%------------------------------------------------------------------------------
% 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 : n021.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 1.84s 1.41s
% Output : Refutation 1.84s
% 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 : 689 ( 199 equ; 0 cnn)
% Maximal formula atoms : 24 ( 32 avg)
% Number of connectives : 1805 ( 283 ~; 228 |; 208 &; 943 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 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)
% ( 137 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 570 ( 487 ^; 75 !; 8 ?; 570 :)
% 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(f42,plain,
$false,
inference(trivial_inequality_removal,[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] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ 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] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f16,f26,f21,f17,f17]) ).
thf(f17,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ivalid
= ( ^ [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] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ! [X1: $i] :
( ( d2unsorted @ ( sK0 @ X1 ) )
= X1 )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( ( Y0 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y4 @ Y6 )
| ( Y1 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y3 ) )
& ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( X3 = X4 )
| ( ( d2unsorted @ X3 )
!= ( d2unsorted @ X4 ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14]) ).
thf(f14,plain,
! [X1: $i] :
( ? [X2: d_unsorted] :
( ( d2unsorted @ X2 )
= X1 )
=> ( ( d2unsorted @ ( sK0 @ X1 ) )
= X1 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ivalid
= ( ^ [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] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ! [X1: $i] :
? [X2: d_unsorted] :
( ( d2unsorted @ X2 )
= X1 )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( ( Y0 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y4 @ Y6 )
| ( Y1 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y3 ) )
& ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( X3 = X4 )
| ( ( d2unsorted @ X3 )
!= ( d2unsorted @ X4 ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
( ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ivalid
= ( ^ [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] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ! [X4: d_unsorted] : ( d_unsorted_0 = X4 )
& ! [X0: $i] :
? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( ( Y0 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y4 @ Y6 )
| ( Y1 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y3 ) )
& ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ! [X2: d_unsorted,X3: d_unsorted] :
( ( X2 = X3 )
| ( ( d2unsorted @ X2 )
!= ( d2unsorted @ X3 ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ! [X2: d_unsorted,X3: d_unsorted] :
( ( ( d2unsorted @ X2 )
= ( d2unsorted @ X3 ) )
=> ( X2 = X3 ) )
& ( isatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ! [X0: $i] :
? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 )
& ( ixor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( ( Y0 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y4 @ Y6 )
| ( Y1 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y3 ) )
& ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ! [X4: d_unsorted] : ( d_unsorted_0 = X4 )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ! [X0: $i] :
? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ! [X2: d_unsorted,X3: d_unsorted] :
( ( ( d2unsorted @ X2 )
= ( d2unsorted @ X3 ) )
=> ( X2 = X3 ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) )
& ! [X4: d_unsorted] : ( d_unsorted_0 = X4 )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( mimplies
= ( ^ [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] :
( ( ( ( Y0 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y4 @ Y6 )
| ( Y1 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y3 ) )
& ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) )
& ( isatisfiable
= ( ^ [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] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) )
& ( ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( inot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( irel @ Y1 @ Y2 ) ) ) ) )
& ! [X8: $i] :
? [X9: d_unsorted] :
( ( d2unsorted @ X9 )
= X8 )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ! [X17: d_unsorted,X18: d_unsorted] :
( ( ( d2unsorted @ X17 )
= ( d2unsorted @ X18 ) )
=> ( X17 = X18 ) )
& ( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) )
& ! [X22: d_unsorted] : ( d_unsorted_0 = X22 )
& ( iimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) )
& ( icountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( iinvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( iatom
= ( ^ [Y0: $i > $o,Y1: $i] : ( Y0 @ Y1 ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( irel @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
& ( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) ) ) )
& ( mimplies
= ( ^ [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] :
( ( ( ( Y0 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( irel @ Y4 @ Y6 )
| ( Y1 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y3 ) )
& ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 )
| ~ ( irel @ Y4 @ Y6 ) ) )
| ~ ( irel @ Y4 @ Y5 )
| ( Y1 @ Y5 ) ) )
| ~ ( irel @ Y2 @ Y4 ) ) ) ) ) ) )
& ( isatisfiable
= ( ^ [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] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( irel @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand )
& ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
& ( ivalid
= ( ^ [X3: $i > $o] :
! [X4: $i] : ( X3 @ X4 ) ) )
& ( ( ^ [X5: $i > $o,X6: $i] :
~ ! [X7: $i] :
( ~ ( irel @ X6 @ X7 )
| ( X5 @ X7 ) ) )
= inot )
& ! [X8: $i] :
? [X9: d_unsorted] :
( ( d2unsorted @ X9 )
= X8 )
& ( ( ^ [X10: $i > $o,X11: $i] :
~ ( X10 @ X11 ) )
= mnot )
& ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
& ( ( ^ [X12: $i > $o,X13: $i > $o,X14: $i] :
( ! [X15: $i] :
( ( X12 @ X15 )
| ~ ( irel @ X14 @ X15 ) )
| ! [X16: $i] :
( ( X13 @ X16 )
| ~ ( irel @ X14 @ X16 ) ) ) )
= ior )
& ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
& ! [X17: d_unsorted,X18: d_unsorted] :
( ( ( d2unsorted @ X17 )
= ( d2unsorted @ X18 ) )
=> ( X17 = X18 ) )
& ( iand
= ( ^ [X19: $i > $o,X20: $i > $o,X21: $i] :
( ( X20 @ X21 )
& ( X19 @ X21 ) ) ) )
& ! [X22: d_unsorted] : ( d_unsorted_0 = X22 )
& ( ( ^ [X23: $i > $o,X24: $i > $o,X25: $i] :
( ! [X26: $i] :
( ~ ( irel @ X25 @ X26 )
| ( X23 @ X26 ) )
| ~ ! [X27: $i] :
( ( X24 @ X27 )
| ~ ( irel @ X25 @ X27 ) ) ) )
= iimplied )
& ( icountersatisfiable
= ( ^ [X28: $i > $o] :
~ ! [X29: $i] : ( X28 @ X29 ) ) )
& ( iinvalid
= ( ^ [X30: $i > $o] :
! [X31: $i] :
~ ( X30 @ X31 ) ) )
& ( ( ^ [X32: $i > $o,X33: $i] : ( X32 @ X33 ) )
= iatom )
& ( ( ^ [X34: $i > $o,X35: $i > $o,X36: $i] :
( ( X34 @ X36 )
| ( X35 @ X36 ) ) )
= mor )
& ( ( ^ [X37: $i > $o,X38: $i] :
! [X39: $i] :
( ( X37 @ X39 )
| ~ ( irel @ X38 @ X39 ) ) )
= mbox_s4 )
& ( iimplies
= ( ^ [X40: $i > $o,X41: $i > $o,X42: $i] :
( ~ ! [X43: $i] :
( ( X40 @ X43 )
| ~ ( irel @ X42 @ X43 ) )
| ! [X44: $i] :
( ( X41 @ X44 )
| ~ ( irel @ X42 @ X44 ) ) ) ) )
& ( ( ^ [X45: $i > $o,X46: $i > $o,X47: $i] :
( ~ ( X45 @ X47 )
| ( X46 @ X47 ) ) )
= mimplies )
& ( ixor
= ( ^ [X48: $i > $o,X49: $i > $o,X50: $i] :
~ ! [X51: $i,X52: $i,X53: $i] :
( ~ ( irel @ X50 @ X52 )
| ( ( ( X49 @ X51 )
| ~ ( irel @ X52 @ X51 )
| ~ ! [X54: $i] :
( ~ ( irel @ X52 @ X54 )
| ( X48 @ X54 ) ) )
& ( ~ ( irel @ X52 @ X53 )
| ~ ! [X55: $i] :
( ( X49 @ X55 )
| ~ ( irel @ X52 @ X55 ) )
| ( X48 @ X53 ) ) ) ) ) )
& ( isatisfiable
= ( ^ [X56: $i > $o] :
~ ! [X57: $i] :
~ ( X56 @ X57 ) ) )
& ( ( ^ [X58: $i > $o,X59: $i > $o,X60: $i] :
( ( ! [X61: $i] :
( ~ ( irel @ X60 @ X61 )
| ( X59 @ X61 ) )
| ~ ! [X62: $i] :
( ( X58 @ X62 )
| ~ ( irel @ X60 @ X62 ) ) )
& ( ! [X63: $i] :
( ( X58 @ X63 )
| ~ ( irel @ X60 @ X63 ) )
| ~ ! [X64: $i] :
( ~ ( irel @ X60 @ X64 )
| ( X59 @ X64 ) ) ) ) )
= iequiv ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ( ^ [X4: $i > $o,X5: $i > $o,X0: $i] :
( ( X4 @ X0 )
& ( X5 @ X0 ) ) )
= mand )
& ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) )
& ( ivalid
= ( ^ [X14: $i > $o] :
! [X15: $i] : ( X14 @ X15 ) ) )
& ( ( ^ [X8: $i > $o,X7: $i] :
~ ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X8 @ X5 ) ) )
= inot )
& ! [X0: $i] :
? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 )
& ( ( ^ [X4: $i > $o,X0: $i] :
~ ( X4 @ X0 ) )
= mnot )
& ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) )
| ! [X5: $i] :
( ( X9 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) ) )
= ior )
& ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
& ! [X2: d_unsorted,X3: d_unsorted] :
( ( ( d2unsorted @ X2 )
= ( d2unsorted @ X3 ) )
=> ( X2 = X3 ) )
& ( iand
= ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ( X9 @ X7 )
& ( X8 @ X7 ) ) ) )
& ! [X1: d_unsorted] : ( d_unsorted_0 = X1 )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X8 @ X5 ) )
| ~ ! [X5: $i] :
( ( X9 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) ) )
= iimplied )
& ( icountersatisfiable
= ( ^ [X14: $i > $o] :
~ ! [X15: $i] : ( X14 @ X15 ) ) )
& ( iinvalid
= ( ^ [X14: $i > $o] :
! [X15: $i] :
~ ( X14 @ X15 ) ) )
& ( ( ^ [X8: $i > $o,X7: $i] : ( X8 @ X7 ) )
= iatom )
& ( ( ^ [X4: $i > $o,X5: $i > $o,X0: $i] :
( ( X4 @ X0 )
| ( X5 @ X0 ) ) )
= mor )
& ( ( ^ [X8: $i > $o,X4: $i] :
! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X4 @ X5 ) ) )
= mbox_s4 )
& ( iimplies
= ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ~ ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) )
| ! [X5: $i] :
( ( X9 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) ) ) )
& ( ( ^ [X0: $i > $o,X6: $i > $o,X7: $i] :
( ~ ( X0 @ X7 )
| ( X6 @ X7 ) ) )
= mimplies )
& ( ixor
= ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
~ ! [X10: $i,X5: $i,X11: $i] :
( ~ ( irel @ X7 @ X5 )
| ( ( ( X9 @ X10 )
| ~ ( irel @ X5 @ X10 )
| ~ ! [X12: $i] :
( ~ ( irel @ X5 @ X12 )
| ( X8 @ X12 ) ) )
& ( ~ ( irel @ X5 @ X11 )
| ~ ! [X13: $i] :
( ( X9 @ X13 )
| ~ ( irel @ X5 @ X13 ) )
| ( X8 @ X11 ) ) ) ) ) )
& ( isatisfiable
= ( ^ [X14: $i > $o] :
~ ! [X15: $i] :
~ ( X14 @ X15 ) ) )
& ( ( ^ [X8: $i > $o,X9: $i > $o,X7: $i] :
( ( ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X9 @ X5 ) )
| ~ ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) ) )
& ( ! [X5: $i] :
( ( X8 @ X5 )
| ~ ( irel @ X7 @ X5 ) )
| ~ ! [X5: $i] :
( ~ ( irel @ X7 @ X5 )
| ( X9 @ X5 ) ) ) ) )
= iequiv ) ),
file('/export/starexec/sandbox2/tmp/tmp.5QJfih9tC7/DTF2THF_10621.p',lcl695_1) ).
thf(f21,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f26,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( irel @ Y2 @ Y3 )
| ( Y0 @ 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,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mimplies @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) )
!= iimplies ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( ( ^ [X8: $i > $o,X9: $i > $o] : ( mimplies @ ( mbox_s4 @ X8 ) @ ( mbox_s4 @ X9 ) ) )
!= iimplies ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( ^ [X8: $i > $o,X9: $i > $o] : ( mimplies @ ( mbox_s4 @ X8 ) @ ( mbox_s4 @ X9 ) ) )
= iimplies ),
file('/export/starexec/sandbox2/tmp/tmp.5QJfih9tC7/DTF2THF_10621.p',iimplies) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.11/0.15 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.35 % Computer : n021.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36 % CPULimit : 300
% 0.17/0.36 % WCLimit : 300
% 0.17/0.36 % DateTime : Tue May 5 09:20:10 EDT 2026
% 0.17/0.36 % CPUTime :
% 0.17/0.36 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.20/0.47 % Domain : Software Verification
% 0.20/0.47 % Problem : Benchmark: LCL695^1, Active target: iimplies
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English :
% 0.20/0.47
% 0.20/0.47 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Kon26]
% 0.20/0.47 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % Rating : ? v9.3.0
% 0.20/0.47 % Syntax : Number of formulae : 26 ( 1 unt; 24 typ; 0 def)
% 0.20/0.47 % Number of atoms : 63 ( 22 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 24 ( 31 avg)
% 0.20/0.47 % Number of connectives : 164 ( 32 ~; 26 |; 26 &; 79 @)
% 0.20/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 26 ( 14 avg)
% 0.20/0.47 % Number of types : 4 ( 2 usr)
% 0.20/0.47 % Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 23 ( 22 usr; 1 con; 0-3 aty)
% 0.20/0.47 % Number of variables : 67 ( 41 ^; 25 !; 1 ?; 67 :)
% 0.20/0.47 % SPC : TH0_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments :
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(unsorted_type,type,
% 0.20/0.47 unsorted: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(irel_decl,type,
% 0.20/0.47 irel: $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(mnot_decl,type,
% 0.20/0.47 mnot: ( $i > $o ) > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(mor_decl,type,
% 0.20/0.47 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(mand_decl,type,
% 0.20/0.47 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(mimplies_decl,type,
% 0.20/0.47 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(mbox_s4_decl,type,
% 0.20/0.47 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(iatom_decl,type,
% 0.20/0.47 iatom: ( $i > $o ) > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(inot_decl,type,
% 0.20/0.47 inot: ( $i > $o ) > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(itrue_decl,type,
% 0.20/0.47 itrue: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(ifalse_decl,type,
% 0.20/0.47 ifalse: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(iand_decl,type,
% 0.20/0.47 iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(ior_decl,type,
% 0.20/0.47 ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(iimplies_decl,type,
% 0.20/0.47 iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(iimplied_decl,type,
% 0.20/0.47 iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(iequiv_decl,type,
% 0.20/0.47 iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(ixor_decl,type,
% 0.20/0.47 ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(ivalid_decl,type,
% 0.20/0.47 ivalid: ( $i > $o ) > $o ).
% 0.20/0.47
% 0.20/0.47 thf(isatisfiable_decl,type,
% 0.20/0.47 isatisfiable: ( $i > $o ) > $o ).
% 0.20/0.47
% 0.20/0.47 thf(icountersatisfiable_decl,type,
% 0.20/0.47 icountersatisfiable: ( $i > $o ) > $o ).
% 0.20/0.47
% 0.20/0.47 thf(iinvalid_decl,type,
% 0.20/0.47 iinvalid: ( $i > $o ) > $o ).
% 0.20/0.47
% 0.20/0.47 %----Types of the domains
% 0.20/0.47 thf(d_unsorted_type,type,
% 0.20/0.47 d_unsorted: $tType ).
% 0.20/0.47
% 0.20/0.47 %----Types of the promotion functions
% 0.20/0.47 thf(d2unsorted_decl,type,
% 0.20/0.47 d2unsorted: d_unsorted > $i ).
% 0.20/0.47
% 0.20/0.47 %----Types of the domain elements
% 0.20/0.47 thf(d_unsorted_0_decl,type,
% 0.20/0.47 d_unsorted_0: d_unsorted ).
% 0.20/0.47
% 0.20/0.47 thf(lcl695_1,axiom,
% 0.20/0.47 ( ! [U: $i] :
% 0.20/0.47 ? [DU: d_unsorted] :
% 0.20/0.47 ( U
% 0.20/0.47 = ( d2unsorted @ DU ) )
% 0.20/0.47 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 0.20/0.47 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 0.20/0.47 ( ( ( d2unsorted @ DU1 )
% 0.20/0.47 = ( d2unsorted @ DU2 ) )
% 0.20/0.47 => ( DU1 = DU2 ) )
% 0.20/0.47 & ( mnot
% 0.20/0.47 = ( ^ [X: $i > $o,U: $i] :
% 0.20/0.47 ~ ( X @ U ) ) )
% 0.20/0.47 & ( mor
% 0.20/0.47 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.20/0.47 ( ( X @ U )
% 0.20/0.47 | ( Y @ U ) ) ) )
% 0.20/0.47 & ( mand
% 0.20/0.47 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.20/0.47 ( ( X @ U )
% 0.20/0.47 & ( Y @ U ) ) ) )
% 0.20/0.47 & ( mimplies
% 0.20/0.47 = ( ^ [U: $i > $o,V: $i > $o,Flatten_var_0: $i] :
% 0.20/0.47 ( ~ ( U @ Flatten_var_0 )
% 0.20/0.47 | ( V @ Flatten_var_0 ) ) ) )
% 0.20/0.47 & ( mbox_s4
% 0.20/0.47 = ( ^ [P: $i > $o,X: $i] :
% 0.20/0.47 ! [Y: $i] :
% 0.20/0.47 ( ~ ( irel @ X @ Y )
% 0.20/0.47 | ( P @ Y ) ) ) )
% 0.20/0.47 & ( iatom
% 0.20/0.47 = ( ^ [P: $i > $o,Flatten_var_0: $i] : ( P @ Flatten_var_0 ) ) )
% 0.20/0.47 & ( inot
% 0.20/0.47 = ( ^ [P: $i > $o,Flatten_var_0: $i] :
% 0.20/0.47 ~ ! [Y: $i] :
% 0.20/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.20/0.47 | ( P @ Y ) ) ) )
% 0.20/0.47 & ( iand
% 0.20/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.20/0.47 ( ( P @ Flatten_var_0 )
% 0.20/0.47 & ( Q @ Flatten_var_0 ) ) ) )
% 0.20/0.47 & ( ior
% 0.20/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.20/0.47 ( ! [Y: $i] :
% 0.20/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.20/0.47 | ( P @ Y ) )
% 0.20/0.47 | ! [Y: $i] :
% 0.20/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.20/0.47 | ( Q @ Y ) ) ) ) )
% 0.20/0.47 & ( iimplies
% 0.20/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.20/0.47 ( ~ ! [Y: $i] :
% 0.20/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.20/0.47 | ( P @ Y ) )
% 0.20/0.47 | ! [Y: $i] :
% 0.20/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.20/0.47 | ( Q @ Y ) ) ) ) )
% 0.20/0.47 & ( iimplied
% 0.20/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.20/0.47 ( ~ ! [Y: $i] :
% 0.20/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.20/0.47 | ( Q @ Y ) )
% 0.20/0.47 | ! [Y: $i] :
% 0.20/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.20/0.47 | ( P @ Y ) ) ) ) )
% 0.20/0.47 & ( iequiv
% 0.20/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.20/0.47 ( ( ~ ! [Y: $i] :
% 0.20/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.20/0.47 | ( P @ Y ) )
% 0.20/0.47 | ! [Y: $i] :
% 0.20/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.20/0.47 | ( Q @ Y ) ) )
% 0.20/0.47 & ( ~ ! [Y: $i] :
% 0.20/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.20/0.47 | ( Q @ Y ) )
% 0.20/0.47 | ! [Y: $i] :
% 0.20/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.20/0.47 | ( P @ Y ) ) ) ) ) )
% 0.20/0.47 & ( ixor
% 0.20/0.47 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 0.20/0.47 ~ ! [Y: $i,Bound_variable_747: $i,Bound_variable_754: $i] :
% 0.20/0.47 ( ~ ( irel @ Flatten_var_0 @ Y )
% 0.20/0.47 | ( ( ~ ! [Bound_variable_709: $i] :
% 0.20/0.47 ( ~ ( irel @ Y @ Bound_variable_709 )
% 0.20/0.47 | ( P @ Bound_variable_709 ) )
% 0.20/0.47 | ~ ( irel @ Y @ Bound_variable_747 )
% 0.20/0.47 | ( Q @ Bound_variable_747 ) )
% 0.20/0.47 & ( ~ ! [Bound_variable_717: $i] :
% 0.20/0.47 ( ~ ( irel @ Y @ Bound_variable_717 )
% 0.20/0.47 | ( Q @ Bound_variable_717 ) )
% 0.20/0.47 | ~ ( irel @ Y @ Bound_variable_754 )
% 0.20/0.47 | ( P @ Bound_variable_754 ) ) ) ) ) )
% 0.20/0.47 & ( ivalid
% 0.20/0.47 = ( ^ [Phi: $i > $o] :
% 0.20/0.47 ! [W: $i] : ( Phi @ W ) ) )
% 0.20/0.47 & ( isatisfiable
% 0.20/0.47 = ( ^ [Phi: $i > $o] :
% 0.20/0.47 ~ ! [W: $i] :
% 0.20/0.47 ~ ( Phi @ W ) ) )
% 0.20/0.47 & ( icountersatisfiable
% 0.20/0.47 = ( ^ [Phi: $i > $o] :
% 0.20/0.47 ~ ! [W: $i] : ( Phi @ W ) ) )
% 0.20/0.47 & ( iinvalid
% 0.20/0.47 = ( ^ [Phi: $i > $o] :
% 0.20/0.47 ! [W: $i] :
% 0.20/0.47 ~ ( Phi @ W ) ) )
% 0.20/0.47 & ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
% 0.20/0.47 & ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
% 0.20/0.47 & ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(iimplies,conjecture,
% 0.20/0.47 ( iimplies
% 0.20/0.47 = ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.68/1.37 ---- Embedded in THF ---
% 1.68/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.68/1.37 %%% Generated on Tue May 05 09:20:11 EDT 2026
% 1.68/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.68/1.37 %%% Logic specification used:
% 1.68/1.37 %%% thf(spec, logic, $$dhol).
% 1.68/1.37
% 1.68/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.5QJfih9tC7/DTF2DTF10621.p
% See solution above
% 1.68/1.37 ------------------------
% 1.68/1.38 ---- Cleaned THF ---
% 1.68/1.39 thf(unsorted_type,type,
% 1.68/1.39 unsorted: $tType ).
% 1.68/1.39
% 1.68/1.39 thf(irel_decl,type,
% 1.68/1.39 irel: $i > $i > $o ).
% 1.68/1.39
% 1.68/1.39 thf(mnot_decl,type,
% 1.68/1.39 mnot: ( $i > $o ) > $i > $o ).
% 1.68/1.39
% 1.68/1.39 thf(mor_decl,type,
% 1.68/1.39 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.68/1.39
% 1.68/1.39 thf(mand_decl,type,
% 1.68/1.39 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.68/1.39
% 1.68/1.39 thf(mimplies_decl,type,
% 1.68/1.39 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.68/1.39
% 1.68/1.39 thf(mbox_s4_decl,type,
% 1.68/1.39 mbox_s4: ( $i > $o ) > $i > $o ).
% 1.68/1.39
% 1.68/1.39 thf(iatom_decl,type,
% 1.68/1.39 iatom: ( $i > $o ) > $i > $o ).
% 1.68/1.39
% 1.68/1.39 thf(inot_decl,type,
% 1.68/1.39 inot: ( $i > $o ) > $i > $o ).
% 1.68/1.39
% 1.68/1.39 thf(itrue_decl,type,
% 1.68/1.39 itrue: $i > $o ).
% 1.68/1.39
% 1.68/1.39 thf(ifalse_decl,type,
% 1.68/1.39 ifalse: $i > $o ).
% 1.68/1.39
% 1.68/1.39 thf(iand_decl,type,
% 1.68/1.39 iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.68/1.39
% 1.68/1.39 thf(ior_decl,type,
% 1.68/1.39 ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.68/1.39
% 1.68/1.39 thf(iimplies_decl,type,
% 1.68/1.39 iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.68/1.39
% 1.68/1.39 thf(iimplied_decl,type,
% 1.68/1.39 iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.68/1.39
% 1.68/1.39 thf(iequiv_decl,type,
% 1.68/1.39 iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.68/1.39
% 1.68/1.39 thf(ixor_decl,type,
% 1.68/1.39 ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.68/1.39
% 1.68/1.39 thf(ivalid_decl,type,
% 1.68/1.39 ivalid: ( $i > $o ) > $o ).
% 1.68/1.39
% 1.68/1.39 thf(isatisfiable_decl,type,
% 1.68/1.39 isatisfiable: ( $i > $o ) > $o ).
% 1.68/1.39
% 1.68/1.39 thf(icountersatisfiable_decl,type,
% 1.68/1.39 icountersatisfiable: ( $i > $o ) > $o ).
% 1.68/1.39
% 1.68/1.39 thf(iinvalid_decl,type,
% 1.68/1.39 iinvalid: ( $i > $o ) > $o ).
% 1.68/1.39
% 1.68/1.39 thf(d_unsorted_type,type,
% 1.68/1.39 d_unsorted: $tType ).
% 1.68/1.39
% 1.68/1.39 thf(d2unsorted_decl,type,
% 1.68/1.39 d2unsorted: d_unsorted > $i ).
% 1.68/1.39
% 1.68/1.39 thf(d_unsorted_0_decl,type,
% 1.68/1.39 d_unsorted_0: d_unsorted ).
% 1.68/1.39
% 1.68/1.39 thf(lcl695_1,axiom,
% 1.68/1.39 ( ! [U: $i] :
% 1.68/1.39 ? [DU: d_unsorted] :
% 1.68/1.39 ( U
% 1.68/1.39 = ( d2unsorted @ DU ) )
% 1.68/1.39 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 1.68/1.39 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 1.68/1.39 ( ( ( d2unsorted @ DU1 )
% 1.68/1.39 = ( d2unsorted @ DU2 ) )
% 1.68/1.39 => ( DU1 = DU2 ) )
% 1.68/1.39 & ( mnot
% 1.68/1.39 = ( ^ [X: $i > $o,U: $i] :
% 1.68/1.39 ~ ( X @ U ) ) )
% 1.68/1.39 & ( mor
% 1.68/1.39 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 1.68/1.39 ( ( X @ U )
% 1.68/1.39 | ( Y @ U ) ) ) )
% 1.68/1.39 & ( mand
% 1.68/1.39 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 1.68/1.39 ( ( X @ U )
% 1.68/1.39 & ( Y @ U ) ) ) )
% 1.68/1.39 & ( mimplies
% 1.68/1.39 = ( ^ [U: $i > $o,V: $i > $o,Flatten_var_0: $i] :
% 1.68/1.39 ( ~ ( U @ Flatten_var_0 )
% 1.68/1.39 | ( V @ Flatten_var_0 ) ) ) )
% 1.68/1.39 & ( mbox_s4
% 1.68/1.39 = ( ^ [P: $i > $o,X: $i] :
% 1.68/1.39 ! [Y: $i] :
% 1.68/1.39 ( ~ ( irel @ X @ Y )
% 1.68/1.39 | ( P @ Y ) ) ) )
% 1.68/1.39 & ( iatom
% 1.68/1.39 = ( ^ [P: $i > $o,Flatten_var_0: $i] : ( P @ Flatten_var_0 ) ) )
% 1.68/1.39 & ( inot
% 1.68/1.39 = ( ^ [P: $i > $o,Flatten_var_0: $i] :
% 1.68/1.39 ~ ! [Y: $i] :
% 1.68/1.39 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.68/1.39 | ( P @ Y ) ) ) )
% 1.68/1.39 & ( iand
% 1.68/1.39 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.68/1.39 ( ( P @ Flatten_var_0 )
% 1.68/1.39 & ( Q @ Flatten_var_0 ) ) ) )
% 1.68/1.39 & ( ior
% 1.68/1.39 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.68/1.39 ( ! [Y: $i] :
% 1.68/1.39 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.68/1.39 | ( P @ Y ) )
% 1.68/1.39 | ! [Y: $i] :
% 1.68/1.39 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.68/1.39 | ( Q @ Y ) ) ) ) )
% 1.68/1.39 & ( iimplies
% 1.68/1.39 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.68/1.39 ( ~ ! [Y: $i] :
% 1.68/1.39 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.68/1.39 | ( P @ Y ) )
% 1.68/1.39 | ! [Y: $i] :
% 1.68/1.39 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.68/1.39 | ( Q @ Y ) ) ) ) )
% 1.68/1.39 & ( iimplied
% 1.68/1.39 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.68/1.39 ( ~ ! [Y: $i] :
% 1.68/1.39 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.68/1.39 | ( Q @ Y ) )
% 1.68/1.39 | ! [Y: $i] :
% 1.68/1.39 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.68/1.39 | ( P @ Y ) ) ) ) )
% 1.68/1.39 & ( iequiv
% 1.68/1.39 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.68/1.39 ( ( ~ ! [Y: $i] :
% 1.68/1.39 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.68/1.39 | ( P @ Y ) )
% 1.68/1.39 | ! [Y: $i] :
% 1.68/1.39 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.68/1.39 | ( Q @ Y ) ) )
% 1.68/1.39 & ( ~ ! [Y: $i] :
% 1.68/1.39 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.68/1.39 | ( Q @ Y ) )
% 1.68/1.39 | ! [Y: $i] :
% 1.68/1.39 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.68/1.39 | ( P @ Y ) ) ) ) ) )
% 1.68/1.39 & ( ixor
% 1.68/1.39 = ( ^ [P: $i > $o,Q: $i > $o,Flatten_var_0: $i] :
% 1.68/1.39 ~ ! [Y: $i,Bound_variable_747: $i,Bound_variable_754: $i] :
% 1.68/1.39 ( ~ ( irel @ Flatten_var_0 @ Y )
% 1.68/1.39 | ( ( ~ ! [Bound_variable_709: $i] :
% 1.68/1.39 ( ~ ( irel @ Y @ Bound_variable_709 )
% 1.68/1.39 | ( P @ Bound_variable_709 ) )
% 1.68/1.39 | ~ ( irel @ Y @ Bound_variable_747 )
% 1.68/1.39 | ( Q @ Bound_variable_747 ) )
% 1.68/1.39 & ( ~ ! [Bound_variable_717: $i] :
% 1.68/1.39 ( ~ ( irel @ Y @ Bound_variable_717 )
% 1.68/1.39 | ( Q @ Bound_variable_717 ) )
% 1.68/1.39 | ~ ( irel @ Y @ Bound_variable_754 )
% 1.68/1.39 | ( P @ Bound_variable_754 ) ) ) ) ) )
% 1.68/1.39 & ( ivalid
% 1.68/1.39 = ( ^ [Phi: $i > $o] :
% 1.68/1.39 ! [W: $i] : ( Phi @ W ) ) )
% 1.68/1.39 & ( isatisfiable
% 1.68/1.39 = ( ^ [Phi: $i > $o] :
% 1.68/1.39 ~ ! [W: $i] :
% 1.68/1.39 ~ ( Phi @ W ) ) )
% 1.68/1.39 & ( icountersatisfiable
% 1.68/1.39 = ( ^ [Phi: $i > $o] :
% 1.68/1.39 ~ ! [W: $i] : ( Phi @ W ) ) )
% 1.68/1.39 & ( iinvalid
% 1.68/1.39 = ( ^ [Phi: $i > $o] :
% 1.68/1.39 ! [W: $i] :
% 1.68/1.39 ~ ( Phi @ W ) ) )
% 1.68/1.39 & ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
% 1.68/1.39 & ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
% 1.68/1.39 & ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ) ).
% 1.68/1.39
% 1.68/1.39 thf(iimplies,conjecture,
% 1.68/1.39 ( iimplies
% 1.68/1.39 = ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
% 1.68/1.39 ------------------------
% 1.84/1.40 % (10752)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_10621 for (2999ds/27Mi)
% 1.84/1.40 % (10756)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10621 for (2999ds/18Mi)
% 1.84/1.40 % (10756)First to succeed.
% 1.84/1.41 % (10756)Refutation found. Thanks to Tanya!
% 1.84/1.41 % SZS status Theorem for DTF2THF_10621
% 1.84/1.41 % SZS output start Proof for DTF2THF_10621
% 1.84/1.41 thf(type_def_6, type, d_unsorted: $tType).
% 1.84/1.41 thf(func_def_0, type, unsorted: $tType).
% 1.84/1.41 thf(func_def_1, type, irel: $i > $i > $o).
% 1.84/1.41 thf(func_def_2, type, mnot: ($i > $o) > $i > $o).
% 1.84/1.41 thf(func_def_3, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 1.84/1.41 thf(func_def_4, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 1.84/1.41 thf(func_def_5, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 1.84/1.41 thf(func_def_6, type, mbox_s4: ($i > $o) > $i > $o).
% 1.84/1.41 thf(func_def_7, type, iatom: ($i > $o) > $i > $o).
% 1.84/1.41 thf(func_def_8, type, inot: ($i > $o) > $i > $o).
% 1.84/1.41 thf(func_def_9, type, itrue: $i > $o).
% 1.84/1.41 thf(func_def_10, type, ifalse: $i > $o).
% 1.84/1.41 thf(func_def_11, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 1.84/1.41 thf(func_def_12, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 1.84/1.41 thf(func_def_13, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 1.84/1.41 thf(func_def_14, type, iimplied: ($i > $o) > ($i > $o) > $i > $o).
% 1.84/1.41 thf(func_def_15, type, iequiv: ($i > $o) > ($i > $o) > $i > $o).
% 1.84/1.41 thf(func_def_16, type, ixor: ($i > $o) > ($i > $o) > $i > $o).
% 1.84/1.41 thf(func_def_17, type, ivalid: ($i > $o) > $o).
% 1.84/1.41 thf(func_def_18, type, isatisfiable: ($i > $o) > $o).
% 1.84/1.41 thf(func_def_19, type, icountersatisfiable: ($i > $o) > $o).
% 1.84/1.41 thf(func_def_20, type, iinvalid: ($i > $o) > $o).
% 1.84/1.41 thf(func_def_21, type, d_unsorted: $tType).
% 1.84/1.41 thf(func_def_22, type, d2unsorted: d_unsorted > $i).
% 1.84/1.41 thf(func_def_23, type, d_unsorted_0: d_unsorted).
% 1.84/1.41 thf(func_def_39, type, sK0: $i > d_unsorted).
% 1.84/1.41 thf(f42,plain,(
% 1.84/1.41 $false),
% 1.84/1.41 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.84/1.41 thf(f41,plain,(
% 1.84/1.41 ((^[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]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))))),
% 1.84/1.41 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.84/1.41 thf(f40,plain,(
% 1.84/1.41 ((^[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]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))))),
% 1.84/1.41 inference(definition_unfolding,[status(thm)],[f16,f26,f21,f17,f17])).
% 1.84/1.41 thf(f17,plain,(
% 1.84/1.41 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 1.84/1.41 inference(cnf_transformation,[status(thm)],[f15])).
% 1.84/1.41 thf(f15,plain,(
% 1.84/1.41 (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ivalid = (^[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]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & ! [X1 : $i] : ((d2unsorted @ (sK0 @ X1)) = X1) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((Y0 @ Y3) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (Y1 @ Y6)))))) | (~ (irel @ Y4 @ Y3))) & (((~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y5))) | (Y1 @ Y5))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((X3 = X4) | ((d2unsorted @ X3) != (d2unsorted @ X4))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 1.84/1.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14])).
% 1.84/1.41 thf(f14,plain,(
% 1.84/1.41 ! [X1 : $i] : (? [X2 : d_unsorted] : ((d2unsorted @ X2) = X1) => ((d2unsorted @ (sK0 @ X1)) = X1))),
% 1.84/1.41 introduced(definition,[],[choice_axiom])).
% 1.84/1.41 thf(f13,plain,(
% 1.84/1.41 (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ivalid = (^[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]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & ! [X1 : $i] : ? [X2 : d_unsorted] : ((d2unsorted @ X2) = X1) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((Y0 @ Y3) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (Y1 @ Y6)))))) | (~ (irel @ Y4 @ Y3))) & (((~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y5))) | (Y1 @ Y5))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((X3 = X4) | ((d2unsorted @ X3) != (d2unsorted @ X4))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 1.84/1.41 inference(rectify,[status(thm)],[f12])).
% 1.84/1.41 thf(f12,plain,(
% 1.84/1.41 (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ivalid = (^[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]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & ! [X0 : $i] : ? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((Y0 @ Y3) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (Y1 @ Y6)))))) | (~ (irel @ Y4 @ Y3))) & (((~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y5))) | (Y1 @ Y5))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((X2 = X3) | ((d2unsorted @ X2) != (d2unsorted @ X3))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 1.84/1.41 inference(ennf_transformation,[status(thm)],[f11])).
% 1.84/1.41 thf(f11,plain,(
% 1.84/1.41 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & ! [X2 : d_unsorted,X3 : d_unsorted] : (((d2unsorted @ X2) = (d2unsorted @ X3)) => (X2 = X3)) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & ((ifalse @ (d2unsorted @ d_unsorted_0)) != $true) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((Y0 @ Y3) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (Y1 @ Y6)))))) | (~ (irel @ Y4 @ Y3))) & (((~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y5))) | (Y1 @ Y5))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2)))))))))),
% 1.84/1.41 inference(flattening,[status(thm)],[f10])).
% 1.84/1.41 thf(f10,plain,(
% 1.84/1.41 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ~((ifalse @ (d2unsorted @ d_unsorted_0)) = $true) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & ! [X2 : d_unsorted,X3 : d_unsorted] : (((d2unsorted @ X2) = (d2unsorted @ X3)) => (X2 = X3)) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (mimplies = (^[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]: (((((Y0 @ Y3) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (Y1 @ Y6)))))) | (~ (irel @ Y4 @ Y3))) & (((~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y5))) | (Y1 @ Y5))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & (isatisfiable = (^[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]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))))),
% 1.84/1.41 inference(rectify,[status(thm)],[f8])).
% 1.84/1.41 thf(f8,plain,(
% 1.84/1.41 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ~((ifalse @ (d2unsorted @ d_unsorted_0)) = $true) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & ! [X8 : $i] : ? [X9 : d_unsorted] : ((d2unsorted @ X9) = X8) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & ((itrue @ (d2unsorted @ d_unsorted_0)) = $true) & ! [X17 : d_unsorted,X18 : d_unsorted] : (((d2unsorted @ X17) = (d2unsorted @ X18)) => (X17 = X18)) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & ! [X22 : d_unsorted] : (d_unsorted_0 = X22) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (mimplies = (^[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]: (((((Y0 @ Y3) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (Y1 @ Y6)))))) | (~ (irel @ Y4 @ Y3))) & (((~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y4 @ Y6)))))) | (~ (irel @ Y4 @ Y5))) | (Y1 @ Y5))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & (isatisfiable = (^[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]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))))),
% 1.84/1.41 inference(fool_elimination,[status(thm)],[f7])).
% 1.84/1.41 thf(f7,plain,(
% 1.84/1.41 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) & (X1 @ X2))) = mand) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (ivalid = (^[X3 : $i > $o] : (! [X4 : $i] : (X3 @ X4)))) & ((^[X5 : $i > $o, X6 : $i] : (~! [X7 : $i] : (~(irel @ X6 @ X7) | (X5 @ X7)))) = inot) & ! [X8 : $i] : ? [X9 : d_unsorted] : ((d2unsorted @ X9) = X8) & ((^[X10 : $i > $o, X11 : $i] : (~(X10 @ X11))) = mnot) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ((^[X12 : $i > $o, X13 : $i > $o, X14 : $i] : (! [X15 : $i] : ((X12 @ X15) | ~(irel @ X14 @ X15)) | ! [X16 : $i] : ((X13 @ X16) | ~(irel @ X14 @ X16)))) = ior) & (itrue @ (d2unsorted @ d_unsorted_0)) & ! [X17 : d_unsorted,X18 : d_unsorted] : (((d2unsorted @ X17) = (d2unsorted @ X18)) => (X17 = X18)) & (iand = (^[X19 : $i > $o, X20 : $i > $o, X21 : $i] : ((X20 @ X21) & (X19 @ X21)))) & ! [X22 : d_unsorted] : (d_unsorted_0 = X22) & ((^[X23 : $i > $o, X24 : $i > $o, X25 : $i] : (! [X26 : $i] : (~(irel @ X25 @ X26) | (X23 @ X26)) | ~! [X27 : $i] : ((X24 @ X27) | ~(irel @ X25 @ X27)))) = iimplied) & (icountersatisfiable = (^[X28 : $i > $o] : (~! [X29 : $i] : (X28 @ X29)))) & (iinvalid = (^[X30 : $i > $o] : (! [X31 : $i] : ~(X30 @ X31)))) & ((^[X32 : $i > $o, X33 : $i] : (X32 @ X33)) = iatom) & ((^[X34 : $i > $o, X35 : $i > $o, X36 : $i] : ((X34 @ X36) | (X35 @ X36))) = mor) & ((^[X37 : $i > $o, X38 : $i] : (! [X39 : $i] : ((X37 @ X39) | ~(irel @ X38 @ X39)))) = mbox_s4) & (iimplies = (^[X40 : $i > $o, X41 : $i > $o, X42 : $i] : (~! [X43 : $i] : ((X40 @ X43) | ~(irel @ X42 @ X43)) | ! [X44 : $i] : ((X41 @ X44) | ~(irel @ X42 @ X44))))) & ((^[X45 : $i > $o, X46 : $i > $o, X47 : $i] : (~(X45 @ X47) | (X46 @ X47))) = mimplies) & (ixor = (^[X48 : $i > $o, X49 : $i > $o, X50 : $i] : (~! [X51 : $i,X52 : $i,X53 : $i] : (~(irel @ X50 @ X52) | (((X49 @ X51) | ~(irel @ X52 @ X51) | ~! [X54 : $i] : (~(irel @ X52 @ X54) | (X48 @ X54))) & (~(irel @ X52 @ X53) | ~! [X55 : $i] : ((X49 @ X55) | ~(irel @ X52 @ X55)) | (X48 @ X53))))))) & (isatisfiable = (^[X56 : $i > $o] : (~! [X57 : $i] : ~(X56 @ X57)))) & ((^[X58 : $i > $o, X59 : $i > $o, X60 : $i] : ((! [X61 : $i] : (~(irel @ X60 @ X61) | (X59 @ X61)) | ~! [X62 : $i] : ((X58 @ X62) | ~(irel @ X60 @ X62))) & (! [X63 : $i] : ((X58 @ X63) | ~(irel @ X60 @ X63)) | ~! [X64 : $i] : (~(irel @ X60 @ X64) | (X59 @ X64))))) = iequiv)),
% 1.84/1.41 inference(rectify,[status(thm)],[f1])).
% 1.84/1.41 thf(f1,axiom,(
% 1.84/1.41 ((^[X4 : $i > $o, X5 : $i > $o, X0 : $i] : ((X4 @ X0) & (X5 @ X0))) = mand) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (ivalid = (^[X14 : $i > $o] : (! [X15 : $i] : (X14 @ X15)))) & ((^[X8 : $i > $o, X7 : $i] : (~! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)))) = inot) & ! [X0 : $i] : ? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0) & ((^[X4 : $i > $o, X0 : $i] : (~(X4 @ X0))) = mnot) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)))) = ior) & (itrue @ (d2unsorted @ d_unsorted_0)) & ! [X2 : d_unsorted,X3 : d_unsorted] : (((d2unsorted @ X2) = (d2unsorted @ X3)) => (X2 = X3)) & (iand = (^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : ((X9 @ X7) & (X8 @ X7)))) & ! [X1 : d_unsorted] : (d_unsorted_0 = X1) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)) | ~! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)))) = iimplied) & (icountersatisfiable = (^[X14 : $i > $o] : (~! [X15 : $i] : (X14 @ X15)))) & (iinvalid = (^[X14 : $i > $o] : (! [X15 : $i] : ~(X14 @ X15)))) & ((^[X8 : $i > $o, X7 : $i] : (X8 @ X7)) = iatom) & ((^[X4 : $i > $o, X5 : $i > $o, X0 : $i] : ((X4 @ X0) | (X5 @ X0))) = mor) & ((^[X8 : $i > $o, X4 : $i] : (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X4 @ X5)))) = mbox_s4) & (iimplies = (^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (~! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5))))) & ((^[X0 : $i > $o, X6 : $i > $o, X7 : $i] : (~(X0 @ X7) | (X6 @ X7))) = mimplies) & (ixor = (^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : (~! [X10 : $i,X5 : $i,X11 : $i] : (~(irel @ X7 @ X5) | (((X9 @ X10) | ~(irel @ X5 @ X10) | ~! [X12 : $i] : (~(irel @ X5 @ X12) | (X8 @ X12))) & (~(irel @ X5 @ X11) | ~! [X13 : $i] : ((X9 @ X13) | ~(irel @ X5 @ X13)) | (X8 @ X11))))))) & (isatisfiable = (^[X14 : $i > $o] : (~! [X15 : $i] : ~(X14 @ X15)))) & ((^[X8 : $i > $o, X9 : $i > $o, X7 : $i] : ((! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)) | ~! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5))) & (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)) | ~! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5))))) = iequiv)),
% 1.84/1.41 file('/export/starexec/sandbox2/tmp/tmp.5QJfih9tC7/DTF2THF_10621.p',lcl695_1)).
% 1.84/1.41 thf(f21,plain,(
% 1.84/1.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2)))))))))),
% 1.84/1.41 inference(cnf_transformation,[status(thm)],[f15])).
% 1.84/1.41 thf(f26,plain,(
% 1.84/1.41 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))))),
% 1.84/1.41 inference(cnf_transformation,[status(thm)],[f15])).
% 1.84/1.41 thf(f16,plain,(
% 1.84/1.41 (iimplies != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 1.84/1.41 inference(cnf_transformation,[status(thm)],[f9])).
% 1.84/1.41 thf(f9,plain,(
% 1.84/1.41 (iimplies != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 1.84/1.41 inference(flattening,[status(thm)],[f6])).
% 1.84/1.41 thf(f6,plain,(
% 1.84/1.41 ~(iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 1.84/1.41 inference(fool_elimination,[status(thm)],[f5])).
% 1.84/1.41 thf(f5,plain,(
% 1.84/1.41 ~((^[X0 : $i > $o, X1 : $i > $o] : (mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1))) = iimplies)),
% 1.84/1.41 inference(rectify,[status(thm)],[f3])).
% 1.84/1.41 thf(f3,negated_conjecture,(
% 1.84/1.41 ~((^[X8 : $i > $o, X9 : $i > $o] : (mimplies @ (mbox_s4 @ X8) @ (mbox_s4 @ X9))) = iimplies)),
% 1.84/1.41 inference(negated_conjecture,[status(cth)],[f2])).
% 1.84/1.41 thf(f2,conjecture,(
% 1.84/1.41 ((^[X8 : $i > $o, X9 : $i > $o] : (mimplies @ (mbox_s4 @ X8) @ (mbox_s4 @ X9))) = iimplies)),
% 1.84/1.41 file('/export/starexec/sandbox2/tmp/tmp.5QJfih9tC7/DTF2THF_10621.p',iimplies)).
% 1.84/1.41 % SZS output end Proof for DTF2THF_10621
% 1.84/1.41 % (10756)------------------------------
% 1.84/1.41 % (10756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.41 % (10756)Termination reason: Refutation
% 1.84/1.41
% 1.84/1.41 % (10756)Memory used [KB]: 5628
% 1.84/1.41 % (10756)Time elapsed: 0.006 s
% 1.84/1.41 % (10756)Instructions burned: 5 (million)
% 1.84/1.41 % (10756)------------------------------
% 1.84/1.41 % (10756)------------------------------
% 1.84/1.41 % (10747)Success in time 0.018 s
%------------------------------------------------------------------------------