true = (irel @ sK63 @ sK64)) | ($true = (sK3 @ X2))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1482])).
% 1.82/1.55 thf(f1482,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = (irel @ sK63 @ sK64)) | ((irel @ sK21 @ X2) = $false) | ($true = (sK4 @ X1)) | ((~ (irel @ sK66 @ sK65)) = $false) | ($true = (sK3 @ X2)) | ((irel @ sK18 @ X1) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1481])).
% 1.82/1.55 thf(f1481,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = (irel @ sK63 @ sK64)) | ((~ (irel @ sK21 @ X2)) = $true) | ((~ (irel @ sK66 @ sK65)) = $false) | ($true = (sK3 @ X2)) | ($true = (sK4 @ X1)) | ((irel @ sK18 @ X1) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1480])).
% 1.82/1.55 thf(f1480,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = (sK4 @ X1)) | ($true = ((~ (irel @ sK21 @ X2)) | (sK3 @ X2))) | ($true = (irel @ sK63 @ sK64)) | ((~ (irel @ sK66 @ sK65)) = $false) | ((irel @ sK18 @ X1) = $false)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1479])).
% 1.82/1.55 thf(f1479,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))) @ X2) = $true) | ($true = (irel @ sK63 @ sK64)) | ($true = (sK4 @ X1)) | ((~ (irel @ sK66 @ sK65)) = $false) | ((irel @ sK18 @ X1) = $false)) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f1462])).
% 1.82/1.55 thf(f1462,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) | ($true = (sK4 @ X1)) | ((~ (irel @ sK66 @ sK65)) = $false) | ($true = (irel @ sK63 @ sK64)) | ((irel @ sK18 @ X1) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1461])).
% 1.82/1.55 thf(f2135,plain,(
% 1.82/1.55 spl1_17 | spl1_20 | spl1_12 | spl1_11),
% 1.82/1.55 inference(avatar_split_clause,[status(thm)],[f1871,f2083,f2087,f2127,f2110])).
% 1.82/1.55 thf(f1871,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ sK79 @ X3) = $false) | ($true = (irel @ sK18 @ sK19)) | ($true = (sK3 @ X2)) | ((irel @ sK77 @ X2) = $false) | ($true = (sK4 @ X3)) | ($true = (sK3 @ X1)) | ((irel @ sK21 @ X1) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1870])).
% 1.82/1.55 thf(f1870,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (irel @ sK18 @ sK19)) | ((irel @ sK21 @ X1) = $false) | ($true = (sK3 @ X2)) | ((~ (irel @ sK79 @ X3)) = $true) | ((irel @ sK77 @ X2) = $false) | ($true = (sK3 @ X1)) | ($true = (sK4 @ X3))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1869])).
% 1.82/1.55 thf(f1869,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (irel @ sK18 @ sK19)) | ($true = (sK3 @ X1)) | ($true = ((~ (irel @ sK79 @ X3)) | (sK4 @ X3))) | ((irel @ sK77 @ X2) = $false) | ($true = (sK3 @ X2)) | ((irel @ sK21 @ X1) = $false)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1868])).
% 1.82/1.55 thf(f1868,plain,(
% 1.82/1.55 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (irel @ sK18 @ sK19)) | ($true = (sK3 @ X2)) | ((irel @ sK21 @ X1) = $false) | ($true = (sK3 @ X1)) | ((irel @ sK77 @ X2) = $false) | ($true = ((^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))) @ X3))) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f1867])).
% 1.82/1.55 thf(f1867,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = (sK3 @ X1)) | ($true = (sK3 @ X2)) | ($true = (irel @ sK18 @ sK19)) | ((irel @ sK77 @ X2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | ((irel @ sK21 @ X1) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1866])).
% 1.82/1.55 thf(f1866,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = (sK3 @ X1)) | ((irel @ sK77 @ X2) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) = $false) | ((irel @ sK21 @ X1) = $false) | ($true = (sK3 @ X2)) | ($true = (irel @ sK18 @ sK19))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1864])).
% 1.82/1.55 thf(f1864,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (((irel @ sK77 @ X2) = $false) | ($true = (sK3 @ X2)) | ($true = (irel @ sK18 @ sK19)) | ((irel @ sK21 @ X1) = $false) | ($true = (sK3 @ X1)) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1863])).
% 1.82/1.55 thf(f1863,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = (sK3 @ X1)) | ($true = (~ (irel @ sK77 @ X2))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) = $false) | ($true = (sK3 @ X2)) | ((irel @ sK21 @ X1) = $false) | ($true = (irel @ sK18 @ sK19))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1861])).
% 1.82/1.55 thf(f1861,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) | (~ (irel @ sK79 @ sK76))) = $false) | ($true = (sK3 @ X2)) | ($true = (irel @ sK18 @ sK19)) | ($true = (~ (irel @ sK77 @ X2))) | ((irel @ sK21 @ X1) = $false) | ($true = (sK3 @ X1))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1860])).
% 1.82/1.55 thf(f1860,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : ((((sK3 @ X2) | (~ (irel @ sK77 @ X2))) = $true) | ($true = (irel @ sK18 @ sK19)) | ($true = (sK3 @ X1)) | ((irel @ sK21 @ X1) = $false) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) | (~ (irel @ sK79 @ sK76))) = $false)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1859])).
% 1.82/1.55 thf(f1859,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = (sK3 @ X1)) | ($true = ((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK77 @ Y0)))) @ X2)) | ($true = (irel @ sK18 @ sK19)) | ((irel @ sK21 @ X1) = $false) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) | (~ (irel @ sK79 @ sK76))) = $false)) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f1858])).
% 1.82/1.55 thf(f1858,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK77 @ Y0))))) = $true) | ($true = (irel @ sK18 @ sK19)) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) | (~ (irel @ sK79 @ sK76))) = $false) | ($true = (sK3 @ X1)) | ((irel @ sK21 @ X1) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1857])).
% 1.82/1.55 thf(f1857,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = (~ (irel @ sK21 @ X1))) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) | (~ (irel @ sK79 @ sK76))) = $false) | ($true = (irel @ sK18 @ sK19)) | ($true = (sK3 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK77 @ Y0))))) = $true)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1856])).
% 1.82/1.55 thf(f1856,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK77 @ Y0)))))) = $false) | ($true = (~ (irel @ sK21 @ X1))) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) | (~ (irel @ sK79 @ sK76))) = $false) | ($true = (sK3 @ X1)) | ($true = (irel @ sK18 @ sK19))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1854])).
% 1.82/1.55 thf(f1854,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = (sK3 @ X1)) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK77 @ Y0)))))) | (~ (irel @ sK23 @ sK77))) = $false) | ($true = (~ (irel @ sK21 @ X1))) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) | (~ (irel @ sK79 @ sK76))) = $false) | ($true = (irel @ sK18 @ sK19))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1852])).
% 1.82/1.55 thf(f1852,plain,(
% 1.82/1.55 ( ! [X1 : $i] : ((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) | (~ (irel @ sK79 @ sK76))) | (~ (irel @ sK23 @ sK79))) = $false) | ($true = (~ (irel @ sK21 @ X1))) | ($true = (sK3 @ X1)) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK77 @ Y0)))))) | (~ (irel @ sK23 @ sK77))) = $false) | ($true = (irel @ sK18 @ sK19))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1850])).
% 1.82/1.55 thf(f1850,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK77 @ Y0)))))) | (~ (irel @ sK23 @ sK77))) | (~ (irel @ sK77 @ sK78))) = $false) | ($true = (~ (irel @ sK21 @ X1))) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) | (~ (irel @ sK79 @ sK76))) | (~ (irel @ sK23 @ sK79))) = $false) | ($true = (sK3 @ X1)) | ($true = (irel @ sK18 @ sK19))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1848])).
% 1.82/1.55 thf(f1848,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = (sK3 @ X1)) | ($true = (irel @ sK18 @ sK19)) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK77 @ Y0)))))) | (~ (irel @ sK23 @ sK77))) | (~ (irel @ sK77 @ sK78))) | (sK4 @ sK78)) = $false) | ($true = (~ (irel @ sK21 @ X1))) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) | (~ (irel @ sK79 @ sK76))) | (~ (irel @ sK23 @ sK79))) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1847])).
% 1.82/1.55 thf(f1847,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = (irel @ sK18 @ sK19)) | (((~ (irel @ sK21 @ X1)) | (sK3 @ X1)) = $true) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK77 @ Y0)))))) | (~ (irel @ sK23 @ sK77))) | (~ (irel @ sK77 @ sK78))) | (sK4 @ sK78)) = $false) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) | (~ (irel @ sK79 @ sK76))) | (~ (irel @ sK23 @ sK79))) = $false)) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1846])).
% 1.82/1.55 thf(f1846,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))) @ X1)) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) | (~ (irel @ sK79 @ sK76))) | (~ (irel @ sK23 @ sK79))) = $false) | ($true = (irel @ sK18 @ sK19)) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK77 @ Y0)))))) | (~ (irel @ sK23 @ sK77))) | (~ (irel @ sK77 @ sK78))) | (sK4 @ sK78)) = $false)) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f1845])).
% 1.82/1.55 thf(f1845,plain,(
% 1.82/1.55 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) | (~ (irel @ sK79 @ sK76))) | (~ (irel @ sK23 @ sK79))) = $false) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK77 @ Y0)))))) | (~ (irel @ sK23 @ sK77))) | (~ (irel @ sK77 @ sK78))) | (sK4 @ sK78)) = $false) | ($true = (irel @ sK18 @ sK19))),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1844])).
% 1.82/1.55 thf(f1844,plain,(
% 1.82/1.55 (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK77 @ Y0)))))) | (~ (irel @ sK23 @ sK77))) | (~ (irel @ sK77 @ sK78))) | (sK4 @ sK78)) = $false) | ($true = (irel @ sK18 @ sK19)) | (((^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ sK76)) | (~ (irel @ Y0 @ sK76))) | (~ (irel @ sK23 @ Y0)))) @ sK79) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0)))))),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f1843])).
% 1.82/1.55 thf(f1843,plain,(
% 1.82/1.55 ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ sK76)) | (~ (irel @ Y0 @ sK76))) | (~ (irel @ sK23 @ Y0))))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK77 @ Y0)))))) | (~ (irel @ sK23 @ sK77))) | (~ (irel @ sK77 @ sK78))) | (sK4 @ sK78)) = $false) | ($true = (irel @ sK18 @ sK19))),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1842])).
% 1.82/1.55 thf(f1842,plain,(
% 1.82/1.55 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ sK76)) | (~ (irel @ Y0 @ sK76))) | (~ (irel @ sK23 @ Y0))))) = $false) | ($true = (irel @ sK18 @ sK19)) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK77 @ Y0)))))) | (~ (irel @ sK23 @ sK77))) | (~ (irel @ sK77 @ sK78))) | (sK4 @ sK78)) = $false)),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1841])).
% 1.82/1.55 thf(f1841,plain,(
% 1.82/1.55 (((^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ sK77 @ Y1)))))) | (~ (irel @ sK23 @ sK77))) | (~ (irel @ sK77 @ Y0))) | (sK4 @ Y0))) @ sK78) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = (irel @ sK18 @ sK19)) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ sK76)) | (~ (irel @ Y0 @ sK76))) | (~ (irel @ sK23 @ Y0))))) = $false)),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f1840])).
% 1.82/1.55 thf(f1840,plain,(
% 1.82/1.55 ($true = (irel @ sK18 @ sK19)) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ sK77 @ Y1)))))) | (~ (irel @ sK23 @ sK77))) | (~ (irel @ sK77 @ Y0))) | (sK4 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ sK76)) | (~ (irel @ Y0 @ sK76))) | (~ (irel @ sK23 @ Y0))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false)),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1839])).
% 1.82/1.55 thf(f1839,plain,(
% 1.82/1.55 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1))))) @ sK77) = $false) | ($true = (irel @ sK18 @ sK19)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ sK76)) | (~ (irel @ Y0 @ sK76))) | (~ (irel @ sK23 @ Y0))))) = $false)),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f1838])).
% 1.82/1.55 thf(f1838,plain,(
% 1.82/1.55 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))) | (sK3 @ sK76)) | (~ (irel @ Y0 @ sK76))) | (~ (irel @ sK23 @ Y0))))) = $false) | ($true = (irel @ sK18 @ sK19)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false)),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1837])).
% 1.82/1.55 thf(f1837,plain,(
% 1.82/1.55 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))) @ sK76) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) = $false) | ($true = (irel @ sK18 @ sK19)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false)),
% 1.82/1.55 inference(sigma_clausification,[status(thm)],[f1836])).
% 1.82/1.55 thf(f1836,plain,(
% 1.82/1.55 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = (irel @ sK18 @ sK19))),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1835])).
% 1.82/1.55 thf(f1835,plain,(
% 1.82/1.55 ($true = (irel @ sK18 @ sK19)) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false)),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1834])).
% 1.82/1.55 thf(f1834,plain,(
% 1.82/1.55 ((~ (irel @ sK18 @ sK19)) = $false) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1549])).
% 1.82/1.55 thf(f1549,plain,(
% 1.82/1.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))))) | (~ (irel @ sK5 @ sK23))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0))))) = $false) | ((~ (irel @ sK18 @ sK19)) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f237])).
% 1.82/1.55 thf(f237,plain,(
% 1.82/1.55 (((((~ (irel @ sK22 @ sK21)) | (sK4 @ sK20)) | (~ (irel @ sK21 @ sK20))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK21 @ Y0)) | (sK3 @ Y0)))))) = $false) | ((~ (irel @ sK18 @ sK19)) = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))))) | (~ (irel @ sK5 @ sK23))) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f236])).
% 1.82/1.55 thf(f2133,plain,(
% 1.82/1.55 spl1_12 | spl1_15 | spl1_20 | spl1_11),
% 1.82/1.55 inference(avatar_split_clause,[status(thm)],[f1873,f2083,f2127,f2100,f2087])).
% 1.82/1.55 thf(f1873,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (((irel @ sK77 @ X2) = $false) | ((irel @ sK79 @ sK76) = $true) | ((irel @ sK21 @ X1) = $false) | ($true = (sK3 @ X2)) | ($true = (irel @ sK18 @ sK19)) | ($true = (sK3 @ X1))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1872])).
% 1.82/1.55 thf(f1872,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (((irel @ sK21 @ X1) = $false) | ((irel @ sK77 @ X2) = $false) | ($true = (sK3 @ X2)) | ($true = (sK3 @ X1)) | ((~ (irel @ sK79 @ sK76)) = $false) | ($true = (irel @ sK18 @ sK19))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1862])).
% 1.82/1.55 thf(f1862,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (($true = (irel @ sK18 @ sK19)) | ($true = (~ (irel @ sK77 @ X2))) | ((irel @ sK21 @ X1) = $false) | ($true = (sK3 @ X1)) | ((~ (irel @ sK79 @ sK76)) = $false) | ($true = (sK3 @ X2))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1861])).
% 1.82/1.55 thf(f2120,plain,(
% 1.82/1.55 spl1_18 | spl1_11 | spl1_12 | spl1_17),
% 1.82/1.55 inference(avatar_split_clause,[status(thm)],[f1912,f2110,f2087,f2083,f2114])).
% 1.82/1.55 thf(f1912,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (((irel @ sK79 @ X2) = $false) | ($true = (irel @ sK18 @ sK19)) | ((sK4 @ X2) = $true) | ((irel @ sK77 @ sK78) = $true) | ($true = (sK3 @ X1)) | ((irel @ sK21 @ X1) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1911])).
% 1.82/1.55 thf(f1911,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (((sK4 @ X2) = $true) | ($true = (sK3 @ X1)) | ($true = (~ (irel @ sK79 @ X2))) | ((irel @ sK77 @ sK78) = $true) | ($true = (irel @ sK18 @ sK19)) | ((irel @ sK21 @ X1) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1910])).
% 1.82/1.55 thf(f1910,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (((irel @ sK77 @ sK78) = $true) | ($true = (irel @ sK18 @ sK19)) | ($true = ((~ (irel @ sK79 @ X2)) | (sK4 @ X2))) | ((irel @ sK21 @ X1) = $false) | ($true = (sK3 @ X1))) )),
% 1.82/1.55 inference(beta_eta_normalization,[status(thm)],[f1909])).
% 1.82/1.55 thf(f1909,plain,(
% 1.82/1.55 ( ! [X2 : $i,X1 : $i] : (((irel @ sK21 @ X1) = $false) | ((irel @ sK77 @ sK78) = $true) | ($true = (irel @ sK18 @ sK19)) | ($true = (sK3 @ X1)) | (((^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))) @ X2) = $true)) )),
% 1.82/1.55 inference(pi_clausification,[status(thm)],[f1908])).
% 1.82/1.55 thf(f1908,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((irel @ sK21 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | ($true = (sK3 @ X1)) | ($true = (irel @ sK18 @ sK19)) | ((irel @ sK77 @ sK78) = $true)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1907])).
% 1.82/1.55 thf(f1907,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = (irel @ sK18 @ sK19)) | ((irel @ sK77 @ sK78) = $true) | ($true = (sK3 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) = $false) | ((irel @ sK21 @ X1) = $false)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1905])).
% 1.82/1.55 thf(f1905,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = (sK3 @ X1)) | ((irel @ sK77 @ sK78) = $true) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) = $false) | ((irel @ sK21 @ X1) = $false) | ($true = (irel @ sK18 @ sK19))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1903])).
% 1.82/1.55 thf(f1903,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((irel @ sK77 @ sK78) = $true) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) | (~ (irel @ sK79 @ sK76))) = $false) | ((irel @ sK21 @ X1) = $false) | ($true = (sK3 @ X1)) | ($true = (irel @ sK18 @ sK19))) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1902])).
% 1.82/1.55 thf(f1902,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((irel @ sK21 @ X1) = $false) | ($true = (sK3 @ X1)) | ((~ (irel @ sK77 @ sK78)) = $false) | ($true = (irel @ sK18 @ sK19)) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) | (~ (irel @ sK79 @ sK76))) = $false)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1901])).
% 1.82/1.55 thf(f1901,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = (~ (irel @ sK21 @ X1))) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) | (~ (irel @ sK79 @ sK76))) = $false) | ((~ (irel @ sK77 @ sK78)) = $false) | ($true = (sK3 @ X1)) | ($true = (irel @ sK18 @ sK19))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1851])).
% 1.82/1.55 thf(f1851,plain,(
% 1.82/1.55 ( ! [X1 : $i] : ((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK79 @ Y0)) | (sK4 @ Y0))))) | (sK3 @ sK76)) | (~ (irel @ sK79 @ sK76))) | (~ (irel @ sK23 @ sK79))) = $false) | ($true = (sK3 @ X1)) | ($true = (~ (irel @ sK21 @ X1))) | ((~ (irel @ sK77 @ sK78)) = $false) | ($true = (irel @ sK18 @ sK19))) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1850])).
% 1.82/1.55 thf(f2118,plain,(
% 1.82/1.55 spl1_15 | spl1_11 | spl1_12 | spl1_18),
% 1.82/1.55 inference(avatar_split_clause,[status(thm)],[f1913,f2114,f2087,f2083,f2100])).
% 1.82/1.55 thf(f1913,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (((irel @ sK21 @ X1) = $false) | ($true = (sK3 @ X1)) | ($true = (irel @ sK18 @ sK19)) | ((irel @ sK77 @ sK78) = $true) | ((irel @ sK79 @ sK76) = $true)) )),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1904])).
% 1.82/1.55 thf(f1904,plain,(
% 1.82/1.55 ( ! [X1 : $i] : (($true = (sK3 @ X1)) | ($true = (irel @ sK18 @ sK19)) | ((irel @ sK21 @ X1) = $false) | ((~ (irel @ sK79 @ sK76)) = $false) | ((irel @ sK77 @ sK78) = $true)) )),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f1903])).
% 1.82/1.55 thf(f2035,plain,(
% 1.82/1.55 spl1_1 | spl1_2),
% 1.82/1.55 inference(avatar_split_clause,[status(thm)],[f2026,f2032,f2028])).
% 1.82/1.55 thf(f2026,plain,(
% 1.82/1.55 ($true = (irel @ sK5 @ sK22)) | ((irel @ sK5 @ sK23) = $true)),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f2025])).
% 1.82/1.55 thf(f2025,plain,(
% 1.82/1.55 ($true = (irel @ sK5 @ sK22)) | ((~ (irel @ sK5 @ sK23)) = $false)),
% 1.82/1.55 inference(not_proxy_clausification,[status(thm)],[f1938])).
% 1.82/1.55 thf(f1938,plain,(
% 1.82/1.55 ((~ (irel @ sK5 @ sK22)) = $false) | ((~ (irel @ sK5 @ sK23)) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f234])).
% 1.82/1.55 thf(f234,plain,(
% 1.82/1.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ sK23 @ Y0))) | (~ (irel @ Y0 @ Y1))) | (sK4 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2))))) | (sK3 @ Y0)) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK23 @ Y1)))))))) | (~ (irel @ sK5 @ sK23))) = $false) | ((~ (irel @ sK5 @ sK22)) = $false)),
% 1.82/1.55 inference(binary_proxy_clausification,[status(thm)],[f233])).
% 1.82/1.55 % SZS output end Proof for DTF2THF_2576
% 1.82/1.55 % (2942)------------------------------
% 1.82/1.55 % (2942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.55 % (2942)Termination reason: Refutation
% 1.82/1.55
% 1.82/1.55 % (2942)Memory used [KB]: 7419
% 1.82/1.55 % (2942)Time elapsed: 0.130 s
% 1.82/1.55 % (2942)Instructions burned: 337 (million)
% 1.82/1.55 % (2942)------------------------------
% 1.82/1.55 % (2942)------------------------------
% 1.82/1.55 % (2912)Success in time 0.209 s
%------------------------------------------------------------------------------