%------------------------------------------------------------------------------
% 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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:58:54 PM UTC 2026
% Result : Theorem 1.77s 1.30s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 10
% Syntax : Number of formulae : 108 ( 24 unt; 0 typ; 7 def)
% Number of atoms : 1627 ( 381 equ; 0 cnn)
% Maximal formula atoms : 24 ( 15 avg)
% Number of connectives : 2900 ( 435 ~; 495 |; 208 &;1538 @)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 245 ( 245 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 39 usr; 17 con; 0-3 aty)
% ( 211 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 729 ( 587 ^; 134 !; 8 ?; 729 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
d_unsorted: $tType ).
thf(func_def_0,type,
unsorted: $tType ).
thf(func_def_1,type,
irel: $i > $i > $o ).
thf(func_def_2,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
iatom: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
inot: ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
itrue: $i > $o ).
thf(func_def_10,type,
ifalse: $i > $o ).
thf(func_def_11,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_16,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
ivalid: ( $i > $o ) > $o ).
thf(func_def_18,type,
isatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_20,type,
iinvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
d_unsorted: $tType ).
thf(func_def_22,type,
d2unsorted: d_unsorted > $i ).
thf(func_def_23,type,
d_unsorted_0: d_unsorted ).
thf(func_def_39,type,
sK0: $i > d_unsorted ).
thf(func_def_41,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
sK3: $i > $o ).
thf(func_def_43,type,
sK4: $i > $o ).
thf(f401,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f221,f244,f319,f351,f364,f370,f392,f400]) ).
thf(f400,plain,
( ~ spl1_1
| ~ spl1_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f399]) ).
thf(f399,plain,
( $false
| ~ spl1_1
| ~ spl1_6 ),
inference(trivial_inequality_removal,[status(thm)],[f395]) ).
thf(f395,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_6 ),
inference(superposition,[status(thm)],[f239,f379]) ).
thf(f379,plain,
( ! [X0: $i] :
( $true
= ( sK3 @ X0 ) )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f378,f54]) ).
thf(f54,plain,
! [X0: $i,X1: $i] : ( X0 = X1 ),
inference(superposition,[status(thm)],[f50,f50]) ).
thf(f50,plain,
! [X0: $i] :
( ( d2unsorted @ d_unsorted_0 )
= X0 ),
inference(superposition,[status(thm)],[f33,f19]) ).
thf(f19,plain,
! [X4: d_unsorted] : ( d_unsorted_0 = X4 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
!= ( d2unsorted @ X0 ) )
| ( X0 = X1 ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ! [X2: $i] :
( ( d2unsorted @ ( sK0 @ X2 ) )
= X2 )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y2 @ Y5 )
| ( ( ~ ( irel @ Y5 @ Y4 )
| ( Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 )
| ~ ( irel @ Y5 @ Y6 ) ) ) )
& ( ~ ( irel @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y5 @ Y6 )
| ( Y1 @ Y6 ) ) )
| ( Y0 @ Y3 ) ) ) ) ) ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) )
& ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ! [X4: d_unsorted] : ( d_unsorted_0 = X4 )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14]) ).
thf(f14,plain,
! [X2: $i] :
( ? [X3: d_unsorted] :
( ( d2unsorted @ X3 )
= X2 )
=> ( ( d2unsorted @ ( sK0 @ X2 ) )
= X2 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
!= ( d2unsorted @ X0 ) )
| ( X0 = X1 ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ! [X2: $i] :
? [X3: d_unsorted] :
( ( d2unsorted @ X3 )
= X2 )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y2 @ Y5 )
| ( ( ~ ( irel @ Y5 @ Y4 )
| ( Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 )
| ~ ( irel @ Y5 @ Y6 ) ) ) )
& ( ~ ( irel @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y5 @ Y6 )
| ( Y1 @ Y6 ) ) )
| ( Y0 @ Y3 ) ) ) ) ) ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) )
& ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ! [X4: d_unsorted] : ( d_unsorted_0 = X4 )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
!= ( d2unsorted @ X0 ) )
| ( X0 = X1 ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ! [X3: $i] :
? [X4: d_unsorted] :
( ( d2unsorted @ X4 )
= X3 )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y2 @ Y5 )
| ( ( ~ ( irel @ Y5 @ Y4 )
| ( Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 )
| ~ ( irel @ Y5 @ Y6 ) ) ) )
& ( ~ ( irel @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y5 @ Y6 )
| ( Y1 @ Y6 ) ) )
| ( Y0 @ Y3 ) ) ) ) ) ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) )
& ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ! [X2: d_unsorted] : ( d_unsorted_0 = X2 )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y2 @ Y5 )
| ( ( ~ ( irel @ Y5 @ Y4 )
| ( Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 )
| ~ ( irel @ Y5 @ Y6 ) ) ) )
& ( ~ ( irel @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y5 @ Y6 )
| ( Y1 @ Y6 ) ) )
| ( Y0 @ Y3 ) ) ) ) ) ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ! [X3: $i] :
? [X4: d_unsorted] :
( ( d2unsorted @ X4 )
= X3 )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ! [X2: d_unsorted] : ( d_unsorted_0 = X2 )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) )
& ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) )
& ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X0 ) )
=> ( X0 = X1 ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) )
& ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X0 ) )
=> ( X0 = X1 ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) )
& ! [X2: d_unsorted] : ( d_unsorted_0 = X2 )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ! [X3: $i] :
? [X4: d_unsorted] :
( ( d2unsorted @ X4 )
= X3 )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y2 @ Y5 )
| ( ( ~ ( irel @ Y5 @ Y4 )
| ( Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 )
| ~ ( irel @ Y5 @ Y6 ) ) ) )
& ( ~ ( irel @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y5 @ Y6 )
| ( Y1 @ Y6 ) ) )
| ( Y0 @ Y3 ) ) ) ) ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) )
& ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ! [X20: d_unsorted,X21: d_unsorted] :
( ( ( d2unsorted @ X21 )
= ( d2unsorted @ X20 ) )
=> ( X20 = X21 ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) )
& ! [X30: d_unsorted] : ( d_unsorted_0 = X30 )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ! [X33: $i] :
? [X34: d_unsorted] :
( ( d2unsorted @ X34 )
= X33 )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y2 @ Y5 )
| ( ( ~ ( irel @ Y5 @ Y4 )
| ( Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 )
| ~ ( irel @ Y5 @ Y6 ) ) ) )
& ( ~ ( irel @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y5 @ Y6 )
| ( Y1 @ Y6 ) ) )
| ( Y0 @ Y3 ) ) ) ) ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( ^ [X0: $i > $o,X1: $i] :
~ ! [X2: $i] :
( ( X0 @ X2 )
| ~ ( irel @ X1 @ X2 ) ) )
= inot )
& ( ( ^ [X3: $i > $o] :
~ ! [X4: $i] : ( X3 @ X4 ) )
= icountersatisfiable )
& ( iatom
= ( ^ [X5: $i > $o,X6: $i] : ( X5 @ X6 ) ) )
& ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
& ( ( ^ [X7: $i > $o,X8: $i > $o,X9: $i] :
( ( X8 @ X9 )
& ( X7 @ X9 ) ) )
= mand )
& ( mimplies
= ( ^ [X10: $i > $o,X11: $i > $o,X12: $i] :
( ( X11 @ X12 )
| ~ ( X10 @ X12 ) ) ) )
& ( iequiv
= ( ^ [X13: $i > $o,X14: $i > $o,X15: $i] :
( ( ~ ! [X16: $i] :
( ( X14 @ X16 )
| ~ ( irel @ X15 @ X16 ) )
| ! [X17: $i] :
( ( X13 @ X17 )
| ~ ( irel @ X15 @ X17 ) ) )
& ( ~ ! [X18: $i] :
( ~ ( irel @ X15 @ X18 )
| ( X13 @ X18 ) )
| ! [X19: $i] :
( ~ ( irel @ X15 @ X19 )
| ( X14 @ X19 ) ) ) ) ) )
& ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
& ! [X20: d_unsorted,X21: d_unsorted] :
( ( ( d2unsorted @ X21 )
= ( d2unsorted @ X20 ) )
=> ( X20 = X21 ) )
& ( ( ^ [X22: $i > $o,X23: $i > $o,X24: $i] :
( ( X22 @ X24 )
& ( X23 @ X24 ) ) )
= iand )
& ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
& ( ( ^ [X25: $i > $o,X26: $i > $o,X27: $i] :
( ~ ! [X28: $i] :
( ( X26 @ X28 )
| ~ ( irel @ X27 @ X28 ) )
| ! [X29: $i] :
( ~ ( irel @ X27 @ X29 )
| ( X25 @ X29 ) ) ) )
= iimplied )
& ! [X30: d_unsorted] : ( d_unsorted_0 = X30 )
& ( ( ^ [X31: $i > $o] :
~ ! [X32: $i] :
~ ( X31 @ X32 ) )
= isatisfiable )
& ! [X33: $i] :
? [X34: d_unsorted] :
( ( d2unsorted @ X34 )
= X33 )
& ( mor
= ( ^ [X35: $i > $o,X36: $i > $o,X37: $i] :
( ( X35 @ X37 )
| ( X36 @ X37 ) ) ) )
& ( ( ^ [X38: $i > $o,X39: $i > $o,X40: $i] :
( ! [X41: $i] :
( ~ ( irel @ X40 @ X41 )
| ( X38 @ X41 ) )
| ! [X42: $i] :
( ~ ( irel @ X40 @ X42 )
| ( X39 @ X42 ) ) ) )
= ior )
& ( iinvalid
= ( ^ [X43: $i > $o] :
! [X44: $i] :
~ ( X43 @ X44 ) ) )
& ( ( ^ [X45: $i > $o,X46: $i > $o,X47: $i] :
~ ! [X48: $i,X49: $i,X50: $i] :
( ( ( ( X45 @ X50 )
| ~ ! [X51: $i] :
( ( X46 @ X51 )
| ~ ( irel @ X48 @ X51 ) )
| ~ ( irel @ X48 @ X50 ) )
& ( ~ ! [X52: $i] :
( ~ ( irel @ X48 @ X52 )
| ( X45 @ X52 ) )
| ( X46 @ X49 )
| ~ ( irel @ X48 @ X49 ) ) )
| ~ ( irel @ X47 @ X48 ) ) )
= ixor )
& ( ( ^ [X53: $i > $o,X54: $i > $o,X55: $i] :
( ! [X56: $i] :
( ~ ( irel @ X55 @ X56 )
| ( X54 @ X56 ) )
| ~ ! [X57: $i] :
( ( X53 @ X57 )
| ~ ( irel @ X55 @ X57 ) ) ) )
= iimplies )
& ( ( ^ [X58: $i > $o,X59: $i] :
~ ( X58 @ X59 ) )
= mnot )
& ( ivalid
= ( ^ [X60: $i > $o] :
! [X61: $i] : ( X60 @ X61 ) ) )
& ( mbox_s4
= ( ^ [X62: $i > $o,X63: $i] :
! [X64: $i] :
( ( X62 @ X64 )
| ~ ( irel @ X63 @ X64 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ( ^ [X8: $i > $o,X7: $i] :
~ ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) )
= inot )
& ( ( ^ [X14: $i > $o] :
~ ! [X15: $i] : ( X14 @ X15 ) )
= icountersatisfiable )
& ( iatom
= ( ^ [X8: $i > $o,X7: $i] : ( X8 @ X7 ) ) )
& ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
& ( ( ^ [X4: $i > $o,X5: $i > $o,X0: $i] :
( ( X5 @ X0 )
& ( X4 @ X0 ) ) )
= mand )
& ( mimplies
= ( ^ [X0: $i > $o,X6: $i > $o,X7: $i] :
( ( X6 @ X7 )
| ~ ( X0 @ X7 ) ) ) )
& ( iequiv
= ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ( ~ ! [X5: $i] :
( ( X9 @ X5 )
| ~ ( irel @ X7 @ X5 ) )
| ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) )
& ( ~ ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X8 @ X5 ) )
| ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X9 @ X5 ) ) ) ) ) )
& ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
& ! [X3: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X2 )
= ( d2unsorted @ X3 ) )
=> ( X2 = X3 ) )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ( X8 @ X7 )
& ( X9 @ X7 ) ) )
= iand )
& ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ~ ! [X5: $i] :
( ( X9 @ X5 )
| ~ ( irel @ X7 @ X5 ) )
| ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X8 @ X5 ) ) ) )
= iimplied )
& ! [X1: d_unsorted] : ( d_unsorted_0 = X1 )
& ( ( ^ [X14: $i > $o] :
~ ! [X15: $i] :
~ ( X14 @ X15 ) )
= isatisfiable )
& ! [X0: $i] :
? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 )
& ( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X0: $i] :
( ( X4 @ X0 )
| ( X5 @ X0 ) ) ) )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X8 @ X5 ) )
| ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X9 @ X5 ) ) ) )
= ior )
& ( iinvalid
= ( ^ [X14: $i > $o] :
! [X15: $i] :
~ ( X14 @ X15 ) ) )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
~ ! [X5: $i,X10: $i,X11: $i] :
( ( ( ( X8 @ X11 )
| ~ ! [X13: $i] :
( ( X9 @ X13 )
| ~ ( irel @ X5 @ X13 ) )
| ~ ( irel @ X5 @ X11 ) )
& ( ~ ! [X12: $i] :
( ~ ( irel @ X5 @ X12 )
| ( X8 @ X12 ) )
| ( X9 @ X10 )
| ~ ( irel @ X5 @ X10 ) ) )
| ~ ( irel @ X7 @ X5 ) ) )
= ixor )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X9 @ X5 ) )
| ~ ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) ) )
= iimplies )
& ( ( ^ [X4: $i > $o,X0: $i] :
~ ( X4 @ X0 ) )
= mnot )
& ( ivalid
= ( ^ [X14: $i > $o] :
! [X15: $i] : ( X14 @ X15 ) ) )
& ( mbox_s4
= ( ^ [X8: $i > $o,X4: $i] :
! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6KYU5pQR7S/DTF2THF_31761.p',lcl695_1) ).
thf(f33,plain,
! [X2: $i] :
( ( d2unsorted @ ( sK0 @ X2 ) )
= X2 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f378,plain,
( ( $true
= ( sK3 @ sK5 ) )
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f376]) ).
thf(f376,plain,
( ( $true = $false )
| ( $true
= ( sK3 @ sK5 ) )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f120,f217]) ).
thf(f217,plain,
( ! [X4: $i] :
( ( ( irel @ sK5 @ X4 )
= $false )
| ( $true
= ( sK3 @ X4 ) ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f216]) ).
thf(f216,definition,
( spl1_1
<=> ! [X4: $i] :
( ( ( irel @ sK5 @ X4 )
= $false )
| ( $true
= ( sK3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f120,plain,
! [X0: $i] :
( $true
= ( irel @ X0 @ X0 ) ),
inference(superposition,[status(thm)],[f38,f54]) ).
thf(f38,plain,
( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f239,plain,
( ( ( sK3 @ sK16 )
= $false )
| ~ spl1_6 ),
inference(avatar_component_clause,[status(thm)],[f237]) ).
thf(f237,definition,
( spl1_6
<=> ( ( sK3 @ sK16 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition]) ).
thf(f392,plain,
( ~ spl1_1
| ~ spl1_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f391]) ).
thf(f391,plain,
( $false
| ~ spl1_1
| ~ spl1_7 ),
inference(trivial_inequality_removal,[status(thm)],[f382]) ).
thf(f382,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_7 ),
inference(superposition,[status(thm)],[f379,f243]) ).
thf(f243,plain,
( ( ( sK3 @ sK15 )
= $false )
| ~ spl1_7 ),
inference(avatar_component_clause,[status(thm)],[f241]) ).
thf(f241,definition,
( spl1_7
<=> ( ( sK3 @ sK15 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition]) ).
thf(f370,plain,
( spl1_12
| ~ spl1_23 ),
inference(avatar_contradiction_clause,[status(thm)],[f369]) ).
thf(f369,plain,
( $false
| spl1_12
| ~ spl1_23 ),
inference(subsumption_resolution,[status(thm)],[f318,f352]) ).
thf(f352,plain,
( ! [X0: $i] :
( ( sK4 @ X0 )
!= $false )
| spl1_12 ),
inference(superposition,[status(thm)],[f266,f54]) ).
thf(f266,plain,
( ( ( sK4 @ sK12 )
!= $false )
| spl1_12 ),
inference(avatar_component_clause,[status(thm)],[f265]) ).
thf(f265,definition,
( spl1_12
<=> ( ( sK4 @ sK12 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_12])],[avatar_definition]) ).
thf(f318,plain,
( ( ( sK4 @ sK8 )
= $false )
| ~ spl1_23 ),
inference(avatar_component_clause,[status(thm)],[f316]) ).
thf(f316,definition,
( spl1_23
<=> ( ( sK4 @ sK8 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_23])],[avatar_definition]) ).
thf(f364,plain,
( ~ spl1_2
| ~ spl1_22 ),
inference(avatar_contradiction_clause,[status(thm)],[f363]) ).
thf(f363,plain,
( $false
| ~ spl1_2
| ~ spl1_22 ),
inference(trivial_inequality_removal,[status(thm)],[f359]) ).
thf(f359,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_22 ),
inference(superposition,[status(thm)],[f313,f340]) ).
thf(f340,plain,
( ! [X0: $i] :
( $true
= ( sK4 @ X0 ) )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f339,f54]) ).
thf(f339,plain,
( ( $true
= ( sK4 @ sK5 ) )
| ~ spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f337]) ).
thf(f337,plain,
( ( $true
= ( sK4 @ sK5 ) )
| ( $true = $false )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f120,f220]) ).
thf(f220,plain,
( ! [X1: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f219]) ).
thf(f219,definition,
( spl1_2
<=> ! [X1: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f313,plain,
( ( ( sK4 @ sK6 )
= $false )
| ~ spl1_22 ),
inference(avatar_component_clause,[status(thm)],[f311]) ).
thf(f311,definition,
( spl1_22
<=> ( ( sK4 @ sK6 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_22])],[avatar_definition]) ).
thf(f351,plain,
( ~ spl1_2
| ~ spl1_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f350]) ).
thf(f350,plain,
( $false
| ~ spl1_2
| ~ spl1_12 ),
inference(trivial_inequality_removal,[status(thm)],[f346]) ).
thf(f346,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_12 ),
inference(superposition,[status(thm)],[f267,f340]) ).
thf(f267,plain,
( ( ( sK4 @ sK12 )
= $false )
| ~ spl1_12 ),
inference(avatar_component_clause,[status(thm)],[f265]) ).
thf(f319,plain,
( spl1_23
| spl1_22 ),
inference(avatar_split_clause,[status(thm)],[f146,f311,f316]) ).
thf(f146,plain,
( ( ( sK4 @ sK6 )
= $false )
| ( ( sK4 @ sK8 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
( ( ( sK4 @ sK6 )
= $false )
| ( ( ( sK4 @ sK8 )
| ~ ( irel @ sK5 @ sK8 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f143]) ).
thf(f143,plain,
( ( ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) )
@ sK8 )
= $false )
| ( ( sK4 @ sK6 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f135]) ).
thf(f135,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false )
| ( ( sK4 @ sK6 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f134]) ).
thf(f134,plain,
( ( ( ~ ( irel @ sK5 @ sK6 )
| ( sK4 @ sK6 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f133]) ).
thf(f133,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK6 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f130]) ).
thf(f130,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK4 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f128]) ).
thf(f128,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f126]) ).
thf(f126,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
!= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f125]) ).
thf(f125,plain,
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) ) )
@ sK5 )
!= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f124]) ).
thf(f124,plain,
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( irel @ Y0 @ Y1 ) ) ) ) )
!= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( irel @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f123]) ).
thf(f123,plain,
( ( ^ [Y0: $i > $o,Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) ) )
@ sK4 )
!= ( ^ [Y0: $i > $o,Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) )
@ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f122]) ).
thf(f122,plain,
( ( ^ [Y0: $i > $o,Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) ) ) )
!= ( ^ [Y0: $i > $o,Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f121]) ).
thf(f121,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) )
@ sK3 )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) )
@ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( irel @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ Y1 ) ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f16,f17,f28,f23,f23]) ).
thf(f23,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f28,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f17,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f16,plain,
( ior
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ior
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ior
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( ior
!= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( ior
!= ( ^ [X8: $i > $o,X9: $i > $o] : ( mor @ ( mbox_s4 @ X8 ) @ ( mbox_s4 @ X9 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ior
= ( ^ [X8: $i > $o,X9: $i > $o] : ( mor @ ( mbox_s4 @ X8 ) @ ( mbox_s4 @ X9 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6KYU5pQR7S/DTF2THF_31761.p',ior) ).
thf(f244,plain,
( spl1_6
| spl1_7 ),
inference(avatar_split_clause,[status(thm)],[f188,f241,f237]) ).
thf(f188,plain,
( ( ( sK3 @ sK15 )
= $false )
| ( ( sK3 @ sK16 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f187]) ).
thf(f187,plain,
( ( ( sK3 @ sK15 )
= $false )
| ( $false
= ( ~ ( irel @ sK5 @ sK16 )
| ( sK3 @ sK16 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f186]) ).
thf(f186,plain,
( ( ( ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) )
@ sK16 )
= $false )
| ( ( sK3 @ sK15 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f185]) ).
thf(f185,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) )
= $false )
| ( ( sK3 @ sK15 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f183]) ).
thf(f183,plain,
( ( ( ( sK3 @ sK15 )
| ~ ( irel @ sK5 @ sK15 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f182]) ).
thf(f182,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) )
@ sK15 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f164]) ).
thf(f164,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f129]) ).
thf(f129,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f128]) ).
thf(f221,plain,
( spl1_1
| spl1_1
| spl1_2
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f214,f219,f219,f216,f216]) ).
thf(f214,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK5 @ X4 )
= $false )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( ( sK3 @ X2 )
= $true )
| ( $true
= ( sK4 @ X3 ) )
| ( ( irel @ sK5 @ X3 )
= $false )
| ( ( irel @ sK5 @ X2 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( sK3 @ X4 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f213]) ).
thf(f213,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( sK3 @ X4 ) )
| ( $true
= ( ~ ( irel @ sK5 @ X4 ) ) )
| ( ( irel @ sK5 @ X3 )
= $false )
| ( ( sK3 @ X2 )
= $true )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( sK4 @ X3 ) )
| ( ( irel @ sK5 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f212]) ).
thf(f212,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( ~ ( irel @ sK5 @ X4 )
| ( sK3 @ X4 ) ) )
| ( $true
= ( sK4 @ X3 ) )
| ( ( irel @ sK5 @ X3 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( ( sK3 @ X2 )
= $true )
| ( ( irel @ sK5 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f211]) ).
thf(f211,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) )
| ( ( irel @ sK5 @ X3 )
= $false )
| ( ( sK3 @ X2 )
= $true )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( ~ ( irel @ sK5 @ X4 )
| ( sK3 @ X4 ) ) )
| ( $true
= ( sK4 @ X3 ) )
| ( ( irel @ sK5 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f210]) ).
thf(f210,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( sK4 @ X3 ) )
| ( ( sK3 @ X2 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) )
| ( ( irel @ sK5 @ X3 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f209]) ).
thf(f209,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( sK4 @ X3 ) )
| ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( sK4 @ X1 ) )
| ( ( irel @ sK5 @ X3 )
= $false )
| ( ( sK3 @ X2 )
= $true )
| ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f208]) ).
thf(f208,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK5 @ X1 )
= $false )
| ( $true
= ( ~ ( irel @ sK5 @ X3 ) ) )
| ( ( sK3 @ X2 )
= $true )
| ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( sK4 @ X3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f207]) ).
thf(f207,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( ~ ( irel @ sK5 @ X1 ) ) )
| ( ( sK3 @ X2 )
= $true )
| ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f206]) ).
thf(f206,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK5 @ X1 ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X3 ) ) )
| ( ( sK3 @ X2 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( sK4 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f205]) ).
thf(f205,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( irel @ sK5 @ X3 )
| ( sK4 @ X3 ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK5 @ X1 ) ) )
| ( ( sK3 @ X2 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f204]) ).
thf(f204,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( ( sK3 @ X2 )
= $true )
| ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK4 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK5 @ X1 ) ) ) ),
inference(pi_clausification,[status(thm)],[f203]) ).
thf(f203,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( irel @ sK5 @ X2 ) ) )
| ( ( sK3 @ X2 )
= $true )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK5 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f202]) ).
thf(f202,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( sK3 @ X2 )
| ~ ( irel @ sK5 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK5 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f201]) ).
thf(f201,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK5 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f200]) ).
thf(f200,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( ( sK4 @ X1 )
| ~ ( irel @ sK5 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f199]) ).
thf(f199,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f198]) ).
thf(f198,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f197]) ).
thf(f197,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f127]) ).
thf(f127,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( irel @ sK5 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( irel @ sK5 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.33 % Computer : n017.cluster.edu
% 0.18/0.33 % Model : x86_64 x86_64
% 0.18/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.33 % Memory : 8042.1875MB
% 0.18/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.33 % CPULimit : 300
% 0.18/0.33 % WCLimit : 300
% 0.18/0.33 % DateTime : Tue May 5 09:16:12 EDT 2026
% 0.18/0.33 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.45 ---- Original DTF file ---
% 0.31/0.45 thf(spec,logic,$$dhol).
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.31/0.45 % Domain : Software Verification
% 0.31/0.45 % Problem : Benchmark: LCL695^1, Active target: ior
% 0.31/0.45 % Version : Especial.
% 0.31/0.45 % English :
% 0.31/0.45
% 0.31/0.45 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.31/0.45 % Source : [Kon26]
% 0.31/0.45 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.31/0.45
% 0.31/0.45 % Status : Theorem
% 0.31/0.45 % Rating : ? v9.3.0
% 0.31/0.45 % Syntax : Number of formulae : 26 ( 1 unt; 24 typ; 0 def)
% 0.31/0.45 % Number of atoms : 63 ( 22 equ; 0 cnn)
% 0.31/0.45 % Maximal formula atoms : 24 ( 31 avg)
% 0.31/0.45 % Number of connectives : 164 ( 32 ~; 26 |; 26 &; 79 @)
% 0.31/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.31/0.45 % Maximal formula depth : 26 ( 14 avg)
% 0.31/0.45 % Number of types : 4 ( 2 usr)
% 0.31/0.45 % Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% 0.31/0.45 % Number of symbols : 23 ( 22 usr; 1 con; 0-3 aty)
% 0.31/0.45 % Number of variables : 67 ( 41 ^; 25 !; 1 ?; 67 :)
% 0.31/0.45 % SPC : TH0_THM_EQU_NAR
% 0.31/0.45
% 0.31/0.45 % Comments :
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 thf(unsorted_type,type,
% 0.31/0.45 unsorted: $tType ).
% 0.31/0.45
% 0.31/0.45 thf(irel_decl,type,
% 0.31/0.45 irel: $i > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(mnot_decl,type,
% 0.31/0.45 mnot: ( $i > $o ) > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(mor_decl,type,
% 0.31/0.45 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(mand_decl,type,
% 0.31/0.45 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(mimplies_decl,type,
% 0.31/0.45 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(mbox_s4_decl,type,
% 0.31/0.45 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(iatom_decl,type,
% 0.31/0.45 iatom: ( $i > $o ) > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(inot_decl,type,
% 0.31/0.45 inot: ( $i > $o ) > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(itrue_decl,type,
% 0.31/0.45 itrue: $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(ifalse_decl,type,
% 0.31/0.45 ifalse: $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(iand_decl,type,
% 0.31/0.45 iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(ior_decl,type,
% 0.31/0.45 ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(iimplies_decl,type,
% 0.31/0.45 iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(iimplied_decl,type,
% 0.31/0.45 iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(iequiv_decl,type,
% 0.31/0.45 iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(ixor_decl,type,
% 0.31/0.45 ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(ivalid_decl,type,
% 0.31/0.45 ivalid: ( $i > $o ) > $o ).
% 0.31/0.45
% 0.31/0.45 thf(isatisfiable_decl,type,
% 0.31/0.45 isatisfiable: ( $i > $o ) > $o ).
% 0.31/0.45
% 0.31/0.45 thf(icountersatisfiable_decl,type,
% 0.31/0.45 icountersatisfiable: ( $i > $o ) > $o ).
% 0.31/0.45
% 0.31/0.45 thf(iinvalid_decl,type,
% 0.31/0.45 iinvalid: ( $i > $o ) > $o ).
% 0.31/0.45
% 0.31/0.45 %----Types of the domains
% 0.31/0.45 thf(d_unsorted_type,type,
% 0.31/0.45 d_unsorted: $tType ).
% 0.31/0.45
% 0.31/0.45 %----Types of the promotion functions
% 0.31/0.45 thf(d2unsorted_decl,type,
% 0.31/0.45 d2unsorted: d_unsorted > $i ).
% 0.31/0.45
% 0.31/0.45 %----Types of the domain elements
% 0.31/0.45 thf(d_unsorted_0_decl,type,
% 0.31/0.45 d_unsorted_0: d_unsorted ).
% 0.31/0.45
% 0.31/0.45 thf(lcl695_1,axiom,
% 0.31/0.45 ( ! [U: $i] :
% 0.31/0.45 ? [DU: d_unsorted] :
% 0.31/0.45 ( U
% 0.31/0.45 = ( d2unsorted @ DU ) )
% 0.31/0.45 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 0.31/0.45 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 0.31/0.45 ( ( ( d2unsorted @ DU1 )
% 0.31/0.45 = ( d2unsorted @ DU2 ) )
% 0.31/0.45 => ( DU1 = DU2 ) )
% 0.31/0.45 & ( mnot
% 0.31/0.45 = ( ^ [X: $i > $o,U: $i] :
% 0.31/0.45 ~ ( X @ U ) ) )
% 0.31/0.45 & ( mor
% 0.31/0.45 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.31/0.45 ( ( X @ U )
% 0.31/0.45 | ( Y @ U ) ) ) )
% 0.31/0.45 & ( mand
% 0.31/0.45 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.31/0.45 ( ( X @ U )
% 0.31/0.45 & ( Y @ U ) ) ) )
% 0.31/0.45 & ( mimplies
% 0.31/0.45 = ( ^ [U: $i > $o,V: $i > $o,Flatten_var_0: $i] :
% 0.31/0.45 ( ~ ( U @ Flatten_var_0 )
% 0.31/0.45 | ( V @ Flatten_var_0 ) ) ) )
% 0.31/0.45 & ( mbox_s4
% 0.31/0.45 = ( ^ [P: $i > $o,X: $i] :
% 0.31/0.45 ! [Y: $i] :
% 0.31/0.45 ( ~ ( irel @ X @ Y )
% 0.31/0.45 | ( P @ Y ) ) ) )
% 0.31/0.45 & ( iatom
% 0.31/0.45 = ( ^ [P: $i > $o,Flatten_var_0: $i] : ( P @ Flatten_var_0 ) ) )
% 0.31/0.45 & ( inot
% 0.31/0.45 = ( ^ [P: $i > $o,Flatten_var_0: $i] :
% 0.31/0.45 ~ ! [Y: $i] :
% 0.31/0.45 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.45 | ( P @ Y ) ) ) )
% 0.31/0.45 & ( iand
% 0.31/0.45 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.31/0.45 ( ( P @ Flatten_var_0 )
% 0.31/0.45 & ( Q @ Flatten_var_0 ) ) ) )
% 0.31/0.45 & ( ior
% 0.31/0.45 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.31/0.45 ( ! [Y: $i] :
% 0.31/0.45 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.45 | ( P @ Y ) )
% 0.31/0.45 | ! [Y: $i] :
% 0.31/0.45 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.45 | ( Q @ Y ) ) ) ) )
% 0.31/0.45 & ( iimplies
% 0.31/0.45 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.31/0.45 ( ~ ! [Y: $i] :
% 0.31/0.45 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.45 | ( P @ Y ) )
% 0.31/0.45 | ! [Y: $i] :
% 0.31/0.45 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.45 | ( Q @ Y ) ) ) ) )
% 0.31/0.45 & ( iimplied
% 0.31/0.45 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.31/0.45 ( ~ ! [Y: $i] :
% 0.31/0.45 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.45 | ( Q @ Y ) )
% 0.31/0.45 | ! [Y: $i] :
% 0.31/0.45 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.45 | ( P @ Y ) ) ) ) )
% 0.31/0.45 & ( iequiv
% 0.31/0.45 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.31/0.45 ( ( ~ ! [Y: $i] :
% 0.31/0.45 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.45 | ( P @ Y ) )
% 0.31/0.45 | ! [Y: $i] :
% 0.31/0.45 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.45 | ( Q @ Y ) ) )
% 0.31/0.45 & ( ~ ! [Y: $i] :
% 0.31/0.45 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.45 | ( Q @ Y ) )
% 0.31/0.45 | ! [Y: $i] :
% 0.31/0.45 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.45 | ( P @ Y ) ) ) ) ) )
% 0.31/0.45 & ( ixor
% 0.31/0.45 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.31/0.45 ~ ! [Y: $i,Bound_variable_747: $i,Bound_variable_754: $i] :
% 0.31/0.45 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.31/0.45 | ( ( ~ ! [Bound_variable_709: $i] :
% 0.31/0.45 ( ~ ( irel @ Y @ Bound_variable_709 )
% 0.31/0.45 | ( P @ Bound_variable_709 ) )
% 0.31/0.45 | ~ ( irel @ Y @ Bound_variable_747 )
% 0.31/0.45 | ( Q @ Bound_variable_747 ) )
% 0.31/0.45 & ( ~ ! [Bound_variable_717: $i] :
% 0.31/0.45 ( ~ ( irel @ Y @ Bound_variable_717 )
% 0.31/0.45 | ( Q @ Bound_variable_717 ) )
% 0.31/0.45 | ~ ( irel @ Y @ Bound_variable_754 )
% 0.31/0.45 | ( P @ Bound_variable_754 ) ) ) ) ) )
% 0.31/0.45 & ( ivalid
% 0.31/0.45 = ( ^ [Phi: $i > $o] :
% 0.31/0.45 ! [W: $i] : ( Phi @ W ) ) )
% 0.31/0.45 & ( isatisfiable
% 0.31/0.45 = ( ^ [Phi: $i > $o] :
% 0.31/0.45 ~ ! [W: $i] :
% 0.31/0.45 ~ ( Phi @ W ) ) )
% 0.31/0.45 & ( icountersatisfiable
% 0.31/0.45 = ( ^ [Phi: $i > $o] :
% 0.31/0.45 ~ ! [W: $i] : ( Phi @ W ) ) )
% 0.31/0.45 & ( iinvalid
% 0.31/0.45 = ( ^ [Phi: $i > $o] :
% 0.31/0.45 ! [W: $i] :
% 0.31/0.45 ~ ( Phi @ W ) ) )
% 0.31/0.45 & ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
% 0.31/0.45 & ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
% 0.31/0.45 & ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(ior,conjecture,
% 0.31/0.45 ( ior
% 0.31/0.45 = ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 ------------------------
% 1.62/1.26 ---- Embedded in THF ---
% 1.62/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.62/1.26 %%% Generated on Tue May 05 09:16:13 EDT 2026
% 1.62/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.62/1.26 %%% Logic specification used:
% 1.62/1.26 %%% thf(spec, logic, $$dhol).
% 1.62/1.26
% 1.62/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.6KYU5pQR7S/DTF2DTF31761.p
% See solution above
% 1.62/1.26 ------------------------
% 1.62/1.27 ---- Cleaned THF ---
% 1.62/1.27 thf(unsorted_type,type,
% 1.62/1.27 unsorted: $tType ).
% 1.62/1.27
% 1.62/1.27 thf(irel_decl,type,
% 1.62/1.27 irel: $i > $i > $o ).
% 1.62/1.27
% 1.62/1.27 thf(mnot_decl,type,
% 1.62/1.27 mnot: ( $i > $o ) > $i > $o ).
% 1.62/1.27
% 1.62/1.27 thf(mor_decl,type,
% 1.62/1.27 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.62/1.27
% 1.62/1.27 thf(mand_decl,type,
% 1.62/1.27 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.62/1.27
% 1.62/1.27 thf(mimplies_decl,type,
% 1.62/1.27 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.62/1.27
% 1.62/1.27 thf(mbox_s4_decl,type,
% 1.62/1.27 mbox_s4: ( $i > $o ) > $i > $o ).
% 1.62/1.27
% 1.62/1.27 thf(iatom_decl,type,
% 1.62/1.27 iatom: ( $i > $o ) > $i > $o ).
% 1.62/1.27
% 1.62/1.27 thf(inot_decl,type,
% 1.62/1.27 inot: ( $i > $o ) > $i > $o ).
% 1.62/1.27
% 1.62/1.27 thf(itrue_decl,type,
% 1.62/1.27 itrue: $i > $o ).
% 1.62/1.27
% 1.62/1.27 thf(ifalse_decl,type,
% 1.62/1.27 ifalse: $i > $o ).
% 1.62/1.27
% 1.62/1.27 thf(iand_decl,type,
% 1.62/1.27 iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.62/1.27
% 1.62/1.27 thf(ior_decl,type,
% 1.62/1.27 ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.62/1.27
% 1.62/1.27 thf(iimplies_decl,type,
% 1.62/1.27 iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.62/1.27
% 1.62/1.27 thf(iimplied_decl,type,
% 1.62/1.27 iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.62/1.27
% 1.62/1.27 thf(iequiv_decl,type,
% 1.62/1.27 iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.62/1.27
% 1.62/1.27 thf(ixor_decl,type,
% 1.62/1.27 ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.62/1.27
% 1.62/1.27 thf(ivalid_decl,type,
% 1.62/1.27 ivalid: ( $i > $o ) > $o ).
% 1.62/1.27
% 1.62/1.27 thf(isatisfiable_decl,type,
% 1.62/1.27 isatisfiable: ( $i > $o ) > $o ).
% 1.62/1.27
% 1.62/1.27 thf(icountersatisfiable_decl,type,
% 1.62/1.27 icountersatisfiable: ( $i > $o ) > $o ).
% 1.62/1.27
% 1.62/1.27 thf(iinvalid_decl,type,
% 1.62/1.27 iinvalid: ( $i > $o ) > $o ).
% 1.62/1.27
% 1.62/1.27 thf(d_unsorted_type,type,
% 1.62/1.27 d_unsorted: $tType ).
% 1.62/1.27
% 1.62/1.27 thf(d2unsorted_decl,type,
% 1.62/1.27 d2unsorted: d_unsorted > $i ).
% 1.62/1.27
% 1.62/1.27 thf(d_unsorted_0_decl,type,
% 1.62/1.27 d_unsorted_0: d_unsorted ).
% 1.62/1.27
% 1.62/1.27 thf(lcl695_1,axiom,
% 1.62/1.27 ( ! [U: $i] :
% 1.62/1.27 ? [DU: d_unsorted] :
% 1.62/1.27 ( U
% 1.62/1.27 = ( d2unsorted @ DU ) )
% 1.62/1.27 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 1.62/1.27 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 1.62/1.27 ( ( ( d2unsorted @ DU1 )
% 1.62/1.27 = ( d2unsorted @ DU2 ) )
% 1.62/1.27 => ( DU1 = DU2 ) )
% 1.62/1.27 & ( mnot
% 1.62/1.27 = ( ^ [X: $i > $o,U: $i] :
% 1.62/1.27 ~ ( X @ U ) ) )
% 1.62/1.27 & ( mor
% 1.62/1.27 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 1.62/1.27 ( ( X @ U )
% 1.62/1.27 | ( Y @ U ) ) ) )
% 1.62/1.27 & ( mand
% 1.62/1.27 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 1.62/1.27 ( ( X @ U )
% 1.62/1.27 & ( Y @ U ) ) ) )
% 1.62/1.27 & ( mimplies
% 1.62/1.27 = ( ^ [U: $i > $o,V: $i > $o,Flatten_var_0: $i] :
% 1.62/1.27 ( ~ ( U @ Flatten_var_0 )
% 1.62/1.27 | ( V @ Flatten_var_0 ) ) ) )
% 1.62/1.27 & ( mbox_s4
% 1.62/1.27 = ( ^ [P: $i > $o,X: $i] :
% 1.62/1.27 ! [Y: $i] :
% 1.62/1.27 ( ~ ( irel @ X @ Y )
% 1.62/1.27 | ( P @ Y ) ) ) )
% 1.62/1.27 & ( iatom
% 1.62/1.27 = ( ^ [P: $i > $o,Flatten_var_0: $i] : ( P @ Flatten_var_0 ) ) )
% 1.62/1.27 & ( inot
% 1.62/1.27 = ( ^ [P: $i > $o,Flatten_var_0: $i] :
% 1.62/1.27 ~ ! [Y: $i] :
% 1.62/1.27 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.62/1.27 | ( P @ Y ) ) ) )
% 1.62/1.27 & ( iand
% 1.62/1.27 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.62/1.27 ( ( P @ Flatten_var_0 )
% 1.62/1.27 & ( Q @ Flatten_var_0 ) ) ) )
% 1.62/1.27 & ( ior
% 1.62/1.27 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.62/1.27 ( ! [Y: $i] :
% 1.62/1.27 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.62/1.27 | ( P @ Y ) )
% 1.62/1.27 | ! [Y: $i] :
% 1.62/1.27 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.62/1.27 | ( Q @ Y ) ) ) ) )
% 1.62/1.27 & ( iimplies
% 1.62/1.27 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.62/1.27 ( ~ ! [Y: $i] :
% 1.62/1.27 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.62/1.27 | ( P @ Y ) )
% 1.62/1.27 | ! [Y: $i] :
% 1.62/1.27 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.62/1.27 | ( Q @ Y ) ) ) ) )
% 1.62/1.27 & ( iimplied
% 1.62/1.27 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.62/1.27 ( ~ ! [Y: $i] :
% 1.62/1.27 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.62/1.27 | ( Q @ Y ) )
% 1.62/1.27 | ! [Y: $i] :
% 1.62/1.27 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.62/1.27 | ( P @ Y ) ) ) ) )
% 1.62/1.27 & ( iequiv
% 1.62/1.27 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.62/1.27 ( ( ~ ! [Y: $i] :
% 1.62/1.27 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.62/1.27 | ( P @ Y ) )
% 1.62/1.27 | ! [Y: $i] :
% 1.62/1.27 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.62/1.27 | ( Q @ Y ) ) )
% 1.62/1.27 & ( ~ ! [Y: $i] :
% 1.62/1.27 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.62/1.27 | ( Q @ Y ) )
% 1.62/1.27 | ! [Y: $i] :
% 1.62/1.27 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.62/1.27 | ( P @ Y ) ) ) ) ) )
% 1.62/1.27 & ( ixor
% 1.62/1.27 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.62/1.27 ~ ! [Y: $i,Bound_variable_747: $i,Bound_variable_754: $i] :
% 1.62/1.27 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.62/1.27 | ( ( ~ ! [Bound_variable_709: $i] :
% 1.62/1.27 ( ~ ( irel @ Y @ Bound_variable_709 )
% 1.62/1.27 | ( P @ Bound_variable_709 ) )
% 1.62/1.27 | ~ ( irel @ Y @ Bound_variable_747 )
% 1.62/1.27 | ( Q @ Bound_variable_747 ) )
% 1.62/1.27 & ( ~ ! [Bound_variable_717: $i] :
% 1.62/1.27 ( ~ ( irel @ Y @ Bound_variable_717 )
% 1.62/1.27 | ( Q @ Bound_variable_717 ) )
% 1.62/1.27 | ~ ( irel @ Y @ Bound_variable_754 )
% 1.62/1.27 | ( P @ Bound_variable_754 ) ) ) ) ) )
% 1.62/1.27 & ( ivalid
% 1.62/1.27 = ( ^ [Phi: $i > $o] :
% 1.62/1.27 ! [W: $i] : ( Phi @ W ) ) )
% 1.62/1.27 & ( isatisfiable
% 1.62/1.27 = ( ^ [Phi: $i > $o] :
% 1.62/1.27 ~ ! [W: $i] :
% 1.62/1.27 ~ ( Phi @ W ) ) )
% 1.62/1.27 & ( icountersatisfiable
% 1.62/1.27 = ( ^ [Phi: $i > $o] :
% 1.62/1.27 ~ ! [W: $i] : ( Phi @ W ) ) )
% 1.62/1.27 & ( iinvalid
% 1.62/1.27 = ( ^ [Phi: $i > $o] :
% 1.62/1.27 ! [W: $i] :
% 1.62/1.27 ~ ( Phi @ W ) ) )
% 1.62/1.27 & ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
% 1.62/1.27 & ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
% 1.62/1.27 & ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ) ).
% 1.62/1.27
% 1.62/1.27 thf(ior,conjecture,
% 1.62/1.27 ( ior
% 1.62/1.27 = ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
% 1.62/1.27 ------------------------
% 1.62/1.28 % (31866)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31761 for (2999ds/183Mi)
% 1.62/1.29 % (31867)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_31761 for (2999ds/4Mi)
% 1.62/1.29 % (31867)Instruction limit reached!
% 1.62/1.29 % (31867)------------------------------
% 1.62/1.29 % (31867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.29 % (31867)Termination reason: Unknown
% 1.62/1.29 % (31867)Termination phase: Property scanning
% 1.62/1.29
% 1.62/1.29 % (31867)Memory used [KB]: 1023
% 1.62/1.29 % (31867)Time elapsed: 0.003 s
% 1.62/1.29 % (31867)Instructions burned: 4 (million)
% 1.62/1.29 % (31867)------------------------------
% 1.62/1.29 % (31867)------------------------------
% 1.62/1.29 % (31868)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_31761 for (2999ds/27Mi)
% 1.62/1.29 % (31869)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31761 for (2999ds/2Mi)
% 1.62/1.29 % (31870)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_31761 for (2999ds/2Mi)
% 1.62/1.29 % (31871)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_31761 for (2999ds/275Mi)
% 1.62/1.29 % (31872)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31761 for (2999ds/18Mi)
% 1.62/1.29 % (31866)First to succeed.
% 1.62/1.29 % (31869)Instruction limit reached!
% 1.62/1.29 % (31869)------------------------------
% 1.62/1.29 % (31869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.29 % (31869)Termination reason: Unknown
% 1.62/1.29 % (31869)Termination phase: shuffling
% 1.62/1.29 % (31870)Instruction limit reached!
% 1.62/1.29 % (31870)------------------------------
% 1.62/1.29 % (31870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.29 % (31870)Termination reason: Unknown
% 1.62/1.29 % (31870)Termination phase: shuffling
% 1.62/1.29
% 1.62/1.29 % (31870)Memory used [KB]: 1023
% 1.62/1.29 % (31870)Time elapsed: 0.003 s
% 1.62/1.29 % (31870)Instructions burned: 2 (million)
% 1.62/1.29 % (31870)------------------------------
% 1.62/1.29 % (31870)------------------------------
% 1.62/1.29
% 1.62/1.29 % (31869)Memory used [KB]: 1023
% 1.62/1.29 % (31869)Time elapsed: 0.003 s
% 1.62/1.29 % (31869)Instructions burned: 2 (million)
% 1.62/1.29 % (31869)------------------------------
% 1.62/1.29 % (31869)------------------------------
% 1.77/1.30 % (31871)Refutation not found, incomplete strategy
% 1.77/1.30 % (31871)------------------------------
% 1.77/1.30 % (31871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.30 % (31871)Termination reason: Refutation not found, incomplete strategy
% 1.77/1.30
% 1.77/1.30 % (31873)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_31761 for (2999ds/3Mi)
% 1.77/1.30
% 1.77/1.30 % (31871)Memory used [KB]: 5500
% 1.77/1.30 % (31871)Time elapsed: 0.005 s
% 1.77/1.30 % (31871)Instructions burned: 5 (million)
% 1.77/1.30 % (31871)------------------------------
% 1.77/1.30 % (31871)------------------------------
% 1.77/1.30 % (31866)Refutation found. Thanks to Tanya!
% 1.77/1.30 % SZS status Theorem for DTF2THF_31761
% 1.77/1.30 % SZS output start Proof for DTF2THF_31761
% 1.77/1.30 thf(type_def_6, type, d_unsorted: $tType).
% 1.77/1.30 thf(func_def_0, type, unsorted: $tType).
% 1.77/1.30 thf(func_def_1, type, irel: $i > $i > $o).
% 1.77/1.30 thf(func_def_2, type, mnot: ($i > $o) > $i > $o).
% 1.77/1.30 thf(func_def_3, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 1.77/1.30 thf(func_def_4, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 1.77/1.30 thf(func_def_5, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 1.77/1.30 thf(func_def_6, type, mbox_s4: ($i > $o) > $i > $o).
% 1.77/1.30 thf(func_def_7, type, iatom: ($i > $o) > $i > $o).
% 1.77/1.30 thf(func_def_8, type, inot: ($i > $o) > $i > $o).
% 1.77/1.30 thf(func_def_9, type, itrue: $i > $o).
% 1.77/1.30 thf(func_def_10, type, ifalse: $i > $o).
% 1.77/1.30 thf(func_def_11, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 1.77/1.30 thf(func_def_12, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 1.77/1.30 thf(func_def_13, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 1.77/1.30 thf(func_def_14, type, iimplied: ($i > $o) > ($i > $o) > $i > $o).
% 1.77/1.30 thf(func_def_15, type, iequiv: ($i > $o) > ($i > $o) > $i > $o).
% 1.77/1.30 thf(func_def_16, type, ixor: ($i > $o) > ($i > $o) > $i > $o).
% 1.77/1.30 thf(func_def_17, type, ivalid: ($i > $o) > $o).
% 1.77/1.30 thf(func_def_18, type, isatisfiable: ($i > $o) > $o).
% 1.77/1.30 thf(func_def_19, type, icountersatisfiable: ($i > $o) > $o).
% 1.77/1.30 thf(func_def_20, type, iinvalid: ($i > $o) > $o).
% 1.77/1.30 thf(func_def_21, type, d_unsorted: $tType).
% 1.77/1.30 thf(func_def_22, type, d2unsorted: d_unsorted > $i).
% 1.77/1.30 thf(func_def_23, type, d_unsorted_0: d_unsorted).
% 1.77/1.30 thf(func_def_39, type, sK0: $i > d_unsorted).
% 1.77/1.30 thf(func_def_41, type, ph2: !>[X0: $tType]:(X0)).
% 1.77/1.30 thf(func_def_42, type, sK3: $i > $o).
% 1.77/1.30 thf(func_def_43, type, sK4: $i > $o).
% 1.77/1.30 thf(f401,plain,(
% 1.77/1.30 $false),
% 1.77/1.30 inference(avatar_sat_refutation,[status(thm)],[f221,f244,f319,f351,f364,f370,f392,f400])).
% 1.77/1.30 thf(f400,plain,(
% 1.77/1.30 ~spl1_1 | ~spl1_6),
% 1.77/1.30 inference(avatar_contradiction_clause,[status(thm)],[f399])).
% 1.77/1.30 thf(f399,plain,(
% 1.77/1.30 $false | (~spl1_1 | ~spl1_6)),
% 1.77/1.30 inference(trivial_inequality_removal,[status(thm)],[f395])).
% 1.77/1.30 thf(f395,plain,(
% 1.77/1.30 ($true = $false) | (~spl1_1 | ~spl1_6)),
% 1.77/1.30 inference(superposition,[status(thm)],[f239,f379])).
% 1.77/1.30 thf(f379,plain,(
% 1.77/1.30 ( ! [X0 : $i] : (($true = (sK3 @ X0))) ) | ~spl1_1),
% 1.77/1.30 inference(superposition,[status(thm)],[f378,f54])).
% 1.77/1.30 thf(f54,plain,(
% 1.77/1.30 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 1.77/1.30 inference(superposition,[status(thm)],[f50,f50])).
% 1.77/1.30 thf(f50,plain,(
% 1.77/1.30 ( ! [X0 : $i] : (((d2unsorted @ d_unsorted_0) = X0)) )),
% 1.77/1.30 inference(superposition,[status(thm)],[f33,f19])).
% 1.77/1.30 thf(f19,plain,(
% 1.77/1.30 ( ! [X4 : d_unsorted] : ((d_unsorted_0 = X4)) )),
% 1.77/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.77/1.30 thf(f15,plain,(
% 1.77/1.30 ! [X0 : d_unsorted,X1 : d_unsorted] : (((d2unsorted @ X1) != (d2unsorted @ X0)) | (X0 = X1)) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & ! [X2 : $i] : ((d2unsorted @ (sK0 @ X2)) = X2) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y2 @ Y5)) | ((((~ (irel @ Y5 @ Y4)) | (Y1 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6))))))) & (((~ (irel @ Y5 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y5 @ Y6)) | (Y1 @ Y6)))))) | (Y0 @ Y3))))))))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))),
% 1.77/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14])).
% 1.77/1.30 thf(f14,plain,(
% 1.77/1.30 ! [X2 : $i] : (? [X3 : d_unsorted] : ((d2unsorted @ X3) = X2) => ((d2unsorted @ (sK0 @ X2)) = X2))),
% 1.77/1.30 introduced(definition,[],[choice_axiom])).
% 1.77/1.30 thf(f13,plain,(
% 1.77/1.30 ! [X0 : d_unsorted,X1 : d_unsorted] : (((d2unsorted @ X1) != (d2unsorted @ X0)) | (X0 = X1)) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & ! [X2 : $i] : ? [X3 : d_unsorted] : ((d2unsorted @ X3) = X2) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y2 @ Y5)) | ((((~ (irel @ Y5 @ Y4)) | (Y1 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6))))))) & (((~ (irel @ Y5 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y5 @ Y6)) | (Y1 @ Y6)))))) | (Y0 @ Y3))))))))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))),
% 1.77/1.30 inference(rectify,[status(thm)],[f12])).
% 1.77/1.30 thf(f12,plain,(
% 1.77/1.30 ! [X0 : d_unsorted,X1 : d_unsorted] : (((d2unsorted @ X1) != (d2unsorted @ X0)) | (X0 = X1)) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & ! [X3 : $i] : ? [X4 : d_unsorted] : ((d2unsorted @ X4) = X3) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y2 @ Y5)) | ((((~ (irel @ Y5 @ Y4)) | (Y1 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6))))))) & (((~ (irel @ Y5 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y5 @ Y6)) | (Y1 @ Y6)))))) | (Y0 @ Y3))))))))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))),
% 1.77/1.30 inference(ennf_transformation,[status(thm)],[f11])).
% 1.77/1.30 thf(f11,plain,(
% 1.77/1.30 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y2 @ Y5)) | ((((~ (irel @ Y5 @ Y4)) | (Y1 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6))))))) & (((~ (irel @ Y5 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y5 @ Y6)) | (Y1 @ Y6)))))) | (Y0 @ Y3))))))))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & ! [X3 : $i] : ? [X4 : d_unsorted] : ((d2unsorted @ X4) = X3) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : (((d2unsorted @ X1) = (d2unsorted @ X0)) => (X0 = X1)) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1)))))),
% 1.77/1.30 inference(flattening,[status(thm)],[f10])).
% 1.77/1.30 thf(f10,plain,(
% 1.77/1.30 (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & ! [X0 : d_unsorted,X1 : d_unsorted] : (((d2unsorted @ X1) = (d2unsorted @ X0)) => (X0 = X1)) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ~((ifalse @ (d2unsorted @ d_unsorted_0)) = $true) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ! [X3 : $i] : ? [X4 : d_unsorted] : ((d2unsorted @ X4) = X3) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y2 @ Y5)) | ((((~ (irel @ Y5 @ Y4)) | (Y1 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6))))))) & (((~ (irel @ Y5 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y5 @ Y6)) | (Y1 @ Y6)))))) | (Y0 @ Y3))))))))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 1.77/1.30 inference(rectify,[status(thm)],[f8])).
% 1.77/1.30 thf(f8,plain,(
% 1.77/1.30 (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & ! [X20 : d_unsorted,X21 : d_unsorted] : (((d2unsorted @ X21) = (d2unsorted @ X20)) => (X20 = X21)) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ~((ifalse @ (d2unsorted @ d_unsorted_0)) = $true) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & ! [X30 : d_unsorted] : (d_unsorted_0 = X30) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ! [X33 : $i] : ? [X34 : d_unsorted] : ((d2unsorted @ X34) = X33) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y2 @ Y5)) | ((((~ (irel @ Y5 @ Y4)) | (Y1 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6))))))) & (((~ (irel @ Y5 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y5 @ Y6)) | (Y1 @ Y6)))))) | (Y0 @ Y3))))))))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 1.77/1.30 inference(fool_elimination,[status(thm)],[f7])).
% 1.77/1.30 thf(f7,plain,(
% 1.77/1.30 ((^[X0 : $i > $o, X1 : $i] : (~! [X2 : $i] : ((X0 @ X2) | ~(irel @ X1 @ X2)))) = inot) & ((^[X3 : $i > $o] : (~! [X4 : $i] : (X3 @ X4))) = icountersatisfiable) & (iatom = (^[X5 : $i > $o, X6 : $i] : (X5 @ X6))) & (itrue @ (d2unsorted @ d_unsorted_0)) & ((^[X7 : $i > $o, X8 : $i > $o, X9 : $i] : ((X8 @ X9) & (X7 @ X9))) = mand) & (mimplies = (^[X10 : $i > $o, X11 : $i > $o, X12 : $i] : ((X11 @ X12) | ~(X10 @ X12)))) & (iequiv = (^[X13 : $i > $o, X14 : $i > $o, X15 : $i] : ((~! [X16 : $i] : ((X14 @ X16) | ~(irel @ X15 @ X16)) | ! [X17 : $i] : ((X13 @ X17) | ~(irel @ X15 @ X17))) & (~! [X18 : $i] : (~(irel @ X15 @ X18) | (X13 @ X18)) | ! [X19 : $i] : (~(irel @ X15 @ X19) | (X14 @ X19)))))) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ! [X20 : d_unsorted,X21 : d_unsorted] : (((d2unsorted @ X21) = (d2unsorted @ X20)) => (X20 = X21)) & ((^[X22 : $i > $o, X23 : $i > $o, X24 : $i] : ((X22 @ X24) & (X23 @ X24))) = iand) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & ((^[X25 : $i > $o, X26 : $i > $o, X27 : $i] : (~! [X28 : $i] : ((X26 @ X28) | ~(irel @ X27 @ X28)) | ! [X29 : $i] : (~(irel @ X27 @ X29) | (X25 @ X29)))) = iimplied) & ! [X30 : d_unsorted] : (d_unsorted_0 = X30) & ((^[X31 : $i > $o] : (~! [X32 : $i] : ~(X31 @ X32))) = isatisfiable) & ! [X33 : $i] : ? [X34 : d_unsorted] : ((d2unsorted @ X34) = X33) & (mor = (^[X35 : $i > $o, X36 : $i > $o, X37 : $i] : ((X35 @ X37) | (X36 @ X37)))) & ((^[X38 : $i > $o, X39 : $i > $o, X40 : $i] : (! [X41 : $i] : (~(irel @ X40 @ X41) | (X38 @ X41)) | ! [X42 : $i] : (~(irel @ X40 @ X42) | (X39 @ X42)))) = ior) & (iinvalid = (^[X43 : $i > $o] : (! [X44 : $i] : ~(X43 @ X44)))) & ((^[X45 : $i > $o, X46 : $i > $o, X47 : $i] : (~! [X48 : $i,X49 : $i,X50 : $i] : ((((X45 @ X50) | ~! [X51 : $i] : ((X46 @ X51) | ~(irel @ X48 @ X51)) | ~(irel @ X48 @ X50)) & (~! [X52 : $i] : (~(irel @ X48 @ X52) | (X45 @ X52)) | (X46 @ X49) | ~(irel @ X48 @ X49))) | ~(irel @ X47 @ X48)))) = ixor) & ((^[X53 : $i > $o, X54 : $i > $o, X55 : $i] : (! [X56 : $i] : (~(irel @ X55 @ X56) | (X54 @ X56)) | ~! [X57 : $i] : ((X53 @ X57) | ~(irel @ X55 @ X57)))) = iimplies) & ((^[X58 : $i > $o, X59 : $i] : (~(X58 @ X59))) = mnot) & (ivalid = (^[X60 : $i > $o] : (! [X61 : $i] : (X60 @ X61)))) & (mbox_s4 = (^[X62 : $i > $o, X63 : $i] : (! [X64 : $i] : ((X62 @ X64) | ~(irel @ X63 @ X64)))))),
% 1.77/1.30 inference(rectify,[status(thm)],[f1])).
% 1.77/1.30 thf(f1,axiom,(
% 1.77/1.30 ((^[X8 : $i > $o, X7 : $i] : (~! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)))) = inot) & ((^[X14 : $i > $o] : (~! [X15 : $i] : (X14 @ X15))) = icountersatisfiable) & (iatom = (^[X8 : $i > $o, X7 : $i] : (X8 @ X7))) & (itrue @ (d2unsorted @ d_unsorted_0)) & ((^[X4 : $i > $o, X5 : $i > $o, X0 : $i] : ((X5 @ X0) & (X4 @ X0))) = mand) & (mimplies = (^[X0 : $i > $o, X6 : $i > $o, X7 : $i] : ((X6 @ X7) | ~(X0 @ X7)))) & (iequiv = (^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : ((~! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5))) & (~! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)) | ! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)))))) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ! [X3 : d_unsorted,X2 : d_unsorted] : (((d2unsorted @ X2) = (d2unsorted @ X3)) => (X2 = X3)) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : ((X8 @ X7) & (X9 @ X7))) = iand) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (~! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)))) = iimplied) & ! [X1 : d_unsorted] : (d_unsorted_0 = X1) & ((^[X14 : $i > $o] : (~! [X15 : $i] : ~(X14 @ X15))) = isatisfiable) & ! [X0 : $i] : ? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0) & (mor = (^[X4 : $i > $o, X5 : $i > $o, X0 : $i] : ((X4 @ X0) | (X5 @ X0)))) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)) | ! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)))) = ior) & (iinvalid = (^[X14 : $i > $o] : (! [X15 : $i] : ~(X14 @ X15)))) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (~! [X5 : $i,X10 : $i,X11 : $i] : ((((X8 @ X11) | ~! [X13 : $i] : ((X9 @ X13) | ~(irel @ X5 @ X13)) | ~(irel @ X5 @ X11)) & (~! [X12 : $i] : (~(irel @ X5 @ X12) | (X8 @ X12)) | (X9 @ X10) | ~(irel @ X5 @ X10))) | ~(irel @ X7 @ X5)))) = ixor) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)) | ~! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)))) = iimplies) & ((^[X4 : $i > $o, X0 : $i] : (~(X4 @ X0))) = mnot) & (ivalid = (^[X14 : $i > $o] : (! [X15 : $i] : (X14 @ X15)))) & (mbox_s4 = (^[X8 : $i > $o, X4 : $i] : (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X4 @ X5)))))),
% 1.77/1.30 file('/export/starexec/sandbox2/tmp/tmp.6KYU5pQR7S/DTF2THF_31761.p',lcl695_1)).
% 1.77/1.30 thf(f33,plain,(
% 1.77/1.30 ( ! [X2 : $i] : (((d2unsorted @ (sK0 @ X2)) = X2)) )),
% 1.77/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.77/1.30 thf(f378,plain,(
% 1.77/1.30 ($true = (sK3 @ sK5)) | ~spl1_1),
% 1.77/1.30 inference(trivial_inequality_removal,[status(thm)],[f376])).
% 1.77/1.30 thf(f376,plain,(
% 1.77/1.30 ($true = $false) | ($true = (sK3 @ sK5)) | ~spl1_1),
% 1.77/1.30 inference(superposition,[status(thm)],[f120,f217])).
% 1.77/1.30 thf(f217,plain,(
% 1.77/1.30 ( ! [X4 : $i] : (((irel @ sK5 @ X4) = $false) | ($true = (sK3 @ X4))) ) | ~spl1_1),
% 1.77/1.30 inference(avatar_component_clause,[status(thm)],[f216])).
% 1.77/1.30 thf(f216,definition,(
% 1.77/1.30 spl1_1 <=> ! [X4 : $i] : (((irel @ sK5 @ X4) = $false) | ($true = (sK3 @ X4)))),
% 1.77/1.30 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.77/1.30 thf(f120,plain,(
% 1.77/1.30 ( ! [X0 : $i] : (($true = (irel @ X0 @ X0))) )),
% 1.77/1.30 inference(superposition,[status(thm)],[f38,f54])).
% 1.77/1.30 thf(f38,plain,(
% 1.77/1.30 ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true)),
% 1.77/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.77/1.30 thf(f239,plain,(
% 1.77/1.30 ((sK3 @ sK16) = $false) | ~spl1_6),
% 1.77/1.30 inference(avatar_component_clause,[status(thm)],[f237])).
% 1.77/1.30 thf(f237,definition,(
% 1.77/1.30 spl1_6 <=> ((sK3 @ sK16) = $false)),
% 1.77/1.30 introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition])).
% 1.77/1.30 thf(f392,plain,(
% 1.77/1.30 ~spl1_1 | ~spl1_7),
% 1.77/1.30 inference(avatar_contradiction_clause,[status(thm)],[f391])).
% 1.77/1.30 thf(f391,plain,(
% 1.77/1.30 $false | (~spl1_1 | ~spl1_7)),
% 1.77/1.30 inference(trivial_inequality_removal,[status(thm)],[f382])).
% 1.77/1.30 thf(f382,plain,(
% 1.77/1.30 ($true = $false) | (~spl1_1 | ~spl1_7)),
% 1.77/1.30 inference(superposition,[status(thm)],[f379,f243])).
% 1.77/1.30 thf(f243,plain,(
% 1.77/1.30 ((sK3 @ sK15) = $false) | ~spl1_7),
% 1.77/1.30 inference(avatar_component_clause,[status(thm)],[f241])).
% 1.77/1.30 thf(f241,definition,(
% 1.77/1.30 spl1_7 <=> ((sK3 @ sK15) = $false)),
% 1.77/1.30 introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition])).
% 1.77/1.30 thf(f370,plain,(
% 1.77/1.30 spl1_12 | ~spl1_23),
% 1.77/1.30 inference(avatar_contradiction_clause,[status(thm)],[f369])).
% 1.77/1.30 thf(f369,plain,(
% 1.77/1.30 $false | (spl1_12 | ~spl1_23)),
% 1.77/1.30 inference(subsumption_resolution,[status(thm)],[f318,f352])).
% 1.77/1.30 thf(f352,plain,(
% 1.77/1.30 ( ! [X0 : $i] : (((sK4 @ X0) != $false)) ) | spl1_12),
% 1.77/1.30 inference(superposition,[status(thm)],[f266,f54])).
% 1.77/1.30 thf(f266,plain,(
% 1.77/1.30 ((sK4 @ sK12) != $false) | spl1_12),
% 1.77/1.30 inference(avatar_component_clause,[status(thm)],[f265])).
% 1.77/1.30 thf(f265,definition,(
% 1.77/1.30 spl1_12 <=> ((sK4 @ sK12) = $false)),
% 1.77/1.30 introduced(definition,[new_symbols(naming,[spl1_12])],[avatar_definition])).
% 1.77/1.30 thf(f318,plain,(
% 1.77/1.30 ((sK4 @ sK8) = $false) | ~spl1_23),
% 1.77/1.30 inference(avatar_component_clause,[status(thm)],[f316])).
% 1.77/1.30 thf(f316,definition,(
% 1.77/1.30 spl1_23 <=> ((sK4 @ sK8) = $false)),
% 1.77/1.30 introduced(definition,[new_symbols(naming,[spl1_23])],[avatar_definition])).
% 1.77/1.30 thf(f364,plain,(
% 1.77/1.30 ~spl1_2 | ~spl1_22),
% 1.77/1.30 inference(avatar_contradiction_clause,[status(thm)],[f363])).
% 1.77/1.30 thf(f363,plain,(
% 1.77/1.30 $false | (~spl1_2 | ~spl1_22)),
% 1.77/1.30 inference(trivial_inequality_removal,[status(thm)],[f359])).
% 1.77/1.30 thf(f359,plain,(
% 1.77/1.30 ($true = $false) | (~spl1_2 | ~spl1_22)),
% 1.77/1.30 inference(superposition,[status(thm)],[f313,f340])).
% 1.77/1.30 thf(f340,plain,(
% 1.77/1.30 ( ! [X0 : $i] : (($true = (sK4 @ X0))) ) | ~spl1_2),
% 1.77/1.30 inference(superposition,[status(thm)],[f339,f54])).
% 1.77/1.30 thf(f339,plain,(
% 1.77/1.30 ($true = (sK4 @ sK5)) | ~spl1_2),
% 1.77/1.30 inference(trivial_inequality_removal,[status(thm)],[f337])).
% 1.77/1.30 thf(f337,plain,(
% 1.77/1.30 ($true = (sK4 @ sK5)) | ($true = $false) | ~spl1_2),
% 1.77/1.30 inference(superposition,[status(thm)],[f120,f220])).
% 1.77/1.30 thf(f220,plain,(
% 1.77/1.30 ( ! [X1 : $i] : (((irel @ sK5 @ X1) = $false) | ($true = (sK4 @ X1))) ) | ~spl1_2),
% 1.77/1.30 inference(avatar_component_clause,[status(thm)],[f219])).
% 1.77/1.30 thf(f219,definition,(
% 1.77/1.30 spl1_2 <=> ! [X1 : $i] : (((irel @ sK5 @ X1) = $false) | ($true = (sK4 @ X1)))),
% 1.77/1.30 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.77/1.30 thf(f313,plain,(
% 1.77/1.30 ((sK4 @ sK6) = $false) | ~spl1_22),
% 1.77/1.30 inference(avatar_component_clause,[status(thm)],[f311])).
% 1.77/1.30 thf(f311,definition,(
% 1.77/1.30 spl1_22 <=> ((sK4 @ sK6) = $false)),
% 1.77/1.30 introduced(definition,[new_symbols(naming,[spl1_22])],[avatar_definition])).
% 1.77/1.30 thf(f351,plain,(
% 1.77/1.30 ~spl1_2 | ~spl1_12),
% 1.77/1.30 inference(avatar_contradiction_clause,[status(thm)],[f350])).
% 1.77/1.30 thf(f350,plain,(
% 1.77/1.30 $false | (~spl1_2 | ~spl1_12)),
% 1.77/1.30 inference(trivial_inequality_removal,[status(thm)],[f346])).
% 1.77/1.30 thf(f346,plain,(
% 1.77/1.30 ($true = $false) | (~spl1_2 | ~spl1_12)),
% 1.77/1.30 inference(superposition,[status(thm)],[f267,f340])).
% 1.77/1.30 thf(f267,plain,(
% 1.77/1.30 ((sK4 @ sK12) = $false) | ~spl1_12),
% 1.77/1.30 inference(avatar_component_clause,[status(thm)],[f265])).
% 1.77/1.30 thf(f319,plain,(
% 1.77/1.30 spl1_23 | spl1_22),
% 1.77/1.30 inference(avatar_split_clause,[status(thm)],[f146,f311,f316])).
% 1.77/1.30 thf(f146,plain,(
% 1.77/1.30 ((sK4 @ sK6) = $false) | ((sK4 @ sK8) = $false)),
% 1.77/1.30 inference(binary_proxy_clausification,[status(thm)],[f144])).
% 1.77/1.30 thf(f144,plain,(
% 1.77/1.30 ((sK4 @ sK6) = $false) | (((sK4 @ sK8) | (~ (irel @ sK5 @ sK8))) = $false)),
% 1.77/1.30 inference(beta_eta_normalization,[status(thm)],[f143])).
% 1.77/1.30 thf(f143,plain,(
% 1.77/1.30 (((^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK5 @ Y0)))) @ sK8) = $false) | ((sK4 @ sK6) = $false)),
% 1.77/1.30 inference(sigma_clausification,[status(thm)],[f135])).
% 1.77/1.30 thf(f135,plain,(
% 1.77/1.30 ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK5 @ Y0))))) = $false) | ((sK4 @ sK6) = $false)),
% 1.77/1.30 inference(binary_proxy_clausification,[status(thm)],[f134])).
% 1.77/1.30 thf(f134,plain,(
% 1.77/1.30 (((~ (irel @ sK5 @ sK6)) | (sK4 @ sK6)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK5 @ Y0))))) = $false)),
% 1.77/1.30 inference(beta_eta_normalization,[status(thm)],[f133])).
% 1.77/1.30 thf(f133,plain,(
% 1.77/1.30 ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK5 @ Y0))))) = $false) | (((^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK4 @ Y0))) @ sK6) = $false)),
% 1.77/1.30 inference(sigma_clausification,[status(thm)],[f132])).
% 1.77/1.30 thf(f132,plain,(
% 1.77/1.30 ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK4 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK5 @ Y0))))) = $false)),
% 1.77/1.30 inference(binary_proxy_clausification,[status(thm)],[f130])).
% 1.77/1.30 thf(f130,plain,(
% 1.77/1.30 (((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK5 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK5 @ Y0)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK4 @ Y0)))) = $false)),
% 1.77/1.30 inference(binary_proxy_clausification,[status(thm)],[f128])).
% 1.77/1.30 thf(f128,plain,(
% 1.77/1.30 (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK4 @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK5 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK5 @ Y0)))))) = $false)),
% 1.77/1.30 inference(binary_proxy_clausification,[status(thm)],[f126])).
% 1.77/1.30 thf(f126,plain,(
% 1.77/1.30 (((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK5 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK5 @ Y0)))))) != ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK4 @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0))))))),
% 1.77/1.30 inference(beta_eta_normalization,[status(thm)],[f125])).
% 1.77/1.30 thf(f125,plain,(
% 1.77/1.30 (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))))) @ sK5) != ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))) @ sK5))),
% 1.77/1.30 inference(negative_extensionality,[status(thm)],[f124])).
% 1.77/1.30 thf(f124,plain,(
% 1.77/1.30 ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (irel @ Y0 @ Y1))))))) != (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK4 @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK3 @ Y1)))))))),
% 1.77/1.30 inference(beta_eta_normalization,[status(thm)],[f123])).
% 1.77/1.30 thf(f123,plain,(
% 1.77/1.30 (((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK3 @ Y2)))))))) @ sK4) != ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) @ sK4))),
% 1.77/1.30 inference(negative_extensionality,[status(thm)],[f122])).
% 1.77/1.30 thf(f122,plain,(
% 1.77/1.30 ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK3 @ Y2)))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (irel @ Y1 @ Y2))))))))))),
% 1.77/1.30 inference(beta_eta_normalization,[status(thm)],[f121])).
% 1.77/1.30 thf(f121,plain,(
% 1.77/1.30 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))) @ sK3) != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))) @ sK3))),
% 1.77/1.30 inference(negative_extensionality,[status(thm)],[f41])).
% 1.77/1.30 thf(f41,plain,(
% 1.77/1.30 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))),
% 1.77/1.30 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.77/1.30 thf(f40,plain,(
% 1.77/1.30 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y2 @ Y4))))))) @ Y1))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))),
% 1.77/1.30 inference(definition_unfolding,[status(thm)],[f16,f17,f28,f23,f23])).
% 1.77/1.30 thf(f23,plain,(
% 1.77/1.30 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 1.77/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.77/1.30 thf(f28,plain,(
% 1.77/1.30 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 1.77/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.77/1.30 thf(f17,plain,(
% 1.77/1.30 (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))),
% 1.77/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.77/1.30 thf(f16,plain,(
% 1.77/1.30 (ior != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 1.77/1.30 inference(cnf_transformation,[status(thm)],[f9])).
% 1.77/1.30 thf(f9,plain,(
% 1.77/1.30 (ior != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 1.77/1.30 inference(flattening,[status(thm)],[f6])).
% 1.77/1.30 thf(f6,plain,(
% 1.77/1.30 ~(ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 1.77/1.30 inference(fool_elimination,[status(thm)],[f5])).
% 1.77/1.30 thf(f5,plain,(
% 1.77/1.30 ~(ior = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mbox_s4 @ X0) @ (mbox_s4 @ X1))))),
% 1.77/1.30 inference(rectify,[status(thm)],[f3])).
% 1.77/1.30 thf(f3,negated_conjecture,(
% 1.77/1.30 ~(ior = (^[X8 : $i > $o, X9 : $i > $o] : (mor @ (mbox_s4 @ X8) @ (mbox_s4 @ X9))))),
% 1.77/1.30 inference(negated_conjecture,[status(cth)],[f2])).
% 1.77/1.30 thf(f2,conjecture,(
% 1.77/1.30 (ior = (^[X8 : $i > $o, X9 : $i > $o] : (mor @ (mbox_s4 @ X8) @ (mbox_s4 @ X9))))),
% 1.77/1.30 file('/export/starexec/sandbox2/tmp/tmp.6KYU5pQR7S/DTF2THF_31761.p',ior)).
% 1.77/1.30 thf(f244,plain,(
% 1.77/1.30 spl1_6 | spl1_7),
% 1.77/1.30 inference(avatar_split_clause,[status(thm)],[f188,f241,f237])).
% 1.77/1.30 thf(f188,plain,(
% 1.77/1.30 ((sK3 @ sK15) = $false) | ((sK3 @ sK16) = $false)),
% 1.77/1.30 inference(binary_proxy_clausification,[status(thm)],[f187])).
% 1.77/1.30 thf(f187,plain,(
% 1.77/1.30 ((sK3 @ sK15) = $false) | ($false = ((~ (irel @ sK5 @ sK16)) | (sK3 @ sK16)))),
% 1.77/1.30 inference(beta_eta_normalization,[status(thm)],[f186])).
% 1.77/1.30 thf(f186,plain,(
% 1.77/1.30 (((^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0))) @ sK16) = $false) | ((sK3 @ sK15) = $false)),
% 1.77/1.30 inference(sigma_clausification,[status(thm)],[f185])).
% 1.77/1.30 thf(f185,plain,(
% 1.77/1.30 ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0)))) = $false) | ((sK3 @ sK15) = $false)),
% 1.77/1.30 inference(binary_proxy_clausification,[status(thm)],[f183])).
% 1.77/1.30 thf(f183,plain,(
% 1.77/1.30 (((sK3 @ sK15) | (~ (irel @ sK5 @ sK15))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0)))) = $false)),
% 1.77/1.30 inference(beta_eta_normalization,[status(thm)],[f182])).
% 1.77/1.30 thf(f182,plain,(
% 1.77/1.30 ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0)))) = $false) | (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK5 @ Y0)))) @ sK15) = $false)),
% 1.77/1.30 inference(sigma_clausification,[status(thm)],[f164])).
% 1.77/1.30 thf(f164,plain,(
% 1.77/1.30 ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK5 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0)))) = $false)),
% 1.77/1.30 inference(binary_proxy_clausification,[status(thm)],[f129])).
% 1.77/1.30 thf(f129,plain,(
% 1.77/1.30 (((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK5 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK5 @ Y0)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0)))) = $false)),
% 1.77/1.30 inference(binary_proxy_clausification,[status(thm)],[f128])).
% 1.77/1.30 thf(f221,plain,(
% 1.77/1.30 spl1_1 | spl1_1 | spl1_2 | spl1_2),
% 1.77/1.30 inference(avatar_split_clause,[status(thm)],[f214,f219,f219,f216,f216])).
% 1.77/1.30 thf(f214,plain,(
% 1.77/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((irel @ sK5 @ X4) = $false) | ((irel @ sK5 @ X1) = $false) | ((sK3 @ X2) = $true) | ($true = (sK4 @ X3)) | ((irel @ sK5 @ X3) = $false) | ((irel @ sK5 @ X2) = $false) | ($true = (sK4 @ X1)) | ($true = (sK3 @ X4))) )),
% 1.77/1.30 inference(not_proxy_clausification,[status(thm)],[f213])).
% 1.77/1.30 thf(f213,plain,(
% 1.77/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (sK4 @ X1)) | ($true = (sK3 @ X4)) | ($true = (~ (irel @ sK5 @ X4))) | ((irel @ sK5 @ X3) = $false) | ((sK3 @ X2) = $true) | ((irel @ sK5 @ X1) = $false) | ($true = (sK4 @ X3)) | ((irel @ sK5 @ X2) = $false)) )),
% 1.77/1.30 inference(binary_proxy_clausification,[status(thm)],[f212])).
% 1.77/1.30 thf(f212,plain,(
% 1.77/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((irel @ sK5 @ X1) = $false) | ($true = ((~ (irel @ sK5 @ X4)) | (sK3 @ X4))) | ($true = (sK4 @ X3)) | ((irel @ sK5 @ X3) = $false) | ($true = (sK4 @ X1)) | ((sK3 @ X2) = $true) | ((irel @ sK5 @ X2) = $false)) )),
% 1.77/1.30 inference(not_proxy_clausification,[status(thm)],[f211])).
% 1.77/1.30 thf(f211,plain,(
% 1.77/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (~ (irel @ sK5 @ X2))) | ((irel @ sK5 @ X3) = $false) | ((sK3 @ X2) = $true) | ($true = (sK4 @ X1)) | ($true = ((~ (irel @ sK5 @ X4)) | (sK3 @ X4))) | ($true = (sK4 @ X3)) | ((irel @ sK5 @ X1) = $false)) )),
% 1.77/1.30 inference(beta_eta_normalization,[status(thm)],[f210])).
% 1.77/1.30 thf(f210,plain,(
% 1.77/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (sK4 @ X1)) | ((irel @ sK5 @ X1) = $false) | ($true = (sK4 @ X3)) | ((sK3 @ X2) = $true) | ($true = ((^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0))) @ X4)) | ($true = (~ (irel @ sK5 @ X2))) | ((irel @ sK5 @ X3) = $false)) )),
% 1.77/1.30 inference(pi_clausification,[status(thm)],[f209])).
% 1.77/1.30 thf(f209,plain,(
% 1.77/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0))))) | ($true = (sK4 @ X3)) | ((irel @ sK5 @ X1) = $false) | ($true = (sK4 @ X1)) | ((irel @ sK5 @ X3) = $false) | ((sK3 @ X2) = $true) | ($true = (~ (irel @ sK5 @ X2)))) )),
% 1.77/1.30 inference(not_proxy_clausification,[status(thm)],[f208])).
% 1.77/1.30 thf(f208,plain,(
% 1.77/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ sK5 @ X1) = $false) | ($true = (~ (irel @ sK5 @ X3))) | ((sK3 @ X2) = $true) | ($true = (~ (irel @ sK5 @ X2))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0))))) | ($true = (sK4 @ X1)) | ($true = (sK4 @ X3))) )),
% 1.77/1.30 inference(not_proxy_clausification,[status(thm)],[f207])).
% 1.77/1.30 thf(f207,plain,(
% 1.77/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK4 @ X1)) | ($true = (sK4 @ X3)) | ($true = (~ (irel @ sK5 @ X1))) | ((sK3 @ X2) = $true) | ($true = (~ (irel @ sK5 @ X2))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0))))) | ($true = (~ (irel @ sK5 @ X3)))) )),
% 1.77/1.30 inference(binary_proxy_clausification,[status(thm)],[f206])).
% 1.77/1.30 thf(f206,plain,(
% 1.77/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((sK4 @ X1) | (~ (irel @ sK5 @ X1)))) | ($true = (~ (irel @ sK5 @ X2))) | ($true = (~ (irel @ sK5 @ X3))) | ((sK3 @ X2) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0))))) | ($true = (sK4 @ X3))) )),
% 1.77/1.30 inference(binary_proxy_clausification,[status(thm)],[f205])).
% 1.77/1.30 thf(f205,plain,(
% 1.77/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((~ (irel @ sK5 @ X3)) | (sK4 @ X3))) | ($true = (~ (irel @ sK5 @ X2))) | ($true = ((sK4 @ X1) | (~ (irel @ sK5 @ X1)))) | ((sK3 @ X2) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0)))))) )),
% 1.77/1.30 inference(beta_eta_normalization,[status(thm)],[f204])).
% 1.77/1.30 thf(f204,plain,(
% 1.77/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0))))) | ((sK3 @ X2) = $true) | ($true = (~ (irel @ sK5 @ X2))) | ($true = ((^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK4 @ Y0))) @ X3)) | ($true = ((sK4 @ X1) | (~ (irel @ sK5 @ X1))))) )),
% 1.77/1.30 inference(pi_clausification,[status(thm)],[f203])).
% 1.77/1.30 thf(f203,plain,(
% 1.77/1.30 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK4 @ Y0))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0))))) | ($true = (~ (irel @ sK5 @ X2))) | ((sK3 @ X2) = $true) | ($true = ((sK4 @ X1) | (~ (irel @ sK5 @ X1))))) )),
% 1.77/1.30 inference(binary_proxy_clausification,[status(thm)],[f202])).
% 1.77/1.30 thf(f202,plain,(
% 1.77/1.30 ( ! [X2 : $i,X1 : $i] : (($true = ((sK3 @ X2) | (~ (irel @ sK5 @ X2)))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0))))) | ($true = ((sK4 @ X1) | (~ (irel @ sK5 @ X1)))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK4 @ Y0)))))) )),
% 1.77/1.30 inference(beta_eta_normalization,[status(thm)],[f201])).
% 1.77/1.30 thf(f201,plain,(
% 1.77/1.30 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK5 @ Y0)))) @ X2)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK4 @ Y0))))) | ($true = ((sK4 @ X1) | (~ (irel @ sK5 @ X1)))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0)))))) )),
% 1.77/1.30 inference(pi_clausification,[status(thm)],[f200])).
% 1.77/1.30 thf(f200,plain,(
% 1.77/1.30 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK5 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK4 @ Y0))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0))))) | ($true = ((sK4 @ X1) | (~ (irel @ sK5 @ X1))))) )),
% 1.77/1.30 inference(beta_eta_normalization,[status(thm)],[f199])).
% 1.77/1.30 thf(f199,plain,(
% 1.77/1.30 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK4 @ Y0))))) | ($true = ((^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK5 @ Y0)))) @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK5 @ Y0))))))) )),
% 1.77/1.30 inference(pi_clausification,[status(thm)],[f198])).
% 1.77/1.30 thf(f198,plain,(
% 1.77/1.30 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK5 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK4 @ Y0))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK5 @ Y0))))))),
% 1.77/1.30 inference(binary_proxy_clausification,[status(thm)],[f197])).
% 1.77/1.30 thf(f197,plain,(
% 1.77/1.30 ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK4 @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK5 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK5 @ Y0))))))),
% 1.77/1.30 inference(binary_proxy_clausification,[status(thm)],[f127])).
% 1.77/1.30 thf(f127,plain,(
% 1.77/1.30 (((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (irel @ sK5 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (irel @ sK5 @ Y0)))))) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK4 @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK3 @ Y0))))))),
% 1.77/1.30 inference(binary_proxy_clausification,[status(thm)],[f126])).
% 1.77/1.30 % SZS output end Proof for DTF2THF_31761
% 1.77/1.30 % (31866)------------------------------
% 1.77/1.30 % (31866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.30 % (31866)Termination reason: Refutation
% 1.77/1.30
% 1.77/1.30 % (31866)Memory used [KB]: 5884
% 1.77/1.30 % (31866)Time elapsed: 0.014 s
% 1.77/1.30 % (31866)Instructions burned: 24 (million)
% 1.77/1.30 % (31866)------------------------------
% 1.77/1.30 % (31866)------------------------------
% 1.77/1.30 % (31865)Success in time 0.015 s
%------------------------------------------------------------------------------