%------------------------------------------------------------------------------
% 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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:58:55 PM UTC 2026
% Result : Theorem 1.64s 1.59s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 30
% Syntax : Number of formulae : 540 ( 24 unt; 0 typ; 27 def)
% Number of atoms : 10788 (1930 equ; 0 cnn)
% Maximal formula atoms : 24 ( 19 avg)
% Number of connectives : 14395 (2321 ~;3239 |; 213 &;7690 @)
% ( 27 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 222 ( 222 >; 0 *; 0 +; 0 <<)
% Number of symbols : 88 ( 84 usr; 50 con; 0-3 aty)
% ( 899 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1899 (1288 ^; 604 !; 7 ?;1899 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
d_unsorted: $tType ).
thf(func_def_0,type,
unsorted: $tType ).
thf(func_def_1,type,
irel: $i > $i > $o ).
thf(func_def_2,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
iatom: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
inot: ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
itrue: $i > $o ).
thf(func_def_10,type,
ifalse: $i > $o ).
thf(func_def_11,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_16,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
ivalid: ( $i > $o ) > $o ).
thf(func_def_18,type,
isatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_20,type,
iinvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
d_unsorted: $tType ).
thf(func_def_22,type,
d2unsorted: d_unsorted > $i ).
thf(func_def_23,type,
d_unsorted_0: d_unsorted ).
thf(func_def_41,type,
sK0: $i > d_unsorted ).
thf(func_def_43,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
sK3: $i > $o ).
thf(func_def_45,type,
sK4: $i > $o ).
thf(func_def_119,type,
sK78: $i > $i ).
thf(func_def_120,type,
sK79: $i > $i ).
thf(func_def_121,type,
sK80: $i > $i ).
thf(func_def_122,type,
sK81: $i > $i ).
thf(func_def_123,type,
sK82: $i > $i ).
thf(func_def_124,type,
sK83: $i > $i ).
thf(func_def_125,type,
sK84: $i > $i ).
thf(func_def_126,type,
sK85: $i > $i ).
thf(func_def_127,type,
sK86: $i > $i ).
thf(func_def_128,type,
sK87: $i > $i ).
thf(func_def_129,type,
sK88: $i > $i ).
thf(func_def_130,type,
sK89: $i > $i ).
thf(f3621,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2083,f2156,f2219,f2506,f2512,f2518,f2520,f2562,f2568,f2576,f2584,f2664,f2668,f2692,f2712,f2726,f2728,f2760,f2832,f3003,f3071,f3073,f3086,f3094,f3105,f3142,f3147,f3161,f3174,f3201,f3223,f3240,f3243,f3246,f3264,f3271,f3281,f3295,f3299,f3568,f3587,f3604,f3620]) ).
thf(f3620,plain,
( spl1_25
| ~ spl1_37 ),
inference(avatar_contradiction_clause,[status(thm)],[f3619]) ).
thf(f3619,plain,
( $false
| spl1_25
| ~ spl1_37 ),
inference(subsumption_resolution,[status(thm)],[f2163,f3343]) ).
thf(f3343,plain,
( ! [X0: $i] :
( ( sK4 @ X0 )
= $false )
| ~ spl1_37 ),
inference(superposition,[status(thm)],[f2218,f3007]) ).
thf(f3007,plain,
! [X0: $i,X1: $i] : ( X0 = X1 ),
inference(superposition,[status(thm)],[f41,f41]) ).
thf(f41,plain,
! [X1: $i] :
( ( d2unsorted @ d_unsorted_0 )
= X1 ),
inference(forward_demodulation,[status(thm)],[f32,f35]) ).
thf(f35,plain,
! [X0: d_unsorted] : ( d_unsorted_0 = X0 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y4 @ Y3 )
| ~ ( irel @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ( Y0 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ( Y1 @ Y4 ) ) ) ) ) ) )
& ! [X1: $i] :
( ( d2unsorted @ ( sK0 @ X1 ) )
= X1 )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( ( 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] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( ( ~ ( irel @ Y5 @ Y7 )
| ~ ( irel @ Y3 @ Y5 )
| ( Y1 @ Y7 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( Y0 @ Y8 )
| ~ ( irel @ Y5 @ Y8 ) ) ) )
& ( ~ ( irel @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y6 @ Y8 )
| ( Y1 @ Y8 ) ) )
| ~ ( irel @ Y6 @ Y4 )
| ( Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( X3 = X4 )
| ( ( d2unsorted @ X3 )
!= ( d2unsorted @ X4 ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f13]) ).
thf(f13,plain,
! [X1: $i] :
( ? [X2: d_unsorted] :
( ( d2unsorted @ X2 )
= X1 )
=> ( ( d2unsorted @ ( sK0 @ X1 ) )
= X1 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y4 @ Y3 )
| ~ ( irel @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ( Y0 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ( Y1 @ Y4 ) ) ) ) ) ) )
& ! [X1: $i] :
? [X2: d_unsorted] :
( ( d2unsorted @ X2 )
= X1 )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( ( 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] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( ( ~ ( irel @ Y5 @ Y7 )
| ~ ( irel @ Y3 @ Y5 )
| ( Y1 @ Y7 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( Y0 @ Y8 )
| ~ ( irel @ Y5 @ Y8 ) ) ) )
& ( ~ ( irel @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y6 @ Y8 )
| ( Y1 @ Y8 ) ) )
| ~ ( irel @ Y6 @ Y4 )
| ( Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( X3 = X4 )
| ( ( d2unsorted @ X3 )
!= ( d2unsorted @ X4 ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ! [X1: $i] :
? [X2: d_unsorted] :
( ( d2unsorted @ X2 )
= X1 )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y4 @ Y3 )
| ~ ( irel @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ( Y0 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ( Y1 @ Y4 ) ) ) ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( ( d2unsorted @ X3 )
= ( d2unsorted @ X4 ) )
=> ( X3 = X4 ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( ( ~ ( irel @ Y5 @ Y7 )
| ~ ( irel @ Y3 @ Y5 )
| ( Y1 @ Y7 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( Y0 @ Y8 )
| ~ ( irel @ Y5 @ Y8 ) ) ) )
& ( ~ ( irel @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y6 @ Y8 )
| ( Y1 @ Y8 ) ) )
| ~ ( irel @ Y6 @ Y4 )
| ( Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( ( ~ ( irel @ Y5 @ Y7 )
| ~ ( irel @ Y3 @ Y5 )
| ( Y1 @ Y7 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( Y0 @ Y8 )
| ~ ( irel @ Y5 @ Y8 ) ) ) )
& ( ~ ( irel @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y6 @ Y8 )
| ( Y1 @ Y8 ) ) )
| ~ ( irel @ Y6 @ Y4 )
| ( Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) )
& ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y4 @ Y3 )
| ~ ( irel @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ( Y0 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ( Y1 @ Y4 ) ) ) ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ! [X1: $i] :
? [X2: d_unsorted] :
( ( d2unsorted @ X2 )
= X1 )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( ( d2unsorted @ X3 )
= ( d2unsorted @ X4 ) )
=> ( X3 = X4 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( ( ~ ( irel @ Y5 @ Y7 )
| ~ ( irel @ Y3 @ Y5 )
| ( Y1 @ Y7 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( Y0 @ Y8 )
| ~ ( irel @ Y5 @ Y8 ) ) ) )
& ( ~ ( irel @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ~ ( irel @ Y6 @ Y8 )
| ( Y1 @ Y8 ) ) )
| ~ ( irel @ Y6 @ Y4 )
| ( Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) )
& ! [X20: d_unsorted] : ( d_unsorted_0 = X20 )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y4 @ Y3 )
| ~ ( irel @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ( Y0 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ( Y1 @ Y4 ) ) ) ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ! [X56: $i] :
? [X57: d_unsorted] :
( ( d2unsorted @ X57 )
= X56 )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ! [X69: d_unsorted,X70: d_unsorted] :
( ( ( d2unsorted @ X70 )
= ( d2unsorted @ X69 ) )
=> ( X69 = X70 ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ~ ( X0 @ X2 ) ) )
= mimplies )
& ( ( ^ [X3: $i > $o] :
! [X4: $i] : ( X3 @ X4 ) )
= ivalid )
& ( ( ^ [X5: $i > $o,X6: $i] :
! [X7: $i] :
( ( X5 @ X7 )
| ~ ( irel @ X6 @ X7 ) ) )
= mbox_s4 )
& ( ( ^ [X8: $i > $o,X9: $i] :
~ ( X8 @ X9 ) )
= mnot )
& ( ( ^ [X10: $i > $o,X11: $i > $o,X12: $i] :
~ ! [X13: $i,X14: $i,X15: $i,X16: $i,X17: $i] :
( ( ( ( X10 @ X16 )
| ~ ( irel @ X14 @ X16 )
| ~ ! [X18: $i] :
( ( X11 @ X18 )
| ~ ( irel @ X14 @ X18 ) )
| ~ ( irel @ X17 @ X14 ) )
& ( ~ ! [X19: $i] :
( ~ ( irel @ X15 @ X19 )
| ( X10 @ X19 ) )
| ( X11 @ X13 )
| ~ ( irel @ X17 @ X15 )
| ~ ( irel @ X15 @ X13 ) ) )
| ~ ( irel @ X12 @ X17 ) ) )
= ixor )
& ! [X20: d_unsorted] : ( d_unsorted_0 = X20 )
& ( iimplies
= ( ^ [X21: $i > $o,X22: $i > $o,X23: $i] :
( ~ ! [X24: $i] :
( ~ ( irel @ X23 @ X24 )
| ( X21 @ X24 ) )
| ! [X25: $i] :
( ( X22 @ X25 )
| ~ ( irel @ X23 @ X25 ) ) ) ) )
& ( iatom
= ( ^ [X26: $i > $o,X27: $i] : ( X26 @ X27 ) ) )
& ( ( ^ [X28: $i > $o] :
! [X29: $i] :
~ ( X28 @ X29 ) )
= iinvalid )
& ( mor
= ( ^ [X30: $i > $o,X31: $i > $o,X32: $i] :
( ( X30 @ X32 )
| ( X31 @ X32 ) ) ) )
& ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
& ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
& ( ( ^ [X33: $i > $o] :
~ ! [X34: $i] :
~ ( X33 @ X34 ) )
= isatisfiable )
& ( ior
= ( ^ [X35: $i > $o,X36: $i > $o,X37: $i] :
( ! [X38: $i] :
( ~ ( irel @ X37 @ X38 )
| ( X36 @ X38 ) )
| ! [X39: $i] :
( ( X35 @ X39 )
| ~ ( irel @ X37 @ X39 ) ) ) ) )
& ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
& ( ( ^ [X40: $i > $o] :
~ ! [X41: $i] : ( X40 @ X41 ) )
= icountersatisfiable )
& ( iequiv
= ( ^ [X42: $i > $o,X43: $i > $o,X44: $i] :
( ! [X45: $i,X46: $i] :
( ( X43 @ X45 )
| ~ ! [X47: $i] :
( ( X42 @ X47 )
| ~ ( irel @ X46 @ X47 ) )
| ~ ( irel @ X44 @ X46 )
| ~ ( irel @ X46 @ X45 ) )
& ! [X48: $i,X49: $i] :
( ( X42 @ X49 )
| ~ ! [X50: $i] :
( ( X43 @ X50 )
| ~ ( irel @ X48 @ X50 ) )
| ~ ( irel @ X44 @ X48 )
| ~ ( irel @ X48 @ X49 ) ) ) ) )
& ( ( ^ [X51: $i > $o,X52: $i > $o,X53: $i] :
( ! [X54: $i] :
( ( X51 @ X54 )
| ~ ( irel @ X53 @ X54 ) )
& ! [X55: $i] :
( ~ ( irel @ X53 @ X55 )
| ( X52 @ X55 ) ) ) )
= iand )
& ! [X56: $i] :
? [X57: d_unsorted] :
( ( d2unsorted @ X57 )
= X56 )
& ( inot
= ( ^ [X58: $i > $o,X59: $i] :
~ ! [X60: $i] :
( ~ ( irel @ X59 @ X60 )
| ( X58 @ X60 ) ) ) )
& ( ( ^ [X61: $i > $o,X62: $i > $o,X63: $i] :
( ( X62 @ X63 )
& ( X61 @ X63 ) ) )
= mand )
& ( ( ^ [X64: $i > $o,X65: $i > $o,X66: $i] :
( ~ ! [X67: $i] :
( ~ ( irel @ X66 @ X67 )
| ( X65 @ X67 ) )
| ! [X68: $i] :
( ( X64 @ X68 )
| ~ ( irel @ X66 @ X68 ) ) ) )
= iimplied )
& ! [X69: d_unsorted,X70: d_unsorted] :
( ( ( d2unsorted @ X70 )
= ( d2unsorted @ X69 ) )
=> ( X69 = X70 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ( ^ [X0: $i > $o,X6: $i > $o,X7: $i] :
( ( X6 @ X7 )
| ~ ( X0 @ X7 ) ) )
= mimplies )
& ( ( ^ [X18: $i > $o] :
! [X19: $i] : ( X18 @ X19 ) )
= ivalid )
& ( ( ^ [X8: $i > $o,X4: $i] :
! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X4 @ X5 ) ) )
= mbox_s4 )
& ( ( ^ [X4: $i > $o,X0: $i] :
~ ( X4 @ X0 ) )
= mnot )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
~ ! [X15: $i,X16: $i,X14: $i,X17: $i,X5: $i] :
( ( ( ( X8 @ X17 )
| ~ ( irel @ X16 @ X17 )
| ~ ! [X13: $i] :
( ( X9 @ X13 )
| ~ ( irel @ X16 @ X13 ) )
| ~ ( irel @ X5 @ X16 ) )
& ( ~ ! [X11: $i] :
( ~ ( irel @ X14 @ X11 )
| ( X8 @ X11 ) )
| ( X9 @ X15 )
| ~ ( irel @ X5 @ X14 )
| ~ ( irel @ X14 @ X15 ) ) )
| ~ ( irel @ X7 @ X5 ) ) )
= ixor )
& ! [X1: d_unsorted] : ( d_unsorted_0 = X1 )
& ( iimplies
= ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ~ ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X8 @ X5 ) )
| ! [X5: $i] :
( ( X9 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) ) ) )
& ( iatom
= ( ^ [X8: $i > $o,X7: $i] : ( X8 @ X7 ) ) )
& ( ( ^ [X18: $i > $o] :
! [X19: $i] :
~ ( X18 @ X19 ) )
= iinvalid )
& ( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X0: $i] :
( ( X4 @ X0 )
| ( X5 @ X0 ) ) ) )
& ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
& ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
& ( ( ^ [X18: $i > $o] :
~ ! [X19: $i] :
~ ( X18 @ X19 ) )
= isatisfiable )
& ( ior
= ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X9 @ X5 ) )
| ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) ) ) )
& ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
& ( ( ^ [X18: $i > $o] :
~ ! [X19: $i] : ( X18 @ X19 ) )
= icountersatisfiable )
& ( iequiv
= ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ! [X10: $i,X5: $i] :
( ( X9 @ X10 )
| ~ ! [X11: $i] :
( ( X8 @ X11 )
| ~ ( irel @ X5 @ X11 ) )
| ~ ( irel @ X7 @ X5 )
| ~ ( irel @ X5 @ X10 ) )
& ! [X5: $i,X12: $i] :
( ( X8 @ X12 )
| ~ ! [X13: $i] :
( ( X9 @ X13 )
| ~ ( irel @ X5 @ X13 ) )
| ~ ( irel @ X7 @ X5 )
| ~ ( irel @ X5 @ X12 ) ) ) ) )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) )
& ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X9 @ X5 ) ) ) )
= iand )
& ! [X0: $i] :
? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 )
& ( inot
= ( ^ [X8: $i > $o,X7: $i] :
~ ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X8 @ X5 ) ) ) )
& ( ( ^ [X4: $i > $o,X5: $i > $o,X0: $i] :
( ( X5 @ X0 )
& ( X4 @ X0 ) ) )
= mand )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ~ ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X9 @ X5 ) )
| ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) ) )
= iimplied )
& ! [X2: d_unsorted,X3: d_unsorted] :
( ( ( d2unsorted @ X2 )
= ( d2unsorted @ X3 ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MacNcZ7HSP/DTF2THF_29558.p',lcl696_1) ).
thf(f32,plain,
! [X1: $i] :
( ( d2unsorted @ ( sK0 @ X1 ) )
= X1 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f2218,plain,
( ( ( sK4 @ sK74 )
= $false )
| ~ spl1_37 ),
inference(avatar_component_clause,[status(thm)],[f2216]) ).
thf(f2216,definition,
( spl1_37
<=> ( ( sK4 @ sK74 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_37])],[avatar_definition]) ).
thf(f2163,plain,
( ( ( sK4 @ sK59 )
!= $false )
| spl1_25 ),
inference(avatar_component_clause,[status(thm)],[f2162]) ).
thf(f2162,definition,
( spl1_25
<=> ( ( sK4 @ sK59 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_25])],[avatar_definition]) ).
thf(f3604,plain,
( ~ spl1_1
| ~ spl1_25
| spl1_26
| spl1_171 ),
inference(avatar_contradiction_clause,[status(thm)],[f3603]) ).
thf(f3603,plain,
( $false
| ~ spl1_1
| ~ spl1_25
| spl1_26
| spl1_171 ),
inference(subsumption_resolution,[status(thm)],[f3602,f3001]) ).
thf(f3001,plain,
( ( $false
!= ( irel @ sK5 @ sK5 ) )
| spl1_171 ),
inference(avatar_component_clause,[status(thm)],[f3000]) ).
thf(f3000,definition,
( spl1_171
<=> ( $false
= ( irel @ sK5 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_171])],[avatar_definition]) ).
thf(f3602,plain,
( ( $false
= ( irel @ sK5 @ sK5 ) )
| ~ spl1_1
| ~ spl1_25
| spl1_26 ),
inference(trivial_inequality_removal,[status(thm)],[f3601]) ).
thf(f3601,plain,
( ( $false != $false )
| ( $false
= ( irel @ sK5 @ sK5 ) )
| ~ spl1_1
| ~ spl1_25
| spl1_26 ),
inference(equality_factoring,[status(thm)],[f3573]) ).
thf(f3573,plain,
( ! [X3: $i,X1: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false ) )
| ~ spl1_1
| ~ spl1_25
| spl1_26 ),
inference(trivial_inequality_removal,[status(thm)],[f3572]) ).
thf(f3572,plain,
( ! [X3: $i,X1: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( $true = $false )
| ( ( irel @ sK5 @ X1 )
= $false ) )
| ~ spl1_1
| ~ spl1_25
| spl1_26 ),
inference(forward_demodulation,[status(thm)],[f3571,f3187]) ).
thf(f3187,plain,
( ! [X0: $i] :
( ( sK4 @ X0 )
= $false )
| ~ spl1_25 ),
inference(superposition,[status(thm)],[f2164,f3007]) ).
thf(f2164,plain,
( ( ( sK4 @ sK59 )
= $false )
| ~ spl1_25 ),
inference(avatar_component_clause,[status(thm)],[f2162]) ).
thf(f3571,plain,
( ! [X3: $i,X1: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( sK4 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false ) )
| ~ spl1_1
| spl1_26 ),
inference(subsumption_resolution,[status(thm)],[f2075,f3326]) ).
thf(f3326,plain,
( ! [X0: $i] :
( $false
!= ( sK3 @ X0 ) )
| spl1_26 ),
inference(superposition,[status(thm)],[f2167,f3007]) ).
thf(f2167,plain,
( ( ( sK3 @ sK8 )
!= $false )
| spl1_26 ),
inference(avatar_component_clause,[status(thm)],[f2166]) ).
thf(f2166,definition,
( spl1_26
<=> ( ( sK3 @ sK8 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_26])],[avatar_definition]) ).
thf(f2075,plain,
( ! [X3: $i,X1: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( sK4 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( sK3 @ ( sK87 @ X1 ) )
= $false ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f2074]) ).
thf(f2074,definition,
( spl1_1
<=> ! [X1: $i,X3: $i] :
( ( ( sK3 @ ( sK87 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( sK4 @ X3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f3587,plain,
( ~ spl1_40
| ~ spl1_125
| spl1_174 ),
inference(avatar_contradiction_clause,[status(thm)],[f3586]) ).
thf(f3586,plain,
( $false
| ~ spl1_40
| ~ spl1_125
| spl1_174 ),
inference(trivial_inequality_removal,[status(thm)],[f3576]) ).
thf(f3576,plain,
( ( $true = $false )
| ~ spl1_40
| ~ spl1_125
| spl1_174 ),
inference(backward_demodulation,[status(thm)],[f2722,f3574]) ).
thf(f3574,plain,
( ! [X1: $i] :
( $false
= ( irel @ sK10 @ X1 ) )
| ~ spl1_40
| spl1_174 ),
inference(subsumption_resolution,[status(thm)],[f2233,f3331]) ).
thf(f3331,plain,
( ! [X0: $i] :
( $true
!= ( sK3 @ X0 ) )
| spl1_174 ),
inference(superposition,[status(thm)],[f3084,f3007]) ).
thf(f3084,plain,
( ( $true
!= ( sK3 @ sK5 ) )
| spl1_174 ),
inference(avatar_component_clause,[status(thm)],[f3083]) ).
thf(f3083,definition,
( spl1_174
<=> ( $true
= ( sK3 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_174])],[avatar_definition]) ).
thf(f2233,plain,
( ! [X1: $i] :
( ( $false
= ( irel @ sK10 @ X1 ) )
| ( ( sK3 @ X1 )
= $true ) )
| ~ spl1_40 ),
inference(avatar_component_clause,[status(thm)],[f2232]) ).
thf(f2232,definition,
( spl1_40
<=> ! [X1: $i] :
( ( $false
= ( irel @ sK10 @ X1 ) )
| ( ( sK3 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1_40])],[avatar_definition]) ).
thf(f2722,plain,
( ( $true
= ( irel @ sK10 @ sK22 ) )
| ~ spl1_125 ),
inference(avatar_component_clause,[status(thm)],[f2720]) ).
thf(f2720,definition,
( spl1_125
<=> ( $true
= ( irel @ sK10 @ sK22 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_125])],[avatar_definition]) ).
thf(f3568,plain,
( spl1_26
| ~ spl1_170 ),
inference(avatar_contradiction_clause,[status(thm)],[f3567]) ).
thf(f3567,plain,
( $false
| spl1_26
| ~ spl1_170 ),
inference(subsumption_resolution,[status(thm)],[f2998,f3326]) ).
thf(f2998,plain,
( ( ( sK3 @ ( sK89 @ sK5 ) )
= $false )
| ~ spl1_170 ),
inference(avatar_component_clause,[status(thm)],[f2996]) ).
thf(f2996,definition,
( spl1_170
<=> ( ( sK3 @ ( sK89 @ sK5 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_170])],[avatar_definition]) ).
thf(f3299,plain,
( ~ spl1_26
| ~ spl1_27
| ~ spl1_120 ),
inference(avatar_contradiction_clause,[status(thm)],[f3298]) ).
thf(f3298,plain,
( $false
| ~ spl1_26
| ~ spl1_27
| ~ spl1_120 ),
inference(trivial_inequality_removal,[status(thm)],[f3297]) ).
thf(f3297,plain,
( ( $true = $false )
| ~ spl1_26
| ~ spl1_27
| ~ spl1_120 ),
inference(forward_demodulation,[status(thm)],[f2691,f3257]) ).
thf(f3257,plain,
( ! [X1: $i] :
( $false
= ( irel @ sK6 @ X1 ) )
| ~ spl1_26
| ~ spl1_27 ),
inference(trivial_inequality_removal,[status(thm)],[f3256]) ).
thf(f3256,plain,
( ! [X1: $i] :
( ( $false
= ( irel @ sK6 @ X1 ) )
| ( $true = $false ) )
| ~ spl1_26
| ~ spl1_27 ),
inference(forward_demodulation,[status(thm)],[f2171,f3098]) ).
thf(f3098,plain,
( ! [X0: $i] :
( $false
= ( sK3 @ X0 ) )
| ~ spl1_26 ),
inference(superposition,[status(thm)],[f2168,f3007]) ).
thf(f2168,plain,
( ( ( sK3 @ sK8 )
= $false )
| ~ spl1_26 ),
inference(avatar_component_clause,[status(thm)],[f2166]) ).
thf(f2171,plain,
( ! [X1: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( $false
= ( irel @ sK6 @ X1 ) ) )
| ~ spl1_27 ),
inference(avatar_component_clause,[status(thm)],[f2170]) ).
thf(f2170,definition,
( spl1_27
<=> ! [X1: $i] :
( ( $false
= ( irel @ sK6 @ X1 ) )
| ( ( sK3 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1_27])],[avatar_definition]) ).
thf(f2691,plain,
( ( ( irel @ sK6 @ sK36 )
= $true )
| ~ spl1_120 ),
inference(avatar_component_clause,[status(thm)],[f2689]) ).
thf(f2689,definition,
( spl1_120
<=> ( ( irel @ sK6 @ sK36 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_120])],[avatar_definition]) ).
thf(f3295,plain,
( ~ spl1_26
| ~ spl1_27
| ~ spl1_131 ),
inference(avatar_contradiction_clause,[status(thm)],[f3294]) ).
thf(f3294,plain,
( $false
| ~ spl1_26
| ~ spl1_27
| ~ spl1_131 ),
inference(trivial_inequality_removal,[status(thm)],[f3293]) ).
thf(f3293,plain,
( ( $true = $false )
| ~ spl1_26
| ~ spl1_27
| ~ spl1_131 ),
inference(forward_demodulation,[status(thm)],[f2759,f3257]) ).
thf(f2759,plain,
( ( ( irel @ sK6 @ sK31 )
= $true )
| ~ spl1_131 ),
inference(avatar_component_clause,[status(thm)],[f2757]) ).
thf(f2757,definition,
( spl1_131
<=> ( ( irel @ sK6 @ sK31 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_131])],[avatar_definition]) ).
thf(f3281,plain,
( ~ spl1_26
| ~ spl1_27
| ~ spl1_124 ),
inference(avatar_contradiction_clause,[status(thm)],[f3280]) ).
thf(f3280,plain,
( $false
| ~ spl1_26
| ~ spl1_27
| ~ spl1_124 ),
inference(trivial_inequality_removal,[status(thm)],[f3279]) ).
thf(f3279,plain,
( ( $true = $false )
| ~ spl1_26
| ~ spl1_27
| ~ spl1_124 ),
inference(forward_demodulation,[status(thm)],[f2711,f3257]) ).
thf(f2711,plain,
( ( $true
= ( irel @ sK6 @ sK34 ) )
| ~ spl1_124 ),
inference(avatar_component_clause,[status(thm)],[f2709]) ).
thf(f2709,definition,
( spl1_124
<=> ( $true
= ( irel @ sK6 @ sK34 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_124])],[avatar_definition]) ).
thf(f3271,plain,
( ~ spl1_26
| ~ spl1_27
| ~ spl1_145 ),
inference(avatar_contradiction_clause,[status(thm)],[f3270]) ).
thf(f3270,plain,
( $false
| ~ spl1_26
| ~ spl1_27
| ~ spl1_145 ),
inference(trivial_inequality_removal,[status(thm)],[f3269]) ).
thf(f3269,plain,
( ( $true = $false )
| ~ spl1_26
| ~ spl1_27
| ~ spl1_145 ),
inference(forward_demodulation,[status(thm)],[f2830,f3257]) ).
thf(f2830,plain,
( ( $true
= ( irel @ sK6 @ sK24 ) )
| ~ spl1_145 ),
inference(avatar_component_clause,[status(thm)],[f2828]) ).
thf(f2828,definition,
( spl1_145
<=> ( $true
= ( irel @ sK6 @ sK24 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_145])],[avatar_definition]) ).
thf(f3264,plain,
( ~ spl1_26
| ~ spl1_27
| ~ spl1_98 ),
inference(avatar_contradiction_clause,[status(thm)],[f3263]) ).
thf(f3263,plain,
( $false
| ~ spl1_26
| ~ spl1_27
| ~ spl1_98 ),
inference(trivial_inequality_removal,[status(thm)],[f3262]) ).
thf(f3262,plain,
( ( $true = $false )
| ~ spl1_26
| ~ spl1_27
| ~ spl1_98 ),
inference(forward_demodulation,[status(thm)],[f2560,f3257]) ).
thf(f2560,plain,
( ( $true
= ( irel @ sK6 @ sK44 ) )
| ~ spl1_98 ),
inference(avatar_component_clause,[status(thm)],[f2558]) ).
thf(f2558,definition,
( spl1_98
<=> ( $true
= ( irel @ sK6 @ sK44 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_98])],[avatar_definition]) ).
thf(f3246,plain,
( ~ spl1_26
| ~ spl1_40
| ~ spl1_101 ),
inference(avatar_contradiction_clause,[status(thm)],[f3245]) ).
thf(f3245,plain,
( $false
| ~ spl1_26
| ~ spl1_40
| ~ spl1_101 ),
inference(trivial_inequality_removal,[status(thm)],[f3244]) ).
thf(f3244,plain,
( ( $true = $false )
| ~ spl1_26
| ~ spl1_40
| ~ spl1_101 ),
inference(forward_demodulation,[status(thm)],[f2582,f3209]) ).
thf(f3209,plain,
( ! [X1: $i] :
( $false
= ( irel @ sK10 @ X1 ) )
| ~ spl1_26
| ~ spl1_40 ),
inference(trivial_inequality_removal,[status(thm)],[f3208]) ).
thf(f3208,plain,
( ! [X1: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK10 @ X1 ) ) )
| ~ spl1_26
| ~ spl1_40 ),
inference(forward_demodulation,[status(thm)],[f2233,f3098]) ).
thf(f2582,plain,
( ( $true
= ( irel @ sK10 @ sK45 ) )
| ~ spl1_101 ),
inference(avatar_component_clause,[status(thm)],[f2580]) ).
thf(f2580,definition,
( spl1_101
<=> ( $true
= ( irel @ sK10 @ sK45 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_101])],[avatar_definition]) ).
thf(f3243,plain,
( ~ spl1_26
| ~ spl1_40
| ~ spl1_99 ),
inference(avatar_contradiction_clause,[status(thm)],[f3242]) ).
thf(f3242,plain,
( $false
| ~ spl1_26
| ~ spl1_40
| ~ spl1_99 ),
inference(trivial_inequality_removal,[status(thm)],[f3241]) ).
thf(f3241,plain,
( ( $true = $false )
| ~ spl1_26
| ~ spl1_40
| ~ spl1_99 ),
inference(forward_demodulation,[status(thm)],[f2567,f3209]) ).
thf(f2567,plain,
( ( $true
= ( irel @ sK10 @ sK46 ) )
| ~ spl1_99 ),
inference(avatar_component_clause,[status(thm)],[f2565]) ).
thf(f2565,definition,
( spl1_99
<=> ( $true
= ( irel @ sK10 @ sK46 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_99])],[avatar_definition]) ).
thf(f3240,plain,
( ~ spl1_26
| ~ spl1_40
| ~ spl1_91 ),
inference(avatar_contradiction_clause,[status(thm)],[f3239]) ).
thf(f3239,plain,
( $false
| ~ spl1_26
| ~ spl1_40
| ~ spl1_91 ),
inference(trivial_inequality_removal,[status(thm)],[f3238]) ).
thf(f3238,plain,
( ( $true = $false )
| ~ spl1_26
| ~ spl1_40
| ~ spl1_91 ),
inference(forward_demodulation,[status(thm)],[f2511,f3209]) ).
thf(f2511,plain,
( ( $true
= ( irel @ sK10 @ sK49 ) )
| ~ spl1_91 ),
inference(avatar_component_clause,[status(thm)],[f2509]) ).
thf(f2509,definition,
( spl1_91
<=> ( $true
= ( irel @ sK10 @ sK49 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_91])],[avatar_definition]) ).
thf(f3223,plain,
( ~ spl1_25
| ~ spl1_31
| ~ spl1_110 ),
inference(avatar_contradiction_clause,[status(thm)],[f3222]) ).
thf(f3222,plain,
( $false
| ~ spl1_25
| ~ spl1_31
| ~ spl1_110 ),
inference(trivial_inequality_removal,[status(thm)],[f3221]) ).
thf(f3221,plain,
( ( $true = $false )
| ~ spl1_25
| ~ spl1_31
| ~ spl1_110 ),
inference(forward_demodulation,[status(thm)],[f2629,f3196]) ).
thf(f3196,plain,
( ! [X1: $i] :
( ( irel @ sK7 @ X1 )
= $false )
| ~ spl1_25
| ~ spl1_31 ),
inference(trivial_inequality_removal,[status(thm)],[f3192]) ).
thf(f3192,plain,
( ! [X1: $i] :
( ( ( irel @ sK7 @ X1 )
= $false )
| ( $true = $false ) )
| ~ spl1_25
| ~ spl1_31 ),
inference(backward_demodulation,[status(thm)],[f2189,f3187]) ).
thf(f2189,plain,
( ! [X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK7 @ X1 )
= $false ) )
| ~ spl1_31 ),
inference(avatar_component_clause,[status(thm)],[f2188]) ).
thf(f2188,definition,
( spl1_31
<=> ! [X1: $i] :
( ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_31])],[avatar_definition]) ).
thf(f2629,plain,
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ~ spl1_110 ),
inference(avatar_component_clause,[status(thm)],[f2627]) ).
thf(f2627,definition,
( spl1_110
<=> ( $true
= ( irel @ sK7 @ sK23 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_110])],[avatar_definition]) ).
thf(f3201,plain,
( ~ spl1_25
| ~ spl1_70
| ~ spl1_78 ),
inference(avatar_contradiction_clause,[status(thm)],[f3200]) ).
thf(f3200,plain,
( $false
| ~ spl1_25
| ~ spl1_70
| ~ spl1_78 ),
inference(trivial_inequality_removal,[status(thm)],[f3199]) ).
thf(f3199,plain,
( ( $true = $false )
| ~ spl1_25
| ~ spl1_70
| ~ spl1_78 ),
inference(backward_demodulation,[status(thm)],[f2433,f3198]) ).
thf(f3198,plain,
( ! [X2: $i] :
( ( irel @ sK9 @ X2 )
= $false )
| ~ spl1_25
| ~ spl1_70 ),
inference(trivial_inequality_removal,[status(thm)],[f3190]) ).
thf(f3190,plain,
( ! [X2: $i] :
( ( ( irel @ sK9 @ X2 )
= $false )
| ( $true = $false ) )
| ~ spl1_25
| ~ spl1_70 ),
inference(backward_demodulation,[status(thm)],[f2388,f3187]) ).
thf(f2388,plain,
( ! [X2: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( ( irel @ sK9 @ X2 )
= $false ) )
| ~ spl1_70 ),
inference(avatar_component_clause,[status(thm)],[f2387]) ).
thf(f2387,definition,
( spl1_70
<=> ! [X2: $i] :
( ( ( irel @ sK9 @ X2 )
= $false )
| ( $true
= ( sK4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_70])],[avatar_definition]) ).
thf(f2433,plain,
( ( $true
= ( irel @ sK9 @ sK8 ) )
| ~ spl1_78 ),
inference(avatar_component_clause,[status(thm)],[f2431]) ).
thf(f2431,definition,
( spl1_78
<=> ( $true
= ( irel @ sK9 @ sK8 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_78])],[avatar_definition]) ).
thf(f3174,plain,
( ~ spl1_23
| spl1_25
| ~ spl1_26
| spl1_171 ),
inference(avatar_contradiction_clause,[status(thm)],[f3173]) ).
thf(f3173,plain,
( $false
| ~ spl1_23
| spl1_25
| ~ spl1_26
| spl1_171 ),
inference(subsumption_resolution,[status(thm)],[f3172,f3001]) ).
thf(f3172,plain,
( ( $false
= ( irel @ sK5 @ sK5 ) )
| ~ spl1_23
| spl1_25
| ~ spl1_26 ),
inference(trivial_inequality_removal,[status(thm)],[f3171]) ).
thf(f3171,plain,
( ( $false != $false )
| ( $false
= ( irel @ sK5 @ sK5 ) )
| ~ spl1_23
| spl1_25
| ~ spl1_26 ),
inference(equality_factoring,[status(thm)],[f3165]) ).
thf(f3165,plain,
( ! [X2: $i,X1: $i] :
( ( ( irel @ sK5 @ X2 )
= $false )
| ( ( irel @ X2 @ X1 )
= $false ) )
| ~ spl1_23
| spl1_25
| ~ spl1_26 ),
inference(trivial_inequality_removal,[status(thm)],[f3164]) ).
thf(f3164,plain,
( ! [X2: $i,X1: $i] :
( ( ( irel @ X2 @ X1 )
= $false )
| ( ( irel @ sK5 @ X2 )
= $false )
| ( $true = $false ) )
| ~ spl1_23
| spl1_25
| ~ spl1_26 ),
inference(forward_demodulation,[status(thm)],[f3163,f3098]) ).
thf(f3163,plain,
( ! [X2: $i,X1: $i] :
( ( ( irel @ sK5 @ X2 )
= $false )
| ( ( sK3 @ X1 )
= $true )
| ( ( irel @ X2 @ X1 )
= $false ) )
| ~ spl1_23
| spl1_25 ),
inference(subsumption_resolution,[status(thm)],[f2155,f3096]) ).
thf(f3096,plain,
( ! [X0: $i] :
( ( sK4 @ X0 )
!= $false )
| spl1_25 ),
inference(superposition,[status(thm)],[f2163,f3007]) ).
thf(f2155,plain,
( ! [X2: $i,X1: $i] :
( ( ( irel @ sK5 @ X2 )
= $false )
| ( ( sK4 @ ( sK79 @ X2 ) )
= $false )
| ( ( sK3 @ X1 )
= $true )
| ( ( irel @ X2 @ X1 )
= $false ) )
| ~ spl1_23 ),
inference(avatar_component_clause,[status(thm)],[f2154]) ).
thf(f2154,definition,
( spl1_23
<=> ! [X2: $i,X1: $i] :
( ( ( sK4 @ ( sK79 @ X2 ) )
= $false )
| ( ( sK3 @ X1 )
= $true )
| ( ( irel @ sK5 @ X2 )
= $false )
| ( ( irel @ X2 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl1_23])],[avatar_definition]) ).
thf(f3161,plain,
( ~ spl1_22
| spl1_25
| ~ spl1_26
| spl1_171 ),
inference(avatar_contradiction_clause,[status(thm)],[f3160]) ).
thf(f3160,plain,
( $false
| ~ spl1_22
| spl1_25
| ~ spl1_26
| spl1_171 ),
inference(subsumption_resolution,[status(thm)],[f3159,f3001]) ).
thf(f3159,plain,
( ( $false
= ( irel @ sK5 @ sK5 ) )
| ~ spl1_22
| spl1_25
| ~ spl1_26 ),
inference(trivial_inequality_removal,[status(thm)],[f3158]) ).
thf(f3158,plain,
( ( $false != $false )
| ( $false
= ( irel @ sK5 @ sK5 ) )
| ~ spl1_22
| spl1_25
| ~ spl1_26 ),
inference(equality_factoring,[status(thm)],[f3152]) ).
thf(f3152,plain,
( ! [X3: $i,X4: $i] :
( ( $false
= ( irel @ sK5 @ X3 ) )
| ( $false
= ( irel @ X3 @ X4 ) ) )
| ~ spl1_22
| spl1_25
| ~ spl1_26 ),
inference(trivial_inequality_removal,[status(thm)],[f3151]) ).
thf(f3151,plain,
( ! [X3: $i,X4: $i] :
( ( $false
= ( irel @ sK5 @ X3 ) )
| ( $false
= ( irel @ X3 @ X4 ) )
| ( $true = $false ) )
| ~ spl1_22
| spl1_25
| ~ spl1_26 ),
inference(forward_demodulation,[status(thm)],[f3150,f3098]) ).
thf(f3150,plain,
( ! [X3: $i,X4: $i] :
( ( $false
= ( irel @ X3 @ X4 ) )
| ( $false
= ( irel @ sK5 @ X3 ) )
| ( ( sK3 @ X4 )
= $true ) )
| ~ spl1_22
| spl1_25 ),
inference(subsumption_resolution,[status(thm)],[f2152,f3096]) ).
thf(f2152,plain,
( ! [X3: $i,X4: $i] :
( ( ( sK4 @ ( sK78 @ X3 ) )
= $false )
| ( $false
= ( irel @ sK5 @ X3 ) )
| ( ( sK3 @ X4 )
= $true )
| ( $false
= ( irel @ X3 @ X4 ) ) )
| ~ spl1_22 ),
inference(avatar_component_clause,[status(thm)],[f2151]) ).
thf(f2151,definition,
( spl1_22
<=> ! [X4: $i,X3: $i] :
( ( ( sK4 @ ( sK78 @ X3 ) )
= $false )
| ( $false
= ( irel @ sK5 @ X3 ) )
| ( ( sK3 @ X4 )
= $true )
| ( $false
= ( irel @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_22])],[avatar_definition]) ).
thf(f3147,plain,
~ spl1_171,
inference(avatar_contradiction_clause,[status(thm)],[f3146]) ).
thf(f3146,plain,
( $false
| ~ spl1_171 ),
inference(trivial_inequality_removal,[status(thm)],[f3145]) ).
thf(f3145,plain,
( ( $true = $false )
| ~ spl1_171 ),
inference(backward_demodulation,[status(thm)],[f37,f3143]) ).
thf(f3143,plain,
( ! [X0: $i] :
( $false
= ( irel @ X0 @ X0 ) )
| ~ spl1_171 ),
inference(superposition,[status(thm)],[f3002,f3007]) ).
thf(f3002,plain,
( ( $false
= ( irel @ sK5 @ sK5 ) )
| ~ spl1_171 ),
inference(avatar_component_clause,[status(thm)],[f3000]) ).
thf(f37,plain,
( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f3142,plain,
( ~ spl1_26
| spl1_36 ),
inference(avatar_contradiction_clause,[status(thm)],[f3141]) ).
thf(f3141,plain,
( $false
| ~ spl1_26
| spl1_36 ),
inference(subsumption_resolution,[status(thm)],[f3137,f3098]) ).
thf(f3137,plain,
( ! [X0: $i] :
( $false
!= ( sK3 @ X0 ) )
| spl1_36 ),
inference(superposition,[status(thm)],[f2213,f3007]) ).
thf(f2213,plain,
( ( ( sK3 @ sK73 )
!= $false )
| spl1_36 ),
inference(avatar_component_clause,[status(thm)],[f2212]) ).
thf(f2212,definition,
( spl1_36
<=> ( ( sK3 @ sK73 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_36])],[avatar_definition]) ).
thf(f3105,plain,
( ~ spl1_26
| ~ spl1_174 ),
inference(avatar_contradiction_clause,[status(thm)],[f3104]) ).
thf(f3104,plain,
( $false
| ~ spl1_26
| ~ spl1_174 ),
inference(trivial_inequality_removal,[status(thm)],[f3102]) ).
thf(f3102,plain,
( ( $true = $false )
| ~ spl1_26
| ~ spl1_174 ),
inference(backward_demodulation,[status(thm)],[f3085,f3098]) ).
thf(f3085,plain,
( ( $true
= ( sK3 @ sK5 ) )
| ~ spl1_174 ),
inference(avatar_component_clause,[status(thm)],[f3083]) ).
thf(f3094,plain,
( ~ spl1_25
| ~ spl1_169 ),
inference(avatar_contradiction_clause,[status(thm)],[f3093]) ).
thf(f3093,plain,
( $false
| ~ spl1_25
| ~ spl1_169 ),
inference(trivial_inequality_removal,[status(thm)],[f3089]) ).
thf(f3089,plain,
( ( $true = $false )
| ~ spl1_25
| ~ spl1_169 ),
inference(backward_demodulation,[status(thm)],[f3037,f3088]) ).
thf(f3088,plain,
( ! [X0: $i] :
( ( sK4 @ X0 )
= $false )
| ~ spl1_25 ),
inference(superposition,[status(thm)],[f2164,f3007]) ).
thf(f3037,plain,
( ! [X0: $i] :
( $true
= ( sK4 @ X0 ) )
| ~ spl1_169 ),
inference(superposition,[status(thm)],[f2994,f3007]) ).
thf(f2994,plain,
( ( $true
= ( sK4 @ sK5 ) )
| ~ spl1_169 ),
inference(avatar_component_clause,[status(thm)],[f2992]) ).
thf(f2992,definition,
( spl1_169
<=> ( $true
= ( sK4 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_169])],[avatar_definition]) ).
thf(f3086,plain,
( spl1_171
| spl1_174
| ~ spl1_22
| ~ spl1_169 ),
inference(avatar_split_clause,[status(thm)],[f3081,f2992,f2151,f3083,f3000]) ).
thf(f3081,plain,
( ( $true
= ( sK3 @ sK5 ) )
| ( $false
= ( irel @ sK5 @ sK5 ) )
| ~ spl1_22
| ~ spl1_169 ),
inference(trivial_inequality_removal,[status(thm)],[f3078]) ).
thf(f3078,plain,
( ( $false != $false )
| ( $false
= ( irel @ sK5 @ sK5 ) )
| ( $true
= ( sK3 @ sK5 ) )
| ~ spl1_22
| ~ spl1_169 ),
inference(equality_factoring,[status(thm)],[f3057]) ).
thf(f3057,plain,
( ! [X3: $i,X4: $i] :
( ( $false
= ( irel @ sK5 @ X3 ) )
| ( $false
= ( irel @ X3 @ X4 ) )
| ( ( sK3 @ X4 )
= $true ) )
| ~ spl1_22
| ~ spl1_169 ),
inference(trivial_inequality_removal,[status(thm)],[f3056]) ).
thf(f3056,plain,
( ! [X3: $i,X4: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK5 @ X3 ) )
| ( ( sK3 @ X4 )
= $true )
| ( $false
= ( irel @ X3 @ X4 ) ) )
| ~ spl1_22
| ~ spl1_169 ),
inference(forward_demodulation,[status(thm)],[f2152,f3037]) ).
thf(f3073,plain,
( spl1_26
| ~ spl1_36 ),
inference(avatar_contradiction_clause,[status(thm)],[f3072]) ).
thf(f3072,plain,
( $false
| spl1_26
| ~ spl1_36 ),
inference(subsumption_resolution,[status(thm)],[f2214,f3058]) ).
thf(f3058,plain,
( ! [X0: $i] :
( $false
!= ( sK3 @ X0 ) )
| spl1_26 ),
inference(superposition,[status(thm)],[f2167,f3007]) ).
thf(f2214,plain,
( ( ( sK3 @ sK73 )
= $false )
| ~ spl1_36 ),
inference(avatar_component_clause,[status(thm)],[f2212]) ).
thf(f3071,plain,
( ~ spl1_37
| ~ spl1_169 ),
inference(avatar_contradiction_clause,[status(thm)],[f3070]) ).
thf(f3070,plain,
( $false
| ~ spl1_37
| ~ spl1_169 ),
inference(trivial_inequality_removal,[status(thm)],[f3066]) ).
thf(f3066,plain,
( ( $true = $false )
| ~ spl1_37
| ~ spl1_169 ),
inference(backward_demodulation,[status(thm)],[f3037,f3065]) ).
thf(f3065,plain,
( ! [X0: $i] :
( ( sK4 @ X0 )
= $false )
| ~ spl1_37 ),
inference(superposition,[status(thm)],[f2218,f3007]) ).
thf(f3003,plain,
( spl1_169
| spl1_170
| spl1_171
| ~ spl1_3 ),
inference(avatar_split_clause,[status(thm)],[f2990,f2081,f3000,f2996,f2992]) ).
thf(f2081,definition,
( spl1_3
<=> ! [X2: $i,X4: $i] :
( ( ( irel @ sK5 @ X2 )
= $false )
| ( $true
= ( sK4 @ X4 ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( sK3 @ ( sK89 @ X2 ) )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f2990,plain,
( ( $true
= ( sK4 @ sK5 ) )
| ( $false
= ( irel @ sK5 @ sK5 ) )
| ( ( sK3 @ ( sK89 @ sK5 ) )
= $false )
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f2989]) ).
thf(f2989,plain,
( ( $true
= ( sK4 @ sK5 ) )
| ( ( sK3 @ ( sK89 @ sK5 ) )
= $false )
| ( $false != $false )
| ( $false
= ( irel @ sK5 @ sK5 ) )
| ~ spl1_3 ),
inference(equality_factoring,[status(thm)],[f2082]) ).
thf(f2082,plain,
( ! [X2: $i,X4: $i] :
( ( ( irel @ sK5 @ X2 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( sK4 @ X4 ) )
| ( ( sK3 @ ( sK89 @ X2 ) )
= $false ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f2081]) ).
thf(f2832,plain,
( spl1_125
| spl1_145
| spl1_110
| spl1_78 ),
inference(avatar_split_clause,[status(thm)],[f480,f2431,f2627,f2828,f2720]) ).
thf(f480,plain,
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( irel @ sK6 @ sK24 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( irel @ sK10 @ sK22 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f479]) ).
thf(f479,plain,
( ( ( ~ ( irel @ sK10 @ sK22 ) )
= $false )
| ( $true
= ( irel @ sK6 @ sK24 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( irel @ sK7 @ sK23 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f477]) ).
thf(f477,plain,
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( irel @ sK6 @ sK24 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $false
= ( ~ ( irel @ sK10 @ sK22 )
| ~ ( irel @ sK5 @ sK10 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f476]) ).
thf(f476,plain,
( ( $false
= ( ~ ( irel @ sK6 @ sK24 ) ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $false
= ( ~ ( irel @ sK10 @ sK22 )
| ~ ( irel @ sK5 @ sK10 ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f475]) ).
thf(f475,plain,
( ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 ) ) )
| ( $false
= ( ~ ( irel @ sK10 @ sK22 )
| ~ ( irel @ sK5 @ sK10 ) ) )
| ( $false
= ( ~ ( irel @ sK6 @ sK24 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f473]) ).
thf(f473,plain,
( ( ( ~ ( irel @ sK6 @ sK24 )
| ( sK4 @ sK24 ) )
= $false )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 ) ) )
| ( $false
= ( ~ ( irel @ sK10 @ sK22 )
| ~ ( irel @ sK5 @ sK10 ) ) )
| ( $true
= ( irel @ sK9 @ sK8 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f472]) ).
thf(f472,plain,
( ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( ( ~ ( irel @ sK6 @ sK24 )
| ( sK4 @ sK24 ) )
= $false )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 ) ) )
| ( $false
= ( ~ ( irel @ sK10 @ sK22 )
| ~ ( irel @ sK5 @ sK10 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f471]) ).
thf(f471,plain,
( ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 ) ) )
| ( $false
= ( ~ ( irel @ sK10 @ sK22 )
| ~ ( irel @ sK5 @ sK10 ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK24 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f470]) ).
thf(f470,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 ) ) )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $false
= ( ~ ( irel @ sK10 @ sK22 )
| ~ ( irel @ sK5 @ sK10 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f468]) ).
thf(f468,plain,
( ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK10 @ sK22 )
| ~ ( irel @ sK5 @ sK10 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f466]) ).
thf(f466,plain,
( ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK10 @ sK22 )
| ~ ( irel @ sK5 @ sK10 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f464]) ).
thf(f464,plain,
( ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( $false
= ( ~ ( irel @ sK10 @ sK22 )
| ~ ( irel @ sK5 @ sK10 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f462]) ).
thf(f462,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK10 @ sK22 )
| ~ ( irel @ sK5 @ sK10 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f460]) ).
thf(f460,plain,
( ( $false
= ( ~ ( irel @ sK10 @ sK22 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f458]) ).
thf(f458,plain,
( ( $false
= ( ~ ( irel @ sK10 @ sK22 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( sK4 @ sK22 ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f457]) ).
thf(f457,plain,
( ( $false
= ( ~ ( irel @ sK10 @ sK22 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( sK4 @ sK22 ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) )
@ sK23 )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f456]) ).
thf(f456,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK10 @ sK22 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( sK4 @ sK22 ) ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f455]) ).
thf(f455,plain,
( ( ( ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) )
@ sK22 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f454]) ).
thf(f454,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f452]) ).
thf(f452,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f450]) ).
thf(f450,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) )
| ~ ( irel @ sK5 @ sK7 ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK8 ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) )
| ~ ( irel @ sK5 @ sK7 ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( ( ( ~ ( irel @ sK5 @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) )
| ~ ( irel @ sK5 @ sK7 ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK8 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK8 ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) )
| ~ ( irel @ sK5 @ sK7 ) )
= $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( sK4 @ Y1 ) ) )
@ sK10 )
= $false )
| ( ( ~ ( irel @ sK5 @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( sK4 @ Y1 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ sK8 ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) )
| ~ ( irel @ sK5 @ sK7 ) )
= $false )
| ( ( ~ ( irel @ sK5 @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) )
| ~ ( irel @ sK5 @ sK7 ) )
= $false )
| ( ( ~ ( irel @ sK5 @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ Y0 @ sK8 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ sK8 ) )
@ sK9 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( sK4 @ Y1 ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ Y0 @ sK8 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ sK8 ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) )
| ~ ( irel @ sK5 @ sK7 ) )
= $false )
| ( ( ~ ( irel @ sK5 @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( sK4 @ Y1 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 ) ) )
@ sK8 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( sK4 @ Y1 ) ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) )
| ~ ( irel @ sK5 @ sK7 ) )
= $false )
| ( ( ~ ( irel @ sK5 @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( sK4 @ Y1 ) ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) )
| ~ ( irel @ sK5 @ sK7 ) )
= $false )
| ( ( ~ ( irel @ sK5 @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) )
@ sK7 )
= $false )
| ( ( ~ ( irel @ sK5 @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( sK4 @ Y1 ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false )
| ( ( ~ ( irel @ sK5 @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( sK4 @ Y1 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( sK4 @ Y1 ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false )
| ( ( ~ ( irel @ sK5 @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( sK4 @ Y1 ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) )
@ sK6 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( sK4 @ Y1 ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( sK4 @ Y1 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( sK4 @ Y1 ) ) ) ) )
!= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y1 @ Y3 )
| ( sK3 @ Y3 ) ) )
| ( sK4 @ Y2 ) ) ) ) )
@ sK5 )
!= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK4 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) )
| ~ ( irel @ Y0 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK4 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) )
| ~ ( irel @ Y0 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) ) ) )
!= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y2 @ Y1 )
| ~ ( irel @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK4 @ Y3 ) ) )
| ( sK3 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ~ ( irel @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y1 @ Y3 )
| ( sK3 @ Y3 ) ) )
| ( sK4 @ Y2 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ^ [Y0: $i > $o,Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y3 @ Y2 )
| ~ ( irel @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ( Y0 @ Y4 ) ) )
| ( sK3 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ~ ( irel @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y2 @ Y4 )
| ( sK3 @ Y4 ) ) )
| ( Y0 @ Y3 ) ) ) ) )
@ sK4 )
!= ( ^ [Y0: $i > $o,Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK3 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
@ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ^ [Y0: $i > $o,Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y3 @ Y2 )
| ~ ( irel @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ( Y0 @ Y4 ) ) )
| ( sK3 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ~ ( irel @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y2 @ Y4 )
| ( sK3 @ Y4 ) ) )
| ( Y0 @ Y3 ) ) ) ) ) )
!= ( ^ [Y0: $i > $o,Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( sK3 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( irel @ Y1 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( sK3 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y4 @ Y3 )
| ~ ( irel @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ( Y0 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ( Y1 @ Y4 ) ) ) ) )
@ sK3 )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ( Y0 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( irel @ Y3 @ Y4 ) ) )
| ~ ( irel @ Y2 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
| ~ ( irel @ Y3 @ Y4 ) ) ) ) ) )
@ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y4 @ Y3 )
| ~ ( irel @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ( Y0 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ( Y1 @ Y4 ) ) ) ) ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ( Y0 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( irel @ Y3 @ Y4 ) ) )
| ~ ( irel @ Y2 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
| ~ ( irel @ Y3 @ Y4 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y4 @ Y3 )
| ~ ( irel @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ( Y0 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ( Y1 @ Y4 ) ) ) ) ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( irel @ Y4 @ Y5 ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y2 @ Y5 ) ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 )
| ~ ( irel @ Y4 @ Y5 ) ) ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 )
| ~ ( irel @ Y4 @ Y5 ) ) ) )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f15,f33,f31,f24,f24]) ).
thf(f24,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f31,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f33,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y4 @ Y3 )
| ~ ( irel @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ( Y0 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( Y0 @ Y5 ) ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f15,plain,
( iequiv
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( iand @ ( iimplies @ Y0 @ Y1 ) @ ( iimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( iequiv
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( iand @ ( iimplies @ Y0 @ Y1 ) @ ( iimplies @ Y1 @ Y0 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( iequiv
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( iand @ ( iimplies @ Y0 @ Y1 ) @ ( iimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( iequiv
!= ( ^ [X0: $i > $o,X1: $i > $o] : ( iand @ ( iimplies @ X0 @ X1 ) @ ( iimplies @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( iequiv
!= ( ^ [X8: $i > $o,X9: $i > $o] : ( iand @ ( iimplies @ X8 @ X9 ) @ ( iimplies @ X9 @ X8 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( iequiv
= ( ^ [X8: $i > $o,X9: $i > $o] : ( iand @ ( iimplies @ X8 @ X9 ) @ ( iimplies @ X9 @ X8 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MacNcZ7HSP/DTF2THF_29558.p',iequiv) ).
thf(f2760,plain,
( spl1_70
| spl1_131
| spl1_125
| spl1_110 ),
inference(avatar_split_clause,[status(thm)],[f555,f2627,f2720,f2757,f2387]) ).
thf(f555,plain,
! [X1: $i] :
( ( ( irel @ sK6 @ sK31 )
= $true )
| ( $true
= ( irel @ sK10 @ sK22 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( irel @ sK9 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f554]) ).
thf(f554,plain,
! [X1: $i] :
( ( $true
= ( ~ ( irel @ sK9 @ X1 ) ) )
| ( ( irel @ sK6 @ sK31 )
= $true )
| ( $true
= ( irel @ sK10 @ sK22 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( irel @ sK7 @ sK23 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f553]) ).
thf(f553,plain,
! [X1: $i] :
( ( ( irel @ sK6 @ sK31 )
= $true )
| ( $true
= ( ~ ( irel @ sK9 @ X1 )
| ( sK4 @ X1 ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( irel @ sK10 @ sK22 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f552]) ).
thf(f552,plain,
! [X1: $i] :
( ( ( irel @ sK6 @ sK31 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) )
@ X1 ) )
| ( $true
= ( irel @ sK10 @ sK22 ) )
| ( $true
= ( irel @ sK7 @ sK23 ) ) ),
inference(pi_clausification,[status(thm)],[f551]) ).
thf(f551,plain,
( ( ( irel @ sK6 @ sK31 )
= $true )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( irel @ sK10 @ sK22 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f550]) ).
thf(f550,plain,
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( irel @ sK10 @ sK22 ) )
| ( $false
= ( ~ ( irel @ sK6 @ sK31 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f548]) ).
thf(f548,plain,
( ( $true
= ( irel @ sK10 @ sK22 ) )
| ( $false
= ( ~ ( irel @ sK6 @ sK31 )
| ( sK4 @ sK31 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f547]) ).
thf(f547,plain,
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( irel @ sK10 @ sK22 ) )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK31 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f546]) ).
thf(f546,plain,
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( irel @ sK10 @ sK22 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f545]) ).
thf(f545,plain,
( ( $true
= ( irel @ sK10 @ sK22 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $true
= ( irel @ sK7 @ sK23 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f544]) ).
thf(f544,plain,
( ( $false
= ( ~ ( irel @ sK7 @ sK23 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $true
= ( irel @ sK10 @ sK22 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f542]) ).
thf(f542,plain,
( ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( $true
= ( irel @ sK10 @ sK22 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f541]) ).
thf(f541,plain,
( ( ( ~ ( irel @ sK10 @ sK22 ) )
= $false )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f465]) ).
thf(f465,plain,
( ( $false
= ( ~ ( irel @ sK10 @ sK22 )
| ~ ( irel @ sK5 @ sK10 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f464]) ).
thf(f2728,plain,
( spl1_78
| spl1_27
| spl1_110
| spl1_125 ),
inference(avatar_split_clause,[status(thm)],[f617,f2720,f2627,f2170,f2431]) ).
thf(f617,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK6 @ X1 ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( irel @ sK10 @ sK22 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( irel @ sK7 @ sK23 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f616]) ).
thf(f616,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( ~ ( irel @ sK6 @ X1 ) ) )
| ( $true
= ( irel @ sK10 @ sK22 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f615]) ).
thf(f615,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK10 @ sK22 ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( ( sK3 @ X1 )
| ~ ( irel @ sK6 @ X1 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f614]) ).
thf(f614,plain,
! [X1: $i] :
( ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( ( sK3 @ X1 )
| ~ ( irel @ sK6 @ X1 ) ) )
| ( $true
= ( irel @ sK10 @ sK22 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f613]) ).
thf(f613,plain,
! [X1: $i] :
( ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( irel @ sK10 @ sK22 ) )
| ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f612]) ).
thf(f612,plain,
( ( $true
= ( irel @ sK10 @ sK22 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f610]) ).
thf(f610,plain,
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
| ( $true
= ( irel @ sK10 @ sK22 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f609]) ).
thf(f609,plain,
( ( $true
= ( irel @ sK10 @ sK22 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f608]) ).
thf(f608,plain,
( ( ( ~ ( irel @ sK10 @ sK22 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false )
| ( $true
= ( irel @ sK7 @ sK23 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f606]) ).
thf(f606,plain,
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK10 @ sK22 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f605]) ).
thf(f605,plain,
( ( $false
= ( ~ ( irel @ sK7 @ sK23 ) ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK10 @ sK22 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f603]) ).
thf(f603,plain,
( ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK10 @ sK22 ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f463]) ).
thf(f463,plain,
( ( $false
= ( ~ ( irel @ sK10 @ sK22 )
| ~ ( irel @ sK5 @ sK10 ) ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f462]) ).
thf(f2726,plain,
( spl1_110
| spl1_70
| spl1_125
| spl1_27 ),
inference(avatar_split_clause,[status(thm)],[f633,f2170,f2720,f2387,f2627]) ).
thf(f633,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK10 @ sK22 ) )
| ( ( sK3 @ X1 )
= $true )
| ( ( irel @ sK9 @ X2 )
= $false )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $false
= ( irel @ sK6 @ X1 ) )
| ( $true
= ( sK4 @ X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f632]) ).
thf(f632,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( irel @ sK10 @ sK22 ) )
| ( $false
= ( irel @ sK6 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK9 @ X2 ) ) )
| ( $true
= ( sK4 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f631]) ).
thf(f631,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $false
= ( irel @ sK6 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK9 @ X2 )
| ( sK4 @ X2 ) ) )
| ( $true
= ( irel @ sK10 @ sK22 ) )
| ( ( sK3 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f630]) ).
thf(f630,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $false
= ( irel @ sK6 @ X1 ) )
| ( $true
= ( irel @ sK10 @ sK22 ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( irel @ sK7 @ sK23 ) ) ),
inference(pi_clausification,[status(thm)],[f629]) ).
thf(f629,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK10 @ sK22 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( $false
= ( irel @ sK6 @ X1 ) )
| ( $true
= ( irel @ sK7 @ sK23 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f628]) ).
thf(f628,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( irel @ sK10 @ sK22 ) )
| ( $true
= ( ~ ( irel @ sK6 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( ( sK3 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f627]) ).
thf(f627,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( ( sK3 @ X1 )
| ~ ( irel @ sK6 @ X1 ) ) )
| ( $true
= ( irel @ sK10 @ sK22 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f626]) ).
thf(f626,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( irel @ sK10 @ sK22 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f625]) ).
thf(f625,plain,
( ( $true
= ( irel @ sK10 @ sK22 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f624]) ).
thf(f624,plain,
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( ~ ( irel @ sK10 @ sK22 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f623]) ).
thf(f623,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( ~ ( irel @ sK10 @ sK22 ) )
= $false )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f607]) ).
thf(f607,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( ~ ( irel @ sK10 @ sK22 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f606]) ).
thf(f2712,plain,
( spl1_40
| spl1_78
| spl1_110
| spl1_124 ),
inference(avatar_split_clause,[status(thm)],[f736,f2709,f2627,f2431,f2232]) ).
thf(f736,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK9 @ sK8 ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $false
= ( irel @ sK10 @ X1 ) )
| ( $true
= ( irel @ sK6 @ sK34 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f735]) ).
thf(f735,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( irel @ sK6 @ sK34 ) )
| ( $true
= ( ~ ( irel @ sK10 @ X1 ) ) )
| ( $true
= ( irel @ sK9 @ sK8 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f734]) ).
thf(f734,plain,
! [X1: $i] :
( ( $true
= ( ~ ( irel @ sK10 @ X1 )
| ( sK3 @ X1 ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( irel @ sK6 @ sK34 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f733]) ).
thf(f733,plain,
! [X1: $i] :
( ( ( ~ ( irel @ sK6 @ sK34 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK10 @ X1 )
| ( sK3 @ X1 ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f732]) ).
thf(f732,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) )
@ X1 ) )
| ( ( ~ ( irel @ sK6 @ sK34 ) )
= $false )
| ( $true
= ( irel @ sK9 @ sK8 ) ) ),
inference(pi_clausification,[status(thm)],[f731]) ).
thf(f731,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( ~ ( irel @ sK6 @ sK34 ) )
= $false )
| ( $true
= ( irel @ sK9 @ sK8 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f729]) ).
thf(f729,plain,
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( ~ ( irel @ sK6 @ sK34 )
| ( sK4 @ sK34 ) )
= $false )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f728]) ).
thf(f728,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( ~ ( irel @ sK6 @ sK34 )
| ( sK4 @ sK34 ) )
= $false )
| ( $true
= ( irel @ sK9 @ sK8 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f727]) ).
thf(f727,plain,
( ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK34 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f726]) ).
thf(f726,plain,
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f725]) ).
thf(f725,plain,
( ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f723]) ).
thf(f723,plain,
( ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f721]) ).
thf(f721,plain,
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f720]) ).
thf(f720,plain,
( ( $false
= ( ~ ( irel @ sK7 @ sK23 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f718]) ).
thf(f718,plain,
( ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f461]) ).
thf(f461,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f460]) ).
thf(f2692,plain,
( spl1_110
| spl1_70
| spl1_120
| spl1_40 ),
inference(avatar_split_clause,[status(thm)],[f768,f2232,f2689,f2387,f2627]) ).
thf(f768,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK9 @ X2 )
= $false )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( sK4 @ X2 ) )
| ( ( irel @ sK6 @ sK36 )
= $true )
| ( $false
= ( irel @ sK10 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f767]) ).
thf(f767,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( irel @ sK6 @ sK36 )
= $true )
| ( ( sK3 @ X1 )
= $true )
| ( $false
= ( irel @ sK10 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK9 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f766]) ).
thf(f766,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( ~ ( irel @ sK9 @ X2 )
| ( sK4 @ X2 ) ) )
| ( $false
= ( irel @ sK10 @ X1 ) )
| ( ( irel @ sK6 @ sK36 )
= $true )
| ( ( sK3 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f765]) ).
thf(f765,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK10 @ X1 ) )
| ( ( ~ ( irel @ sK6 @ sK36 ) )
= $false )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( ~ ( irel @ sK9 @ X2 )
| ( sK4 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f764]) ).
thf(f764,plain,
! [X2: $i,X1: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( ~ ( irel @ sK6 @ sK36 ) )
= $false )
| ( $false
= ( irel @ sK10 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f763]) ).
thf(f763,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK10 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( ( ~ ( irel @ sK6 @ sK36 ) )
= $false )
| ( $true
= ( irel @ sK7 @ sK23 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f762]) ).
thf(f762,plain,
! [X1: $i] :
( ( $true
= ( ~ ( irel @ sK10 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( ( ~ ( irel @ sK6 @ sK36 ) )
= $false )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( irel @ sK7 @ sK23 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f760]) ).
thf(f760,plain,
! [X1: $i] :
( ( ( ~ ( irel @ sK6 @ sK36 )
| ( sK4 @ sK36 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( ~ ( irel @ sK10 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f759]) ).
thf(f759,plain,
! [X1: $i] :
( ( $true
= ( ~ ( irel @ sK10 @ X1 )
| ( sK3 @ X1 ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( ~ ( irel @ sK6 @ sK36 )
| ( sK4 @ sK36 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f758]) ).
thf(f758,plain,
! [X1: $i] :
( ( $true
= ( ~ ( irel @ sK10 @ X1 )
| ( sK3 @ X1 ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK36 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f757]) ).
thf(f757,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( ~ ( irel @ sK10 @ X1 )
| ( sK3 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f756]) ).
thf(f756,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f755]) ).
thf(f755,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f754]) ).
thf(f754,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f722]) ).
thf(f722,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f721]) ).
thf(f2668,plain,
( spl1_40
| spl1_110
| spl1_78
| spl1_27 ),
inference(avatar_split_clause,[status(thm)],[f838,f2170,f2431,f2627,f2232]) ).
thf(f838,plain,
! [X2: $i,X1: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( $false
= ( irel @ sK6 @ X1 ) )
| ( ( irel @ sK10 @ X2 )
= $false )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f837]) ).
thf(f837,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( ~ ( irel @ sK10 @ X2 ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $false
= ( irel @ sK6 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f836]) ).
thf(f836,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( ~ ( irel @ sK6 @ X1 ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( ~ ( irel @ sK10 @ X2 ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f835]) ).
thf(f835,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( sK3 @ X1 )
| ~ ( irel @ sK6 @ X1 ) ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( ~ ( irel @ sK10 @ X2 ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f834]) ).
thf(f834,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( ( ~ ( irel @ sK10 @ X2 )
| ( sK3 @ X2 ) )
= $true )
| ( $true
= ( ( sK3 @ X1 )
| ~ ( irel @ sK6 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f833]) ).
thf(f833,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( sK3 @ X1 )
| ~ ( irel @ sK6 @ X1 ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) ) ),
inference(pi_clausification,[status(thm)],[f832]) ).
thf(f832,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( ( sK3 @ X1 )
| ~ ( irel @ sK6 @ X1 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f831]) ).
thf(f831,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK9 @ sK8 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( ( sK3 @ X1 )
| ~ ( irel @ sK6 @ X1 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f830]) ).
thf(f830,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $true
= ( ( sK3 @ X1 )
| ~ ( irel @ sK6 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f829]) ).
thf(f829,plain,
! [X1: $i] :
( ( $false
= ( ~ ( irel @ sK7 @ sK23 ) ) )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $true
= ( ( sK3 @ X1 )
| ~ ( irel @ sK6 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f828]) ).
thf(f828,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) )
@ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 ) ) ) ),
inference(pi_clausification,[status(thm)],[f827]) ).
thf(f827,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f825]) ).
thf(f825,plain,
( ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f823]) ).
thf(f823,plain,
( ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f822]) ).
thf(f822,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f717]) ).
thf(f717,plain,
( ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f461]) ).
thf(f2664,plain,
( spl1_27
| spl1_40
| spl1_70
| spl1_110 ),
inference(avatar_split_clause,[status(thm)],[f889,f2627,f2387,f2232,f2170]) ).
thf(f889,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( $true
= ( sK4 @ X2 ) )
| ( $false
= ( irel @ sK6 @ X1 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $false
= ( irel @ sK10 @ X3 ) )
| ( ( irel @ sK9 @ X2 )
= $false )
| ( $true
= ( irel @ sK7 @ sK23 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f888]) ).
thf(f888,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( ( sK3 @ X1 )
= $true )
| ( ( irel @ sK9 @ X2 )
= $false )
| ( $true
= ( ~ ( irel @ sK10 @ X3 ) ) )
| ( $false
= ( irel @ sK6 @ X1 ) )
| ( $true
= ( sK4 @ X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f887]) ).
thf(f887,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $false
= ( irel @ sK6 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK9 @ X2 ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( ~ ( irel @ sK10 @ X3 ) ) )
| ( $true
= ( sK3 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f886]) ).
thf(f886,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK10 @ X3 )
| ( sK3 @ X3 ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( ~ ( irel @ sK9 @ X2 ) ) )
| ( $false
= ( irel @ sK6 @ X1 ) )
| ( $true
= ( sK4 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f885]) ).
thf(f885,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK9 @ X2 )
| ( sK4 @ X2 ) ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $false
= ( irel @ sK6 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK10 @ X3 )
| ( sK3 @ X3 ) ) )
| ( ( sK3 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f884]) ).
thf(f884,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( $false
= ( irel @ sK6 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK9 @ X2 )
| ( sK4 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( irel @ sK7 @ sK23 ) ) ),
inference(pi_clausification,[status(thm)],[f883]) ).
thf(f883,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $false
= ( irel @ sK6 @ X1 ) )
| ( $true
= ( irel @ sK7 @ sK23 ) )
| ( $true
= ( ~ ( irel @ sK9 @ X2 )
| ( sK4 @ X2 ) ) )
| ( ( sK3 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f882]) ).
thf(f882,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK6 @ X1 ) )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( irel @ sK9 @ X2 )
| ( sK4 @ X2 ) ) )
| ( ( sK3 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f881]) ).
thf(f881,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $false
= ( irel @ sK6 @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f880]) ).
thf(f880,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK6 @ X1 ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f879]) ).
thf(f879,plain,
! [X1: $i] :
( ( $true
= ( ~ ( irel @ sK6 @ X1 ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f877]) ).
thf(f877,plain,
! [X1: $i] :
( ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( ~ ( irel @ sK6 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f876]) ).
thf(f876,plain,
! [X1: $i] :
( ( $true
= ( ( sK3 @ X1 )
| ~ ( irel @ sK6 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f875]) ).
thf(f875,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ( sK3 @ X1 )
| ~ ( irel @ sK6 @ X1 ) ) )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f874]) ).
thf(f874,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f873]) ).
thf(f873,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f872]) ).
thf(f872,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f821]) ).
thf(f821,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( irel @ sK7 @ sK23 )
| ( sK3 @ sK23 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f717]) ).
thf(f2584,plain,
( spl1_78
| spl1_31
| spl1_101
| spl1_98 ),
inference(avatar_split_clause,[status(thm)],[f1031,f2558,f2580,f2188,f2431]) ).
thf(f1031,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK10 @ sK45 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( ( irel @ sK7 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1030]) ).
thf(f1030,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( irel @ sK10 @ sK45 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1029]) ).
thf(f1029,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( irel @ sK10 @ sK45 ) )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK7 @ X1 ) ) )
| ( $true
= ( irel @ sK9 @ sK8 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1028]) ).
thf(f1028,plain,
! [X1: $i] :
( ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK7 @ X1 ) ) )
| ( $true
= ( irel @ sK10 @ sK45 ) )
| ( $true
= ( irel @ sK6 @ sK44 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1027]) ).
thf(f1027,plain,
! [X1: $i] :
( ( ( ~ ( irel @ sK10 @ sK45 ) )
= $false )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK7 @ X1 ) ) )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1026]) ).
thf(f1026,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( ( ~ ( irel @ sK10 @ sK45 ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f1025]) ).
thf(f1025,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( ( ~ ( irel @ sK10 @ sK45 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1023]) ).
thf(f1023,plain,
( ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( ( ~ ( irel @ sK10 @ sK45 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1021]) ).
thf(f1021,plain,
( ( $true
= ( irel @ sK6 @ sK44 ) )
| ( ( ~ ( irel @ sK10 @ sK45 )
| ~ ( irel @ sK5 @ sK10 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1019]) ).
thf(f1019,plain,
( ( $true
= ( irel @ sK6 @ sK44 ) )
| ( ( ~ ( irel @ sK10 @ sK45 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1018]) ).
thf(f1018,plain,
( ( $false
= ( ~ ( irel @ sK6 @ sK44 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false )
| ( ( ~ ( irel @ sK10 @ sK45 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1016]) ).
thf(f1016,plain,
( ( ( ~ ( irel @ sK10 @ sK45 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( sK4 @ sK45 ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) )
| ( $false
= ( ~ ( irel @ sK6 @ sK44 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1015]) ).
thf(f1015,plain,
( ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) )
@ sK45 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) )
| ( $false
= ( ~ ( irel @ sK6 @ sK44 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f1014]) ).
thf(f1014,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) )
| ( $false
= ( ~ ( irel @ sK6 @ sK44 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1012]) ).
thf(f1012,plain,
( ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK6 @ sK44 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1010]) ).
thf(f1010,plain,
( ( $false
= ( ~ ( irel @ sK6 @ sK44 )
| ( sK4 @ sK44 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1009]) ).
thf(f1009,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK44 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f1008]) ).
thf(f1008,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1006]) ).
thf(f1006,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f453]) ).
thf(f453,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f452]) ).
thf(f2576,plain,
( spl1_78
| spl1_40
| spl1_31
| spl1_98 ),
inference(avatar_split_clause,[status(thm)],[f1058,f2558,f2188,f2232,f2431]) ).
thf(f1058,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK10 @ X2 )
= $false )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1057]) ).
thf(f1057,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK10 @ X2 )
= $false )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1056]) ).
thf(f1056,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( ~ ( irel @ sK10 @ X2 ) ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( $true
= ( irel @ sK6 @ sK44 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1055]) ).
thf(f1055,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $true
= ( ~ ( irel @ sK10 @ X2 ) ) )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( $true
= ( sK3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1054]) ).
thf(f1054,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( irel @ sK10 @ X2 )
| ( sK3 @ X2 ) )
= $true )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1053]) ).
thf(f1053,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f1052]) ).
thf(f1052,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1051]) ).
thf(f1051,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $true
= ( irel @ sK6 @ sK44 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1049]) ).
thf(f1049,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1048]) ).
thf(f1048,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK7 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1047]) ).
thf(f1047,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) )
@ X1 ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f1020]) ).
thf(f1020,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false )
| ( $true
= ( irel @ sK6 @ sK44 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1019]) ).
thf(f2568,plain,
( spl1_98
| spl1_99
| spl1_70
| spl1_31 ),
inference(avatar_split_clause,[status(thm)],[f1097,f2188,f2387,f2565,f2558]) ).
thf(f1097,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK9 @ X2 )
= $false )
| ( $true
= ( irel @ sK10 @ sK46 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1096]) ).
thf(f1096,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK9 @ X2 )
= $false )
| ( ( ~ ( irel @ sK10 @ sK46 ) )
= $false )
| ( $true
= ( irel @ sK6 @ sK44 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1094]) ).
thf(f1094,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK9 @ X2 )
= $false )
| ( $true
= ( sK4 @ X2 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( ( ~ ( irel @ sK10 @ sK46 )
| ~ ( irel @ sK5 @ sK10 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1093]) ).
thf(f1093,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( ( irel @ sK9 @ X2 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( sK4 @ X2 ) )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( ( ~ ( irel @ sK10 @ sK46 )
| ~ ( irel @ sK5 @ sK10 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1091]) ).
thf(f1091,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( ( ~ ( irel @ sK10 @ sK46 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( $true
= ( sK4 @ X2 ) )
| ( ( irel @ sK9 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1090]) ).
thf(f1090,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK9 @ X2 ) ) )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( $true
= ( sK4 @ X2 ) )
| ( ( ~ ( irel @ sK10 @ sK46 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1089]) ).
thf(f1089,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK9 @ X2 )
| ( sK4 @ X2 ) ) )
| ( ( ~ ( irel @ sK10 @ sK46 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( $true
= ( irel @ sK6 @ sK44 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1088]) ).
thf(f1088,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( irel @ sK10 @ sK46 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f1087]) ).
thf(f1087,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( ( ~ ( irel @ sK10 @ sK46 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1085]) ).
thf(f1085,plain,
! [X1: $i] :
( ( ( ~ ( irel @ sK10 @ sK46 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( sK4 @ sK46 ) )
= $false )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1084]) ).
thf(f1084,plain,
! [X1: $i] :
( ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK7 @ X1 ) ) )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( ( ~ ( irel @ sK10 @ sK46 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( sK4 @ sK46 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1083]) ).
thf(f1083,plain,
! [X1: $i] :
( ( $false
= ( ~ ( irel @ sK6 @ sK44 ) ) )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK7 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( ( ~ ( irel @ sK10 @ sK46 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( sK4 @ sK46 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1082]) ).
thf(f1082,plain,
! [X1: $i] :
( ( $false
= ( ~ ( irel @ sK6 @ sK44 ) ) )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK7 @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) )
@ sK46 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f1081]) ).
thf(f1081,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK7 @ X1 ) ) )
| ( $false
= ( ~ ( irel @ sK6 @ sK44 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1080]) ).
thf(f1080,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( irel @ sK6 @ sK44 ) ) )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK7 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1079]) ).
thf(f1079,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK6 @ sK44 ) ) ) ),
inference(pi_clausification,[status(thm)],[f1013]) ).
thf(f1013,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK6 @ sK44 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1012]) ).
thf(f2562,plain,
( spl1_40
| spl1_98
| spl1_70
| spl1_31 ),
inference(avatar_split_clause,[status(thm)],[f1104,f2188,f2387,f2558,f2232]) ).
thf(f1104,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK7 @ X1 )
= $false )
| ( $false
= ( irel @ sK10 @ X3 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( sK4 @ X2 ) )
| ( ( irel @ sK9 @ X2 )
= $false )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( sK3 @ X3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1103]) ).
thf(f1103,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK9 @ X2 )
= $false )
| ( $true
= ( sK4 @ X2 ) )
| ( $true
= ( ~ ( irel @ sK10 @ X3 ) ) )
| ( $true
= ( sK3 @ X3 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( irel @ sK6 @ sK44 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1102]) ).
thf(f1102,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( ~ ( irel @ sK10 @ X3 )
| ( sK3 @ X3 ) ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( ( irel @ sK9 @ X2 )
= $false )
| ( $true
= ( sK4 @ X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1101]) ).
thf(f1101,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK9 @ X2 )
= $false )
| ( $true
= ( ~ ( irel @ sK10 @ X3 )
| ( sK3 @ X3 ) ) )
| ( $true
= ( irel @ sK6 @ sK44 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1100]) ).
thf(f1100,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ sK6 @ sK44 ) )
| ( ( irel @ sK9 @ X2 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( sK4 @ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f1099]) ).
thf(f1099,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( sK4 @ X2 ) )
| ( $true
= ( irel @ sK6 @ sK44 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( ( irel @ sK9 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1092]) ).
thf(f1092,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( sK4 @ X2 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( irel @ sK9 @ X2 )
= $false )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( $true
= ( irel @ sK6 @ sK44 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1091]) ).
thf(f2520,plain,
( spl1_27
| spl1_31
| spl1_78
| spl1_91 ),
inference(avatar_split_clause,[status(thm)],[f1226,f2509,f2431,f2188,f2170]) ).
thf(f1226,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( $false
= ( irel @ sK6 @ X2 ) )
| ( $true
= ( irel @ sK10 @ sK49 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1225]) ).
thf(f1225,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( irel @ sK10 @ sK49 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( ~ ( irel @ sK6 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1224]) ).
thf(f1224,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( irel @ sK10 @ sK49 ) )
| ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK6 @ X2 ) ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( irel @ sK9 @ sK8 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1223]) ).
thf(f1223,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK10 @ sK49 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) )
@ X2 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) ) ),
inference(pi_clausification,[status(thm)],[f1222]) ).
thf(f1222,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( irel @ sK10 @ sK49 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1221]) ).
thf(f1221,plain,
! [X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( ( ~ ( irel @ sK10 @ sK49 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
| ( $true
= ( irel @ sK9 @ sK8 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1220]) ).
thf(f1220,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( ( ~ ( irel @ sK10 @ sK49 ) )
= $false )
| ( $true
= ( irel @ sK9 @ sK8 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1218]) ).
thf(f1218,plain,
! [X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $true
= ( irel @ sK9 @ sK8 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1217]) ).
thf(f1217,plain,
! [X1: $i] :
( ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 ) )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( irel @ sK7 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1215]) ).
thf(f1215,plain,
! [X1: $i] :
( ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( ( irel @ sK7 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1214]) ).
thf(f1214,plain,
! [X1: $i] :
( ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1212]) ).
thf(f1212,plain,
! [X1: $i] :
( ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( sK4 @ sK49 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1210]) ).
thf(f1210,plain,
! [X1: $i] :
( ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( sK4 @ sK49 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1209]) ).
thf(f1209,plain,
! [X1: $i] :
( ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK7 @ X1 ) ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 ) )
= $false )
| ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( sK4 @ sK49 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1207]) ).
thf(f1207,plain,
! [X1: $i] :
( ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( sK4 @ sK49 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK7 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1206]) ).
thf(f1206,plain,
! [X1: $i] :
( ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK7 @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) )
@ sK49 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f1205]) ).
thf(f1205,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK7 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1204]) ).
thf(f1204,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) )
@ X1 ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f1007]) ).
thf(f1007,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) )
| ( ( ~ ( irel @ sK9 @ sK8 )
| ~ ( irel @ sK5 @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1006]) ).
thf(f2518,plain,
( spl1_78
| spl1_40
| spl1_31
| spl1_27 ),
inference(avatar_split_clause,[status(thm)],[f1243,f2170,f2188,f2232,f2431]) ).
thf(f1243,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $false
= ( irel @ sK6 @ X2 ) )
| ( $false
= ( irel @ sK10 @ X3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1242]) ).
thf(f1242,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK6 @ X2 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( ~ ( irel @ sK10 @ X3 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1241]) ).
thf(f1241,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK6 @ X2 ) ) )
| ( $true
= ( ~ ( irel @ sK10 @ X3 ) ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1240]) ).
thf(f1240,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK10 @ X3 )
| ( sK3 @ X3 ) ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( ~ ( irel @ sK6 @ X2 ) ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK7 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1239]) ).
thf(f1239,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( irel @ sK6 @ X2 ) ) ) ),
inference(pi_clausification,[status(thm)],[f1238]) ).
thf(f1238,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( ~ ( irel @ sK6 @ X2 ) ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1237]) ).
thf(f1237,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK9 @ sK8 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( ~ ( irel @ sK6 @ X2 ) ) )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1236]) ).
thf(f1236,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK6 @ X2 ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1235]) ).
thf(f1235,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK9 @ sK8 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) )
@ X2 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f1234]) ).
thf(f1234,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1233]) ).
thf(f1233,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $true
= ( irel @ sK9 @ sK8 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK7 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1216]) ).
thf(f1216,plain,
! [X1: $i] :
( ( ( irel @ sK7 @ X1 )
= $false )
| ( $false
= ( ~ ( irel @ sK9 @ sK8 ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1215]) ).
thf(f2512,plain,
( spl1_91
| spl1_31
| spl1_27
| spl1_70 ),
inference(avatar_split_clause,[status(thm)],[f1309,f2387,f2170,f2188,f2509]) ).
thf(f1309,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK6 @ X2 ) )
| ( $false
= ( irel @ sK9 @ X3 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( irel @ sK10 @ sK49 ) )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1308]) ).
thf(f1308,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( irel @ sK10 @ sK49 ) )
| ( $false
= ( irel @ sK6 @ X2 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( ( ~ ( irel @ sK9 @ X3 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1307]) ).
thf(f1307,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK6 @ X2 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( ~ ( irel @ sK9 @ X3 )
| ( sK4 @ X3 ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( irel @ sK10 @ sK49 ) )
| ( ( irel @ sK7 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1306]) ).
thf(f1306,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( irel @ sK10 @ sK49 ) )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $false
= ( irel @ sK6 @ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f1305]) ).
thf(f1305,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( irel @ sK10 @ sK49 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $false
= ( irel @ sK6 @ X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1304]) ).
thf(f1304,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( irel @ sK10 @ sK49 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $false
= ( irel @ sK6 @ X2 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1303]) ).
thf(f1303,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $false
= ( irel @ sK6 @ X2 ) )
| ( ( ~ ( irel @ sK10 @ sK49 ) )
= $false )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1301]) ).
thf(f1301,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK7 @ X1 )
= $false )
| ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $false
= ( irel @ sK6 @ X2 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1300]) ).
thf(f1300,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK6 @ X2 ) ) )
| ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( irel @ sK7 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1299]) ).
thf(f1299,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK6 @ X2 ) ) )
| ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 ) )
= $false )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1298]) ).
thf(f1298,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 ) )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f1297]) ).
thf(f1297,plain,
! [X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
| ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 ) )
= $false )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1295]) ).
thf(f1295,plain,
! [X1: $i] :
( ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( irel @ sK7 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1294]) ).
thf(f1294,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( irel @ sK7 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1293]) ).
thf(f1293,plain,
! [X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) )
| ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1291]) ).
thf(f1291,plain,
! [X1: $i] :
( ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( sK4 @ sK49 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( irel @ sK7 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1208]) ).
thf(f1208,plain,
! [X1: $i] :
( ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK7 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( ~ ( irel @ sK10 @ sK49 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( sK4 @ sK49 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1207]) ).
thf(f2506,plain,
( spl1_70
| spl1_40
| spl1_31
| spl1_27 ),
inference(avatar_split_clause,[status(thm)],[f1329,f2170,f2188,f2232,f2387]) ).
thf(f1329,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK10 @ X3 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK4 @ X4 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK3 @ X3 ) )
| ( ( irel @ sK9 @ X4 )
= $false )
| ( $false
= ( irel @ sK6 @ X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1328]) ).
thf(f1328,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK4 @ X4 ) )
| ( $false
= ( irel @ sK10 @ X3 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $false
= ( irel @ sK6 @ X2 ) )
| ( $true
= ( ~ ( irel @ sK9 @ X4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1327]) ).
thf(f1327,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $false
= ( irel @ sK6 @ X2 ) )
| ( $false
= ( irel @ sK10 @ X3 ) )
| ( $true
= ( ~ ( irel @ sK9 @ X4 )
| ( sK4 @ X4 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1326]) ).
thf(f1326,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK6 @ X2 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $false
= ( irel @ sK10 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) )
@ X4 ) )
| ( $true
= ( sK3 @ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f1325]) ).
thf(f1325,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $false
= ( irel @ sK6 @ X2 ) )
| ( $false
= ( irel @ sK10 @ X3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1324]) ).
thf(f1324,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK10 @ X3 ) ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $false
= ( irel @ sK6 @ X2 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1323]) ).
thf(f1323,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK6 @ X2 ) ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( ~ ( irel @ sK10 @ X3 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( sK3 @ X2 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1322]) ).
thf(f1322,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK10 @ X3 )
| ( sK3 @ X3 ) ) )
| ( $true
= ( sK3 @ X2 ) )
| ( $true
= ( ~ ( irel @ sK6 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1321]) ).
thf(f1321,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK3 @ X2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( irel @ sK10 @ X3 )
| ( sK3 @ X3 ) ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK6 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1320]) ).
thf(f1320,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK6 @ X2 ) ) )
| ( $true
= ( ~ ( irel @ sK10 @ X3 )
| ( sK3 @ X3 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1319]) ).
thf(f1319,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) )
@ X3 ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK6 @ X2 ) ) ) ),
inference(pi_clausification,[status(thm)],[f1318]) ).
thf(f1318,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK6 @ X2 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( irel @ sK7 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1317]) ).
thf(f1317,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) )
@ X2 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f1316]) ).
thf(f1316,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
| ( ( irel @ sK7 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1296]) ).
thf(f1296,plain,
! [X1: $i] :
( ( ( irel @ sK7 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK9 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $true
= ( sK4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1295]) ).
thf(f2219,plain,
( spl1_25
| spl1_36
| spl1_26
| spl1_37 ),
inference(avatar_split_clause,[status(thm)],[f1838,f2216,f2166,f2212,f2162]) ).
thf(f1838,plain,
( ( ( sK3 @ sK8 )
= $false )
| ( ( sK3 @ sK73 )
= $false )
| ( ( sK4 @ sK59 )
= $false )
| ( ( sK4 @ sK74 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1831]) ).
thf(f1831,plain,
( ( $false
= ( ~ ( irel @ sK6 @ sK74 )
| ( sK4 @ sK74 ) ) )
| ( ( sK3 @ sK8 )
= $false )
| ( ( sK4 @ sK59 )
= $false )
| ( ( sK3 @ sK73 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1830]) ).
thf(f1830,plain,
( ( ( sK3 @ sK8 )
= $false )
| ( ( ~ ( irel @ sK7 @ sK73 )
| ( sK3 @ sK73 ) )
= $false )
| ( $false
= ( ~ ( irel @ sK6 @ sK74 )
| ( sK4 @ sK74 ) ) )
| ( ( sK4 @ sK59 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1829]) ).
thf(f1829,plain,
( ( ( ~ ( irel @ sK7 @ sK73 )
| ( sK3 @ sK73 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK74 )
= $false )
| ( ( sK3 @ sK8 )
= $false )
| ( ( sK4 @ sK59 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f1828]) ).
thf(f1828,plain,
( ( ( sK4 @ sK59 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( sK3 @ sK8 )
= $false )
| ( ( ~ ( irel @ sK7 @ sK73 )
| ( sK3 @ sK73 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1827]) ).
thf(f1827,plain,
( ( ( sK3 @ sK8 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) )
@ sK73 ) )
| ( ( sK4 @ sK59 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f1826]) ).
thf(f1826,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
= $false )
| ( ( sK4 @ sK59 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( sK3 @ sK8 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1824]) ).
thf(f1824,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( sK4 @ sK59 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
= $false )
| ( ( sK3 @ sK8 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1822]) ).
thf(f1822,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( sK3 @ sK8 )
= $false )
| ( ( sK4 @ sK59 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1587]) ).
thf(f1587,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) )
| ~ ( irel @ sK5 @ sK7 ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( sK3 @ sK8 )
= $false )
| ( ( sK4 @ sK59 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1586]) ).
thf(f1586,plain,
( ( ( sK3 @ sK8 )
= $false )
| ( ( ~ ( irel @ sK10 @ sK59 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( sK4 @ sK59 ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) )
| ~ ( irel @ sK5 @ sK7 ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1585]) ).
thf(f1585,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) )
@ sK59 )
= $false )
| ( ( sK3 @ sK8 )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) )
| ~ ( irel @ sK5 @ sK7 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f449]) ).
thf(f449,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK10 @ Y0 )
| ~ ( irel @ sK5 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ sK10 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( sK3 @ sK8 )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK7 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK7 @ Y0 ) ) )
| ~ ( irel @ sK5 @ sK7 ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK6 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK6 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f2156,plain,
( spl1_22
| spl1_23 ),
inference(avatar_split_clause,[status(thm)],[f1915,f2154,f2151]) ).
thf(f1915,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( sK4 @ ( sK79 @ X2 ) )
= $false )
| ( ( irel @ X2 @ X1 )
= $false )
| ( ( sK4 @ ( sK78 @ X3 ) )
= $false )
| ( $false
= ( irel @ X3 @ X4 ) )
| ( ( sK3 @ X4 )
= $true )
| ( ( irel @ sK5 @ X2 )
= $false )
| ( $false
= ( irel @ sK5 @ X3 ) )
| ( ( sK3 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1914]) ).
thf(f1914,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ X3 @ X4 ) )
| ( ( sK4 @ ( sK78 @ X3 ) )
= $false )
| ( ( irel @ X2 @ X1 )
= $false )
| ( ( ~ ( irel @ X2 @ ( sK79 @ X2 ) )
| ( sK4 @ ( sK79 @ X2 ) ) )
= $false )
| ( ( sK3 @ X1 )
= $true )
| ( ( sK3 @ X4 )
= $true )
| ( $false
= ( irel @ sK5 @ X3 ) )
| ( ( irel @ sK5 @ X2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1913]) ).
thf(f1913,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( $false
= ( irel @ sK5 @ X3 ) )
| ( ( irel @ X2 @ X1 )
= $false )
| ( ( sK3 @ X4 )
= $true )
| ( ( sK4 @ ( sK78 @ X3 ) )
= $false )
| ( ( irel @ sK5 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) )
@ ( sK79 @ X2 ) )
= $false )
| ( $false
= ( irel @ X3 @ X4 ) ) ),
inference(sigma_clausification,[status(thm)],[f1912]) ).
thf(f1912,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X1 )
= $false )
| ( ( sK3 @ X4 )
= $true )
| ( ( sK4 @ ( sK78 @ X3 ) )
= $false )
| ( $false
= ( irel @ X3 @ X4 ) )
| ( $false
= ( irel @ sK5 @ X3 ) )
| ( ( irel @ sK5 @ X2 )
= $false )
| ( ( sK3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1911]) ).
thf(f1911,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK5 @ X3 ) )
| ( ( sK3 @ X4 )
= $true )
| ( ( sK4 @ ( sK78 @ X3 ) )
= $false )
| ( ( irel @ X2 @ X1 )
= $false )
| ( ( irel @ sK5 @ X2 )
= $false )
| ( $true
= ( ~ ( irel @ X3 @ X4 ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1910]) ).
thf(f1910,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) )
| ( $false
= ( irel @ sK5 @ X3 ) )
| ( $true
= ( ~ ( irel @ X3 @ X4 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( sK3 @ X4 )
= $true )
| ( ( sK4 @ ( sK78 @ X3 ) )
= $false )
| ( ( irel @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1909]) ).
thf(f1909,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( sK4 @ ( sK78 @ X3 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK5 @ X3 ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( ( irel @ X2 @ X1 )
= $false )
| ( ( sK3 @ X4 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) )
| ( $true
= ( ~ ( irel @ X3 @ X4 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1908]) ).
thf(f1908,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( irel @ X2 @ X1 )
= $false )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( ~ ( irel @ sK5 @ X3 ) ) )
| ( ( sK3 @ X4 )
= $true )
| ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) )
| ( $true
= ( ~ ( irel @ X3 @ X4 ) ) )
| ( ( sK4 @ ( sK78 @ X3 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1907]) ).
thf(f1907,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( irel @ X2 @ X1 ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) )
| ( $true
= ( ~ ( irel @ X3 @ X4 ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X3 ) ) )
| ( ( sK3 @ X4 )
= $true )
| ( ( sK4 @ ( sK78 @ X3 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1906]) ).
thf(f1906,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( irel @ X3 @ X4 )
| ( sK3 @ X4 ) ) )
| ( $true
= ( ~ ( irel @ X2 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( ( sK4 @ ( sK78 @ X3 ) )
= $false )
| ( $true
= ( ~ ( irel @ sK5 @ X3 ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1905]) ).
thf(f1905,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( ( sK4 @ ( sK78 @ X3 ) )
= $false )
| ( $true
= ( ~ ( irel @ X2 @ X1 )
| ~ ( irel @ sK5 @ X2 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X3 ) ) )
| ( $true
= ( ~ ( irel @ X3 @ X4 )
| ( sK3 @ X4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1903]) ).
thf(f1903,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( ( ( sK4 @ ( sK78 @ X3 ) )
| ~ ( irel @ X3 @ ( sK78 @ X3 ) ) )
= $false )
| ( $true
= ( ~ ( irel @ X2 @ X1 )
| ~ ( irel @ sK5 @ X2 ) ) )
| ( $true
= ( ~ ( irel @ X3 @ X4 )
| ( sK3 @ X4 ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X3 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1902]) ).
thf(f1902,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( irel @ sK5 @ X3 ) ) )
| ( $true
= ( ~ ( irel @ X2 @ X1 )
| ~ ( irel @ sK5 @ X2 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( ~ ( irel @ X3 @ X4 )
| ( sK3 @ X4 ) ) )
| ( ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X3 @ Y0 ) )
@ ( sK78 @ X3 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f1901]) ).
thf(f1901,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X3 @ Y0 ) ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( irel @ X3 @ X4 )
| ( sK3 @ X4 ) ) )
| ( $true
= ( ~ ( irel @ X2 @ X1 )
| ~ ( irel @ sK5 @ X2 ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X3 ) ) )
| ( ( sK3 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1900]) ).
thf(f1900,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( irel @ X2 @ X1 )
| ~ ( irel @ sK5 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( ~ ( irel @ X3 @ X4 )
| ( sK3 @ X4 ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X3 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1899]) ).
thf(f1899,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( sK3 @ X1 )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( irel @ X3 @ X4 )
| ( sK3 @ X4 ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X3 ) ) )
| ( $true
= ( ~ ( irel @ X2 @ X1 )
| ~ ( irel @ sK5 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1898]) ).
thf(f1898,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( irel @ sK5 @ X3 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X3 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ X3 @ Y0 )
| ( sK3 @ Y0 ) )
@ X4 ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( ~ ( irel @ X2 @ X1 )
| ~ ( irel @ sK5 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f1897]) ).
thf(f1897,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X3 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X3 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X3 @ Y0 ) ) ) ) )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( ~ ( irel @ X2 @ X1 )
| ~ ( irel @ sK5 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1896]) ).
thf(f1896,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X3 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X3 @ Y0 ) ) ) )
= $true )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( ~ ( irel @ sK5 @ X3 ) ) )
| ( $true
= ( ~ ( irel @ X2 @ X1 )
| ~ ( irel @ sK5 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1895]) ).
thf(f1895,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X3 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X3 @ Y0 ) ) )
| ~ ( irel @ sK5 @ X3 ) )
= $true )
| ( ( sK3 @ X1 )
= $true )
| ( $true
= ( ~ ( irel @ X2 @ X1 )
| ~ ( irel @ sK5 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1894]) ).
thf(f1894,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( irel @ X2 @ X1 )
| ~ ( irel @ sK5 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X1 ) )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X3 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ X3 @ Y0 ) ) )
| ~ ( irel @ sK5 @ X3 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1893]) ).
thf(f1893,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) )
@ X3 ) )
| ( ( ~ ( irel @ X2 @ X1 )
| ~ ( irel @ sK5 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X1 ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f1892]) ).
thf(f1892,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
| ( ( ~ ( irel @ X2 @ X1 )
| ~ ( irel @ sK5 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1890]) ).
thf(f1890,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) ) ) ) )
| ( ( ~ ( irel @ X2 @ X1 )
| ~ ( irel @ sK5 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( sK3 @ X1 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1889]) ).
thf(f1889,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ Y0 @ X1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ X1 ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f1888]) ).
thf(f1888,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ Y0 @ X1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( sK3 @ X1 ) ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1887]) ).
thf(f1887,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f1886]) ).
thf(f1886,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y1 @ Y0 )
| ~ ( irel @ sK5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK4 @ Y2 ) ) )
| ( sK3 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( sK4 @ Y1 ) ) ) ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f2083,plain,
( spl1_1
| spl1_3 ),
inference(avatar_split_clause,[status(thm)],[f2071,f2081,f2074]) ).
thf(f2071,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK5 @ X2 )
= $false )
| ( ( sK3 @ ( sK89 @ X2 ) )
= $false )
| ( $true
= ( sK4 @ X3 ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( sK3 @ ( sK87 @ X1 ) )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( sK4 @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2069]) ).
thf(f2069,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( sK3 @ ( sK87 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ sK5 @ X2 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( sK4 @ X4 ) )
| ( $true
= ( sK4 @ X3 ) )
| ( ( ( sK3 @ ( sK89 @ X2 ) )
| ~ ( irel @ X2 @ ( sK89 @ X2 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f2068]) ).
thf(f2068,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) )
@ ( sK89 @ X2 ) )
= $false )
| ( ( irel @ sK5 @ X2 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( sK4 @ X4 ) )
| ( ( sK3 @ ( sK87 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f2067]) ).
thf(f2067,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( sK3 @ ( sK87 @ X1 ) )
= $false )
| ( $true
= ( sK4 @ X4 ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) )
= $false )
| ( ( irel @ sK5 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( sK4 @ X3 ) )
| ( ( irel @ sK5 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f2066]) ).
thf(f2066,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( irel @ X2 @ X4 ) )
= $true )
| ( $true
= ( sK4 @ X4 ) )
| ( ( sK3 @ ( sK87 @ X1 ) )
= $false )
| ( ( irel @ sK5 @ X2 )
= $false )
| ( $true
= ( sK4 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f2065]) ).
thf(f2065,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( irel @ X2 @ X4 )
| ( sK4 @ X4 ) ) )
| ( ( irel @ sK5 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( sK3 @ ( sK87 @ X1 ) )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) )
= $false )
| ( $true
= ( sK4 @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2064]) ).
thf(f2064,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) )
@ X4 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ sK5 @ X2 )
= $false )
| ( ( sK3 @ ( sK87 @ X1 ) )
= $false )
| ( $true
= ( sK4 @ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f2063]) ).
thf(f2063,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( sK4 @ X3 ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( sK3 @ ( sK87 @ X1 ) )
= $false )
| ( ( irel @ sK5 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f2062]) ).
thf(f2062,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( sK4 @ X3 ) )
| ( ( irel @ sK5 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( ( sK3 @ ( sK87 @ X1 ) )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f2061]) ).
thf(f2061,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( ( sK3 @ ( sK87 @ X1 ) )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f2044]) ).
thf(f2044,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X3 ) )
| ( ( sK3 @ ( sK87 @ X1 ) )
= $false )
| ( ( ~ ( irel @ sK5 @ X1 ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2043]) ).
thf(f2043,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ( irel @ X1 @ ( sK87 @ X1 ) )
| ( sK3 @ ( sK87 @ X1 ) ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ~ ( irel @ sK5 @ X1 ) )
= $true )
| ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) ) ) )
| ( $true
= ( sK4 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2042]) ).
thf(f2042,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) ) )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ~ ( irel @ sK5 @ X1 ) )
= $true )
| ( $false
= ( ~ ( irel @ X1 @ ( sK87 @ X1 ) )
| ( sK3 @ ( sK87 @ X1 ) ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) )
| ( $true
= ( sK4 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2041]) ).
thf(f2041,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK5 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) ) ) )
| ( $true
= ( sK4 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ~ ( irel @ sK5 @ X1 ) )
= $true )
| ( $false
= ( ~ ( irel @ X1 @ ( sK87 @ X1 ) )
| ( sK3 @ ( sK87 @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f2040]) ).
thf(f2040,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( ~ ( irel @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( irel @ X1 @ ( sK87 @ X1 ) )
| ( sK3 @ ( sK87 @ X1 ) ) ) )
| ( ( ~ ( irel @ sK5 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f2039]) ).
thf(f2039,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( irel @ X1 @ X3 )
| ~ ( irel @ sK5 @ X1 ) )
= $true )
| ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( ~ ( irel @ sK5 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( irel @ X1 @ ( sK87 @ X1 ) )
| ( sK3 @ ( sK87 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2038]) ).
thf(f2038,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK3 @ Y0 ) )
@ ( sK87 @ X1 ) )
= $false )
| ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( ~ ( irel @ sK5 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) ) ) )
| ( ( ~ ( irel @ X1 @ X3 )
| ~ ( irel @ sK5 @ X1 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f2037]) ).
thf(f2037,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
= $false )
| ( ( ~ ( irel @ X1 @ X3 )
| ~ ( irel @ sK5 @ X1 ) )
= $true )
| ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( ~ ( irel @ sK5 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f2036]) ).
thf(f2036,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( ( ~ ( irel @ X1 @ X3 )
| ~ ( irel @ sK5 @ X1 ) )
= $true )
| ( $true
= ( ~ ( irel @ sK5 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2035]) ).
thf(f2035,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( ~ ( irel @ X1 @ X3 )
| ~ ( irel @ sK5 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2034]) ).
thf(f2034,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ X1 @ X3 )
| ~ ( irel @ sK5 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( sK4 @ X3 ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2033]) ).
thf(f2033,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ~ ( irel @ sK5 @ X1 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ X1 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( irel @ sK5 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f2032]) ).
thf(f2032,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ~ ( irel @ sK5 @ X1 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ X1 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X2 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ X2 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2031]) ).
thf(f2031,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ~ ( irel @ sK5 @ X1 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ X1 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f2030]) ).
thf(f2030,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ X1 @ Y0 )
| ~ ( irel @ sK5 @ X1 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ X1 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( sK4 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2029]) ).
thf(f2029,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( sK4 @ Y1 ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f1984]) ).
thf(f1984,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( sK4 @ Y1 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1885]) ).
thf(f1885,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ~ ( irel @ sK5 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ~ ( irel @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y0 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( sK4 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.08 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.27 % Computer : n012.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Tue May 5 09:24:45 EDT 2026
% 0.09/0.27 % CPUTime :
% 0.09/0.27 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.36 ---- Original DTF file ---
% 0.16/0.36 thf(spec,logic,$$dhol).
% 0.16/0.36 %------------------------------------------------------------------------------
% 0.16/0.36 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.16/0.36 % Domain : Software Verification
% 0.16/0.36 % Problem : Benchmark: LCL696^1, Active target: iequiv
% 0.16/0.36 % Version : Especial.
% 0.16/0.36 % English :
% 0.16/0.36
% 0.16/0.36 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.16/0.36 % Source : [Kon26]
% 0.16/0.36 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.16/0.36
% 0.16/0.36 % Status : Theorem
% 0.16/0.36 % Rating : ? v9.3.0
% 0.16/0.36 % Syntax : Number of formulae : 26 ( 1 unt; 24 typ; 0 def)
% 0.16/0.36 % Number of atoms : 69 ( 22 equ; 0 cnn)
% 0.16/0.36 % Maximal formula atoms : 24 ( 34 avg)
% 0.16/0.36 % Number of connectives : 190 ( 38 ~; 32 |; 26 &; 93 @)
% 0.16/0.36 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.16/0.36 % Maximal formula depth : 26 ( 14 avg)
% 0.16/0.36 % Number of types : 4 ( 2 usr)
% 0.16/0.36 % Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% 0.16/0.36 % Number of symbols : 23 ( 22 usr; 1 con; 0-3 aty)
% 0.16/0.36 % Number of variables : 73 ( 41 ^; 31 !; 1 ?; 73 :)
% 0.16/0.36 % SPC : TH0_THM_EQU_NAR
% 0.16/0.36
% 0.16/0.36 % Comments :
% 0.16/0.36 %------------------------------------------------------------------------------
% 0.16/0.36 thf(unsorted_type,type,
% 0.16/0.36 unsorted: $tType ).
% 0.16/0.36
% 0.16/0.36 thf(irel_decl,type,
% 0.16/0.36 irel: $i > $i > $o ).
% 0.16/0.36
% 0.16/0.36 thf(mnot_decl,type,
% 0.16/0.36 mnot: ( $i > $o ) > $i > $o ).
% 0.16/0.36
% 0.16/0.36 thf(mor_decl,type,
% 0.16/0.36 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.36
% 0.16/0.36 thf(mand_decl,type,
% 0.16/0.36 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.36
% 0.16/0.36 thf(mimplies_decl,type,
% 0.16/0.36 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.36
% 0.16/0.36 thf(mbox_s4_decl,type,
% 0.16/0.36 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.16/0.36
% 0.16/0.36 thf(iatom_decl,type,
% 0.16/0.36 iatom: ( $i > $o ) > $i > $o ).
% 0.16/0.36
% 0.16/0.36 thf(inot_decl,type,
% 0.16/0.36 inot: ( $i > $o ) > $i > $o ).
% 0.16/0.36
% 0.16/0.36 thf(itrue_decl,type,
% 0.16/0.36 itrue: $i > $o ).
% 0.16/0.36
% 0.16/0.36 thf(ifalse_decl,type,
% 0.16/0.36 ifalse: $i > $o ).
% 0.16/0.36
% 0.16/0.36 thf(iand_decl,type,
% 0.16/0.36 iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.36
% 0.16/0.36 thf(ior_decl,type,
% 0.16/0.36 ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.36
% 0.16/0.36 thf(iimplies_decl,type,
% 0.16/0.36 iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.36
% 0.16/0.36 thf(iimplied_decl,type,
% 0.16/0.36 iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.36
% 0.16/0.36 thf(iequiv_decl,type,
% 0.16/0.36 iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.36
% 0.16/0.36 thf(ixor_decl,type,
% 0.16/0.36 ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.36
% 0.16/0.36 thf(ivalid_decl,type,
% 0.16/0.36 ivalid: ( $i > $o ) > $o ).
% 0.16/0.36
% 0.16/0.36 thf(isatisfiable_decl,type,
% 0.16/0.36 isatisfiable: ( $i > $o ) > $o ).
% 0.16/0.36
% 0.16/0.36 thf(icountersatisfiable_decl,type,
% 0.16/0.36 icountersatisfiable: ( $i > $o ) > $o ).
% 0.16/0.36
% 0.16/0.36 thf(iinvalid_decl,type,
% 0.16/0.36 iinvalid: ( $i > $o ) > $o ).
% 0.16/0.36
% 0.16/0.36 %----Types of the domains
% 0.16/0.36 thf(d_unsorted_type,type,
% 0.16/0.36 d_unsorted: $tType ).
% 0.16/0.36
% 0.16/0.36 %----Types of the promotion functions
% 0.16/0.36 thf(d2unsorted_decl,type,
% 0.16/0.36 d2unsorted: d_unsorted > $i ).
% 0.16/0.36
% 0.16/0.36 %----Types of the domain elements
% 0.16/0.36 thf(d_unsorted_0_decl,type,
% 0.16/0.36 d_unsorted_0: d_unsorted ).
% 0.16/0.36
% 0.16/0.36 thf(lcl696_1,axiom,
% 0.16/0.36 ( ! [U: $i] :
% 0.16/0.36 ? [DU: d_unsorted] :
% 0.16/0.36 ( U
% 0.16/0.36 = ( d2unsorted @ DU ) )
% 0.16/0.36 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 0.16/0.36 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 0.16/0.36 ( ( ( d2unsorted @ DU1 )
% 0.16/0.36 = ( d2unsorted @ DU2 ) )
% 0.16/0.36 => ( DU1 = DU2 ) )
% 0.16/0.36 & ( mnot
% 0.16/0.36 = ( ^ [X: $i > $o,U: $i] :
% 0.16/0.36 ~ ( X @ U ) ) )
% 0.16/0.36 & ( mor
% 0.16/0.36 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.16/0.36 ( ( X @ U )
% 0.16/0.36 | ( Y @ U ) ) ) )
% 0.16/0.36 & ( mand
% 0.16/0.36 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.16/0.36 ( ( X @ U )
% 0.16/0.36 & ( Y @ U ) ) ) )
% 0.16/0.36 & ( mimplies
% 0.16/0.36 = ( ^ [U: $i > $o,V: $i > $o,Flatten_var_0: $i] :
% 0.16/0.36 ( ~ ( U @ Flatten_var_0 )
% 0.16/0.36 | ( V @ Flatten_var_0 ) ) ) )
% 0.16/0.36 & ( mbox_s4
% 0.16/0.36 = ( ^ [P: $i > $o,X: $i] :
% 0.16/0.36 ! [Y: $i] :
% 0.16/0.36 ( ~ ( irel @ X @ Y )
% 0.16/0.36 | ( P @ Y ) ) ) )
% 0.16/0.36 & ( iatom
% 0.16/0.36 = ( ^ [P: $i > $o,Flatten_var_0: $i] : ( P @ Flatten_var_0 ) ) )
% 0.16/0.36 & ( inot
% 0.16/0.36 = ( ^ [P: $i > $o,Flatten_var_0: $i] :
% 0.16/0.36 ~ ! [Y: $i] :
% 0.16/0.36 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.16/0.36 | ( P @ Y ) ) ) )
% 0.16/0.36 & ( iand
% 0.16/0.36 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.16/0.36 ( ! [Y: $i] :
% 0.16/0.36 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.16/0.36 | ( P @ Y ) )
% 0.16/0.36 & ! [Y: $i] :
% 0.16/0.36 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.16/0.36 | ( Q @ Y ) ) ) ) )
% 0.16/0.36 & ( ior
% 0.16/0.36 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.16/0.36 ( ! [Y: $i] :
% 0.16/0.36 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.16/0.36 | ( P @ Y ) )
% 0.16/0.36 | ! [Y: $i] :
% 0.16/0.36 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.16/0.36 | ( Q @ Y ) ) ) ) )
% 0.16/0.36 & ( iimplies
% 0.16/0.36 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.16/0.36 ( ~ ! [Y: $i] :
% 0.16/0.36 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.16/0.36 | ( P @ Y ) )
% 0.16/0.36 | ! [Y: $i] :
% 0.16/0.36 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.16/0.36 | ( Q @ Y ) ) ) ) )
% 0.16/0.36 & ( iimplied
% 0.16/0.36 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.16/0.36 ( ~ ! [Y: $i] :
% 0.16/0.36 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.16/0.36 | ( Q @ Y ) )
% 0.16/0.36 | ! [Y: $i] :
% 0.16/0.36 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.16/0.36 | ( P @ Y ) ) ) ) )
% 0.16/0.36 & ( iequiv
% 0.16/0.36 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.16/0.36 ( ! [Y: $i,Bound_variable_718: $i] :
% 0.16/0.36 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.16/0.36 | ~ ! [Bound_variable_693: $i] :
% 0.16/0.36 ( ~ ( irel @ Y @ Bound_variable_693 )
% 0.16/0.36 | ( P @ Bound_variable_693 ) )
% 0.16/0.36 | ~ ( irel @ Y @ Bound_variable_718 )
% 0.16/0.36 | ( Q @ Bound_variable_718 ) )
% 0.16/0.36 & ! [Y: $i,Bound_variable_771: $i] :
% 0.16/0.36 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.16/0.36 | ~ ! [Bound_variable_746: $i] :
% 0.16/0.36 ( ~ ( irel @ Y @ Bound_variable_746 )
% 0.16/0.36 | ( Q @ Bound_variable_746 ) )
% 0.16/0.36 | ~ ( irel @ Y @ Bound_variable_771 )
% 0.16/0.36 | ( P @ Bound_variable_771 ) ) ) ) )
% 0.16/0.36 & ( ixor
% 0.16/0.36 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.16/0.36 ~ ! [Y: $i,Bound_variable_849: $i,Bound_variable_851: $i,Bound_variable_864: $i,Bound_variable_866: $i] :
% 0.16/0.36 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.16/0.36 | ( ( ~ ( irel @ Y @ Bound_variable_849 )
% 0.16/0.36 | ~ ! [Bound_variable_693: $i] :
% 0.16/0.36 ( ~ ( irel @ Bound_variable_849 @ Bound_variable_693 )
% 0.16/0.36 | ( P @ Bound_variable_693 ) )
% 0.16/0.36 | ~ ( irel @ Bound_variable_849 @ Bound_variable_851 )
% 0.16/0.36 | ( Q @ Bound_variable_851 ) )
% 0.16/0.36 & ( ~ ( irel @ Y @ Bound_variable_864 )
% 0.16/0.36 | ~ ! [Bound_variable_746: $i] :
% 0.16/0.36 ( ~ ( irel @ Bound_variable_864 @ Bound_variable_746 )
% 0.16/0.36 | ( Q @ Bound_variable_746 ) )
% 0.16/0.36 | ~ ( irel @ Bound_variable_864 @ Bound_variable_866 )
% 0.16/0.36 | ( P @ Bound_variable_866 ) ) ) ) ) )
% 0.16/0.36 & ( ivalid
% 0.16/0.36 = ( ^ [Phi: $i > $o] :
% 0.16/0.36 ! [W: $i] : ( Phi @ W ) ) )
% 0.16/0.36 & ( isatisfiable
% 0.16/0.36 = ( ^ [Phi: $i > $o] :
% 0.16/0.36 ~ ! [W: $i] :
% 0.16/0.36 ~ ( Phi @ W ) ) )
% 0.16/0.36 & ( icountersatisfiable
% 0.16/0.36 = ( ^ [Phi: $i > $o] :
% 0.16/0.36 ~ ! [W: $i] : ( Phi @ W ) ) )
% 0.16/0.36 & ( iinvalid
% 0.16/0.36 = ( ^ [Phi: $i > $o] :
% 0.16/0.36 ! [W: $i] :
% 0.16/0.36 ~ ( Phi @ W ) ) )
% 0.16/0.36 & ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
% 0.16/0.36 & ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
% 0.16/0.36 & ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ) ).
% 0.16/0.36
% 0.16/0.36 thf(iequiv,conjecture,
% 0.16/0.36 ( iequiv
% 0.16/0.36 = ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ) ).
% 0.16/0.36
% 0.16/0.36 %------------------------------------------------------------------------------
% 0.16/0.36 ------------------------
% 1.43/1.28 ---- Embedded in THF ---
% 1.43/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.28 %%% Generated on Tue May 05 09:24:46 EDT 2026
% 1.43/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.28 %%% Logic specification used:
% 1.43/1.28 %%% thf(spec, logic, $$dhol).
% 1.43/1.28
% 1.43/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.MacNcZ7HSP/DTF2DTF29558.p
% See solution above
% 1.43/1.28 ------------------------
% 1.43/1.29 ---- Cleaned THF ---
% 1.43/1.29 thf(unsorted_type,type,
% 1.43/1.29 unsorted: $tType ).
% 1.43/1.29
% 1.43/1.29 thf(irel_decl,type,
% 1.43/1.29 irel: $i > $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(mnot_decl,type,
% 1.43/1.29 mnot: ( $i > $o ) > $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(mor_decl,type,
% 1.43/1.29 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(mand_decl,type,
% 1.43/1.29 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(mimplies_decl,type,
% 1.43/1.29 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(mbox_s4_decl,type,
% 1.43/1.29 mbox_s4: ( $i > $o ) > $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(iatom_decl,type,
% 1.43/1.29 iatom: ( $i > $o ) > $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(inot_decl,type,
% 1.43/1.29 inot: ( $i > $o ) > $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(itrue_decl,type,
% 1.43/1.29 itrue: $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(ifalse_decl,type,
% 1.43/1.29 ifalse: $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(iand_decl,type,
% 1.43/1.29 iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(ior_decl,type,
% 1.43/1.29 ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(iimplies_decl,type,
% 1.43/1.29 iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(iimplied_decl,type,
% 1.43/1.29 iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(iequiv_decl,type,
% 1.43/1.29 iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(ixor_decl,type,
% 1.43/1.29 ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.43/1.29
% 1.43/1.29 thf(ivalid_decl,type,
% 1.43/1.29 ivalid: ( $i > $o ) > $o ).
% 1.43/1.29
% 1.43/1.29 thf(isatisfiable_decl,type,
% 1.43/1.29 isatisfiable: ( $i > $o ) > $o ).
% 1.43/1.29
% 1.43/1.29 thf(icountersatisfiable_decl,type,
% 1.43/1.29 icountersatisfiable: ( $i > $o ) > $o ).
% 1.43/1.29
% 1.43/1.29 thf(iinvalid_decl,type,
% 1.43/1.29 iinvalid: ( $i > $o ) > $o ).
% 1.43/1.29
% 1.43/1.29 thf(d_unsorted_type,type,
% 1.43/1.29 d_unsorted: $tType ).
% 1.43/1.29
% 1.43/1.29 thf(d2unsorted_decl,type,
% 1.43/1.29 d2unsorted: d_unsorted > $i ).
% 1.43/1.29
% 1.43/1.29 thf(d_unsorted_0_decl,type,
% 1.43/1.29 d_unsorted_0: d_unsorted ).
% 1.43/1.29
% 1.43/1.29 thf(lcl696_1,axiom,
% 1.43/1.29 ( ! [U: $i] :
% 1.43/1.29 ? [DU: d_unsorted] :
% 1.43/1.29 ( U
% 1.43/1.29 = ( d2unsorted @ DU ) )
% 1.43/1.29 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 1.43/1.29 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 1.43/1.29 ( ( ( d2unsorted @ DU1 )
% 1.43/1.29 = ( d2unsorted @ DU2 ) )
% 1.43/1.29 => ( DU1 = DU2 ) )
% 1.43/1.29 & ( mnot
% 1.43/1.29 = ( ^ [X: $i > $o,U: $i] :
% 1.43/1.29 ~ ( X @ U ) ) )
% 1.43/1.29 & ( mor
% 1.43/1.29 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 1.43/1.29 ( ( X @ U )
% 1.43/1.29 | ( Y @ U ) ) ) )
% 1.43/1.29 & ( mand
% 1.43/1.29 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 1.43/1.29 ( ( X @ U )
% 1.43/1.29 & ( Y @ U ) ) ) )
% 1.43/1.29 & ( mimplies
% 1.43/1.29 = ( ^ [U: $i > $o,V: $i > $o,Flatten_var_0: $i] :
% 1.43/1.29 ( ~ ( U @ Flatten_var_0 )
% 1.43/1.29 | ( V @ Flatten_var_0 ) ) ) )
% 1.43/1.29 & ( mbox_s4
% 1.43/1.29 = ( ^ [P: $i > $o,X: $i] :
% 1.43/1.29 ! [Y: $i] :
% 1.43/1.29 ( ~ ( irel @ X @ Y )
% 1.43/1.29 | ( P @ Y ) ) ) )
% 1.43/1.29 & ( iatom
% 1.43/1.29 = ( ^ [P: $i > $o,Flatten_var_0: $i] : ( P @ Flatten_var_0 ) ) )
% 1.43/1.29 & ( inot
% 1.43/1.29 = ( ^ [P: $i > $o,Flatten_var_0: $i] :
% 1.43/1.29 ~ ! [Y: $i] :
% 1.43/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.43/1.29 | ( P @ Y ) ) ) )
% 1.43/1.29 & ( iand
% 1.43/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.43/1.29 ( ! [Y: $i] :
% 1.43/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.43/1.29 | ( P @ Y ) )
% 1.43/1.29 & ! [Y: $i] :
% 1.43/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.43/1.29 | ( Q @ Y ) ) ) ) )
% 1.43/1.29 & ( ior
% 1.43/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.43/1.29 ( ! [Y: $i] :
% 1.43/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.43/1.29 | ( P @ Y ) )
% 1.43/1.29 | ! [Y: $i] :
% 1.43/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.43/1.29 | ( Q @ Y ) ) ) ) )
% 1.43/1.29 & ( iimplies
% 1.43/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.43/1.29 ( ~ ! [Y: $i] :
% 1.43/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.43/1.29 | ( P @ Y ) )
% 1.43/1.29 | ! [Y: $i] :
% 1.43/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.43/1.29 | ( Q @ Y ) ) ) ) )
% 1.43/1.29 & ( iimplied
% 1.43/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.43/1.29 ( ~ ! [Y: $i] :
% 1.43/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.43/1.29 | ( Q @ Y ) )
% 1.43/1.29 | ! [Y: $i] :
% 1.43/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.43/1.29 | ( P @ Y ) ) ) ) )
% 1.43/1.29 & ( iequiv
% 1.43/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.43/1.29 ( ! [Y: $i,Bound_variable_718: $i] :
% 1.43/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.43/1.29 | ~ ! [Bound_variable_693: $i] :
% 1.43/1.29 ( ~ ( irel @ Y @ Bound_variable_693 )
% 1.43/1.29 | ( P @ Bound_variable_693 ) )
% 1.43/1.29 | ~ ( irel @ Y @ Bound_variable_718 )
% 1.43/1.29 | ( Q @ Bound_variable_718 ) )
% 1.43/1.29 & ! [Y: $i,Bound_variable_771: $i] :
% 1.43/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.43/1.29 | ~ ! [Bound_variable_746: $i] :
% 1.43/1.29 ( ~ ( irel @ Y @ Bound_variable_746 )
% 1.43/1.29 | ( Q @ Bound_variable_746 ) )
% 1.43/1.29 | ~ ( irel @ Y @ Bound_variable_771 )
% 1.43/1.29 | ( P @ Bound_variable_771 ) ) ) ) )
% 1.43/1.29 & ( ixor
% 1.43/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.43/1.29 ~ ! [Y: $i,Bound_variable_849: $i,Bound_variable_851: $i,Bound_variable_864: $i,Bound_variable_866: $i] :
% 1.43/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.43/1.29 | ( ( ~ ( irel @ Y @ Bound_variable_849 )
% 1.43/1.29 | ~ ! [Bound_variable_693: $i] :
% 1.43/1.29 ( ~ ( irel @ Bound_variable_849 @ Bound_variable_693 )
% 1.43/1.29 | ( P @ Bound_variable_693 ) )
% 1.43/1.29 | ~ ( irel @ Bound_variable_849 @ Bound_variable_851 )
% 1.43/1.29 | ( Q @ Bound_variable_851 ) )
% 1.43/1.29 & ( ~ ( irel @ Y @ Bound_variable_864 )
% 1.43/1.29 | ~ ! [Bound_variable_746: $i] :
% 1.43/1.29 ( ~ ( irel @ Bound_variable_864 @ Bound_variable_746 )
% 1.43/1.29 | ( Q @ Bound_variable_746 ) )
% 1.43/1.29 | ~ ( irel @ Bound_variable_864 @ Bound_variable_866 )
% 1.43/1.29 | ( P @ Bound_variable_866 ) ) ) ) ) )
% 1.43/1.29 & ( ivalid
% 1.43/1.29 = ( ^ [Phi: $i > $o] :
% 1.43/1.29 ! [W: $i] : ( Phi @ W ) ) )
% 1.43/1.29 & ( isatisfiable
% 1.43/1.29 = ( ^ [Phi: $i > $o] :
% 1.43/1.29 ~ ! [W: $i] :
% 1.43/1.29 ~ ( Phi @ W ) ) )
% 1.43/1.29 & ( icountersatisfiable
% 1.43/1.29 = ( ^ [Phi: $i > $o] :
% 1.43/1.29 ~ ! [W: $i] : ( Phi @ W ) ) )
% 1.43/1.29 & ( iinvalid
% 1.43/1.29 = ( ^ [Phi: $i > $o] :
% 1.43/1.29 ! [W: $i] :
% 1.43/1.29 ~ ( Phi @ W ) ) )
% 1.43/1.29 & ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
% 1.43/1.29 & ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
% 1.43/1.29 & ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ) ).
% 1.43/1.29
% 1.43/1.29 thf(iequiv,conjecture,
% 1.43/1.29 ( iequiv
% 1.43/1.29 = ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ) ).
% 1.43/1.29 ------------------------
% 1.64/1.30 % (29656)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/183Mi)
% 1.64/1.31 % (29657)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_29558 for (2999ds/4Mi)
% 1.64/1.31 % (29662)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/18Mi)
% 1.64/1.31 % (29658)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_29558 for (2999ds/27Mi)
% 1.64/1.31 % (29660)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_29558 for (2999ds/2Mi)
% 1.64/1.31 % (29661)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_29558 for (2999ds/275Mi)
% 1.64/1.31 % (29659)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/2Mi)
% 1.64/1.31 % (29659)Instruction limit reached!
% 1.64/1.31 % (29659)------------------------------
% 1.64/1.31 % (29659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (29659)Termination reason: Unknown
% 1.64/1.31 % (29660)Instruction limit reached!
% 1.64/1.31 % (29660)------------------------------
% 1.64/1.31 % (29660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (29659)Termination phase: shuffling
% 1.64/1.31
% 1.64/1.31 % (29659)Memory used [KB]: 1023
% 1.64/1.31 % (29659)Time elapsed: 0.002 s
% 1.64/1.31 % (29659)Instructions burned: 2 (million)
% 1.64/1.31 % (29659)------------------------------
% 1.64/1.31 % (29659)------------------------------
% 1.64/1.31 % (29660)Termination reason: Unknown
% 1.64/1.31 % (29660)Termination phase: shuffling
% 1.64/1.31
% 1.64/1.31 % (29660)Memory used [KB]: 1023
% 1.64/1.31 % (29660)Time elapsed: 0.003 s
% 1.64/1.31 % (29660)Instructions burned: 2 (million)
% 1.64/1.31 % (29660)------------------------------
% 1.64/1.31 % (29660)------------------------------
% 1.64/1.31 % (29657)Instruction limit reached!
% 1.64/1.31 % (29657)------------------------------
% 1.64/1.31 % (29657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (29657)Termination reason: Unknown
% 1.64/1.31 % (29657)Termination phase: Property scanning
% 1.64/1.31
% 1.64/1.31 % (29657)Memory used [KB]: 1023
% 1.64/1.31 % (29657)Time elapsed: 0.004 s
% 1.64/1.31 % (29657)Instructions burned: 4 (million)
% 1.64/1.31 % (29657)------------------------------
% 1.64/1.31 % (29657)------------------------------
% 1.64/1.31 % (29661)Refutation not found, incomplete strategy
% 1.64/1.31 % (29661)------------------------------
% 1.64/1.31 % (29661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (29661)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.31
% 1.64/1.31
% 1.64/1.31 % (29661)Memory used [KB]: 5628
% 1.64/1.31 % (29661)Time elapsed: 0.005 s
% 1.64/1.31 % (29661)Instructions burned: 6 (million)
% 1.64/1.31 % (29661)------------------------------
% 1.64/1.31 % (29661)------------------------------
% 1.64/1.32 % (29662)Instruction limit reached!
% 1.64/1.32 % (29662)------------------------------
% 1.64/1.32 % (29662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (29662)Termination reason: Unknown
% 1.64/1.32 % (29662)Termination phase: Saturation
% 1.64/1.32
% 1.64/1.32 % (29662)Memory used [KB]: 5628
% 1.64/1.32 % (29662)Time elapsed: 0.011 s
% 1.64/1.32 % (29662)Instructions burned: 18 (million)
% 1.64/1.32 % (29662)------------------------------
% 1.64/1.32 % (29662)------------------------------
% 1.64/1.32 % (29658)Instruction limit reached!
% 1.64/1.32 % (29658)------------------------------
% 1.64/1.32 % (29658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (29658)Termination reason: Unknown
% 1.64/1.32 % (29658)Termination phase: Saturation
% 1.64/1.32
% 1.64/1.32 % (29658)Memory used [KB]: 5756
% 1.64/1.32 % (29658)Time elapsed: 0.014 s
% 1.64/1.32 % (29658)Instructions burned: 27 (million)
% 1.64/1.32 % (29658)------------------------------
% 1.64/1.32 % (29658)------------------------------
% 1.64/1.32 % (29663)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/3Mi)
% 1.64/1.32 % (29664)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_29558 for (2999ds/37Mi)
% 1.64/1.32 % (29663)Instruction limit reached!
% 1.64/1.32 % (29663)------------------------------
% 1.64/1.32 % (29663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (29663)Termination reason: Unknown
% 1.64/1.32 % (29663)Termination phase: shuffling
% 1.64/1.32
% 1.64/1.32 % (29663)Memory used [KB]: 1023
% 1.64/1.32 % (29663)Time elapsed: 0.003 s
% 1.64/1.32 % (29663)Instructions burned: 3 (million)
% 1.64/1.32 % (29663)------------------------------
% 1.64/1.32 % (29663)------------------------------
% 1.64/1.33 % (29666)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_29558 for (2999ds/3Mi)
% 1.64/1.33 % (29666)Instruction limit reached!
% 1.64/1.33 % (29666)------------------------------
% 1.64/1.33 % (29666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.33 % (29666)Termination reason: Unknown
% 1.64/1.33 % (29666)Termination phase: shuffling
% 1.64/1.33
% 1.64/1.33 % (29666)Memory used [KB]: 1023
% 1.64/1.33 % (29666)Time elapsed: 0.003 s
% 1.64/1.33 % (29666)Instructions burned: 3 (million)
% 1.64/1.33 % (29666)------------------------------
% 1.64/1.33 % (29666)------------------------------
% 1.64/1.33 % (29665)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_29558 for (2999ds/15Mi)
% 1.64/1.33 % (29667)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_29558 for (2999ds/1041Mi)
% 1.64/1.34 % (29665)Instruction limit reached!
% 1.64/1.34 % (29665)------------------------------
% 1.64/1.34 % (29665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (29665)Termination reason: Unknown
% 1.64/1.34 % (29665)Termination phase: Saturation
% 1.64/1.34
% 1.64/1.34 % (29665)Memory used [KB]: 5756
% 1.64/1.34 % (29665)Time elapsed: 0.009 s
% 1.64/1.34 % (29665)Instructions burned: 17 (million)
% 1.64/1.34 % (29665)------------------------------
% 1.64/1.34 % (29665)------------------------------
% 1.64/1.34 % (29668)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/7Mi)
% 1.64/1.34 % (29664)Instruction limit reached!
% 1.64/1.34 % (29664)------------------------------
% 1.64/1.34 % (29664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (29664)Termination reason: Unknown
% 1.64/1.34 % (29664)Termination phase: Saturation
% 1.64/1.34
% 1.64/1.34 % (29664)Memory used [KB]: 5628
% 1.64/1.34 % (29664)Time elapsed: 0.019 s
% 1.64/1.34 % (29664)Instructions burned: 38 (million)
% 1.64/1.34 % (29664)------------------------------
% 1.64/1.34 % (29664)------------------------------
% 1.64/1.34 % (29668)Instruction limit reached!
% 1.64/1.34 % (29668)------------------------------
% 1.64/1.34 % (29668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (29670)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_29558 for (2999ds/3Mi)
% 1.64/1.34 % (29668)Termination reason: Unknown
% 1.64/1.34 % (29668)Termination phase: Property scanning
% 1.64/1.34
% 1.64/1.34 % (29668)Memory used [KB]: 1023
% 1.64/1.34 % (29668)Time elapsed: 0.006 s
% 1.64/1.34 % (29668)Instructions burned: 9 (million)
% 1.64/1.34 % (29668)------------------------------
% 1.64/1.34 % (29668)------------------------------
% 1.64/1.34 % (29670)Instruction limit reached!
% 1.64/1.34 % (29670)------------------------------
% 1.64/1.34 % (29670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (29670)Termination reason: Unknown
% 1.64/1.34 % (29670)Termination phase: Property scanning
% 1.64/1.34
% 1.64/1.34 % (29670)Memory used [KB]: 1023
% 1.64/1.34 % (29670)Time elapsed: 0.004 s
% 1.64/1.34 % (29670)Instructions burned: 5 (million)
% 1.64/1.34 % (29670)------------------------------
% 1.64/1.34 % (29670)------------------------------
% 1.64/1.35 % (29671)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_29558 for (2999ds/3Mi)
% 1.64/1.35 % (29656)Instruction limit reached!
% 1.64/1.35 % (29656)------------------------------
% 1.64/1.35 % (29656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.35 % (29656)Termination reason: Unknown
% 1.64/1.35 % (29656)Termination phase: Saturation
% 1.64/1.35
% 1.64/1.35 % (29656)Memory used [KB]: 6652
% 1.64/1.35 % (29656)Time elapsed: 0.055 s
% 1.64/1.35 % (29656)Instructions burned: 183 (million)
% 1.64/1.35 % (29656)------------------------------
% 1.64/1.35 % (29656)------------------------------
% 1.64/1.36 % (29671)Instruction limit reached!
% 1.64/1.36 % (29671)------------------------------
% 1.64/1.36 % (29671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.36 % (29671)Termination reason: Unknown
% 1.64/1.36 % (29671)Termination phase: Property scanning
% 1.64/1.36
% 1.64/1.36 % (29671)Memory used [KB]: 1023
% 1.64/1.36 % (29672)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/7Mi)
% 1.64/1.36 % (29671)Time elapsed: 0.003 s
% 1.64/1.36 % (29671)Instructions burned: 4 (million)
% 1.64/1.36 % (29671)------------------------------
% 1.64/1.36 % (29671)------------------------------
% 1.64/1.36 % (29669)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/16Mi)
% 1.64/1.36 % (29672)Instruction limit reached!
% 1.64/1.36 % (29672)------------------------------
% 1.64/1.36 % (29672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.36 % (29672)Termination reason: Unknown
% 1.64/1.36 % (29672)Termination phase: Function definition elimination
% 1.64/1.36
% 1.64/1.36 % (29672)Memory used [KB]: 1023
% 1.64/1.36 % (29672)Time elapsed: 0.005 s
% 1.64/1.36 % (29672)Instructions burned: 8 (million)
% 1.64/1.36 % (29672)------------------------------
% 1.64/1.36 % (29672)------------------------------
% 1.64/1.36 % (29674)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/4Mi)
% 1.64/1.36 % (29674)Instruction limit reached!
% 1.64/1.36 % (29674)------------------------------
% 1.64/1.36 % (29674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.36 % (29674)Termination reason: Unknown
% 1.64/1.36 % (29674)Termination phase: Property scanning
% 1.64/1.36
% 1.64/1.36 % (29674)Memory used [KB]: 1023
% 1.64/1.36 % (29674)Time elapsed: 0.004 s
% 1.64/1.36 % (29674)Instructions burned: 5 (million)
% 1.64/1.36 % (29674)------------------------------
% 1.64/1.36 % (29674)------------------------------
% 1.64/1.36 % (29673)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/3Mi)
% 1.64/1.36 % (29669)Instruction limit reached!
% 1.64/1.36 % (29669)------------------------------
% 1.64/1.36 % (29669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.36 % (29669)Termination reason: Unknown
% 1.64/1.36 % (29669)Termination phase: Saturation
% 1.64/1.36
% 1.64/1.36 % (29669)Memory used [KB]: 5756
% 1.64/1.36 % (29669)Time elapsed: 0.040 s
% 1.64/1.36 % (29669)Instructions burned: 16 (million)
% 1.64/1.36 % (29669)------------------------------
% 1.64/1.36 % (29669)------------------------------
% 1.64/1.36 % (29673)Instruction limit reached!
% 1.64/1.36 % (29673)------------------------------
% 1.64/1.36 % (29673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.36 % (29673)Termination reason: Unknown
% 1.64/1.36 % (29673)Termination phase: Property scanning
% 1.64/1.36
% 1.64/1.36 % (29673)Memory used [KB]: 1023
% 1.64/1.36 % (29673)Time elapsed: 0.003 s
% 1.64/1.36 % (29673)Instructions burned: 5 (million)
% 1.64/1.36 % (29673)------------------------------
% 1.64/1.36 % (29673)------------------------------
% 1.64/1.37 % (29675)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/18Mi)
% 1.64/1.37 % (29676)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/710Mi)
% 1.64/1.37 % (29675)Instruction limit reached!
% 1.64/1.37 % (29675)------------------------------
% 1.64/1.37 % (29675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (29675)Termination reason: Unknown
% 1.64/1.37 % (29675)Termination phase: Saturation
% 1.64/1.37
% 1.64/1.37 % (29675)Memory used [KB]: 5628
% 1.64/1.37 % (29675)Time elapsed: 0.008 s
% 1.64/1.37 % (29675)Instructions burned: 20 (million)
% 1.64/1.37 % (29675)------------------------------
% 1.64/1.37 % (29675)------------------------------
% 1.64/1.37 % (29677)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/6Mi)
% 1.64/1.38 % (29677)Instruction limit reached!
% 1.64/1.38 % (29677)------------------------------
% 1.64/1.38 % (29677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (29677)Termination reason: Unknown
% 1.64/1.38 % (29677)Termination phase: Function definition elimination
% 1.64/1.38
% 1.64/1.38 % (29677)Memory used [KB]: 1023
% 1.64/1.38 % (29677)Time elapsed: 0.005 s
% 1.64/1.38 % (29677)Instructions burned: 8 (million)
% 1.64/1.38 % (29677)------------------------------
% 1.64/1.38 % (29677)------------------------------
% 1.64/1.38 % (29678)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/902Mi)
% 1.64/1.38 % (29680)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/5Mi)
% 1.64/1.38 % (29679)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/21Mi)
% 1.64/1.38 % (29680)Instruction limit reached!
% 1.64/1.38 % (29680)------------------------------
% 1.64/1.38 % (29680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (29680)Termination reason: Unknown
% 1.64/1.38 % (29680)Termination phase: Property scanning
% 1.64/1.38
% 1.64/1.38 % (29680)Memory used [KB]: 1023
% 1.64/1.38 % (29680)Time elapsed: 0.004 s
% 1.64/1.38 % (29680)Instructions burned: 7 (million)
% 1.64/1.38 % (29680)------------------------------
% 1.64/1.38 % (29680)------------------------------
% 1.64/1.38 % (29678)Refutation not found, incomplete strategy
% 1.64/1.38 % (29678)------------------------------
% 1.64/1.38 % (29678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (29678)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.38
% 1.64/1.38
% 1.64/1.38 % (29678)Memory used [KB]: 5628
% 1.64/1.38 % (29678)Time elapsed: 0.007 s
% 1.64/1.38 % (29678)Instructions burned: 10 (million)
% 1.64/1.38 % (29678)------------------------------
% 1.64/1.38 % (29678)------------------------------
% 1.64/1.39 % (29681)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/6Mi)
% 1.64/1.39 % (29682)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/377Mi)
% 1.64/1.39 % (29681)Instruction limit reached!
% 1.64/1.39 % (29681)------------------------------
% 1.64/1.39 % (29681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.39 % (29681)Termination reason: Unknown
% 1.64/1.39 % (29681)Termination phase: Saturation
% 1.64/1.39
% 1.64/1.39 % (29681)Memory used [KB]: 1023
% 1.64/1.39 % (29681)Time elapsed: 0.005 s
% 1.64/1.39 % (29681)Instructions burned: 7 (million)
% 1.64/1.39 % (29681)------------------------------
% 1.64/1.39 % (29681)------------------------------
% 1.64/1.39 % (29679)Instruction limit reached!
% 1.64/1.39 % (29679)------------------------------
% 1.64/1.39 % (29679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.39 % (29679)Termination reason: Unknown
% 1.64/1.39 % (29679)Termination phase: Saturation
% 1.64/1.39
% 1.64/1.39 % (29679)Memory used [KB]: 5756
% 1.64/1.39 % (29679)Time elapsed: 0.013 s
% 1.64/1.39 % (29679)Instructions burned: 22 (million)
% 1.64/1.39 % (29679)------------------------------
% 1.64/1.39 % (29679)------------------------------
% 1.64/1.40 % (29683)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/779Mi)
% 1.64/1.40 % (29684)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/19Mi)
% 1.64/1.40 % (29684)Refutation not found, incomplete strategy
% 1.64/1.40 % (29684)------------------------------
% 1.64/1.40 % (29684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.40 % (29684)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.40
% 1.64/1.40
% 1.64/1.40 % (29684)Memory used [KB]: 5628
% 1.64/1.40 % (29684)Time elapsed: 0.006 s
% 1.64/1.40 % (29684)Instructions burned: 9 (million)
% 1.64/1.40 % (29684)------------------------------
% 1.64/1.40 % (29684)------------------------------
% 1.64/1.41 % (29686)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_29558 for (2998ds/17Mi)
% 1.64/1.41 % (29685)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_29558 for (2999ds/879Mi)
% 1.64/1.41 % (29686)Instruction limit reached!
% 1.64/1.41 % (29686)------------------------------
% 1.64/1.41 % (29686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.41 % (29686)Termination reason: Unknown
% 1.64/1.41 % (29686)Termination phase: Saturation
% 1.64/1.41
% 1.64/1.41 % (29686)Memory used [KB]: 6012
% 1.64/1.41 % (29686)Time elapsed: 0.011 s
% 1.64/1.41 % (29686)Instructions burned: 18 (million)
% 1.64/1.41 % (29686)------------------------------
% 1.64/1.41 % (29686)------------------------------
% 1.64/1.42 % (29687)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_29558 for (2998ds/3Mi)
% 1.64/1.42 % (29687)Instruction limit reached!
% 1.64/1.42 % (29687)------------------------------
% 1.64/1.42 % (29687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.42 % (29687)Termination reason: Unknown
% 1.64/1.42 % (29687)Termination phase: Property scanning
% 1.64/1.42
% 1.64/1.42 % (29687)Memory used [KB]: 1023
% 1.64/1.42 % (29687)Time elapsed: 0.003 s
% 1.64/1.42 % (29687)Instructions burned: 4 (million)
% 1.64/1.42 % (29687)------------------------------
% 1.64/1.42 % (29687)------------------------------
% 1.64/1.43 % (29688)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_29558 for (2998ds/30Mi)
% 1.64/1.44 % (29689)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_29558 for (2998ds/127Mi)
% 1.64/1.44 % (29688)Refutation not found, incomplete strategy
% 1.64/1.44 % (29688)------------------------------
% 1.64/1.44 % (29688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.44 % (29688)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.44
% 1.64/1.44
% 1.64/1.44 % (29688)Memory used [KB]: 5628
% 1.64/1.44 % (29688)Time elapsed: 0.012 s
% 1.64/1.44 % (29688)Instructions burned: 21 (million)
% 1.64/1.44 % (29688)------------------------------
% 1.64/1.44 % (29688)------------------------------
% 1.64/1.46 % (29690)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_29558 for (2998ds/100Mi)
% 1.64/1.48 % (29689)Instruction limit reached!
% 1.64/1.48 % (29689)------------------------------
% 1.64/1.48 % (29689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.48 % (29689)Termination reason: Unknown
% 1.64/1.48 % (29689)Termination phase: Saturation
% 1.64/1.48
% 1.64/1.48 % (29689)Memory used [KB]: 6396
% 1.64/1.48 % (29689)Time elapsed: 0.039 s
% 1.64/1.48 % (29689)Instructions burned: 128 (million)
% 1.64/1.48 % (29689)------------------------------
% 1.64/1.48 % (29689)------------------------------
% 1.64/1.49 % (29691)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_29558 for (2998ds/3Mi)
% 1.64/1.49 % (29691)Instruction limit reached!
% 1.64/1.49 % (29691)------------------------------
% 1.64/1.49 % (29691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.49 % (29691)Termination reason: Unknown
% 1.64/1.49 % (29691)Termination phase: Property scanning
% 1.64/1.49
% 1.64/1.49 % (29691)Memory used [KB]: 1023
% 1.64/1.49 % (29691)Time elapsed: 0.003 s
% 1.64/1.49 % (29691)Instructions burned: 5 (million)
% 1.64/1.49 % (29691)------------------------------
% 1.64/1.49 % (29691)------------------------------
% 1.64/1.50 % (29692)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_29558 for (2997ds/20Mi)
% 1.64/1.50 % (29692)Refutation not found, incomplete strategy
% 1.64/1.50 % (29692)------------------------------
% 1.64/1.50 % (29692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.50 % (29692)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.50
% 1.64/1.50
% 1.64/1.50 % (29692)Memory used [KB]: 5500
% 1.64/1.50 % (29692)Time elapsed: 0.004 s
% 1.64/1.50 % (29692)Instructions burned: 7 (million)
% 1.64/1.50 % (29692)------------------------------
% 1.64/1.50 % (29692)------------------------------
% 1.64/1.51 % (29690)Instruction limit reached!
% 1.64/1.51 % (29690)------------------------------
% 1.64/1.51 % (29690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.51 % (29690)Termination reason: Unknown
% 1.64/1.51 % (29690)Termination phase: Saturation
% 1.64/1.51
% 1.64/1.51 % (29690)Memory used [KB]: 5884
% 1.64/1.51 % (29690)Time elapsed: 0.052 s
% 1.64/1.51 % (29690)Instructions burned: 101 (million)
% 1.64/1.51 % (29690)------------------------------
% 1.64/1.51 % (29690)------------------------------
% 1.64/1.51 % (29693)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_29558 for (2997ds/86Mi)
% 1.64/1.53 % (29682)Refutation not found, non-redundant clauses discarded% (29682)------------------------------
% 1.64/1.53 % (29682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.53 % (29682)Termination reason: Refutation not found, non-redundant clauses discarded
% 1.64/1.53
% 1.64/1.53 % (29682)Memory used [KB]: 7291
% 1.64/1.53 % (29682)Time elapsed: 0.157 s
% 1.64/1.53 % (29682)Instructions burned: 327 (million)
% 1.64/1.53 % (29682)------------------------------
% 1.64/1.53 % (29682)------------------------------
% 1.64/1.53 % (29694)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_29558 for (2997ds/107Mi)
% 1.64/1.54 % (29693)Instruction limit reached!
% 1.64/1.54 % (29693)------------------------------
% 1.64/1.54 % (29693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.54 % (29693)Termination reason: Unknown
% 1.64/1.54 % (29693)Termination phase: Saturation
% 1.64/1.54
% 1.64/1.54 % (29693)Memory used [KB]: 6012
% 1.64/1.54 % (29693)Time elapsed: 0.025 s
% 1.64/1.54 % (29693)Instructions burned: 86 (million)
% 1.64/1.54 % (29693)------------------------------
% 1.64/1.54 % (29693)------------------------------
% 1.64/1.54 % (29695)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_29558 for (2997ds/39Mi)
% 1.64/1.55 % (29696)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_29558 for (2997ds/448Mi)
% 1.64/1.55 % (29696)Refutation not found, incomplete strategy
% 1.64/1.55 % (29696)------------------------------
% 1.64/1.55 % (29696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.55 % (29696)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.55
% 1.64/1.55
% 1.64/1.55 % (29696)Memory used [KB]: 5628
% 1.64/1.55 % (29696)Time elapsed: 0.004 s
% 1.64/1.55 % (29696)Instructions burned: 9 (million)
% 1.64/1.55 % (29696)------------------------------
% 1.64/1.55 % (29696)------------------------------
% 1.64/1.56 % (29697)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_29558 for (2997ds/46Mi)
% 1.64/1.56 % (29695)Instruction limit reached!
% 1.64/1.56 % (29695)------------------------------
% 1.64/1.56 % (29695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.56 % (29695)Termination reason: Unknown
% 1.64/1.56 % (29695)Termination phase: Saturation
% 1.64/1.56
% 1.64/1.56 % (29695)Memory used [KB]: 6012
% 1.64/1.56 % (29695)Time elapsed: 0.019 s
% 1.64/1.56 % (29695)Instructions burned: 39 (million)
% 1.64/1.56 % (29695)------------------------------
% 1.64/1.56 % (29695)------------------------------
% 1.64/1.57 % (29685)First to succeed.
% 1.64/1.57 % (29694)Instruction limit reached!
% 1.64/1.57 % (29694)------------------------------
% 1.64/1.57 % (29694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.57 % (29694)Termination reason: Unknown
% 1.64/1.57 % (29694)Termination phase: Saturation
% 1.64/1.57
% 1.64/1.57 % (29694)Memory used [KB]: 6140
% 1.64/1.57 % (29694)Time elapsed: 0.050 s
% 1.64/1.57 % (29694)Instructions burned: 107 (million)
% 1.64/1.57 % (29694)------------------------------
% 1.64/1.57 % (29694)------------------------------
% 1.64/1.58 % (29697)Instruction limit reached!
% 1.64/1.58 % (29697)------------------------------
% 1.64/1.58 % (29697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.58 % (29697)Termination reason: Unknown
% 1.64/1.58 % (29697)Termination phase: Saturation
% 1.64/1.58
% 1.64/1.58 % (29697)Memory used [KB]: 5756
% 1.64/1.58 % (29697)Time elapsed: 0.017 s
% 1.64/1.58 % (29697)Instructions burned: 48 (million)
% 1.64/1.58 % (29697)------------------------------
% 1.64/1.58 % (29697)------------------------------
% 1.64/1.58 % (29698)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_29558 for (2997ds/98Mi)
% 1.64/1.59 % (29700)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_29558 for (2997ds/149Mi)
% 1.64/1.59 % (29699)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_29558 for (2997ds/507Mi)
% 1.64/1.59 % (29685)Refutation found. Thanks to Tanya!
% 1.64/1.59 % SZS status Theorem for DTF2THF_29558
% 1.64/1.59 % SZS output start Proof for DTF2THF_29558
% 1.64/1.59 thf(type_def_6, type, d_unsorted: $tType).
% 1.64/1.59 thf(func_def_0, type, unsorted: $tType).
% 1.64/1.59 thf(func_def_1, type, irel: $i > $i > $o).
% 1.64/1.59 thf(func_def_2, type, mnot: ($i > $o) > $i > $o).
% 1.64/1.59 thf(func_def_3, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 1.64/1.59 thf(func_def_4, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 1.64/1.59 thf(func_def_5, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 1.64/1.59 thf(func_def_6, type, mbox_s4: ($i > $o) > $i > $o).
% 1.64/1.59 thf(func_def_7, type, iatom: ($i > $o) > $i > $o).
% 1.64/1.59 thf(func_def_8, type, inot: ($i > $o) > $i > $o).
% 1.64/1.59 thf(func_def_9, type, itrue: $i > $o).
% 1.64/1.59 thf(func_def_10, type, ifalse: $i > $o).
% 1.64/1.59 thf(func_def_11, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 1.64/1.59 thf(func_def_12, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 1.64/1.59 thf(func_def_13, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 1.64/1.59 thf(func_def_14, type, iimplied: ($i > $o) > ($i > $o) > $i > $o).
% 1.64/1.59 thf(func_def_15, type, iequiv: ($i > $o) > ($i > $o) > $i > $o).
% 1.64/1.59 thf(func_def_16, type, ixor: ($i > $o) > ($i > $o) > $i > $o).
% 1.64/1.59 thf(func_def_17, type, ivalid: ($i > $o) > $o).
% 1.64/1.59 thf(func_def_18, type, isatisfiable: ($i > $o) > $o).
% 1.64/1.59 thf(func_def_19, type, icountersatisfiable: ($i > $o) > $o).
% 1.64/1.59 thf(func_def_20, type, iinvalid: ($i > $o) > $o).
% 1.64/1.59 thf(func_def_21, type, d_unsorted: $tType).
% 1.64/1.59 thf(func_def_22, type, d2unsorted: d_unsorted > $i).
% 1.64/1.59 thf(func_def_23, type, d_unsorted_0: d_unsorted).
% 1.64/1.59 thf(func_def_41, type, sK0: $i > d_unsorted).
% 1.64/1.59 thf(func_def_43, type, ph2: !>[X0: $tType]:(X0)).
% 1.64/1.59 thf(func_def_44, type, sK3: $i > $o).
% 1.64/1.59 thf(func_def_45, type, sK4: $i > $o).
% 1.64/1.59 thf(func_def_119, type, sK78: $i > $i).
% 1.64/1.59 thf(func_def_120, type, sK79: $i > $i).
% 1.64/1.59 thf(func_def_121, type, sK80: $i > $i).
% 1.64/1.59 thf(func_def_122, type, sK81: $i > $i).
% 1.64/1.59 thf(func_def_123, type, sK82: $i > $i).
% 1.64/1.59 thf(func_def_124, type, sK83: $i > $i).
% 1.64/1.59 thf(func_def_125, type, sK84: $i > $i).
% 1.64/1.59 thf(func_def_126, type, sK85: $i > $i).
% 1.64/1.59 thf(func_def_127, type, sK86: $i > $i).
% 1.64/1.59 thf(func_def_128, type, sK87: $i > $i).
% 1.64/1.59 thf(func_def_129, type, sK88: $i > $i).
% 1.64/1.59 thf(func_def_130, type, sK89: $i > $i).
% 1.64/1.59 thf(f3621,plain,(
% 1.64/1.59 $false),
% 1.64/1.59 inference(avatar_sat_refutation,[status(thm)],[f2083,f2156,f2219,f2506,f2512,f2518,f2520,f2562,f2568,f2576,f2584,f2664,f2668,f2692,f2712,f2726,f2728,f2760,f2832,f3003,f3071,f3073,f3086,f3094,f3105,f3142,f3147,f3161,f3174,f3201,f3223,f3240,f3243,f3246,f3264,f3271,f3281,f3295,f3299,f3568,f3587,f3604,f3620])).
% 1.64/1.59 thf(f3620,plain,(
% 1.64/1.59 spl1_25 | ~spl1_37),
% 1.64/1.59 inference(avatar_contradiction_clause,[status(thm)],[f3619])).
% 1.64/1.59 thf(f3619,plain,(
% 1.64/1.59 $false | (spl1_25 | ~spl1_37)),
% 1.64/1.59 inference(subsumption_resolution,[status(thm)],[f2163,f3343])).
% 1.64/1.59 thf(f3343,plain,(
% 1.64/1.59 ( ! [X0 : $i] : (((sK4 @ X0) = $false)) ) | ~spl1_37),
% 1.64/1.59 inference(superposition,[status(thm)],[f2218,f3007])).
% 1.64/1.59 thf(f3007,plain,(
% 1.64/1.59 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 1.64/1.59 inference(superposition,[status(thm)],[f41,f41])).
% 1.64/1.59 thf(f41,plain,(
% 1.64/1.59 ( ! [X1 : $i] : (((d2unsorted @ d_unsorted_0) = X1)) )),
% 1.64/1.59 inference(forward_demodulation,[status(thm)],[f32,f35])).
% 1.64/1.59 thf(f35,plain,(
% 1.64/1.60 ( ! [X0 : d_unsorted] : ((d_unsorted_0 = X0)) )),
% 1.64/1.60 inference(cnf_transformation,[status(thm)],[f14])).
% 1.64/1.60 thf(f14,plain,(
% 1.64/1.60 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (Y0 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y3 @ Y4)) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y0 @ Y5)))))) | (Y1 @ Y4))))))))))))) & ! [X1 : $i] : ((d2unsorted @ (sK0 @ X1)) = X1) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ((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]: (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y3)) | (((((~ (irel @ Y5 @ Y7)) | (~ (irel @ Y3 @ Y5))) | (Y1 @ Y7)) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y5 @ Y8))))))) & ((((~ (irel @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y6 @ Y4))) | (Y0 @ Y4))))))))))))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((X3 = X4) | ((d2unsorted @ X3) != (d2unsorted @ X4))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 1.64/1.60 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f13])).
% 1.64/1.60 thf(f13,plain,(
% 1.64/1.60 ! [X1 : $i] : (? [X2 : d_unsorted] : ((d2unsorted @ X2) = X1) => ((d2unsorted @ (sK0 @ X1)) = X1))),
% 1.64/1.60 introduced(definition,[],[choice_axiom])).
% 1.64/1.60 thf(f12,plain,(
% 1.64/1.60 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (Y0 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y3 @ Y4)) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y0 @ Y5)))))) | (Y1 @ Y4))))))))))))) & ! [X1 : $i] : ? [X2 : d_unsorted] : ((d2unsorted @ X2) = X1) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ((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]: (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y3)) | (((((~ (irel @ Y5 @ Y7)) | (~ (irel @ Y3 @ Y5))) | (Y1 @ Y7)) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y5 @ Y8))))))) & ((((~ (irel @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y6 @ Y4))) | (Y0 @ Y4))))))))))))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((X3 = X4) | ((d2unsorted @ X3) != (d2unsorted @ X4))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 1.64/1.60 inference(ennf_transformation,[status(thm)],[f11])).
% 1.64/1.60 thf(f11,plain,(
% 1.64/1.60 ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & ! [X1 : $i] : ? [X2 : d_unsorted] : ((d2unsorted @ X2) = X1) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (Y0 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y3 @ Y4)) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y0 @ Y5)))))) | (Y1 @ Y4))))))))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : (((d2unsorted @ X3) = (d2unsorted @ X4)) => (X3 = X4)) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y3)) | (((((~ (irel @ Y5 @ Y7)) | (~ (irel @ Y3 @ Y5))) | (Y1 @ Y7)) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y5 @ Y8))))))) & ((((~ (irel @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y6 @ Y4))) | (Y0 @ Y4))))))))))))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true)),
% 1.64/1.60 inference(flattening,[status(thm)],[f10])).
% 1.64/1.60 thf(f10,plain,(
% 1.64/1.60 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y3)) | (((((~ (irel @ Y5 @ Y7)) | (~ (irel @ Y3 @ Y5))) | (Y1 @ Y7)) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y5 @ Y8))))))) & ((((~ (irel @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y6 @ Y4))) | (Y0 @ Y4))))))))))))))))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & ~((ifalse @ (d2unsorted @ d_unsorted_0)) = $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (Y0 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y3 @ Y4)) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y0 @ Y5)))))) | (Y1 @ Y4))))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & ! [X1 : $i] : ? [X2 : d_unsorted] : ((d2unsorted @ X2) = X1) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : (((d2unsorted @ X3) = (d2unsorted @ X4)) => (X3 = X4))),
% 1.64/1.60 inference(rectify,[status(thm)],[f8])).
% 1.64/1.60 thf(f8,plain,(
% 1.64/1.60 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y3)) | (((((~ (irel @ Y5 @ Y7)) | (~ (irel @ Y3 @ Y5))) | (Y1 @ Y7)) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y5 @ Y8))))))) & ((((~ (irel @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y6 @ Y4))) | (Y0 @ Y4))))))))))))))))))))) & ! [X20 : d_unsorted] : (d_unsorted_0 = X20) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & ~((ifalse @ (d2unsorted @ d_unsorted_0)) = $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (Y0 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y3 @ Y4)) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y0 @ Y5)))))) | (Y1 @ Y4))))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & ! [X56 : $i] : ? [X57 : d_unsorted] : ((d2unsorted @ X57) = X56) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & ! [X69 : d_unsorted,X70 : d_unsorted] : (((d2unsorted @ X70) = (d2unsorted @ X69)) => (X69 = X70))),
% 1.64/1.60 inference(fool_elimination,[status(thm)],[f7])).
% 1.64/1.60 thf(f7,plain,(
% 1.64/1.60 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | ~(X0 @ X2))) = mimplies) & ((^[X3 : $i > $o] : (! [X4 : $i] : (X3 @ X4))) = ivalid) & ((^[X5 : $i > $o, X6 : $i] : (! [X7 : $i] : ((X5 @ X7) | ~(irel @ X6 @ X7)))) = mbox_s4) & ((^[X8 : $i > $o, X9 : $i] : (~(X8 @ X9))) = mnot) & ((^[X10 : $i > $o, X11 : $i > $o, X12 : $i] : (~! [X13 : $i,X14 : $i,X15 : $i,X16 : $i,X17 : $i] : ((((X10 @ X16) | ~(irel @ X14 @ X16) | ~! [X18 : $i] : ((X11 @ X18) | ~(irel @ X14 @ X18)) | ~(irel @ X17 @ X14)) & (~! [X19 : $i] : (~(irel @ X15 @ X19) | (X10 @ X19)) | (X11 @ X13) | ~(irel @ X17 @ X15) | ~(irel @ X15 @ X13))) | ~(irel @ X12 @ X17)))) = ixor) & ! [X20 : d_unsorted] : (d_unsorted_0 = X20) & (iimplies = (^[X21 : $i > $o, X22 : $i > $o, X23 : $i] : (~! [X24 : $i] : (~(irel @ X23 @ X24) | (X21 @ X24)) | ! [X25 : $i] : ((X22 @ X25) | ~(irel @ X23 @ X25))))) & (iatom = (^[X26 : $i > $o, X27 : $i] : (X26 @ X27))) & ((^[X28 : $i > $o] : (! [X29 : $i] : ~(X28 @ X29))) = iinvalid) & (mor = (^[X30 : $i > $o, X31 : $i > $o, X32 : $i] : ((X30 @ X32) | (X31 @ X32)))) & (itrue @ (d2unsorted @ d_unsorted_0)) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & ((^[X33 : $i > $o] : (~! [X34 : $i] : ~(X33 @ X34))) = isatisfiable) & (ior = (^[X35 : $i > $o, X36 : $i > $o, X37 : $i] : (! [X38 : $i] : (~(irel @ X37 @ X38) | (X36 @ X38)) | ! [X39 : $i] : ((X35 @ X39) | ~(irel @ X37 @ X39))))) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ((^[X40 : $i > $o] : (~! [X41 : $i] : (X40 @ X41))) = icountersatisfiable) & (iequiv = (^[X42 : $i > $o, X43 : $i > $o, X44 : $i] : (! [X45 : $i,X46 : $i] : ((X43 @ X45) | ~! [X47 : $i] : ((X42 @ X47) | ~(irel @ X46 @ X47)) | ~(irel @ X44 @ X46) | ~(irel @ X46 @ X45)) & ! [X48 : $i,X49 : $i] : ((X42 @ X49) | ~! [X50 : $i] : ((X43 @ X50) | ~(irel @ X48 @ X50)) | ~(irel @ X44 @ X48) | ~(irel @ X48 @ X49))))) & ((^[X51 : $i > $o, X52 : $i > $o, X53 : $i] : (! [X54 : $i] : ((X51 @ X54) | ~(irel @ X53 @ X54)) & ! [X55 : $i] : (~(irel @ X53 @ X55) | (X52 @ X55)))) = iand) & ! [X56 : $i] : ? [X57 : d_unsorted] : ((d2unsorted @ X57) = X56) & (inot = (^[X58 : $i > $o, X59 : $i] : (~! [X60 : $i] : (~(irel @ X59 @ X60) | (X58 @ X60))))) & ((^[X61 : $i > $o, X62 : $i > $o, X63 : $i] : ((X62 @ X63) & (X61 @ X63))) = mand) & ((^[X64 : $i > $o, X65 : $i > $o, X66 : $i] : (~! [X67 : $i] : (~(irel @ X66 @ X67) | (X65 @ X67)) | ! [X68 : $i] : ((X64 @ X68) | ~(irel @ X66 @ X68)))) = iimplied) & ! [X69 : d_unsorted,X70 : d_unsorted] : (((d2unsorted @ X70) = (d2unsorted @ X69)) => (X69 = X70))),
% 1.64/1.60 inference(rectify,[status(thm)],[f1])).
% 1.64/1.60 thf(f1,axiom,(
% 1.64/1.60 ((^[X0 : $i > $o, X6 : $i > $o, X7 : $i] : ((X6 @ X7) | ~(X0 @ X7))) = mimplies) & ((^[X18 : $i > $o] : (! [X19 : $i] : (X18 @ X19))) = ivalid) & ((^[X8 : $i > $o, X4 : $i] : (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X4 @ X5)))) = mbox_s4) & ((^[X4 : $i > $o, X0 : $i] : (~(X4 @ X0))) = mnot) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (~! [X15 : $i,X16 : $i,X14 : $i,X17 : $i,X5 : $i] : ((((X8 @ X17) | ~(irel @ X16 @ X17) | ~! [X13 : $i] : ((X9 @ X13) | ~(irel @ X16 @ X13)) | ~(irel @ X5 @ X16)) & (~! [X11 : $i] : (~(irel @ X14 @ X11) | (X8 @ X11)) | (X9 @ X15) | ~(irel @ X5 @ X14) | ~(irel @ X14 @ X15))) | ~(irel @ X7 @ X5)))) = ixor) & ! [X1 : d_unsorted] : (d_unsorted_0 = X1) & (iimplies = (^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (~! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)) | ! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5))))) & (iatom = (^[X8 : $i > $o, X7 : $i] : (X8 @ X7))) & ((^[X18 : $i > $o] : (! [X19 : $i] : ~(X18 @ X19))) = iinvalid) & (mor = (^[X4 : $i > $o, X5 : $i > $o, X0 : $i] : ((X4 @ X0) | (X5 @ X0)))) & (itrue @ (d2unsorted @ d_unsorted_0)) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & ((^[X18 : $i > $o] : (~! [X19 : $i] : ~(X18 @ X19))) = isatisfiable) & (ior = (^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)) | ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5))))) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ((^[X18 : $i > $o] : (~! [X19 : $i] : (X18 @ X19))) = icountersatisfiable) & (iequiv = (^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (! [X10 : $i,X5 : $i] : ((X9 @ X10) | ~! [X11 : $i] : ((X8 @ X11) | ~(irel @ X5 @ X11)) | ~(irel @ X7 @ X5) | ~(irel @ X5 @ X10)) & ! [X5 : $i,X12 : $i] : ((X8 @ X12) | ~! [X13 : $i] : ((X9 @ X13) | ~(irel @ X5 @ X13)) | ~(irel @ X7 @ X5) | ~(irel @ X5 @ X12))))) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)) & ! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)))) = iand) & ! [X0 : $i] : ? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0) & (inot = (^[X8 : $i > $o, X7 : $i] : (~! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5))))) & ((^[X4 : $i > $o, X5 : $i > $o, X0 : $i] : ((X5 @ X0) & (X4 @ X0))) = mand) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (~! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)) | ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)))) = iimplied) & ! [X2 : d_unsorted,X3 : d_unsorted] : (((d2unsorted @ X2) = (d2unsorted @ X3)) => (X2 = X3))),
% 1.64/1.60 file('/export/starexec/sandbox2/tmp/tmp.MacNcZ7HSP/DTF2THF_29558.p',lcl696_1)).
% 1.64/1.60 thf(f32,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((d2unsorted @ (sK0 @ X1)) = X1)) )),
% 1.64/1.60 inference(cnf_transformation,[status(thm)],[f14])).
% 1.64/1.60 thf(f2218,plain,(
% 1.64/1.60 ((sK4 @ sK74) = $false) | ~spl1_37),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2216])).
% 1.64/1.60 thf(f2216,definition,(
% 1.64/1.60 spl1_37 <=> ((sK4 @ sK74) = $false)),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_37])],[avatar_definition])).
% 1.64/1.60 thf(f2163,plain,(
% 1.64/1.60 ((sK4 @ sK59) != $false) | spl1_25),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2162])).
% 1.64/1.60 thf(f2162,definition,(
% 1.64/1.60 spl1_25 <=> ((sK4 @ sK59) = $false)),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_25])],[avatar_definition])).
% 1.64/1.60 thf(f3604,plain,(
% 1.64/1.60 ~spl1_1 | ~spl1_25 | spl1_26 | spl1_171),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3603])).
% 1.64/1.60 thf(f3603,plain,(
% 1.64/1.60 $false | (~spl1_1 | ~spl1_25 | spl1_26 | spl1_171)),
% 1.64/1.60 inference(subsumption_resolution,[status(thm)],[f3602,f3001])).
% 1.64/1.60 thf(f3001,plain,(
% 1.64/1.60 ($false != (irel @ sK5 @ sK5)) | spl1_171),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f3000])).
% 1.64/1.60 thf(f3000,definition,(
% 1.64/1.60 spl1_171 <=> ($false = (irel @ sK5 @ sK5))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_171])],[avatar_definition])).
% 1.64/1.60 thf(f3602,plain,(
% 1.64/1.60 ($false = (irel @ sK5 @ sK5)) | (~spl1_1 | ~spl1_25 | spl1_26)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3601])).
% 1.64/1.60 thf(f3601,plain,(
% 1.64/1.60 ($false != $false) | ($false = (irel @ sK5 @ sK5)) | (~spl1_1 | ~spl1_25 | spl1_26)),
% 1.64/1.60 inference(equality_factoring,[status(thm)],[f3573])).
% 1.64/1.60 thf(f3573,plain,(
% 1.64/1.60 ( ! [X3 : $i,X1 : $i] : (((irel @ sK5 @ X1) = $false) | ((irel @ X1 @ X3) = $false)) ) | (~spl1_1 | ~spl1_25 | spl1_26)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3572])).
% 1.64/1.60 thf(f3572,plain,(
% 1.64/1.60 ( ! [X3 : $i,X1 : $i] : (((irel @ X1 @ X3) = $false) | ($true = $false) | ((irel @ sK5 @ X1) = $false)) ) | (~spl1_1 | ~spl1_25 | spl1_26)),
% 1.64/1.60 inference(forward_demodulation,[status(thm)],[f3571,f3187])).
% 1.64/1.60 thf(f3187,plain,(
% 1.64/1.60 ( ! [X0 : $i] : (((sK4 @ X0) = $false)) ) | ~spl1_25),
% 1.64/1.60 inference(superposition,[status(thm)],[f2164,f3007])).
% 1.64/1.60 thf(f2164,plain,(
% 1.64/1.60 ((sK4 @ sK59) = $false) | ~spl1_25),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2162])).
% 1.64/1.60 thf(f3571,plain,(
% 1.64/1.60 ( ! [X3 : $i,X1 : $i] : (((irel @ sK5 @ X1) = $false) | ($true = (sK4 @ X3)) | ((irel @ X1 @ X3) = $false)) ) | (~spl1_1 | spl1_26)),
% 1.64/1.60 inference(subsumption_resolution,[status(thm)],[f2075,f3326])).
% 1.64/1.60 thf(f3326,plain,(
% 1.64/1.60 ( ! [X0 : $i] : (($false != (sK3 @ X0))) ) | spl1_26),
% 1.64/1.60 inference(superposition,[status(thm)],[f2167,f3007])).
% 1.64/1.60 thf(f2167,plain,(
% 1.64/1.60 ((sK3 @ sK8) != $false) | spl1_26),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2166])).
% 1.64/1.60 thf(f2166,definition,(
% 1.64/1.60 spl1_26 <=> ((sK3 @ sK8) = $false)),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_26])],[avatar_definition])).
% 1.64/1.60 thf(f2075,plain,(
% 1.64/1.60 ( ! [X3 : $i,X1 : $i] : (((irel @ sK5 @ X1) = $false) | ($true = (sK4 @ X3)) | ((irel @ X1 @ X3) = $false) | ((sK3 @ (sK87 @ X1)) = $false)) ) | ~spl1_1),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2074])).
% 1.64/1.60 thf(f2074,definition,(
% 1.64/1.60 spl1_1 <=> ! [X1 : $i,X3 : $i] : (((sK3 @ (sK87 @ X1)) = $false) | ((irel @ X1 @ X3) = $false) | ((irel @ sK5 @ X1) = $false) | ($true = (sK4 @ X3)))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.64/1.60 thf(f3587,plain,(
% 1.64/1.60 ~spl1_40 | ~spl1_125 | spl1_174),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3586])).
% 1.64/1.60 thf(f3586,plain,(
% 1.64/1.60 $false | (~spl1_40 | ~spl1_125 | spl1_174)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3576])).
% 1.64/1.60 thf(f3576,plain,(
% 1.64/1.60 ($true = $false) | (~spl1_40 | ~spl1_125 | spl1_174)),
% 1.64/1.60 inference(backward_demodulation,[status(thm)],[f2722,f3574])).
% 1.64/1.60 thf(f3574,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($false = (irel @ sK10 @ X1))) ) | (~spl1_40 | spl1_174)),
% 1.64/1.60 inference(subsumption_resolution,[status(thm)],[f2233,f3331])).
% 1.64/1.60 thf(f3331,plain,(
% 1.64/1.60 ( ! [X0 : $i] : (($true != (sK3 @ X0))) ) | spl1_174),
% 1.64/1.60 inference(superposition,[status(thm)],[f3084,f3007])).
% 1.64/1.60 thf(f3084,plain,(
% 1.64/1.60 ($true != (sK3 @ sK5)) | spl1_174),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f3083])).
% 1.64/1.60 thf(f3083,definition,(
% 1.64/1.60 spl1_174 <=> ($true = (sK3 @ sK5))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_174])],[avatar_definition])).
% 1.64/1.60 thf(f2233,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($false = (irel @ sK10 @ X1)) | ((sK3 @ X1) = $true)) ) | ~spl1_40),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2232])).
% 1.64/1.60 thf(f2232,definition,(
% 1.64/1.60 spl1_40 <=> ! [X1 : $i] : (($false = (irel @ sK10 @ X1)) | ((sK3 @ X1) = $true))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_40])],[avatar_definition])).
% 1.64/1.60 thf(f2722,plain,(
% 1.64/1.60 ($true = (irel @ sK10 @ sK22)) | ~spl1_125),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2720])).
% 1.64/1.60 thf(f2720,definition,(
% 1.64/1.60 spl1_125 <=> ($true = (irel @ sK10 @ sK22))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_125])],[avatar_definition])).
% 1.64/1.60 thf(f3568,plain,(
% 1.64/1.60 spl1_26 | ~spl1_170),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3567])).
% 1.64/1.60 thf(f3567,plain,(
% 1.64/1.60 $false | (spl1_26 | ~spl1_170)),
% 1.64/1.60 inference(subsumption_resolution,[status(thm)],[f2998,f3326])).
% 1.64/1.60 thf(f2998,plain,(
% 1.64/1.60 ((sK3 @ (sK89 @ sK5)) = $false) | ~spl1_170),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2996])).
% 1.64/1.60 thf(f2996,definition,(
% 1.64/1.60 spl1_170 <=> ((sK3 @ (sK89 @ sK5)) = $false)),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_170])],[avatar_definition])).
% 1.64/1.60 thf(f3299,plain,(
% 1.64/1.60 ~spl1_26 | ~spl1_27 | ~spl1_120),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3298])).
% 1.64/1.60 thf(f3298,plain,(
% 1.64/1.60 $false | (~spl1_26 | ~spl1_27 | ~spl1_120)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3297])).
% 1.64/1.60 thf(f3297,plain,(
% 1.64/1.60 ($true = $false) | (~spl1_26 | ~spl1_27 | ~spl1_120)),
% 1.64/1.60 inference(forward_demodulation,[status(thm)],[f2691,f3257])).
% 1.64/1.60 thf(f3257,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($false = (irel @ sK6 @ X1))) ) | (~spl1_26 | ~spl1_27)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3256])).
% 1.64/1.60 thf(f3256,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($false = (irel @ sK6 @ X1)) | ($true = $false)) ) | (~spl1_26 | ~spl1_27)),
% 1.64/1.60 inference(forward_demodulation,[status(thm)],[f2171,f3098])).
% 1.64/1.60 thf(f3098,plain,(
% 1.64/1.60 ( ! [X0 : $i] : (($false = (sK3 @ X0))) ) | ~spl1_26),
% 1.64/1.60 inference(superposition,[status(thm)],[f2168,f3007])).
% 1.64/1.60 thf(f2168,plain,(
% 1.64/1.60 ((sK3 @ sK8) = $false) | ~spl1_26),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2166])).
% 1.64/1.60 thf(f2171,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((sK3 @ X1) = $true) | ($false = (irel @ sK6 @ X1))) ) | ~spl1_27),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2170])).
% 1.64/1.60 thf(f2170,definition,(
% 1.64/1.60 spl1_27 <=> ! [X1 : $i] : (($false = (irel @ sK6 @ X1)) | ((sK3 @ X1) = $true))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_27])],[avatar_definition])).
% 1.64/1.60 thf(f2691,plain,(
% 1.64/1.60 ((irel @ sK6 @ sK36) = $true) | ~spl1_120),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2689])).
% 1.64/1.60 thf(f2689,definition,(
% 1.64/1.60 spl1_120 <=> ((irel @ sK6 @ sK36) = $true)),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_120])],[avatar_definition])).
% 1.64/1.60 thf(f3295,plain,(
% 1.64/1.60 ~spl1_26 | ~spl1_27 | ~spl1_131),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3294])).
% 1.64/1.60 thf(f3294,plain,(
% 1.64/1.60 $false | (~spl1_26 | ~spl1_27 | ~spl1_131)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3293])).
% 1.64/1.60 thf(f3293,plain,(
% 1.64/1.60 ($true = $false) | (~spl1_26 | ~spl1_27 | ~spl1_131)),
% 1.64/1.60 inference(forward_demodulation,[status(thm)],[f2759,f3257])).
% 1.64/1.60 thf(f2759,plain,(
% 1.64/1.60 ((irel @ sK6 @ sK31) = $true) | ~spl1_131),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2757])).
% 1.64/1.60 thf(f2757,definition,(
% 1.64/1.60 spl1_131 <=> ((irel @ sK6 @ sK31) = $true)),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_131])],[avatar_definition])).
% 1.64/1.60 thf(f3281,plain,(
% 1.64/1.60 ~spl1_26 | ~spl1_27 | ~spl1_124),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3280])).
% 1.64/1.60 thf(f3280,plain,(
% 1.64/1.60 $false | (~spl1_26 | ~spl1_27 | ~spl1_124)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3279])).
% 1.64/1.60 thf(f3279,plain,(
% 1.64/1.60 ($true = $false) | (~spl1_26 | ~spl1_27 | ~spl1_124)),
% 1.64/1.60 inference(forward_demodulation,[status(thm)],[f2711,f3257])).
% 1.64/1.60 thf(f2711,plain,(
% 1.64/1.60 ($true = (irel @ sK6 @ sK34)) | ~spl1_124),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2709])).
% 1.64/1.60 thf(f2709,definition,(
% 1.64/1.60 spl1_124 <=> ($true = (irel @ sK6 @ sK34))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_124])],[avatar_definition])).
% 1.64/1.60 thf(f3271,plain,(
% 1.64/1.60 ~spl1_26 | ~spl1_27 | ~spl1_145),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3270])).
% 1.64/1.60 thf(f3270,plain,(
% 1.64/1.60 $false | (~spl1_26 | ~spl1_27 | ~spl1_145)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3269])).
% 1.64/1.60 thf(f3269,plain,(
% 1.64/1.60 ($true = $false) | (~spl1_26 | ~spl1_27 | ~spl1_145)),
% 1.64/1.60 inference(forward_demodulation,[status(thm)],[f2830,f3257])).
% 1.64/1.60 thf(f2830,plain,(
% 1.64/1.60 ($true = (irel @ sK6 @ sK24)) | ~spl1_145),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2828])).
% 1.64/1.60 thf(f2828,definition,(
% 1.64/1.60 spl1_145 <=> ($true = (irel @ sK6 @ sK24))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_145])],[avatar_definition])).
% 1.64/1.60 thf(f3264,plain,(
% 1.64/1.60 ~spl1_26 | ~spl1_27 | ~spl1_98),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3263])).
% 1.64/1.60 thf(f3263,plain,(
% 1.64/1.60 $false | (~spl1_26 | ~spl1_27 | ~spl1_98)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3262])).
% 1.64/1.60 thf(f3262,plain,(
% 1.64/1.60 ($true = $false) | (~spl1_26 | ~spl1_27 | ~spl1_98)),
% 1.64/1.60 inference(forward_demodulation,[status(thm)],[f2560,f3257])).
% 1.64/1.60 thf(f2560,plain,(
% 1.64/1.60 ($true = (irel @ sK6 @ sK44)) | ~spl1_98),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2558])).
% 1.64/1.60 thf(f2558,definition,(
% 1.64/1.60 spl1_98 <=> ($true = (irel @ sK6 @ sK44))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_98])],[avatar_definition])).
% 1.64/1.60 thf(f3246,plain,(
% 1.64/1.60 ~spl1_26 | ~spl1_40 | ~spl1_101),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3245])).
% 1.64/1.60 thf(f3245,plain,(
% 1.64/1.60 $false | (~spl1_26 | ~spl1_40 | ~spl1_101)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3244])).
% 1.64/1.60 thf(f3244,plain,(
% 1.64/1.60 ($true = $false) | (~spl1_26 | ~spl1_40 | ~spl1_101)),
% 1.64/1.60 inference(forward_demodulation,[status(thm)],[f2582,f3209])).
% 1.64/1.60 thf(f3209,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($false = (irel @ sK10 @ X1))) ) | (~spl1_26 | ~spl1_40)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3208])).
% 1.64/1.60 thf(f3208,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = $false) | ($false = (irel @ sK10 @ X1))) ) | (~spl1_26 | ~spl1_40)),
% 1.64/1.60 inference(forward_demodulation,[status(thm)],[f2233,f3098])).
% 1.64/1.60 thf(f2582,plain,(
% 1.64/1.60 ($true = (irel @ sK10 @ sK45)) | ~spl1_101),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2580])).
% 1.64/1.60 thf(f2580,definition,(
% 1.64/1.60 spl1_101 <=> ($true = (irel @ sK10 @ sK45))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_101])],[avatar_definition])).
% 1.64/1.60 thf(f3243,plain,(
% 1.64/1.60 ~spl1_26 | ~spl1_40 | ~spl1_99),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3242])).
% 1.64/1.60 thf(f3242,plain,(
% 1.64/1.60 $false | (~spl1_26 | ~spl1_40 | ~spl1_99)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3241])).
% 1.64/1.60 thf(f3241,plain,(
% 1.64/1.60 ($true = $false) | (~spl1_26 | ~spl1_40 | ~spl1_99)),
% 1.64/1.60 inference(forward_demodulation,[status(thm)],[f2567,f3209])).
% 1.64/1.60 thf(f2567,plain,(
% 1.64/1.60 ($true = (irel @ sK10 @ sK46)) | ~spl1_99),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2565])).
% 1.64/1.60 thf(f2565,definition,(
% 1.64/1.60 spl1_99 <=> ($true = (irel @ sK10 @ sK46))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_99])],[avatar_definition])).
% 1.64/1.60 thf(f3240,plain,(
% 1.64/1.60 ~spl1_26 | ~spl1_40 | ~spl1_91),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3239])).
% 1.64/1.60 thf(f3239,plain,(
% 1.64/1.60 $false | (~spl1_26 | ~spl1_40 | ~spl1_91)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3238])).
% 1.64/1.60 thf(f3238,plain,(
% 1.64/1.60 ($true = $false) | (~spl1_26 | ~spl1_40 | ~spl1_91)),
% 1.64/1.60 inference(forward_demodulation,[status(thm)],[f2511,f3209])).
% 1.64/1.60 thf(f2511,plain,(
% 1.64/1.60 ($true = (irel @ sK10 @ sK49)) | ~spl1_91),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2509])).
% 1.64/1.60 thf(f2509,definition,(
% 1.64/1.60 spl1_91 <=> ($true = (irel @ sK10 @ sK49))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_91])],[avatar_definition])).
% 1.64/1.60 thf(f3223,plain,(
% 1.64/1.60 ~spl1_25 | ~spl1_31 | ~spl1_110),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3222])).
% 1.64/1.60 thf(f3222,plain,(
% 1.64/1.60 $false | (~spl1_25 | ~spl1_31 | ~spl1_110)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3221])).
% 1.64/1.60 thf(f3221,plain,(
% 1.64/1.60 ($true = $false) | (~spl1_25 | ~spl1_31 | ~spl1_110)),
% 1.64/1.60 inference(forward_demodulation,[status(thm)],[f2629,f3196])).
% 1.64/1.60 thf(f3196,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((irel @ sK7 @ X1) = $false)) ) | (~spl1_25 | ~spl1_31)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3192])).
% 1.64/1.60 thf(f3192,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((irel @ sK7 @ X1) = $false) | ($true = $false)) ) | (~spl1_25 | ~spl1_31)),
% 1.64/1.60 inference(backward_demodulation,[status(thm)],[f2189,f3187])).
% 1.64/1.60 thf(f2189,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (sK4 @ X1)) | ((irel @ sK7 @ X1) = $false)) ) | ~spl1_31),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2188])).
% 1.64/1.60 thf(f2188,definition,(
% 1.64/1.60 spl1_31 <=> ! [X1 : $i] : (((irel @ sK7 @ X1) = $false) | ($true = (sK4 @ X1)))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_31])],[avatar_definition])).
% 1.64/1.60 thf(f2629,plain,(
% 1.64/1.60 ($true = (irel @ sK7 @ sK23)) | ~spl1_110),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2627])).
% 1.64/1.60 thf(f2627,definition,(
% 1.64/1.60 spl1_110 <=> ($true = (irel @ sK7 @ sK23))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_110])],[avatar_definition])).
% 1.64/1.60 thf(f3201,plain,(
% 1.64/1.60 ~spl1_25 | ~spl1_70 | ~spl1_78),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3200])).
% 1.64/1.60 thf(f3200,plain,(
% 1.64/1.60 $false | (~spl1_25 | ~spl1_70 | ~spl1_78)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3199])).
% 1.64/1.60 thf(f3199,plain,(
% 1.64/1.60 ($true = $false) | (~spl1_25 | ~spl1_70 | ~spl1_78)),
% 1.64/1.60 inference(backward_demodulation,[status(thm)],[f2433,f3198])).
% 1.64/1.60 thf(f3198,plain,(
% 1.64/1.60 ( ! [X2 : $i] : (((irel @ sK9 @ X2) = $false)) ) | (~spl1_25 | ~spl1_70)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3190])).
% 1.64/1.60 thf(f3190,plain,(
% 1.64/1.60 ( ! [X2 : $i] : (((irel @ sK9 @ X2) = $false) | ($true = $false)) ) | (~spl1_25 | ~spl1_70)),
% 1.64/1.60 inference(backward_demodulation,[status(thm)],[f2388,f3187])).
% 1.64/1.60 thf(f2388,plain,(
% 1.64/1.60 ( ! [X2 : $i] : (($true = (sK4 @ X2)) | ((irel @ sK9 @ X2) = $false)) ) | ~spl1_70),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2387])).
% 1.64/1.60 thf(f2387,definition,(
% 1.64/1.60 spl1_70 <=> ! [X2 : $i] : (((irel @ sK9 @ X2) = $false) | ($true = (sK4 @ X2)))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_70])],[avatar_definition])).
% 1.64/1.60 thf(f2433,plain,(
% 1.64/1.60 ($true = (irel @ sK9 @ sK8)) | ~spl1_78),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2431])).
% 1.64/1.60 thf(f2431,definition,(
% 1.64/1.60 spl1_78 <=> ($true = (irel @ sK9 @ sK8))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_78])],[avatar_definition])).
% 1.64/1.60 thf(f3174,plain,(
% 1.64/1.60 ~spl1_23 | spl1_25 | ~spl1_26 | spl1_171),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3173])).
% 1.64/1.60 thf(f3173,plain,(
% 1.64/1.60 $false | (~spl1_23 | spl1_25 | ~spl1_26 | spl1_171)),
% 1.64/1.60 inference(subsumption_resolution,[status(thm)],[f3172,f3001])).
% 1.64/1.60 thf(f3172,plain,(
% 1.64/1.60 ($false = (irel @ sK5 @ sK5)) | (~spl1_23 | spl1_25 | ~spl1_26)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3171])).
% 1.64/1.60 thf(f3171,plain,(
% 1.64/1.60 ($false != $false) | ($false = (irel @ sK5 @ sK5)) | (~spl1_23 | spl1_25 | ~spl1_26)),
% 1.64/1.60 inference(equality_factoring,[status(thm)],[f3165])).
% 1.64/1.60 thf(f3165,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (((irel @ sK5 @ X2) = $false) | ((irel @ X2 @ X1) = $false)) ) | (~spl1_23 | spl1_25 | ~spl1_26)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3164])).
% 1.64/1.60 thf(f3164,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X2 @ X1) = $false) | ((irel @ sK5 @ X2) = $false) | ($true = $false)) ) | (~spl1_23 | spl1_25 | ~spl1_26)),
% 1.64/1.60 inference(forward_demodulation,[status(thm)],[f3163,f3098])).
% 1.64/1.60 thf(f3163,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (((irel @ sK5 @ X2) = $false) | ((sK3 @ X1) = $true) | ((irel @ X2 @ X1) = $false)) ) | (~spl1_23 | spl1_25)),
% 1.64/1.60 inference(subsumption_resolution,[status(thm)],[f2155,f3096])).
% 1.64/1.60 thf(f3096,plain,(
% 1.64/1.60 ( ! [X0 : $i] : (((sK4 @ X0) != $false)) ) | spl1_25),
% 1.64/1.60 inference(superposition,[status(thm)],[f2163,f3007])).
% 1.64/1.60 thf(f2155,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (((irel @ sK5 @ X2) = $false) | ((sK4 @ (sK79 @ X2)) = $false) | ((sK3 @ X1) = $true) | ((irel @ X2 @ X1) = $false)) ) | ~spl1_23),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2154])).
% 1.64/1.60 thf(f2154,definition,(
% 1.64/1.60 spl1_23 <=> ! [X2 : $i,X1 : $i] : (((sK4 @ (sK79 @ X2)) = $false) | ((sK3 @ X1) = $true) | ((irel @ sK5 @ X2) = $false) | ((irel @ X2 @ X1) = $false))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_23])],[avatar_definition])).
% 1.64/1.60 thf(f3161,plain,(
% 1.64/1.60 ~spl1_22 | spl1_25 | ~spl1_26 | spl1_171),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3160])).
% 1.64/1.60 thf(f3160,plain,(
% 1.64/1.60 $false | (~spl1_22 | spl1_25 | ~spl1_26 | spl1_171)),
% 1.64/1.60 inference(subsumption_resolution,[status(thm)],[f3159,f3001])).
% 1.64/1.60 thf(f3159,plain,(
% 1.64/1.60 ($false = (irel @ sK5 @ sK5)) | (~spl1_22 | spl1_25 | ~spl1_26)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3158])).
% 1.64/1.60 thf(f3158,plain,(
% 1.64/1.60 ($false != $false) | ($false = (irel @ sK5 @ sK5)) | (~spl1_22 | spl1_25 | ~spl1_26)),
% 1.64/1.60 inference(equality_factoring,[status(thm)],[f3152])).
% 1.64/1.60 thf(f3152,plain,(
% 1.64/1.60 ( ! [X3 : $i,X4 : $i] : (($false = (irel @ sK5 @ X3)) | ($false = (irel @ X3 @ X4))) ) | (~spl1_22 | spl1_25 | ~spl1_26)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3151])).
% 1.64/1.60 thf(f3151,plain,(
% 1.64/1.60 ( ! [X3 : $i,X4 : $i] : (($false = (irel @ sK5 @ X3)) | ($false = (irel @ X3 @ X4)) | ($true = $false)) ) | (~spl1_22 | spl1_25 | ~spl1_26)),
% 1.64/1.60 inference(forward_demodulation,[status(thm)],[f3150,f3098])).
% 1.64/1.60 thf(f3150,plain,(
% 1.64/1.60 ( ! [X3 : $i,X4 : $i] : (($false = (irel @ X3 @ X4)) | ($false = (irel @ sK5 @ X3)) | ((sK3 @ X4) = $true)) ) | (~spl1_22 | spl1_25)),
% 1.64/1.60 inference(subsumption_resolution,[status(thm)],[f2152,f3096])).
% 1.64/1.60 thf(f2152,plain,(
% 1.64/1.60 ( ! [X3 : $i,X4 : $i] : (((sK4 @ (sK78 @ X3)) = $false) | ($false = (irel @ sK5 @ X3)) | ((sK3 @ X4) = $true) | ($false = (irel @ X3 @ X4))) ) | ~spl1_22),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2151])).
% 1.64/1.60 thf(f2151,definition,(
% 1.64/1.60 spl1_22 <=> ! [X4 : $i,X3 : $i] : (((sK4 @ (sK78 @ X3)) = $false) | ($false = (irel @ sK5 @ X3)) | ((sK3 @ X4) = $true) | ($false = (irel @ X3 @ X4)))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_22])],[avatar_definition])).
% 1.64/1.60 thf(f3147,plain,(
% 1.64/1.60 ~spl1_171),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3146])).
% 1.64/1.60 thf(f3146,plain,(
% 1.64/1.60 $false | ~spl1_171),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3145])).
% 1.64/1.60 thf(f3145,plain,(
% 1.64/1.60 ($true = $false) | ~spl1_171),
% 1.64/1.60 inference(backward_demodulation,[status(thm)],[f37,f3143])).
% 1.64/1.60 thf(f3143,plain,(
% 1.64/1.60 ( ! [X0 : $i] : (($false = (irel @ X0 @ X0))) ) | ~spl1_171),
% 1.64/1.60 inference(superposition,[status(thm)],[f3002,f3007])).
% 1.64/1.60 thf(f3002,plain,(
% 1.64/1.60 ($false = (irel @ sK5 @ sK5)) | ~spl1_171),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f3000])).
% 1.64/1.60 thf(f37,plain,(
% 1.64/1.60 ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true)),
% 1.64/1.60 inference(cnf_transformation,[status(thm)],[f14])).
% 1.64/1.60 thf(f3142,plain,(
% 1.64/1.60 ~spl1_26 | spl1_36),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3141])).
% 1.64/1.60 thf(f3141,plain,(
% 1.64/1.60 $false | (~spl1_26 | spl1_36)),
% 1.64/1.60 inference(subsumption_resolution,[status(thm)],[f3137,f3098])).
% 1.64/1.60 thf(f3137,plain,(
% 1.64/1.60 ( ! [X0 : $i] : (($false != (sK3 @ X0))) ) | spl1_36),
% 1.64/1.60 inference(superposition,[status(thm)],[f2213,f3007])).
% 1.64/1.60 thf(f2213,plain,(
% 1.64/1.60 ((sK3 @ sK73) != $false) | spl1_36),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2212])).
% 1.64/1.60 thf(f2212,definition,(
% 1.64/1.60 spl1_36 <=> ((sK3 @ sK73) = $false)),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_36])],[avatar_definition])).
% 1.64/1.60 thf(f3105,plain,(
% 1.64/1.60 ~spl1_26 | ~spl1_174),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3104])).
% 1.64/1.60 thf(f3104,plain,(
% 1.64/1.60 $false | (~spl1_26 | ~spl1_174)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3102])).
% 1.64/1.60 thf(f3102,plain,(
% 1.64/1.60 ($true = $false) | (~spl1_26 | ~spl1_174)),
% 1.64/1.60 inference(backward_demodulation,[status(thm)],[f3085,f3098])).
% 1.64/1.60 thf(f3085,plain,(
% 1.64/1.60 ($true = (sK3 @ sK5)) | ~spl1_174),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f3083])).
% 1.64/1.60 thf(f3094,plain,(
% 1.64/1.60 ~spl1_25 | ~spl1_169),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3093])).
% 1.64/1.60 thf(f3093,plain,(
% 1.64/1.60 $false | (~spl1_25 | ~spl1_169)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3089])).
% 1.64/1.60 thf(f3089,plain,(
% 1.64/1.60 ($true = $false) | (~spl1_25 | ~spl1_169)),
% 1.64/1.60 inference(backward_demodulation,[status(thm)],[f3037,f3088])).
% 1.64/1.60 thf(f3088,plain,(
% 1.64/1.60 ( ! [X0 : $i] : (((sK4 @ X0) = $false)) ) | ~spl1_25),
% 1.64/1.60 inference(superposition,[status(thm)],[f2164,f3007])).
% 1.64/1.60 thf(f3037,plain,(
% 1.64/1.60 ( ! [X0 : $i] : (($true = (sK4 @ X0))) ) | ~spl1_169),
% 1.64/1.60 inference(superposition,[status(thm)],[f2994,f3007])).
% 1.64/1.60 thf(f2994,plain,(
% 1.64/1.60 ($true = (sK4 @ sK5)) | ~spl1_169),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2992])).
% 1.64/1.60 thf(f2992,definition,(
% 1.64/1.60 spl1_169 <=> ($true = (sK4 @ sK5))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_169])],[avatar_definition])).
% 1.64/1.60 thf(f3086,plain,(
% 1.64/1.60 spl1_171 | spl1_174 | ~spl1_22 | ~spl1_169),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f3081,f2992,f2151,f3083,f3000])).
% 1.64/1.60 thf(f3081,plain,(
% 1.64/1.60 ($true = (sK3 @ sK5)) | ($false = (irel @ sK5 @ sK5)) | (~spl1_22 | ~spl1_169)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3078])).
% 1.64/1.60 thf(f3078,plain,(
% 1.64/1.60 ($false != $false) | ($false = (irel @ sK5 @ sK5)) | ($true = (sK3 @ sK5)) | (~spl1_22 | ~spl1_169)),
% 1.64/1.60 inference(equality_factoring,[status(thm)],[f3057])).
% 1.64/1.60 thf(f3057,plain,(
% 1.64/1.60 ( ! [X3 : $i,X4 : $i] : (($false = (irel @ sK5 @ X3)) | ($false = (irel @ X3 @ X4)) | ((sK3 @ X4) = $true)) ) | (~spl1_22 | ~spl1_169)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3056])).
% 1.64/1.60 thf(f3056,plain,(
% 1.64/1.60 ( ! [X3 : $i,X4 : $i] : (($true = $false) | ($false = (irel @ sK5 @ X3)) | ((sK3 @ X4) = $true) | ($false = (irel @ X3 @ X4))) ) | (~spl1_22 | ~spl1_169)),
% 1.64/1.60 inference(forward_demodulation,[status(thm)],[f2152,f3037])).
% 1.64/1.60 thf(f3073,plain,(
% 1.64/1.60 spl1_26 | ~spl1_36),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3072])).
% 1.64/1.60 thf(f3072,plain,(
% 1.64/1.60 $false | (spl1_26 | ~spl1_36)),
% 1.64/1.60 inference(subsumption_resolution,[status(thm)],[f2214,f3058])).
% 1.64/1.60 thf(f3058,plain,(
% 1.64/1.60 ( ! [X0 : $i] : (($false != (sK3 @ X0))) ) | spl1_26),
% 1.64/1.60 inference(superposition,[status(thm)],[f2167,f3007])).
% 1.64/1.60 thf(f2214,plain,(
% 1.64/1.60 ((sK3 @ sK73) = $false) | ~spl1_36),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2212])).
% 1.64/1.60 thf(f3071,plain,(
% 1.64/1.60 ~spl1_37 | ~spl1_169),
% 1.64/1.60 inference(avatar_contradiction_clause,[status(thm)],[f3070])).
% 1.64/1.60 thf(f3070,plain,(
% 1.64/1.60 $false | (~spl1_37 | ~spl1_169)),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f3066])).
% 1.64/1.60 thf(f3066,plain,(
% 1.64/1.60 ($true = $false) | (~spl1_37 | ~spl1_169)),
% 1.64/1.60 inference(backward_demodulation,[status(thm)],[f3037,f3065])).
% 1.64/1.60 thf(f3065,plain,(
% 1.64/1.60 ( ! [X0 : $i] : (((sK4 @ X0) = $false)) ) | ~spl1_37),
% 1.64/1.60 inference(superposition,[status(thm)],[f2218,f3007])).
% 1.64/1.60 thf(f3003,plain,(
% 1.64/1.60 spl1_169 | spl1_170 | spl1_171 | ~spl1_3),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f2990,f2081,f3000,f2996,f2992])).
% 1.64/1.60 thf(f2081,definition,(
% 1.64/1.60 spl1_3 <=> ! [X2 : $i,X4 : $i] : (((irel @ sK5 @ X2) = $false) | ($true = (sK4 @ X4)) | ((irel @ X2 @ X4) = $false) | ((sK3 @ (sK89 @ X2)) = $false))),
% 1.64/1.60 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.64/1.60 thf(f2990,plain,(
% 1.64/1.60 ($true = (sK4 @ sK5)) | ($false = (irel @ sK5 @ sK5)) | ((sK3 @ (sK89 @ sK5)) = $false) | ~spl1_3),
% 1.64/1.60 inference(trivial_inequality_removal,[status(thm)],[f2989])).
% 1.64/1.60 thf(f2989,plain,(
% 1.64/1.60 ($true = (sK4 @ sK5)) | ((sK3 @ (sK89 @ sK5)) = $false) | ($false != $false) | ($false = (irel @ sK5 @ sK5)) | ~spl1_3),
% 1.64/1.60 inference(equality_factoring,[status(thm)],[f2082])).
% 1.64/1.60 thf(f2082,plain,(
% 1.64/1.60 ( ! [X2 : $i,X4 : $i] : (((irel @ sK5 @ X2) = $false) | ((irel @ X2 @ X4) = $false) | ($true = (sK4 @ X4)) | ((sK3 @ (sK89 @ X2)) = $false)) ) | ~spl1_3),
% 1.64/1.60 inference(avatar_component_clause,[status(thm)],[f2081])).
% 1.64/1.60 thf(f2832,plain,(
% 1.64/1.60 spl1_125 | spl1_145 | spl1_110 | spl1_78),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f480,f2431,f2627,f2828,f2720])).
% 1.64/1.60 thf(f480,plain,(
% 1.64/1.60 ($true = (irel @ sK7 @ sK23)) | ($true = (irel @ sK6 @ sK24)) | ($true = (irel @ sK9 @ sK8)) | ($true = (irel @ sK10 @ sK22))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f479])).
% 1.64/1.60 thf(f479,plain,(
% 1.64/1.60 ((~ (irel @ sK10 @ sK22)) = $false) | ($true = (irel @ sK6 @ sK24)) | ($true = (irel @ sK9 @ sK8)) | ($true = (irel @ sK7 @ sK23))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f477])).
% 1.64/1.60 thf(f477,plain,(
% 1.64/1.60 ($true = (irel @ sK7 @ sK23)) | ($true = (irel @ sK6 @ sK24)) | ($true = (irel @ sK9 @ sK8)) | ($false = ((~ (irel @ sK10 @ sK22)) | (~ (irel @ sK5 @ sK10))))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f476])).
% 1.64/1.60 thf(f476,plain,(
% 1.64/1.60 ($false = (~ (irel @ sK6 @ sK24))) | ($true = (irel @ sK9 @ sK8)) | ($false = ((~ (irel @ sK10 @ sK22)) | (~ (irel @ sK5 @ sK10)))) | ($true = (irel @ sK7 @ sK23))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f475])).
% 1.64/1.60 thf(f475,plain,(
% 1.64/1.60 ($true = (irel @ sK9 @ sK8)) | ($false = (~ (irel @ sK7 @ sK23))) | ($false = ((~ (irel @ sK10 @ sK22)) | (~ (irel @ sK5 @ sK10)))) | ($false = (~ (irel @ sK6 @ sK24)))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f473])).
% 1.64/1.60 thf(f473,plain,(
% 1.64/1.60 (((~ (irel @ sK6 @ sK24)) | (sK4 @ sK24)) = $false) | ($false = (~ (irel @ sK7 @ sK23))) | ($false = ((~ (irel @ sK10 @ sK22)) | (~ (irel @ sK5 @ sK10)))) | ($true = (irel @ sK9 @ sK8))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f472])).
% 1.64/1.60 thf(f472,plain,(
% 1.64/1.60 ($false = (~ (irel @ sK9 @ sK8))) | (((~ (irel @ sK6 @ sK24)) | (sK4 @ sK24)) = $false) | ($false = (~ (irel @ sK7 @ sK23))) | ($false = ((~ (irel @ sK10 @ sK22)) | (~ (irel @ sK5 @ sK10))))),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f471])).
% 1.64/1.60 thf(f471,plain,(
% 1.64/1.60 ($false = (~ (irel @ sK9 @ sK8))) | ($false = (~ (irel @ sK7 @ sK23))) | ($false = ((~ (irel @ sK10 @ sK22)) | (~ (irel @ sK5 @ sK10)))) | (((^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0))) @ sK24) = $false)),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f470])).
% 1.64/1.60 thf(f470,plain,(
% 1.64/1.60 ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ($false = (~ (irel @ sK7 @ sK23))) | ($false = (~ (irel @ sK9 @ sK8))) | ($false = ((~ (irel @ sK10 @ sK22)) | (~ (irel @ sK5 @ sK10))))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f468])).
% 1.64/1.60 thf(f468,plain,(
% 1.64/1.60 ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | ($false = (~ (irel @ sK9 @ sK8))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ($false = ((~ (irel @ sK10 @ sK22)) | (~ (irel @ sK5 @ sK10))))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f466])).
% 1.64/1.60 thf(f466,plain,(
% 1.64/1.60 (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ($false = ((~ (irel @ sK10 @ sK22)) | (~ (irel @ sK5 @ sK10))))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f464])).
% 1.64/1.60 thf(f464,plain,(
% 1.64/1.60 ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | ($false = ((~ (irel @ sK10 @ sK22)) | (~ (irel @ sK5 @ sK10)))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f462])).
% 1.64/1.60 thf(f462,plain,(
% 1.64/1.60 (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ($false = ((~ (irel @ sK10 @ sK22)) | (~ (irel @ sK5 @ sK10))))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f460])).
% 1.64/1.60 thf(f460,plain,(
% 1.64/1.60 ($false = (((~ (irel @ sK10 @ sK22)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))))) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f458])).
% 1.64/1.60 thf(f458,plain,(
% 1.64/1.60 ($false = ((((~ (irel @ sK10 @ sK22)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) | (sK4 @ sK22))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23)))),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f457])).
% 1.64/1.60 thf(f457,plain,(
% 1.64/1.60 ($false = ((((~ (irel @ sK10 @ sK22)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) | (sK4 @ sK22))) | (((^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0))) @ sK23) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false)),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f456])).
% 1.64/1.60 thf(f456,plain,(
% 1.64/1.60 ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false) | ($false = ((((~ (irel @ sK10 @ sK22)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) | (sK4 @ sK22))) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false)),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f455])).
% 1.64/1.60 thf(f455,plain,(
% 1.64/1.60 (((^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0))) @ sK22) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false)),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f454])).
% 1.64/1.60 thf(f454,plain,(
% 1.64/1.60 ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) = $false) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f452])).
% 1.64/1.60 thf(f452,plain,(
% 1.64/1.60 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))))))) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f450])).
% 1.64/1.60 thf(f450,plain,(
% 1.64/1.60 ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0))))))) | (~ (irel @ sK5 @ sK7))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.64/1.60 thf(f65,plain,(
% 1.64/1.60 (((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | (sK3 @ sK8)) = $false) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0))))))) | (~ (irel @ sK5 @ sK7))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.64/1.60 thf(f64,plain,(
% 1.64/1.60 (((~ (irel @ sK5 @ sK6)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))))) = $false) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0))))))) | (~ (irel @ sK5 @ sK7))) = $false) | (((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | (sK3 @ sK8)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false)),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.64/1.60 thf(f63,plain,(
% 1.64/1.60 (((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | (sK3 @ sK8)) = $false) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0))))))) | (~ (irel @ sK5 @ sK7))) = $false) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y0 @ Y1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2)))))) | (sK4 @ Y1))))) @ sK10) = $false) | (((~ (irel @ sK5 @ sK6)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))))) = $false)),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f62])).
% 1.64/1.60 thf(f62,plain,(
% 1.64/1.60 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y0 @ Y1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2)))))) | (sK4 @ Y1)))))) = $false) | (((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | (sK3 @ sK8)) = $false) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0))))))) | (~ (irel @ sK5 @ sK7))) = $false) | (((~ (irel @ sK5 @ sK6)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))))) = $false)),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f61])).
% 1.64/1.60 thf(f61,plain,(
% 1.64/1.60 ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0))))))) | (~ (irel @ sK5 @ sK7))) = $false) | (((~ (irel @ sK5 @ sK6)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))))) = $false) | (((^[Y0 : $i]: ((((~ (irel @ Y0 @ sK8)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))))) | (sK3 @ sK8))) @ sK9) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y0 @ Y1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2)))))) | (sK4 @ Y1)))))) = $false)),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f60])).
% 1.64/1.60 thf(f60,plain,(
% 1.64/1.60 ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ Y0 @ sK8)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))))) | (sK3 @ sK8)))) = $false) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0))))))) | (~ (irel @ sK5 @ sK7))) = $false) | (((~ (irel @ sK5 @ sK6)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y0 @ Y1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2)))))) | (sK4 @ Y1)))))) = $false)),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.64/1.60 thf(f59,plain,(
% 1.64/1.60 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK5 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))))) | (sK3 @ Y0))))) @ sK8) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y0 @ Y1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2)))))) | (sK4 @ Y1)))))) = $false) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0))))))) | (~ (irel @ sK5 @ sK7))) = $false) | (((~ (irel @ sK5 @ sK6)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))))) = $false)),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f58])).
% 1.64/1.60 thf(f58,plain,(
% 1.64/1.60 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK5 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))))) | (sK3 @ Y0)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y0 @ Y1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2)))))) | (sK4 @ Y1)))))) = $false) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0))))))) | (~ (irel @ sK5 @ sK7))) = $false) | (((~ (irel @ sK5 @ sK6)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))))) = $false)),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.64/1.60 thf(f57,plain,(
% 1.64/1.60 (((^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ sK5 @ Y0)))) @ sK7) = $false) | (((~ (irel @ sK5 @ sK6)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK5 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))))) | (sK3 @ Y0)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y0 @ Y1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2)))))) | (sK4 @ Y1)))))) = $false)),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f56])).
% 1.64/1.60 thf(f56,plain,(
% 1.64/1.60 ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ sK5 @ Y0))))) = $false) | (((~ (irel @ sK5 @ sK6)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y0 @ Y1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2)))))) | (sK4 @ Y1)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK5 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))))) | (sK3 @ Y0)))))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.64/1.60 thf(f55,plain,(
% 1.64/1.60 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK5 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))))) | (sK3 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y0 @ Y1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2)))))) | (sK4 @ Y1))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ sK5 @ Y0))))) = $false) | (((~ (irel @ sK5 @ sK6)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))))) = $false)),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.64/1.60 thf(f54,plain,(
% 1.64/1.60 ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ sK5 @ Y0))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK5 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))))) | (sK3 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y0 @ Y1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2)))))) | (sK4 @ Y1))))))) = $false) | (((^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))))) @ sK6) = $false)),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f53])).
% 1.64/1.60 thf(f53,plain,(
% 1.64/1.60 ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1)))))))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK5 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))))) | (sK3 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y0 @ Y1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2)))))) | (sK4 @ Y1))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ sK5 @ Y0))))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.64/1.60 thf(f52,plain,(
% 1.64/1.60 ($false = ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ sK5 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1)))))))))))) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK5 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))))) | (sK3 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y0 @ Y1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2)))))) | (sK4 @ Y1))))))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.64/1.60 thf(f50,plain,(
% 1.64/1.60 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK5 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))))) | (sK3 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y0 @ Y1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2)))))) | (sK4 @ Y1))))))) != ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ sK5 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))))))))),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.64/1.60 thf(f49,plain,(
% 1.64/1.60 (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3)))))) | (sK3 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y1 @ Y2)) | (~ (irel @ Y0 @ Y1))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK3 @ Y3)))))) | (sK4 @ Y2)))))))) @ sK5) != ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK3 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (~ (irel @ Y0 @ Y1))))) & (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))))) @ sK5))),
% 1.64/1.60 inference(negative_extensionality,[status(thm)],[f46])).
% 1.64/1.60 thf(f46,plain,(
% 1.64/1.60 ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK3 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK4 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (~ (irel @ Y0 @ Y1))))) & (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))))) != (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK4 @ Y3)))))) | (sK3 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y1 @ Y2)) | (~ (irel @ Y0 @ Y1))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK3 @ Y3)))))) | (sK4 @ Y2)))))))))),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.64/1.60 thf(f45,plain,(
% 1.64/1.60 (((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (irel @ Y3 @ Y2)) | (~ (irel @ Y1 @ Y3))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y0 @ Y4)))))) | (sK3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (irel @ Y2 @ Y3)) | (~ (irel @ Y1 @ Y2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK3 @ Y4)))))) | (Y0 @ Y3)))))))))) @ sK4) != ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK3 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))) | (~ (irel @ Y1 @ Y2))))) & (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))))) @ sK4))),
% 1.64/1.60 inference(negative_extensionality,[status(thm)],[f43])).
% 1.64/1.60 thf(f43,plain,(
% 1.64/1.60 ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (irel @ Y3 @ Y2)) | (~ (irel @ Y1 @ Y3))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y0 @ Y4)))))) | (sK3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (irel @ Y2 @ Y3)) | (~ (irel @ Y1 @ Y2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK3 @ Y4)))))) | (Y0 @ Y3)))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK3 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))) | (~ (irel @ Y1 @ Y2))))) & (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK3 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))))))),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.64/1.60 thf(f42,plain,(
% 1.64/1.60 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (Y0 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y3 @ Y4)) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y0 @ Y5)))))) | (Y1 @ Y4)))))))))))) @ sK3) != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (((!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y0 @ Y4)))) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (irel @ Y3 @ Y4))))))) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | ((!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y1 @ Y4)))) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4) | (~ (irel @ Y3 @ Y4)))))))))))))))) @ sK3))),
% 1.64/1.60 inference(negative_extensionality,[status(thm)],[f40])).
% 1.64/1.60 thf(f40,plain,(
% 1.64/1.60 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (Y0 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y3 @ Y4)) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y0 @ Y5)))))) | (Y1 @ Y4)))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (((!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y0 @ Y4)))) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (irel @ Y3 @ Y4))))))) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | ((!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y1 @ Y4)))) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4) | (~ (irel @ Y3 @ Y4)))))))))))))))))),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.64/1.60 thf(f39,plain,(
% 1.64/1.60 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (Y0 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y3 @ Y4)) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y0 @ Y5)))))) | (Y1 @ Y4)))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (irel @ Y4 @ Y5))))) & (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y2 @ Y5)))))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y3 @ Y5)))) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y5) | (~ (irel @ Y4 @ Y5)))))))))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y3 @ Y5)))) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y5) | (~ (irel @ Y4 @ Y5)))))))))))) @ Y1 @ Y0))))))),
% 1.64/1.60 inference(definition_unfolding,[status(thm)],[f15,f33,f31,f24,f24])).
% 1.64/1.60 thf(f24,plain,(
% 1.64/1.60 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))))),
% 1.64/1.60 inference(cnf_transformation,[status(thm)],[f14])).
% 1.64/1.60 thf(f31,plain,(
% 1.64/1.60 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))),
% 1.64/1.60 inference(cnf_transformation,[status(thm)],[f14])).
% 1.64/1.60 thf(f33,plain,(
% 1.64/1.60 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (Y0 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y3 @ Y4)) | (~ (irel @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y0 @ Y5)))))) | (Y1 @ Y4)))))))))))))),
% 1.64/1.60 inference(cnf_transformation,[status(thm)],[f14])).
% 1.64/1.60 thf(f15,plain,(
% 1.64/1.60 (iequiv != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
% 1.64/1.60 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.60 thf(f9,plain,(
% 1.64/1.60 (iequiv != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
% 1.64/1.60 inference(flattening,[status(thm)],[f6])).
% 1.64/1.60 thf(f6,plain,(
% 1.64/1.60 ~(iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
% 1.64/1.60 inference(fool_elimination,[status(thm)],[f5])).
% 1.64/1.60 thf(f5,plain,(
% 1.64/1.60 ~(iequiv = (^[X0 : $i > $o, X1 : $i > $o] : (iand @ (iimplies @ X0 @ X1) @ (iimplies @ X1 @ X0))))),
% 1.64/1.60 inference(rectify,[status(thm)],[f3])).
% 1.64/1.60 thf(f3,negated_conjecture,(
% 1.64/1.60 ~(iequiv = (^[X8 : $i > $o, X9 : $i > $o] : (iand @ (iimplies @ X8 @ X9) @ (iimplies @ X9 @ X8))))),
% 1.64/1.60 inference(negated_conjecture,[status(cth)],[f2])).
% 1.64/1.60 thf(f2,conjecture,(
% 1.64/1.60 (iequiv = (^[X8 : $i > $o, X9 : $i > $o] : (iand @ (iimplies @ X8 @ X9) @ (iimplies @ X9 @ X8))))),
% 1.64/1.60 file('/export/starexec/sandbox2/tmp/tmp.MacNcZ7HSP/DTF2THF_29558.p',iequiv)).
% 1.64/1.60 thf(f2760,plain,(
% 1.64/1.60 spl1_70 | spl1_131 | spl1_125 | spl1_110),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f555,f2627,f2720,f2757,f2387])).
% 1.64/1.60 thf(f555,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((irel @ sK6 @ sK31) = $true) | ($true = (irel @ sK10 @ sK22)) | ($true = (sK4 @ X1)) | ($true = (irel @ sK7 @ sK23)) | ((irel @ sK9 @ X1) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f554])).
% 1.64/1.60 thf(f554,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (~ (irel @ sK9 @ X1))) | ((irel @ sK6 @ sK31) = $true) | ($true = (irel @ sK10 @ sK22)) | ($true = (sK4 @ X1)) | ($true = (irel @ sK7 @ sK23))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f553])).
% 1.64/1.60 thf(f553,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((irel @ sK6 @ sK31) = $true) | ($true = ((~ (irel @ sK9 @ X1)) | (sK4 @ X1))) | ($true = (irel @ sK7 @ sK23)) | ($true = (irel @ sK10 @ sK22))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f552])).
% 1.64/1.60 thf(f552,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((irel @ sK6 @ sK31) = $true) | ($true = ((^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))) @ X1)) | ($true = (irel @ sK10 @ sK22)) | ($true = (irel @ sK7 @ sK23))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f551])).
% 1.64/1.60 thf(f551,plain,(
% 1.64/1.60 ((irel @ sK6 @ sK31) = $true) | ($true = (irel @ sK7 @ sK23)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ($true = (irel @ sK10 @ sK22))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f550])).
% 1.64/1.60 thf(f550,plain,(
% 1.64/1.60 ($true = (irel @ sK7 @ sK23)) | ($true = (irel @ sK10 @ sK22)) | ($false = (~ (irel @ sK6 @ sK31))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f548])).
% 1.64/1.60 thf(f548,plain,(
% 1.64/1.60 ($true = (irel @ sK10 @ sK22)) | ($false = ((~ (irel @ sK6 @ sK31)) | (sK4 @ sK31))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ($true = (irel @ sK7 @ sK23))),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f547])).
% 1.64/1.60 thf(f547,plain,(
% 1.64/1.60 ($true = (irel @ sK7 @ sK23)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ($true = (irel @ sK10 @ sK22)) | (((^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0))) @ sK31) = $false)),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f546])).
% 1.64/1.60 thf(f546,plain,(
% 1.64/1.60 ($true = (irel @ sK7 @ sK23)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ($true = (irel @ sK10 @ sK22))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f545])).
% 1.64/1.60 thf(f545,plain,(
% 1.64/1.60 ($true = (irel @ sK10 @ sK22)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ($true = (irel @ sK7 @ sK23))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f544])).
% 1.64/1.60 thf(f544,plain,(
% 1.64/1.60 ($false = (~ (irel @ sK7 @ sK23))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ($true = (irel @ sK10 @ sK22))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f542])).
% 1.64/1.60 thf(f542,plain,(
% 1.64/1.60 ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | ($true = (irel @ sK10 @ sK22)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f541])).
% 1.64/1.60 thf(f541,plain,(
% 1.64/1.60 ((~ (irel @ sK10 @ sK22)) = $false) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f465])).
% 1.64/1.60 thf(f465,plain,(
% 1.64/1.60 ($false = ((~ (irel @ sK10 @ sK22)) | (~ (irel @ sK5 @ sK10)))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23)))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f464])).
% 1.64/1.60 thf(f2728,plain,(
% 1.64/1.60 spl1_78 | spl1_27 | spl1_110 | spl1_125),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f617,f2720,f2627,f2170,f2431])).
% 1.64/1.60 thf(f617,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($false = (irel @ sK6 @ X1)) | ((sK3 @ X1) = $true) | ($true = (irel @ sK10 @ sK22)) | ($true = (irel @ sK9 @ sK8)) | ($true = (irel @ sK7 @ sK23))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f616])).
% 1.64/1.60 thf(f616,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK7 @ sK23)) | ((sK3 @ X1) = $true) | ($true = (irel @ sK9 @ sK8)) | ($true = (~ (irel @ sK6 @ X1))) | ($true = (irel @ sK10 @ sK22))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f615])).
% 1.64/1.60 thf(f615,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK10 @ sK22)) | ($true = (irel @ sK7 @ sK23)) | ($true = (irel @ sK9 @ sK8)) | ($true = ((sK3 @ X1) | (~ (irel @ sK6 @ X1))))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f614])).
% 1.64/1.60 thf(f614,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($false = (~ (irel @ sK9 @ sK8))) | ($true = (irel @ sK7 @ sK23)) | ($true = ((sK3 @ X1) | (~ (irel @ sK6 @ X1)))) | ($true = (irel @ sK10 @ sK22))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f613])).
% 1.64/1.60 thf(f613,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($false = (~ (irel @ sK9 @ sK8))) | ($true = (irel @ sK7 @ sK23)) | ($true = (irel @ sK10 @ sK22)) | (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))) @ X1) = $true)) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f612])).
% 1.64/1.60 thf(f612,plain,(
% 1.64/1.60 ($true = (irel @ sK10 @ sK22)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) | ($false = (~ (irel @ sK9 @ sK8))) | ($true = (irel @ sK7 @ sK23))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f610])).
% 1.64/1.60 thf(f610,plain,(
% 1.64/1.60 ($true = (irel @ sK7 @ sK23)) | (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) | ($true = (irel @ sK10 @ sK22))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f609])).
% 1.64/1.60 thf(f609,plain,(
% 1.64/1.60 ($true = (irel @ sK10 @ sK22)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($true = (irel @ sK7 @ sK23)) | (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false)),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f608])).
% 1.64/1.60 thf(f608,plain,(
% 1.64/1.60 ((~ (irel @ sK10 @ sK22)) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false) | ($true = (irel @ sK7 @ sK23))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f606])).
% 1.64/1.60 thf(f606,plain,(
% 1.64/1.60 ($true = (irel @ sK7 @ sK23)) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ((~ (irel @ sK10 @ sK22)) = $false)),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f605])).
% 1.64/1.60 thf(f605,plain,(
% 1.64/1.60 ($false = (~ (irel @ sK7 @ sK23))) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ((~ (irel @ sK10 @ sK22)) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f603])).
% 1.64/1.60 thf(f603,plain,(
% 1.64/1.60 ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ((~ (irel @ sK10 @ sK22)) = $false) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f463])).
% 1.64/1.60 thf(f463,plain,(
% 1.64/1.60 ($false = ((~ (irel @ sK10 @ sK22)) | (~ (irel @ sK5 @ sK10)))) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23)))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f462])).
% 1.64/1.60 thf(f2726,plain,(
% 1.64/1.60 spl1_110 | spl1_70 | spl1_125 | spl1_27),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f633,f2170,f2720,f2387,f2627])).
% 1.64/1.60 thf(f633,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (irel @ sK10 @ sK22)) | ((sK3 @ X1) = $true) | ((irel @ sK9 @ X2) = $false) | ($true = (irel @ sK7 @ sK23)) | ($false = (irel @ sK6 @ X1)) | ($true = (sK4 @ X2))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f632])).
% 1.64/1.60 thf(f632,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (irel @ sK7 @ sK23)) | ((sK3 @ X1) = $true) | ($true = (irel @ sK10 @ sK22)) | ($false = (irel @ sK6 @ X1)) | ($true = (~ (irel @ sK9 @ X2))) | ($true = (sK4 @ X2))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f631])).
% 1.64/1.60 thf(f631,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (irel @ sK7 @ sK23)) | ($false = (irel @ sK6 @ X1)) | ($true = ((~ (irel @ sK9 @ X2)) | (sK4 @ X2))) | ($true = (irel @ sK10 @ sK22)) | ((sK3 @ X1) = $true)) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f630])).
% 1.64/1.60 thf(f630,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))) @ X2)) | ($false = (irel @ sK6 @ X1)) | ($true = (irel @ sK10 @ sK22)) | ((sK3 @ X1) = $true) | ($true = (irel @ sK7 @ sK23))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f629])).
% 1.64/1.60 thf(f629,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK10 @ sK22)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ((sK3 @ X1) = $true) | ($false = (irel @ sK6 @ X1)) | ($true = (irel @ sK7 @ sK23))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f628])).
% 1.64/1.60 thf(f628,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK7 @ sK23)) | ($true = (irel @ sK10 @ sK22)) | ($true = (~ (irel @ sK6 @ X1))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ((sK3 @ X1) = $true)) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f627])).
% 1.64/1.60 thf(f627,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK7 @ sK23)) | ($true = ((sK3 @ X1) | (~ (irel @ sK6 @ X1)))) | ($true = (irel @ sK10 @ sK22)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f626])).
% 1.64/1.60 thf(f626,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK7 @ sK23)) | ($true = (irel @ sK10 @ sK22)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))) @ X1) = $true)) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f625])).
% 1.64/1.60 thf(f625,plain,(
% 1.64/1.60 ($true = (irel @ sK10 @ sK22)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ($true = (irel @ sK7 @ sK23))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f624])).
% 1.64/1.60 thf(f624,plain,(
% 1.64/1.60 ($true = (irel @ sK7 @ sK23)) | ((~ (irel @ sK10 @ sK22)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f623])).
% 1.64/1.60 thf(f623,plain,(
% 1.64/1.60 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ((~ (irel @ sK10 @ sK22)) = $false) | ($true = (irel @ sK7 @ sK23)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f607])).
% 1.64/1.60 thf(f607,plain,(
% 1.64/1.60 ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($true = (irel @ sK7 @ sK23)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ((~ (irel @ sK10 @ sK22)) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f606])).
% 1.64/1.60 thf(f2712,plain,(
% 1.64/1.60 spl1_40 | spl1_78 | spl1_110 | spl1_124),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f736,f2709,f2627,f2431,f2232])).
% 1.64/1.60 thf(f736,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK9 @ sK8)) | ((sK3 @ X1) = $true) | ($true = (irel @ sK7 @ sK23)) | ($false = (irel @ sK10 @ X1)) | ($true = (irel @ sK6 @ sK34))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f735])).
% 1.64/1.60 thf(f735,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK7 @ sK23)) | ((sK3 @ X1) = $true) | ($true = (irel @ sK6 @ sK34)) | ($true = (~ (irel @ sK10 @ X1))) | ($true = (irel @ sK9 @ sK8))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f734])).
% 1.64/1.60 thf(f734,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = ((~ (irel @ sK10 @ X1)) | (sK3 @ X1))) | ($true = (irel @ sK7 @ sK23)) | ($true = (irel @ sK6 @ sK34)) | ($true = (irel @ sK9 @ sK8))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f733])).
% 1.64/1.60 thf(f733,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((~ (irel @ sK6 @ sK34)) = $false) | ($true = ((~ (irel @ sK10 @ X1)) | (sK3 @ X1))) | ($true = (irel @ sK7 @ sK23)) | ($true = (irel @ sK9 @ sK8))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f732])).
% 1.64/1.60 thf(f732,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK7 @ sK23)) | ($true = ((^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))) @ X1)) | ((~ (irel @ sK6 @ sK34)) = $false) | ($true = (irel @ sK9 @ sK8))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f731])).
% 1.64/1.60 thf(f731,plain,(
% 1.64/1.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) | ($true = (irel @ sK7 @ sK23)) | ((~ (irel @ sK6 @ sK34)) = $false) | ($true = (irel @ sK9 @ sK8))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f729])).
% 1.64/1.60 thf(f729,plain,(
% 1.64/1.60 ($true = (irel @ sK7 @ sK23)) | (((~ (irel @ sK6 @ sK34)) | (sK4 @ sK34)) = $false) | ($true = (irel @ sK9 @ sK8)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f728])).
% 1.64/1.60 thf(f728,plain,(
% 1.64/1.60 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = (irel @ sK7 @ sK23)) | (((~ (irel @ sK6 @ sK34)) | (sK4 @ sK34)) = $false) | ($true = (irel @ sK9 @ sK8))),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f727])).
% 1.64/1.60 thf(f727,plain,(
% 1.64/1.60 ($true = (irel @ sK9 @ sK8)) | ($true = (irel @ sK7 @ sK23)) | (((^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0))) @ sK34) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false)),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f726])).
% 1.64/1.60 thf(f726,plain,(
% 1.64/1.60 ($true = (irel @ sK7 @ sK23)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ($true = (irel @ sK9 @ sK8)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false)),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f725])).
% 1.64/1.60 thf(f725,plain,(
% 1.64/1.60 ($false = (~ (irel @ sK9 @ sK8))) | ($true = (irel @ sK7 @ sK23)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f723])).
% 1.64/1.60 thf(f723,plain,(
% 1.64/1.60 (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false) | ($true = (irel @ sK7 @ sK23)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f721])).
% 1.64/1.60 thf(f721,plain,(
% 1.64/1.60 ($true = (irel @ sK7 @ sK23)) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false)),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f720])).
% 1.64/1.60 thf(f720,plain,(
% 1.64/1.60 ($false = (~ (irel @ sK7 @ sK23))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f718])).
% 1.64/1.60 thf(f718,plain,(
% 1.64/1.60 ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f461])).
% 1.64/1.60 thf(f461,plain,(
% 1.64/1.60 (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23)))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f460])).
% 1.64/1.60 thf(f2692,plain,(
% 1.64/1.60 spl1_110 | spl1_70 | spl1_120 | spl1_40),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f768,f2232,f2689,f2387,f2627])).
% 1.64/1.60 thf(f768,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (((irel @ sK9 @ X2) = $false) | ($true = (irel @ sK7 @ sK23)) | ((sK3 @ X1) = $true) | ($true = (sK4 @ X2)) | ((irel @ sK6 @ sK36) = $true) | ($false = (irel @ sK10 @ X1))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f767])).
% 1.64/1.60 thf(f767,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (sK4 @ X2)) | ($true = (irel @ sK7 @ sK23)) | ((irel @ sK6 @ sK36) = $true) | ((sK3 @ X1) = $true) | ($false = (irel @ sK10 @ X1)) | ($true = (~ (irel @ sK9 @ X2)))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f766])).
% 1.64/1.60 thf(f766,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (irel @ sK7 @ sK23)) | ($true = ((~ (irel @ sK9 @ X2)) | (sK4 @ X2))) | ($false = (irel @ sK10 @ X1)) | ((irel @ sK6 @ sK36) = $true) | ((sK3 @ X1) = $true)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f765])).
% 1.64/1.60 thf(f765,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($false = (irel @ sK10 @ X1)) | ((~ (irel @ sK6 @ sK36)) = $false) | ((sK3 @ X1) = $true) | ($true = (irel @ sK7 @ sK23)) | ($true = ((~ (irel @ sK9 @ X2)) | (sK4 @ X2)))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f764])).
% 1.64/1.60 thf(f764,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (((sK3 @ X1) = $true) | ($true = (irel @ sK7 @ sK23)) | ((~ (irel @ sK6 @ sK36)) = $false) | ($false = (irel @ sK10 @ X1)) | ($true = ((^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))) @ X2))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f763])).
% 1.64/1.60 thf(f763,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($false = (irel @ sK10 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ((sK3 @ X1) = $true) | ((~ (irel @ sK6 @ sK36)) = $false) | ($true = (irel @ sK7 @ sK23))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f762])).
% 1.64/1.60 thf(f762,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (~ (irel @ sK10 @ X1))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ((~ (irel @ sK6 @ sK36)) = $false) | ((sK3 @ X1) = $true) | ($true = (irel @ sK7 @ sK23))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f760])).
% 1.64/1.60 thf(f760,plain,(
% 1.64/1.60 ( ! [X1 : $i] : ((((~ (irel @ sK6 @ sK36)) | (sK4 @ sK36)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ((sK3 @ X1) = $true) | ($true = (irel @ sK7 @ sK23)) | ($true = (~ (irel @ sK10 @ X1)))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f759])).
% 1.64/1.60 thf(f759,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = ((~ (irel @ sK10 @ X1)) | (sK3 @ X1))) | ($true = (irel @ sK7 @ sK23)) | (((~ (irel @ sK6 @ sK36)) | (sK4 @ sK36)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f758])).
% 1.64/1.60 thf(f758,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = ((~ (irel @ sK10 @ X1)) | (sK3 @ X1))) | ($true = (irel @ sK7 @ sK23)) | (((^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0))) @ sK36) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) )),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f757])).
% 1.64/1.60 thf(f757,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ($true = (irel @ sK7 @ sK23)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ($true = ((~ (irel @ sK10 @ X1)) | (sK3 @ X1)))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f756])).
% 1.64/1.60 thf(f756,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ($true = (irel @ sK7 @ sK23)) | ($true = ((^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))) @ X1))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f755])).
% 1.64/1.60 thf(f755,plain,(
% 1.64/1.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) | ($true = (irel @ sK7 @ sK23)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f754])).
% 1.64/1.60 thf(f754,plain,(
% 1.64/1.60 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ($true = (irel @ sK7 @ sK23)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false)),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f722])).
% 1.64/1.60 thf(f722,plain,(
% 1.64/1.60 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = (irel @ sK7 @ sK23)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f721])).
% 1.64/1.60 thf(f2668,plain,(
% 1.64/1.60 spl1_40 | spl1_110 | spl1_78 | spl1_27),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f838,f2170,f2431,f2627,f2232])).
% 1.64/1.60 thf(f838,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (((sK3 @ X1) = $true) | ($false = (irel @ sK6 @ X1)) | ((irel @ sK10 @ X2) = $false) | ($true = (irel @ sK7 @ sK23)) | ($true = (irel @ sK9 @ sK8)) | ($true = (sK3 @ X2))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f837])).
% 1.64/1.60 thf(f837,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (irel @ sK9 @ sK8)) | ($true = (~ (irel @ sK10 @ X2))) | ((sK3 @ X1) = $true) | ($true = (irel @ sK7 @ sK23)) | ($true = (sK3 @ X2)) | ($false = (irel @ sK6 @ X1))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f836])).
% 1.64/1.60 thf(f836,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (irel @ sK9 @ sK8)) | ($true = (~ (irel @ sK6 @ X1))) | ((sK3 @ X1) = $true) | ($true = (sK3 @ X2)) | ($true = (~ (irel @ sK10 @ X2))) | ($true = (irel @ sK7 @ sK23))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f835])).
% 1.64/1.60 thf(f835,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = ((sK3 @ X1) | (~ (irel @ sK6 @ X1)))) | ($true = (sK3 @ X2)) | ($true = (~ (irel @ sK10 @ X2))) | ($true = (irel @ sK7 @ sK23)) | ($true = (irel @ sK9 @ sK8))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f834])).
% 1.64/1.60 thf(f834,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (irel @ sK7 @ sK23)) | ($true = (irel @ sK9 @ sK8)) | (((~ (irel @ sK10 @ X2)) | (sK3 @ X2)) = $true) | ($true = ((sK3 @ X1) | (~ (irel @ sK6 @ X1))))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f833])).
% 1.64/1.60 thf(f833,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))) @ X2)) | ($true = ((sK3 @ X1) | (~ (irel @ sK6 @ X1)))) | ($true = (irel @ sK7 @ sK23)) | ($true = (irel @ sK9 @ sK8))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f832])).
% 1.64/1.60 thf(f832,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) | ($true = (irel @ sK7 @ sK23)) | ($true = (irel @ sK9 @ sK8)) | ($true = ((sK3 @ X1) | (~ (irel @ sK6 @ X1))))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f831])).
% 1.64/1.60 thf(f831,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK9 @ sK8)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = (irel @ sK7 @ sK23)) | ($true = ((sK3 @ X1) | (~ (irel @ sK6 @ X1))))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f830])).
% 1.64/1.60 thf(f830,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK7 @ sK23)) | ($false = (~ (irel @ sK9 @ sK8))) | ($true = ((sK3 @ X1) | (~ (irel @ sK6 @ X1)))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f829])).
% 1.64/1.60 thf(f829,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($false = (~ (irel @ sK7 @ sK23))) | ($false = (~ (irel @ sK9 @ sK8))) | ($true = ((sK3 @ X1) | (~ (irel @ sK6 @ X1)))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false)) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f828])).
% 1.64/1.60 thf(f828,plain,(
% 1.64/1.60 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))) @ X1) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ($false = (~ (irel @ sK9 @ sK8))) | ($false = (~ (irel @ sK7 @ sK23)))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f827])).
% 1.64/1.60 thf(f827,plain,(
% 1.64/1.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) | ($false = (~ (irel @ sK9 @ sK8))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ($false = (~ (irel @ sK7 @ sK23)))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f825])).
% 1.64/1.60 thf(f825,plain,(
% 1.64/1.60 ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | ($false = (~ (irel @ sK9 @ sK8))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f823])).
% 1.64/1.60 thf(f823,plain,(
% 1.64/1.60 (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f822])).
% 1.64/1.60 thf(f822,plain,(
% 1.64/1.60 ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f717])).
% 1.64/1.60 thf(f717,plain,(
% 1.64/1.60 ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23)))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f461])).
% 1.64/1.60 thf(f2664,plain,(
% 1.64/1.60 spl1_27 | spl1_40 | spl1_70 | spl1_110),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f889,f2627,f2387,f2232,f2170])).
% 1.64/1.60 thf(f889,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((sK3 @ X1) = $true) | ($true = (sK4 @ X2)) | ($false = (irel @ sK6 @ X1)) | ($true = (sK3 @ X3)) | ($false = (irel @ sK10 @ X3)) | ((irel @ sK9 @ X2) = $false) | ($true = (irel @ sK7 @ sK23))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f888])).
% 1.64/1.60 thf(f888,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (irel @ sK7 @ sK23)) | ($true = (sK3 @ X3)) | ((sK3 @ X1) = $true) | ((irel @ sK9 @ X2) = $false) | ($true = (~ (irel @ sK10 @ X3))) | ($false = (irel @ sK6 @ X1)) | ($true = (sK4 @ X2))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f887])).
% 1.64/1.60 thf(f887,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK4 @ X2)) | ($false = (irel @ sK6 @ X1)) | ($true = (~ (irel @ sK9 @ X2))) | ((sK3 @ X1) = $true) | ($true = (irel @ sK7 @ sK23)) | ($true = (~ (irel @ sK10 @ X3))) | ($true = (sK3 @ X3))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f886])).
% 1.64/1.60 thf(f886,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((~ (irel @ sK10 @ X3)) | (sK3 @ X3))) | ($true = (irel @ sK7 @ sK23)) | ((sK3 @ X1) = $true) | ($true = (~ (irel @ sK9 @ X2))) | ($false = (irel @ sK6 @ X1)) | ($true = (sK4 @ X2))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f885])).
% 1.64/1.60 thf(f885,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((~ (irel @ sK9 @ X2)) | (sK4 @ X2))) | ($true = (irel @ sK7 @ sK23)) | ($false = (irel @ sK6 @ X1)) | ($true = ((~ (irel @ sK10 @ X3)) | (sK3 @ X3))) | ((sK3 @ X1) = $true)) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f884])).
% 1.64/1.60 thf(f884,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((sK3 @ X1) = $true) | ($false = (irel @ sK6 @ X1)) | ($true = ((~ (irel @ sK9 @ X2)) | (sK4 @ X2))) | ($true = ((^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))) @ X3)) | ($true = (irel @ sK7 @ sK23))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f883])).
% 1.64/1.60 thf(f883,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) | ($false = (irel @ sK6 @ X1)) | ($true = (irel @ sK7 @ sK23)) | ($true = ((~ (irel @ sK9 @ X2)) | (sK4 @ X2))) | ((sK3 @ X1) = $true)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f882])).
% 1.64/1.60 thf(f882,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($false = (irel @ sK6 @ X1)) | ($false = (~ (irel @ sK7 @ sK23))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) | ($true = ((~ (irel @ sK9 @ X2)) | (sK4 @ X2))) | ((sK3 @ X1) = $true)) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f881])).
% 1.64/1.60 thf(f881,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) | ((sK3 @ X1) = $true) | ($false = (~ (irel @ sK7 @ sK23))) | ($true = ((^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))) @ X2)) | ($false = (irel @ sK6 @ X1))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f880])).
% 1.64/1.60 thf(f880,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($false = (irel @ sK6 @ X1)) | ((sK3 @ X1) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ($false = (~ (irel @ sK7 @ sK23))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f879])).
% 1.64/1.60 thf(f879,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (~ (irel @ sK6 @ X1))) | ((sK3 @ X1) = $true) | ($false = (~ (irel @ sK7 @ sK23))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f877])).
% 1.64/1.60 thf(f877,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | ((sK3 @ X1) = $true) | ($true = (~ (irel @ sK6 @ X1))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f876])).
% 1.64/1.60 thf(f876,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = ((sK3 @ X1) | (~ (irel @ sK6 @ X1)))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f875])).
% 1.64/1.60 thf(f875,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = ((sK3 @ X1) | (~ (irel @ sK6 @ X1)))) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f874])).
% 1.64/1.60 thf(f874,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))) @ X1) = $true) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f873])).
% 1.64/1.60 thf(f873,plain,(
% 1.64/1.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f872])).
% 1.64/1.60 thf(f872,plain,(
% 1.64/1.60 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f821])).
% 1.64/1.60 thf(f821,plain,(
% 1.64/1.60 ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ($false = ((~ (irel @ sK7 @ sK23)) | (sK3 @ sK23))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f717])).
% 1.64/1.60 thf(f2584,plain,(
% 1.64/1.60 spl1_78 | spl1_31 | spl1_101 | spl1_98),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f1031,f2558,f2580,f2188,f2431])).
% 1.64/1.60 thf(f1031,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK10 @ sK45)) | ($true = (sK4 @ X1)) | ($true = (irel @ sK6 @ sK44)) | ($true = (irel @ sK9 @ sK8)) | ((irel @ sK7 @ X1) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1030])).
% 1.64/1.60 thf(f1030,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK6 @ sK44)) | ($true = (sK4 @ X1)) | ($true = (~ (irel @ sK7 @ X1))) | ($true = (irel @ sK9 @ sK8)) | ($true = (irel @ sK10 @ sK45))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1029])).
% 1.64/1.60 thf(f1029,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK6 @ sK44)) | ($true = (irel @ sK10 @ sK45)) | ($true = ((sK4 @ X1) | (~ (irel @ sK7 @ X1)))) | ($true = (irel @ sK9 @ sK8))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1028])).
% 1.64/1.60 thf(f1028,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($false = (~ (irel @ sK9 @ sK8))) | ($true = ((sK4 @ X1) | (~ (irel @ sK7 @ X1)))) | ($true = (irel @ sK10 @ sK45)) | ($true = (irel @ sK6 @ sK44))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1027])).
% 1.64/1.60 thf(f1027,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((~ (irel @ sK10 @ sK45)) = $false) | ($true = (irel @ sK6 @ sK44)) | ($true = ((sK4 @ X1) | (~ (irel @ sK7 @ X1)))) | ($false = (~ (irel @ sK9 @ sK8)))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1026])).
% 1.64/1.60 thf(f1026,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK6 @ sK44)) | ($true = ((^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))) @ X1)) | ($false = (~ (irel @ sK9 @ sK8))) | ((~ (irel @ sK10 @ sK45)) = $false)) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1025])).
% 1.64/1.60 thf(f1025,plain,(
% 1.64/1.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))))) | ($false = (~ (irel @ sK9 @ sK8))) | ($true = (irel @ sK6 @ sK44)) | ((~ (irel @ sK10 @ sK45)) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1023])).
% 1.64/1.60 thf(f1023,plain,(
% 1.64/1.60 (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))))) | ($true = (irel @ sK6 @ sK44)) | ((~ (irel @ sK10 @ sK45)) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1021])).
% 1.64/1.60 thf(f1021,plain,(
% 1.64/1.60 ($true = (irel @ sK6 @ sK44)) | (((~ (irel @ sK10 @ sK45)) | (~ (irel @ sK5 @ sK10))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))))) | (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1019])).
% 1.64/1.60 thf(f1019,plain,(
% 1.64/1.60 ($true = (irel @ sK6 @ sK44)) | ((((~ (irel @ sK10 @ sK45)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))))) | (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false)),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1018])).
% 1.64/1.60 thf(f1018,plain,(
% 1.64/1.60 ($false = (~ (irel @ sK6 @ sK44))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))))) | (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false) | ((((~ (irel @ sK10 @ sK45)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1016])).
% 1.64/1.60 thf(f1016,plain,(
% 1.64/1.60 (((((~ (irel @ sK10 @ sK45)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) | (sK4 @ sK45)) = $false) | (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))))) | ($false = (~ (irel @ sK6 @ sK44)))),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1015])).
% 1.64/1.60 thf(f1015,plain,(
% 1.64/1.60 (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false) | (((^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0))) @ sK45) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))))) | ($false = (~ (irel @ sK6 @ sK44)))),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f1014])).
% 1.64/1.60 thf(f1014,plain,(
% 1.64/1.60 ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false) | (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))))) | ($false = (~ (irel @ sK6 @ sK44)))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1012])).
% 1.64/1.60 thf(f1012,plain,(
% 1.64/1.60 ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false) | ($false = (~ (irel @ sK6 @ sK44))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0))))))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1010])).
% 1.64/1.60 thf(f1010,plain,(
% 1.64/1.60 ($false = ((~ (irel @ sK6 @ sK44)) | (sK4 @ sK44))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))))) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false)),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1009])).
% 1.64/1.60 thf(f1009,plain,(
% 1.64/1.60 ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))))) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | (((^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0))) @ sK44) = $false)),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f1008])).
% 1.64/1.60 thf(f1008,plain,(
% 1.64/1.60 ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0))))))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1006])).
% 1.64/1.60 thf(f1006,plain,(
% 1.64/1.60 (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0))))))),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f453])).
% 1.64/1.60 thf(f453,plain,(
% 1.64/1.60 ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f452])).
% 1.64/1.60 thf(f2576,plain,(
% 1.64/1.60 spl1_78 | spl1_40 | spl1_31 | spl1_98),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f1058,f2558,f2188,f2232,f2431])).
% 1.64/1.60 thf(f1058,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (((irel @ sK10 @ X2) = $false) | ($true = (irel @ sK9 @ sK8)) | ((irel @ sK7 @ X1) = $false) | ($true = (sK3 @ X2)) | ($true = (irel @ sK6 @ sK44)) | ($true = (sK4 @ X1))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1057])).
% 1.64/1.60 thf(f1057,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (irel @ sK6 @ sK44)) | ($true = (sK4 @ X1)) | ($true = (sK3 @ X2)) | ((irel @ sK10 @ X2) = $false) | ($true = (irel @ sK9 @ sK8)) | ($true = (~ (irel @ sK7 @ X1)))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1056])).
% 1.64/1.60 thf(f1056,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (sK4 @ X1)) | ($true = (sK3 @ X2)) | ($true = (~ (irel @ sK10 @ X2))) | ($true = (irel @ sK9 @ sK8)) | ($true = (~ (irel @ sK7 @ X1))) | ($true = (irel @ sK6 @ sK44))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1055])).
% 1.64/1.60 thf(f1055,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($false = (~ (irel @ sK9 @ sK8))) | ($true = (~ (irel @ sK10 @ X2))) | ($true = (irel @ sK6 @ sK44)) | ($true = (sK4 @ X1)) | ($true = (~ (irel @ sK7 @ X1))) | ($true = (sK3 @ X2))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1054])).
% 1.64/1.60 thf(f1054,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : ((((~ (irel @ sK10 @ X2)) | (sK3 @ X2)) = $true) | ($false = (~ (irel @ sK9 @ sK8))) | ($true = (~ (irel @ sK7 @ X1))) | ($true = (irel @ sK6 @ sK44)) | ($true = (sK4 @ X1))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1053])).
% 1.64/1.60 thf(f1053,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))) @ X2)) | ($true = (~ (irel @ sK7 @ X1))) | ($false = (~ (irel @ sK9 @ sK8))) | ($true = (irel @ sK6 @ sK44)) | ($true = (sK4 @ X1))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1052])).
% 1.64/1.60 thf(f1052,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK6 @ sK44)) | ($true = (sK4 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) | ($false = (~ (irel @ sK9 @ sK8))) | ($true = (~ (irel @ sK7 @ X1)))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1051])).
% 1.64/1.60 thf(f1051,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = (sK4 @ X1)) | ($true = (~ (irel @ sK7 @ X1))) | ($false = (~ (irel @ sK9 @ sK8))) | ($true = (irel @ sK6 @ sK44))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1049])).
% 1.64/1.60 thf(f1049,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK6 @ sK44)) | ($true = (sK4 @ X1)) | (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false) | ($true = (~ (irel @ sK7 @ X1))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false)) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1048])).
% 1.64/1.60 thf(f1048,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (irel @ sK6 @ sK44)) | ($true = ((sK4 @ X1) | (~ (irel @ sK7 @ X1)))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false)) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1047])).
% 1.64/1.60 thf(f1047,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = (irel @ sK6 @ sK44)) | ($true = ((^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))) @ X1)) | (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false)) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1020])).
% 1.64/1.60 thf(f1020,plain,(
% 1.64/1.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false) | ($true = (irel @ sK6 @ sK44))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1019])).
% 1.64/1.60 thf(f2568,plain,(
% 1.64/1.60 spl1_98 | spl1_99 | spl1_70 | spl1_31),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f1097,f2188,f2387,f2565,f2558])).
% 1.64/1.60 thf(f1097,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (sK4 @ X2)) | ($true = (irel @ sK6 @ sK44)) | ((irel @ sK7 @ X1) = $false) | ($true = (sK4 @ X1)) | ((irel @ sK9 @ X2) = $false) | ($true = (irel @ sK10 @ sK46))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1096])).
% 1.64/1.60 thf(f1096,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (sK4 @ X2)) | ((irel @ sK7 @ X1) = $false) | ($true = (sK4 @ X1)) | ((irel @ sK9 @ X2) = $false) | ((~ (irel @ sK10 @ sK46)) = $false) | ($true = (irel @ sK6 @ sK44))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1094])).
% 1.64/1.60 thf(f1094,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (((irel @ sK9 @ X2) = $false) | ($true = (sK4 @ X2)) | ((irel @ sK7 @ X1) = $false) | ($true = (sK4 @ X1)) | ($true = (irel @ sK6 @ sK44)) | (((~ (irel @ sK10 @ sK46)) | (~ (irel @ sK5 @ sK10))) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1093])).
% 1.64/1.60 thf(f1093,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (irel @ sK7 @ X1))) | ((irel @ sK9 @ X2) = $false) | ($true = (sK4 @ X1)) | ($true = (sK4 @ X2)) | ($true = (irel @ sK6 @ sK44)) | (((~ (irel @ sK10 @ sK46)) | (~ (irel @ sK5 @ sK10))) = $false)) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1091])).
% 1.64/1.60 thf(f1091,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (sK4 @ X1)) | ((((~ (irel @ sK10 @ sK46)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) = $false) | ($true = (irel @ sK6 @ sK44)) | ($true = (~ (irel @ sK7 @ X1))) | ($true = (sK4 @ X2)) | ((irel @ sK9 @ X2) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1090])).
% 1.64/1.60 thf(f1090,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (sK4 @ X1)) | ($true = (~ (irel @ sK9 @ X2))) | ($true = (irel @ sK6 @ sK44)) | ($true = (~ (irel @ sK7 @ X1))) | ($true = (sK4 @ X2)) | ((((~ (irel @ sK10 @ sK46)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) = $false)) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1089])).
% 1.64/1.60 thf(f1089,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (irel @ sK9 @ X2)) | (sK4 @ X2))) | ((((~ (irel @ sK10 @ sK46)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) = $false) | ($true = (sK4 @ X1)) | ($true = (~ (irel @ sK7 @ X1))) | ($true = (irel @ sK6 @ sK44))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1088])).
% 1.64/1.60 thf(f1088,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (((((~ (irel @ sK10 @ sK46)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) = $false) | ($true = (~ (irel @ sK7 @ X1))) | ($true = ((^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))) @ X2)) | ($true = (irel @ sK6 @ sK44)) | ($true = (sK4 @ X1))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1087])).
% 1.64/1.60 thf(f1087,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ($true = (irel @ sK6 @ sK44)) | ((((~ (irel @ sK10 @ sK46)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) = $false) | ($true = (sK4 @ X1)) | ($true = (~ (irel @ sK7 @ X1)))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1085])).
% 1.64/1.60 thf(f1085,plain,(
% 1.64/1.60 ( ! [X1 : $i] : ((((((~ (irel @ sK10 @ sK46)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) | (sK4 @ sK46)) = $false) | ($true = (irel @ sK6 @ sK44)) | ($true = (~ (irel @ sK7 @ X1))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ($true = (sK4 @ X1))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1084])).
% 1.64/1.60 thf(f1084,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = ((sK4 @ X1) | (~ (irel @ sK7 @ X1)))) | ($true = (irel @ sK6 @ sK44)) | (((((~ (irel @ sK10 @ sK46)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) | (sK4 @ sK46)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1083])).
% 1.64/1.60 thf(f1083,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($false = (~ (irel @ sK6 @ sK44))) | ($true = ((sK4 @ X1) | (~ (irel @ sK7 @ X1)))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | (((((~ (irel @ sK10 @ sK46)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) | (sK4 @ sK46)) = $false)) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1082])).
% 1.64/1.60 thf(f1082,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($false = (~ (irel @ sK6 @ sK44))) | ($true = ((sK4 @ X1) | (~ (irel @ sK7 @ X1)))) | (((^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0))) @ sK46) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) )),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f1081])).
% 1.64/1.60 thf(f1081,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ($true = ((sK4 @ X1) | (~ (irel @ sK7 @ X1)))) | ($false = (~ (irel @ sK6 @ sK44)))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1080])).
% 1.64/1.60 thf(f1080,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ($false = (~ (irel @ sK6 @ sK44))) | ($true = ((sK4 @ X1) | (~ (irel @ sK7 @ X1)))) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false)) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1079])).
% 1.64/1.60 thf(f1079,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))) @ X1)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false) | ($false = (~ (irel @ sK6 @ sK44)))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1013])).
% 1.64/1.60 thf(f1013,plain,(
% 1.64/1.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false) | ($false = (~ (irel @ sK6 @ sK44)))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1012])).
% 1.64/1.60 thf(f2562,plain,(
% 1.64/1.60 spl1_40 | spl1_98 | spl1_70 | spl1_31),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f1104,f2188,f2387,f2558,f2232])).
% 1.64/1.60 thf(f1104,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ sK7 @ X1) = $false) | ($false = (irel @ sK10 @ X3)) | ($true = (sK4 @ X1)) | ($true = (sK4 @ X2)) | ((irel @ sK9 @ X2) = $false) | ($true = (irel @ sK6 @ sK44)) | ($true = (sK3 @ X3))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1103])).
% 1.64/1.60 thf(f1103,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK4 @ X1)) | ((irel @ sK9 @ X2) = $false) | ($true = (sK4 @ X2)) | ($true = (~ (irel @ sK10 @ X3))) | ($true = (sK3 @ X3)) | ((irel @ sK7 @ X1) = $false) | ($true = (irel @ sK6 @ sK44))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1102])).
% 1.64/1.60 thf(f1102,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK4 @ X1)) | ($true = (irel @ sK6 @ sK44)) | ($true = ((~ (irel @ sK10 @ X3)) | (sK3 @ X3))) | ((irel @ sK7 @ X1) = $false) | ((irel @ sK9 @ X2) = $false) | ($true = (sK4 @ X2))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1101])).
% 1.64/1.60 thf(f1101,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK4 @ X2)) | ($true = (~ (irel @ sK7 @ X1))) | ($true = (sK4 @ X1)) | ((irel @ sK9 @ X2) = $false) | ($true = ((~ (irel @ sK10 @ X3)) | (sK3 @ X3))) | ($true = (irel @ sK6 @ sK44))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1100])).
% 1.64/1.60 thf(f1100,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (irel @ sK6 @ sK44)) | ((irel @ sK9 @ X2) = $false) | ($true = (sK4 @ X1)) | ($true = (~ (irel @ sK7 @ X1))) | ($true = ((^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))) @ X3)) | ($true = (sK4 @ X2))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1099])).
% 1.64/1.60 thf(f1099,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) | ($true = (sK4 @ X2)) | ($true = (irel @ sK6 @ sK44)) | ($true = (sK4 @ X1)) | ($true = (~ (irel @ sK7 @ X1))) | ((irel @ sK9 @ X2) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1092])).
% 1.64/1.60 thf(f1092,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (sK4 @ X1)) | ($true = (sK4 @ X2)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ((irel @ sK9 @ X2) = $false) | ($true = (~ (irel @ sK7 @ X1))) | ($true = (irel @ sK6 @ sK44))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1091])).
% 1.64/1.60 thf(f2520,plain,(
% 1.64/1.60 spl1_27 | spl1_31 | spl1_78 | spl1_91),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f1226,f2509,f2431,f2188,f2170])).
% 1.64/1.60 thf(f1226,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (sK4 @ X1)) | ((irel @ sK7 @ X1) = $false) | ($true = (sK3 @ X2)) | ($false = (irel @ sK6 @ X2)) | ($true = (irel @ sK10 @ sK49)) | ($true = (irel @ sK9 @ sK8))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1225])).
% 1.64/1.60 thf(f1225,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (sK3 @ X2)) | ($true = (sK4 @ X1)) | ($true = (irel @ sK10 @ sK49)) | ((irel @ sK7 @ X1) = $false) | ($true = (irel @ sK9 @ sK8)) | ($true = (~ (irel @ sK6 @ X2)))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1224])).
% 1.64/1.60 thf(f1224,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (sK4 @ X1)) | ($true = (irel @ sK10 @ sK49)) | ($true = ((sK3 @ X2) | (~ (irel @ sK6 @ X2)))) | ((irel @ sK7 @ X1) = $false) | ($true = (irel @ sK9 @ sK8))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1223])).
% 1.64/1.60 thf(f1223,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (irel @ sK10 @ sK49)) | ((irel @ sK7 @ X1) = $false) | ($true = (sK4 @ X1)) | ($true = ((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))) @ X2)) | ($true = (irel @ sK9 @ sK8))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1222])).
% 1.64/1.60 thf(f1222,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) | ($true = (sK4 @ X1)) | ((irel @ sK7 @ X1) = $false) | ($true = (irel @ sK10 @ sK49)) | ($true = (irel @ sK9 @ sK8))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1221])).
% 1.64/1.60 thf(f1221,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (sK4 @ X1)) | ((irel @ sK7 @ X1) = $false) | ((~ (irel @ sK10 @ sK49)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) | ($true = (irel @ sK9 @ sK8))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1220])).
% 1.64/1.60 thf(f1220,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($true = (sK4 @ X1)) | ((irel @ sK7 @ X1) = $false) | ((~ (irel @ sK10 @ sK49)) = $false) | ($true = (irel @ sK9 @ sK8))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1218])).
% 1.64/1.60 thf(f1218,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (sK4 @ X1)) | ((irel @ sK7 @ X1) = $false) | (((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($true = (irel @ sK9 @ sK8))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1217])).
% 1.64/1.60 thf(f1217,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($false = (~ (irel @ sK9 @ sK8))) | (((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) = $false) | ($true = (sK4 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ((irel @ sK7 @ X1) = $false)) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1215])).
% 1.64/1.60 thf(f1215,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($true = (sK4 @ X1)) | ($false = (~ (irel @ sK9 @ sK8))) | ((irel @ sK7 @ X1) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1214])).
% 1.64/1.60 thf(f1214,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (~ (irel @ sK7 @ X1))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($false = (~ (irel @ sK9 @ sK8))) | ((((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) = $false) | ($true = (sK4 @ X1))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1212])).
% 1.64/1.60 thf(f1212,plain,(
% 1.64/1.60 ( ! [X1 : $i] : ((((((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) | (sK4 @ sK49)) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($true = (~ (irel @ sK7 @ X1))) | ($false = (~ (irel @ sK9 @ sK8))) | ($true = (sK4 @ X1))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1210])).
% 1.64/1.60 thf(f1210,plain,(
% 1.64/1.60 ( ! [X1 : $i] : ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false) | ($true = (sK4 @ X1)) | (((((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) | (sK4 @ sK49)) = $false) | ($true = (~ (irel @ sK7 @ X1))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false)) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1209])).
% 1.64/1.60 thf(f1209,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = ((sK4 @ X1) | (~ (irel @ sK7 @ X1)))) | (((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) = $false) | (((((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) | (sK4 @ sK49)) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false)) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1207])).
% 1.64/1.60 thf(f1207,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | (((((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) | (sK4 @ sK49)) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($true = ((sK4 @ X1) | (~ (irel @ sK7 @ X1))))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1206])).
% 1.64/1.60 thf(f1206,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ($true = ((sK4 @ X1) | (~ (irel @ sK7 @ X1)))) | (((^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0))) @ sK49) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false)) )),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f1205])).
% 1.64/1.60 thf(f1205,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ($true = ((sK4 @ X1) | (~ (irel @ sK7 @ X1)))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false)) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1204])).
% 1.64/1.60 thf(f1204,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($true = ((^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))) @ X1)) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false)) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1007])).
% 1.64/1.60 thf(f1007,plain,(
% 1.64/1.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))))) | ((((~ (irel @ sK9 @ sK8)) | (~ (irel @ sK5 @ sK9))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1006])).
% 1.64/1.60 thf(f2518,plain,(
% 1.64/1.60 spl1_78 | spl1_40 | spl1_31 | spl1_27),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f1243,f2170,f2188,f2232,f2431])).
% 1.64/1.60 thf(f1243,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (irel @ sK9 @ sK8)) | ($true = (sK3 @ X2)) | ($true = (sK3 @ X3)) | ($true = (sK4 @ X1)) | ((irel @ sK7 @ X1) = $false) | ($false = (irel @ sK6 @ X2)) | ($false = (irel @ sK10 @ X3))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1242])).
% 1.64/1.60 thf(f1242,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ sK6 @ X2)) | ($true = (sK3 @ X3)) | ($true = (irel @ sK9 @ sK8)) | ($true = (sK4 @ X1)) | ($true = (sK3 @ X2)) | ((irel @ sK7 @ X1) = $false) | ($true = (~ (irel @ sK10 @ X3)))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1241])).
% 1.64/1.60 thf(f1241,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (irel @ sK6 @ X2))) | ($true = (~ (irel @ sK10 @ X3))) | ($true = (irel @ sK9 @ sK8)) | ($true = (sK3 @ X3)) | ($true = (sK3 @ X2)) | ((irel @ sK7 @ X1) = $false) | ($true = (sK4 @ X1))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1240])).
% 1.64/1.60 thf(f1240,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((~ (irel @ sK10 @ X3)) | (sK3 @ X3))) | ($true = (sK3 @ X2)) | ($true = (~ (irel @ sK6 @ X2))) | ($true = (irel @ sK9 @ sK8)) | ($true = (sK4 @ X1)) | ((irel @ sK7 @ X1) = $false)) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1239])).
% 1.64/1.60 thf(f1239,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK3 @ X2)) | ((irel @ sK7 @ X1) = $false) | ($true = (sK4 @ X1)) | ($true = (irel @ sK9 @ sK8)) | ($true = ((^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))) @ X3)) | ($true = (~ (irel @ sK6 @ X2)))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1238])).
% 1.64/1.60 thf(f1238,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) | ($true = (irel @ sK9 @ sK8)) | ($true = (~ (irel @ sK6 @ X2))) | ((irel @ sK7 @ X1) = $false) | ($true = (sK4 @ X1)) | ($true = (sK3 @ X2))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1237])).
% 1.64/1.60 thf(f1237,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (irel @ sK9 @ sK8)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ((irel @ sK7 @ X1) = $false) | ($true = (sK3 @ X2)) | ($true = (~ (irel @ sK6 @ X2))) | ($true = (sK4 @ X1))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1236])).
% 1.64/1.60 thf(f1236,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (((irel @ sK7 @ X1) = $false) | ($true = (irel @ sK9 @ sK8)) | ($true = ((sK3 @ X2) | (~ (irel @ sK6 @ X2)))) | ($true = (sK4 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false)) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1235])).
% 1.64/1.60 thf(f1235,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (irel @ sK9 @ sK8)) | ($true = ((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))) @ X2)) | ((irel @ sK7 @ X1) = $false) | ($true = (sK4 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false)) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1234])).
% 1.64/1.60 thf(f1234,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) | ((irel @ sK7 @ X1) = $false) | ($true = (sK4 @ X1)) | ($true = (irel @ sK9 @ sK8)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1233])).
% 1.64/1.60 thf(f1233,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($true = (irel @ sK9 @ sK8)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = (sK4 @ X1)) | ((irel @ sK7 @ X1) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1216])).
% 1.64/1.60 thf(f1216,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((irel @ sK7 @ X1) = $false) | ($false = (~ (irel @ sK9 @ sK8))) | ($true = (sK4 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false)) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1215])).
% 1.64/1.60 thf(f2512,plain,(
% 1.64/1.60 spl1_91 | spl1_31 | spl1_27 | spl1_70),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f1309,f2387,f2170,f2188,f2509])).
% 1.64/1.60 thf(f1309,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ sK6 @ X2)) | ($false = (irel @ sK9 @ X3)) | ((irel @ sK7 @ X1) = $false) | ($true = (sK4 @ X3)) | ($true = (sK3 @ X2)) | ($true = (irel @ sK10 @ sK49)) | ($true = (sK4 @ X1))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1308])).
% 1.64/1.60 thf(f1308,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK3 @ X2)) | ($true = (sK4 @ X3)) | ($true = (sK4 @ X1)) | ($true = (irel @ sK10 @ sK49)) | ($false = (irel @ sK6 @ X2)) | ((irel @ sK7 @ X1) = $false) | ((~ (irel @ sK9 @ X3)) = $true)) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1307])).
% 1.64/1.60 thf(f1307,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ sK6 @ X2)) | ($true = (sK3 @ X2)) | ($true = ((~ (irel @ sK9 @ X3)) | (sK4 @ X3))) | ($true = (sK4 @ X1)) | ($true = (irel @ sK10 @ sK49)) | ((irel @ sK7 @ X1) = $false)) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1306])).
% 1.64/1.60 thf(f1306,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK3 @ X2)) | ($true = (irel @ sK10 @ sK49)) | (((^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))) @ X3) = $true) | ($true = (sK4 @ X1)) | ((irel @ sK7 @ X1) = $false) | ($false = (irel @ sK6 @ X2))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1305])).
% 1.64/1.60 thf(f1305,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (sK3 @ X2)) | ($true = (sK4 @ X1)) | ($true = (irel @ sK10 @ sK49)) | ((irel @ sK7 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ($false = (irel @ sK6 @ X2))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1304])).
% 1.64/1.60 thf(f1304,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (((~ (irel @ sK10 @ sK49)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ($false = (irel @ sK6 @ X2)) | ($true = (sK4 @ X1)) | ((irel @ sK7 @ X1) = $false) | ($true = (sK3 @ X2))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1303])).
% 1.64/1.60 thf(f1303,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (sK3 @ X2)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ((irel @ sK7 @ X1) = $false) | ($false = (irel @ sK6 @ X2)) | ((~ (irel @ sK10 @ sK49)) = $false) | ($true = (sK4 @ X1))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1301])).
% 1.64/1.60 thf(f1301,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (((irel @ sK7 @ X1) = $false) | (((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ($false = (irel @ sK6 @ X2)) | ($true = (sK4 @ X1)) | ($true = (sK3 @ X2))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1300])).
% 1.64/1.60 thf(f1300,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (sK3 @ X2)) | ($true = (sK4 @ X1)) | ($true = (~ (irel @ sK6 @ X2))) | (((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ((irel @ sK7 @ X1) = $false)) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1299])).
% 1.64/1.60 thf(f1299,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = ((sK3 @ X2) | (~ (irel @ sK6 @ X2)))) | (((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) = $false) | ((irel @ sK7 @ X1) = $false) | ($true = (sK4 @ X1)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1298])).
% 1.64/1.60 thf(f1298,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : ((((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) = $false) | ($true = (sK4 @ X1)) | ((irel @ sK7 @ X1) = $false) | ($true = ((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))) @ X2)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1297])).
% 1.64/1.60 thf(f1297,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (sK4 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) | (((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) = $false) | ((irel @ sK7 @ X1) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1295])).
% 1.64/1.60 thf(f1295,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) = $false) | ($true = (sK4 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ((irel @ sK7 @ X1) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1294])).
% 1.64/1.60 thf(f1294,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($true = (sK4 @ X1)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ((((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) = $false) | ((irel @ sK7 @ X1) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1293])).
% 1.64/1.60 thf(f1293,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (sK4 @ X1)) | ($true = (~ (irel @ sK7 @ X1))) | ((((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1291])).
% 1.64/1.60 thf(f1291,plain,(
% 1.64/1.60 ( ! [X1 : $i] : ((((((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) | (sK4 @ sK49)) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($true = (sK4 @ X1)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ($true = (~ (irel @ sK7 @ X1)))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1208])).
% 1.64/1.60 thf(f1208,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = ((sK4 @ X1) | (~ (irel @ sK7 @ X1)))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | (((((~ (irel @ sK10 @ sK49)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) | (sK4 @ sK49)) = $false)) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1207])).
% 1.64/1.60 thf(f2506,plain,(
% 1.64/1.60 spl1_70 | spl1_40 | spl1_31 | spl1_27),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f1329,f2170,f2188,f2232,f2387])).
% 1.64/1.60 thf(f1329,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (irel @ sK10 @ X3)) | ($true = (sK4 @ X1)) | ($true = (sK3 @ X2)) | ($true = (sK4 @ X4)) | ((irel @ sK7 @ X1) = $false) | ($true = (sK3 @ X3)) | ((irel @ sK9 @ X4) = $false) | ($false = (irel @ sK6 @ X2))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1328])).
% 1.64/1.60 thf(f1328,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (sK4 @ X1)) | ((irel @ sK7 @ X1) = $false) | ($true = (sK3 @ X2)) | ($true = (sK4 @ X4)) | ($false = (irel @ sK10 @ X3)) | ($true = (sK3 @ X3)) | ($false = (irel @ sK6 @ X2)) | ($true = (~ (irel @ sK9 @ X4)))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1327])).
% 1.64/1.60 thf(f1327,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (sK3 @ X2)) | ($true = (sK4 @ X1)) | ($true = (sK3 @ X3)) | ((irel @ sK7 @ X1) = $false) | ($false = (irel @ sK6 @ X2)) | ($false = (irel @ sK10 @ X3)) | ($true = ((~ (irel @ sK9 @ X4)) | (sK4 @ X4)))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1326])).
% 1.64/1.60 thf(f1326,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (irel @ sK6 @ X2)) | ($true = (sK3 @ X3)) | ((irel @ sK7 @ X1) = $false) | ($true = (sK4 @ X1)) | ($false = (irel @ sK10 @ X3)) | ($true = ((^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))) @ X4)) | ($true = (sK3 @ X2))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1325])).
% 1.64/1.60 thf(f1325,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ sK7 @ X1) = $false) | ($true = (sK3 @ X3)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ($true = (sK3 @ X2)) | ($true = (sK4 @ X1)) | ($false = (irel @ sK6 @ X2)) | ($false = (irel @ sK10 @ X3))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1324])).
% 1.64/1.60 thf(f1324,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (irel @ sK10 @ X3))) | ($true = (sK3 @ X3)) | ($true = (sK3 @ X2)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ($false = (irel @ sK6 @ X2)) | ((irel @ sK7 @ X1) = $false) | ($true = (sK4 @ X1))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1323])).
% 1.64/1.60 thf(f1323,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (irel @ sK6 @ X2))) | ($true = (sK3 @ X3)) | ($true = (~ (irel @ sK10 @ X3))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ($true = (sK3 @ X2)) | ((irel @ sK7 @ X1) = $false) | ($true = (sK4 @ X1))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1322])).
% 1.64/1.60 thf(f1322,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((~ (irel @ sK10 @ X3)) | (sK3 @ X3))) | ($true = (sK3 @ X2)) | ($true = (~ (irel @ sK6 @ X2))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))) | ((irel @ sK7 @ X1) = $false) | ($true = (sK4 @ X1))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1321])).
% 1.64/1.60 thf(f1321,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK3 @ X2)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ($true = ((~ (irel @ sK10 @ X3)) | (sK3 @ X3))) | ((irel @ sK7 @ X1) = $false) | ($true = (sK4 @ X1)) | ($true = (~ (irel @ sK6 @ X2)))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1320])).
% 1.64/1.60 thf(f1320,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ sK7 @ X1) = $false) | ($true = ((sK3 @ X2) | (~ (irel @ sK6 @ X2)))) | ($true = ((~ (irel @ sK10 @ X3)) | (sK3 @ X3))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ($true = (sK4 @ X1))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1319])).
% 1.64/1.60 thf(f1319,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))) @ X3)) | ((irel @ sK7 @ X1) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ($true = (sK4 @ X1)) | ($true = ((sK3 @ X2) | (~ (irel @ sK6 @ X2))))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1318])).
% 1.64/1.60 thf(f1318,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (sK4 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) | ($true = ((sK3 @ X2) | (~ (irel @ sK6 @ X2)))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ((irel @ sK7 @ X1) = $false)) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1317])).
% 1.64/1.60 thf(f1317,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) | ((irel @ sK7 @ X1) = $false) | ($true = ((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))) @ X2)) | ($true = (sK4 @ X1)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1316])).
% 1.64/1.60 thf(f1316,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) | ((irel @ sK7 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) | ($true = (sK4 @ X1)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0))))))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1296])).
% 1.64/1.60 thf(f1296,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (((irel @ sK7 @ X1) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0))))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0)))))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK9 @ Y0)) | (sK4 @ Y0)))))) | ($true = (sK4 @ X1))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1295])).
% 1.64/1.60 thf(f2219,plain,(
% 1.64/1.60 spl1_25 | spl1_36 | spl1_26 | spl1_37),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f1838,f2216,f2166,f2212,f2162])).
% 1.64/1.60 thf(f1838,plain,(
% 1.64/1.60 ((sK3 @ sK8) = $false) | ((sK3 @ sK73) = $false) | ((sK4 @ sK59) = $false) | ((sK4 @ sK74) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1831])).
% 1.64/1.60 thf(f1831,plain,(
% 1.64/1.60 ($false = ((~ (irel @ sK6 @ sK74)) | (sK4 @ sK74))) | ((sK3 @ sK8) = $false) | ((sK4 @ sK59) = $false) | ((sK3 @ sK73) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1830])).
% 1.64/1.60 thf(f1830,plain,(
% 1.64/1.60 ((sK3 @ sK8) = $false) | (((~ (irel @ sK7 @ sK73)) | (sK3 @ sK73)) = $false) | ($false = ((~ (irel @ sK6 @ sK74)) | (sK4 @ sK74))) | ((sK4 @ sK59) = $false)),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1829])).
% 1.64/1.60 thf(f1829,plain,(
% 1.64/1.60 (((~ (irel @ sK7 @ sK73)) | (sK3 @ sK73)) = $false) | (((^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0))) @ sK74) = $false) | ((sK3 @ sK8) = $false) | ((sK4 @ sK59) = $false)),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f1828])).
% 1.64/1.60 thf(f1828,plain,(
% 1.64/1.60 ((sK4 @ sK59) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ((sK3 @ sK8) = $false) | (((~ (irel @ sK7 @ sK73)) | (sK3 @ sK73)) = $false)),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1827])).
% 1.64/1.60 thf(f1827,plain,(
% 1.64/1.60 ((sK3 @ sK8) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ($false = ((^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0))) @ sK73)) | ((sK4 @ sK59) = $false)),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f1826])).
% 1.64/1.60 thf(f1826,plain,(
% 1.64/1.60 ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) = $false) | ((sK4 @ sK59) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) = $false) | ((sK3 @ sK8) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1824])).
% 1.64/1.60 thf(f1824,plain,(
% 1.64/1.60 (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false) | ((sK4 @ sK59) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) = $false) | ((sK3 @ sK8) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1822])).
% 1.64/1.60 thf(f1822,plain,(
% 1.64/1.60 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0)))))))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false) | ((sK3 @ sK8) = $false) | ((sK4 @ sK59) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1587])).
% 1.64/1.60 thf(f1587,plain,(
% 1.64/1.60 ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0))))))) | (~ (irel @ sK5 @ sK7))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false) | ((sK3 @ sK8) = $false) | ((sK4 @ sK59) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1586])).
% 1.64/1.60 thf(f1586,plain,(
% 1.64/1.60 ((sK3 @ sK8) = $false) | (((((~ (irel @ sK10 @ sK59)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK10 @ Y0)) | (sK3 @ Y0)))))) | (sK4 @ sK59)) = $false) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0))))))) | (~ (irel @ sK5 @ sK7))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false)),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1585])).
% 1.64/1.60 thf(f1585,plain,(
% 1.64/1.60 (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false) | (((^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0))) @ sK59) = $false) | ((sK3 @ sK8) = $false) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0))))))) | (~ (irel @ sK5 @ sK7))) = $false)),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f449])).
% 1.64/1.60 thf(f449,plain,(
% 1.64/1.60 ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ sK10 @ Y0)) | (~ (irel @ sK5 @ sK10))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK10 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))) = $false) | ((sK3 @ sK8) = $false) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK7 @ Y0))))))) | (~ (irel @ sK5 @ sK7))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK6 @ Y0))))))) = $false)),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.64/1.60 thf(f2156,plain,(
% 1.64/1.60 spl1_22 | spl1_23),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f1915,f2154,f2151])).
% 1.64/1.60 thf(f1915,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((sK4 @ (sK79 @ X2)) = $false) | ((irel @ X2 @ X1) = $false) | ((sK4 @ (sK78 @ X3)) = $false) | ($false = (irel @ X3 @ X4)) | ((sK3 @ X4) = $true) | ((irel @ sK5 @ X2) = $false) | ($false = (irel @ sK5 @ X3)) | ((sK3 @ X1) = $true)) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1914])).
% 1.64/1.60 thf(f1914,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (irel @ X3 @ X4)) | ((sK4 @ (sK78 @ X3)) = $false) | ((irel @ X2 @ X1) = $false) | (((~ (irel @ X2 @ (sK79 @ X2))) | (sK4 @ (sK79 @ X2))) = $false) | ((sK3 @ X1) = $true) | ((sK3 @ X4) = $true) | ($false = (irel @ sK5 @ X3)) | ((irel @ sK5 @ X2) = $false)) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1913])).
% 1.64/1.60 thf(f1913,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((sK3 @ X1) = $true) | ($false = (irel @ sK5 @ X3)) | ((irel @ X2 @ X1) = $false) | ((sK3 @ X4) = $true) | ((sK4 @ (sK78 @ X3)) = $false) | ((irel @ sK5 @ X2) = $false) | (((^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0))) @ (sK79 @ X2)) = $false) | ($false = (irel @ X3 @ X4))) )),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f1912])).
% 1.64/1.60 thf(f1912,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((irel @ X2 @ X1) = $false) | ((sK3 @ X4) = $true) | ((sK4 @ (sK78 @ X3)) = $false) | ($false = (irel @ X3 @ X4)) | ($false = (irel @ sK5 @ X3)) | ((irel @ sK5 @ X2) = $false) | ((sK3 @ X1) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1911])).
% 1.64/1.60 thf(f1911,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (irel @ sK5 @ X3)) | ((sK3 @ X4) = $true) | ((sK4 @ (sK78 @ X3)) = $false) | ((irel @ X2 @ X1) = $false) | ((irel @ sK5 @ X2) = $false) | ($true = (~ (irel @ X3 @ X4))) | ((sK3 @ X1) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1910])).
% 1.64/1.60 thf(f1910,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((sK3 @ X1) = $true) | ($true = (~ (irel @ sK5 @ X2))) | ($false = (irel @ sK5 @ X3)) | ($true = (~ (irel @ X3 @ X4))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) = $false) | ((sK3 @ X4) = $true) | ((sK4 @ (sK78 @ X3)) = $false) | ((irel @ X2 @ X1) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1909])).
% 1.64/1.60 thf(f1909,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((sK4 @ (sK78 @ X3)) = $false) | ($true = (~ (irel @ sK5 @ X3))) | ((sK3 @ X1) = $true) | ((irel @ X2 @ X1) = $false) | ((sK3 @ X4) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) = $false) | ($true = (~ (irel @ sK5 @ X2))) | ($true = (~ (irel @ X3 @ X4)))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1908])).
% 1.64/1.60 thf(f1908,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | ((irel @ X2 @ X1) = $false) | ((sK3 @ X1) = $true) | ($true = (~ (irel @ sK5 @ X3))) | ((sK3 @ X4) = $true) | ($true = (~ (irel @ sK5 @ X2))) | ($true = (~ (irel @ X3 @ X4))) | ((sK4 @ (sK78 @ X3)) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1907])).
% 1.64/1.60 thf(f1907,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (~ (irel @ X2 @ X1))) | ($true = (~ (irel @ sK5 @ X2))) | ($true = (~ (irel @ X3 @ X4))) | ((sK3 @ X1) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | ($true = (~ (irel @ sK5 @ X3))) | ((sK3 @ X4) = $true) | ((sK4 @ (sK78 @ X3)) = $false)) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1906])).
% 1.64/1.60 thf(f1906,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((~ (irel @ X3 @ X4)) | (sK3 @ X4))) | ($true = (~ (irel @ X2 @ X1))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | ((sK3 @ X1) = $true) | ((sK4 @ (sK78 @ X3)) = $false) | ($true = (~ (irel @ sK5 @ X3))) | ($true = (~ (irel @ sK5 @ X2)))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1905])).
% 1.64/1.60 thf(f1905,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((sK3 @ X1) = $true) | ((sK4 @ (sK78 @ X3)) = $false) | ($true = ((~ (irel @ X2 @ X1)) | (~ (irel @ sK5 @ X2)))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | ($true = (~ (irel @ sK5 @ X3))) | ($true = ((~ (irel @ X3 @ X4)) | (sK3 @ X4)))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1903])).
% 1.64/1.60 thf(f1903,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((sK3 @ X1) = $true) | (((sK4 @ (sK78 @ X3)) | (~ (irel @ X3 @ (sK78 @ X3)))) = $false) | ($true = ((~ (irel @ X2 @ X1)) | (~ (irel @ sK5 @ X2)))) | ($true = ((~ (irel @ X3 @ X4)) | (sK3 @ X4))) | ($true = (~ (irel @ sK5 @ X3))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0))))))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1902])).
% 1.64/1.60 thf(f1902,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (~ (irel @ sK5 @ X3))) | ($true = ((~ (irel @ X2 @ X1)) | (~ (irel @ sK5 @ X2)))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | ((sK3 @ X1) = $true) | ($true = ((~ (irel @ X3 @ X4)) | (sK3 @ X4))) | (((^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X3 @ Y0)))) @ (sK78 @ X3)) = $false)) )),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f1901])).
% 1.64/1.60 thf(f1901,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X3 @ Y0))))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | ($true = ((~ (irel @ X3 @ X4)) | (sK3 @ X4))) | ($true = ((~ (irel @ X2 @ X1)) | (~ (irel @ sK5 @ X2)))) | ($true = (~ (irel @ sK5 @ X3))) | ((sK3 @ X1) = $true)) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1900])).
% 1.64/1.60 thf(f1900,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (irel @ X2 @ X1)) | (~ (irel @ sK5 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0))))))) | ((sK3 @ X1) = $true) | ($true = ((~ (irel @ X3 @ X4)) | (sK3 @ X4))) | ($true = (~ (irel @ sK5 @ X3))) | ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X3 @ Y0))))) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f1899])).
% 1.64/1.60 thf(f1899,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((sK3 @ X1) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X3 @ Y0))))))) | ($true = ((~ (irel @ X3 @ X4)) | (sK3 @ X4))) | ($true = (~ (irel @ sK5 @ X3))) | ($true = (((~ (irel @ X2 @ X1)) | (~ (irel @ sK5 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1898])).
% 1.64/1.60 thf(f1898,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (~ (irel @ sK5 @ X3))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X3 @ Y0))))))) | ($true = ((^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK3 @ Y0))) @ X4)) | ((sK3 @ X1) = $true) | ($true = (((~ (irel @ X2 @ X1)) | (~ (irel @ sK5 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1897])).
% 1.64/1.60 thf(f1897,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK3 @ Y0))))) | ($true = (~ (irel @ sK5 @ X3))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X3 @ Y0))))))) | ((sK3 @ X1) = $true) | ($true = (((~ (irel @ X2 @ X1)) | (~ (irel @ sK5 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1896])).
% 1.64/1.60 thf(f1896,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X3 @ Y0))))))) = $true) | ((sK3 @ X1) = $true) | ($true = (~ (irel @ sK5 @ X3))) | ($true = (((~ (irel @ X2 @ X1)) | (~ (irel @ sK5 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1895])).
% 1.64/1.60 thf(f1895,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X3 @ Y0))))))) | (~ (irel @ sK5 @ X3))) = $true) | ((sK3 @ X1) = $true) | ($true = (((~ (irel @ X2 @ X1)) | (~ (irel @ sK5 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1894])).
% 1.64/1.60 thf(f1894,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((((~ (irel @ X2 @ X1)) | (~ (irel @ sK5 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | (sK3 @ X1)) = $true) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ X3 @ Y0))))))) | (~ (irel @ sK5 @ X3))) = $true)) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1893])).
% 1.64/1.60 thf(f1893,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ sK5 @ Y0)))) @ X3)) | (((((~ (irel @ X2 @ X1)) | (~ (irel @ sK5 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | (sK3 @ X1)) = $true)) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1892])).
% 1.64/1.60 thf(f1892,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ sK5 @ Y0)))))) | (((((~ (irel @ X2 @ X1)) | (~ (irel @ sK5 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | (sK3 @ X1)) = $true)) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1890])).
% 1.64/1.60 thf(f1890,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ sK5 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1)))))))))))) | (((((~ (irel @ X2 @ X1)) | (~ (irel @ sK5 @ X2))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))))) | (sK3 @ X1)) = $true)) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1889])).
% 1.64/1.60 thf(f1889,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ sK5 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1)))))))))))) | ($true = ((^[Y0 : $i]: ((((~ (irel @ Y0 @ X1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))))) | (sK3 @ X1))) @ X2))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1888])).
% 1.64/1.60 thf(f1888,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ Y0 @ X1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))))) | (sK3 @ X1))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ sK5 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))))))))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f1887])).
% 1.64/1.60 thf(f1887,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK5 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))))) | (sK3 @ Y0))))) @ X1)) | ($true = ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ sK5 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))))))))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1886])).
% 1.64/1.60 thf(f1886,plain,(
% 1.64/1.60 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK5 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))))) | (sK3 @ Y0))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ sK5 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))))))))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.64/1.60 thf(f51,plain,(
% 1.64/1.60 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK5 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK4 @ Y2)))))) | (sK3 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y0 @ Y1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2)))))) | (sK4 @ Y1)))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ sK5 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))))))))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.64/1.60 thf(f2083,plain,(
% 1.64/1.60 spl1_1 | spl1_3),
% 1.64/1.60 inference(avatar_split_clause,[status(thm)],[f2071,f2081,f2074])).
% 1.64/1.60 thf(f2071,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((irel @ sK5 @ X2) = $false) | ((sK3 @ (sK89 @ X2)) = $false) | ($true = (sK4 @ X3)) | ((irel @ sK5 @ X1) = $false) | ((sK3 @ (sK87 @ X1)) = $false) | ((irel @ X2 @ X4) = $false) | ((irel @ X1 @ X3) = $false) | ($true = (sK4 @ X4))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f2069])).
% 1.64/1.60 thf(f2069,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((sK3 @ (sK87 @ X1)) = $false) | ((irel @ X1 @ X3) = $false) | ((irel @ sK5 @ X1) = $false) | ((irel @ sK5 @ X2) = $false) | ((irel @ X2 @ X4) = $false) | ($true = (sK4 @ X4)) | ($true = (sK4 @ X3)) | (((sK3 @ (sK89 @ X2)) | (~ (irel @ X2 @ (sK89 @ X2)))) = $false)) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f2068])).
% 1.64/1.60 thf(f2068,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((irel @ X2 @ X4) = $false) | (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0)))) @ (sK89 @ X2)) = $false) | ((irel @ sK5 @ X2) = $false) | ((irel @ sK5 @ X1) = $false) | ($true = (sK4 @ X3)) | ($true = (sK4 @ X4)) | ((sK3 @ (sK87 @ X1)) = $false) | ((irel @ X1 @ X3) = $false)) )),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f2067])).
% 1.64/1.60 thf(f2067,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((sK3 @ (sK87 @ X1)) = $false) | ($true = (sK4 @ X4)) | ((irel @ X2 @ X4) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0))))) = $false) | ((irel @ sK5 @ X2) = $false) | ((irel @ X1 @ X3) = $false) | ($true = (sK4 @ X3)) | ((irel @ sK5 @ X1) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f2066])).
% 1.64/1.60 thf(f2066,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((~ (irel @ X2 @ X4)) = $true) | ($true = (sK4 @ X4)) | ((sK3 @ (sK87 @ X1)) = $false) | ((irel @ sK5 @ X2) = $false) | ($true = (sK4 @ X3)) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0))))) = $false) | ((irel @ X1 @ X3) = $false) | ((irel @ sK5 @ X1) = $false)) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f2065])).
% 1.64/1.60 thf(f2065,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((~ (irel @ X2 @ X4)) | (sK4 @ X4))) | ((irel @ sK5 @ X2) = $false) | ((irel @ X1 @ X3) = $false) | ((sK3 @ (sK87 @ X1)) = $false) | ((irel @ sK5 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0))))) = $false) | ($true = (sK4 @ X3))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f2064])).
% 1.64/1.60 thf(f2064,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((irel @ X1 @ X3) = $false) | (((^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0))) @ X4) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0))))) = $false) | ((irel @ sK5 @ X1) = $false) | ((irel @ sK5 @ X2) = $false) | ((sK3 @ (sK87 @ X1)) = $false) | ($true = (sK4 @ X3))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f2063])).
% 1.64/1.60 thf(f2063,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0))))) | ($true = (sK4 @ X3)) | ((irel @ sK5 @ X1) = $false) | ((irel @ X1 @ X3) = $false) | ((sK3 @ (sK87 @ X1)) = $false) | ((irel @ sK5 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0))))) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f2062])).
% 1.64/1.60 thf(f2062,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0))))))) | ((irel @ X1 @ X3) = $false) | ($true = (sK4 @ X3)) | ((irel @ sK5 @ X2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0))))) | ((sK3 @ (sK87 @ X1)) = $false) | ((irel @ sK5 @ X1) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f2061])).
% 1.64/1.60 thf(f2061,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK4 @ X3)) | ($true = (~ (irel @ sK5 @ X2))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0))))) | ((sK3 @ (sK87 @ X1)) = $false) | ((irel @ sK5 @ X1) = $false) | ((irel @ X1 @ X3) = $false)) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f2044])).
% 1.64/1.60 thf(f2044,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK4 @ X3)) | ((sK3 @ (sK87 @ X1)) = $false) | ((~ (irel @ sK5 @ X1)) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0))))) | ((irel @ X1 @ X3) = $false) | ($true = (~ (irel @ sK5 @ X2)))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f2043])).
% 1.64/1.60 thf(f2043,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((~ (irel @ X1 @ (sK87 @ X1))) | (sK3 @ (sK87 @ X1)))) | ((irel @ X1 @ X3) = $false) | ((~ (irel @ sK5 @ X1)) = $true) | ($true = (~ (irel @ sK5 @ X2))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0))))))) | ($true = (sK4 @ X3))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f2042])).
% 1.64/1.60 thf(f2042,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0))))))) = $true) | ((irel @ X1 @ X3) = $false) | ((~ (irel @ sK5 @ X1)) = $true) | ($false = ((~ (irel @ X1 @ (sK87 @ X1))) | (sK3 @ (sK87 @ X1)))) | ($true = (~ (irel @ sK5 @ X2))) | ($true = (sK4 @ X3))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f2041])).
% 1.64/1.60 thf(f2041,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((~ (irel @ sK5 @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0))))))))) | ($true = (sK4 @ X3)) | ((irel @ X1 @ X3) = $false) | ((~ (irel @ sK5 @ X1)) = $true) | ($false = ((~ (irel @ X1 @ (sK87 @ X1))) | (sK3 @ (sK87 @ X1))))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f2040])).
% 1.64/1.60 thf(f2040,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK4 @ X3)) | ($true = (~ (irel @ X1 @ X3))) | ($true = ((~ (irel @ sK5 @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0))))))))) | ($false = ((~ (irel @ X1 @ (sK87 @ X1))) | (sK3 @ (sK87 @ X1)))) | ((~ (irel @ sK5 @ X1)) = $true)) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f2039])).
% 1.64/1.60 thf(f2039,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((~ (irel @ X1 @ X3)) | (~ (irel @ sK5 @ X1))) = $true) | ($true = (sK4 @ X3)) | ($true = ((~ (irel @ sK5 @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0))))))))) | ($false = ((~ (irel @ X1 @ (sK87 @ X1))) | (sK3 @ (sK87 @ X1))))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f2038])).
% 1.64/1.60 thf(f2038,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK3 @ Y0))) @ (sK87 @ X1)) = $false) | ($true = (sK4 @ X3)) | ($true = ((~ (irel @ sK5 @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0))))))))) | (((~ (irel @ X1 @ X3)) | (~ (irel @ sK5 @ X1))) = $true)) )),
% 1.64/1.60 inference(sigma_clausification,[status(thm)],[f2037])).
% 1.64/1.60 thf(f2037,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK3 @ Y0)))) = $false) | (((~ (irel @ X1 @ X3)) | (~ (irel @ sK5 @ X1))) = $true) | ($true = (sK4 @ X3)) | ($true = ((~ (irel @ sK5 @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0)))))))))) )),
% 1.64/1.60 inference(not_proxy_clausification,[status(thm)],[f2036])).
% 1.64/1.60 thf(f2036,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK4 @ X3)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK3 @ Y0)))))) | (((~ (irel @ X1 @ X3)) | (~ (irel @ sK5 @ X1))) = $true) | ($true = ((~ (irel @ sK5 @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0)))))))))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f2035])).
% 1.64/1.60 thf(f2035,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK4 @ X3)) | ($true = (((~ (irel @ X1 @ X3)) | (~ (irel @ sK5 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK3 @ Y0))))))) | ($true = ((~ (irel @ sK5 @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0)))))))))) )),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f2034])).
% 1.64/1.60 thf(f2034,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((((~ (irel @ X1 @ X3)) | (~ (irel @ sK5 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK3 @ Y0)))))) | (sK4 @ X3))) | ($true = ((~ (irel @ sK5 @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0)))))))))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f2033])).
% 1.64/1.60 thf(f2033,plain,(
% 1.64/1.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((((~ (irel @ X1 @ Y0)) | (~ (irel @ sK5 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X1 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0))) @ X3)) | ($true = ((~ (irel @ sK5 @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0)))))))))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f2032])).
% 1.64/1.60 thf(f2032,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ X1 @ Y0)) | (~ (irel @ sK5 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X1 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0))))) | ($true = ((~ (irel @ sK5 @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ X2 @ Y0)))))))))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f2031])).
% 1.64/1.60 thf(f2031,plain,(
% 1.64/1.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ X1 @ Y0)) | (~ (irel @ sK5 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X1 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0))))) | ($true = ((^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))))) @ X2))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f2030])).
% 1.64/1.60 thf(f2030,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ X1 @ Y0)) | (~ (irel @ sK5 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X1 @ Y1)) | (sK3 @ Y1)))))) | (sK4 @ Y0)))))) )),
% 1.64/1.60 inference(beta_eta_normalization,[status(thm)],[f2029])).
% 1.64/1.60 thf(f2029,plain,(
% 1.64/1.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y0 @ Y1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2)))))) | (sK4 @ Y1))))) @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1)))))))))))) )),
% 1.64/1.60 inference(pi_clausification,[status(thm)],[f1984])).
% 1.64/1.60 thf(f1984,plain,(
% 1.64/1.60 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y0 @ Y1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2)))))) | (sK4 @ Y1))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1)))))))))))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f1885])).
% 1.64/1.60 thf(f1885,plain,(
% 1.64/1.60 ($true = ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ sK5 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1)))))))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y0 @ Y1)) | (~ (irel @ sK5 @ Y0))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK3 @ Y2)))))) | (sK4 @ Y1)))))))),
% 1.64/1.60 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.64/1.60 % SZS output end Proof for DTF2THF_29558
% 1.64/1.60 % (29685)------------------------------
% 1.64/1.60 % (29685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.60 % (29685)Termination reason: Refutation
% 1.64/1.60
% 1.64/1.60 % (29685)Memory used [KB]: 7419
% 1.64/1.60 % (29685)Time elapsed: 0.212 s
% 1.64/1.60 % (29685)Instructions burned: 329 (million)
% 1.64/1.60 % (29685)------------------------------
% 1.64/1.60 % (29685)------------------------------
% 1.64/1.60 % (29655)Success in time 0.312 s
%------------------------------------------------------------------------------