%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 06:58:54 PM UTC 2026
% Result : Theorem 1.76s 1.37s
% Output : Refutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 24
% Syntax : Number of formulae : 284 ( 26 unt; 0 typ; 21 def)
% Number of atoms : 5233 ( 924 equ; 0 cnn)
% Maximal formula atoms : 24 ( 18 avg)
% Number of connectives : 8939 (1437 ~;1792 |; 303 &;4722 @)
% ( 21 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 244 ( 244 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 65 usr; 33 con; 0-3 aty)
% ( 658 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1435 (1049 ^; 378 !; 8 ?;1435 :)
% 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_39,type,
sK0: $i > d_unsorted ).
thf(func_def_41,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
sK3: $i > $o ).
thf(func_def_43,type,
sK4: $i > $o ).
thf(func_def_45,type,
sK6: $i > $i ).
thf(func_def_46,type,
sK7: $i > $i ).
thf(func_def_47,type,
sK8: $i > $i ).
thf(func_def_48,type,
sK9: $i > $i ).
thf(func_def_49,type,
sK10: $i > $i ).
thf(func_def_50,type,
sK11: $i > $i ).
thf(func_def_51,type,
sK12: $i > $i ).
thf(func_def_52,type,
sK13: $i > $i ).
thf(func_def_53,type,
sK14: $i > $i ).
thf(func_def_54,type,
sK15: $i > $i ).
thf(f1804,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f997,f1038,f1087,f1235,f1300,f1422,f1559,f1567,f1569,f1571,f1576,f1608,f1612,f1634,f1648,f1650,f1671,f1751,f1758,f1760,f1762,f1771,f1803]) ).
thf(f1803,plain,
( ~ spl1_7
| ~ spl1_62 ),
inference(avatar_contradiction_clause,[status(thm)],[f1802]) ).
thf(f1802,plain,
( $false
| ~ spl1_7
| ~ spl1_62 ),
inference(trivial_inequality_removal,[status(thm)],[f1798]) ).
thf(f1798,plain,
( ( $false = $true )
| ~ spl1_7
| ~ spl1_62 ),
inference(superposition,[status(thm)],[f1781,f1015]) ).
thf(f1015,plain,
( ( $false
= ( sK4 @ sK17 ) )
| ~ spl1_7 ),
inference(avatar_component_clause,[status(thm)],[f1013]) ).
thf(f1013,definition,
( spl1_7
<=> ( $false
= ( sK4 @ sK17 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition]) ).
thf(f1781,plain,
( ! [X0: $i] :
( ( sK4 @ X0 )
= $true )
| ~ spl1_62 ),
inference(superposition,[status(thm)],[f1421,f55]) ).
thf(f55,plain,
! [X0: $i,X1: $i] : ( X0 = X1 ),
inference(superposition,[status(thm)],[f25,f49]) ).
thf(f49,plain,
! [X0: $i,X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 ),
inference(superposition,[status(thm)],[f25,f42]) ).
thf(f42,plain,
! [X0: d_unsorted,X1: d_unsorted] : ( X0 = X1 ),
inference(superposition,[status(thm)],[f29,f29]) ).
thf(f29,plain,
! [X0: d_unsorted] : ( d_unsorted_0 = X0 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) )
& ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ! [X1: $i] :
( ( d2unsorted @ ( sK0 @ X1 ) )
= X1 )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( ixor
= ( ^ [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 @ Y4 @ Y3 )
| ( Y1 @ Y3 ) )
& ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( ( d2unsorted @ X3 )
!= ( d2unsorted @ X4 ) )
| ( X3 = X4 ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14]) ).
thf(f14,plain,
! [X1: $i] :
( ? [X2: d_unsorted] :
( ( d2unsorted @ X2 )
= X1 )
=> ( ( d2unsorted @ ( sK0 @ X1 ) )
= X1 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) )
& ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ! [X1: $i] :
? [X2: d_unsorted] :
( ( d2unsorted @ X2 )
= X1 )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( ixor
= ( ^ [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 @ Y4 @ Y3 )
| ( Y1 @ Y3 ) )
& ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( ( d2unsorted @ X3 )
!= ( d2unsorted @ X4 ) )
| ( X3 = X4 ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) )
& ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ! [X4: d_unsorted] : ( d_unsorted_0 = X4 )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ! [X2: $i] :
? [X3: d_unsorted] :
( ( d2unsorted @ X3 )
= X2 )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( ixor
= ( ^ [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 @ Y4 @ Y3 )
| ( Y1 @ Y3 ) )
& ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
!= ( d2unsorted @ X0 ) )
| ( X0 = X1 ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ixor
= ( ^ [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 @ Y4 @ Y3 )
| ( Y1 @ Y3 ) )
& ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ! [X4: d_unsorted] : ( d_unsorted_0 = X4 )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) )
& ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ! [X2: $i] :
? [X3: d_unsorted] :
( ( d2unsorted @ X3 )
= X2 )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X0 ) )
=> ( X0 = X1 ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X0 ) )
=> ( X0 = X1 ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ! [X2: $i] :
? [X3: d_unsorted] :
( ( d2unsorted @ X3 )
= X2 )
& ! [X4: d_unsorted] : ( d_unsorted_0 = X4 )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) )
& ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( ( itrue @ ( 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] :
( ( Y0 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y3 )
| ( Y1 @ Y3 ) )
& ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X0 ) )
=> ( X0 = X1 ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ! [X9: $i] :
? [X10: d_unsorted] :
( ( d2unsorted @ X10 )
= X9 )
& ! [X11: d_unsorted] : ( d_unsorted_0 = X11 )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) )
& ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( ( itrue @ ( 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] :
( ( Y0 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y3 )
| ( Y1 @ Y3 ) )
& ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X0 ) )
=> ( X0 = X1 ) )
& ( ivalid
= ( ^ [X2: $i > $o] :
! [X3: $i] : ( X2 @ X3 ) ) )
& ( isatisfiable
= ( ^ [X4: $i > $o] :
~ ! [X5: $i] :
~ ( X4 @ X5 ) ) )
& ( iand
= ( ^ [X6: $i > $o,X7: $i > $o,X8: $i] :
( ( X6 @ X8 )
& ( X7 @ X8 ) ) ) )
& ! [X9: $i] :
? [X10: d_unsorted] :
( ( d2unsorted @ X10 )
= X9 )
& ! [X11: d_unsorted] : ( d_unsorted_0 = X11 )
& ( ( ^ [X12: $i > $o,X13: $i > $o,X14: $i] :
( ( ~ ! [X15: $i] :
( ( X13 @ X15 )
| ~ ( irel @ X14 @ X15 ) )
| ! [X16: $i] :
( ( X12 @ X16 )
| ~ ( irel @ X14 @ X16 ) ) )
& ( ~ ! [X17: $i] :
( ~ ( irel @ X14 @ X17 )
| ( X12 @ X17 ) )
| ! [X18: $i] :
( ( X13 @ X18 )
| ~ ( irel @ X14 @ X18 ) ) ) ) )
= iequiv )
& ( mnot
= ( ^ [X19: $i > $o,X20: $i] :
~ ( X19 @ X20 ) ) )
& ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
& ( icountersatisfiable
= ( ^ [X21: $i > $o] :
~ ! [X22: $i] : ( X21 @ X22 ) ) )
& ( mand
= ( ^ [X23: $i > $o,X24: $i > $o,X25: $i] :
( ( X23 @ X25 )
& ( X24 @ X25 ) ) ) )
& ( inot
= ( ^ [X26: $i > $o,X27: $i] :
~ ! [X28: $i] :
( ( X26 @ X28 )
| ~ ( irel @ X27 @ X28 ) ) ) )
& ( mor
= ( ^ [X29: $i > $o,X30: $i > $o,X31: $i] :
( ( X29 @ X31 )
| ( X30 @ X31 ) ) ) )
& ( mbox_s4
= ( ^ [X32: $i > $o,X33: $i] :
! [X34: $i] :
( ( X32 @ X34 )
| ~ ( irel @ X33 @ X34 ) ) ) )
& ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
& ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
& ( ( ^ [X35: $i > $o,X36: $i > $o,X37: $i] :
~ ! [X38: $i,X39: $i,X40: $i] :
( ~ ( irel @ X37 @ X39 )
| ( ( ( X35 @ X38 )
| ~ ( irel @ X39 @ X38 )
| ~ ! [X41: $i] :
( ~ ( irel @ X39 @ X41 )
| ( X36 @ X41 ) ) )
& ( ( X36 @ X40 )
| ~ ( irel @ X39 @ X40 )
| ~ ! [X42: $i] :
( ~ ( irel @ X39 @ X42 )
| ( X35 @ X42 ) ) ) ) ) )
= ixor )
& ( iatom
= ( ^ [X43: $i > $o,X44: $i] : ( X43 @ X44 ) ) )
& ( ( ^ [X45: $i > $o,X46: $i > $o,X47: $i] :
( ~ ! [X48: $i] :
( ~ ( irel @ X47 @ X48 )
| ( X46 @ X48 ) )
| ! [X49: $i] :
( ~ ( irel @ X47 @ X49 )
| ( X45 @ X49 ) ) ) )
= iimplied )
& ( iimplies
= ( ^ [X50: $i > $o,X51: $i > $o,X52: $i] :
( ~ ! [X53: $i] :
( ( X50 @ X53 )
| ~ ( irel @ X52 @ X53 ) )
| ! [X54: $i] :
( ~ ( irel @ X52 @ X54 )
| ( X51 @ X54 ) ) ) ) )
& ( iinvalid
= ( ^ [X55: $i > $o] :
! [X56: $i] :
~ ( X55 @ X56 ) ) )
& ( ior
= ( ^ [X57: $i > $o,X58: $i > $o,X59: $i] :
( ! [X60: $i] :
( ~ ( irel @ X59 @ X60 )
| ( X57 @ X60 ) )
| ! [X61: $i] :
( ~ ( irel @ X59 @ X61 )
| ( X58 @ X61 ) ) ) ) )
& ( ( ^ [X62: $i > $o,X63: $i > $o,X64: $i] :
( ~ ( X62 @ X64 )
| ( X63 @ X64 ) ) )
= mimplies ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ! [X3: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X2 )
= ( d2unsorted @ X3 ) )
=> ( X2 = X3 ) )
& ( ivalid
= ( ^ [X14: $i > $o] :
! [X15: $i] : ( X14 @ X15 ) ) )
& ( isatisfiable
= ( ^ [X14: $i > $o] :
~ ! [X15: $i] :
~ ( X14 @ X15 ) ) )
& ( iand
= ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ( X8 @ X7 )
& ( X9 @ X7 ) ) ) )
& ! [X0: $i] :
? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 )
& ! [X1: d_unsorted] : ( d_unsorted_0 = X1 )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ( ~ ! [X5: $i] :
( ( X9 @ X5 )
| ~ ( irel @ X7 @ X5 ) )
| ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) )
& ( ~ ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X8 @ X5 ) )
| ! [X5: $i] :
( ( X9 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) ) ) )
= iequiv )
& ( mnot
= ( ^ [X4: $i > $o,X0: $i] :
~ ( X4 @ X0 ) ) )
& ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
& ( icountersatisfiable
= ( ^ [X14: $i > $o] :
~ ! [X15: $i] : ( X14 @ X15 ) ) )
& ( mand
= ( ^ [X4: $i > $o,X5: $i > $o,X0: $i] :
( ( X4 @ X0 )
& ( X5 @ X0 ) ) ) )
& ( inot
= ( ^ [X8: $i > $o,X7: $i] :
~ ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) ) )
& ( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X0: $i] :
( ( X4 @ X0 )
| ( X5 @ X0 ) ) ) )
& ( mbox_s4
= ( ^ [X8: $i > $o,X4: $i] :
! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X4 @ X5 ) ) ) )
& ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
& ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
~ ! [X11: $i,X5: $i,X10: $i] :
( ~ ( irel @ X7 @ X5 )
| ( ( ( X8 @ X11 )
| ~ ( irel @ X5 @ X11 )
| ~ ! [X13: $i] :
( ~ ( irel @ X5 @ X13 )
| ( X9 @ X13 ) ) )
& ( ( X9 @ X10 )
| ~ ( irel @ X5 @ X10 )
| ~ ! [X12: $i] :
( ~ ( irel @ X5 @ X12 )
| ( X8 @ X12 ) ) ) ) ) )
= ixor )
& ( iatom
= ( ^ [X8: $i > $o,X7: $i] : ( X8 @ X7 ) ) )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ~ ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X9 @ X5 ) )
| ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X8 @ X5 ) ) ) )
= iimplied )
& ( iimplies
= ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ~ ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) )
| ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X9 @ X5 ) ) ) ) )
& ( iinvalid
= ( ^ [X14: $i > $o] :
! [X15: $i] :
~ ( X14 @ X15 ) ) )
& ( ior
= ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X8 @ X5 ) )
| ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X9 @ X5 ) ) ) ) )
& ( ( ^ [X0: $i > $o,X6: $i > $o,X7: $i] :
( ~ ( X0 @ X7 )
| ( X6 @ X7 ) ) )
= mimplies ) ),
file('/export/starexec/sandbox2/tmp/tmp.iSg9Oe0LVX/DTF2THF_27148.p',lcl695_1) ).
thf(f25,plain,
! [X1: $i] :
( ( d2unsorted @ ( sK0 @ X1 ) )
= X1 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f1421,plain,
( ( ( sK4 @ sK5 )
= $true )
| ~ spl1_62 ),
inference(avatar_component_clause,[status(thm)],[f1419]) ).
thf(f1419,definition,
( spl1_62
<=> ( ( sK4 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_62])],[avatar_definition]) ).
thf(f1771,plain,
( spl1_6
| ~ spl1_60 ),
inference(avatar_contradiction_clause,[status(thm)],[f1770]) ).
thf(f1770,plain,
( $false
| spl1_6
| ~ spl1_60 ),
inference(subsumption_resolution,[status(thm)],[f1010,f1697]) ).
thf(f1697,plain,
( ! [X0: $i] :
( $false
= ( sK3 @ X0 ) )
| ~ spl1_60 ),
inference(superposition,[status(thm)],[f1410,f55]) ).
thf(f1410,plain,
( ( $false
= ( sK3 @ ( sK6 @ sK5 ) ) )
| ~ spl1_60 ),
inference(avatar_component_clause,[status(thm)],[f1408]) ).
thf(f1408,definition,
( spl1_60
<=> ( $false
= ( sK3 @ ( sK6 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_60])],[avatar_definition]) ).
thf(f1010,plain,
( ( ( sK3 @ sK21 )
!= $false )
| spl1_6 ),
inference(avatar_component_clause,[status(thm)],[f1009]) ).
thf(f1009,definition,
( spl1_6
<=> ( ( sK3 @ sK21 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition]) ).
thf(f1762,plain,
( spl1_6
| ~ spl1_63 ),
inference(avatar_contradiction_clause,[status(thm)],[f1761]) ).
thf(f1761,plain,
( $false
| spl1_6
| ~ spl1_63 ),
inference(subsumption_resolution,[status(thm)],[f1010,f1702]) ).
thf(f1702,plain,
( ! [X0: $i] :
( $false
= ( sK3 @ X0 ) )
| ~ spl1_63 ),
inference(superposition,[status(thm)],[f1575,f55]) ).
thf(f1575,plain,
( ( $false
= ( sK3 @ ( sK7 @ sK5 ) ) )
| ~ spl1_63 ),
inference(avatar_component_clause,[status(thm)],[f1573]) ).
thf(f1573,definition,
( spl1_63
<=> ( $false
= ( sK3 @ ( sK7 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_63])],[avatar_definition]) ).
thf(f1760,plain,
( spl1_7
| ~ spl1_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f1759]) ).
thf(f1759,plain,
( $false
| spl1_7
| ~ spl1_14 ),
inference(subsumption_resolution,[status(thm)],[f1068,f1642]) ).
thf(f1642,plain,
( ! [X0: $i] :
( ( sK4 @ X0 )
!= $false )
| spl1_7 ),
inference(superposition,[status(thm)],[f1014,f55]) ).
thf(f1014,plain,
( ( $false
!= ( sK4 @ sK17 ) )
| spl1_7 ),
inference(avatar_component_clause,[status(thm)],[f1013]) ).
thf(f1068,plain,
( ( ( sK4 @ sK22 )
= $false )
| ~ spl1_14 ),
inference(avatar_component_clause,[status(thm)],[f1066]) ).
thf(f1066,definition,
( spl1_14
<=> ( ( sK4 @ sK22 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_14])],[avatar_definition]) ).
thf(f1758,plain,
( spl1_7
| ~ spl1_39
| spl1_61
| spl1_68 ),
inference(avatar_contradiction_clause,[status(thm)],[f1757]) ).
thf(f1757,plain,
( $false
| spl1_7
| ~ spl1_39
| spl1_61
| spl1_68 ),
inference(subsumption_resolution,[status(thm)],[f1416,f1734]) ).
thf(f1734,plain,
( ! [X0: $i] :
( $false
= ( irel @ sK5 @ X0 ) )
| spl1_7
| ~ spl1_39
| spl1_68 ),
inference(trivial_inequality_removal,[status(thm)],[f1727]) ).
thf(f1727,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( irel @ sK5 @ X0 ) ) )
| spl1_7
| ~ spl1_39
| spl1_68 ),
inference(superposition,[status(thm)],[f91,f1721]) ).
thf(f1721,plain,
( ! [X4: $i,X5: $i] :
( ( $false
= ( irel @ sK5 @ X4 ) )
| ( ( irel @ X4 @ X5 )
= $false ) )
| spl1_7
| ~ spl1_39
| spl1_68 ),
inference(subsumption_resolution,[status(thm)],[f1720,f1642]) ).
thf(f1720,plain,
( ! [X4: $i,X5: $i] :
( ( $false
= ( irel @ sK5 @ X4 ) )
| ( ( irel @ X4 @ X5 )
= $false )
| ( ( sK4 @ ( sK15 @ X4 ) )
= $false ) )
| ~ spl1_39
| spl1_68 ),
inference(subsumption_resolution,[status(thm)],[f1234,f1652]) ).
thf(f1652,plain,
( ! [X0: $i] :
( ( sK3 @ X0 )
!= $true )
| spl1_68 ),
inference(superposition,[status(thm)],[f1632,f55]) ).
thf(f1632,plain,
( ( ( sK3 @ sK5 )
!= $true )
| spl1_68 ),
inference(avatar_component_clause,[status(thm)],[f1631]) ).
thf(f1631,definition,
( spl1_68
<=> ( ( sK3 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_68])],[avatar_definition]) ).
thf(f1234,plain,
( ! [X4: $i,X5: $i] :
( ( ( sK3 @ X5 )
= $true )
| ( ( irel @ X4 @ X5 )
= $false )
| ( $false
= ( irel @ sK5 @ X4 ) )
| ( ( sK4 @ ( sK15 @ X4 ) )
= $false ) )
| ~ spl1_39 ),
inference(avatar_component_clause,[status(thm)],[f1233]) ).
thf(f1233,definition,
( spl1_39
<=> ! [X4: $i,X5: $i] :
( ( ( sK4 @ ( sK15 @ X4 ) )
= $false )
| ( $false
= ( irel @ sK5 @ X4 ) )
| ( ( sK3 @ X5 )
= $true )
| ( ( irel @ X4 @ X5 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl1_39])],[avatar_definition]) ).
thf(f91,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(superposition,[status(thm)],[f27,f55]) ).
thf(f27,plain,
( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f1416,plain,
( ( $false
!= ( irel @ sK5 @ sK5 ) )
| spl1_61 ),
inference(avatar_component_clause,[status(thm)],[f1415]) ).
thf(f1415,definition,
( spl1_61
<=> ( $false
= ( irel @ sK5 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_61])],[avatar_definition]) ).
thf(f1751,plain,
~ spl1_61,
inference(avatar_contradiction_clause,[status(thm)],[f1750]) ).
thf(f1750,plain,
( $false
| ~ spl1_61 ),
inference(trivial_inequality_removal,[status(thm)],[f1745]) ).
thf(f1745,plain,
( ( $false = $true )
| ~ spl1_61 ),
inference(superposition,[status(thm)],[f91,f1417]) ).
thf(f1417,plain,
( ( $false
= ( irel @ sK5 @ sK5 ) )
| ~ spl1_61 ),
inference(avatar_component_clause,[status(thm)],[f1415]) ).
thf(f1671,plain,
( ~ spl1_2
| spl1_68 ),
inference(avatar_contradiction_clause,[status(thm)],[f1670]) ).
thf(f1670,plain,
( $false
| ~ spl1_2
| spl1_68 ),
inference(subsumption_resolution,[status(thm)],[f1659,f1652]) ).
thf(f1659,plain,
( ( ( sK3 @ sK16 )
= $true )
| ~ spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f1657]) ).
thf(f1657,plain,
( ( ( sK3 @ sK16 )
= $true )
| ( $false = $true )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f91,f992]) ).
thf(f992,plain,
( ! [X1: $i] :
( ( ( irel @ sK16 @ X1 )
= $false )
| ( ( sK3 @ X1 )
= $true ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f991]) ).
thf(f991,definition,
( spl1_2
<=> ! [X1: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( ( irel @ sK16 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f1650,plain,
( spl1_7
| ~ spl1_65 ),
inference(avatar_contradiction_clause,[status(thm)],[f1649]) ).
thf(f1649,plain,
( $false
| spl1_7
| ~ spl1_65 ),
inference(subsumption_resolution,[status(thm)],[f1618,f1642]) ).
thf(f1618,plain,
( ( $false
= ( sK4 @ ( sK11 @ sK5 ) ) )
| ~ spl1_65 ),
inference(avatar_component_clause,[status(thm)],[f1616]) ).
thf(f1616,definition,
( spl1_65
<=> ( $false
= ( sK4 @ ( sK11 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_65])],[avatar_definition]) ).
thf(f1648,plain,
( ~ spl1_6
| ~ spl1_68 ),
inference(avatar_contradiction_clause,[status(thm)],[f1647]) ).
thf(f1647,plain,
( $false
| ~ spl1_6
| ~ spl1_68 ),
inference(trivial_inequality_removal,[status(thm)],[f1643]) ).
thf(f1643,plain,
( ( $false = $true )
| ~ spl1_6
| ~ spl1_68 ),
inference(superposition,[status(thm)],[f1637,f1011]) ).
thf(f1011,plain,
( ( ( sK3 @ sK21 )
= $false )
| ~ spl1_6 ),
inference(avatar_component_clause,[status(thm)],[f1009]) ).
thf(f1637,plain,
( ! [X0: $i] :
( ( sK3 @ X0 )
= $true )
| ~ spl1_68 ),
inference(superposition,[status(thm)],[f1633,f55]) ).
thf(f1633,plain,
( ( ( sK3 @ sK5 )
= $true )
| ~ spl1_68 ),
inference(avatar_component_clause,[status(thm)],[f1631]) ).
thf(f1634,plain,
( spl1_68
| spl1_65
| spl1_61
| ~ spl1_37 ),
inference(avatar_split_clause,[status(thm)],[f1364,f1226,f1415,f1616,f1631]) ).
thf(f1226,definition,
( spl1_37
<=> ! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( $false
= ( sK4 @ ( sK11 @ X1 ) ) )
| ( ( sK3 @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1_37])],[avatar_definition]) ).
thf(f1364,plain,
( ( $false
= ( irel @ sK5 @ sK5 ) )
| ( ( sK3 @ sK5 )
= $true )
| ( $false
= ( sK4 @ ( sK11 @ sK5 ) ) )
| ~ spl1_37 ),
inference(trivial_inequality_removal,[status(thm)],[f1351]) ).
thf(f1351,plain,
( ( $false != $false )
| ( $false
= ( sK4 @ ( sK11 @ sK5 ) ) )
| ( ( sK3 @ sK5 )
= $true )
| ( $false
= ( irel @ sK5 @ sK5 ) )
| ~ spl1_37 ),
inference(equality_factoring,[status(thm)],[f1227]) ).
thf(f1227,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( sK3 @ X2 )
= $true )
| ( $false
= ( sK4 @ ( sK11 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) )
| ~ spl1_37 ),
inference(avatar_component_clause,[status(thm)],[f1226]) ).
thf(f1612,plain,
( spl1_6
| ~ spl1_17 ),
inference(avatar_contradiction_clause,[status(thm)],[f1611]) ).
thf(f1611,plain,
( $false
| spl1_6
| ~ spl1_17 ),
inference(subsumption_resolution,[status(thm)],[f1086,f1585]) ).
thf(f1585,plain,
( ! [X0: $i] :
( $false
!= ( sK3 @ X0 ) )
| spl1_6 ),
inference(superposition,[status(thm)],[f1010,f55]) ).
thf(f1086,plain,
( ( ( sK3 @ sK28 )
= $false )
| ~ spl1_17 ),
inference(avatar_component_clause,[status(thm)],[f1084]) ).
thf(f1084,definition,
( spl1_17
<=> ( ( sK3 @ sK28 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_17])],[avatar_definition]) ).
thf(f1608,plain,
( ~ spl1_1
| ~ spl1_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f1607]) ).
thf(f1607,plain,
( $false
| ~ spl1_1
| ~ spl1_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1604]) ).
thf(f1604,plain,
( ( $false = $true )
| ~ spl1_1
| ~ spl1_7 ),
inference(superposition,[status(thm)],[f1015,f1600]) ).
thf(f1600,plain,
( ! [X0: $i] :
( ( sK4 @ X0 )
= $true )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f1597,f55]) ).
thf(f1597,plain,
( ( ( sK4 @ sK16 )
= $true )
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f1591]) ).
thf(f1591,plain,
( ( $false = $true )
| ( ( sK4 @ sK16 )
= $true )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f989,f91]) ).
thf(f989,plain,
( ! [X2: $i] :
( ( $false
= ( irel @ sK16 @ X2 ) )
| ( ( sK4 @ X2 )
= $true ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f988]) ).
thf(f988,definition,
( spl1_1
<=> ! [X2: $i] :
( ( ( sK4 @ X2 )
= $true )
| ( $false
= ( irel @ sK16 @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f1576,plain,
( spl1_61
| spl1_63
| spl1_62
| ~ spl1_56 ),
inference(avatar_split_clause,[status(thm)],[f1496,f1298,f1419,f1573,f1415]) ).
thf(f1298,definition,
( spl1_56
<=> ! [X4: $i,X3: $i] :
( ( $false
= ( irel @ X4 @ X3 ) )
| ( ( sK3 @ ( sK7 @ X4 ) )
= $false )
| ( ( sK4 @ X3 )
= $true )
| ( $false
= ( irel @ sK5 @ X4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_56])],[avatar_definition]) ).
thf(f1496,plain,
( ( $false
= ( irel @ sK5 @ sK5 ) )
| ( ( sK4 @ sK5 )
= $true )
| ( $false
= ( sK3 @ ( sK7 @ sK5 ) ) )
| ~ spl1_56 ),
inference(trivial_inequality_removal,[status(thm)],[f1486]) ).
thf(f1486,plain,
( ( $false
= ( sK3 @ ( sK7 @ sK5 ) ) )
| ( $false != $false )
| ( ( sK4 @ sK5 )
= $true )
| ( $false
= ( irel @ sK5 @ sK5 ) )
| ~ spl1_56 ),
inference(equality_factoring,[status(thm)],[f1299]) ).
thf(f1299,plain,
( ! [X3: $i,X4: $i] :
( ( $false
= ( irel @ sK5 @ X4 ) )
| ( ( sK4 @ X3 )
= $true )
| ( $false
= ( irel @ X4 @ X3 ) )
| ( ( sK3 @ ( sK7 @ X4 ) )
= $false ) )
| ~ spl1_56 ),
inference(avatar_component_clause,[status(thm)],[f1298]) ).
thf(f1571,plain,
( ~ spl1_3
| spl1_31 ),
inference(avatar_contradiction_clause,[status(thm)],[f1570]) ).
thf(f1570,plain,
( $false
| ~ spl1_3
| spl1_31 ),
inference(subsumption_resolution,[status(thm)],[f1195,f1311]) ).
thf(f1311,plain,
( ! [X0: $i] :
( ( irel @ sK5 @ X0 )
= $true )
| ~ spl1_3 ),
inference(superposition,[status(thm)],[f996,f55]) ).
thf(f996,plain,
( ( ( irel @ sK5 @ sK20 )
= $true )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f994]) ).
thf(f994,definition,
( spl1_3
<=> ( ( irel @ sK5 @ sK20 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f1195,plain,
( ( ( irel @ sK5 @ sK18 )
!= $true )
| spl1_31 ),
inference(avatar_component_clause,[status(thm)],[f1194]) ).
thf(f1194,definition,
( spl1_31
<=> ( ( irel @ sK5 @ sK18 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_31])],[avatar_definition]) ).
thf(f1569,plain,
( spl1_8
| ~ spl1_31 ),
inference(avatar_contradiction_clause,[status(thm)],[f1568]) ).
thf(f1568,plain,
( $false
| spl1_8
| ~ spl1_31 ),
inference(subsumption_resolution,[status(thm)],[f1019,f1437]) ).
thf(f1437,plain,
( ! [X0: $i,X1: $i] :
( ( irel @ X1 @ X0 )
= $true )
| ~ spl1_31 ),
inference(superposition,[status(thm)],[f1430,f55]) ).
thf(f1430,plain,
( ! [X0: $i] :
( ( irel @ X0 @ sK18 )
= $true )
| ~ spl1_31 ),
inference(superposition,[status(thm)],[f1196,f55]) ).
thf(f1196,plain,
( ( ( irel @ sK5 @ sK18 )
= $true )
| ~ spl1_31 ),
inference(avatar_component_clause,[status(thm)],[f1194]) ).
thf(f1019,plain,
( ( ( irel @ sK20 @ sK17 )
!= $true )
| spl1_8 ),
inference(avatar_component_clause,[status(thm)],[f1018]) ).
thf(f1018,definition,
( spl1_8
<=> ( ( irel @ sK20 @ sK17 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition]) ).
thf(f1567,plain,
( ~ spl1_6
| ~ spl1_8
| ~ spl1_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f1566]) ).
thf(f1566,plain,
( $false
| ~ spl1_6
| ~ spl1_8
| ~ spl1_9 ),
inference(trivial_inequality_removal,[status(thm)],[f1563]) ).
thf(f1563,plain,
( ( $false = $true )
| ~ spl1_6
| ~ spl1_8
| ~ spl1_9 ),
inference(superposition,[status(thm)],[f1424,f1011]) ).
thf(f1424,plain,
( ! [X0: $i] :
( ( sK3 @ X0 )
= $true )
| ~ spl1_8
| ~ spl1_9 ),
inference(superposition,[status(thm)],[f1329,f55]) ).
thf(f1329,plain,
( ( ( sK3 @ sK17 )
= $true )
| ~ spl1_8
| ~ spl1_9 ),
inference(trivial_inequality_removal,[status(thm)],[f1324]) ).
thf(f1324,plain,
( ( ( sK3 @ sK17 )
= $true )
| ( $false = $true )
| ~ spl1_8
| ~ spl1_9 ),
inference(superposition,[status(thm)],[f1024,f1020]) ).
thf(f1020,plain,
( ( ( irel @ sK20 @ sK17 )
= $true )
| ~ spl1_8 ),
inference(avatar_component_clause,[status(thm)],[f1018]) ).
thf(f1024,plain,
( ! [X3: $i] :
( ( $false
= ( irel @ sK20 @ X3 ) )
| ( ( sK3 @ X3 )
= $true ) )
| ~ spl1_9 ),
inference(avatar_component_clause,[status(thm)],[f1023]) ).
thf(f1023,definition,
( spl1_9
<=> ! [X3: $i] :
( ( $false
= ( irel @ sK20 @ X3 ) )
| ( ( sK3 @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1_9])],[avatar_definition]) ).
thf(f1559,plain,
( ~ spl1_3
| ~ spl1_7
| ~ spl1_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f1558]) ).
thf(f1558,plain,
( $false
| ~ spl1_3
| ~ spl1_7
| ~ spl1_11 ),
inference(trivial_inequality_removal,[status(thm)],[f1554]) ).
thf(f1554,plain,
( ( $false = $true )
| ~ spl1_3
| ~ spl1_7
| ~ spl1_11 ),
inference(superposition,[status(thm)],[f1551,f1301]) ).
thf(f1301,plain,
( ! [X0: $i] :
( ( sK4 @ X0 )
= $false )
| ~ spl1_7 ),
inference(superposition,[status(thm)],[f1015,f55]) ).
thf(f1551,plain,
( ( ( sK4 @ sK20 )
= $true )
| ~ spl1_3
| ~ spl1_11 ),
inference(trivial_inequality_removal,[status(thm)],[f1537]) ).
thf(f1537,plain,
( ( ( sK4 @ sK20 )
= $true )
| ( $false = $true )
| ~ spl1_3
| ~ spl1_11 ),
inference(superposition,[status(thm)],[f1314,f1033]) ).
thf(f1033,plain,
( ! [X2: $i] :
( ( $false
= ( irel @ sK20 @ X2 ) )
| ( ( sK4 @ X2 )
= $true ) )
| ~ spl1_11 ),
inference(avatar_component_clause,[status(thm)],[f1032]) ).
thf(f1032,definition,
( spl1_11
<=> ! [X2: $i] :
( ( ( sK4 @ X2 )
= $true )
| ( $false
= ( irel @ sK20 @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_11])],[avatar_definition]) ).
thf(f1314,plain,
( ! [X0: $i] :
( ( irel @ X0 @ sK20 )
= $true )
| ~ spl1_3 ),
inference(superposition,[status(thm)],[f996,f55]) ).
thf(f1422,plain,
( spl1_60
| spl1_61
| spl1_62
| ~ spl1_53 ),
inference(avatar_split_clause,[status(thm)],[f1387,f1286,f1419,f1415,f1408]) ).
thf(f1286,definition,
( spl1_53
<=> ! [X2: $i,X1: $i] :
( ( ( sK3 @ ( sK6 @ X1 ) )
= $false )
| ( ( sK4 @ X2 )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl1_53])],[avatar_definition]) ).
thf(f1387,plain,
( ( ( sK4 @ sK5 )
= $true )
| ( $false
= ( irel @ sK5 @ sK5 ) )
| ( $false
= ( sK3 @ ( sK6 @ sK5 ) ) )
| ~ spl1_53 ),
inference(trivial_inequality_removal,[status(thm)],[f1379]) ).
thf(f1379,plain,
( ( ( sK4 @ sK5 )
= $true )
| ( $false != $false )
| ( $false
= ( irel @ sK5 @ sK5 ) )
| ( $false
= ( sK3 @ ( sK6 @ sK5 ) ) )
| ~ spl1_53 ),
inference(equality_factoring,[status(thm)],[f1287]) ).
thf(f1287,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( sK4 @ X2 )
= $true )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false ) )
| ~ spl1_53 ),
inference(avatar_component_clause,[status(thm)],[f1286]) ).
thf(f1300,plain,
( spl1_53
| spl1_56 ),
inference(avatar_split_clause,[status(thm)],[f137,f1298,f1286]) ).
thf(f137,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ X4 @ X3 ) )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ sK5 @ X4 ) )
| ( ( sK4 @ X3 )
= $true )
| ( ( sK4 @ X2 )
= $true )
| ( ( sK3 @ ( sK7 @ X4 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f135]) ).
thf(f135,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( sK4 @ X3 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X4 @ X3 ) )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false )
| ( $false
= ( irel @ sK5 @ X4 ) )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( sK4 @ X2 )
= $true )
| ( $false
= ( ( sK3 @ ( sK7 @ X4 ) )
| ~ ( irel @ X4 @ ( sK7 @ X4 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f134]) ).
thf(f134,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK5 @ X4 ) )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false )
| ( ( sK4 @ X2 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X4 @ X3 ) )
| ( ( sK4 @ X3 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) )
@ ( sK7 @ X4 ) ) )
| ( $false
= ( irel @ sK5 @ X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f133]) ).
thf(f133,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X4 @ X3 ) )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) ) )
| ( $false
= ( irel @ sK5 @ X4 ) )
| ( ( sK4 @ X2 )
= $true )
| ( ( sK4 @ X3 )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK5 @ X4 ) )
| ( ( sK4 @ X3 )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false )
| ( ( sK4 @ X2 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X4 @ X3 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f131]) ).
thf(f131,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( $false
= ( irel @ sK5 @ X4 ) )
| ( ( ~ ( irel @ X4 @ X3 ) )
= $true )
| ( ( sK4 @ X3 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) ) )
= $true )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false )
| ( ( sK4 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f130]) ).
thf(f130,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( sK4 @ X3 )
= $true )
| ( $false
= ( irel @ sK5 @ X4 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X3 ) )
= $true )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( sK4 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f129]) ).
thf(f129,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X3 )
| ( sK4 @ X3 ) )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( sK4 @ X2 )
= $true )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false )
| ( $false
= ( irel @ sK5 @ X4 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f128]) ).
thf(f128,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( sK4 @ X2 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ~ ( irel @ sK5 @ X4 ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X3 )
| ( sK4 @ X3 ) )
= $true )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false )
| ( $false
= ( irel @ sK5 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f126]) ).
thf(f126,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X5 )
| ( sK3 @ X5 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( ~ ( irel @ sK5 @ X4 ) )
= $true )
| ( ( sK4 @ X2 )
= $true )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f125]) ).
thf(f125,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X5 )
| ( sK3 @ X5 ) ) )
| ~ ( irel @ sK5 @ X4 ) )
= $true )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false )
| ( ( sK4 @ X2 )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f124]) ).
thf(f124,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ~ ( irel @ X1 @ X2 ) )
= $true )
| ( ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X5 )
| ( sK3 @ X5 ) ) )
| ~ ( irel @ sK5 @ X4 ) )
= $true )
| ( ( sK4 @ X2 )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f123]) ).
thf(f123,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( sK3 @ ( sK6 @ X1 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X4 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X4 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( irel @ sK5 @ X4 ) )
@ X5 )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( ~ ( irel @ X1 @ X2 ) )
= $true )
| ( ( sK4 @ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X4 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X4 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( irel @ sK5 @ X4 ) ) )
= $true )
| ( ( ~ ( irel @ X1 @ X2 ) )
= $true )
| ( ( sK4 @ X2 )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f121]) ).
thf(f121,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( irel @ X1 @ X2 )
| ( sK4 @ X2 ) )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X4 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X4 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( irel @ sK5 @ X4 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f120]) ).
thf(f120,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false )
| ( ( ~ ( irel @ X1 @ X2 )
| ( sK4 @ X2 ) )
= $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK4 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
@ X4 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK4 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
= $true )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false )
| ( ( ~ ( irel @ X1 @ X2 )
| ( sK4 @ X2 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f118]) ).
thf(f118,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK3 @ ( sK6 @ X1 ) )
= $false )
| ( ( ~ ( irel @ X1 @ X2 )
| ( sK4 @ X2 ) )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) )
@ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f117]) ).
thf(f117,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) )
= $true )
| ( ( sK3 @ ( sK6 @ X1 ) )
= $false )
| ( ( ~ ( irel @ X1 @ X2 )
| ( sK4 @ X2 ) )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f115]) ).
thf(f115,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK3 @ ( sK6 @ X1 ) )
| ~ ( irel @ X1 @ ( sK6 @ X1 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) )
= $true )
| ( ( ~ ( irel @ X1 @ X2 )
| ( sK4 @ X2 ) )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f114]) ).
thf(f114,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X1 @ Y0 ) )
@ ( sK6 @ X1 ) ) )
| ( ( ~ ( irel @ X1 @ X2 )
| ( sK4 @ X2 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f113]) ).
thf(f113,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK5 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X1 @ Y0 ) ) ) )
| ( ( ~ ( irel @ X1 @ X2 )
| ( sK4 @ X2 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f112]) ).
thf(f112,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X1 @ Y0 ) ) ) )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X1 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X1 @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f108]) ).
thf(f108,plain,
! [X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X1 @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
! [X1: $i] :
( ( ( ~ ( irel @ sK5 @ X1 ) )
= $true )
| ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X1 @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
! [X1: $i] :
( ( ( ~ ( irel @ sK5 @ X1 )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X1 @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f103]) ).
thf(f103,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) ) ) )
@ X1 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) ) )
!= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f98]) ).
thf(f98,plain,
( ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( sK3 @ Y4 )
| ~ ( irel @ Y2 @ Y4 ) ) )
| ~ ( irel @ Y2 @ Y1 )
| ( sK4 @ Y1 ) )
& ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( sK4 @ Y4 )
| ~ ( irel @ Y2 @ Y4 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ( sK3 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) )
@ sK5 )
!= ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) )
& ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) ) ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f97]) ).
thf(f97,plain,
( ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( sK3 @ Y4 )
| ~ ( irel @ Y2 @ Y4 ) ) )
| ~ ( irel @ Y2 @ Y1 )
| ( sK4 @ Y1 ) )
& ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( sK4 @ Y4 )
| ~ ( irel @ Y2 @ Y4 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ( sK3 @ Y3 ) ) )
| ~ ( irel @ Y0 @ Y2 ) ) ) ) ) )
!= ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) )
& ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f96]) ).
thf(f96,plain,
( ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( sK3 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y3 @ Y2 )
| ( Y0 @ Y2 ) )
& ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y3 @ Y4 )
| ( sK3 @ Y4 ) ) )
| ~ ( irel @ Y1 @ Y3 ) ) ) ) )
@ sK4 )
!= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) )
& ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK3 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) ) )
@ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f95]) ).
thf(f95,plain,
( ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) )
& ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK3 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) ) ) )
!= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( sK3 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y3 @ Y2 )
| ( Y0 @ Y2 ) )
& ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y3 @ Y4 )
| ( sK3 @ Y4 ) ) )
| ~ ( irel @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f94]) ).
thf(f94,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( ( ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
| ~ ( irel @ Y3 @ Y4 ) ) ) )
& ( ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ( Y0 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) ) ) ) ) )
@ 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 @ Y4 @ Y3 )
| ( Y1 @ Y3 ) )
& ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) )
@ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( ( ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
| ~ ( irel @ Y3 @ Y4 ) ) ) )
& ( ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ( Y0 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) ) ) ) ) ) )
!= ( ^ [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 @ Y4 @ Y3 )
| ( Y1 @ Y3 ) )
& ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 )
| ~ ( irel @ Y4 @ Y5 ) ) ) )
& ( ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y2 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) ) ) )
@ Y0
@ Y1 ) ) )
!= ( ^ [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 @ Y4 @ Y3 )
| ( Y1 @ Y3 ) )
& ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f39,f23,f18,f37]) ).
thf(f37,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) )
& ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f18,plain,
( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f23,plain,
( ixor
= ( ^ [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 @ Y4 @ Y3 )
| ( Y1 @ Y3 ) )
& ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f39,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)],[f6]) ).
thf(f6,plain,
( ixor
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( inot @ ( iequiv @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,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/sandbox2/tmp/tmp.iSg9Oe0LVX/DTF2THF_27148.p',ixor) ).
thf(f1235,plain,
( spl1_37
| spl1_39 ),
inference(avatar_split_clause,[status(thm)],[f245,f1233,f1226]) ).
thf(f245,plain,
! [X2: $i,X1: $i,X4: $i,X5: $i] :
( ( ( sK4 @ ( sK15 @ X4 ) )
= $false )
| ( ( irel @ X4 @ X5 )
= $false )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( sK3 @ X5 )
= $true )
| ( $false
= ( irel @ sK5 @ X4 ) )
| ( ( sK3 @ X2 )
= $true )
| ( $false
= ( sK4 @ ( sK11 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f243]) ).
thf(f243,plain,
! [X2: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( sK4 @ ( sK11 @ X1 ) ) )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X4 @ X5 )
= $false )
| ( ( ( sK4 @ ( sK15 @ X4 ) )
| ~ ( irel @ X4 @ ( sK15 @ X4 ) ) )
= $false )
| ( $false
= ( irel @ sK5 @ X4 ) )
| ( ( sK3 @ X2 )
= $true )
| ( ( sK3 @ X5 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f242]) ).
thf(f242,plain,
! [X2: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) )
@ ( sK15 @ X4 ) ) )
| ( ( sK3 @ X2 )
= $true )
| ( ( irel @ X4 @ X5 )
= $false )
| ( $false
= ( sK4 @ ( sK11 @ X1 ) ) )
| ( ( sK3 @ X5 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( $false
= ( irel @ sK5 @ X4 ) ) ),
inference(sigma_clausification,[status(thm)],[f241]) ).
thf(f241,plain,
! [X2: $i,X1: $i,X4: $i,X5: $i] :
( ( ( irel @ X4 @ X5 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
= $false )
| ( $false
= ( irel @ sK5 @ X4 ) )
| ( $false
= ( sK4 @ ( sK11 @ X1 ) ) )
| ( ( sK3 @ X5 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( sK3 @ X2 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f240]) ).
thf(f240,plain,
! [X2: $i,X1: $i,X4: $i,X5: $i] :
( ( ( sK3 @ X2 )
= $true )
| ( $false
= ( irel @ sK5 @ X4 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) ) )
= $true )
| ( $false
= ( sK4 @ ( sK11 @ X1 ) ) )
| ( ( irel @ X4 @ X5 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( sK3 @ X5 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f239]) ).
thf(f239,plain,
! [X2: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( irel @ sK5 @ X4 ) )
| ( ( ~ ( irel @ X4 @ X5 ) )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( sK4 @ ( sK11 @ X1 ) ) )
| ( ( sK3 @ X2 )
= $true )
| ( ( sK3 @ X5 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f238]) ).
thf(f238,plain,
! [X2: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( sK4 @ ( sK11 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ sK5 @ X4 ) )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( sK3 @ X2 )
= $true )
| ( ( sK3 @ X5 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f227]) ).
thf(f227,plain,
! [X2: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X5 )
| ( sK3 @ X5 ) )
= $true )
| ( $false
= ( irel @ sK5 @ X4 ) )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( sK4 @ ( sK11 @ X1 ) ) )
| ( ( sK3 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f226]) ).
thf(f226,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( irel @ sK5 @ X1 ) )
| ( $false
= ( irel @ sK5 @ X4 ) )
| ( ( sK3 @ X2 )
= $true )
| ( $false
= ( sK4 @ ( sK11 @ X1 ) ) )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X5 )
| ( sK3 @ X5 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f225]) ).
thf(f225,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ~ ( irel @ sK5 @ X4 ) )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( $false
= ( sK4 @ ( sK11 @ X1 ) ) )
| ( ( sK3 @ X2 )
= $true )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X5 )
| ( sK3 @ X5 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f224]) ).
thf(f224,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( sK3 @ X2 )
= $true )
| ( ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X5 )
| ( sK3 @ X5 ) ) )
| ~ ( irel @ sK5 @ X4 ) )
= $true )
| ( $false
= ( sK4 @ ( sK11 @ X1 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f223]) ).
thf(f223,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( sK3 @ X2 )
= $true )
| ( ( ~ ( irel @ X1 @ X2 ) )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X4 @ Y0 ) ) )
| ~ ( irel @ X4 @ X5 )
| ( sK3 @ X5 ) ) )
| ~ ( irel @ sK5 @ X4 ) )
= $true )
| ( $false
= ( sK4 @ ( sK11 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f222]) ).
thf(f222,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( sK3 @ X2 )
= $true )
| ( $false
= ( sK4 @ ( sK11 @ X1 ) ) )
| ( ( ~ ( irel @ X1 @ X2 ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X4 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X4 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( irel @ sK5 @ X4 ) )
@ X5 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f221]) ).
thf(f221,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X4 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X4 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( irel @ sK5 @ X4 ) ) )
= $true )
| ( $false
= ( sK4 @ ( sK11 @ X1 ) ) )
| ( ( sK3 @ X2 )
= $true )
| ( ( ~ ( irel @ X1 @ X2 ) )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f192]) ).
thf(f192,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( irel @ X1 @ X2 )
| ( sK3 @ X2 ) )
= $true )
| ( $false
= ( sK4 @ ( sK11 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X4 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X4 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( irel @ sK5 @ X4 ) ) )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f191]) ).
thf(f191,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK5 @ X1 ) )
| ( $false
= ( ~ ( irel @ X1 @ ( sK11 @ X1 ) )
| ( sK4 @ ( sK11 @ X1 ) ) ) )
| ( ( ~ ( irel @ X1 @ X2 )
| ( sK3 @ X2 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X4 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ X4 @ Y1 ) ) )
| ~ ( irel @ X4 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( irel @ sK5 @ X4 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f190]) ).
thf(f190,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( irel @ X1 @ X2 )
| ( sK3 @ X2 ) )
= $true )
| ( $false
= ( ~ ( irel @ X1 @ ( sK11 @ X1 ) )
| ( sK4 @ ( sK11 @ X1 ) ) ) )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK4 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
@ X4 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f189]) ).
thf(f189,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK4 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ~ ( irel @ X1 @ ( sK11 @ X1 ) )
| ( sK4 @ ( sK11 @ X1 ) ) ) )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( ~ ( irel @ X1 @ X2 )
| ( sK3 @ X2 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f188]) ).
thf(f188,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( irel @ X1 @ X2 )
| ( sK3 @ X2 ) )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ ( sK11 @ X1 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK4 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f187]) ).
thf(f187,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ X3 )
| ( sK4 @ X3 ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK4 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
= $true )
| ( ( ~ ( irel @ X1 @ X2 )
| ( sK3 @ X2 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f186]) ).
thf(f186,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) )
@ X3 )
= $true )
| ( ( ~ ( irel @ X1 @ X2 )
| ( sK3 @ X2 ) )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f185]) ).
thf(f185,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( ~ ( irel @ X1 @ X2 )
| ( sK3 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f184]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) )
= $true )
| ( ( ~ ( irel @ X1 @ X2 )
| ( sK3 @ X2 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f183]) ).
thf(f183,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK3 @ Y0 ) )
@ X2 )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f182]) ).
thf(f182,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f181]) ).
thf(f181,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
= $true )
| ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK5 @ X1 ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f106]) ).
thf(f1087,plain,
( spl1_14
| spl1_6
| spl1_17
| spl1_7 ),
inference(avatar_split_clause,[status(thm)],[f676,f1013,f1084,f1009,f1066]) ).
thf(f676,plain,
( ( $false
= ( sK4 @ sK17 ) )
| ( ( sK3 @ sK28 )
= $false )
| ( ( sK3 @ sK21 )
= $false )
| ( ( sK4 @ sK22 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f675]) ).
thf(f675,plain,
( ( ( sK4 @ sK22 )
= $false )
| ( ( sK3 @ sK21 )
= $false )
| ( $false
= ( sK4 @ sK17 ) )
| ( $false
= ( ~ ( irel @ sK16 @ sK28 )
| ( sK3 @ sK28 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f674]) ).
thf(f674,plain,
( ( $false
= ( sK4 @ sK17 ) )
| ( ( sK4 @ sK22 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) )
@ sK28 ) )
| ( ( sK3 @ sK21 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f651]) ).
thf(f651,plain,
( ( ( sK4 @ sK22 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
= $false )
| ( ( sK3 @ sK21 )
= $false )
| ( $false
= ( sK4 @ sK17 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f650]) ).
thf(f650,plain,
( ( ( sK4 @ sK22 )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 )
| ( sK4 @ sK17 ) ) )
| ( ( sK3 @ sK21 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f492]) ).
thf(f492,plain,
( ( ( sK4 @ sK22 )
= $false )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( sK3 @ sK21 )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 )
| ( sK4 @ sK17 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f491]) ).
thf(f491,plain,
( ( ( sK4 @ sK22 )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK21 )
| ( sK3 @ sK21 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 )
| ( sK4 @ sK17 ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f490]) ).
thf(f490,plain,
( ( $false
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 )
| ( sK4 @ sK17 ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK21 )
| ( sK3 @ sK21 ) ) ) )
| ( ( sK4 @ sK22 )
= $false )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f319]) ).
thf(f319,plain,
( ( $false
= ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 )
| ( sK4 @ sK17 ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK21 )
| ( sK3 @ sK21 ) ) )
| ~ ( irel @ sK5 @ sK20 ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( sK4 @ sK22 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f318]) ).
thf(f318,plain,
( ( $false
= ( ~ ( irel @ sK16 @ sK22 )
| ( sK4 @ sK22 ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $false
= ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 )
| ( sK4 @ sK17 ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK21 )
| ( sK3 @ sK21 ) ) )
| ~ ( irel @ sK5 @ sK20 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f317]) ).
thf(f317,plain,
( ( ( ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK22 )
= $false )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $false
= ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 )
| ( sK4 @ sK17 ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK21 )
| ( sK3 @ sK21 ) ) )
| ~ ( irel @ sK5 @ sK20 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f316]) ).
thf(f316,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $false
= ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 )
| ( sK4 @ sK17 ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK21 )
| ( sK3 @ sK21 ) ) )
| ~ ( irel @ sK5 @ sK20 ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f314]) ).
thf(f314,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $false
= ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 )
| ( sK4 @ sK17 ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK21 )
| ( sK3 @ sK21 ) ) )
| ~ ( irel @ sK5 @ sK20 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f313]) ).
thf(f313,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ sK20 @ Y1 ) ) )
| ~ ( irel @ sK20 @ sK17 )
| ( sK4 @ sK17 ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ sK20 @ Y1 ) ) )
| ~ ( irel @ sK20 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( irel @ sK5 @ sK20 ) )
@ sK21 )
= $false )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f312]) ).
thf(f312,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ sK20 @ Y1 ) ) )
| ~ ( irel @ sK20 @ sK17 )
| ( sK4 @ sK17 ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ sK20 @ Y1 ) ) )
| ~ ( irel @ sK20 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( irel @ sK5 @ sK20 ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f311]) ).
thf(f311,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ sK17 )
| ( sK4 @ sK17 ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK4 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
@ sK20 ) ) ),
inference(sigma_clausification,[status(thm)],[f310]) ).
thf(f310,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ sK17 )
| ( sK4 @ sK17 ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK4 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f253]) ).
thf(f253,plain,
( ( $false
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ sK17 )
| ( sK4 @ sK17 ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK4 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f252]) ).
thf(f252,plain,
( ( ( ~ ( irel @ sK5 @ sK16 )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ sK17 )
| ( sK4 @ sK17 ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK4 @ Y2 )
| ~ ( irel @ Y0 @ Y2 ) ) )
| ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f251]) ).
thf(f251,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) )
@ sK17 )
= $false )
| ( ( ~ ( irel @ sK5 @ sK16 )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f250]) ).
thf(f250,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) ) )
| ( ( ~ ( irel @ sK5 @ sK16 )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f249]) ).
thf(f249,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) ) ) )
@ sK16 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f248]) ).
thf(f248,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f247]) ).
thf(f247,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y0 )
| ( sK4 @ Y0 ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK4 @ Y3 )
| ~ ( irel @ Y1 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( irel @ sK5 @ Y1 ) ) ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f1038,plain,
( spl1_2
| spl1_11
| spl1_9
| spl1_1 ),
inference(avatar_split_clause,[status(thm)],[f879,f988,f1023,f1032,f991]) ).
thf(f879,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( sK4 @ X3 )
= $true )
| ( $false
= ( irel @ sK16 @ X3 ) )
| ( $false
= ( irel @ sK20 @ X2 ) )
| ( $false
= ( irel @ sK20 @ X4 ) )
| ( ( sK3 @ X1 )
= $true )
| ( ( sK3 @ X4 )
= $true )
| ( ( irel @ sK16 @ X1 )
= $false )
| ( ( sK4 @ X2 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f878]) ).
thf(f878,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK16 @ X3 ) )
| ( ( sK3 @ X1 )
= $true )
| ( ( irel @ sK16 @ X1 )
= $false )
| ( ( sK4 @ X3 )
= $true )
| ( ( sK4 @ X2 )
= $true )
| ( ( sK3 @ X4 )
= $true )
| ( ( ~ ( irel @ sK20 @ X4 ) )
= $true )
| ( $false
= ( irel @ sK20 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f877]) ).
thf(f877,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK20 @ X2 ) )
| ( ( sK3 @ X1 )
= $true )
| ( ( sK4 @ X2 )
= $true )
| ( ( sK4 @ X3 )
= $true )
| ( ( irel @ sK16 @ X1 )
= $false )
| ( $false
= ( irel @ sK16 @ X3 ) )
| ( ( ( sK3 @ X4 )
| ~ ( irel @ sK20 @ X4 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f876]) ).
thf(f876,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( sK4 @ X2 )
= $true )
| ( ( sK4 @ X3 )
= $true )
| ( $false
= ( irel @ sK20 @ X2 ) )
| ( ( sK3 @ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) )
@ X4 )
= $true )
| ( $false
= ( irel @ sK16 @ X3 ) )
| ( ( irel @ sK16 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f875]) ).
thf(f875,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK16 @ X1 )
= $false )
| ( $false
= ( irel @ sK16 @ X3 ) )
| ( ( sK4 @ X3 )
= $true )
| ( ( sK4 @ X2 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
= $true )
| ( $false
= ( irel @ sK20 @ X2 ) )
| ( ( sK3 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f874]) ).
thf(f874,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) ) ) )
| ( $false
= ( irel @ sK16 @ X3 ) )
| ( $false
= ( irel @ sK20 @ X2 ) )
| ( ( sK4 @ X2 )
= $true )
| ( ( sK4 @ X3 )
= $true )
| ( ( irel @ sK16 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f872]) ).
thf(f872,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 ) ) )
| ( $false
= ( irel @ sK16 @ X3 ) )
| ( ( sK4 @ X2 )
= $true )
| ( ( sK3 @ X1 )
= $true )
| ( ( sK4 @ X3 )
= $true )
| ( ( irel @ sK16 @ X1 )
= $false )
| ( $false
= ( irel @ sK20 @ X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f871]) ).
thf(f871,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( irel @ sK20 @ X2 ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 ) ) )
| ( ( sK4 @ X2 )
= $true )
| ( ( irel @ sK16 @ X1 )
= $false )
| ( ( sK3 @ X1 )
= $true )
| ( $false
= ( irel @ sK16 @ X3 ) )
| ( ( sK4 @ X3 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f870]) ).
thf(f870,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( irel @ sK16 @ X3 ) )
= $true )
| ( ( sK4 @ X3 )
= $true )
| ( ( ~ ( irel @ sK20 @ X2 ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 ) ) )
| ( ( irel @ sK16 @ X1 )
= $false )
| ( ( sK4 @ X2 )
= $true )
| ( ( sK3 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f869]) ).
thf(f869,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( irel @ sK16 @ X3 )
| ( sK4 @ X3 ) )
= $true )
| ( ( sK4 @ X2 )
= $true )
| ( ( irel @ sK16 @ X1 )
= $false )
| ( ( ~ ( irel @ sK20 @ X2 ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 ) ) )
| ( ( sK3 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f868]) ).
thf(f868,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( sK4 @ X2 )
| ~ ( irel @ sK20 @ X2 ) )
= $true )
| ( ( irel @ sK16 @ X1 )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( ( ~ ( irel @ sK16 @ X3 )
| ( sK4 @ X3 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f867]) ).
thf(f867,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( ( ( sK4 @ X2 )
| ~ ( irel @ sK20 @ X2 ) )
= $true )
| ( ( irel @ sK16 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f866]) ).
thf(f866,plain,
! [X2: $i,X1: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( ( irel @ sK16 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true )
| ( ( ( sK4 @ X2 )
| ~ ( irel @ sK20 @ X2 ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f865]) ).
thf(f865,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK16 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) )
@ X2 )
= $true )
| ( ( sK3 @ X1 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 ) ) ) ),
inference(pi_clausification,[status(thm)],[f864]) ).
thf(f864,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
= $true )
| ( ( sK3 @ X1 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 ) ) )
| ( ( irel @ sK16 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f863]) ).
thf(f863,plain,
! [X1: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( ( irel @ sK16 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f862]) ).
thf(f862,plain,
! [X1: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( ( ~ ( irel @ sK16 @ X1 ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f861]) ).
thf(f861,plain,
! [X1: $i] :
( ( ( ( sK3 @ X1 )
| ~ ( irel @ sK16 @ X1 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f859]) ).
thf(f859,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK21 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 ) ) )
| ( ( ( sK3 @ X1 )
| ~ ( irel @ sK16 @ X1 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f858]) ).
thf(f858,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK21 ) ) )
| ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f857]) ).
thf(f857,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK21 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f856]) ).
thf(f856,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK21 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f855]) ).
thf(f855,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK21 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f853]) ).
thf(f853,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 )
| ( sK4 @ sK17 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK21 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f720]) ).
thf(f720,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK21 )
| ( sK3 @ sK21 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 )
| ( sK4 @ sK17 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f719]) ).
thf(f719,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK21 )
| ( sK3 @ sK21 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 )
| ( sK4 @ sK17 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f718]) ).
thf(f718,plain,
( ( $false
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 )
| ( sK4 @ sK17 ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK21 )
| ( sK3 @ sK21 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f315]) ).
thf(f315,plain,
( ( $false
= ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK17 )
| ( sK4 @ sK17 ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK20 @ Y0 ) ) )
| ~ ( irel @ sK20 @ sK21 )
| ( sK3 @ sK21 ) ) )
| ~ ( irel @ sK5 @ sK20 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f314]) ).
thf(f997,plain,
( spl1_1
| spl1_2
| spl1_3 ),
inference(avatar_split_clause,[status(thm)],[f986,f994,f991,f988]) ).
thf(f986,plain,
! [X2: $i,X1: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( ( sK4 @ X2 )
= $true )
| ( ( irel @ sK5 @ sK20 )
= $true )
| ( $false
= ( irel @ sK16 @ X2 ) )
| ( ( irel @ sK16 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f985]) ).
thf(f985,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK5 @ sK20 )
= $true )
| ( ( sK4 @ X2 )
= $true )
| ( ( irel @ sK16 @ X1 )
= $false )
| ( ( ~ ( irel @ sK16 @ X2 ) )
= $true )
| ( ( sK3 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f984]) ).
thf(f984,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( irel @ sK16 @ X2 )
| ( sK4 @ X2 ) )
= $true )
| ( ( sK3 @ X1 )
= $true )
| ( ( irel @ sK16 @ X1 )
= $false )
| ( ( irel @ sK5 @ sK20 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f983]) ).
thf(f983,plain,
! [X2: $i,X1: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( ( ~ ( irel @ sK16 @ X1 ) )
= $true )
| ( ( ~ ( irel @ sK16 @ X2 )
| ( sK4 @ X2 ) )
= $true )
| ( ( irel @ sK5 @ sK20 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f982]) ).
thf(f982,plain,
! [X2: $i,X1: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( ( irel @ sK5 @ sK20 )
= $true )
| ( ( ~ ( irel @ sK16 @ X1 ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f981]) ).
thf(f981,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true )
| ( ( ~ ( irel @ sK16 @ X1 ) )
= $true )
| ( ( irel @ sK5 @ sK20 )
= $true )
| ( ( sK3 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f980]) ).
thf(f980,plain,
! [X1: $i] :
( ( ( ( sK3 @ X1 )
| ~ ( irel @ sK16 @ X1 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true )
| ( ( irel @ sK5 @ sK20 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f979]) ).
thf(f979,plain,
! [X1: $i] :
( ( ( irel @ sK5 @ sK20 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) )
@ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f978]) ).
thf(f978,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) )
= $true )
| ( ( irel @ sK5 @ sK20 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f977]) ).
thf(f977,plain,
( ( ( ~ ( irel @ sK5 @ sK20 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f976]) ).
thf(f976,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) ) )
| ( ( ~ ( irel @ sK5 @ sK20 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f958]) ).
thf(f958,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) ) )
| ( ( ~ ( irel @ sK5 @ sK20 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f717]) ).
thf(f717,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK16 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( ~ ( irel @ sK5 @ sK20 ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK16 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f315]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n008.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 09:19:58 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.31/0.47 % Domain : Software Verification
% 0.31/0.47 % Problem : Benchmark: LCL695^1, Active target: ixor
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English :
% 0.31/0.47
% 0.31/0.47 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.31/0.47 % Source : [Kon26]
% 0.31/0.47 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : ? v9.3.0
% 0.31/0.47 % Syntax : Number of formulae : 26 ( 1 unt; 24 typ; 0 def)
% 0.31/0.47 % Number of atoms : 62 ( 22 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 24 ( 31 avg)
% 0.31/0.47 % Number of connectives : 163 ( 32 ~; 26 |; 26 &; 78 @)
% 0.31/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 26 ( 14 avg)
% 0.31/0.47 % Number of types : 4 ( 2 usr)
% 0.31/0.47 % Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 23 ( 22 usr; 1 con; 0-3 aty)
% 0.31/0.47 % Number of variables : 67 ( 41 ^; 25 !; 1 ?; 67 :)
% 0.31/0.47 % SPC : TH0_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments :
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(unsorted_type,type,
% 0.31/0.47 unsorted: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(irel_decl,type,
% 0.31/0.47 irel: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(mnot_decl,type,
% 0.31/0.47 mnot: ( $i > $o ) > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(mor_decl,type,
% 0.31/0.47 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(mand_decl,type,
% 0.31/0.47 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(mimplies_decl,type,
% 0.31/0.47 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(mbox_s4_decl,type,
% 0.31/0.47 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(iatom_decl,type,
% 0.31/0.47 iatom: ( $i > $o ) > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(inot_decl,type,
% 0.31/0.47 inot: ( $i > $o ) > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(itrue_decl,type,
% 0.31/0.47 itrue: $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(ifalse_decl,type,
% 0.31/0.47 ifalse: $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(iand_decl,type,
% 0.31/0.47 iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(ior_decl,type,
% 0.31/0.47 ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(iimplies_decl,type,
% 0.31/0.47 iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(iimplied_decl,type,
% 0.31/0.47 iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(iequiv_decl,type,
% 0.31/0.47 iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(ixor_decl,type,
% 0.31/0.47 ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(ivalid_decl,type,
% 0.31/0.47 ivalid: ( $i > $o ) > $o ).
% 0.31/0.47
% 0.31/0.47 thf(isatisfiable_decl,type,
% 0.31/0.47 isatisfiable: ( $i > $o ) > $o ).
% 0.31/0.47
% 0.31/0.47 thf(icountersatisfiable_decl,type,
% 0.31/0.47 icountersatisfiable: ( $i > $o ) > $o ).
% 0.31/0.47
% 0.31/0.47 thf(iinvalid_decl,type,
% 0.31/0.47 iinvalid: ( $i > $o ) > $o ).
% 0.31/0.47
% 0.31/0.47 %----Types of the domains
% 0.31/0.47 thf(d_unsorted_type,type,
% 0.31/0.47 d_unsorted: $tType ).
% 0.31/0.47
% 0.31/0.47 %----Types of the promotion functions
% 0.31/0.47 thf(d2unsorted_decl,type,
% 0.31/0.47 d2unsorted: d_unsorted > $i ).
% 0.31/0.47
% 0.31/0.47 %----Types of the domain elements
% 0.31/0.47 thf(d_unsorted_0_decl,type,
% 0.31/0.47 d_unsorted_0: d_unsorted ).
% 0.31/0.47
% 0.31/0.47 thf(lcl695_1,axiom,
% 0.31/0.47 ( ! [U: $i] :
% 0.31/0.47 ? [DU: d_unsorted] :
% 0.31/0.47 ( U
% 0.31/0.47 = ( d2unsorted @ DU ) )
% 0.31/0.47 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 0.31/0.47 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 0.31/0.47 ( ( ( d2unsorted @ DU1 )
% 0.31/0.47 = ( d2unsorted @ DU2 ) )
% 0.31/0.47 => ( DU1 = DU2 ) )
% 0.31/0.47 & ( mnot
% 0.31/0.47 = ( ^ [X: $i > $o,U: $i] :
% 0.31/0.47 ~ ( X @ U ) ) )
% 0.31/0.47 & ( mor
% 0.31/0.47 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.31/0.47 ( ( X @ U )
% 0.31/0.47 | ( Y @ U ) ) ) )
% 0.31/0.47 & ( mand
% 0.31/0.47 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.31/0.47 ( ( X @ U )
% 0.31/0.47 & ( Y @ U ) ) ) )
% 0.31/0.47 & ( mimplies
% 0.31/0.47 = ( ^ [U: $i > $o,V: $i > $o,Flatten_var_0: $i] :
% 0.31/0.47 ( ~ ( U @ Flatten_var_0 )
% 0.31/0.47 | ( V @ Flatten_var_0 ) ) ) )
% 0.31/0.47 & ( mbox_s4
% 0.31/0.47 = ( ^ [P: $i > $o,X: $i] :
% 0.31/0.47 ! [Y: $i] :
% 0.31/0.47 ( ~ ( irel @ X @ Y )
% 0.31/0.47 | ( P @ Y ) ) ) )
% 0.31/0.47 & ( iatom
% 0.31/0.47 = ( ^ [P: $i > $o,Flatten_var_0: $i] : ( P @ Flatten_var_0 ) ) )
% 0.31/0.47 & ( inot
% 0.31/0.47 = ( ^ [P: $i > $o,Flatten_var_0: $i] :
% 0.31/0.47 ~ ! [Y: $i] :
% 0.31/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.47 | ( P @ Y ) ) ) )
% 0.31/0.47 & ( iand
% 0.31/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.31/0.47 ( ( P @ Flatten_var_0 )
% 0.31/0.47 & ( Q @ Flatten_var_0 ) ) ) )
% 0.31/0.47 & ( ior
% 0.31/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.31/0.47 ( ! [Y: $i] :
% 0.31/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.47 | ( P @ Y ) )
% 0.31/0.47 | ! [Y: $i] :
% 0.31/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.47 | ( Q @ Y ) ) ) ) )
% 0.31/0.47 & ( iimplies
% 0.31/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.31/0.47 ( ~ ! [Y: $i] :
% 0.31/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.47 | ( P @ Y ) )
% 0.31/0.47 | ! [Y: $i] :
% 0.31/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.47 | ( Q @ Y ) ) ) ) )
% 0.31/0.47 & ( iimplied
% 0.31/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.31/0.47 ( ~ ! [Y: $i] :
% 0.31/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.47 | ( Q @ Y ) )
% 0.31/0.47 | ! [Y: $i] :
% 0.31/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.47 | ( P @ Y ) ) ) ) )
% 0.31/0.47 & ( iequiv
% 0.31/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.31/0.47 ( ( ~ ! [Y: $i] :
% 0.31/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.47 | ( P @ Y ) )
% 0.31/0.47 | ! [Y: $i] :
% 0.31/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.47 | ( Q @ Y ) ) )
% 0.31/0.47 & ( ~ ! [Y: $i] :
% 0.31/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.47 | ( Q @ Y ) )
% 0.31/0.47 | ! [Y: $i] :
% 0.31/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.47 | ( P @ Y ) ) ) ) ) )
% 0.31/0.47 & ( ixor
% 0.31/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.31/0.47 ~ ! [Y: $i,Bound_variable_747: $i,Bound_variable_754: $i] :
% 0.31/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.47 | ( ( ~ ! [Bound_variable_709: $i] :
% 0.31/0.47 ( ~ ( irel @ Y @ Bound_variable_709 )
% 0.31/0.47 | ( P @ Bound_variable_709 ) )
% 0.31/0.47 | ~ ( irel @ Y @ Bound_variable_747 )
% 0.31/0.47 | ( Q @ Bound_variable_747 ) )
% 0.31/0.47 & ( ~ ! [Bound_variable_717: $i] :
% 0.31/0.47 ( ~ ( irel @ Y @ Bound_variable_717 )
% 0.31/0.47 | ( Q @ Bound_variable_717 ) )
% 0.31/0.47 | ~ ( irel @ Y @ Bound_variable_754 )
% 0.31/0.47 | ( P @ Bound_variable_754 ) ) ) ) ) )
% 0.31/0.47 & ( ivalid
% 0.31/0.47 = ( ^ [Phi: $i > $o] :
% 0.31/0.47 ! [W: $i] : ( Phi @ W ) ) )
% 0.31/0.47 & ( isatisfiable
% 0.31/0.47 = ( ^ [Phi: $i > $o] :
% 0.31/0.47 ~ ! [W: $i] :
% 0.31/0.47 ~ ( Phi @ W ) ) )
% 0.31/0.47 & ( icountersatisfiable
% 0.31/0.47 = ( ^ [Phi: $i > $o] :
% 0.31/0.47 ~ ! [W: $i] : ( Phi @ W ) ) )
% 0.31/0.47 & ( iinvalid
% 0.31/0.47 = ( ^ [Phi: $i > $o] :
% 0.31/0.47 ! [W: $i] :
% 0.31/0.47 ~ ( Phi @ W ) ) )
% 0.31/0.47 & ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
% 0.31/0.47 & ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
% 0.31/0.47 & ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(ixor,conjecture,
% 0.31/0.47 ( ixor
% 0.31/0.47 = ( ^ [P: $i > $o,Q: $i > $o] : ( inot @ ( iequiv @ P @ Q ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.57/1.27 ---- Embedded in THF ---
% 1.57/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.57/1.27 %%% Generated on Tue May 05 09:19:59 EDT 2026
% 1.57/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.57/1.27 %%% Logic specification used:
% 1.57/1.27 %%% thf(spec, logic, $$dhol).
% 1.57/1.27
% 1.57/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.iSg9Oe0LVX/DTF2DTF27148.p
% See solution above
% 1.57/1.27 ------------------------
% 1.57/1.28 ---- Cleaned THF ---
% 1.57/1.29 thf(unsorted_type,type,
% 1.57/1.29 unsorted: $tType ).
% 1.57/1.29
% 1.57/1.29 thf(irel_decl,type,
% 1.57/1.29 irel: $i > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(mnot_decl,type,
% 1.57/1.29 mnot: ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(mor_decl,type,
% 1.57/1.29 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(mand_decl,type,
% 1.57/1.29 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(mimplies_decl,type,
% 1.57/1.29 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(mbox_s4_decl,type,
% 1.57/1.29 mbox_s4: ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(iatom_decl,type,
% 1.57/1.29 iatom: ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(inot_decl,type,
% 1.57/1.29 inot: ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(itrue_decl,type,
% 1.57/1.29 itrue: $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(ifalse_decl,type,
% 1.57/1.29 ifalse: $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(iand_decl,type,
% 1.57/1.29 iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(ior_decl,type,
% 1.57/1.29 ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(iimplies_decl,type,
% 1.57/1.29 iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(iimplied_decl,type,
% 1.57/1.29 iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(iequiv_decl,type,
% 1.57/1.29 iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(ixor_decl,type,
% 1.57/1.29 ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(ivalid_decl,type,
% 1.57/1.29 ivalid: ( $i > $o ) > $o ).
% 1.57/1.29
% 1.57/1.29 thf(isatisfiable_decl,type,
% 1.57/1.29 isatisfiable: ( $i > $o ) > $o ).
% 1.57/1.29
% 1.57/1.29 thf(icountersatisfiable_decl,type,
% 1.57/1.29 icountersatisfiable: ( $i > $o ) > $o ).
% 1.57/1.29
% 1.57/1.29 thf(iinvalid_decl,type,
% 1.57/1.29 iinvalid: ( $i > $o ) > $o ).
% 1.57/1.29
% 1.57/1.29 thf(d_unsorted_type,type,
% 1.57/1.29 d_unsorted: $tType ).
% 1.57/1.29
% 1.57/1.29 thf(d2unsorted_decl,type,
% 1.57/1.29 d2unsorted: d_unsorted > $i ).
% 1.57/1.29
% 1.57/1.29 thf(d_unsorted_0_decl,type,
% 1.57/1.29 d_unsorted_0: d_unsorted ).
% 1.57/1.29
% 1.57/1.29 thf(lcl695_1,axiom,
% 1.57/1.29 ( ! [U: $i] :
% 1.57/1.29 ? [DU: d_unsorted] :
% 1.57/1.29 ( U
% 1.57/1.29 = ( d2unsorted @ DU ) )
% 1.57/1.29 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 1.57/1.29 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 1.57/1.29 ( ( ( d2unsorted @ DU1 )
% 1.57/1.29 = ( d2unsorted @ DU2 ) )
% 1.57/1.29 => ( DU1 = DU2 ) )
% 1.57/1.29 & ( mnot
% 1.57/1.29 = ( ^ [X: $i > $o,U: $i] :
% 1.57/1.29 ~ ( X @ U ) ) )
% 1.57/1.29 & ( mor
% 1.57/1.29 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 1.57/1.29 ( ( X @ U )
% 1.57/1.29 | ( Y @ U ) ) ) )
% 1.57/1.29 & ( mand
% 1.57/1.29 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 1.57/1.29 ( ( X @ U )
% 1.57/1.29 & ( Y @ U ) ) ) )
% 1.57/1.29 & ( mimplies
% 1.57/1.29 = ( ^ [U: $i > $o,V: $i > $o,Flatten_var_0: $i] :
% 1.57/1.29 ( ~ ( U @ Flatten_var_0 )
% 1.57/1.29 | ( V @ Flatten_var_0 ) ) ) )
% 1.57/1.29 & ( mbox_s4
% 1.57/1.29 = ( ^ [P: $i > $o,X: $i] :
% 1.57/1.29 ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ X @ Y )
% 1.57/1.29 | ( P @ Y ) ) ) )
% 1.57/1.29 & ( iatom
% 1.57/1.29 = ( ^ [P: $i > $o,Flatten_var_0: $i] : ( P @ Flatten_var_0 ) ) )
% 1.57/1.29 & ( inot
% 1.57/1.29 = ( ^ [P: $i > $o,Flatten_var_0: $i] :
% 1.57/1.29 ~ ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( P @ Y ) ) ) )
% 1.57/1.29 & ( iand
% 1.57/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.57/1.29 ( ( P @ Flatten_var_0 )
% 1.57/1.29 & ( Q @ Flatten_var_0 ) ) ) )
% 1.57/1.29 & ( ior
% 1.57/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.57/1.29 ( ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( P @ Y ) )
% 1.57/1.29 | ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( Q @ Y ) ) ) ) )
% 1.57/1.29 & ( iimplies
% 1.57/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.57/1.29 ( ~ ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( P @ Y ) )
% 1.57/1.29 | ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( Q @ Y ) ) ) ) )
% 1.57/1.29 & ( iimplied
% 1.57/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.57/1.29 ( ~ ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( Q @ Y ) )
% 1.57/1.29 | ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( P @ Y ) ) ) ) )
% 1.57/1.29 & ( iequiv
% 1.57/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.57/1.29 ( ( ~ ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( P @ Y ) )
% 1.57/1.29 | ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( Q @ Y ) ) )
% 1.57/1.29 & ( ~ ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( Q @ Y ) )
% 1.57/1.29 | ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( P @ Y ) ) ) ) ) )
% 1.57/1.29 & ( ixor
% 1.57/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.57/1.29 ~ ! [Y: $i,Bound_variable_747: $i,Bound_variable_754: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( ( ~ ! [Bound_variable_709: $i] :
% 1.57/1.29 ( ~ ( irel @ Y @ Bound_variable_709 )
% 1.57/1.29 | ( P @ Bound_variable_709 ) )
% 1.57/1.29 | ~ ( irel @ Y @ Bound_variable_747 )
% 1.57/1.29 | ( Q @ Bound_variable_747 ) )
% 1.57/1.29 & ( ~ ! [Bound_variable_717: $i] :
% 1.57/1.29 ( ~ ( irel @ Y @ Bound_variable_717 )
% 1.57/1.29 | ( Q @ Bound_variable_717 ) )
% 1.57/1.29 | ~ ( irel @ Y @ Bound_variable_754 )
% 1.57/1.29 | ( P @ Bound_variable_754 ) ) ) ) ) )
% 1.57/1.29 & ( ivalid
% 1.57/1.29 = ( ^ [Phi: $i > $o] :
% 1.57/1.29 ! [W: $i] : ( Phi @ W ) ) )
% 1.57/1.29 & ( isatisfiable
% 1.57/1.29 = ( ^ [Phi: $i > $o] :
% 1.57/1.29 ~ ! [W: $i] :
% 1.57/1.29 ~ ( Phi @ W ) ) )
% 1.57/1.29 & ( icountersatisfiable
% 1.57/1.29 = ( ^ [Phi: $i > $o] :
% 1.57/1.29 ~ ! [W: $i] : ( Phi @ W ) ) )
% 1.57/1.29 & ( iinvalid
% 1.57/1.29 = ( ^ [Phi: $i > $o] :
% 1.57/1.29 ! [W: $i] :
% 1.57/1.29 ~ ( Phi @ W ) ) )
% 1.57/1.29 & ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
% 1.57/1.29 & ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
% 1.57/1.29 & ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ) ).
% 1.57/1.29
% 1.57/1.29 thf(ixor,conjecture,
% 1.57/1.29 ( ixor
% 1.57/1.29 = ( ^ [P: $i > $o,Q: $i > $o] : ( inot @ ( iequiv @ P @ Q ) ) ) ) ).
% 1.57/1.29 ------------------------
% 1.76/1.30 % (27248)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_27148 for (2999ds/27Mi)
% 1.76/1.30 % (27246)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27148 for (2999ds/183Mi)
% 1.76/1.31 % (27247)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_27148 for (2999ds/4Mi)
% 1.76/1.31 % (27249)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27148 for (2999ds/2Mi)
% 1.76/1.31 % (27250)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_27148 for (2999ds/2Mi)
% 1.76/1.31 % (27251)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_27148 for (2999ds/275Mi)
% 1.76/1.31 % (27249)Instruction limit reached!
% 1.76/1.31 % (27249)------------------------------
% 1.76/1.31 % (27249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.31 % (27249)Termination reason: Unknown
% 1.76/1.31 % (27249)Termination phase: shuffling
% 1.76/1.31
% 1.76/1.31 % (27249)Memory used [KB]: 1023
% 1.76/1.31 % (27249)Time elapsed: 0.003 s
% 1.76/1.31 % (27249)Instructions burned: 2 (million)
% 1.76/1.31 % (27249)------------------------------
% 1.76/1.31 % (27249)------------------------------
% 1.76/1.31 % (27250)Instruction limit reached!
% 1.76/1.31 % (27250)------------------------------
% 1.76/1.31 % (27250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.31 % (27250)Termination reason: Unknown
% 1.76/1.31 % (27250)Termination phase: shuffling
% 1.76/1.31
% 1.76/1.31 % (27250)Memory used [KB]: 1023
% 1.76/1.31 % (27250)Time elapsed: 0.003 s
% 1.76/1.31 % (27250)Instructions burned: 2 (million)
% 1.76/1.31 % (27250)------------------------------
% 1.76/1.31 % (27250)------------------------------
% 1.76/1.31 % (27247)Instruction limit reached!
% 1.76/1.31 % (27247)------------------------------
% 1.76/1.31 % (27247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.31 % (27247)Termination reason: Unknown
% 1.76/1.31 % (27247)Termination phase: Property scanning
% 1.76/1.31 % (27248)Instruction limit reached!
% 1.76/1.31 % (27248)------------------------------
% 1.76/1.31 % (27248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.31
% 1.76/1.31 % (27248)Termination reason: Unknown
% 1.76/1.31 % (27247)Memory used [KB]: 1023
% 1.76/1.31 % (27248)Termination phase: Saturation
% 1.76/1.31
% 1.76/1.31 % (27247)Time elapsed: 0.004 s
% 1.76/1.31 % (27248)Memory used [KB]: 5628
% 1.76/1.31 % (27247)Instructions burned: 4 (million)
% 1.76/1.31 % (27248)Time elapsed: 0.010 s
% 1.76/1.31 % (27248)Instructions burned: 28 (million)
% 1.76/1.31 % (27247)------------------------------
% 1.76/1.31 % (27247)------------------------------
% 1.76/1.31 % (27248)------------------------------
% 1.76/1.31 % (27248)------------------------------
% 1.76/1.31 % (27251)Refutation not found, incomplete strategy
% 1.76/1.31 % (27251)------------------------------
% 1.76/1.31 % (27251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.31 % (27251)Termination reason: Refutation not found, incomplete strategy
% 1.76/1.31
% 1.76/1.31
% 1.76/1.31 % (27251)Memory used [KB]: 5500
% 1.76/1.31 % (27251)Time elapsed: 0.005 s
% 1.76/1.31 % (27251)Instructions burned: 5 (million)
% 1.76/1.31 % (27251)------------------------------
% 1.76/1.31 % (27251)------------------------------
% 1.76/1.32 % (27256)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_27148 for (2999ds/3Mi)
% 1.76/1.32 % (27252)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27148 for (2999ds/18Mi)
% 1.76/1.32 % (27256)Instruction limit reached!
% 1.76/1.32 % (27256)------------------------------
% 1.76/1.32 % (27256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.32 % (27256)Termination reason: Unknown
% 1.76/1.32 % (27256)Termination phase: Preprocessing 3
% 1.76/1.32
% 1.76/1.32 % (27256)Memory used [KB]: 1023
% 1.76/1.32 % (27256)Time elapsed: 0.003 s
% 1.76/1.32 % (27256)Instructions burned: 4 (million)
% 1.76/1.32 % (27256)------------------------------
% 1.76/1.32 % (27256)------------------------------
% 1.76/1.32 % (27253)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27148 for (2999ds/3Mi)
% 1.76/1.32 % (27254)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_27148 for (2999ds/37Mi)
% 1.76/1.33 % (27255)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_27148 for (2999ds/15Mi)
% 1.76/1.33 % (27253)Instruction limit reached!
% 1.76/1.33 % (27253)------------------------------
% 1.76/1.33 % (27253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.33 % (27253)Termination reason: Unknown
% 1.76/1.33 % (27253)Termination phase: Preprocessing 2
% 1.76/1.33
% 1.76/1.33 % (27253)Memory used [KB]: 1023
% 1.76/1.33 % (27253)Time elapsed: 0.004 s
% 1.76/1.33 % (27253)Instructions burned: 4 (million)
% 1.76/1.33 % (27253)------------------------------
% 1.76/1.33 % (27253)------------------------------
% 1.76/1.33 % (27257)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_27148 for (2999ds/1041Mi)
% 1.76/1.33 % (27258)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27148 for (2999ds/7Mi)
% 1.76/1.33 % (27258)Instruction limit reached!
% 1.76/1.33 % (27258)------------------------------
% 1.76/1.33 % (27258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.33 % (27258)Termination reason: Unknown
% 1.76/1.33 % (27258)Termination phase: Saturation
% 1.76/1.33
% 1.76/1.33 % (27258)Memory used [KB]: 1023
% 1.76/1.33 % (27258)Time elapsed: 0.004 s
% 1.76/1.33 % (27258)Instructions burned: 8 (million)
% 1.76/1.33 % (27258)------------------------------
% 1.76/1.33 % (27258)------------------------------
% 1.76/1.33 % (27255)Instruction limit reached!
% 1.76/1.33 % (27255)------------------------------
% 1.76/1.33 % (27255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.33 % (27255)Termination reason: Unknown
% 1.76/1.33 % (27255)Termination phase: Saturation
% 1.76/1.33
% 1.76/1.33 % (27255)Memory used [KB]: 5756
% 1.76/1.33 % (27255)Time elapsed: 0.010 s
% 1.76/1.33 % (27255)Instructions burned: 15 (million)
% 1.76/1.33 % (27255)------------------------------
% 1.76/1.33 % (27255)------------------------------
% 1.76/1.34 % (27252)Instruction limit reached!
% 1.76/1.34 % (27252)------------------------------
% 1.76/1.34 % (27252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.34 % (27252)Termination reason: Unknown
% 1.76/1.34 % (27252)Termination phase: Saturation
% 1.76/1.34
% 1.76/1.34 % (27252)Memory used [KB]: 5628
% 1.76/1.34 % (27252)Time elapsed: 0.019 s
% 1.76/1.34 % (27252)Instructions burned: 18 (million)
% 1.76/1.34 % (27252)------------------------------
% 1.76/1.34 % (27252)------------------------------
% 1.76/1.34 % (27260)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_27148 for (2999ds/3Mi)
% 1.76/1.34 % (27260)Instruction limit reached!
% 1.76/1.34 % (27260)------------------------------
% 1.76/1.34 % (27260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.34 % (27260)Termination reason: Unknown
% 1.76/1.34 % (27260)Termination phase: SInE selection
% 1.76/1.34
% 1.76/1.34 % (27260)Memory used [KB]: 1023
% 1.76/1.34 % (27260)Time elapsed: 0.003 s
% 1.76/1.34 % (27260)Instructions burned: 5 (million)
% 1.76/1.34 % (27260)------------------------------
% 1.76/1.34 % (27260)------------------------------
% 1.76/1.34 % (27259)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27148 for (2999ds/16Mi)
% 1.76/1.34 % (27254)Instruction limit reached!
% 1.76/1.34 % (27254)------------------------------
% 1.76/1.34 % (27254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.34 % (27254)Termination reason: Unknown
% 1.76/1.34 % (27254)Termination phase: Saturation
% 1.76/1.34
% 1.76/1.34 % (27254)Memory used [KB]: 5628
% 1.76/1.34 % (27254)Time elapsed: 0.022 s
% 1.76/1.34 % (27254)Instructions burned: 37 (million)
% 1.76/1.34 % (27254)------------------------------
% 1.76/1.34 % (27254)------------------------------
% 1.76/1.35 % (27262)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27148 for (2999ds/7Mi)
% 1.76/1.35 % (27262)Instruction limit reached!
% 1.76/1.35 % (27262)------------------------------
% 1.76/1.35 % (27262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.35 % (27262)Termination reason: Unknown
% 1.76/1.35 % (27262)Termination phase: Saturation
% 1.76/1.35
% 1.76/1.35 % (27262)Memory used [KB]: 1023
% 1.76/1.35 % (27262)Time elapsed: 0.003 s
% 1.76/1.35 % (27262)Instructions burned: 7 (million)
% 1.76/1.35 % (27262)------------------------------
% 1.76/1.35 % (27262)------------------------------
% 1.76/1.35 % (27261)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_27148 for (2999ds/3Mi)
% 1.76/1.35 % (27261)Instruction limit reached!
% 1.76/1.35 % (27261)------------------------------
% 1.76/1.35 % (27261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.35 % (27261)Termination reason: Unknown
% 1.76/1.35 % (27261)Termination phase: Property scanning
% 1.76/1.35
% 1.76/1.35 % (27261)Memory used [KB]: 1023
% 1.76/1.35 % (27261)Time elapsed: 0.004 s
% 1.76/1.35 % (27261)Instructions burned: 4 (million)
% 1.76/1.35 % (27261)------------------------------
% 1.76/1.35 % (27261)------------------------------
% 1.76/1.35 % (27263)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_27148 for (2999ds/3Mi)
% 1.76/1.35 % (27259)Instruction limit reached!
% 1.76/1.35 % (27259)------------------------------
% 1.76/1.35 % (27259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.35 % (27259)Termination reason: Unknown
% 1.76/1.35 % (27259)Termination phase: Saturation
% 1.76/1.35
% 1.76/1.35 % (27259)Memory used [KB]: 5756
% 1.76/1.35 % (27259)Time elapsed: 0.012 s
% 1.76/1.35 % (27259)Instructions burned: 16 (million)
% 1.76/1.35 % (27259)------------------------------
% 1.76/1.35 % (27259)------------------------------
% 1.76/1.35 % (27263)Instruction limit reached!
% 1.76/1.35 % (27263)------------------------------
% 1.76/1.35 % (27263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.35 % (27263)Termination reason: Unknown
% 1.76/1.35 % (27263)Termination phase: Property scanning
% 1.76/1.35
% 1.76/1.35 % (27263)Memory used [KB]: 1023
% 1.76/1.35 % (27263)Time elapsed: 0.003 s
% 1.76/1.35 % (27263)Instructions burned: 4 (million)
% 1.76/1.35 % (27263)------------------------------
% 1.76/1.35 % (27263)------------------------------
% 1.76/1.36 % (27246)First to succeed.
% 1.76/1.36 % (27265)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_27148 for (2999ds/18Mi)
% 1.76/1.36 % (27264)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_27148 for (2999ds/4Mi)
% 1.76/1.36 % (27265)Instruction limit reached!
% 1.76/1.36 % (27265)------------------------------
% 1.76/1.36 % (27265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.36 % (27265)Termination reason: Unknown
% 1.76/1.36 % (27265)Termination phase: Saturation
% 1.76/1.36
% 1.76/1.36 % (27265)Memory used [KB]: 5628
% 1.76/1.36 % (27265)Time elapsed: 0.007 s
% 1.76/1.36 % (27265)Instructions burned: 18 (million)
% 1.76/1.36 % (27265)------------------------------
% 1.76/1.36 % (27265)------------------------------
% 1.76/1.36 % (27264)Instruction limit reached!
% 1.76/1.36 % (27264)------------------------------
% 1.76/1.36 % (27264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.36 % (27264)Termination reason: Unknown
% 1.76/1.36 % (27264)Termination phase: Property scanning
% 1.76/1.36
% 1.76/1.36 % (27264)Memory used [KB]: 1023
% 1.76/1.36 % (27264)Time elapsed: 0.004 s
% 1.76/1.36 % (27264)Instructions burned: 4 (million)
% 1.76/1.36 % (27264)------------------------------
% 1.76/1.36 % (27264)------------------------------
% 1.76/1.36 % (27267)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27148 for (2999ds/6Mi)
% 1.76/1.37 % (27267)Instruction limit reached!
% 1.76/1.37 % (27267)------------------------------
% 1.76/1.37 % (27267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.37 % (27267)Termination reason: Unknown
% 1.76/1.37 % (27267)Termination phase: Saturation
% 1.76/1.37
% 1.76/1.37 % (27267)Memory used [KB]: 5500
% 1.76/1.37 % (27267)Time elapsed: 0.004 s
% 1.76/1.37 % (27267)Instructions burned: 8 (million)
% 1.76/1.37 % (27267)------------------------------
% 1.76/1.37 % (27267)------------------------------
% 1.76/1.37 % (27246)Refutation found. Thanks to Tanya!
% 1.76/1.37 % SZS status Theorem for DTF2THF_27148
% 1.76/1.37 % SZS output start Proof for DTF2THF_27148
% 1.76/1.37 thf(type_def_6, type, d_unsorted: $tType).
% 1.76/1.37 thf(func_def_0, type, unsorted: $tType).
% 1.76/1.37 thf(func_def_1, type, irel: $i > $i > $o).
% 1.76/1.37 thf(func_def_2, type, mnot: ($i > $o) > $i > $o).
% 1.76/1.37 thf(func_def_3, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 1.76/1.37 thf(func_def_4, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 1.76/1.37 thf(func_def_5, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 1.76/1.37 thf(func_def_6, type, mbox_s4: ($i > $o) > $i > $o).
% 1.76/1.37 thf(func_def_7, type, iatom: ($i > $o) > $i > $o).
% 1.76/1.37 thf(func_def_8, type, inot: ($i > $o) > $i > $o).
% 1.76/1.37 thf(func_def_9, type, itrue: $i > $o).
% 1.76/1.37 thf(func_def_10, type, ifalse: $i > $o).
% 1.76/1.37 thf(func_def_11, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 1.76/1.37 thf(func_def_12, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 1.76/1.37 thf(func_def_13, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 1.76/1.37 thf(func_def_14, type, iimplied: ($i > $o) > ($i > $o) > $i > $o).
% 1.76/1.37 thf(func_def_15, type, iequiv: ($i > $o) > ($i > $o) > $i > $o).
% 1.76/1.37 thf(func_def_16, type, ixor: ($i > $o) > ($i > $o) > $i > $o).
% 1.76/1.37 thf(func_def_17, type, ivalid: ($i > $o) > $o).
% 1.76/1.37 thf(func_def_18, type, isatisfiable: ($i > $o) > $o).
% 1.76/1.37 thf(func_def_19, type, icountersatisfiable: ($i > $o) > $o).
% 1.76/1.37 thf(func_def_20, type, iinvalid: ($i > $o) > $o).
% 1.76/1.37 thf(func_def_21, type, d_unsorted: $tType).
% 1.76/1.37 thf(func_def_22, type, d2unsorted: d_unsorted > $i).
% 1.76/1.37 thf(func_def_23, type, d_unsorted_0: d_unsorted).
% 1.76/1.37 thf(func_def_39, type, sK0: $i > d_unsorted).
% 1.76/1.37 thf(func_def_41, type, ph2: !>[X0: $tType]:(X0)).
% 1.76/1.37 thf(func_def_42, type, sK3: $i > $o).
% 1.76/1.37 thf(func_def_43, type, sK4: $i > $o).
% 1.76/1.37 thf(func_def_45, type, sK6: $i > $i).
% 1.76/1.37 thf(func_def_46, type, sK7: $i > $i).
% 1.76/1.37 thf(func_def_47, type, sK8: $i > $i).
% 1.76/1.37 thf(func_def_48, type, sK9: $i > $i).
% 1.76/1.37 thf(func_def_49, type, sK10: $i > $i).
% 1.76/1.37 thf(func_def_50, type, sK11: $i > $i).
% 1.76/1.37 thf(func_def_51, type, sK12: $i > $i).
% 1.76/1.37 thf(func_def_52, type, sK13: $i > $i).
% 1.76/1.37 thf(func_def_53, type, sK14: $i > $i).
% 1.76/1.37 thf(func_def_54, type, sK15: $i > $i).
% 1.76/1.37 thf(f1804,plain,(
% 1.76/1.37 $false),
% 1.76/1.37 inference(avatar_sat_refutation,[status(thm)],[f997,f1038,f1087,f1235,f1300,f1422,f1559,f1567,f1569,f1571,f1576,f1608,f1612,f1634,f1648,f1650,f1671,f1751,f1758,f1760,f1762,f1771,f1803])).
% 1.76/1.37 thf(f1803,plain,(
% 1.76/1.37 ~spl1_7 | ~spl1_62),
% 1.76/1.37 inference(avatar_contradiction_clause,[status(thm)],[f1802])).
% 1.76/1.37 thf(f1802,plain,(
% 1.76/1.37 $false | (~spl1_7 | ~spl1_62)),
% 1.76/1.37 inference(trivial_inequality_removal,[status(thm)],[f1798])).
% 1.76/1.37 thf(f1798,plain,(
% 1.76/1.37 ($false = $true) | (~spl1_7 | ~spl1_62)),
% 1.76/1.37 inference(superposition,[status(thm)],[f1781,f1015])).
% 1.76/1.37 thf(f1015,plain,(
% 1.76/1.37 ($false = (sK4 @ sK17)) | ~spl1_7),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1013])).
% 1.76/1.37 thf(f1013,definition,(
% 1.76/1.37 spl1_7 <=> ($false = (sK4 @ sK17))),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition])).
% 1.76/1.37 thf(f1781,plain,(
% 1.76/1.37 ( ! [X0 : $i] : (((sK4 @ X0) = $true)) ) | ~spl1_62),
% 1.76/1.37 inference(superposition,[status(thm)],[f1421,f55])).
% 1.76/1.37 thf(f55,plain,(
% 1.76/1.37 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 1.76/1.37 inference(superposition,[status(thm)],[f25,f49])).
% 1.76/1.37 thf(f49,plain,(
% 1.76/1.37 ( ! [X0 : $i,X1 : d_unsorted] : (((d2unsorted @ X1) = X0)) )),
% 1.76/1.37 inference(superposition,[status(thm)],[f25,f42])).
% 1.76/1.37 thf(f42,plain,(
% 1.76/1.37 ( ! [X0 : d_unsorted,X1 : d_unsorted] : ((X0 = X1)) )),
% 1.76/1.37 inference(superposition,[status(thm)],[f29,f29])).
% 1.76/1.37 thf(f29,plain,(
% 1.76/1.37 ( ! [X0 : d_unsorted] : ((d_unsorted_0 = X0)) )),
% 1.76/1.37 inference(cnf_transformation,[status(thm)],[f15])).
% 1.76/1.37 thf(f15,plain,(
% 1.76/1.37 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ! [X1 : $i] : ((d2unsorted @ (sK0 @ X1)) = X1) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (ixor = (^[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 @ Y4 @ Y3))) | (Y1 @ Y3)) & (((~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y5))) | (Y0 @ Y5))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & ! [X3 : d_unsorted,X4 : d_unsorted] : (((d2unsorted @ X3) != (d2unsorted @ X4)) | (X3 = X4)) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.76/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14])).
% 1.76/1.37 thf(f14,plain,(
% 1.76/1.37 ! [X1 : $i] : (? [X2 : d_unsorted] : ((d2unsorted @ X2) = X1) => ((d2unsorted @ (sK0 @ X1)) = X1))),
% 1.76/1.37 introduced(definition,[],[choice_axiom])).
% 1.76/1.37 thf(f13,plain,(
% 1.76/1.37 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ! [X1 : $i] : ? [X2 : d_unsorted] : ((d2unsorted @ X2) = X1) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (ixor = (^[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 @ Y4 @ Y3))) | (Y1 @ Y3)) & (((~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y5))) | (Y0 @ Y5))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & ! [X3 : d_unsorted,X4 : d_unsorted] : (((d2unsorted @ X3) != (d2unsorted @ X4)) | (X3 = X4)) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.76/1.37 inference(rectify,[status(thm)],[f12])).
% 1.76/1.37 thf(f12,plain,(
% 1.76/1.37 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ! [X2 : $i] : ? [X3 : d_unsorted] : ((d2unsorted @ X3) = X2) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (ixor = (^[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 @ Y4 @ Y3))) | (Y1 @ Y3)) & (((~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y5))) | (Y0 @ Y5))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & ! [X0 : d_unsorted,X1 : d_unsorted] : (((d2unsorted @ X1) != (d2unsorted @ X0)) | (X0 = X1)) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.76/1.37 inference(ennf_transformation,[status(thm)],[f11])).
% 1.76/1.37 thf(f11,plain,(
% 1.76/1.37 (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (ixor = (^[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 @ Y4 @ Y3))) | (Y1 @ Y3)) & (((~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y5))) | (Y0 @ Y5))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & ! [X2 : $i] : ? [X3 : d_unsorted] : ((d2unsorted @ X3) = X2) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : (((d2unsorted @ X1) = (d2unsorted @ X0)) => (X0 = X1))),
% 1.76/1.37 inference(flattening,[status(thm)],[f10])).
% 1.76/1.37 thf(f10,plain,(
% 1.76/1.37 ! [X0 : d_unsorted,X1 : d_unsorted] : (((d2unsorted @ X1) = (d2unsorted @ X0)) => (X0 = X1)) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ! [X2 : $i] : ? [X3 : d_unsorted] : ((d2unsorted @ X3) = X2) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & ~((ifalse @ (d2unsorted @ d_unsorted_0)) = $true) & ((itrue @ (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]: ((Y0 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) & (((~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y5))) | (Y0 @ Y5))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2)))))))))),
% 1.76/1.37 inference(rectify,[status(thm)],[f8])).
% 1.76/1.37 thf(f8,plain,(
% 1.76/1.37 ! [X0 : d_unsorted,X1 : d_unsorted] : (((d2unsorted @ X1) = (d2unsorted @ X0)) => (X0 = X1)) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ! [X9 : $i] : ? [X10 : d_unsorted] : ((d2unsorted @ X10) = X9) & ! [X11 : d_unsorted] : (d_unsorted_0 = X11) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & ~((ifalse @ (d2unsorted @ d_unsorted_0)) = $true) & ((itrue @ (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]: ((Y0 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) & (((~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y5))) | (Y0 @ Y5))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2)))))))))),
% 1.76/1.37 inference(fool_elimination,[status(thm)],[f7])).
% 1.76/1.37 thf(f7,plain,(
% 1.76/1.37 ! [X0 : d_unsorted,X1 : d_unsorted] : (((d2unsorted @ X1) = (d2unsorted @ X0)) => (X0 = X1)) & (ivalid = (^[X2 : $i > $o] : (! [X3 : $i] : (X2 @ X3)))) & (isatisfiable = (^[X4 : $i > $o] : (~! [X5 : $i] : ~(X4 @ X5)))) & (iand = (^[X6 : $i > $o, X7 : $i > $o, X8 : $i] : ((X6 @ X8) & (X7 @ X8)))) & ! [X9 : $i] : ? [X10 : d_unsorted] : ((d2unsorted @ X10) = X9) & ! [X11 : d_unsorted] : (d_unsorted_0 = X11) & ((^[X12 : $i > $o, X13 : $i > $o, X14 : $i] : ((~! [X15 : $i] : ((X13 @ X15) | ~(irel @ X14 @ X15)) | ! [X16 : $i] : ((X12 @ X16) | ~(irel @ X14 @ X16))) & (~! [X17 : $i] : (~(irel @ X14 @ X17) | (X12 @ X17)) | ! [X18 : $i] : ((X13 @ X18) | ~(irel @ X14 @ X18))))) = iequiv) & (mnot = (^[X19 : $i > $o, X20 : $i] : (~(X19 @ X20)))) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & (icountersatisfiable = (^[X21 : $i > $o] : (~! [X22 : $i] : (X21 @ X22)))) & (mand = (^[X23 : $i > $o, X24 : $i > $o, X25 : $i] : ((X23 @ X25) & (X24 @ X25)))) & (inot = (^[X26 : $i > $o, X27 : $i] : (~! [X28 : $i] : ((X26 @ X28) | ~(irel @ X27 @ X28))))) & (mor = (^[X29 : $i > $o, X30 : $i > $o, X31 : $i] : ((X29 @ X31) | (X30 @ X31)))) & (mbox_s4 = (^[X32 : $i > $o, X33 : $i] : (! [X34 : $i] : ((X32 @ X34) | ~(irel @ X33 @ X34))))) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (itrue @ (d2unsorted @ d_unsorted_0)) & ((^[X35 : $i > $o, X36 : $i > $o, X37 : $i] : (~! [X38 : $i,X39 : $i,X40 : $i] : (~(irel @ X37 @ X39) | (((X35 @ X38) | ~(irel @ X39 @ X38) | ~! [X41 : $i] : (~(irel @ X39 @ X41) | (X36 @ X41))) & ((X36 @ X40) | ~(irel @ X39 @ X40) | ~! [X42 : $i] : (~(irel @ X39 @ X42) | (X35 @ X42))))))) = ixor) & (iatom = (^[X43 : $i > $o, X44 : $i] : (X43 @ X44))) & ((^[X45 : $i > $o, X46 : $i > $o, X47 : $i] : (~! [X48 : $i] : (~(irel @ X47 @ X48) | (X46 @ X48)) | ! [X49 : $i] : (~(irel @ X47 @ X49) | (X45 @ X49)))) = iimplied) & (iimplies = (^[X50 : $i > $o, X51 : $i > $o, X52 : $i] : (~! [X53 : $i] : ((X50 @ X53) | ~(irel @ X52 @ X53)) | ! [X54 : $i] : (~(irel @ X52 @ X54) | (X51 @ X54))))) & (iinvalid = (^[X55 : $i > $o] : (! [X56 : $i] : ~(X55 @ X56)))) & (ior = (^[X57 : $i > $o, X58 : $i > $o, X59 : $i] : (! [X60 : $i] : (~(irel @ X59 @ X60) | (X57 @ X60)) | ! [X61 : $i] : (~(irel @ X59 @ X61) | (X58 @ X61))))) & ((^[X62 : $i > $o, X63 : $i > $o, X64 : $i] : (~(X62 @ X64) | (X63 @ X64))) = mimplies)),
% 1.76/1.37 inference(rectify,[status(thm)],[f1])).
% 1.76/1.37 thf(f1,axiom,(
% 1.76/1.37 ! [X3 : d_unsorted,X2 : d_unsorted] : (((d2unsorted @ X2) = (d2unsorted @ X3)) => (X2 = X3)) & (ivalid = (^[X14 : $i > $o] : (! [X15 : $i] : (X14 @ X15)))) & (isatisfiable = (^[X14 : $i > $o] : (~! [X15 : $i] : ~(X14 @ X15)))) & (iand = (^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : ((X8 @ X7) & (X9 @ X7)))) & ! [X0 : $i] : ? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0) & ! [X1 : d_unsorted] : (d_unsorted_0 = X1) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : ((~! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5))) & (~! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)) | ! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5))))) = iequiv) & (mnot = (^[X4 : $i > $o, X0 : $i] : (~(X4 @ X0)))) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & (icountersatisfiable = (^[X14 : $i > $o] : (~! [X15 : $i] : (X14 @ X15)))) & (mand = (^[X4 : $i > $o, X5 : $i > $o, X0 : $i] : ((X4 @ X0) & (X5 @ X0)))) & (inot = (^[X8 : $i > $o, X7 : $i] : (~! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5))))) & (mor = (^[X4 : $i > $o, X5 : $i > $o, X0 : $i] : ((X4 @ X0) | (X5 @ X0)))) & (mbox_s4 = (^[X8 : $i > $o, X4 : $i] : (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X4 @ X5))))) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (itrue @ (d2unsorted @ d_unsorted_0)) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (~! [X11 : $i,X5 : $i,X10 : $i] : (~(irel @ X7 @ X5) | (((X8 @ X11) | ~(irel @ X5 @ X11) | ~! [X13 : $i] : (~(irel @ X5 @ X13) | (X9 @ X13))) & ((X9 @ X10) | ~(irel @ X5 @ X10) | ~! [X12 : $i] : (~(irel @ X5 @ X12) | (X8 @ X12))))))) = ixor) & (iatom = (^[X8 : $i > $o, X7 : $i] : (X8 @ X7))) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (~! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)) | ! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)))) = iimplied) & (iimplies = (^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (~! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5))))) & (iinvalid = (^[X14 : $i > $o] : (! [X15 : $i] : ~(X14 @ X15)))) & (ior = (^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)) | ! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5))))) & ((^[X0 : $i > $o, X6 : $i > $o, X7 : $i] : (~(X0 @ X7) | (X6 @ X7))) = mimplies)),
% 1.76/1.37 file('/export/starexec/sandbox2/tmp/tmp.iSg9Oe0LVX/DTF2THF_27148.p',lcl695_1)).
% 1.76/1.37 thf(f25,plain,(
% 1.76/1.37 ( ! [X1 : $i] : (((d2unsorted @ (sK0 @ X1)) = X1)) )),
% 1.76/1.37 inference(cnf_transformation,[status(thm)],[f15])).
% 1.76/1.37 thf(f1421,plain,(
% 1.76/1.37 ((sK4 @ sK5) = $true) | ~spl1_62),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1419])).
% 1.76/1.37 thf(f1419,definition,(
% 1.76/1.37 spl1_62 <=> ((sK4 @ sK5) = $true)),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_62])],[avatar_definition])).
% 1.76/1.37 thf(f1771,plain,(
% 1.76/1.37 spl1_6 | ~spl1_60),
% 1.76/1.37 inference(avatar_contradiction_clause,[status(thm)],[f1770])).
% 1.76/1.37 thf(f1770,plain,(
% 1.76/1.37 $false | (spl1_6 | ~spl1_60)),
% 1.76/1.37 inference(subsumption_resolution,[status(thm)],[f1010,f1697])).
% 1.76/1.37 thf(f1697,plain,(
% 1.76/1.37 ( ! [X0 : $i] : (($false = (sK3 @ X0))) ) | ~spl1_60),
% 1.76/1.37 inference(superposition,[status(thm)],[f1410,f55])).
% 1.76/1.37 thf(f1410,plain,(
% 1.76/1.37 ($false = (sK3 @ (sK6 @ sK5))) | ~spl1_60),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1408])).
% 1.76/1.37 thf(f1408,definition,(
% 1.76/1.37 spl1_60 <=> ($false = (sK3 @ (sK6 @ sK5)))),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_60])],[avatar_definition])).
% 1.76/1.37 thf(f1010,plain,(
% 1.76/1.37 ((sK3 @ sK21) != $false) | spl1_6),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1009])).
% 1.76/1.37 thf(f1009,definition,(
% 1.76/1.37 spl1_6 <=> ((sK3 @ sK21) = $false)),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition])).
% 1.76/1.37 thf(f1762,plain,(
% 1.76/1.37 spl1_6 | ~spl1_63),
% 1.76/1.37 inference(avatar_contradiction_clause,[status(thm)],[f1761])).
% 1.76/1.37 thf(f1761,plain,(
% 1.76/1.37 $false | (spl1_6 | ~spl1_63)),
% 1.76/1.37 inference(subsumption_resolution,[status(thm)],[f1010,f1702])).
% 1.76/1.37 thf(f1702,plain,(
% 1.76/1.37 ( ! [X0 : $i] : (($false = (sK3 @ X0))) ) | ~spl1_63),
% 1.76/1.37 inference(superposition,[status(thm)],[f1575,f55])).
% 1.76/1.37 thf(f1575,plain,(
% 1.76/1.37 ($false = (sK3 @ (sK7 @ sK5))) | ~spl1_63),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1573])).
% 1.76/1.37 thf(f1573,definition,(
% 1.76/1.37 spl1_63 <=> ($false = (sK3 @ (sK7 @ sK5)))),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_63])],[avatar_definition])).
% 1.76/1.37 thf(f1760,plain,(
% 1.76/1.37 spl1_7 | ~spl1_14),
% 1.76/1.37 inference(avatar_contradiction_clause,[status(thm)],[f1759])).
% 1.76/1.37 thf(f1759,plain,(
% 1.76/1.37 $false | (spl1_7 | ~spl1_14)),
% 1.76/1.37 inference(subsumption_resolution,[status(thm)],[f1068,f1642])).
% 1.76/1.37 thf(f1642,plain,(
% 1.76/1.37 ( ! [X0 : $i] : (((sK4 @ X0) != $false)) ) | spl1_7),
% 1.76/1.37 inference(superposition,[status(thm)],[f1014,f55])).
% 1.76/1.37 thf(f1014,plain,(
% 1.76/1.37 ($false != (sK4 @ sK17)) | spl1_7),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1013])).
% 1.76/1.37 thf(f1068,plain,(
% 1.76/1.37 ((sK4 @ sK22) = $false) | ~spl1_14),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1066])).
% 1.76/1.37 thf(f1066,definition,(
% 1.76/1.37 spl1_14 <=> ((sK4 @ sK22) = $false)),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_14])],[avatar_definition])).
% 1.76/1.37 thf(f1758,plain,(
% 1.76/1.37 spl1_7 | ~spl1_39 | spl1_61 | spl1_68),
% 1.76/1.37 inference(avatar_contradiction_clause,[status(thm)],[f1757])).
% 1.76/1.37 thf(f1757,plain,(
% 1.76/1.37 $false | (spl1_7 | ~spl1_39 | spl1_61 | spl1_68)),
% 1.76/1.37 inference(subsumption_resolution,[status(thm)],[f1416,f1734])).
% 1.76/1.37 thf(f1734,plain,(
% 1.76/1.37 ( ! [X0 : $i] : (($false = (irel @ sK5 @ X0))) ) | (spl1_7 | ~spl1_39 | spl1_68)),
% 1.76/1.37 inference(trivial_inequality_removal,[status(thm)],[f1727])).
% 1.76/1.37 thf(f1727,plain,(
% 1.76/1.37 ( ! [X0 : $i] : (($false = $true) | ($false = (irel @ sK5 @ X0))) ) | (spl1_7 | ~spl1_39 | spl1_68)),
% 1.76/1.37 inference(superposition,[status(thm)],[f91,f1721])).
% 1.76/1.37 thf(f1721,plain,(
% 1.76/1.37 ( ! [X4 : $i,X5 : $i] : (($false = (irel @ sK5 @ X4)) | ((irel @ X4 @ X5) = $false)) ) | (spl1_7 | ~spl1_39 | spl1_68)),
% 1.76/1.37 inference(subsumption_resolution,[status(thm)],[f1720,f1642])).
% 1.76/1.37 thf(f1720,plain,(
% 1.76/1.37 ( ! [X4 : $i,X5 : $i] : (($false = (irel @ sK5 @ X4)) | ((irel @ X4 @ X5) = $false) | ((sK4 @ (sK15 @ X4)) = $false)) ) | (~spl1_39 | spl1_68)),
% 1.76/1.37 inference(subsumption_resolution,[status(thm)],[f1234,f1652])).
% 1.76/1.37 thf(f1652,plain,(
% 1.76/1.37 ( ! [X0 : $i] : (((sK3 @ X0) != $true)) ) | spl1_68),
% 1.76/1.37 inference(superposition,[status(thm)],[f1632,f55])).
% 1.76/1.37 thf(f1632,plain,(
% 1.76/1.37 ((sK3 @ sK5) != $true) | spl1_68),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1631])).
% 1.76/1.37 thf(f1631,definition,(
% 1.76/1.37 spl1_68 <=> ((sK3 @ sK5) = $true)),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_68])],[avatar_definition])).
% 1.76/1.37 thf(f1234,plain,(
% 1.76/1.37 ( ! [X4 : $i,X5 : $i] : (((sK3 @ X5) = $true) | ((irel @ X4 @ X5) = $false) | ($false = (irel @ sK5 @ X4)) | ((sK4 @ (sK15 @ X4)) = $false)) ) | ~spl1_39),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1233])).
% 1.76/1.37 thf(f1233,definition,(
% 1.76/1.37 spl1_39 <=> ! [X4 : $i,X5 : $i] : (((sK4 @ (sK15 @ X4)) = $false) | ($false = (irel @ sK5 @ X4)) | ((sK3 @ X5) = $true) | ((irel @ X4 @ X5) = $false))),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_39])],[avatar_definition])).
% 1.76/1.37 thf(f91,plain,(
% 1.76/1.37 ( ! [X0 : $i] : (((irel @ X0 @ X0) = $true)) )),
% 1.76/1.37 inference(superposition,[status(thm)],[f27,f55])).
% 1.76/1.37 thf(f27,plain,(
% 1.76/1.37 ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true)),
% 1.76/1.37 inference(cnf_transformation,[status(thm)],[f15])).
% 1.76/1.37 thf(f1416,plain,(
% 1.76/1.37 ($false != (irel @ sK5 @ sK5)) | spl1_61),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1415])).
% 1.76/1.37 thf(f1415,definition,(
% 1.76/1.37 spl1_61 <=> ($false = (irel @ sK5 @ sK5))),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_61])],[avatar_definition])).
% 1.76/1.37 thf(f1751,plain,(
% 1.76/1.37 ~spl1_61),
% 1.76/1.37 inference(avatar_contradiction_clause,[status(thm)],[f1750])).
% 1.76/1.37 thf(f1750,plain,(
% 1.76/1.37 $false | ~spl1_61),
% 1.76/1.37 inference(trivial_inequality_removal,[status(thm)],[f1745])).
% 1.76/1.37 thf(f1745,plain,(
% 1.76/1.37 ($false = $true) | ~spl1_61),
% 1.76/1.37 inference(superposition,[status(thm)],[f91,f1417])).
% 1.76/1.37 thf(f1417,plain,(
% 1.76/1.37 ($false = (irel @ sK5 @ sK5)) | ~spl1_61),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1415])).
% 1.76/1.37 thf(f1671,plain,(
% 1.76/1.37 ~spl1_2 | spl1_68),
% 1.76/1.37 inference(avatar_contradiction_clause,[status(thm)],[f1670])).
% 1.76/1.37 thf(f1670,plain,(
% 1.76/1.37 $false | (~spl1_2 | spl1_68)),
% 1.76/1.37 inference(subsumption_resolution,[status(thm)],[f1659,f1652])).
% 1.76/1.37 thf(f1659,plain,(
% 1.76/1.37 ((sK3 @ sK16) = $true) | ~spl1_2),
% 1.76/1.37 inference(trivial_inequality_removal,[status(thm)],[f1657])).
% 1.76/1.37 thf(f1657,plain,(
% 1.76/1.37 ((sK3 @ sK16) = $true) | ($false = $true) | ~spl1_2),
% 1.76/1.37 inference(superposition,[status(thm)],[f91,f992])).
% 1.76/1.37 thf(f992,plain,(
% 1.76/1.37 ( ! [X1 : $i] : (((irel @ sK16 @ X1) = $false) | ((sK3 @ X1) = $true)) ) | ~spl1_2),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f991])).
% 1.76/1.37 thf(f991,definition,(
% 1.76/1.37 spl1_2 <=> ! [X1 : $i] : (((sK3 @ X1) = $true) | ((irel @ sK16 @ X1) = $false))),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.76/1.37 thf(f1650,plain,(
% 1.76/1.37 spl1_7 | ~spl1_65),
% 1.76/1.37 inference(avatar_contradiction_clause,[status(thm)],[f1649])).
% 1.76/1.37 thf(f1649,plain,(
% 1.76/1.37 $false | (spl1_7 | ~spl1_65)),
% 1.76/1.37 inference(subsumption_resolution,[status(thm)],[f1618,f1642])).
% 1.76/1.37 thf(f1618,plain,(
% 1.76/1.37 ($false = (sK4 @ (sK11 @ sK5))) | ~spl1_65),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1616])).
% 1.76/1.37 thf(f1616,definition,(
% 1.76/1.37 spl1_65 <=> ($false = (sK4 @ (sK11 @ sK5)))),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_65])],[avatar_definition])).
% 1.76/1.37 thf(f1648,plain,(
% 1.76/1.37 ~spl1_6 | ~spl1_68),
% 1.76/1.37 inference(avatar_contradiction_clause,[status(thm)],[f1647])).
% 1.76/1.37 thf(f1647,plain,(
% 1.76/1.37 $false | (~spl1_6 | ~spl1_68)),
% 1.76/1.37 inference(trivial_inequality_removal,[status(thm)],[f1643])).
% 1.76/1.37 thf(f1643,plain,(
% 1.76/1.37 ($false = $true) | (~spl1_6 | ~spl1_68)),
% 1.76/1.37 inference(superposition,[status(thm)],[f1637,f1011])).
% 1.76/1.37 thf(f1011,plain,(
% 1.76/1.37 ((sK3 @ sK21) = $false) | ~spl1_6),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1009])).
% 1.76/1.37 thf(f1637,plain,(
% 1.76/1.37 ( ! [X0 : $i] : (((sK3 @ X0) = $true)) ) | ~spl1_68),
% 1.76/1.37 inference(superposition,[status(thm)],[f1633,f55])).
% 1.76/1.37 thf(f1633,plain,(
% 1.76/1.37 ((sK3 @ sK5) = $true) | ~spl1_68),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1631])).
% 1.76/1.37 thf(f1634,plain,(
% 1.76/1.37 spl1_68 | spl1_65 | spl1_61 | ~spl1_37),
% 1.76/1.37 inference(avatar_split_clause,[status(thm)],[f1364,f1226,f1415,f1616,f1631])).
% 1.76/1.37 thf(f1226,definition,(
% 1.76/1.37 spl1_37 <=> ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (irel @ sK5 @ X1)) | ($false = (sK4 @ (sK11 @ X1))) | ((sK3 @ X2) = $true))),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_37])],[avatar_definition])).
% 1.76/1.37 thf(f1364,plain,(
% 1.76/1.37 ($false = (irel @ sK5 @ sK5)) | ((sK3 @ sK5) = $true) | ($false = (sK4 @ (sK11 @ sK5))) | ~spl1_37),
% 1.76/1.37 inference(trivial_inequality_removal,[status(thm)],[f1351])).
% 1.76/1.37 thf(f1351,plain,(
% 1.76/1.37 ($false != $false) | ($false = (sK4 @ (sK11 @ sK5))) | ((sK3 @ sK5) = $true) | ($false = (irel @ sK5 @ sK5)) | ~spl1_37),
% 1.76/1.37 inference(equality_factoring,[status(thm)],[f1227])).
% 1.76/1.37 thf(f1227,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i] : (($false = (irel @ sK5 @ X1)) | ((sK3 @ X2) = $true) | ($false = (sK4 @ (sK11 @ X1))) | ((irel @ X1 @ X2) = $false)) ) | ~spl1_37),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1226])).
% 1.76/1.37 thf(f1612,plain,(
% 1.76/1.37 spl1_6 | ~spl1_17),
% 1.76/1.37 inference(avatar_contradiction_clause,[status(thm)],[f1611])).
% 1.76/1.37 thf(f1611,plain,(
% 1.76/1.37 $false | (spl1_6 | ~spl1_17)),
% 1.76/1.37 inference(subsumption_resolution,[status(thm)],[f1086,f1585])).
% 1.76/1.37 thf(f1585,plain,(
% 1.76/1.37 ( ! [X0 : $i] : (($false != (sK3 @ X0))) ) | spl1_6),
% 1.76/1.37 inference(superposition,[status(thm)],[f1010,f55])).
% 1.76/1.37 thf(f1086,plain,(
% 1.76/1.37 ((sK3 @ sK28) = $false) | ~spl1_17),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1084])).
% 1.76/1.37 thf(f1084,definition,(
% 1.76/1.37 spl1_17 <=> ((sK3 @ sK28) = $false)),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_17])],[avatar_definition])).
% 1.76/1.37 thf(f1608,plain,(
% 1.76/1.37 ~spl1_1 | ~spl1_7),
% 1.76/1.37 inference(avatar_contradiction_clause,[status(thm)],[f1607])).
% 1.76/1.37 thf(f1607,plain,(
% 1.76/1.37 $false | (~spl1_1 | ~spl1_7)),
% 1.76/1.37 inference(trivial_inequality_removal,[status(thm)],[f1604])).
% 1.76/1.37 thf(f1604,plain,(
% 1.76/1.37 ($false = $true) | (~spl1_1 | ~spl1_7)),
% 1.76/1.37 inference(superposition,[status(thm)],[f1015,f1600])).
% 1.76/1.37 thf(f1600,plain,(
% 1.76/1.37 ( ! [X0 : $i] : (((sK4 @ X0) = $true)) ) | ~spl1_1),
% 1.76/1.37 inference(superposition,[status(thm)],[f1597,f55])).
% 1.76/1.37 thf(f1597,plain,(
% 1.76/1.37 ((sK4 @ sK16) = $true) | ~spl1_1),
% 1.76/1.37 inference(trivial_inequality_removal,[status(thm)],[f1591])).
% 1.76/1.37 thf(f1591,plain,(
% 1.76/1.37 ($false = $true) | ((sK4 @ sK16) = $true) | ~spl1_1),
% 1.76/1.37 inference(superposition,[status(thm)],[f989,f91])).
% 1.76/1.37 thf(f989,plain,(
% 1.76/1.37 ( ! [X2 : $i] : (($false = (irel @ sK16 @ X2)) | ((sK4 @ X2) = $true)) ) | ~spl1_1),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f988])).
% 1.76/1.37 thf(f988,definition,(
% 1.76/1.37 spl1_1 <=> ! [X2 : $i] : (((sK4 @ X2) = $true) | ($false = (irel @ sK16 @ X2)))),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.76/1.37 thf(f1576,plain,(
% 1.76/1.37 spl1_61 | spl1_63 | spl1_62 | ~spl1_56),
% 1.76/1.37 inference(avatar_split_clause,[status(thm)],[f1496,f1298,f1419,f1573,f1415])).
% 1.76/1.37 thf(f1298,definition,(
% 1.76/1.37 spl1_56 <=> ! [X4 : $i,X3 : $i] : (($false = (irel @ X4 @ X3)) | ((sK3 @ (sK7 @ X4)) = $false) | ((sK4 @ X3) = $true) | ($false = (irel @ sK5 @ X4)))),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_56])],[avatar_definition])).
% 1.76/1.37 thf(f1496,plain,(
% 1.76/1.37 ($false = (irel @ sK5 @ sK5)) | ((sK4 @ sK5) = $true) | ($false = (sK3 @ (sK7 @ sK5))) | ~spl1_56),
% 1.76/1.37 inference(trivial_inequality_removal,[status(thm)],[f1486])).
% 1.76/1.37 thf(f1486,plain,(
% 1.76/1.37 ($false = (sK3 @ (sK7 @ sK5))) | ($false != $false) | ((sK4 @ sK5) = $true) | ($false = (irel @ sK5 @ sK5)) | ~spl1_56),
% 1.76/1.37 inference(equality_factoring,[status(thm)],[f1299])).
% 1.76/1.37 thf(f1299,plain,(
% 1.76/1.37 ( ! [X3 : $i,X4 : $i] : (($false = (irel @ sK5 @ X4)) | ((sK4 @ X3) = $true) | ($false = (irel @ X4 @ X3)) | ((sK3 @ (sK7 @ X4)) = $false)) ) | ~spl1_56),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1298])).
% 1.76/1.37 thf(f1571,plain,(
% 1.76/1.37 ~spl1_3 | spl1_31),
% 1.76/1.37 inference(avatar_contradiction_clause,[status(thm)],[f1570])).
% 1.76/1.37 thf(f1570,plain,(
% 1.76/1.37 $false | (~spl1_3 | spl1_31)),
% 1.76/1.37 inference(subsumption_resolution,[status(thm)],[f1195,f1311])).
% 1.76/1.37 thf(f1311,plain,(
% 1.76/1.37 ( ! [X0 : $i] : (((irel @ sK5 @ X0) = $true)) ) | ~spl1_3),
% 1.76/1.37 inference(superposition,[status(thm)],[f996,f55])).
% 1.76/1.37 thf(f996,plain,(
% 1.76/1.37 ((irel @ sK5 @ sK20) = $true) | ~spl1_3),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f994])).
% 1.76/1.37 thf(f994,definition,(
% 1.76/1.37 spl1_3 <=> ((irel @ sK5 @ sK20) = $true)),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.76/1.37 thf(f1195,plain,(
% 1.76/1.37 ((irel @ sK5 @ sK18) != $true) | spl1_31),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1194])).
% 1.76/1.37 thf(f1194,definition,(
% 1.76/1.37 spl1_31 <=> ((irel @ sK5 @ sK18) = $true)),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_31])],[avatar_definition])).
% 1.76/1.37 thf(f1569,plain,(
% 1.76/1.37 spl1_8 | ~spl1_31),
% 1.76/1.37 inference(avatar_contradiction_clause,[status(thm)],[f1568])).
% 1.76/1.37 thf(f1568,plain,(
% 1.76/1.37 $false | (spl1_8 | ~spl1_31)),
% 1.76/1.37 inference(subsumption_resolution,[status(thm)],[f1019,f1437])).
% 1.76/1.37 thf(f1437,plain,(
% 1.76/1.37 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $true)) ) | ~spl1_31),
% 1.76/1.37 inference(superposition,[status(thm)],[f1430,f55])).
% 1.76/1.37 thf(f1430,plain,(
% 1.76/1.37 ( ! [X0 : $i] : (((irel @ X0 @ sK18) = $true)) ) | ~spl1_31),
% 1.76/1.37 inference(superposition,[status(thm)],[f1196,f55])).
% 1.76/1.37 thf(f1196,plain,(
% 1.76/1.37 ((irel @ sK5 @ sK18) = $true) | ~spl1_31),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1194])).
% 1.76/1.37 thf(f1019,plain,(
% 1.76/1.37 ((irel @ sK20 @ sK17) != $true) | spl1_8),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1018])).
% 1.76/1.37 thf(f1018,definition,(
% 1.76/1.37 spl1_8 <=> ((irel @ sK20 @ sK17) = $true)),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition])).
% 1.76/1.37 thf(f1567,plain,(
% 1.76/1.37 ~spl1_6 | ~spl1_8 | ~spl1_9),
% 1.76/1.37 inference(avatar_contradiction_clause,[status(thm)],[f1566])).
% 1.76/1.37 thf(f1566,plain,(
% 1.76/1.37 $false | (~spl1_6 | ~spl1_8 | ~spl1_9)),
% 1.76/1.37 inference(trivial_inequality_removal,[status(thm)],[f1563])).
% 1.76/1.37 thf(f1563,plain,(
% 1.76/1.37 ($false = $true) | (~spl1_6 | ~spl1_8 | ~spl1_9)),
% 1.76/1.37 inference(superposition,[status(thm)],[f1424,f1011])).
% 1.76/1.37 thf(f1424,plain,(
% 1.76/1.37 ( ! [X0 : $i] : (((sK3 @ X0) = $true)) ) | (~spl1_8 | ~spl1_9)),
% 1.76/1.37 inference(superposition,[status(thm)],[f1329,f55])).
% 1.76/1.37 thf(f1329,plain,(
% 1.76/1.37 ((sK3 @ sK17) = $true) | (~spl1_8 | ~spl1_9)),
% 1.76/1.37 inference(trivial_inequality_removal,[status(thm)],[f1324])).
% 1.76/1.37 thf(f1324,plain,(
% 1.76/1.37 ((sK3 @ sK17) = $true) | ($false = $true) | (~spl1_8 | ~spl1_9)),
% 1.76/1.37 inference(superposition,[status(thm)],[f1024,f1020])).
% 1.76/1.37 thf(f1020,plain,(
% 1.76/1.37 ((irel @ sK20 @ sK17) = $true) | ~spl1_8),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1018])).
% 1.76/1.37 thf(f1024,plain,(
% 1.76/1.37 ( ! [X3 : $i] : (($false = (irel @ sK20 @ X3)) | ((sK3 @ X3) = $true)) ) | ~spl1_9),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1023])).
% 1.76/1.37 thf(f1023,definition,(
% 1.76/1.37 spl1_9 <=> ! [X3 : $i] : (($false = (irel @ sK20 @ X3)) | ((sK3 @ X3) = $true))),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_9])],[avatar_definition])).
% 1.76/1.37 thf(f1559,plain,(
% 1.76/1.37 ~spl1_3 | ~spl1_7 | ~spl1_11),
% 1.76/1.37 inference(avatar_contradiction_clause,[status(thm)],[f1558])).
% 1.76/1.37 thf(f1558,plain,(
% 1.76/1.37 $false | (~spl1_3 | ~spl1_7 | ~spl1_11)),
% 1.76/1.37 inference(trivial_inequality_removal,[status(thm)],[f1554])).
% 1.76/1.37 thf(f1554,plain,(
% 1.76/1.37 ($false = $true) | (~spl1_3 | ~spl1_7 | ~spl1_11)),
% 1.76/1.37 inference(superposition,[status(thm)],[f1551,f1301])).
% 1.76/1.37 thf(f1301,plain,(
% 1.76/1.37 ( ! [X0 : $i] : (((sK4 @ X0) = $false)) ) | ~spl1_7),
% 1.76/1.37 inference(superposition,[status(thm)],[f1015,f55])).
% 1.76/1.37 thf(f1551,plain,(
% 1.76/1.37 ((sK4 @ sK20) = $true) | (~spl1_3 | ~spl1_11)),
% 1.76/1.37 inference(trivial_inequality_removal,[status(thm)],[f1537])).
% 1.76/1.37 thf(f1537,plain,(
% 1.76/1.37 ((sK4 @ sK20) = $true) | ($false = $true) | (~spl1_3 | ~spl1_11)),
% 1.76/1.37 inference(superposition,[status(thm)],[f1314,f1033])).
% 1.76/1.37 thf(f1033,plain,(
% 1.76/1.37 ( ! [X2 : $i] : (($false = (irel @ sK20 @ X2)) | ((sK4 @ X2) = $true)) ) | ~spl1_11),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1032])).
% 1.76/1.37 thf(f1032,definition,(
% 1.76/1.37 spl1_11 <=> ! [X2 : $i] : (((sK4 @ X2) = $true) | ($false = (irel @ sK20 @ X2)))),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_11])],[avatar_definition])).
% 1.76/1.37 thf(f1314,plain,(
% 1.76/1.37 ( ! [X0 : $i] : (((irel @ X0 @ sK20) = $true)) ) | ~spl1_3),
% 1.76/1.37 inference(superposition,[status(thm)],[f996,f55])).
% 1.76/1.37 thf(f1422,plain,(
% 1.76/1.37 spl1_60 | spl1_61 | spl1_62 | ~spl1_53),
% 1.76/1.37 inference(avatar_split_clause,[status(thm)],[f1387,f1286,f1419,f1415,f1408])).
% 1.76/1.37 thf(f1286,definition,(
% 1.76/1.37 spl1_53 <=> ! [X2 : $i,X1 : $i] : (((sK3 @ (sK6 @ X1)) = $false) | ((sK4 @ X2) = $true) | ($false = (irel @ sK5 @ X1)) | ((irel @ X1 @ X2) = $false))),
% 1.76/1.37 introduced(definition,[new_symbols(naming,[spl1_53])],[avatar_definition])).
% 1.76/1.37 thf(f1387,plain,(
% 1.76/1.37 ((sK4 @ sK5) = $true) | ($false = (irel @ sK5 @ sK5)) | ($false = (sK3 @ (sK6 @ sK5))) | ~spl1_53),
% 1.76/1.37 inference(trivial_inequality_removal,[status(thm)],[f1379])).
% 1.76/1.37 thf(f1379,plain,(
% 1.76/1.37 ((sK4 @ sK5) = $true) | ($false != $false) | ($false = (irel @ sK5 @ sK5)) | ($false = (sK3 @ (sK6 @ sK5))) | ~spl1_53),
% 1.76/1.37 inference(equality_factoring,[status(thm)],[f1287])).
% 1.76/1.37 thf(f1287,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i] : (($false = (irel @ sK5 @ X1)) | ((irel @ X1 @ X2) = $false) | ((sK4 @ X2) = $true) | ((sK3 @ (sK6 @ X1)) = $false)) ) | ~spl1_53),
% 1.76/1.37 inference(avatar_component_clause,[status(thm)],[f1286])).
% 1.76/1.37 thf(f1300,plain,(
% 1.76/1.37 spl1_53 | spl1_56),
% 1.76/1.37 inference(avatar_split_clause,[status(thm)],[f137,f1298,f1286])).
% 1.76/1.37 thf(f137,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (irel @ X4 @ X3)) | ($false = (irel @ sK5 @ X1)) | ((sK3 @ (sK6 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ sK5 @ X4)) | ((sK4 @ X3) = $true) | ((sK4 @ X2) = $true) | ((sK3 @ (sK7 @ X4)) = $false)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f135])).
% 1.76/1.37 thf(f135,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((sK4 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X4 @ X3)) | ((sK3 @ (sK6 @ X1)) = $false) | ($false = (irel @ sK5 @ X4)) | ($false = (irel @ sK5 @ X1)) | ((sK4 @ X2) = $true) | ($false = ((sK3 @ (sK7 @ X4)) | (~ (irel @ X4 @ (sK7 @ X4)))))) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f134])).
% 1.76/1.37 thf(f134,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (irel @ sK5 @ X4)) | ((sK3 @ (sK6 @ X1)) = $false) | ((sK4 @ X2) = $true) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X4 @ X3)) | ((sK4 @ X3) = $true) | ($false = ((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))) @ (sK7 @ X4))) | ($false = (irel @ sK5 @ X1))) )),
% 1.76/1.37 inference(sigma_clausification,[status(thm)],[f133])).
% 1.76/1.37 thf(f133,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (irel @ X4 @ X3)) | ((sK3 @ (sK6 @ X1)) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | ($false = (irel @ sK5 @ X4)) | ((sK4 @ X2) = $true) | ((sK4 @ X3) = $true) | ($false = (irel @ sK5 @ X1))) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f132])).
% 1.76/1.37 thf(f132,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (irel @ sK5 @ X4)) | ((sK4 @ X3) = $true) | ($false = (irel @ sK5 @ X1)) | ((sK3 @ (sK6 @ X1)) = $false) | ((sK4 @ X2) = $true) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X4 @ X3)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) = $true)) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f131])).
% 1.76/1.37 thf(f131,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (irel @ sK5 @ X1)) | ($false = (irel @ sK5 @ X4)) | ((~ (irel @ X4 @ X3)) = $true) | ((sK4 @ X3) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) = $true) | ((sK3 @ (sK6 @ X1)) = $false) | ((sK4 @ X2) = $true)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f130])).
% 1.76/1.37 thf(f130,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((sK4 @ X3) = $true) | ($false = (irel @ sK5 @ X4)) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X3))) = $true) | ((sK3 @ (sK6 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ sK5 @ X1)) | ((sK4 @ X2) = $true)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f129])).
% 1.76/1.37 thf(f129,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X3))) | (sK4 @ X3)) = $true) | ($false = (irel @ sK5 @ X1)) | ((irel @ X1 @ X2) = $false) | ((sK4 @ X2) = $true) | ((sK3 @ (sK6 @ X1)) = $false) | ($false = (irel @ sK5 @ X4))) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f128])).
% 1.76/1.37 thf(f128,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((sK4 @ X2) = $true) | ((irel @ X1 @ X2) = $false) | ((~ (irel @ sK5 @ X4)) = $true) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X3))) | (sK4 @ X3)) = $true) | ((sK3 @ (sK6 @ X1)) = $false) | ($false = (irel @ sK5 @ X1))) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f126])).
% 1.76/1.37 thf(f126,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X5))) | (sK3 @ X5))) = $true) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ sK5 @ X1)) | ((~ (irel @ sK5 @ X4)) = $true) | ((sK4 @ X2) = $true) | ((sK3 @ (sK6 @ X1)) = $false)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f125])).
% 1.76/1.37 thf(f125,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (((((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X5))) | (sK3 @ X5))) | (~ (irel @ sK5 @ X4))) = $true) | ((sK3 @ (sK6 @ X1)) = $false) | ((sK4 @ X2) = $true) | ($false = (irel @ sK5 @ X1)) | ((irel @ X1 @ X2) = $false)) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f124])).
% 1.76/1.37 thf(f124,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (((~ (irel @ X1 @ X2)) = $true) | ((((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X5))) | (sK3 @ X5))) | (~ (irel @ sK5 @ X4))) = $true) | ((sK4 @ X2) = $true) | ($false = (irel @ sK5 @ X1)) | ((sK3 @ (sK6 @ X1)) = $false)) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f123])).
% 1.76/1.37 thf(f123,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (((sK3 @ (sK6 @ X1)) = $false) | (((^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X4 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X4 @ Y0))) | (sK3 @ Y0))) | (~ (irel @ sK5 @ X4)))) @ X5) = $true) | ($false = (irel @ sK5 @ X1)) | ((~ (irel @ X1 @ X2)) = $true) | ((sK4 @ X2) = $true)) )),
% 1.76/1.37 inference(pi_clausification,[status(thm)],[f122])).
% 1.76/1.37 thf(f122,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X4 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X4 @ Y0))) | (sK3 @ Y0))) | (~ (irel @ sK5 @ X4))))) = $true) | ((~ (irel @ X1 @ X2)) = $true) | ((sK4 @ X2) = $true) | ($false = (irel @ sK5 @ X1)) | ((sK3 @ (sK6 @ X1)) = $false)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f121])).
% 1.76/1.37 thf(f121,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((~ (irel @ X1 @ X2)) | (sK4 @ X2)) = $true) | ($false = (irel @ sK5 @ X1)) | ((sK3 @ (sK6 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X4 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X4 @ Y0))) | (sK3 @ Y0))) | (~ (irel @ sK5 @ X4))))) = $true)) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f120])).
% 1.76/1.37 thf(f120,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (irel @ sK5 @ X1)) | ((sK3 @ (sK6 @ X1)) = $false) | (((~ (irel @ X1 @ X2)) | (sK4 @ X2)) = $true) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ Y1))) | (sK3 @ Y1))) | (~ (irel @ sK5 @ Y0)))))) @ X4) = $true)) )),
% 1.76/1.37 inference(pi_clausification,[status(thm)],[f119])).
% 1.76/1.37 thf(f119,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ sK5 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ Y1))) | (sK3 @ Y1))) | (~ (irel @ sK5 @ Y0))))))) = $true) | ((sK3 @ (sK6 @ X1)) = $false) | (((~ (irel @ X1 @ X2)) | (sK4 @ X2)) = $true)) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f118])).
% 1.76/1.37 thf(f118,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((sK3 @ (sK6 @ X1)) = $false) | (((~ (irel @ X1 @ X2)) | (sK4 @ X2)) = $true) | ($false = (irel @ sK5 @ X1)) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1)))))))) @ X3) = $true)) )),
% 1.76/1.37 inference(pi_clausification,[status(thm)],[f117])).
% 1.76/1.37 thf(f117,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1))))))))) = $true) | ((sK3 @ (sK6 @ X1)) = $false) | (((~ (irel @ X1 @ X2)) | (sK4 @ X2)) = $true) | ($false = (irel @ sK5 @ X1))) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f115])).
% 1.76/1.37 thf(f115,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i] : (($false = ((sK3 @ (sK6 @ X1)) | (~ (irel @ X1 @ (sK6 @ X1))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1))))))))) = $true) | (((~ (irel @ X1 @ X2)) | (sK4 @ X2)) = $true) | ($false = (irel @ sK5 @ X1))) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f114])).
% 1.76/1.37 thf(f114,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X1 @ Y0)))) @ (sK6 @ X1))) | (((~ (irel @ X1 @ X2)) | (sK4 @ X2)) = $true) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1))))))))) = $true) | ($false = (irel @ sK5 @ X1))) )),
% 1.76/1.37 inference(sigma_clausification,[status(thm)],[f113])).
% 1.76/1.37 thf(f113,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i] : (($false = (irel @ sK5 @ X1)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X1 @ Y0)))))) | (((~ (irel @ X1 @ X2)) | (sK4 @ X2)) = $true) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1))))))))) = $true)) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f112])).
% 1.76/1.37 thf(f112,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X1 @ Y0)))))) | ($false = (irel @ sK5 @ X1)) | (((^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0))) @ X2) = $true) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1))))))))) = $true)) )),
% 1.76/1.37 inference(pi_clausification,[status(thm)],[f111])).
% 1.76/1.37 thf(f111,plain,(
% 1.76/1.37 ( ! [X1 : $i] : (($false = (irel @ sK5 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0)))) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X1 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1))))))))) = $true)) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f110])).
% 1.76/1.37 thf(f110,plain,(
% 1.76/1.37 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X1 @ Y0)))))) = $true) | ($false = (irel @ sK5 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1))))))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0)))) = $true)) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f109])).
% 1.76/1.37 thf(f109,plain,(
% 1.76/1.37 ( ! [X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1))))))))))) | ($false = (irel @ sK5 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X1 @ Y0)))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0)))) = $true)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f108])).
% 1.76/1.37 thf(f108,plain,(
% 1.76/1.37 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X1 @ Y0))))))) = $true) | ($false = (irel @ sK5 @ X1)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1)))))))))))) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f106])).
% 1.76/1.37 thf(f106,plain,(
% 1.76/1.37 ( ! [X1 : $i] : (($false = (irel @ sK5 @ X1)) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X1 @ Y0))))))) & ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0))))))) = $true) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1)))))))))))) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f105])).
% 1.76/1.37 thf(f105,plain,(
% 1.76/1.37 ( ! [X1 : $i] : (((~ (irel @ sK5 @ X1)) = $true) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X1 @ Y0))))))) & ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0))))))) = $true) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1)))))))))))) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f104])).
% 1.76/1.37 thf(f104,plain,(
% 1.76/1.37 ( ! [X1 : $i] : ((((~ (irel @ sK5 @ X1)) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X1 @ Y0))))))) & ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0)))))))) = $true) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1)))))))))))) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f103])).
% 1.76/1.37 thf(f103,plain,(
% 1.76/1.37 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))))))) @ X1) = $true) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1)))))))))))) )),
% 1.76/1.37 inference(pi_clausification,[status(thm)],[f102])).
% 1.76/1.37 thf(f102,plain,(
% 1.76/1.37 ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))))))))) = $true) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1)))))))))))),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f101])).
% 1.76/1.37 thf(f101,plain,(
% 1.76/1.37 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))))))))))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1)))))))))))),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 1.76/1.37 thf(f99,plain,(
% 1.76/1.37 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1)))))))))) != (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))))))))))),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f98])).
% 1.76/1.37 thf(f98,plain,(
% 1.76/1.37 (((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((((~ (!! @ $i @ (^[Y4 : $i]: ((sK3 @ Y4) | (~ (irel @ Y2 @ Y4)))))) | (~ (irel @ Y2 @ Y1))) | (sK4 @ Y1)) & (((~ (!! @ $i @ (^[Y4 : $i]: ((sK4 @ Y4) | (~ (irel @ Y2 @ Y4)))))) | (~ (irel @ Y2 @ Y3))) | (sK3 @ Y3))) | (~ (irel @ Y0 @ Y2))))))))))) @ sK5) != ((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y1 @ Y2))))))) & ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK3 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))))))))))) @ sK5))),
% 1.76/1.37 inference(negative_extensionality,[status(thm)],[f97])).
% 1.76/1.37 thf(f97,plain,(
% 1.76/1.37 ((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((((~ (!! @ $i @ (^[Y4 : $i]: ((sK3 @ Y4) | (~ (irel @ Y2 @ Y4)))))) | (~ (irel @ Y2 @ Y1))) | (sK4 @ Y1)) & (((~ (!! @ $i @ (^[Y4 : $i]: ((sK4 @ Y4) | (~ (irel @ Y2 @ Y4)))))) | (~ (irel @ Y2 @ Y3))) | (sK3 @ Y3))) | (~ (irel @ Y0 @ Y2))))))))))) != (^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y1 @ Y2))))))) & ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK3 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))))))))))))),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f96])).
% 1.76/1.37 thf(f96,plain,(
% 1.76/1.37 (((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((((~ (!! @ $i @ (^[Y5 : $i]: ((sK3 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y3 @ Y2))) | (Y0 @ Y2)) & (((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y3 @ Y4))) | (sK3 @ Y4))) | (~ (irel @ Y1 @ Y3))))))))))))) @ sK4) != ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y2 @ Y3))))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK3 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))))) @ sK4))),
% 1.76/1.37 inference(negative_extensionality,[status(thm)],[f95])).
% 1.76/1.37 thf(f95,plain,(
% 1.76/1.37 ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y2 @ Y3))))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK3 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((((~ (!! @ $i @ (^[Y5 : $i]: ((sK3 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y3 @ Y2))) | (Y0 @ Y2)) & (((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y3 @ Y4))) | (sK3 @ Y4))) | (~ (irel @ Y1 @ Y3))))))))))))))),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f94])).
% 1.76/1.37 thf(f94,plain,(
% 1.76/1.37 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (((!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y1 @ Y4)))) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4) | (~ (irel @ Y3 @ Y4))))))) & ((!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y0 @ Y4)))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y1 @ Y4)))))))))))))))) @ 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 @ Y4 @ Y3))) | (Y1 @ Y3)) & (((~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y5))) | (Y0 @ Y5))) | (~ (irel @ Y2 @ Y4))))))))))))))) @ sK3))),
% 1.76/1.37 inference(negative_extensionality,[status(thm)],[f41])).
% 1.76/1.37 thf(f41,plain,(
% 1.76/1.37 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (((!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y1 @ Y4)))) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4) | (~ (irel @ Y3 @ Y4))))))) & ((!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y0 @ Y4)))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y1 @ Y4)))))))))))))))) != (^[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 @ Y4 @ Y3))) | (Y1 @ Y3)) & (((~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y5))) | (Y0 @ Y5))) | (~ (irel @ Y2 @ Y4))))))))))))))))),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.76/1.37 thf(f40,plain,(
% 1.76/1.37 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y2 @ Y4)))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (((!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y3 @ Y5)))) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y5) | (~ (irel @ Y4 @ Y5))))))) & ((!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y2 @ Y5)))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y3 @ Y5)))))))))))) @ Y0 @ Y1))))) != (^[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 @ Y4 @ Y3))) | (Y1 @ Y3)) & (((~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y5))) | (Y0 @ Y5))) | (~ (irel @ Y2 @ Y4))))))))))))))))),
% 1.76/1.37 inference(definition_unfolding,[status(thm)],[f39,f23,f18,f37])).
% 1.76/1.37 thf(f37,plain,(
% 1.76/1.37 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))))),
% 1.76/1.37 inference(cnf_transformation,[status(thm)],[f15])).
% 1.76/1.37 thf(f18,plain,(
% 1.76/1.37 (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))))),
% 1.76/1.37 inference(cnf_transformation,[status(thm)],[f15])).
% 1.76/1.37 thf(f23,plain,(
% 1.76/1.37 (ixor = (^[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 @ Y4 @ Y3))) | (Y1 @ Y3)) & (((~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y5))) | (Y0 @ Y5))) | (~ (irel @ Y2 @ Y4))))))))))))))))),
% 1.76/1.37 inference(cnf_transformation,[status(thm)],[f15])).
% 1.76/1.37 thf(f39,plain,(
% 1.76/1.37 (ixor != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (inot @ (iequiv @ Y0 @ Y1))))))),
% 1.76/1.37 inference(cnf_transformation,[status(thm)],[f9])).
% 1.76/1.37 thf(f9,plain,(
% 1.76/1.37 (ixor != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (inot @ (iequiv @ Y0 @ Y1))))))),
% 1.76/1.37 inference(flattening,[status(thm)],[f6])).
% 1.76/1.37 thf(f6,plain,(
% 1.76/1.37 ~(ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (inot @ (iequiv @ Y0 @ Y1))))))),
% 1.76/1.37 inference(fool_elimination,[status(thm)],[f5])).
% 1.76/1.37 thf(f5,plain,(
% 1.76/1.37 ~((^[X0 : $i > $o, X1 : $i > $o] : (inot @ (iequiv @ X0 @ X1))) = ixor)),
% 1.76/1.37 inference(rectify,[status(thm)],[f3])).
% 1.76/1.37 thf(f3,negated_conjecture,(
% 1.76/1.37 ~((^[X8 : $i > $o, X9 : $i > $o] : (inot @ (iequiv @ X8 @ X9))) = ixor)),
% 1.76/1.37 inference(negated_conjecture,[status(cth)],[f2])).
% 1.76/1.37 thf(f2,conjecture,(
% 1.76/1.37 ((^[X8 : $i > $o, X9 : $i > $o] : (inot @ (iequiv @ X8 @ X9))) = ixor)),
% 1.76/1.37 file('/export/starexec/sandbox2/tmp/tmp.iSg9Oe0LVX/DTF2THF_27148.p',ixor)).
% 1.76/1.37 thf(f1235,plain,(
% 1.76/1.37 spl1_37 | spl1_39),
% 1.76/1.37 inference(avatar_split_clause,[status(thm)],[f245,f1233,f1226])).
% 1.76/1.37 thf(f245,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i,X4 : $i,X5 : $i] : (((sK4 @ (sK15 @ X4)) = $false) | ((irel @ X4 @ X5) = $false) | ($false = (irel @ sK5 @ X1)) | ((sK3 @ X5) = $true) | ($false = (irel @ sK5 @ X4)) | ((sK3 @ X2) = $true) | ($false = (sK4 @ (sK11 @ X1))) | ((irel @ X1 @ X2) = $false)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f243])).
% 1.76/1.37 thf(f243,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = (sK4 @ (sK11 @ X1))) | ($false = (irel @ sK5 @ X1)) | ((irel @ X1 @ X2) = $false) | ((irel @ X4 @ X5) = $false) | (((sK4 @ (sK15 @ X4)) | (~ (irel @ X4 @ (sK15 @ X4)))) = $false) | ($false = (irel @ sK5 @ X4)) | ((sK3 @ X2) = $true) | ((sK3 @ X5) = $true)) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f242])).
% 1.76/1.37 thf(f242,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X4 @ Y0)))) @ (sK15 @ X4))) | ((sK3 @ X2) = $true) | ((irel @ X4 @ X5) = $false) | ($false = (sK4 @ (sK11 @ X1))) | ((sK3 @ X5) = $true) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ sK5 @ X1)) | ($false = (irel @ sK5 @ X4))) )),
% 1.76/1.37 inference(sigma_clausification,[status(thm)],[f241])).
% 1.76/1.37 thf(f241,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i,X4 : $i,X5 : $i] : (((irel @ X4 @ X5) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X4 @ Y0))))) = $false) | ($false = (irel @ sK5 @ X4)) | ($false = (sK4 @ (sK11 @ X1))) | ((sK3 @ X5) = $true) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ sK5 @ X1)) | ((sK3 @ X2) = $true)) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f240])).
% 1.76/1.37 thf(f240,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i,X4 : $i,X5 : $i] : (((sK3 @ X2) = $true) | ($false = (irel @ sK5 @ X4)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X4 @ Y0)))))) = $true) | ($false = (sK4 @ (sK11 @ X1))) | ((irel @ X4 @ X5) = $false) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ sK5 @ X1)) | ((sK3 @ X5) = $true)) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f239])).
% 1.76/1.37 thf(f239,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = (irel @ sK5 @ X4)) | ((~ (irel @ X4 @ X5)) = $true) | ($false = (irel @ sK5 @ X1)) | ((irel @ X1 @ X2) = $false) | ($false = (sK4 @ (sK11 @ X1))) | ((sK3 @ X2) = $true) | ((sK3 @ X5) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X4 @ Y0)))))) = $true)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f238])).
% 1.76/1.37 thf(f238,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = (sK4 @ (sK11 @ X1))) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ sK5 @ X4)) | ($false = (irel @ sK5 @ X1)) | ((sK3 @ X2) = $true) | ((sK3 @ X5) = $true) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X5))) = $true)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f227])).
% 1.76/1.37 thf(f227,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i,X4 : $i,X5 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X5))) | (sK3 @ X5)) = $true) | ($false = (irel @ sK5 @ X4)) | ($false = (irel @ sK5 @ X1)) | ((irel @ X1 @ X2) = $false) | ($false = (sK4 @ (sK11 @ X1))) | ((sK3 @ X2) = $true)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f226])).
% 1.76/1.37 thf(f226,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = (irel @ sK5 @ X1)) | ($false = (irel @ sK5 @ X4)) | ((sK3 @ X2) = $true) | ($false = (sK4 @ (sK11 @ X1))) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X5))) | (sK3 @ X5))) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f225])).
% 1.76/1.37 thf(f225,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (((~ (irel @ sK5 @ X4)) = $true) | ($false = (irel @ sK5 @ X1)) | ($false = (sK4 @ (sK11 @ X1))) | ((sK3 @ X2) = $true) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X5))) | (sK3 @ X5))) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f224])).
% 1.76/1.37 thf(f224,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = (irel @ sK5 @ X1)) | ((irel @ X1 @ X2) = $false) | ((sK3 @ X2) = $true) | ((((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X5))) | (sK3 @ X5))) | (~ (irel @ sK5 @ X4))) = $true) | ($false = (sK4 @ (sK11 @ X1)))) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f223])).
% 1.76/1.37 thf(f223,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (((sK3 @ X2) = $true) | ((~ (irel @ X1 @ X2)) = $true) | ($false = (irel @ sK5 @ X1)) | ((((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X4 @ Y0)))))) | (~ (irel @ X4 @ X5))) | (sK3 @ X5))) | (~ (irel @ sK5 @ X4))) = $true) | ($false = (sK4 @ (sK11 @ X1)))) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f222])).
% 1.76/1.37 thf(f222,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = (irel @ sK5 @ X1)) | ((sK3 @ X2) = $true) | ($false = (sK4 @ (sK11 @ X1))) | ((~ (irel @ X1 @ X2)) = $true) | (((^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X4 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X4 @ Y0))) | (sK3 @ Y0))) | (~ (irel @ sK5 @ X4)))) @ X5) = $true)) )),
% 1.76/1.37 inference(pi_clausification,[status(thm)],[f221])).
% 1.76/1.37 thf(f221,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X4 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X4 @ Y0))) | (sK3 @ Y0))) | (~ (irel @ sK5 @ X4))))) = $true) | ($false = (sK4 @ (sK11 @ X1))) | ((sK3 @ X2) = $true) | ((~ (irel @ X1 @ X2)) = $true) | ($false = (irel @ sK5 @ X1))) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f192])).
% 1.76/1.37 thf(f192,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((~ (irel @ X1 @ X2)) | (sK3 @ X2)) = $true) | ($false = (sK4 @ (sK11 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X4 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X4 @ Y0))) | (sK3 @ Y0))) | (~ (irel @ sK5 @ X4))))) = $true) | ($false = (irel @ sK5 @ X1))) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f191])).
% 1.76/1.37 thf(f191,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (irel @ sK5 @ X1)) | ($false = ((~ (irel @ X1 @ (sK11 @ X1))) | (sK4 @ (sK11 @ X1)))) | (((~ (irel @ X1 @ X2)) | (sK3 @ X2)) = $true) | ((!! @ $i @ (^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X4 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ X4 @ Y1)))))) | (~ (irel @ X4 @ Y0))) | (sK3 @ Y0))) | (~ (irel @ sK5 @ X4))))) = $true)) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f190])).
% 1.76/1.37 thf(f190,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((~ (irel @ X1 @ X2)) | (sK3 @ X2)) = $true) | ($false = ((~ (irel @ X1 @ (sK11 @ X1))) | (sK4 @ (sK11 @ X1)))) | ($false = (irel @ sK5 @ X1)) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ Y1))) | (sK3 @ Y1))) | (~ (irel @ sK5 @ Y0)))))) @ X4) = $true)) )),
% 1.76/1.37 inference(pi_clausification,[status(thm)],[f189])).
% 1.76/1.37 thf(f189,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ Y1))) | (sK3 @ Y1))) | (~ (irel @ sK5 @ Y0))))))) = $true) | ($false = ((~ (irel @ X1 @ (sK11 @ X1))) | (sK4 @ (sK11 @ X1)))) | ($false = (irel @ sK5 @ X1)) | (((~ (irel @ X1 @ X2)) | (sK3 @ X2)) = $true)) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f188])).
% 1.76/1.37 thf(f188,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((~ (irel @ X1 @ X2)) | (sK3 @ X2)) = $true) | ($false = (irel @ sK5 @ X1)) | (((^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0))) @ (sK11 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ Y1))) | (sK3 @ Y1))) | (~ (irel @ sK5 @ Y0))))))) = $true)) )),
% 1.76/1.37 inference(sigma_clausification,[status(thm)],[f187])).
% 1.76/1.37 thf(f187,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0)))) = $false) | ($false = (irel @ sK5 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ X3))) | (sK4 @ X3)) & (((~ (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ Y1))) | (sK3 @ Y1))) | (~ (irel @ sK5 @ Y0))))))) = $true) | (((~ (irel @ X1 @ X2)) | (sK3 @ X2)) = $true)) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f186])).
% 1.76/1.37 thf(f186,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1)))))))) @ X3) = $true) | (((~ (irel @ X1 @ X2)) | (sK3 @ X2)) = $true) | ($false = (irel @ sK5 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0)))) = $false)) )),
% 1.76/1.37 inference(pi_clausification,[status(thm)],[f185])).
% 1.76/1.37 thf(f185,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1))))))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0)))) = $false) | ($false = (irel @ sK5 @ X1)) | (((~ (irel @ X1 @ X2)) | (sK3 @ X2)) = $true)) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f184])).
% 1.76/1.37 thf(f184,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i] : (($false = (irel @ sK5 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1))))))))) = $true) | (((~ (irel @ X1 @ X2)) | (sK3 @ X2)) = $true)) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f183])).
% 1.76/1.37 thf(f183,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK3 @ Y0))) @ X2) = $true) | ($false = (irel @ sK5 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1))))))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0))))) = $true)) )),
% 1.76/1.37 inference(pi_clausification,[status(thm)],[f182])).
% 1.76/1.37 thf(f182,plain,(
% 1.76/1.37 ( ! [X1 : $i] : (($false = (irel @ sK5 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK3 @ Y0)))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1))))))))) = $true)) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f181])).
% 1.76/1.37 thf(f181,plain,(
% 1.76/1.37 ( ! [X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1))))))))))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK3 @ Y0)))) = $true) | ($false = (irel @ sK5 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0))))) = $true)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.76/1.37 thf(f107,plain,(
% 1.76/1.37 ( ! [X1 : $i] : (($false = (irel @ sK5 @ X1)) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK4 @ Y0)))))) = $true) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1)))))))))))) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f106])).
% 1.76/1.37 thf(f1087,plain,(
% 1.76/1.37 spl1_14 | spl1_6 | spl1_17 | spl1_7),
% 1.76/1.37 inference(avatar_split_clause,[status(thm)],[f676,f1013,f1084,f1009,f1066])).
% 1.76/1.37 thf(f676,plain,(
% 1.76/1.37 ($false = (sK4 @ sK17)) | ((sK3 @ sK28) = $false) | ((sK3 @ sK21) = $false) | ((sK4 @ sK22) = $false)),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f675])).
% 1.76/1.37 thf(f675,plain,(
% 1.76/1.37 ((sK4 @ sK22) = $false) | ((sK3 @ sK21) = $false) | ($false = (sK4 @ sK17)) | ($false = ((~ (irel @ sK16 @ sK28)) | (sK3 @ sK28)))),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f674])).
% 1.76/1.37 thf(f674,plain,(
% 1.76/1.37 ($false = (sK4 @ sK17)) | ((sK4 @ sK22) = $false) | ($false = ((^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0))) @ sK28)) | ((sK3 @ sK21) = $false)),
% 1.76/1.37 inference(sigma_clausification,[status(thm)],[f651])).
% 1.76/1.37 thf(f651,plain,(
% 1.76/1.37 ((sK4 @ sK22) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) = $false) | ((sK3 @ sK21) = $false) | ($false = (sK4 @ sK17))),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f650])).
% 1.76/1.37 thf(f650,plain,(
% 1.76/1.37 ((sK4 @ sK22) = $false) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17))) | (sK4 @ sK17))) | ((sK3 @ sK21) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) = $false)),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f492])).
% 1.76/1.37 thf(f492,plain,(
% 1.76/1.37 ((sK4 @ sK22) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0))))))) | ((sK3 @ sK21) = $false) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17))) | (sK4 @ sK17)))),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f491])).
% 1.76/1.37 thf(f491,plain,(
% 1.76/1.37 ((sK4 @ sK22) = $false) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK21))) | (sK3 @ sK21))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17))) | (sK4 @ sK17))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))))))),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f490])).
% 1.76/1.37 thf(f490,plain,(
% 1.76/1.37 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17))) | (sK4 @ sK17)) & (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK21))) | (sK3 @ sK21)))) | ((sK4 @ sK22) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))))))),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f319])).
% 1.76/1.37 thf(f319,plain,(
% 1.76/1.37 ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17))) | (sK4 @ sK17)) & (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK21))) | (sK3 @ sK21))) | (~ (irel @ sK5 @ sK20)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0))))))) | ((sK4 @ sK22) = $false)),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f318])).
% 1.76/1.37 thf(f318,plain,(
% 1.76/1.37 ($false = ((~ (irel @ sK16 @ sK22)) | (sK4 @ sK22))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0))))))) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17))) | (sK4 @ sK17)) & (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK21))) | (sK3 @ sK21))) | (~ (irel @ sK5 @ sK20))))),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f317])).
% 1.76/1.37 thf(f317,plain,(
% 1.76/1.37 (((^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0))) @ sK22) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0))))))) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17))) | (sK4 @ sK17)) & (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK21))) | (sK3 @ sK21))) | (~ (irel @ sK5 @ sK20))))),
% 1.76/1.37 inference(sigma_clausification,[status(thm)],[f316])).
% 1.76/1.37 thf(f316,plain,(
% 1.76/1.37 ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) = $false) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17))) | (sK4 @ sK17)) & (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK21))) | (sK3 @ sK21))) | (~ (irel @ sK5 @ sK20)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))))))),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f314])).
% 1.76/1.37 thf(f314,plain,(
% 1.76/1.37 (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0))))))) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17))) | (sK4 @ sK17)) & (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK21))) | (sK3 @ sK21))) | (~ (irel @ sK5 @ sK20))))),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f313])).
% 1.76/1.37 thf(f313,plain,(
% 1.76/1.37 (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))))) = $false) | (((^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ sK20 @ Y1)))))) | (~ (irel @ sK20 @ sK17))) | (sK4 @ sK17)) & (((~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ sK20 @ Y1)))))) | (~ (irel @ sK20 @ Y0))) | (sK3 @ Y0))) | (~ (irel @ sK5 @ sK20)))) @ sK21) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))))))),
% 1.76/1.37 inference(sigma_clausification,[status(thm)],[f312])).
% 1.76/1.37 thf(f312,plain,(
% 1.76/1.37 ($false = (!! @ $i @ (^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ sK20 @ Y1)))))) | (~ (irel @ sK20 @ sK17))) | (sK4 @ sK17)) & (((~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ sK20 @ Y1)))))) | (~ (irel @ sK20 @ Y0))) | (sK3 @ Y0))) | (~ (irel @ sK5 @ sK20)))))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))))))),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f311])).
% 1.76/1.37 thf(f311,plain,(
% 1.76/1.37 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0))))))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))))) = $false) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ sK17))) | (sK4 @ sK17)) & (((~ (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ Y1))) | (sK3 @ Y1))) | (~ (irel @ sK5 @ Y0)))))) @ sK20))),
% 1.76/1.37 inference(sigma_clausification,[status(thm)],[f310])).
% 1.76/1.37 thf(f310,plain,(
% 1.76/1.37 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ sK17))) | (sK4 @ sK17)) & (((~ (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ Y1))) | (sK3 @ Y1))) | (~ (irel @ sK5 @ Y0)))))))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))))))),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f253])).
% 1.76/1.37 thf(f253,plain,(
% 1.76/1.37 ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))))) & ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))))))) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ sK17))) | (sK4 @ sK17)) & (((~ (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ Y1))) | (sK3 @ Y1))) | (~ (irel @ sK5 @ Y0))))))))),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f252])).
% 1.76/1.37 thf(f252,plain,(
% 1.76/1.37 (((~ (irel @ sK5 @ sK16)) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))))) & ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ sK17))) | (sK4 @ sK17)) & (((~ (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y2) | (~ (irel @ Y0 @ Y2)))))) | (~ (irel @ Y0 @ Y1))) | (sK3 @ Y1))) | (~ (irel @ sK5 @ Y0))))))))),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f251])).
% 1.76/1.37 thf(f251,plain,(
% 1.76/1.37 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1)))))))) @ sK17) = $false) | (((~ (irel @ sK5 @ sK16)) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))))) & ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))))))) = $false)),
% 1.76/1.37 inference(sigma_clausification,[status(thm)],[f250])).
% 1.76/1.37 thf(f250,plain,(
% 1.76/1.37 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1)))))))))) | (((~ (irel @ sK5 @ sK16)) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))))) & ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))))))) = $false)),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f249])).
% 1.76/1.37 thf(f249,plain,(
% 1.76/1.37 ($false = ((^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))))))) @ sK16)) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1))))))))))),
% 1.76/1.37 inference(sigma_clausification,[status(thm)],[f248])).
% 1.76/1.37 thf(f248,plain,(
% 1.76/1.37 ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))))))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1))))))))))),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f247])).
% 1.76/1.37 thf(f247,plain,(
% 1.76/1.37 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))))))))) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1))))))))))),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f100])).
% 1.76/1.37 thf(f100,plain,(
% 1.76/1.37 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y0))) | (sK4 @ Y0)) & (((~ (!! @ $i @ (^[Y3 : $i]: ((sK4 @ Y3) | (~ (irel @ Y1 @ Y3)))))) | (~ (irel @ Y1 @ Y2))) | (sK3 @ Y2))) | (~ (irel @ sK5 @ Y1)))))))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1))))))))))) = $true)),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 1.76/1.37 thf(f1038,plain,(
% 1.76/1.37 spl1_2 | spl1_11 | spl1_9 | spl1_1),
% 1.76/1.37 inference(avatar_split_clause,[status(thm)],[f879,f988,f1023,f1032,f991])).
% 1.76/1.37 thf(f879,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((sK4 @ X3) = $true) | ($false = (irel @ sK16 @ X3)) | ($false = (irel @ sK20 @ X2)) | ($false = (irel @ sK20 @ X4)) | ((sK3 @ X1) = $true) | ((sK3 @ X4) = $true) | ((irel @ sK16 @ X1) = $false) | ((sK4 @ X2) = $true)) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f878])).
% 1.76/1.37 thf(f878,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (irel @ sK16 @ X3)) | ((sK3 @ X1) = $true) | ((irel @ sK16 @ X1) = $false) | ((sK4 @ X3) = $true) | ((sK4 @ X2) = $true) | ((sK3 @ X4) = $true) | ((~ (irel @ sK20 @ X4)) = $true) | ($false = (irel @ sK20 @ X2))) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f877])).
% 1.76/1.37 thf(f877,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (irel @ sK20 @ X2)) | ((sK3 @ X1) = $true) | ((sK4 @ X2) = $true) | ((sK4 @ X3) = $true) | ((irel @ sK16 @ X1) = $false) | ($false = (irel @ sK16 @ X3)) | (((sK3 @ X4) | (~ (irel @ sK20 @ X4))) = $true)) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f876])).
% 1.76/1.37 thf(f876,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((sK4 @ X2) = $true) | ((sK4 @ X3) = $true) | ($false = (irel @ sK20 @ X2)) | ((sK3 @ X1) = $true) | (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))) @ X4) = $true) | ($false = (irel @ sK16 @ X3)) | ((irel @ sK16 @ X1) = $false)) )),
% 1.76/1.37 inference(pi_clausification,[status(thm)],[f875])).
% 1.76/1.37 thf(f875,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ sK16 @ X1) = $false) | ($false = (irel @ sK16 @ X3)) | ((sK4 @ X3) = $true) | ((sK4 @ X2) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0))))) = $true) | ($false = (irel @ sK20 @ X2)) | ((sK3 @ X1) = $true)) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f874])).
% 1.76/1.37 thf(f874,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((sK3 @ X1) = $true) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0))))))) | ($false = (irel @ sK16 @ X3)) | ($false = (irel @ sK20 @ X2)) | ((sK4 @ X2) = $true) | ((sK4 @ X3) = $true) | ((irel @ sK16 @ X1) = $false)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f872])).
% 1.76/1.37 thf(f872,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17)))) | ($false = (irel @ sK16 @ X3)) | ((sK4 @ X2) = $true) | ((sK3 @ X1) = $true) | ((sK4 @ X3) = $true) | ((irel @ sK16 @ X1) = $false) | ($false = (irel @ sK20 @ X2))) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f871])).
% 1.76/1.37 thf(f871,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((~ (irel @ sK20 @ X2)) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17)))) | ((sK4 @ X2) = $true) | ((irel @ sK16 @ X1) = $false) | ((sK3 @ X1) = $true) | ($false = (irel @ sK16 @ X3)) | ((sK4 @ X3) = $true)) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f870])).
% 1.76/1.37 thf(f870,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((~ (irel @ sK16 @ X3)) = $true) | ((sK4 @ X3) = $true) | ((~ (irel @ sK20 @ X2)) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17)))) | ((irel @ sK16 @ X1) = $false) | ((sK4 @ X2) = $true) | ((sK3 @ X1) = $true)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f869])).
% 1.76/1.37 thf(f869,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((~ (irel @ sK16 @ X3)) | (sK4 @ X3)) = $true) | ((sK4 @ X2) = $true) | ((irel @ sK16 @ X1) = $false) | ((~ (irel @ sK20 @ X2)) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17)))) | ((sK3 @ X1) = $true)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f868])).
% 1.76/1.37 thf(f868,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((sK4 @ X2) | (~ (irel @ sK20 @ X2))) = $true) | ((irel @ sK16 @ X1) = $false) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17)))) | ((sK3 @ X1) = $true) | (((~ (irel @ sK16 @ X3)) | (sK4 @ X3)) = $true)) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f867])).
% 1.76/1.37 thf(f867,plain,(
% 1.76/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17)))) | ((sK3 @ X1) = $true) | (((sK4 @ X2) | (~ (irel @ sK20 @ X2))) = $true) | ((irel @ sK16 @ X1) = $false) | (((^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0))) @ X3) = $true)) )),
% 1.76/1.37 inference(pi_clausification,[status(thm)],[f866])).
% 1.76/1.37 thf(f866,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i] : (((sK3 @ X1) = $true) | ((irel @ sK16 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) = $true) | (((sK4 @ X2) | (~ (irel @ sK20 @ X2))) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17))))) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f865])).
% 1.76/1.37 thf(f865,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i] : (((irel @ sK16 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) = $true) | (((^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))) @ X2) = $true) | ((sK3 @ X1) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17))))) )),
% 1.76/1.37 inference(pi_clausification,[status(thm)],[f864])).
% 1.76/1.37 thf(f864,plain,(
% 1.76/1.37 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0))))) = $true) | ((sK3 @ X1) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17)))) | ((irel @ sK16 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) = $true)) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f863])).
% 1.76/1.37 thf(f863,plain,(
% 1.76/1.37 ( ! [X1 : $i] : (((sK3 @ X1) = $true) | ((irel @ sK16 @ X1) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) = $false) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17)))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) = $true)) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f862])).
% 1.76/1.37 thf(f862,plain,(
% 1.76/1.37 ( ! [X1 : $i] : (((sK3 @ X1) = $true) | ((~ (irel @ sK16 @ X1)) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17)))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) = $true)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f861])).
% 1.76/1.37 thf(f861,plain,(
% 1.76/1.37 ( ! [X1 : $i] : ((((sK3 @ X1) | (~ (irel @ sK16 @ X1))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17)))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) = $false)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f859])).
% 1.76/1.37 thf(f859,plain,(
% 1.76/1.37 ( ! [X1 : $i] : (($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK21)))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17)))) | (((sK3 @ X1) | (~ (irel @ sK16 @ X1))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) = $true)) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f858])).
% 1.76/1.37 thf(f858,plain,(
% 1.76/1.37 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17)))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK21)))) | (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0)))) @ X1) = $true)) )),
% 1.76/1.37 inference(pi_clausification,[status(thm)],[f857])).
% 1.76/1.37 thf(f857,plain,(
% 1.76/1.37 ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK21)))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17)))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) = $true)),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f856])).
% 1.76/1.37 thf(f856,plain,(
% 1.76/1.37 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17)))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK21))))),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f855])).
% 1.76/1.37 thf(f855,plain,(
% 1.76/1.37 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK21)))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0))))) = $false) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17))))),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f853])).
% 1.76/1.37 thf(f853,plain,(
% 1.76/1.37 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17))) | (sK4 @ sK17))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0))))) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK21))))),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f720])).
% 1.76/1.37 thf(f720,plain,(
% 1.76/1.37 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK21))) | (sK3 @ sK21))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0))))) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17))) | (sK4 @ sK17)))),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f719])).
% 1.76/1.37 thf(f719,plain,(
% 1.76/1.37 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK21))) | (sK3 @ sK21))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17))) | (sK4 @ sK17)))),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f718])).
% 1.76/1.37 thf(f718,plain,(
% 1.76/1.37 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17))) | (sK4 @ sK17)) & (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK21))) | (sK3 @ sK21)))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))))))),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f315])).
% 1.76/1.37 thf(f315,plain,(
% 1.76/1.37 ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK17))) | (sK4 @ sK17)) & (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK20 @ Y0)))))) | (~ (irel @ sK20 @ sK21))) | (sK3 @ sK21))) | (~ (irel @ sK5 @ sK20)))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))))))),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f314])).
% 1.76/1.37 thf(f997,plain,(
% 1.76/1.37 spl1_1 | spl1_2 | spl1_3),
% 1.76/1.37 inference(avatar_split_clause,[status(thm)],[f986,f994,f991,f988])).
% 1.76/1.37 thf(f986,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i] : (((sK3 @ X1) = $true) | ((sK4 @ X2) = $true) | ((irel @ sK5 @ sK20) = $true) | ($false = (irel @ sK16 @ X2)) | ((irel @ sK16 @ X1) = $false)) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f985])).
% 1.76/1.37 thf(f985,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i] : (((irel @ sK5 @ sK20) = $true) | ((sK4 @ X2) = $true) | ((irel @ sK16 @ X1) = $false) | ((~ (irel @ sK16 @ X2)) = $true) | ((sK3 @ X1) = $true)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f984])).
% 1.76/1.37 thf(f984,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i] : ((((~ (irel @ sK16 @ X2)) | (sK4 @ X2)) = $true) | ((sK3 @ X1) = $true) | ((irel @ sK16 @ X1) = $false) | ((irel @ sK5 @ sK20) = $true)) )),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f983])).
% 1.76/1.37 thf(f983,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i] : (((sK3 @ X1) = $true) | ((~ (irel @ sK16 @ X1)) = $true) | (((~ (irel @ sK16 @ X2)) | (sK4 @ X2)) = $true) | ((irel @ sK5 @ sK20) = $true)) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f982])).
% 1.76/1.37 thf(f982,plain,(
% 1.76/1.37 ( ! [X2 : $i,X1 : $i] : (((sK3 @ X1) = $true) | ((irel @ sK5 @ sK20) = $true) | ((~ (irel @ sK16 @ X1)) = $true) | (((^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0))) @ X2) = $true)) )),
% 1.76/1.37 inference(pi_clausification,[status(thm)],[f981])).
% 1.76/1.37 thf(f981,plain,(
% 1.76/1.37 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) = $true) | ((~ (irel @ sK16 @ X1)) = $true) | ((irel @ sK5 @ sK20) = $true) | ((sK3 @ X1) = $true)) )),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f980])).
% 1.76/1.37 thf(f980,plain,(
% 1.76/1.37 ( ! [X1 : $i] : ((((sK3 @ X1) | (~ (irel @ sK16 @ X1))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) = $true) | ((irel @ sK5 @ sK20) = $true)) )),
% 1.76/1.37 inference(beta_eta_normalization,[status(thm)],[f979])).
% 1.76/1.37 thf(f979,plain,(
% 1.76/1.37 ( ! [X1 : $i] : (((irel @ sK5 @ sK20) = $true) | (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0)))) @ X1) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) = $true)) )),
% 1.76/1.37 inference(pi_clausification,[status(thm)],[f978])).
% 1.76/1.37 thf(f978,plain,(
% 1.76/1.37 ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))) = $true) | ((irel @ sK5 @ sK20) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) = $true)),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f977])).
% 1.76/1.37 thf(f977,plain,(
% 1.76/1.37 ((~ (irel @ sK5 @ sK20)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) = $true)),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f976])).
% 1.76/1.37 thf(f976,plain,(
% 1.76/1.37 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))))) | ((~ (irel @ sK5 @ sK20)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0)))) = $true)),
% 1.76/1.37 inference(not_proxy_clausification,[status(thm)],[f958])).
% 1.76/1.37 thf(f958,plain,(
% 1.76/1.37 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0))))) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0))))))) | ((~ (irel @ sK5 @ sK20)) = $false)),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f717])).
% 1.76/1.37 thf(f717,plain,(
% 1.76/1.37 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK16 @ Y0)) | (sK4 @ Y0))))))) | ((~ (irel @ sK5 @ sK20)) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK16 @ Y0)))))))),
% 1.76/1.37 inference(binary_proxy_clausification,[status(thm)],[f315])).
% 1.76/1.37 % SZS output end Proof for DTF2THF_27148
% 1.76/1.37 % (27246)------------------------------
% 1.76/1.37 % (27246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.37 % (27246)Termination reason: Refutation
% 1.76/1.37
% 1.76/1.37 % (27246)Memory used [KB]: 6652
% 1.76/1.37 % (27246)Time elapsed: 0.068 s
% 1.76/1.37 % (27246)Instructions burned: 168 (million)
% 1.76/1.37 % (27246)------------------------------
% 1.76/1.37 % (27246)------------------------------
% 1.76/1.37 % (27245)Success in time 0.07 s
%------------------------------------------------------------------------------