%------------------------------------------------------------------------------
% 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 : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:58:55 PM UTC 2026
% Result : Theorem 1.78s 1.31s
% Output : Refutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 773 ( 199 equ; 0 cnn)
% Maximal formula atoms : 24 ( 36 avg)
% Number of connectives : 2105 ( 331 ~; 276 |; 208 &;1111 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 10 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 237 ( 237 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 23 usr; 4 con; 0-3 aty)
% ( 173 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 618 ( 523 ^; 87 !; 8 ?; 618 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
d_unsorted: $tType ).
thf(func_def_0,type,
unsorted: $tType ).
thf(func_def_1,type,
irel: $i > $i > $o ).
thf(func_def_2,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
iatom: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
inot: ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
itrue: $i > $o ).
thf(func_def_10,type,
ifalse: $i > $o ).
thf(func_def_11,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_16,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
ivalid: ( $i > $o ) > $o ).
thf(func_def_18,type,
isatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_20,type,
iinvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
d_unsorted: $tType ).
thf(func_def_22,type,
d2unsorted: d_unsorted > $i ).
thf(func_def_23,type,
d_unsorted_0: d_unsorted ).
thf(func_def_41,type,
sK0: $i > d_unsorted ).
thf(f42,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ~ ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( irel @ Y3 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( irel @ Y3 @ Y4 ) ) )
@ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f16,f29,f36,f34,f34]) ).
thf(f34,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
!= ( d2unsorted @ X0 ) )
| ( X0 = X1 ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y4 )
| ~ ( irel @ Y3 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( irel @ Y3 @ Y4 ) ) ) ) ) ) )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( ( Y1 @ Y6 )
| ~ ( irel @ Y5 @ Y7 )
| ~ ( irel @ Y7 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( Y0 @ Y8 )
| ~ ( irel @ Y7 @ Y8 ) ) ) )
& ( ( Y0 @ Y4 )
| ~ ( irel @ Y3 @ Y4 )
| ~ ( irel @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( Y1 @ Y8 )
| ~ ( irel @ Y3 @ Y8 ) ) ) ) )
| ~ ( irel @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,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 ) ) ) ) ) )
& ! [X2: d_unsorted] : ( d_unsorted_0 = X2 )
& ! [X3: $i] :
( ( d2unsorted @ ( sK0 @ X3 ) )
= X3 )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14]) ).
thf(f14,plain,
! [X3: $i] :
( ? [X4: d_unsorted] :
( ( d2unsorted @ X4 )
= X3 )
=> ( ( d2unsorted @ ( sK0 @ X3 ) )
= X3 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
!= ( d2unsorted @ X0 ) )
| ( X0 = X1 ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y4 )
| ~ ( irel @ Y3 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( irel @ Y3 @ Y4 ) ) ) ) ) ) )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( ( Y1 @ Y6 )
| ~ ( irel @ Y5 @ Y7 )
| ~ ( irel @ Y7 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( Y0 @ Y8 )
| ~ ( irel @ Y7 @ Y8 ) ) ) )
& ( ( Y0 @ Y4 )
| ~ ( irel @ Y3 @ Y4 )
| ~ ( irel @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( Y1 @ Y8 )
| ~ ( irel @ Y3 @ Y8 ) ) ) ) )
| ~ ( irel @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,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 ) ) ) ) ) )
& ! [X2: d_unsorted] : ( d_unsorted_0 = X2 )
& ! [X3: $i] :
? [X4: d_unsorted] :
( ( d2unsorted @ X4 )
= X3 )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
( ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( ( d2unsorted @ X3 )
!= ( d2unsorted @ X4 ) )
| ( X3 = X4 ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y4 )
| ~ ( irel @ Y3 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( irel @ Y3 @ Y4 ) ) ) ) ) ) )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( ( Y1 @ Y6 )
| ~ ( irel @ Y5 @ Y7 )
| ~ ( irel @ Y7 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( Y0 @ Y8 )
| ~ ( irel @ Y7 @ Y8 ) ) ) )
& ( ( Y0 @ Y4 )
| ~ ( irel @ Y3 @ Y4 )
| ~ ( irel @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( Y1 @ Y8 )
| ~ ( irel @ Y3 @ Y8 ) ) ) ) )
| ~ ( irel @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,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 ) ) ) ) ) )
& ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ! [X1: $i] :
? [X2: d_unsorted] :
( ( d2unsorted @ X2 )
= X1 )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ! [X1: $i] :
? [X2: d_unsorted] :
( ( d2unsorted @ X2 )
= X1 )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y4 )
| ~ ( irel @ Y3 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( irel @ Y3 @ Y4 ) ) ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( ( Y1 @ Y6 )
| ~ ( irel @ Y5 @ Y7 )
| ~ ( irel @ Y7 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( Y0 @ Y8 )
| ~ ( irel @ Y7 @ Y8 ) ) ) )
& ( ( Y0 @ Y4 )
| ~ ( irel @ Y3 @ Y4 )
| ~ ( irel @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( Y1 @ Y8 )
| ~ ( irel @ Y3 @ Y8 ) ) ) ) )
| ~ ( irel @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( ( d2unsorted @ X3 )
= ( d2unsorted @ X4 ) )
=> ( X3 = X4 ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( 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] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( ( Y1 @ Y6 )
| ~ ( irel @ Y5 @ Y7 )
| ~ ( irel @ Y7 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( Y0 @ Y8 )
| ~ ( irel @ Y7 @ Y8 ) ) ) )
& ( ( Y0 @ Y4 )
| ~ ( irel @ Y3 @ Y4 )
| ~ ( irel @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( Y1 @ Y8 )
| ~ ( irel @ Y3 @ Y8 ) ) ) ) )
| ~ ( irel @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y4 )
| ~ ( irel @ Y3 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( irel @ Y3 @ Y4 ) ) ) ) ) ) )
& ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ! [X1: $i] :
? [X2: d_unsorted] :
( ( d2unsorted @ X2 )
= X1 )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( ( d2unsorted @ X3 )
= ( d2unsorted @ X4 ) )
=> ( X3 = X4 ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( 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] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( ( Y1 @ Y6 )
| ~ ( irel @ Y5 @ Y7 )
| ~ ( irel @ Y7 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( Y0 @ Y8 )
| ~ ( irel @ Y7 @ Y8 ) ) ) )
& ( ( Y0 @ Y4 )
| ~ ( irel @ Y3 @ Y4 )
| ~ ( irel @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( Y1 @ Y8 )
| ~ ( irel @ Y3 @ Y8 ) ) ) ) )
| ~ ( irel @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 )
| ~ ( irel @ Y3 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y4 )
| ~ ( irel @ Y3 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( irel @ Y3 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y3 )
| ~ ( irel @ Y3 @ Y4 ) ) ) ) ) ) )
& ! [X31: d_unsorted] : ( d_unsorted_0 = X31 )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ! [X47: $i] :
? [X48: d_unsorted] :
( ( d2unsorted @ X48 )
= X47 )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ! [X64: d_unsorted,X65: d_unsorted] :
( ( ( d2unsorted @ X65 )
= ( d2unsorted @ X64 ) )
=> ( X64 = X65 ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ~ ( X0 @ X2 ) ) )
= mimplies )
& ( ( ^ [X3: $i > $o,X4: $i > $o,X5: $i] :
~ ! [X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
( ~ ( irel @ X5 @ X8 )
| ( ( ~ ! [X11: $i] :
( ~ ( irel @ X10 @ X11 )
| ( X4 @ X11 ) )
| ~ ( irel @ X8 @ X10 )
| ~ ( irel @ X10 @ X9 )
| ( X3 @ X9 ) )
& ( ~ ! [X12: $i] :
( ~ ( irel @ X6 @ X12 )
| ( X3 @ X12 ) )
| ~ ( irel @ X6 @ X7 )
| ~ ( irel @ X8 @ X6 )
| ( X4 @ X7 ) ) ) ) )
= ixor )
& ( ( ^ [X13: $i > $o] :
! [X14: $i] : ( X13 @ X14 ) )
= ivalid )
& ( ( ^ [X15: $i > $o,X16: $i > $o,X17: $i] :
( ! [X18: $i] :
( ( X15 @ X18 )
| ~ ( irel @ X17 @ X18 ) )
& ! [X19: $i] :
( ( X16 @ X19 )
| ~ ( irel @ X17 @ X19 ) ) ) )
= iand )
& ( ( ^ [X20: $i > $o,X21: $i] :
~ ( X20 @ X21 ) )
= mnot )
& ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
& ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
& ( ( ^ [X22: $i > $o,X23: $i > $o,X24: $i] :
( ! [X25: $i,X26: $i] :
( ~ ( irel @ X26 @ X25 )
| ~ ( irel @ X24 @ X26 )
| ~ ! [X27: $i] :
( ( X23 @ X27 )
| ~ ( irel @ X26 @ X27 ) )
| ( X22 @ X25 ) )
& ! [X28: $i,X29: $i] :
( ~ ( irel @ X29 @ X28 )
| ( X23 @ X28 )
| ~ ( irel @ X24 @ X29 )
| ~ ! [X30: $i] :
( ~ ( irel @ X29 @ X30 )
| ( X22 @ X30 ) ) ) ) )
= iequiv )
& ! [X31: d_unsorted] : ( d_unsorted_0 = X31 )
& ( ( ^ [X32: $i > $o,X33: $i > $o,X34: $i] :
( ( X33 @ X34 )
| ( X32 @ X34 ) ) )
= mor )
& ( ior
= ( ^ [X35: $i > $o,X36: $i > $o,X37: $i] :
( ! [X38: $i] :
( ~ ( irel @ X37 @ X38 )
| ( X35 @ X38 ) )
| ! [X39: $i] :
( ~ ( irel @ X37 @ X39 )
| ( X36 @ X39 ) ) ) ) )
& ( iimplies
= ( ^ [X40: $i > $o,X41: $i > $o,X42: $i] :
( ! [X43: $i] :
( ~ ( irel @ X42 @ X43 )
| ( X41 @ X43 ) )
| ~ ! [X44: $i] :
( ~ ( irel @ X42 @ X44 )
| ( X40 @ X44 ) ) ) ) )
& ( ( ^ [X45: $i > $o,X46: $i] : ( X45 @ X46 ) )
= iatom )
& ! [X47: $i] :
? [X48: d_unsorted] :
( ( d2unsorted @ X48 )
= X47 )
& ( iimplied
= ( ^ [X49: $i > $o,X50: $i > $o,X51: $i] :
( ~ ! [X52: $i] :
( ( X50 @ X52 )
| ~ ( irel @ X51 @ X52 ) )
| ! [X53: $i] :
( ( X49 @ X53 )
| ~ ( irel @ X51 @ X53 ) ) ) ) )
& ( ( ^ [X54: $i > $o] :
~ ! [X55: $i] :
~ ( X54 @ X55 ) )
= isatisfiable )
& ( ( ^ [X56: $i > $o,X57: $i] :
! [X58: $i] :
( ~ ( irel @ X57 @ X58 )
| ( X56 @ X58 ) ) )
= mbox_s4 )
& ( iinvalid
= ( ^ [X59: $i > $o] :
! [X60: $i] :
~ ( X59 @ X60 ) ) )
& ( ( ^ [X61: $i > $o,X62: $i > $o,X63: $i] :
( ( X61 @ X63 )
& ( X62 @ X63 ) ) )
= mand )
& ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
& ! [X64: d_unsorted,X65: d_unsorted] :
( ( ( d2unsorted @ X65 )
= ( d2unsorted @ X64 ) )
=> ( X64 = X65 ) )
& ( inot
= ( ^ [X66: $i > $o,X67: $i] :
~ ! [X68: $i] :
( ( X66 @ X68 )
| ~ ( irel @ X67 @ X68 ) ) ) )
& ( icountersatisfiable
= ( ^ [X69: $i > $o] :
~ ! [X70: $i] : ( X69 @ X70 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ( ^ [X0: $i > $o,X6: $i > $o,X7: $i] :
( ( X6 @ X7 )
| ~ ( X0 @ X7 ) ) )
= mimplies )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
~ ! [X14: $i,X15: $i,X5: $i,X17: $i,X16: $i] :
( ~ ( irel @ X7 @ X5 )
| ( ( ~ ! [X13: $i] :
( ~ ( irel @ X16 @ X13 )
| ( X9 @ X13 ) )
| ~ ( irel @ X5 @ X16 )
| ~ ( irel @ X16 @ X17 )
| ( X8 @ X17 ) )
& ( ~ ! [X11: $i] :
( ~ ( irel @ X14 @ X11 )
| ( X8 @ X11 ) )
| ~ ( irel @ X14 @ X15 )
| ~ ( irel @ X5 @ X14 )
| ( X9 @ X15 ) ) ) ) )
= ixor )
& ( ( ^ [X18: $i > $o] :
! [X19: $i] : ( X18 @ X19 ) )
= ivalid )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) )
& ! [X5: $i] :
( ( X9 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) ) )
= iand )
& ( ( ^ [X4: $i > $o,X0: $i] :
~ ( X4 @ X0 ) )
= mnot )
& ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
& ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ! [X12: $i,X5: $i] :
( ~ ( irel @ X5 @ X12 )
| ~ ( irel @ X7 @ X5 )
| ~ ! [X13: $i] :
( ( X9 @ X13 )
| ~ ( irel @ X5 @ X13 ) )
| ( X8 @ X12 ) )
& ! [X10: $i,X5: $i] :
( ~ ( irel @ X5 @ X10 )
| ( X9 @ X10 )
| ~ ( irel @ X7 @ X5 )
| ~ ! [X11: $i] :
( ~ ( irel @ X5 @ X11 )
| ( X8 @ X11 ) ) ) ) )
= iequiv )
& ! [X1: d_unsorted] : ( d_unsorted_0 = X1 )
& ( ( ^ [X4: $i > $o,X5: $i > $o,X0: $i] :
( ( X5 @ X0 )
| ( X4 @ X0 ) ) )
= mor )
& ( ior
= ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X8 @ X5 ) )
| ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X9 @ X5 ) ) ) ) )
& ( iimplies
= ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X9 @ X5 ) )
| ~ ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X8 @ X5 ) ) ) ) )
& ( ( ^ [X8: $i > $o,X7: $i] : ( X8 @ X7 ) )
= iatom )
& ! [X0: $i] :
? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 )
& ( iimplied
= ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ~ ! [X5: $i] :
( ( X9 @ X5 )
| ~ ( irel @ X7 @ X5 ) )
| ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) ) ) )
& ( ( ^ [X18: $i > $o] :
~ ! [X19: $i] :
~ ( X18 @ X19 ) )
= isatisfiable )
& ( ( ^ [X8: $i > $o,X4: $i] :
! [X5: $i] :
( ~ ( irel @ X4 @ X5 )
| ( X8 @ X5 ) ) )
= mbox_s4 )
& ( iinvalid
= ( ^ [X18: $i > $o] :
! [X19: $i] :
~ ( X18 @ X19 ) ) )
& ( ( ^ [X4: $i > $o,X5: $i > $o,X0: $i] :
( ( X4 @ X0 )
& ( X5 @ X0 ) ) )
= mand )
& ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
& ! [X3: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X2 )
= ( d2unsorted @ X3 ) )
=> ( X2 = X3 ) )
& ( inot
= ( ^ [X8: $i > $o,X7: $i] :
~ ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) ) )
& ( icountersatisfiable
= ( ^ [X18: $i > $o] :
~ ! [X19: $i] : ( X18 @ X19 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZBAnisbwE3/DTF2THF_3132.p',lcl696_1) ).
thf(f36,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f29,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f16,plain,
( iimplies
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( iimplies
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( iimplies
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( iimplies
!= ( ^ [X0: $i > $o,X1: $i > $o] : ( mimplies @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( iimplies
!= ( ^ [X8: $i > $o,X9: $i > $o] : ( mimplies @ ( mbox_s4 @ X8 ) @ ( mbox_s4 @ X9 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( iimplies
= ( ^ [X8: $i > $o,X9: $i > $o] : ( mimplies @ ( mbox_s4 @ X8 ) @ ( mbox_s4 @ X9 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZBAnisbwE3/DTF2THF_3132.p',iimplies) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.35 % Computer : n031.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue May 5 09:25:08 EDT 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.28/0.47 % Domain : Software Verification
% 0.28/0.47 % Problem : Benchmark: LCL696^1, Active target: iimplies
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Kon26]
% 0.28/0.47 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : ? v9.3.0
% 0.28/0.47 % Syntax : Number of formulae : 26 ( 1 unt; 24 typ; 0 def)
% 0.28/0.47 % Number of atoms : 69 ( 22 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 24 ( 34 avg)
% 0.28/0.47 % Number of connectives : 188 ( 38 ~; 32 |; 26 &; 91 @)
% 0.28/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 26 ( 14 avg)
% 0.28/0.47 % Number of types : 4 ( 2 usr)
% 0.28/0.47 % Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 23 ( 22 usr; 1 con; 0-3 aty)
% 0.28/0.47 % Number of variables : 73 ( 41 ^; 31 !; 1 ?; 73 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments :
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(unsorted_type,type,
% 0.28/0.47 unsorted: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(irel_decl,type,
% 0.28/0.47 irel: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(mnot_decl,type,
% 0.28/0.47 mnot: ( $i > $o ) > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(mor_decl,type,
% 0.28/0.47 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(mand_decl,type,
% 0.28/0.47 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(mimplies_decl,type,
% 0.28/0.47 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(mbox_s4_decl,type,
% 0.28/0.47 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(iatom_decl,type,
% 0.28/0.47 iatom: ( $i > $o ) > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(inot_decl,type,
% 0.28/0.47 inot: ( $i > $o ) > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(itrue_decl,type,
% 0.28/0.47 itrue: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(ifalse_decl,type,
% 0.28/0.47 ifalse: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(iand_decl,type,
% 0.28/0.47 iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(ior_decl,type,
% 0.28/0.47 ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(iimplies_decl,type,
% 0.28/0.47 iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(iimplied_decl,type,
% 0.28/0.47 iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(iequiv_decl,type,
% 0.28/0.47 iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(ixor_decl,type,
% 0.28/0.47 ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(ivalid_decl,type,
% 0.28/0.47 ivalid: ( $i > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(isatisfiable_decl,type,
% 0.28/0.47 isatisfiable: ( $i > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(icountersatisfiable_decl,type,
% 0.28/0.47 icountersatisfiable: ( $i > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(iinvalid_decl,type,
% 0.28/0.47 iinvalid: ( $i > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 %----Types of the domains
% 0.28/0.47 thf(d_unsorted_type,type,
% 0.28/0.47 d_unsorted: $tType ).
% 0.28/0.47
% 0.28/0.47 %----Types of the promotion functions
% 0.28/0.47 thf(d2unsorted_decl,type,
% 0.28/0.47 d2unsorted: d_unsorted > $i ).
% 0.28/0.47
% 0.28/0.47 %----Types of the domain elements
% 0.28/0.47 thf(d_unsorted_0_decl,type,
% 0.28/0.47 d_unsorted_0: d_unsorted ).
% 0.28/0.47
% 0.28/0.47 thf(lcl696_1,axiom,
% 0.28/0.47 ( ! [U: $i] :
% 0.28/0.47 ? [DU: d_unsorted] :
% 0.28/0.47 ( U
% 0.28/0.47 = ( d2unsorted @ DU ) )
% 0.28/0.47 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 0.28/0.47 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 0.28/0.47 ( ( ( d2unsorted @ DU1 )
% 0.28/0.47 = ( d2unsorted @ DU2 ) )
% 0.28/0.47 => ( DU1 = DU2 ) )
% 0.28/0.47 & ( mnot
% 0.28/0.47 = ( ^ [X: $i > $o,U: $i] :
% 0.28/0.47 ~ ( X @ U ) ) )
% 0.28/0.47 & ( mor
% 0.28/0.47 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.28/0.47 ( ( X @ U )
% 0.28/0.47 | ( Y @ U ) ) ) )
% 0.28/0.47 & ( mand
% 0.28/0.47 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.28/0.47 ( ( X @ U )
% 0.28/0.47 & ( Y @ U ) ) ) )
% 0.28/0.47 & ( mimplies
% 0.28/0.47 = ( ^ [U: $i > $o,V: $i > $o,Flatten_var_0: $i] :
% 0.28/0.47 ( ~ ( U @ Flatten_var_0 )
% 0.28/0.47 | ( V @ Flatten_var_0 ) ) ) )
% 0.28/0.47 & ( mbox_s4
% 0.28/0.47 = ( ^ [P: $i > $o,X: $i] :
% 0.28/0.47 ! [Y: $i] :
% 0.28/0.47 ( ~ ( irel @ X @ Y )
% 0.28/0.47 | ( P @ Y ) ) ) )
% 0.28/0.47 & ( iatom
% 0.28/0.47 = ( ^ [P: $i > $o,Flatten_var_0: $i] : ( P @ Flatten_var_0 ) ) )
% 0.28/0.47 & ( inot
% 0.28/0.47 = ( ^ [P: $i > $o,Flatten_var_0: $i] :
% 0.28/0.47 ~ ! [Y: $i] :
% 0.28/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.28/0.47 | ( P @ Y ) ) ) )
% 0.28/0.47 & ( iand
% 0.28/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.28/0.47 ( ! [Y: $i] :
% 0.28/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.28/0.47 | ( P @ Y ) )
% 0.28/0.47 & ! [Y: $i] :
% 0.28/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.28/0.47 | ( Q @ Y ) ) ) ) )
% 0.28/0.47 & ( ior
% 0.28/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.28/0.47 ( ! [Y: $i] :
% 0.28/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.28/0.47 | ( P @ Y ) )
% 0.28/0.47 | ! [Y: $i] :
% 0.28/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.28/0.47 | ( Q @ Y ) ) ) ) )
% 0.28/0.47 & ( iimplies
% 0.28/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.28/0.47 ( ~ ! [Y: $i] :
% 0.28/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.28/0.47 | ( P @ Y ) )
% 0.28/0.47 | ! [Y: $i] :
% 0.28/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.28/0.47 | ( Q @ Y ) ) ) ) )
% 0.28/0.47 & ( iimplied
% 0.28/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.28/0.47 ( ~ ! [Y: $i] :
% 0.28/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.28/0.47 | ( Q @ Y ) )
% 0.28/0.47 | ! [Y: $i] :
% 0.28/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.28/0.47 | ( P @ Y ) ) ) ) )
% 0.28/0.47 & ( iequiv
% 0.28/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.28/0.47 ( ! [Y: $i,Bound_variable_718: $i] :
% 0.28/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.28/0.47 | ~ ! [Bound_variable_693: $i] :
% 0.28/0.47 ( ~ ( irel @ Y @ Bound_variable_693 )
% 0.28/0.47 | ( P @ Bound_variable_693 ) )
% 0.28/0.47 | ~ ( irel @ Y @ Bound_variable_718 )
% 0.28/0.47 | ( Q @ Bound_variable_718 ) )
% 0.28/0.47 & ! [Y: $i,Bound_variable_771: $i] :
% 0.28/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.28/0.47 | ~ ! [Bound_variable_746: $i] :
% 0.28/0.47 ( ~ ( irel @ Y @ Bound_variable_746 )
% 0.28/0.47 | ( Q @ Bound_variable_746 ) )
% 0.28/0.47 | ~ ( irel @ Y @ Bound_variable_771 )
% 0.28/0.47 | ( P @ Bound_variable_771 ) ) ) ) )
% 0.28/0.47 & ( ixor
% 0.28/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.28/0.47 ~ ! [Y: $i,Bound_variable_849: $i,Bound_variable_851: $i,Bound_variable_864: $i,Bound_variable_866: $i] :
% 0.28/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.28/0.47 | ( ( ~ ( irel @ Y @ Bound_variable_849 )
% 0.28/0.47 | ~ ! [Bound_variable_693: $i] :
% 0.28/0.47 ( ~ ( irel @ Bound_variable_849 @ Bound_variable_693 )
% 0.28/0.47 | ( P @ Bound_variable_693 ) )
% 0.28/0.47 | ~ ( irel @ Bound_variable_849 @ Bound_variable_851 )
% 0.28/0.47 | ( Q @ Bound_variable_851 ) )
% 0.28/0.47 & ( ~ ( irel @ Y @ Bound_variable_864 )
% 0.28/0.47 | ~ ! [Bound_variable_746: $i] :
% 0.28/0.47 ( ~ ( irel @ Bound_variable_864 @ Bound_variable_746 )
% 0.28/0.47 | ( Q @ Bound_variable_746 ) )
% 0.28/0.47 | ~ ( irel @ Bound_variable_864 @ Bound_variable_866 )
% 0.28/0.47 | ( P @ Bound_variable_866 ) ) ) ) ) )
% 0.28/0.47 & ( ivalid
% 0.28/0.47 = ( ^ [Phi: $i > $o] :
% 0.28/0.47 ! [W: $i] : ( Phi @ W ) ) )
% 0.28/0.47 & ( isatisfiable
% 0.28/0.47 = ( ^ [Phi: $i > $o] :
% 0.28/0.47 ~ ! [W: $i] :
% 0.28/0.47 ~ ( Phi @ W ) ) )
% 0.28/0.47 & ( icountersatisfiable
% 0.28/0.47 = ( ^ [Phi: $i > $o] :
% 0.28/0.47 ~ ! [W: $i] : ( Phi @ W ) ) )
% 0.28/0.47 & ( iinvalid
% 0.28/0.47 = ( ^ [Phi: $i > $o] :
% 0.28/0.47 ! [W: $i] :
% 0.28/0.47 ~ ( Phi @ W ) ) )
% 0.28/0.47 & ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
% 0.28/0.47 & ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
% 0.28/0.47 & ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iimplies,conjecture,
% 0.28/0.47 ( iimplies
% 0.28/0.47 = ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.57/1.28 ---- Embedded in THF ---
% 1.57/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.57/1.28 %%% Generated on Tue May 05 09:25:09 EDT 2026
% 1.57/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.57/1.28 %%% Logic specification used:
% 1.57/1.28 %%% thf(spec, logic, $$dhol).
% 1.57/1.28
% 1.57/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ZBAnisbwE3/DTF2DTF3132.p
% See solution above
% 1.57/1.28 ------------------------
% 1.57/1.29 ---- Cleaned THF ---
% 1.57/1.29 thf(unsorted_type,type,
% 1.57/1.29 unsorted: $tType ).
% 1.57/1.29
% 1.57/1.29 thf(irel_decl,type,
% 1.57/1.29 irel: $i > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(mnot_decl,type,
% 1.57/1.29 mnot: ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(mor_decl,type,
% 1.57/1.29 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(mand_decl,type,
% 1.57/1.29 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(mimplies_decl,type,
% 1.57/1.29 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(mbox_s4_decl,type,
% 1.57/1.29 mbox_s4: ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(iatom_decl,type,
% 1.57/1.29 iatom: ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(inot_decl,type,
% 1.57/1.29 inot: ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(itrue_decl,type,
% 1.57/1.29 itrue: $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(ifalse_decl,type,
% 1.57/1.29 ifalse: $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(iand_decl,type,
% 1.57/1.29 iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(ior_decl,type,
% 1.57/1.29 ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(iimplies_decl,type,
% 1.57/1.29 iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(iimplied_decl,type,
% 1.57/1.29 iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(iequiv_decl,type,
% 1.57/1.29 iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(ixor_decl,type,
% 1.57/1.29 ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.57/1.29
% 1.57/1.29 thf(ivalid_decl,type,
% 1.57/1.29 ivalid: ( $i > $o ) > $o ).
% 1.57/1.29
% 1.57/1.29 thf(isatisfiable_decl,type,
% 1.57/1.29 isatisfiable: ( $i > $o ) > $o ).
% 1.57/1.29
% 1.57/1.29 thf(icountersatisfiable_decl,type,
% 1.57/1.29 icountersatisfiable: ( $i > $o ) > $o ).
% 1.57/1.29
% 1.57/1.29 thf(iinvalid_decl,type,
% 1.57/1.29 iinvalid: ( $i > $o ) > $o ).
% 1.57/1.29
% 1.57/1.29 thf(d_unsorted_type,type,
% 1.57/1.29 d_unsorted: $tType ).
% 1.57/1.29
% 1.57/1.29 thf(d2unsorted_decl,type,
% 1.57/1.29 d2unsorted: d_unsorted > $i ).
% 1.57/1.29
% 1.57/1.29 thf(d_unsorted_0_decl,type,
% 1.57/1.29 d_unsorted_0: d_unsorted ).
% 1.57/1.29
% 1.57/1.29 thf(lcl696_1,axiom,
% 1.57/1.29 ( ! [U: $i] :
% 1.57/1.29 ? [DU: d_unsorted] :
% 1.57/1.29 ( U
% 1.57/1.29 = ( d2unsorted @ DU ) )
% 1.57/1.29 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 1.57/1.29 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 1.57/1.29 ( ( ( d2unsorted @ DU1 )
% 1.57/1.29 = ( d2unsorted @ DU2 ) )
% 1.57/1.29 => ( DU1 = DU2 ) )
% 1.57/1.29 & ( mnot
% 1.57/1.29 = ( ^ [X: $i > $o,U: $i] :
% 1.57/1.29 ~ ( X @ U ) ) )
% 1.57/1.29 & ( mor
% 1.57/1.29 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 1.57/1.29 ( ( X @ U )
% 1.57/1.29 | ( Y @ U ) ) ) )
% 1.57/1.29 & ( mand
% 1.57/1.29 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 1.57/1.29 ( ( X @ U )
% 1.57/1.29 & ( Y @ U ) ) ) )
% 1.57/1.29 & ( mimplies
% 1.57/1.29 = ( ^ [U: $i > $o,V: $i > $o,Flatten_var_0: $i] :
% 1.57/1.29 ( ~ ( U @ Flatten_var_0 )
% 1.57/1.29 | ( V @ Flatten_var_0 ) ) ) )
% 1.57/1.29 & ( mbox_s4
% 1.57/1.29 = ( ^ [P: $i > $o,X: $i] :
% 1.57/1.29 ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ X @ Y )
% 1.57/1.29 | ( P @ Y ) ) ) )
% 1.57/1.29 & ( iatom
% 1.57/1.29 = ( ^ [P: $i > $o,Flatten_var_0: $i] : ( P @ Flatten_var_0 ) ) )
% 1.57/1.29 & ( inot
% 1.57/1.29 = ( ^ [P: $i > $o,Flatten_var_0: $i] :
% 1.57/1.29 ~ ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( P @ Y ) ) ) )
% 1.57/1.29 & ( iand
% 1.57/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.57/1.29 ( ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( P @ Y ) )
% 1.57/1.29 & ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( Q @ Y ) ) ) ) )
% 1.57/1.29 & ( ior
% 1.57/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.57/1.29 ( ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( P @ Y ) )
% 1.57/1.29 | ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( Q @ Y ) ) ) ) )
% 1.57/1.29 & ( iimplies
% 1.57/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.57/1.29 ( ~ ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( P @ Y ) )
% 1.57/1.29 | ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( Q @ Y ) ) ) ) )
% 1.57/1.29 & ( iimplied
% 1.57/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.57/1.29 ( ~ ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( Q @ Y ) )
% 1.57/1.29 | ! [Y: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( P @ Y ) ) ) ) )
% 1.57/1.29 & ( iequiv
% 1.57/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.57/1.29 ( ! [Y: $i,Bound_variable_718: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ~ ! [Bound_variable_693: $i] :
% 1.57/1.29 ( ~ ( irel @ Y @ Bound_variable_693 )
% 1.57/1.29 | ( P @ Bound_variable_693 ) )
% 1.57/1.29 | ~ ( irel @ Y @ Bound_variable_718 )
% 1.57/1.29 | ( Q @ Bound_variable_718 ) )
% 1.57/1.29 & ! [Y: $i,Bound_variable_771: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ~ ! [Bound_variable_746: $i] :
% 1.57/1.29 ( ~ ( irel @ Y @ Bound_variable_746 )
% 1.57/1.29 | ( Q @ Bound_variable_746 ) )
% 1.57/1.29 | ~ ( irel @ Y @ Bound_variable_771 )
% 1.57/1.29 | ( P @ Bound_variable_771 ) ) ) ) )
% 1.57/1.29 & ( ixor
% 1.57/1.29 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.57/1.29 ~ ! [Y: $i,Bound_variable_849: $i,Bound_variable_851: $i,Bound_variable_864: $i,Bound_variable_866: $i] :
% 1.57/1.29 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.57/1.29 | ( ( ~ ( irel @ Y @ Bound_variable_849 )
% 1.57/1.29 | ~ ! [Bound_variable_693: $i] :
% 1.57/1.29 ( ~ ( irel @ Bound_variable_849 @ Bound_variable_693 )
% 1.57/1.29 | ( P @ Bound_variable_693 ) )
% 1.57/1.29 | ~ ( irel @ Bound_variable_849 @ Bound_variable_851 )
% 1.57/1.29 | ( Q @ Bound_variable_851 ) )
% 1.57/1.29 & ( ~ ( irel @ Y @ Bound_variable_864 )
% 1.57/1.29 | ~ ! [Bound_variable_746: $i] :
% 1.57/1.29 ( ~ ( irel @ Bound_variable_864 @ Bound_variable_746 )
% 1.57/1.29 | ( Q @ Bound_variable_746 ) )
% 1.57/1.29 | ~ ( irel @ Bound_variable_864 @ Bound_variable_866 )
% 1.57/1.29 | ( P @ Bound_variable_866 ) ) ) ) ) )
% 1.57/1.29 & ( ivalid
% 1.57/1.29 = ( ^ [Phi: $i > $o] :
% 1.57/1.29 ! [W: $i] : ( Phi @ W ) ) )
% 1.57/1.29 & ( isatisfiable
% 1.57/1.29 = ( ^ [Phi: $i > $o] :
% 1.57/1.29 ~ ! [W: $i] :
% 1.57/1.29 ~ ( Phi @ W ) ) )
% 1.57/1.29 & ( icountersatisfiable
% 1.57/1.29 = ( ^ [Phi: $i > $o] :
% 1.57/1.29 ~ ! [W: $i] : ( Phi @ W ) ) )
% 1.57/1.29 & ( iinvalid
% 1.57/1.29 = ( ^ [Phi: $i > $o] :
% 1.57/1.29 ! [W: $i] :
% 1.57/1.29 ~ ( Phi @ W ) ) )
% 1.57/1.29 & ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
% 1.57/1.29 & ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
% 1.57/1.29 & ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ) ).
% 1.57/1.29
% 1.57/1.29 thf(iimplies,conjecture,
% 1.57/1.29 ( iimplies
% 1.57/1.29 = ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
% 1.57/1.29 ------------------------
% 1.78/1.31 % (3248)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_3132 for (2999ds/275Mi)
% 1.78/1.31 % (3243)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3132 for (2999ds/183Mi)
% 1.78/1.31 % (3249)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3132 for (2999ds/18Mi)
% 1.78/1.31 % (3248)Refutation not found, incomplete strategy
% 1.78/1.31 % (3248)------------------------------
% 1.78/1.31 % (3248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.31 % (3248)Termination reason: Refutation not found, incomplete strategy
% 1.78/1.31
% 1.78/1.31
% 1.78/1.31 % (3248)Memory used [KB]: 5628
% 1.78/1.31 % (3248)Time elapsed: 0.003 s
% 1.78/1.31 % (3248)Instructions burned: 6 (million)
% 1.78/1.31 % (3248)------------------------------
% 1.78/1.31 % (3248)------------------------------
% 1.78/1.31 % (3249)First to succeed.
% 1.78/1.31 % (3249)Refutation found. Thanks to Tanya!
% 1.78/1.31 % SZS status Theorem for DTF2THF_3132
% 1.78/1.31 % SZS output start Proof for DTF2THF_3132
% 1.78/1.31 thf(type_def_6, type, d_unsorted: $tType).
% 1.78/1.31 thf(func_def_0, type, unsorted: $tType).
% 1.78/1.31 thf(func_def_1, type, irel: $i > $i > $o).
% 1.78/1.31 thf(func_def_2, type, mnot: ($i > $o) > $i > $o).
% 1.78/1.31 thf(func_def_3, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 1.78/1.31 thf(func_def_4, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 1.78/1.31 thf(func_def_5, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 1.78/1.31 thf(func_def_6, type, mbox_s4: ($i > $o) > $i > $o).
% 1.78/1.31 thf(func_def_7, type, iatom: ($i > $o) > $i > $o).
% 1.78/1.31 thf(func_def_8, type, inot: ($i > $o) > $i > $o).
% 1.78/1.31 thf(func_def_9, type, itrue: $i > $o).
% 1.78/1.31 thf(func_def_10, type, ifalse: $i > $o).
% 1.78/1.31 thf(func_def_11, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 1.78/1.31 thf(func_def_12, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 1.78/1.31 thf(func_def_13, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 1.78/1.31 thf(func_def_14, type, iimplied: ($i > $o) > ($i > $o) > $i > $o).
% 1.78/1.31 thf(func_def_15, type, iequiv: ($i > $o) > ($i > $o) > $i > $o).
% 1.78/1.31 thf(func_def_16, type, ixor: ($i > $o) > ($i > $o) > $i > $o).
% 1.78/1.31 thf(func_def_17, type, ivalid: ($i > $o) > $o).
% 1.78/1.31 thf(func_def_18, type, isatisfiable: ($i > $o) > $o).
% 1.78/1.31 thf(func_def_19, type, icountersatisfiable: ($i > $o) > $o).
% 1.78/1.31 thf(func_def_20, type, iinvalid: ($i > $o) > $o).
% 1.78/1.31 thf(func_def_21, type, d_unsorted: $tType).
% 1.78/1.31 thf(func_def_22, type, d2unsorted: d_unsorted > $i).
% 1.78/1.31 thf(func_def_23, type, d_unsorted_0: d_unsorted).
% 1.78/1.31 thf(func_def_41, type, sK0: $i > d_unsorted).
% 1.78/1.31 thf(f42,plain,(
% 1.78/1.31 $false),
% 1.78/1.31 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.78/1.31 thf(f41,plain,(
% 1.78/1.31 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))),
% 1.78/1.31 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.78/1.31 thf(f40,plain,(
% 1.78/1.31 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((~ (Y2 @ Y4)) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (irel @ Y3 @ Y4)))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (irel @ Y3 @ Y4)))))))) @ Y1))))))),
% 1.78/1.31 inference(definition_unfolding,[status(thm)],[f16,f29,f36,f34,f34])).
% 1.78/1.31 thf(f34,plain,(
% 1.78/1.31 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))),
% 1.78/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.78/1.31 thf(f15,plain,(
% 1.78/1.31 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : (((d2unsorted @ X1) != (d2unsorted @ X0)) | (X0 = X1)) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4)))))))))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y1 @ Y6) | (~ (irel @ Y5 @ Y7))) | (~ (irel @ Y7 @ Y6))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y7 @ Y8))))))) & ((((Y0 @ Y4) | (~ (irel @ Y3 @ Y4))) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y1 @ Y8) | (~ (irel @ Y3 @ Y8)))))))) | (~ (irel @ Y2 @ Y5)))))))))))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[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)))))))))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & ! [X3 : $i] : ((d2unsorted @ (sK0 @ X3)) = X3) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true)),
% 1.78/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14])).
% 1.78/1.31 thf(f14,plain,(
% 1.78/1.31 ! [X3 : $i] : (? [X4 : d_unsorted] : ((d2unsorted @ X4) = X3) => ((d2unsorted @ (sK0 @ X3)) = X3))),
% 1.78/1.31 introduced(definition,[],[choice_axiom])).
% 1.78/1.31 thf(f13,plain,(
% 1.78/1.31 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : (((d2unsorted @ X1) != (d2unsorted @ X0)) | (X0 = X1)) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4)))))))))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y1 @ Y6) | (~ (irel @ Y5 @ Y7))) | (~ (irel @ Y7 @ Y6))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y7 @ Y8))))))) & ((((Y0 @ Y4) | (~ (irel @ Y3 @ Y4))) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y1 @ Y8) | (~ (irel @ Y3 @ Y8)))))))) | (~ (irel @ Y2 @ Y5)))))))))))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[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)))))))))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & ! [X3 : $i] : ? [X4 : d_unsorted] : ((d2unsorted @ X4) = X3) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true)),
% 1.78/1.31 inference(rectify,[status(thm)],[f12])).
% 1.78/1.31 thf(f12,plain,(
% 1.78/1.31 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : (((d2unsorted @ X3) != (d2unsorted @ X4)) | (X3 = X4)) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4)))))))))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y1 @ Y6) | (~ (irel @ Y5 @ Y7))) | (~ (irel @ Y7 @ Y6))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y7 @ Y8))))))) & ((((Y0 @ Y4) | (~ (irel @ Y3 @ Y4))) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y1 @ Y8) | (~ (irel @ Y3 @ Y8)))))))) | (~ (irel @ Y2 @ Y5)))))))))))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[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)))))))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & ! [X1 : $i] : ? [X2 : d_unsorted] : ((d2unsorted @ X2) = X1) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true)),
% 1.78/1.31 inference(ennf_transformation,[status(thm)],[f11])).
% 1.78/1.31 thf(f11,plain,(
% 1.78/1.31 ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & ! [X1 : $i] : ? [X2 : d_unsorted] : ((d2unsorted @ X2) = X1) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4)))))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y1 @ Y6) | (~ (irel @ Y5 @ Y7))) | (~ (irel @ Y7 @ Y6))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y7 @ Y8))))))) & ((((Y0 @ Y4) | (~ (irel @ Y3 @ Y4))) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y1 @ Y8) | (~ (irel @ Y3 @ Y8)))))))) | (~ (irel @ Y2 @ Y5)))))))))))))))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : (((d2unsorted @ X3) = (d2unsorted @ X4)) => (X3 = X4)) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))),
% 1.78/1.31 inference(flattening,[status(thm)],[f10])).
% 1.78/1.31 thf(f10,plain,(
% 1.78/1.31 (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]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y1 @ Y6) | (~ (irel @ Y5 @ Y7))) | (~ (irel @ Y7 @ Y6))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y7 @ Y8))))))) & ((((Y0 @ Y4) | (~ (irel @ Y3 @ Y4))) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y1 @ Y8) | (~ (irel @ Y3 @ Y8)))))))) | (~ (irel @ Y2 @ Y5)))))))))))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4)))))))))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & ! [X1 : $i] : ? [X2 : d_unsorted] : ((d2unsorted @ X2) = X1) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ~((ifalse @ (d2unsorted @ d_unsorted_0)) = $true) & ! [X3 : d_unsorted,X4 : d_unsorted] : (((d2unsorted @ X3) = (d2unsorted @ X4)) => (X3 = X4)) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.78/1.31 inference(rectify,[status(thm)],[f8])).
% 1.78/1.31 thf(f8,plain,(
% 1.78/1.31 (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]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y1 @ Y6) | (~ (irel @ Y5 @ Y7))) | (~ (irel @ Y7 @ Y6))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y7 @ Y8))))))) & ((((Y0 @ Y4) | (~ (irel @ Y3 @ Y4))) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y1 @ Y8) | (~ (irel @ Y3 @ Y8)))))))) | (~ (irel @ Y2 @ Y5)))))))))))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4)))))))))))))) & ! [X31 : d_unsorted] : (d_unsorted_0 = X31) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & ! [X47 : $i] : ? [X48 : d_unsorted] : ((d2unsorted @ X48) = X47) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ~((ifalse @ (d2unsorted @ d_unsorted_0)) = $true) & ! [X64 : d_unsorted,X65 : d_unsorted] : (((d2unsorted @ X65) = (d2unsorted @ X64)) => (X64 = X65)) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.78/1.31 inference(fool_elimination,[status(thm)],[f7])).
% 1.78/1.31 thf(f7,plain,(
% 1.78/1.31 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | ~(X0 @ X2))) = mimplies) & ((^[X3 : $i > $o, X4 : $i > $o, X5 : $i] : (~! [X6 : $i,X7 : $i,X8 : $i,X9 : $i,X10 : $i] : (~(irel @ X5 @ X8) | ((~! [X11 : $i] : (~(irel @ X10 @ X11) | (X4 @ X11)) | ~(irel @ X8 @ X10) | ~(irel @ X10 @ X9) | (X3 @ X9)) & (~! [X12 : $i] : (~(irel @ X6 @ X12) | (X3 @ X12)) | ~(irel @ X6 @ X7) | ~(irel @ X8 @ X6) | (X4 @ X7)))))) = ixor) & ((^[X13 : $i > $o] : (! [X14 : $i] : (X13 @ X14))) = ivalid) & ((^[X15 : $i > $o, X16 : $i > $o, X17 : $i] : (! [X18 : $i] : ((X15 @ X18) | ~(irel @ X17 @ X18)) & ! [X19 : $i] : ((X16 @ X19) | ~(irel @ X17 @ X19)))) = iand) & ((^[X20 : $i > $o, X21 : $i] : (~(X20 @ X21))) = mnot) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & (itrue @ (d2unsorted @ d_unsorted_0)) & ((^[X22 : $i > $o, X23 : $i > $o, X24 : $i] : (! [X25 : $i,X26 : $i] : (~(irel @ X26 @ X25) | ~(irel @ X24 @ X26) | ~! [X27 : $i] : ((X23 @ X27) | ~(irel @ X26 @ X27)) | (X22 @ X25)) & ! [X28 : $i,X29 : $i] : (~(irel @ X29 @ X28) | (X23 @ X28) | ~(irel @ X24 @ X29) | ~! [X30 : $i] : (~(irel @ X29 @ X30) | (X22 @ X30))))) = iequiv) & ! [X31 : d_unsorted] : (d_unsorted_0 = X31) & ((^[X32 : $i > $o, X33 : $i > $o, X34 : $i] : ((X33 @ X34) | (X32 @ X34))) = mor) & (ior = (^[X35 : $i > $o, X36 : $i > $o, X37 : $i] : (! [X38 : $i] : (~(irel @ X37 @ X38) | (X35 @ X38)) | ! [X39 : $i] : (~(irel @ X37 @ X39) | (X36 @ X39))))) & (iimplies = (^[X40 : $i > $o, X41 : $i > $o, X42 : $i] : (! [X43 : $i] : (~(irel @ X42 @ X43) | (X41 @ X43)) | ~! [X44 : $i] : (~(irel @ X42 @ X44) | (X40 @ X44))))) & ((^[X45 : $i > $o, X46 : $i] : (X45 @ X46)) = iatom) & ! [X47 : $i] : ? [X48 : d_unsorted] : ((d2unsorted @ X48) = X47) & (iimplied = (^[X49 : $i > $o, X50 : $i > $o, X51 : $i] : (~! [X52 : $i] : ((X50 @ X52) | ~(irel @ X51 @ X52)) | ! [X53 : $i] : ((X49 @ X53) | ~(irel @ X51 @ X53))))) & ((^[X54 : $i > $o] : (~! [X55 : $i] : ~(X54 @ X55))) = isatisfiable) & ((^[X56 : $i > $o, X57 : $i] : (! [X58 : $i] : (~(irel @ X57 @ X58) | (X56 @ X58)))) = mbox_s4) & (iinvalid = (^[X59 : $i > $o] : (! [X60 : $i] : ~(X59 @ X60)))) & ((^[X61 : $i > $o, X62 : $i > $o, X63 : $i] : ((X61 @ X63) & (X62 @ X63))) = mand) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & ! [X64 : d_unsorted,X65 : d_unsorted] : (((d2unsorted @ X65) = (d2unsorted @ X64)) => (X64 = X65)) & (inot = (^[X66 : $i > $o, X67 : $i] : (~! [X68 : $i] : ((X66 @ X68) | ~(irel @ X67 @ X68))))) & (icountersatisfiable = (^[X69 : $i > $o] : (~! [X70 : $i] : (X69 @ X70))))),
% 1.78/1.31 inference(rectify,[status(thm)],[f1])).
% 1.78/1.31 thf(f1,axiom,(
% 1.78/1.31 ((^[X0 : $i > $o, X6 : $i > $o, X7 : $i] : ((X6 @ X7) | ~(X0 @ X7))) = mimplies) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (~! [X14 : $i,X15 : $i,X5 : $i,X17 : $i,X16 : $i] : (~(irel @ X7 @ X5) | ((~! [X13 : $i] : (~(irel @ X16 @ X13) | (X9 @ X13)) | ~(irel @ X5 @ X16) | ~(irel @ X16 @ X17) | (X8 @ X17)) & (~! [X11 : $i] : (~(irel @ X14 @ X11) | (X8 @ X11)) | ~(irel @ X14 @ X15) | ~(irel @ X5 @ X14) | (X9 @ X15)))))) = ixor) & ((^[X18 : $i > $o] : (! [X19 : $i] : (X18 @ X19))) = ivalid) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)) & ! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)))) = iand) & ((^[X4 : $i > $o, X0 : $i] : (~(X4 @ X0))) = mnot) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & (itrue @ (d2unsorted @ d_unsorted_0)) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (! [X12 : $i,X5 : $i] : (~(irel @ X5 @ X12) | ~(irel @ X7 @ X5) | ~! [X13 : $i] : ((X9 @ X13) | ~(irel @ X5 @ X13)) | (X8 @ X12)) & ! [X10 : $i,X5 : $i] : (~(irel @ X5 @ X10) | (X9 @ X10) | ~(irel @ X7 @ X5) | ~! [X11 : $i] : (~(irel @ X5 @ X11) | (X8 @ X11))))) = iequiv) & ! [X1 : d_unsorted] : (d_unsorted_0 = X1) & ((^[X4 : $i > $o, X5 : $i > $o, X0 : $i] : ((X5 @ X0) | (X4 @ X0))) = mor) & (ior = (^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)) | ! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5))))) & (iimplies = (^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)) | ~! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5))))) & ((^[X8 : $i > $o, X7 : $i] : (X8 @ X7)) = iatom) & ! [X0 : $i] : ? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0) & (iimplied = (^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (~! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5))))) & ((^[X18 : $i > $o] : (~! [X19 : $i] : ~(X18 @ X19))) = isatisfiable) & ((^[X8 : $i > $o, X4 : $i] : (! [X5 : $i] : (~(irel @ X4 @ X5) | (X8 @ X5)))) = mbox_s4) & (iinvalid = (^[X18 : $i > $o] : (! [X19 : $i] : ~(X18 @ X19)))) & ((^[X4 : $i > $o, X5 : $i > $o, X0 : $i] : ((X4 @ X0) & (X5 @ X0))) = mand) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & ! [X3 : d_unsorted,X2 : d_unsorted] : (((d2unsorted @ X2) = (d2unsorted @ X3)) => (X2 = X3)) & (inot = (^[X8 : $i > $o, X7 : $i] : (~! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5))))) & (icountersatisfiable = (^[X18 : $i > $o] : (~! [X19 : $i] : (X18 @ X19))))),
% 1.78/1.31 file('/export/starexec/sandbox2/tmp/tmp.ZBAnisbwE3/DTF2THF_3132.p',lcl696_1)).
% 1.78/1.31 thf(f36,plain,(
% 1.78/1.31 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2))))))))),
% 1.78/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.78/1.31 thf(f29,plain,(
% 1.78/1.31 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))),
% 1.78/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.78/1.31 thf(f16,plain,(
% 1.78/1.31 (iimplies != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 1.78/1.31 inference(cnf_transformation,[status(thm)],[f9])).
% 1.78/1.31 thf(f9,plain,(
% 1.78/1.31 (iimplies != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 1.78/1.31 inference(flattening,[status(thm)],[f6])).
% 1.78/1.31 thf(f6,plain,(
% 1.78/1.31 ~(iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 1.78/1.31 inference(fool_elimination,[status(thm)],[f5])).
% 1.78/1.31 thf(f5,plain,(
% 1.78/1.31 ~(iimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1))))),
% 1.78/1.31 inference(rectify,[status(thm)],[f3])).
% 1.78/1.31 thf(f3,negated_conjecture,(
% 1.78/1.31 ~(iimplies = (^[X8 : $i > $o, X9 : $i > $o] : (mimplies @ (mbox_s4 @ X8) @ (mbox_s4 @ X9))))),
% 1.78/1.31 inference(negated_conjecture,[status(cth)],[f2])).
% 1.78/1.31 thf(f2,conjecture,(
% 1.78/1.31 (iimplies = (^[X8 : $i > $o, X9 : $i > $o] : (mimplies @ (mbox_s4 @ X8) @ (mbox_s4 @ X9))))),
% 1.78/1.31 file('/export/starexec/sandbox2/tmp/tmp.ZBAnisbwE3/DTF2THF_3132.p',iimplies)).
% 1.78/1.31 % SZS output end Proof for DTF2THF_3132
% 1.78/1.31 % (3249)------------------------------
% 1.78/1.31 % (3249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.31 % (3249)Termination reason: Refutation
% 1.78/1.31
% 1.78/1.31 % (3249)Memory used [KB]: 5628
% 1.78/1.31 % (3249)Time elapsed: 0.007 s
% 1.78/1.31 % (3249)Instructions burned: 8 (million)
% 1.78/1.31 % (3249)------------------------------
% 1.78/1.31 % (3249)------------------------------
% 1.78/1.31 % (3242)Success in time 0.01 s
%------------------------------------------------------------------------------